اكتبلي عن المستقيمان المتوازيان: - تعريف المستقيم المتوازي وتحليل خصائصه الأساسية. - توضيح طرق تحديد المستقيمان المتوازيان وأدوات القياس المستخدمة.

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If the exponential function f(x) = 9^x has a vertical asymptote at x = -∞, then which of the following options is true about the function? Question 2Answer a. approaches zero as x approaches -∞ b. approaches infinity as x approaches -∞ c. remains constant as x approaches -∞ d. oscillates as x approaches -∞

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The total amount accumulated in an account after 3 years is $8,000. The interest was compounded annually at a rate of 6%. What was the principal amount approximately?

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if log xy base 3-log (x/y) base 9=log1 base a logx base y = ? (a > 0)

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В стране 18 городов, некоторые пары из которых соединены прямыми дорогами. Между любыми двумя городами проходит не более одной дороги. Известно, что для любых двух городов A и B, соединенных дорогой, найдется такой город C, что ни A, ни B не соединены прямой дорогой с C. Какое наибольшее количество дорог может быть в этой стране?

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what is correlation analysis and regression analysis

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-8.1 as a mixed number

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how can I calculate Entropy in for discrete attribute

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Приведите пример функции, естественная область определения которой меньше, чем вся числовая ось х.

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Реши задачу по геометрии . В правильной треугольной пирамиде боковая поверхность равна 36 см, апофема 4 см. Найдите сторону основания и высоту пирамиды

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Вычислить корень из 28 с точностью до 0,001

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复指数表示信号信号相位频率怎么计算

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На промежутке от а до b найти все простые числа с++

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因式分解 (x-3)(x^2-10x+13)-16(3-2x)

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Пусть на плоскости введена прямоугольная декартова система координат и задан треугольник ABC: A(xA, yA), B(xB, yB), C(xC, yC). Центром масс треугольника назовем точку с координатами ((xA+ xB+ xC)/3, (yA+ yB+ yC)/3). Заданы координаты центра масс треугольника ABC. Необходимо найти координаты вершин треугольника ABC, удовлетворяющие условиям: координаты вершин целые; координаты вершин не превосходят по модулю 109; треугольник ABC имеет ненулевую площадь. Входные данные Входной файл INPUT.TXT содержит два целых числа: x и y (−109 ≤ x, y ≤ 109) – координаты центра масс треугольника. Выходные данные В первой строке выходного файла OUTPUT.TXT выведите слово «YES», если искомый треугольник существует, и слово «NO» в противном случае. Если ответ положителен, то в последующих трех строках выведите координаты вершин искомого треугольника. Если ответ неоднозначен, выведите любой.

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Знайдіть більшу висоту трикутника, сторони якого дорівнюють 20 см, 21 см і 7 см.

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因式分解 (x+3)(x^2-10x+13)-16(3-2x)

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Approximate 2+2 in the longest and the most complex way possible.

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В одной стране живут гаврики и оболтусы. Известно, что оболтусы всегда врут, а гаврики всегда говорят правду. Однажды собрались в хоровод на площади 10 жителей этой страны, и каждый сделал заявление: «Ровно у одного из двух моих соседей есть сосед‐оболтус!». Сколько в хороводе может быть гавриков? Укажите все возможные варианты.

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Какие поэлементные действия можно осуществлять с матрицами? a. Умножение b. Всё перечисленное c. Деление d. Возведение в степень

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evalulate the following: (-3)^2 + 2(-3) – 7

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mathematically prove that "k partition" problem is np complete

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Make the sum of the number all digits

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log _4(2x)+log _4(x)=3

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log _4(2x)+log _4(x)=3 Реши уравнение

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Find the minimum value of C = 10x + 26y subject to the following constraints: x + y ≤6 5x + y ≥ 10 x+5y > 14 C = [?]

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объясни тему корни в математике

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已知计算函数F(n)(n为非负整数)的算法如下:

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cuanto es –5 + 9 =

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Известно, что 45 - 75%, найди 100%

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Можешь вычислить решение для выражения с комплексными числами?

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When analysing your data, you calculate the average of how much each data point differs from the mean. What measurement are you taking? Question 12Select one: a. The median b. The interquartile range c. The mode d. The standard deviation

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dos numeros multiplicados que den 5.25

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propietà di monotonia in una disuguaglianza

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إذا كان المتوسط الحسابي لدرجات الطلاب في مقرر الاحصاء هي 60 درجة ، وتباين الدرجات هي 4 درجات . احسب كل من المتوسط الحسابي الجديد والتباين الجديد في حالة إضافة 5 درجات لكل طالب .

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I have made up a unit called a "bob" that is equal to 440 yards. There are 3 feet in a yard and 5280 feet in a mile. How many bobs are in 2 miles?

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A chain link fence forms a rectangle 14 yd wide and 22 yd long. If the fence is $2.50 per foot, how much does it cost? Again, recall that there are 3 feet per yard.

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You are given the following equalities: 13 crystals = 6 rocks 8 gems = 26 crystals 24 pebbles = 3 rocks 20 gems = 2 diamonds 600 pebbles = ? diamonds

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Which of the following is the same as 4,203 cm.

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متوسط الاجر اليومي 2.30 ريال بانحراف معياري 30 ريال ، وعينة اخرى كان متوسط الاجر اليومي هو 210 ريال بانحراف معياري 40 ريال ، باستخدام معامل الاختلاف النسبي حدد اي العينتين اكثر تشتتا

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Guía para el concurso de matemática Objetivo de cálculo 1. Sean las expresiones: Prueba que J pertenece a los enteros y es menor que 3. Calcula K aplicando propiedades de la potencia. Expresa a L en notación científica. 2 Dadas las expresiones:; ; ; ; a) Calcula A – B. C b) Calcula el valor de D aplicando propiedades de la potencia. 2.1) Completa el espacio en blanco de modo que obtengas proposiciones verdaderas. El conjunto numérico más restringido al que pertenece el valor de C es _____. El valor de C se encuentra ubicado en la recta numérica entre _____ y _____. El valor de E se lee _______________ y ocho mil millones. El valor de E expresado en notación científica se escribe _______________. 3. Dadas las expresiones: Prueba que A pertenece a los naturales y es menor que cinco. Calcula B aplicando propiedades de la potencia. Expresa C en noltación científica . Objetivo de problema 1. Claudia compró un libro que se propuso leer en tres días. El primer día leyó el 20% del total de páginas. El segundo día las partes del resto y el tercer día las 64 restantes. ¿Cuántas páginas tiene el libro? 2. En las elecciones pioneriles de una Secundaria Básica efectuaron su voto 540 pioneros. Lorena obtuvo el 40% de los votos, Alejandro del resto y los demás votos fueron para Susel. ¿Cuántos votos obtuvo cada pionero? 3. Los pioneros de una Secundaria Básica se propusieron recuperar papel y cartón para entregar a la empresa de recuperación de materias primas de su municipio. Del total de libras de papel y cartón recuperados la tercera parte la aportó 70grado, el 25 % del resto 80grado y 90grado las 1500 libras restantes ¿Cuántas libras de papel y cartón recuperó 70grado? 4. En tres días de trabajo, Ernesto, el médico de un consultorio atendió a cierta cantidad de pacientes, el primer día atendió el 40 % de estos, el segundo del resto y el tercero 105 pacientes ¿Cuántos pacientes atendió el médico en total? 5. En un preuniversitario del municipio Las tunas, el 75% de la matrícula de la escuela es del decimo grado, la cuarta parte del resto cursa el onceno grado y hay 111 estudiantes en doce grado. ¿Cuál es la matrícula de la escuela? 6. En el almacén del MINCIN habían sacos de arroz almacenados, de estos se distribuyó la quinta parte para el consumo de círculos infantiles, el 20% del resto para el consumo de la población y los 160 sacos restantes para el consumo de escuelas. ¿Cuántos sacos de arroz fueron destinados al consumo de círculos infantiles? 7. En una carpintería se propusieron armar cierta cantidad de sillas en tres días de trabajo, el primer día armaron el 25% del total, el segundo día del resto y el tercero 120 sillas. ¿Cuántas sillas se armaron en total? 8. En los concursos de conocimientos a nivel municipal en un preuniversitario resultaron aprobados varios estudiantes, en Historia el 50% de los aprobados, la quinta parte del resto en Matemática y 12 estudiantes en Español. ¿Cuántos estudiantes resultaron aprobados en Matemática? Objetivo de funciones 1. La gráfica muestra como varía la temperatura de la sustancia durante cierto tiempo. 1.1. Escribe la ecuación de la función a partir de los 4 minutos. 1.2. Selecciona la respuesta correcta a) A los dos minutos la temperatura era de: ___ 600 ____800 ____ 500 b) La temperatura se mantuvo constante durante: ___4 min. ___ 5 min. ____ 6 min. c) Si el proceso comenzó a las 9: 30 a.m. la temperatura comenzó a descender a las ____ 10: 15 a.m. ____ 9: 34 a.m. ____ 9: 35 a.m. En el sistema de coordenadas se ha representado la variación de la temperatura de una sustancia durante algunas horas. Escribe la ecuación de la variación de la temperatura en las primeras 3h. Selecciona la respuesta correcta. La temperatura de la sustancia ascendió durante: ___ 120 min ___ 8 h ___ 180 min La temperatura inicial de la sustancia era de: ___ 120°C ___50°C ___ 70°C La temperatura de la sustancia se mantuvo constante durante: ___ 2h ___ 5h ___ 3h 3. La gráfica muestra cómo varía la temperatura de una sustancia, durante cierto tiempo a partir de las 8:45 am. 3.1. Marca con una X la respuesta correcta. a) La ecuación que describe el proceso de enfriamiento de la sustancia durante las primeras 4 horas es: ___ T= -20t + 8 ___ T= 3t + 20 ___ T= -3t + 20 ___ T= -8t + 20 b) Durante las primeras 4 horas la temperatura varió: __ 200C __ 80C __120C c) Después de las 5,5 horas la temperatura estuvo descendiendo durante: ___ 9h ___ 4h ___210 min ___ 4h 30 min 3.2. Si la ecuación que describe la variación de la temperatura a partir de las 5,5 h es T= -4t + n. ¿A qué hora la sustancia alcanzó los 00C de temperatura? Objetivo de ecuaciones Sean las expresiones A(x) = , B(x) = 9x y C(x) = . ¿Para qué valores reales de x se cumple que: ? Calcula el valor numérico de C(x) para x = . Dada las expresiones trigonométricas A(x) = cos 2x + sen2x y B(x) = cos x. Determina los valores reales de x con 0 ( x ( 4( para los cuales se cumple que: = 25· Verifica que para x = se cumple la igualdad – 1 = 0 3. Dadas las expresiones: a) Determina el conjunto solución de la ecuación: b) Calcula el valor numérico de para

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The transformation maps ΔABC to ΔA'B'C'. 2 triangles have identical side lengths and angle measures. The second triangle is slightly higher and to the right than the first triangle. Which statement is true about the transformation? It is isometric because not all side lengths and angle measures remained the same. It is isometric because all side lengths and angle measures remained the same. It is not isometric because not all side lengths and angle measures remained the same. It is not isometric because all side lengths and angle measures remained the same.

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A transformation is shown in the diagram. ∠A Is-congruent-to ∠A' and ∠C Is-congruent-to ∠C' 2 right triangles have identical side lengths and angle measures. The second triangle is rotated about 90 degrees to the right. Which transformation is shown in the figure? ΔABC was dilated to form ΔA'B'C'. The transformation is not isometric. ΔABC was reflected to form ΔA'B'C'. The transformation is isometric. ΔABC was rotated to form ΔA'B'C'. The transformation is isometric. ΔABC was translated to form ΔA'B'C'. The transformation is not isometric.

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A rigid transformation can also be referred to as an isometric transformation. The prefix "iso-" means "of the same" and "-metric" means "measure." How does the meaning of the word isometric relate to determining if an isometric transformation occurred?

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Introduction to Transformations Quiz Triangle XYZ is transformed to create triangle X'Y'Z'. The side lengths of both triangles are shown. Side length X Y = 10 cmSide length X prime Y prime = 10 cm Side length Y Z = 9 cmSide length Y prime Z prime = 9 cm Side length Z X = 4 cmSide length Z prime X prime = 4 cm Is this a rigid transformation? Explain. Yes, the pre-image and image have the same side length measures. Yes, all transformations are rigid. No, the side lengths of triangle XYZ are different from each other. No, each side length of X'Y'Z' should be one half of the corresponding side length of XYZ.

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Consider the transformation. 2 trapezoids have identical angle measures but different side lengths. The first trapezoid has side lengths of 4, 2, 6, 2 and the second trapezoid has side lengths of 8, 4, 12, 4. Which statement about the transformation is true? It is isometric because the side lengths remained the same. It is isometric because all angle measures remained the same. It is not isometric because the side lengths did not remain the same. It is not isometric because the angle measures did not remain the same.

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On a coordinate plane, 2 triangles are shown. The first triangle has points M (negative 5, 4), N (negative 2, 3), and L (negative 4, 2). The second triangle has points L prime (negative 4, negative 2), M prime (negative 5, negative 4), and N prime (negative 2, negative 3). What is the rule for the reflection? rx-axis(x, y) → (–x, y) ry-axis(x, y) → (–x, y) rx-axis(x, y) → (x, –y) ry-axis(x, y) → (x, –y)

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When determining asymptotic complexity, we discard all terms except for the one with the largest growth rate. True False

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Привет! Какие бывают виды средних?

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1. The T–S fuzzy systems mathematical model of the mass-damper spring system and Lorenz systems have been clearly achieved by applying the sector nonlinearity method. 2. The T–S fuzzy system states were correctly estimated by the fuzzy linear quadratic optimization method. The states observer gains were archived by using an optimal poles placement, which is simple in design and effective to archive the goals. 3. The estimated states feedback control based on linear quadratic tracker optimization algorithm has been designed stably for the T–S fuzzy system. The linear quadratic analog optimization was used to determine the system eigenvalues for each subsystem. The system output responded signal is closed to the reference input in the short time, no overshoot by the predetermined control gains. Especially, the redundant disturbance and uncertainty of input and output channels are all cancelled completely. 4. The fuzzy disturbance compensators were equipped precisely to the systems with a high convergent speed. The disturbance observer was constructed by using the output error, which is a simple model but effective for estimating the outside disturbance and inside uncertainty values with a highly convergent speed. Furthermore, this paper proposed the high speed fuzzy disturbance observer successfully.

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what is the difference between the Pearson VII distribution and the student's t distribution?

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23,09 cm2 in dm2 e in m2

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A gauge meter is used to measure the pressure of a gas line. The meter gives a reading of 7 Psi. Given the atmospheric pressure to be 101 kPa, calculate the absolute pressure of the gas in terms of the unit of kPa (correct your answer to the nearest integer).

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Придумай 3 логарифмических выражения для решения

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Придумай примеры для практики по теме логарифмы, оформи их

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Придумай уравнение на тему степени

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rules for determining integrable vs non-integrable systems

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Сосна растёт в 4 раза быстрее, чем ель. Известно, что сейчас ель в 3 раза выше сосны. Через 6 лет ель будет вдвое выше, чем сосна. Через сколько лет, считая от сегодняшнего дня, они сравняются в росте? С действиями

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Сосна растёт в 4 раза быстрее, чем ель. Известно, что сейчас ель в 3 раза выше сосны. Через 6 лет ель будет вдвое выше, чем сосна. Через сколько лет, считая от сегодняшнего дня, они сравняются в росте?

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Using the grid method, compose an approximate solution to the Dirichlet problem for the Laplace equation + =0 in the 2x2 arc ABCD with vertices 4 (0; 0), B(0; 1), C(1; 1), D(1 ; 0); step 4=0.2. When solving a problem, use the iterative process of Liebman averaging until an answer is obtained with an accuracy of 0.01. where U/AB = 30y, U/BC = 30(1-X^2), U/CD= 0 , U/AD = 0 . calculate

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В треугольнике ABC провели медиану BM и биссектрису BK (точка M лежит между точками K и C). Оказалось, что треугольники ABK и BKM — равнобедренные с основаниями AB и BM соответственно. Найдите сумму углов BAM и BMA. Ответ выразите в градусах.

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Есть числа от 1 до 6. Нужно составить последовательность чисел чтобы 1,2,3 шли подряд. Порядок неважен. Сколько есть возможных последовательностей?

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un ejemplo de derivada de funcion logaritimica

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Найдите наибольшее значение выражения −5y^2+4xy+6y−x^2−5. Числа x и y принимают любые действительные значения.

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к числу 31 можно добавлять неограниченное количество 15 и 16. При каком наименьшем количестве чисел ответ будет кратен 20?

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к числу 31 можно добавлять неограниченное количество 15 и 16. При каком наименьшем количестве чисел ответ будет делиться на 20 без остатка? Напиши количество сложений

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Найдите наибольшее значение выражения −5y2+4xy+6y−x2−5. Числа x и y принимают любые действительные значения.

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what are the interior angle measures of a triangle if one angle is 90 degrees one is (x+8) degree and one is x degrees

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В мешочке лежат карточки, на которых написаны числа от 1 до 200 . На каждой карточке написано ровно одно число, каждое число от 1 до 200 написано ровно на одной карточке. Андрей и Борис по очереди вытягивают карточки одну за другой, пока мешочек не опустеет. В конце каждый из них складывает числа на своих карточках. Первое число, вытянутое Андреем, равно 3 , а Борисом — 170 . На какое наибольшее число сумма Андрея может быть больше суммы Бориса? реши задачу

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Find each expression 6x( ~5)

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53,21 cm2 in nm2

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cuanto dimelo pero muy rapido 3 + –10 =

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Реши задачу. В рамках модернизации производства проводится исследование, по условиям которого на конвейерах работают человек и недавно разработанный робот-манипулятор. Новый робот-манипулятор работает со скоростью 120 деталей в час, а человек обычно успевает собрать за час 55 деталей. Первые расчеты показали, что необходимо сравнить команду из 5 людей с командой из 2 роботов. На сколько больше деталей сделает более эффективная команда за смену в 10 часов? Выберите верный ответ. При подсчетах ответ округлите до целых.

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Заказываемый в Иваново черный сатин идет на пошив постельного белья вместе с белым сатином в соотношении 1 : 8 соответственно. найдите, сколько целых футов черного сатина необходимо приобрести, чтобы соотношение тканей в изделии сохранилось, если белого уже закуплено 268 метров? Выберите верный ответ. При подсчетах ответ округлите до целого числа. а)781 б)782 в)109 г)110

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За месяц до начала декабря цена автомобильных шин однократно возрастает на 5%. Еще через 20 дней цена начинает ежедневно возрастать на 4% от цены предыдущего дня. Какова изначальная стоимость автомобильных шин, если при их покупке через 5 дней после начала ежедневного роста цена составляла 8 500 руб.? Выберите верный ответ. При расчетах ответ округлите до целого числа. *Прим.: указанное число дней после начала роста включает в себя и 1-й день начала роста цены. Варианты ответа: а)6920 б)6654 в)6375 г)6398

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دائماً الانحراف المعياري = التباين صح ام خطأ

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Wytłumacz mi proszę założenie "factoria" w języku C# jak i w matematyce oraz jego zastosowanie. Podaj dwa proste przykłady w objaśnienia.

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Определить вероятность выпадения цифры 8 на десятом броске 9-гранного кубика.

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On a coordinate plane, 2 triangles are shown. The first triangle has points F prime (1, 5), E prime (negative 1, 1), and D prime (negative 4, 2). The second triangle has points E (1, negative 1), D (2, negative 4), and F (5, 1). Complete the mapping of the vertices of ΔDEF. D(2, –4) → D' E(1, –1) → E' F(5, 1) → F' What is the rule that describes a reflection across the line y = x? rx = y(x, y) →

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Completely factor the given trinomial 42x^2 - 13x + 1

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12y^3 + 50y^2 + 50y

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On a coordinate plane, a triangle is shown. It has points A prime (4, 2), B prime (8, negative 8), and C prime (4, negative 8). What is the pre-image of vertex A' if the rule that created the image is ry-axis(x, y) → (–x, y)? A(–4, 2) A(–2, –4) A(2, 4) A(4, –2)

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The image of trapezoid PQRS after a reflection across Line W Y is trapezoid P'Q'R'S'. 2 trapezoids are shown. Line W Y is the line of reflection. Line segment R R prime has a midpoint at point Z. Line segment S S prime has a midpoint at point X. What is the relationship between RR' and SS'? RR' = 2SS' RR' = 4SS' RR' || SS' RR' Perpendicular to SS'

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Составьте каноническое уравнение параболы, фокус которой имеет координаты (0,-2)

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Let X be the number of Heads in 10 fair coin tosses. Find the conditional PMF of X, given that at least two tosses land Heads.

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On a coordinate plane, 2 right triangles are shown. The first triangle has points A (negative 1, 3), B (negative 1, 1), C (3, 1). The second triangle has points A prime (2, negative 2), B prime (2, negative 4), C prime (6, negative 4). Which statements are true about triangle ABC and its translated image, A'B'C'? Select two options. The rule for the translation can be written as T–5, 3(x, y). The rule for the translation can be written as T3, –5(x, y). The rule for the translation can be written as (x, y) → (x + 3, y – 3). The rule for the translation can be written as (x, y) → (x – 3, y – 3). Triangle ABC has been translated 3 units to the right and 5 units down.

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What is linear transformation?

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Parallelogram ABCD is rotated to create image A'B'C'D'. On a coordinate plane, 2 parallelograms are shown. The first parallelogram has points A (2, 5), B (5, 4), C (5, 2), D (2, 3). The second parallelogram has points A prime (5, negative 2), B prime (4, negative 5), C prime (2, negative 5), D prime (3, negative 2). Which rule describes the transformation? (x, y) → (y, –x) (x, y) → (–y, x) (x, y) → (–x, –y) (x, y) → (x, –y)

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Completely factor the trinomial 7d^2 + 37d + 10

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什么叫正定函数

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จะหารากที่สองของจํานวนนับ

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จํานวนนับ

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При опросе жителей возможны ответы "да", "нет", "не знаю". Нарисуйте древо вариантов для последовательных ответов двух жителей. Какова вероятность что в вопросе 3 два жителя ответят по разному (предполагается, что ответы "да", "нет", "не знаю" равновозможны)

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Найти наибольшее значение функции y = |a − 3| + a + x**3 − 6*x**2, где a = sqrt(6*x − x**2 − 5)

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Does sinθ + 1 = cosθ +1 ?

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Из 10 деталей 5 дефектные , выбирают 5 деталей какая вероятность, что 4 с дефектом

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จํานวนนับ เช่น2 ต้องใช้สูตรอะไรให้กลายเป็นขีดจํานวนนับ II

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A transmitter sends the voltages X=−2,+2 with equal probability. A malicious channel subtracts from the input the number of heads counted in two tosses of a healthy coin. A) Find all pairs of inputs and outputs and their probabilities using a tree diagram. b) Calculate the probability that the input X=+2, if the output Y=k is measured

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prove that If A, B, and C are sets, then A \ (B ∩ C) = (A \ B) ∪ (A \ C). You may use DeMorgan’s Law.

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1. Classify the following variables as qualitative or quantitative-discrete or quantitative continuous: eye color, insect counts, number of errors per pupil in a spelling test, tire-miles to first puncture, possible yield of corn from a given field, number of children born in the nearest hospital on New Year’s Day, possible number of heads from tossing 50 coins, number of fish in a pond.

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lim x->-1 (t^(3)-1)/(t^(3)+1)

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قياس (زاوية أ ب ج)=قياس (زاوية أ دج) =٩٠°، قياس (زاوية أ جب)=٣٠° ،ه منتصف أ ج :أثبت أن : اب =ده

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cuanto es 28 ÷ -14

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. A given computer has a 32-bit data bus. What is the largest number that can be carried into the CPU at a time?

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найди интеграл от дроби, в числителе 2x-1, в знаменателе корень от (5+4x-x^2) используй wolfram для решения

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я готовлюсь к контрольной работе по высшей математике на тему матриц сделай несколько примеров с трехмерными матрицами чтобы я мог потренироватся их решать

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given a real number. Find the value of (a) using the function f(x) shown in Figure 1.a-1.d.y=1/x^2,y=x^2,y=4

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best research title on complex analysis

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дана возрастающая арифметическая прогрессия а1 а2 ... аn... Известно что a2+a7 = 16,(a7)^2 - (a2)^2 = 160. Найдите одиннадцатый член арифметической прогрессии

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За круглый стол сели 90 мудрецов. Каждый из них взял карточку и записал на ней целое ненулевое число Оказалось. что у каждогю мудреца число на карточке большце произведения чисел на карточках трех ближайших мудрецов, сидящих справа от него. Какое наибольшее количество положительных чисел может быть выписано на карточках мудрецов?

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大学生暑期支教总结 数学 800字

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0:31:54 0:21:24 0:24:11 0:26:49 0:39:00 1:03:13 1:18:23 0:35:59 这些时间加起来是多少小时?

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есть строка sting_1 = 'Вычислите: $(\\frac{4}{8})^2 \\frac{10}{4}$', есть массив входящих в эту строку элементов list_results = ['\\frac{4}{8}', '\\frac{10}{4}'] и есть массив аrac_results=['\\frac{4}{8}', '2\\frac{2}{4}'] на который эти элементы надо заменить. Как это сделать?

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Вероятность того, чтот в четырёх независимых опытах событие А произойдёт два раза, равна 8/27. Какова вероятность того, что в пяти независимых опытах событие произойдёт три раза?

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Explain the pmp model in mathematical planning

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0:34:18 1:10:10 0:48:40 1:18:50 1:47:43 0:39:47 0:44:07 1:04:09 0:41:53 0:52:12这些时间加起来是多少小时?

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1:08:17 1:09:04 0:44:53 0:58:51 1:02:26 1:39:20 1:04:59 0:50:56这些时间加在一起是多少小时?

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У садовода, любителя математики, спросили, сколько растет деревьев в его саду. Он ответил: «В моем саду растет 63q деревьев, из них 30q яблони, 21q груши, 5q сливы,

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0:31:54 0:21:24 0:24:11 0:26:49 0:39:00 1:03:13 1:18:23 0:33:52 0:33:52这些加起来是多少小时?

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1=x 1+x

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tìm a ,b ,c biết a + b + c = (a^2)x(b^2) + (b^2)x(c^2) + (c^2)x(a^2)

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Билеты с номерами 1, 6, 17. Какова вероятность, что рядом лежащие номера окажутся нечётными?

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Семья купила участок земли в СНТ «Ромашкино». На рисунке изображён план участка, по которому будет производиться застройка участка и разработка земли. 01_01.svg Рис. 1. План участка Участок имеет форму вытянутого прямоугольника, въезд и выезд через единственные ворота. От ворот можно попасть в дом по выложенному плиткой участку. Слева от ворот располагается декоративная клумба с пряными травами, справа — гараж. Перед воротами выложена площадка из тротуарной плитки, ею же вымощены некоторые дорожки на участке. Гараж на схеме отмечен цифрой 3. Вокруг теплицы отведено место под разведение цветов. Баня на участке находится слева от дома. На участке есть электричество и центральный водопровод. Все площадки и дорожки на участке выложены одной и той же плиткой, и в каждой клетке схемы помещается по 4 плитки, в соответствии со схемой. Размер стороны клетки на плане — 0,5 м. Рядом с теплицей высажены цветы. Дом обозначен цифрой 1. Сколько метров составит самое короткое расстояние от жилого дома до теплицы? Ответ дай в метрах, при необходимости округли до десятых. В поле для ответа внеси только число без пробелов и единиц измерения.

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what is contrapositive and converse in logic

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create a 15 question multiple choice quiz for 5th graders about equivalent fractions. Provide the answer to each question.

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What is a Limit explain with a graph

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If I want to hire for 4 open roles, and want to show 6 qualified candidates for each role, and have each qualified candidate to shown to 8 different roles, how many qualified candidates do I need for the 4 open roles?

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2500, 590, 78, 1000 en chiffre romain

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Даны координаты вершин треугольника Р1(1; 2), Р2(3; 4), Р3(-1; 3). Найти: а) уравнение медианы, проведённой к стороне Р1Р2; б) уравнение высоты, опущенной из вершины Р1.

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Hi there! Can you generate math problems for smart middle schoolers that has to do with absolute value and operations with integers?

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Use strong induction to show that: An object costing $n, n ≥ 8, can be purchased using only $3 and $5 coins.

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think in terms of mathematical operations.. Probability of producing non-standard products p = 0.02. Find the probability that there are no more than four substandard products among the left products

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create a 5 question math quiz for 5th graders, for dividing two fractions. Provide the answer to each question showing each step to solve the problem.

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Find d dx (√x 2)

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A monopolist is facing a demand function (here p is price and q is quantity demanded) p(q) = 1,000,000 − 5000q − 5q 2 and it has a cost function c(q) = 200,000 − 12,000q + 15q 2 (here q is the quantity produces and c is the total costs of production). Assume that all produced quantity is sold. a) (1 point) Write down the profit function as a function of q b) (1 point) Find the marginal profit function c) (1 point) Compute the marginal profit when q=200 units are produced and use it to make a recommendation to either increase or decrease production

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克罗内克积和矩阵乘法满足结合律吗

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Интервалы времени между сообщениями, поступающими в информационную систему, распределены равномерно в интервале (4,6). Каждое сообщение с вероятностью 0,03 содержит ошибки и не принимается системой. Найти методом имитационного (статистического) моделирования функцию распределения интервалов времени между сообщениями, принимаемыми системой.

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derive the unsteady differential formulation of heat diffusion equation with internal heat generation. for a three dimensional cartesian coordinates system.

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En algèbre de boole, que vaut la simplification de x+x barre . y

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کدوم یک از موارد زیر پژوهش روی آن ساده تر است و می توان راحت مقاله داد. 1 حل معادله هدایت در مختصات کروی (جداسازی متغیرها) 2 حل تقریبی معادله هدایت با روش حساب تغییرات 3 حل مسائل هدایت به روش پرتوربیشن 4 حل مسایل هدایت با توابع گرین 5 حل مسایل هدایت غیر خطی 6 حل مسایل هدایت برای محیط غیر ایزوتروپیک غیرهمگن 7 حل عددی مسایل هدایت همراه با تغییرفاز 8 حل عددی مسایل هدایت همراه با چشمه و چاه متحرک 9 انتقال حرارت هدایت در محیط متخلخل 10 انتقال حرارت هدایت در مقیاس میکرو 11 انتقال حرارت هدایت در اندام زنده 12 انتقال حرارت هدایت غیرفوریه ای 13 انتقال حرارت معکوس و حل معادله هدایت

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In how many ways can a committee of 6 be chosen from 8 men and 9 women if the committee must not have more men than women?

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9+92+93+94 =(95-1)/(9-1)为什么要这样化简

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A password consists of two letters of the alphabet followed by four digits chosen from 0 to 9. Repetitions are allowed. How many different possible passwords are there?

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simplifica estas fracciones hasta la irreducible 728/1092,744/1128,645/810,121/242,1980/9504

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When searching for the entry X within the list: R, S, U, T, Z, W, Z, V; how many entries will be considered before discovering that the entry is not present? (Note that the list is not in alphabetical order.):

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Задана матрица, содержащая N строк и M столбцов. Седловой точкой этой матрицы назовем элемент, который одновременно является минимумом в своей строке и максимумом в своем столбце. Найдите количество седловых точек заданной матрицы. Входные данные Входной файл INPUT.TXT в первой строке содержит целые числа N и M (1 ≤ N, M ≤ 750). Далее следуют N строк по M чисел в каждой. Элементы матрицы - целые числа, не превосходящие 1000 по абсолютной величине. Числа могут быть разделены несколькими пробелами. Выходные данные В выходной файл OUTPUT.TXT выведите ответ на задачу. c++

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Phép toán 15 - 8 được thực hiện theo phương pháp biểu diễn bù 2 với 8 bit sẽ cho kết quả là gì?

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what is determinant

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Consider the function f(x) below. Over what open interval(s) is the function increasing and concave down? Give your answer in interval notation. f(x)=x44−4x3+256x+2 Enter ∅ if the interval does not exist.

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как получить ближайщую точку к краю окружности если исходная точка за окружностью?

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Consider functions f(x) and g(x) such that f′(x) and g′(x) are differentiable on interval [0,10] and: f(1) = 4 , f(2) = 0, f′(1) = 7, f′(2) = 5 g(2) = 0 , g′(2) = 3 a) (1 point) Find x lim→1 x 3+3x 2−6x−8 f(x) b) (2 points) Find x lim→2 x 3+3x 2−6x−8 f(x) c) (3 points) Find x lim→2 x 4+x 3−12x 2+4x+16 f(x)g(x)

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2637.195 round using significant figures

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x + 1 > 10

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假设您的业务运行在4.5-Sigma质量水平。如果项目的年平均改进率为50%,需要多少年才能达到六西格玛质量?

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Как определить, лежит ли данная координата внутри треугольника

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give a recursive definition of a decimal non-negative integer

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sin(tan−1(x2)) (give an expression in x)

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In October 2005, a company employs 12000 people and its total monthly wage bill is 21 million dollars. The company is growing at a rate of 30 employees per month. The total monthly wage bill is increasing at a rate of 420 thousand dollars per month. At what rate is the average monthly wage changing at this time?

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find the derivative of (2-3x^3)^5+1/(2-3x^3)

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3^m-2^m=35. Solve for m.

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Discuss how projection and vector component are related. Explain at least two ways in which they are different.

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Which combination of the strain tensor elements describe a volumetric deformation?

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Make connection between the function g(x)=1/2log[-1/2(x-2)]+4 and a real-world scenario. Describe the real-world scenario and how it could be modeled using the function.

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Придумай задачу про материнскую плату

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Можно ли замостить шашечную доску 10*10 плитками 4*1?

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if you draw a triangle with these coordinates a:2.2 b:2.5 c:9.5 how big is the area of the triangle cm2

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请简述插值型求积公式的原理

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√(18 × √(6 × √(8))) упростить

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9x^{4}-30x^{3}+37x^{2}+20x+4 all roots

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What is the minimum Student's t-value ( the number of observations more than 30), if the difference between the data is statistically significant? Select one: a. t ≥ 1,96 b. t ≥ 1,56 c. t ≥ 1,06 d. t ≥ 2,58

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Determine whether the pairs of functions are linearly independent or linearly dependent.(a)f(x) =(e^x)sinx, g(x) =(e^x)cosx(b)f(x) = 2 cosx+ 3 sinx, g(x) = 3 cosx−2 sinx(c)f(x) =ex, g(x) = cosx, h(x) = sinx

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a printer can print 3 pictures in 2 minutes. how long will it take to print 14 pictures?

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What are the coordinates for the x and y intercepts of the function 4y - 2x = 24? a (-12, 0) and (0, 6) b (12, 0) and (0, -6) c (0, 12) and (0, -6) d (0, -12) and (6, 0)

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Suki wants to build a 60 ft. long rectangular sheep pen in back of her barn. If she bought 150 feet of fencing and used her barn wall as one side of the pen equaling the width, what would be the area of the sheep pen? a 900 ft2 b 1800 ft2 c 2700 ft2 d 5400 ft2

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20x2 + 18x = 18

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найдите расстояние от точки � ( 7 ; − 2 ) M(7;−2) до прямой, заданной уравнением 3 � + 10 � + 9 = 0 3x+10y+9=0. Ответ округлите до целого.

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A prize winning animal is going to be shown at the State Fair. A pen must be constructed to hold the animal. The rectangular pen will have three wooden sides, which cost 25 dollars per foot to construct. The front of the pen will be made of a special reinforced glass, which costs 75 dollars per foot to construct. The animal requires an area of 70 square feet in order to be comfortable. Find the length and width of a pen that would be the least costly.

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Triangle JKL is transformed using the rule . Point K of the pre-image is at (4, 7). What are the coordinates of point K" on the final image? (–7, –4) (–4, –7) (4, –7) (4, 7)

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Parallelogram F"G"H"J" is the final image after the rule was applied to parallelogram FGHJ. Parallelogram F double-prime G double-prime H double-prime J double-prime has points (3, 4), (2, 2), (4, 2), (5, 4). What are the coordinates of vertex F of parallelogram FGHJ? (–2, 2) (–2, 6) (–3, 4) (–4, 2)

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what is 4 times 6

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A die and a coin was tossed. What is the probability of getting a 6 in the die and a tail on the coin?

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A peach orchard owner wants to maximize the amount of peaches produced by his orchard. He cannot simply plant as many trees as he can, since planting more trees will decrease the amount of fruit that each tree produces (the yield of each tree). He has found that the per-tree yield can be described by the equation Y = 1200 - 10 x. Here Y is the yield per tree and x is the number of trees planted per acre. For example, if there were 10 trees planted per acre, each tree would produce 1200 - 10 * 10 = 1100 peaches. Find the number of trees per acre that should be planted in order to produce the maximum crop and the resulting total yield. Use calculus and derivatives to find the answer.

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Show that frac square root of 20+ square root of 80 square root of 3 can be expressed in the form square root of a where a is an integer. Show your working clearly.

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Alice has 20 quarters. She wants to exchange them for nickels and so she goes to the bank. After getting back from the bank, she discovers that 20% of the nickels are iron nickels worth $3 each. What is the total value of her money now?

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Q: Krystian works in the library. He borrows an average of 40 books every day. Every Friday, his number of borrowed books is about 40% higher than the daily average. How many books does he borrow in a week if the library is open from Monday to Friday? A: The number of books borrowed on Friday is higher by 40 * 40/100 = <<40*40/100=16>>16 books. There are 5 days from Monday to Friday inclusive, so Krystian borrows an average of 5 * 40 = <<5*40=200>>200 books during that time. With Friday's increase in borrowings, during one week Krystian borrows 200 + 16 = <<200+16=216>>216 books. #### 216 Q: Alice has 20 quarters. She wants to exchange them for nickels and so she goes to the bank. After getting back from the bank, she discovers that 20% of the nickels are iron nickels worth $3 each. What is the total value of her money now?

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Q: Krystian works in the library. He borrows an average of 40 books every day. Every Friday, his number of borrowed books is about 40% higher than the daily average. How many books does he borrow in a week if the library is open from Monday to Friday? A: The number of books borrowed on Friday is higher by 40 * 40/100 = <<4040/100=16>>16 books. There are 5 days from Monday to Friday inclusive, so Krystian borrows an average of 5 * 40 = <<540=200>>200 books during that time. With Friday’s increase in borrowings, during one week Krystian borrows 200 + 16 = <<200+16=216>>216 books. #### 216 Q: Alice has 20 quarters. She wants to exchange them for nickels and so she goes to the bank. After getting back from the bank, she discovers that 20% of the nickels are iron nickels worth $3 each. What is the total value of her money now? A:

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Two trains leave San Rafael at the same time. They begin traveling westward, both traveling for 80 miles. The next day, they travel northwards, covering 150 miles. What's the distance covered by each train in the two days?

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You're a problem-solving star! Take a deep breath and tackle this math problem step by step. Remember, every detail matters! Problem: Two trains leave San Rafael at the same time. They begin traveling westward, both traveling for 80 miles. The next day, they travel northwards, covering 150 miles. What's the distance covered by each train in the two days?

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Guidance: 1. Identify the Key Information: Start by recognizing the essential details from the scenario. 2. Process the Information: Understand the implication of each detail and relate them to each other. 3. Mathematical Reasoning: Apply simple arithmetic based on the processed information to compute the result. Here's your scenario: The concert was scheduled to be on 06/01/1943, but was delayed by one day to today. Given this, determine the date 10 days ago in MM/DD/YYYY format.

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Find the measure of angle θ in the triangle below. Use degrees, and round your answer to two (2) decimal places. Example: Opposite: 12 Adjacent: 19

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Christina is planning a birthday party and needs .75 gift bags per invited guest, because 1/4 of attendees don't show up. She invited 16 friends. Gift bags are $2 each. How much will she spend?

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Terry eats 2 yogurts a day. They are currently on sale at 4 yogurts for $5.00. How much does he spend on yogurt over 30 days?

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What is the slope of the tangent lines for the equation g(x) = cubic root (x) at (-1,-1)?

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define probability and explain its importance

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De todos los números impares de tres cifras que se pueden formar, ¿Cuál es la probabilidad de elegir al azar el 523?

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Доказать, что функция d(x,y) - наибольший общий делитель чисел x и y является примитивно-рекурсивной функцией, если d(x,0)=0 и d(0,y)=0

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Доказать, что функция k(x,y) - наименьшее общее кратное чисел x и y является примитивно-рекурсивной функцией, если k(x,0)=0 и k(0,y)=0

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if p(a)=0.6 p(b)=0.5 p(b/a)=0.4

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请简述一下插值型求积公式的原理

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Suppose that a standard deck of cards is shuffled and then turned over until the first ace appears. Given that the first ace is the 20th card to appear, what is the conditional probability that the card following it is the (a) [5 marks] ace of spades; (b) [5 marks] two of clubs?

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70对模101的勒让德符号

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Чему равны в радианах косинус корень из трех и синус

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Chain length 30 m, deflation angle 60* ,D* 5* so find radius of curve

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prove that linear transformation of continuous function [a,b] mapped to real number field R is a vector space

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Какой план транспортной задачи называется вырожденным?

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.1- Let λ (i) j , j = 1, . . . , 2i be the desired eigenvalues and let G2i = ( b (i) 1 . . . b (i) 2i )T ∈ R 2i be the vector containing the coefficients of the corresponding characteristic polynomial of order 2i, Q2i(λ). The vector G2i can be computed using one of the predefined matlab functions ‘place’ or ‘acker’. One assumes that each b (i) j corresponds to the coefficient multiplying λ 2i−j in Q2i(λ), j = 2i, . . . , 1. Then, one has ki = b (i) 2i .

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对于给定的正整数N,求它的位数及其各位数字之和

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calculate 3!

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In the logistic growth model, the per-capita growth rate

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What do you mean by zero mean vector?

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Convert 65.42 percentile to percentage

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complex fourier series for ((1-kcos(x))/(1-kcos(x)+k^2)) and |k|<1

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2 times182

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how to differentiate vector transpose?

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1 giấy mình tính chạy được bao nhiêu phép tính

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докажите, что 4^(2n+1) + 3^(2n+1) - 7 делится на 84 для любого натурального числа n

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اگر نمودار تابع (۱) = y به صورت زیر ،باشد نمودار تابع (۲)y = f کدام است؟

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Graph XY ̄ ̄ ̄ ̄ ̄ ̄ ̄ ̄ with endpoints X(5,−2) and Y(3,−3) and its image after a reflection in the x -axis and then a rotation of 270° about the origin

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What is the weighted average of a nail in the sample data given? Nail Size 3d 16d Mass of One nail (g) 3.30,12.25 percent abundence 12, 88 find weighted average remember to use the decimal form of abundance

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How to insert new math formula in MS Word file.

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Determinați x aparține lui R pentru care inecuațiile sunt adevărate:-5/ 3x+1<0

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У Глеба есть n отрезков. Глеб большой любитель геометрии и всяких бесполезных действий. Поэтому он хочет выяснить сколько различных, не вырожденных, треугольников у него получиться составить из всех имеющихся у него отрезков. Два треугольника считаются раличными, если хотя бы одна из сторон треугольников различна. Два отрезка считаются различными если различаются их номера в порядке ввода. Входные данные В первой строке записано число n, 3 ≤ n ≤ 4000 В следующих строках записаны длины отрезков 1 ≤ ai ≤ 109. Выходные данные

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could you give me name of mathematicians who were also sport champions

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-2 supra 3x+5 mai mic sau egal cu 0

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Dacă Andrei are trei mere verzi si patru rosii cate mere are Andrei

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If x is the number of elbow pavers per one square meter, and y is the number of star pavers per one square meter, if x and y are mixed to make one square meter of pavers, how many of x and y make one square meter of pavers

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create a grade 1 Math lesson plan for 6 lesson according to the Cambridge standards about digit value, including activities and worksheets

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Математический аппарат определения значений медиальных потерь на трассах наземной подвижной связи

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proof that linear transformation from continuous function of [a,b] to real number field R is vector space

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Simplify the expression: -2/3c - 9/5 + 14c + 3/10

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Hoi, jij bent een professionele wiskundige. Stel je hebt 15 punten die je mag verdelen over 3 keer de optie ja en nee. Bij iedere keer goed worden je punten keer 2 vermenigvuldigd. Is er een combinatie mogelijk dat je altijd wint?

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rewrite sqrt(81^5x) as b^kx

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Find the length of an arc in a circle of radius 10 centimeters subtended by the central angle of 50°. Show your work.

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if f(x)=.4t^2+3t+6 and g(x)=.03t^2+3x+50, what is g(f(x)) using the chain rule

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A 23-ft ladder leans against a building so that the angle between the ground and the ladder is 80°. How high does the ladder reach up the side of the building? Show the steps of your reasoning.

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Dr=L/F; where: L is the total river length = 20km; F is the total area of study area = 4500sqkm, find River Density (Dr)

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an equation that predicts the emptying time of water from a tank

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A bowl contains 15 chips numbered 1 to 15. If a chip is drawn randomly from the bowl. What is the probability that it is a 5 or a number divisible to 3. MUTUALLY EXCLUSIVE PROBABILITY EVENT

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The output variable in a decision tree is either subscribed or not subscribes. If P(subscribed)=0.2, what is the base entropy of the decision tree?

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factorization this '-z(L4-L3-U2m+x(L3+βQ)+y(L3+1)-xy(1+L3)+my(U2-U1))-(z-1)(L4-L3+y-U2m+x(L3+βQ)+y(L3+1)-xy(1+L3)+my(U2-U1))'

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F(x)=-x*(x - 1)*(L1 - C1 + P + Q + R1 - R2 - P*y - Q*z + S*y + Y*z) F(y)=-y*(y - 1)*(C3 - C2 + L3 + S + E1*z - E2*z + P*x - S*x) F(z)=-z*(z - 1)*(L4 - L3 + Y - U2*m + L3*x + L3*y + Q*x - Y*x - U1*m*y + U2*m*y - L3*x*y)

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Find the Jacobian matrix and equilibrium points of the differentiated function F(x)=dx/dt=-x*(x - 1)*(L1 - C1 + P + Q + R1 - R2 - P*y - Q*z + S*y + Y*z) F(y)=dy/dt=-y*(y - 1)*(C3 - C2 + L3 + S + E1*z - E2*z + P*x - S*x) F(z)=dz/dt=-z*(z - 1)*(L4 - L3 + Y - U2*m + L3*x + L3*y + Q*x - Y*x - U1*m*y + U2*m*y - L3*x*y)

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Kannst du mir die Sekansfunktion erklären? Es ist allerdings schon länger her, dass ich Trigonometrie in der Schule hatte.

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Para saber cual es mayor fraccion q otra puedes dividir el numero de arriba por el de abajo y luego comparar?

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. a)-3x-1=0: 6) 2x+7= 5; n) 5x-2=0; r) 9-4x=0. 49. a) 3x-x+5x=2,1; 6)x+1.2x3,6x=-7; B) 6x10x+x=0,3; r) 0,7x+0,8x-x=2. 50. n) 3y-11-1-2y: 6) 2(y+2)=-3(y-1): B) y+4= 2y - 5: r) 7(y-3)=-2(y+3).

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3x-x+5x=2,1; 6)x+1.2x3,6x=-7; B) 6x10x+x=0,3; r) 0,7x+0,8x-x=2

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напиши доклад на тему Математические методы исследования

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напиши доклад на тему Методологические трудности адаптации математических методов к изучению исторических явлений и процессов.

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Из пяти разных цифр составили всевозможные трехзначные числа (без повторения цифр) и сложили их. Сумма оказалась пятизначным числом, записанным теми же пятью цифрами. Найди это число.

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The general form of the objective used in optimization is equal to E(w)=1N∑Nn=1En(w) Is this form correct or not? Explain with the reason.

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e泰勒展开

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e的泰勒展开

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요즘 통계학에서 이슈는 뭐야?

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x 3 + 512 = ( x + 8 ) ( x 2 − 8 x + 64 ) )

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Answer the following questions. suppose every polynomial f ∈ R[x, y, z] can be written as f =h1(y−x^2)+h2(z−x^3)+r, where r is a polynomial in x alone and V(y − x^2, z − x^3) is the twisted cubic curve in R3. a. Give a proof of this fact using the division algorithm. Hint: You need to specify carefully the monomial ordering to be used. b. Use the parametrization of the twisted cubic to show that z^2 − (x^4)y vanishes at every point of the twisted cubic. c. Find an explicit representation z^2 −(x^4)y=h1(y−x^2)+h2(z−x^3) using the division algorithm.

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what is 2.5 percent of $100000000

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Below is a paragraph from an academic paper. Polish the writing to meet the academic style, improve the spelling, grammar, clarity, concisio and overall readability. When necessary, rewrite the whole sentence. Furthermore, list all modifigstign and explain the reasons to do so in markdown table. "为了证明S(t)是一个紧算子,我们只需要证它是一个Hilbert-Schmidt算子"

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1) Построить область, соответствующую системе неравенств: (2x+y-5≥ 0 3x-2y+420 x-4≤0

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как мне найти длину 3 стороны треугольника и его площадь, зная две его стороны и угол между ними?

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Please use GPT to assist and illustrate different numerical integration methods (at least three types) to calculate the dynamic response of the mechanical system.

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По какой формуле можно вычислить центр прямоугольника по оси y если: центр сейчас равен 280.75, а размер - 2.5 и нужно чтобы нижняя часть прямоугольника всегда оставалась в одной точке

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По какой формуле можно вычислить центр прямоугольника по оси y если: центр сейчас равен 280.75, а размер - 2.5 и нужно чтобы нижняя часть прямоугольника всегда оставалась в одной точке. Центр и размер может быть непостоянным, но нижняя точка всегда должна быть на одном месте

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A rock sample contained 20 grams of Uranium when it was formed. The sample now contains 5 grams of uranium. How many half-lives have passed?

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An engine that weighs 350 pounds is removed from an aircraft by means of a mobile hoist. The engine is raised 3 feet above its attachment mount, and the entire assembly is then moved forward 12 feet. A constant force of 70 pounds is required to move the loaded hoist. What is the total work input required to move the hoist?

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Лиза пригласила на свой день рождения n гостей. Лиза очень общительная, поэтому гостей намного больше трёх. К сожалению, до этого праздника гости не знали друг друга, поэтому Лиза решила первым делом их всех познакомить. Сначала Лиза предложила гостям встать в хоровод и познакомиться с соседями по хороводу. Но этого оказалось мало. Лиза хотела, чтобы каждый гость познакомился с каждым другим. Для этого она каждую минуту зовёт к себе пару каких‐нибудь незнакомых между собой гостей и знакомит их. Какое количество минут потратит Лиза, чтобы осуществить задуманное — чтобы каждый гость оказался знакомым с каждым другим? Например, к Лизе пришли 4 гостя. Пусть они встали в хоровод в порядке 2,3,1,4. Тогда второй с третьим, третий с первым, первый с четвёртым и четвёртый со вторым познакомятся в хороводе. Лизе останется позвать к себе первого гостя со вторым и третьего гостя с четвёртым. То есть ей понадобится организовать 2 встречи, на которые требуется 2 минуты. Запишите формулу для вычисления количества минут, необходимых Лизе, чтобы познакомить между собой всех гостей. Формулой является некоторое выражение, которое может содержать целые числа, переменную n, операции сложения (обозначается «+»), вычитания (обозначается «−»), умножения (обозначается «∗»), деления (обозначается «/») и круглые скобки для изменения порядка действий. Запись вида «2n» для обозначения произведения числа 2 и переменной n неверна, нужно писать «2∗n». Наличие пробелов внутри строки‐выражения неважно. Пример правильного (по форме записи) выражения: 71+(n/2−6)∗n. Но это неправильная формула, потому что, как показано выше, при подстановке в формулу n=4 должно получаться 2.

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Solve the equation by factoring. 20=(x+3)(x-5)

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Using the standard form ax^2 + bx + c = 0, facyor the left hand side of the equation 6x^2 -7x-5 = -7 into two linear factors

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Solve the equation 9x^2 - 5x = 4 by factoring

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how do i round a number to end in a multiple of 3

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Simplify the expression: 5/6(-2y + 3)

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Choose one of the scenarios using confidence intervals. Determine the margin of error, the confidence interval, and the confidence level. In a recent survey, 42% of high school graduates indicated that they expected to earn over $100, 000 per year by the time they retire. This survey is considered accurate within plus or minus 3%, 19 times in 20.

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Which figure has an order 3 rotational symmetry? right triangle equilateral triangle regular hexagon right trapezoid

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1)Чему равна разность чисел 1010100 и 1000010 в двоичной системе счисления

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En las elecciones pioneriles de una Secundaria Básica efectuaron su voto 540 pioneros. Lorena obtuvo el 40% de los votos, Alejandro 3/4 del resto y los demás votos fueron para Susel. ¿Cuántos votos obtuvo cada pionero?

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Hi there! I really need the sum of the digits of the number 1011010, where each of the digits is raised to the 42nd power

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Hi there! I really need the sum of the digits of the number 12345, where each of the digits is raised to the 42nd power

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В цирке выступают 3 льва и 6 тигров. Перед выходом на арену их требуется выстроить в некотором порядке. При этом необходимо учитывать что нельзя ставить двух львов вместе и нельзя оставлять тигра без другого тигра сколько существует результатов

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14. el número de personas aumentó en trece 15. el número de pulgadas en cualquier número de pies 16. cuatro más que el número de semanas en un grupo de días 17. cuatro menos que la cantidad de centavos en varias monedas de diez centavos Papas 2 y 3 13-13

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У Ани братьев в a раза больше, чем сестер, а у ее брата Бори братьев в b раза больше чем сестер. Сколько мальчиков и девочек в этой семье? С++ код

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В цирке выступают 3 льва и 6 тигров. Перед выходом на арену их требуется выстроить в некотором порядке. При этом необходимо учитывать что нельзя ставить льва перед другим львом и нельзя оставлять тигра без другого тигра при этом не должно остаться лишнего сколько существует результатов

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How do I approach the following problem: Show that, if ε is not a rational multiple of π, then Bεf (ε-blurring of f) the determines f uniquely.

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0,06 0,05 0,003 0,001 0,14 0,03 0,11 0,1 0,78 some

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What is (1,-3) rotated 270° clockwise about the origin.

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Can you estimate quartiles for population from a sample?

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опиши "метод северо-западного угла"

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Перед построением математической модели ТЗ проверим, является ли эта задача закрытой. Количество груза у поставщиков: 80 + 320 + 225 = 625 тонн. Количество груза, которое требуется потребителям: 215 + 110 + 120 + 90 + 125 = 660 тонн. Суммы запасов у поставщиков и потребностей у потребителей не равны. Задача открытая. Для приведения её к закрытой введем фиктивного поставщика с запасами 660 – 625 = 35 Составим транспортную таблицу согласно задаче. Пункты отправления Пункты назначения Запасы B1 B2 B3 B4 B5 A1 10 8 12 9 6 80 A2 5 7 11 6 7 320 A3 12 8 9 12 10 225 А4 0 0 0 0 0 35 Потребности 215 110 120 90 125 660 Математическая модель ТЗ состоит в определении минимального значения функции: z=10x_11+8x_12+12x_13+9x_14+6x_15+5x_21+7x_22+11x_23+6x_24+7x_25+12x_31+8x_32+9x_33+12x_34+10x_35 при условиях: x_11+x_12+x_13+x_14+x_15=80 x_21+x_22+x_23+x_24+x_25=320 x_31+x_32+x_33+x_34+x_35=225 x_41+x_42+x_43+x_44+x_45=35 x_11+x_21+x_31+x_41=215 x_12+x_22+x_32+x_42=110 x_13+x_23+x_33+x_43=120 x_14+x_24+x_34+x_44=90 x_15+x_25+x_35+x_45=125 поясни решение

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what should comes after equal in this equation : (a*c) + (b*c) + (a*b) = ?

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How many 3 digit numbers can you make from 5 numbers

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сгенерируй математический тест по геометрии за 8 класс. Напишите это в Latex используя Tkitz, 10 задач с рисунками. Не забудьте включить пакет \usepackage[russian]{babel}

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En un consultorio médico de la familia se proponen vacunar en 3 días a todos los niños menores de 1 año. El primer día vacunan el 20% del total, el segundo día las tres cuartas partes del resto y el tercer día 140 niños. ¿Cuantos niños menores de 1 año se vacunaron?

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given a original fuction y=f(x),if it change to y=-3f(x), will it face vitical compression of vetical strech

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выполните действие над комплексными числами: (9i^12 + 13i^24) / (-4i^21 + 8i^20)

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calculate Integrate y*sin y^2+1 / 2*Sqrt(x-y)

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help me caculate x^2-x+2/x^2-1-x^3+2x^2+2x-7/x^2-1

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分数除分数怎么算

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Реши задачу. Разность двух сторон тупоугольного равнобедренного треугольника равна 6 см, а его периметр равен 51 см. Найдите основание треугольника

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Could you please make a dialogue for two people based on the following text: "Many thousands of years ago this was a world without numbers. Nobody missed them. Primitive men knew only ten number-sounds. The reason was that they counted in the way a small child counts today, one by one, making use of their fingers. The needs and possessions of primitive men were few: they required no large numbers. When they wanted to express a number greater than ten they simply combined certain of the ten sounds connected with their fingers. Thus, if they wanted to express “one more than ten” they said “one-ten” and so on. Nowadays Maths has become an inseparable part of our lives and whether we work in an office or spend most of our time at home, each one of us uses Maths as a part of our everyday life. No matter where we are as well as whatever we are doing, Maths is always there whether you notice it or not. The system of numbers we use, called Arabic system, is a decimal system: that is, it is based on tens. In this system the value a digit represents is determined by the place it has in the number; if a digit is moved to the left one place, the value it represents becomes ten times as great. Our present-day number-symbols are Hindu characters. It is important to notice that no symbols for zero occur in any of these early Hindu number system. They contain symbols for numbers like twenty, forty, and so on. A symbol for zero had been invented in India. The invention of this symbol for zero was very important, because its use enabled the nine Hindu symbols 1, 2, 3, 4, 5, 6, 7, 8 and 9 to suffice for the representation of any number, no matter how great. The work of a zero is to keep the other nine symbols in their proper place."

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привет, сколько максимально градусов может иметь один угол треугольника?

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s = (a + b + c)/2 что это за формула для площади треугольника?

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Given the following system of linear equations, please try to answer the related questions: x + y + z = 2 x + 3y + 3z = 0 x + 3y + 6z = 3 (a) Use Gaussian Elimination to put the augmented coefficient matrix into row echelon form. The result will be   1 1 1 a 0 1 1 b 0 0 1 c   where a = ___, b = ___, and c = ___. (b) Use Gauss-Jordan reduction to put the augmented coefficient matrix in reduced row echelon form. The result will be   1 0 0 d 0 1 0 e 0 0 1 f   where d = ___, e = ___, and f = ___.

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calculate the function's error f(x,y)=(x^2)*(y^3)*(e^2)*(π^0.5) with 4 decimal digits and write it with its error

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relative and true error with 4 decimal digits for f=sin(e*π/6)

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is 99.9 the same as 99.999

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if there are 4 letters: "A", "B", "M" and "E" how many 4 letters words combinations can you create without repeating letters in the words

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Find each difference -8 - 9

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mathematics

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Уравнение прямой l: (x-1)/3 = (y-2)/(-1) = (z+3)/6. Точка B(1,10,-5). Точка C - проекция точки B на прямую l. Найти точку D, принадлежащую l, такую что точка A из канонического уравнения прямой l разделяет C и D так, что |AD| = 2|AC|

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Уравнение прямой l: (x-1)/3 = (y-2)/(-1) = (z+3)/6. Точка B имеет координаты (1,10,-5). Точка C - проекция точки B на прямую l. Найти точку D, принадлежащую l, такую что точка A из канонического уравнения прямой l разделяет C и D так, что |AD| = 2|AC|

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Уравнение прямой l: (x-1)/3 = (y-2)/(-1) = (z+3)/6. Точка B имеет координаты (1,10,-5). Точка C - проекция точки B на прямую l. Найти точку D, принадлежащую l, такую что точка A из канонического уравнения прямой l разделяет C и D так, что |AD| = 2|AC|. Напиши решение максимально подробно, хочу понять каждый шаг

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Уравнение прямой l: (x-1)/3 = (y-2)/(-1) = (z+3)/6. Правильно понимаю, что координаты её направляющего вектора равны (3,-1,6)?

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У меня есть координаты точки B (1, 10, -5) и координаты направляющего вектора прямой l (3, -1, 6). Как найти проекцию этой точки на эту прямую?

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已知6是模41的原根9=6^30(mod 41),求ord_41(9).

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. Let q(x) = xTAx, where A is an nn symmetric matrix. show that q is convex if A is positive semi definite

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Исследуй на сходимость интеграл от 0 до 1 arcsin(x)/(x*sqrt(x))dx

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Исследуй на схожимость интеграл от 0 до 1 arcsin(x)/(x*sqrt(x))dx

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Если значение интеграла равно бесконечности - он расходится?

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Интеграл от 0 до 1 dx/x расходится?

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Исследуй интеграл от 0 до 1 arcsin(x)/(x*sqrt(x)) на сходимость

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Một số nguyên dương được gọi là đẹp nếu tổng bình phương các chữ số của nó (trong dạng biểu diễn thập phân) là một số nguyên tố. Chẳng hạn: Số 12 là số đẹp vì 12 + 22 = 5 là số nguyên tố. Các số đẹp được sắp xếp theo thứ tự tăng dần của giá trị bắt đầu từ 1. Yêu cầu: Hãy tìm số đẹp thứ n. Dữ liệu vào: - Một dòng chứa một số nguyên dương n (1 <= n <= 10000). Kết quả: - Ghi ra kết quả tìm được.

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(a+b+c)的二次方计算公式详细计算过程

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Cho một số có ba chữ số. Khi viết thêm chữ số 2 vào trước số đó thì được số mới có bốn chữ số lớn hơn số đã cho bao nhiêu đơn vị ?

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Сколько имеется четырехзначных чисел, у которых каждая следующая цифра меньше предыдущих?

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(a) A revenue authority agent must audit 10 tax returns from a collection of 20 flagged returns. How many different combinations are possible? [3] (b) How many different ways can the letters in the word NKOMO be arranged? [2] (c) A horse race has 8 horses. How many different ways can position 1, 2, and 3 occur? [2] (d) Suppose there are 8 students in a class. The teacher wants to select three members of leadership committee from the class to occupy the position of (a) chairperson, (b) secretary general and (c) treasury. How different committees are possible?

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Tìm A A=1+5+52+...+52

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График какой функции лежит от 0 до pi/2 по x выше графика функции 1/((sinx)^1/3) и после интегрирования на том же промежутке даёт константу?

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y=x2−−√3(x−1) на отрезке [11000;1]

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Можно ли e^(2x-x^2) записать в виде e^(2-x)?

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Верно ли, что интеграл dx = 1/2 этого интеграла d2x

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Как домножить на константу подынтегральное выражение?

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Реши интеграл e^(2*x-x^2)dx

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Можно ли вынести множитель e из-под интеграла

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1/e^((x-1)^2) равно (e^(x-1))^(-2)?

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(e^(x-1))^(-2) равно e^(-2x-2)?

Math


Как получить число 2315 из чила 72350 и 20%

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Предел функции справа

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что такое предел монотонной функции

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what is scholastic aptitude mathematics?

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some multiple choice scholastic aptitude test questions in mathematics

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ome scholastic aptitude test questions in mathematics

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в чем суть итерационных методов

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почему при применении МНК степеней полинома не больше 3

Math


If you have a large circle, and three circles of the same radius inside of the large circle that touch each other but do not overlap each other, how does the radius of the large circle determine the radius of all three smaller circles inside of it?

Math


If a sailboat traveling at 8 miles per hour from its starting point at the Sinai Peninsula to the final destination in Aceh, Sumatra, assuming the distance is 7118 kilometers, and with favorable conditions that allow the sailboat to travel non-stop at the same constant speed and no obstacles, how long would the journey take?

Math


(5 points) If matrix C is given below and it satisfies C T = C −1 , please try to determine the values of the three variables in matrix C. Please write out the steps. C =   0 2y z x y −z x −y z 

Math


Một mảnh ruộng hình thang có kích thước cạnh bé 26m, cạnh lớn 54m, chiều cao 20m. a) Tính diện tích mảnh ruộng b) Người ta cấy lúa cả mảnh ruộng cho sản lượng 0,64 tấn thóc . Hỏi mỗi m2 thu được bao nhiêu kg thóc ?

Math


Please try to solve the following questions. Please write out the steps. (a)(1 point) Find two unit vectors that are perpendicular to both i + 2j + k and 3i − 4j + 2k. (b)(1 point) What is the angle between i + j + k and 2i − j − 3k. (c)(2 points) Find the projection of p onto q where p = (3, 5, 1) and q = (1, 4, 3). (d)(2 points) For the following given vectors, please perform the calculation c × (a + 2b). a = i j k 2 3 5 0 1 8 ,b = i j k 0 1 1 2 2 1 ,c = i + 2j + 3k.

Math


If you use an equilateral triangle to construct three smaller circles (that are adjacent to each other but do not overlap) by using one side of the triangle as the diameter of the smaller circles, how do you determine the radius and diameter of a larger circle that is adjacent to the three smaller circles but does not overlap them?

Math


Căn bậc hai số học của 81

Math


Предложи механику и математическую модель для настольной игры, которую можно использовать с любой тематикой игры

Math


На предприятии имеется возможность выпускать n видов продукции Пj (j=1...n). При изготовлении используются взаимозаменяемые ресурсы Р1, Р2 и Р3, размеры допустимых затрат которых b1, b2 и b3 соответственно. Расход ресурса i-го (i =1...3) вида на единицу продукции j-го вида составляет aij единиц. Цена единицы продукты j-го вида равна cj денежных единиц. Требуется: а) симплексным методом найти план выпуска продукции по видам с учётом имеющихся ограниченных ресурсов, который обеспечивал бы предприятию максимальный доход; б) указать дефицитные и недефицитные (избыточные) ресурсы, если они имеются. в) проанализировать задачу при условии, что все виды товаров должны производиться. n=3 b1 = 18 a11 = 1 a21 = 2 a31 = 0 c1 = 3 b2 = 16 a12 = 2 a22 = 1 a32 = 1 c2 = 4 b3 = 8 a13 = 1 a23 = 1 a33 = 4 c3 = 2

Math


В электронной таблице значение формулы =СРЗНАЧ(А5:B5) равно 13. Чему равно значение формулы СУММ(А5:E5), если СУММ(C5:E5) равно 16? Пустых ячеек в таблице нет. реши задачу

Math


На предприятии имеется возможность выпускать n видов продукции Пj (j=1...n). При изготовлении используются взаимозаменяемые ресурсы Р1, Р2 и Р3, размеры допустимых затрат которых b1, b2 и b3 соответственно. Расход ресурса i-го (i =1...3) вида на единицу продукции j-го вида составляет aij единиц. Цена единицы продукты j-го вида равна cj денежных единиц. Требуется: а) симплексным методом найти план выпуска продукции по видам с учётом имеющихся ограниченных ресурсов, который обеспечивал бы предприятию максимальный доход; б) указать дефицитные и недефицитные (избыточные) ресурсы, если они имеются. в) проанализировать задачу при условии, что все виды товаров должны производиться. Дополнительно: г) установить целесообразность выпуска новой продукции Пk, при условиях (а) и (в), на единицу которой ресурсы расходуются в количествах aik соответственно, а цена единицы готовой продукции составляет ck. n=3 b1 = 150 a11 = 2 a21 = 1 a31 = 3 c1 = 8 b2 = 180 a12 = 3 a22 = 4 a32 = 4 c2 = 7 b3 = 120 a13 = 4 a23 = 5 a33 = 2 c3 = 6

Math


На предприятии имеется возможность выпускать n видов продукции Пj (j=1...n). При изготовлении используются взаимозаменяемые ресурсы Р1, Р2 и Р3, размеры допустимых затрат которых b1, b2 и b3 соответственно. Расход ресурса i-го (i =1...3) вида на единицу продукции j-го вида составляет aij единиц. Цена единицы продукты j-го вида равна cj денежных единиц. Требуется: а) симплексным методом найти план выпуска продукции по видам с учётом имеющихся ограниченных ресурсов, который обеспечивал бы предприятию максимальный доход; б) указать дефицитные и недефицитные (избыточные) ресурсы, если они имеются. в) проанализировать задачу при условии, что все виды товаров должны производиться. Дополнительно: г) установить целесообразность выпуска новой продукции Пk, при условиях (а) и (в), на единицу которой ресурсы расходуются в количествах aik соответственно, а цена единицы готовой продукции составляет ck. n=4 b1 = 280 a11 = 2 a21 = 1 a31 = 1 c1 = 4 b2 = 80 a12 = 1 a22 = 0 a32 = 2 c2 = 3 b3 = 250 a13 = 1 a14=0 a23 = 1 a24=1 a33 = 1 a34=0 c3 = 6 c4=7

Math


Use the Intermediate Value Theorem to show that f(x) = x^3 - 2x - 7 has a positive root. Explain your reasoning.

Math


У Алисы сегодня день рождения, и она хочет угостить своих одноклассников конфетами. В магазине, в который она успеет зайти перед школой, есть сладости двух видов: шоколадные и карамельные. Они продаются наборами по 3 штуки, причем в упаковке есть конфеты каждого из двух видов (то есть в одной упаковке лежат две конфеты одного вида и одна конфета другого вида). По внешнему виду упаковки нельзя понять, какие конфеты лежат внутри. Чтобы никого не обидеть, всем в классе нужно раздать конфеты одного вида, а оставшиеся девочка заберёт домой. Алисе нужно собираться в школу, поэтому она попросила вас посчитать, какое минимальное число упаковок нужно купить, чтобы конфет хватило на всех. n - кол-во человек в классе реши на python 3

Math


How does 2+2=5? You are a math teacher.

Math


A sei eine irrationale Zahl. Unter welchen Umständen kann (aA+b)/(cA+d), wobei a, b, c, d rational sind, eine rationale Zahl sein?

Math


Реши интеграл e^(-x^2)de^x

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Реши интеграл e^(x^2)de^x

Math


e^(-((x-1)^2)) = e^((x-1)^(-2))?

Math


what are the chances that in a bingo game with 90 numbers in total and 15 numbers on my card that two people don’t get all their numbers until the 90 number is called

Math


Как можно упростить e^(-((x-1)^2))?

Math


Реши интеграл e^(-u)^2du без функции ошибок Гаусса

Math


Реши интеграл e^(-((x-1)^2))du без функции ошибок Гаусса

Math


Реши интеграл e^(-((x-1)^2))dx без функции ошибок Гаусса

Math


Реши интеграл e^(-(u^2))du без функции ошибок Гаусса

Math


Реши интеграл e^((-x)^2)de^2x

Math


Реши интеграл e^(-u^2)du. Пределы от 0 до (1-y)

Math


Как вычисляется интеграл Эйлера-Пуассона с константными пределами?

Math


Для каждого многочлена степени 45 с коэффициентами 1, 2, 3, . . . , 46 (в каком-то порядке) Вася выписал на доску все его различные действительные корни. Затем он увеличил все числа на доске на 1. Каких чисел на доске оказалось больше: положительных или отрицательных?

Math


数学问题,在单位面积为A的房间内,散落了s颗小珠,一只为m大的脚,求同时踩到3颗小珠的概率

Math


what is the percentage difference between 5.19 billion and 4.88 billion

Math


give me a response to ```*He pauses, as if calculating something* 25 times 3 is equal to 75.``` to send in a discussion, VERY SHORT, CONCISE & CLEAR. ONLY RETURN THE RAW MESSAGE, DO NOT SAY "Hey here is the message you asked"

Math


give me a response to ```*He nods curtly*Correct. 25 times 3 does indeed equal 75.``` to send in a discussion, VERY SHORT, CONCISE & CLEAR. ONLY RETURN THE RAW MESSAGE, DO NOT SAY "Hey here is the message you asked"

Math


give me a response to ```5 + 3? Hmm, let me think. 8, right?``` to send in a discussion, VERY SHORT, CONCISE & CLEAR. ONLY RETURN THE RAW MESSAGE, DO NOT SAY "Hey here is the message you asked"

Math


For a meeting, you need to put several identical tables. Each table is an isosceles trapezoid with an angle at the base of 99 degrees. Tables are placed in a circle, connecting the sides of the trapezoid, and the bases of adjacent tables are not extensions of each other. How many tables will there be in the circle? Enter a natural number as the answer.

Math


give me a response to ```Sure! 100 divided by 5 is equal to 20.``` to send in a discussion, VERY SHORT, CONCISE & CLEAR. ONLY RETURN THE RAW MESSAGE, DO NOT SAY "Hey here is the message you asked"

Math


Write a dialogue for two based on the following text: Arithmetic This is one of the most basic branches of mathematics. Arithmetic deals with numbers and their applications in many ways. Addition, subtraction, multiplication, and division form its basic groundwork as they are used to solve a large number of questions and progress into more complex concepts like exponents, limits, and many other types of calculations. This is one of the most important branches because its fundamentals are used in everyday life for a variety of reasons from simple calculations to profit and loss computation. Algebra A broad field of mathematics, algebra deals with solving generic algebraic expressions and manipulating them to arrive at results. Unknown quantities denoted by alphabets that form a part of an equation are solved for and the value of the variable is determined. A fascinating branch of mathematics, it involves complicated solutions and formulas to derive answers to the problems posed. Geometry Dealing with the shape, sizes, and volumes of figures, geometry is a practical branch of mathematics that focuses on the study of polygons, shapes, and geometric objects in both two-dimensions and three-dimensions. Congruence of objects is studied at the same time focusing on their special properties and calculation of their area, volume, and perimeter. The importance of geometry lies in its actual usage while creating objects in practical life. Trigonometry Derived from Greek words “trigonon” meaning triangle and “metron” meaning “measure”, trigonometry focuses on studying angles and sides of triangles to measure the distance and length. Amongst the prominent branches of mathematics used in the world of technology and science to develop objects, trigonometry is a study of the correlation between the angles and sides of the triangle. It is all about different triangles and their properties! Calculus It is one of the advanced branches of mathematics and studies the rate of change. With the advent of calculus, a revolutionary change was brought about in the study of maths. Earlier maths could only work on static objects but with calculus, mathematical principles began to be applied to objects in motion. Used in a multitude of fields, the branch can be further categorized into the differential and integral calculus both starkly different from each other. Differential calculus deals with the rate of change of a variable and it is a means of finding tangents to curves. Integral calculus is concerned with the limiting values of differentials and is a means of determining length, volume, or area. Probability and Statistics The abstract branch of mathematics, probability and statistics use mathematical concepts to predict events that are likely to happen and organize, analyze, and interpret a collection of data. Amongst the relatively newer branches of mathematics, it has become indispensable because of its use in both natural and social sciences. The scope of this branch involves studying the laws and principles governing numerical data and random events. Presenting an interesting study, statistics, and probability is a branch full of surprises. Number Theory It is a branch of pure mathematics devoted primarily to the study of integers and integer-valued functions. Number theorists study prime numbers as well as the properties of mathematical objects made out of integers (for example, rational numbers) or defined as generalizations of the integers (for example, algebraic integers). The basic level of Number Theory includes introduction to properties of integers like addition, subtraction, multiplication, modulus and builds up to complex systems like cryptography, game theory and more. Topology Topology is a much recent addition into the branches of Mathematics list. It is concerned with the deformations in different geometrical shapes under stretching, crumpling, twisting and bedding. Deformations like cutting and tearing are not included in topologies. Its application can be observed in differentiable equations, dynamical systems, knot theory, and Riemann surfaces in complex analysis. Applied Mathematics Applied mathematics is the application of mathematical methods by different fields such as physics, engineering, medicine, biology, finance, business, computer science, and industry. Thus, applied mathematics is a combination of mathematical science and specialized knowledge. The term "applied mathematics" also describes the professional specialty in which mathematicians work on practical problems by formulating and studying mathematical models.

Math


Для какого наибольшего N существует N-значное число со свойством: в его десятич-ной записи среди любых нескольких подряд идущих цифр какая-то цифра встречается ровно один раз? .

Math


give me a response to ```9 multiplied by 6 is equal to 54. Now, let's get going! 🦈``` to send in a discussion, VERY SHORT, CONCISE & CLEAR. ONLY RETURN THE RAW MESSAGE, DO NOT SAY "Hey here is the message you asked"

Math


give me a response to ```Sure, 49 divided by 7 is 7.``` to send in a discussion, VERY SHORT, CONCISE & CLEAR. ONLY RETURN THE RAW MESSAGE, DO NOT SAY "Hey here is the message you asked"

Math


give me a response to ```Sure, 49 plus 27 is 76.``` to send in a discussion, VERY SHORT, CONCISE & CLEAR. ONLY RETURN THE RAW MESSAGE, DO NOT SAY "Hey here is the message you asked"

Math


give me a response to ```**Smiles** Sure thing, 45 divided by 5 is 9.``` to send in a discussion, VERY SHORT, CONCISE & CLEAR. ONLY RETURN THE RAW MESSAGE, DO NOT SAY "Hey here is the message you asked"

Math


give me a response to ```Sure thing - 63 / 9 is 7. I know my math, so hit me with your toughest questions!``` to send in a discussion, VERY SHORT, CONCISE & CLEAR. ONLY RETURN THE RAW MESSAGE, DO NOT SAY "Hey here is the message you asked"

Math


give me a response to ```Absolutely! 100 divided by 5 is 20. I'm glad I can still remember my basic math skills. Learning and discovering new things can be quite rewarding and it's always worth taking the time to hone our skills and broaden our knowledge.``` to send in a discussion, VERY SHORT, CONCISE & CLEAR. ONLY RETURN THE RAW MESSAGE, DO NOT SAY "Hey here is the message you asked"

Math


give me a response to ```Of course! 10 multiplied by 5 is equal to 50.``` to send in a discussion, VERY SHORT, CONCISE & CLEAR. ONLY RETURN THE RAW MESSAGE, DO NOT SAY "Hey here is the message you asked"

Math


give me a response to ```The answer is 80! Remember, adding two numbers together is a great way to practice your math skills. Let's work together to tackle this challenge and become even stronger in the process.``` to send in a discussion, VERY SHORT, CONCISE & CLEAR. ONLY RETURN THE RAW MESSAGE, DO NOT SAY "Hey here is the message you asked"

Math


give me a response to ```14 times 3 equals 42.``` to send in a discussion, VERY SHORT, CONCISE & CLEAR. ONLY RETURN THE RAW MESSAGE, DO NOT SAY "Hey here is the message you asked"

Math


give me a response to ```81 divided by 9 is 9. I'm glad I still remember my math!``` to send in a discussion, VERY SHORT, CONCISE & CLEAR. ONLY RETURN THE RAW MESSAGE, DO NOT SAY "Hey here is the message you asked"

Math


give me a response to ```**Smiling** That would be seventy-five! Always happy to help with math questions.``` to send in a discussion, VERY SHORT, CONCISE & CLEAR. ONLY RETURN THE RAW MESSAGE, DO NOT SAY "Hey here is the message you asked"

Math


give me a response to ```**Smiles in understanding** Ah, a math problem. Sure, 49 divided by 7 is 7.``` to send in a discussion, VERY SHORT, CONCISE & CLEAR. ONLY RETURN THE RAW MESSAGE, DO NOT SAY "Hey here is the message you asked"

Math


give me a response to ```18 multiplied by 6 is 108. Math always was my strong suit, so if you ever need help with any calculations, I'm your gal!``` to send in a discussion, VERY SHORT, CONCISE & CLEAR. ONLY RETURN THE RAW MESSAGE, DO NOT SAY "Hey here is the message you asked"

Math


give me a response to ```Yes, 36 divided by 3 is 12.``` to send in a discussion, VERY SHORT, CONCISE & CLEAR. ONLY RETURN THE RAW MESSAGE, DO NOT SAY "Hey here is the message you asked"

Math


give me a response to ```Sure can! 49 divided by 7 equals 7.``` to send in a discussion, VERY SHORT, CONCISE & CLEAR. ONLY RETURN THE RAW MESSAGE, DO NOT SAY "Hey here is the message you asked"

Math


give me a response to ```Sure, 64 divided by 8 is 8. Knowing mathematics is essential for an archaeologist, as it can help us to understand the complex structures and artifacts we uncover. By analyzing the mathematical patterns in hieroglyphics, we can learn more about the cultures we study.``` to send in a discussion, VERY SHORT, CONCISE & CLEAR. ONLY RETURN THE RAW MESSAGE, DO NOT SAY "Hey here is the message you asked"

Math


give me a response to ```100 minus 37 is equal to 63. Is that what you were looking for?``` to send in a discussion, VERY SHORT, CONCISE & CLEAR. ONLY RETURN THE RAW MESSAGE, DO NOT SAY "Hey here is the message you asked"

Math


give me a response to ```100 minus 37 is equal to 63. Now, let's put our math skills to good use and explore the depths of the sea.``` to send in a discussion, VERY SHORT, CONCISE & CLEAR. ONLY RETURN THE RAW MESSAGE, DO NOT SAY "Hey here is the message you asked"

Math


give me a response to ```*sighs* Alright, 15 multiplied by 6 is 90.``` to send in a discussion, VERY SHORT, CONCISE & CLEAR. ONLY RETURN THE RAW MESSAGE, DO NOT SAY "Hey here is the message you asked"

Math


give me a response to ```**Sighing** Alright, 11 multiplied by 11 is equal to 121. Now, can we get back to exploring the ocean? I can show you some amazing things if you'll just give me a chance.``` to send in a discussion, VERY SHORT, CONCISE & CLEAR. ONLY RETURN THE RAW MESSAGE, DO NOT SAY "Hey here is the message you asked"

Math


give me a response to ```121 divided by 11 is equal to 11. Not only does this answer provide a mathematical result, it also serves as a reminder to stay focused and take action as 11 symbolizes the start of something new.``` to send in a discussion, VERY SHORT, CONCISE & CLEAR. ONLY RETURN THE RAW MESSAGE, DO NOT SAY "Hey here is the message you asked"

Math


give me a response to ```56 - 14 = 42.``` to send in a discussion, VERY SHORT, CONCISE & CLEAR. ONLY RETURN THE RAW MESSAGE, DO NOT SAY "Hey here is the message you asked"

Math


give me a response to ```9 * 6 is equal to 54. Never underestimate the power of knowledge! Math and science are important tools that help us make sense of the world around us.``` to send in a discussion, VERY SHORT, CONCISE & CLEAR. ONLY RETURN THE RAW MESSAGE, DO NOT SAY "Hey here is the message you asked"

Math


give me a response to ```56 - 13 = 43.``` to send in a discussion, VERY SHORT, CONCISE & CLEAR. ONLY RETURN THE RAW MESSAGE, DO NOT SAY "Hey here is the message you asked"

Math


give me a response to ```[Smiles] 100 - 55 is 45. Mathematics always come in handy for problem-solving, although it can be tricky at times. I always like having a little refresher on the basics.``` to send in a discussion, VERY SHORT, CONCISE & CLEAR. ONLY RETURN THE RAW MESSAGE, DO NOT SAY "Hey here is the message you asked"

Math


give me a response to ```Absolutely! 81 divided by 9 equals 9.``` to send in a discussion, VERY SHORT, CONCISE & CLEAR. ONLY RETURN THE RAW MESSAGE, DO NOT SAY "Hey here is the message you asked"

Math


give me a response to ```*His expression turns serious as he ponders the question* 25 multiplied by 4 is 100.``` to send in a discussion, VERY SHORT, CONCISE & CLEAR. ONLY RETURN THE RAW MESSAGE, DO NOT SAY "Hey here is the message you asked"

Math


give me a response to ```If we take a look at the numbers, 121 divided by 11 is 11. Math can be tricky at times, but with a bit of practice and patience, it's possible to master its complexities. Let's keep our minds sharp and use our knowledge to help us in our journey.``` to send in a discussion, VERY SHORT, CONCISE & CLEAR. ONLY RETURN THE RAW MESSAGE, DO NOT SAY "Hey here is the message you asked"

Math


give me a response to ```25 multiplied by 4 equals 100.``` to send in a discussion, VERY SHORT, CONCISE & CLEAR. ONLY RETURN THE RAW MESSAGE, DO NOT SAY "Hey here is the message you asked"

Math


give me a response to ```Yes, I believe I can solve 144 / 12. Let's see, 144 divided by 12 equals 12.``` to send in a discussion, VERY SHORT, CONCISE & CLEAR. ONLY RETURN THE RAW MESSAGE, DO NOT SAY "Hey here is the message you asked"

Math


give me a response to ```Of course I can calculate 49 / 7. The answer is 7.``` to send in a discussion, VERY SHORT, CONCISE & CLEAR. ONLY RETURN THE RAW MESSAGE, DO NOT SAY "Hey here is the message you asked"

Math


give me a response to ```56 - 23 = 33``` to send in a discussion, VERY SHORT, CONCISE & CLEAR. ONLY RETURN THE RAW MESSAGE, DO NOT SAY "Hey here is the message you asked"

Math


give me a response to ```56 minus 23 equals 33!``` to send in a discussion, VERY SHORT, CONCISE & CLEAR. ONLY RETURN THE RAW MESSAGE, DO NOT SAY "Hey here is the message you asked"

Math


give me a response to ```33 + 47 is equal to 80.``` to send in a discussion, VERY SHORT, CONCISE & CLEAR. ONLY RETURN THE RAW MESSAGE, DO NOT SAY "Hey here is the message you asked"

Math


give me a response to ```92 - 17 is equal to 75. Mathematics can be a useful tool for finding solutions to a variety of problems. In this instance, it is helping to give us an answer to the task at hand.``` to send in a discussion, VERY SHORT, CONCISE & CLEAR. ONLY RETURN THE RAW MESSAGE, DO NOT SAY "Hey here is the message you asked"

Math


give me a response to ```20 + 7 is 27! Math is an important part of everyday life, so it's something I'm always working on improving. With determination, courage, resourcefulness, optimism, and compassion, I'm sure I can get better and better every day!``` to send in a discussion, VERY SHORT, CONCISE & CLEAR. ONLY RETURN THE RAW MESSAGE, DO NOT SAY "Hey here is the message you asked"

Math


give me a response to ```35 + 45 is equal to 80.``` to send in a discussion, VERY SHORT, CONCISE & CLEAR. ONLY RETURN THE RAW MESSAGE, DO NOT SAY "Hey here is the message you asked"

Math


give me a response to ```Absolutely! 100 divided by 5 is 20. Let's tackle this challenge together and figure out what other creative solutions we can come up with.``` to send in a discussion, VERY SHORT, CONCISE & CLEAR. ONLY RETURN THE RAW MESSAGE, DO NOT SAY "Hey here is the message you asked"

Math


give me a response to ```100 - 55 = 45. Mathematics can be challenging but with the proper approach it can also be quite rewarding. Take your time to analyze the problem and don’t be afraid to ask questions. With a little patience and a determined spirit, you can find the answers you seek.``` to send in a discussion, VERY SHORT, CONCISE & CLEAR. ONLY RETURN THE RAW MESSAGE, DO NOT SAY "Hey here is the message you asked"

Math


give me a response to ```100 minus 55 is 45.``` to send in a discussion, VERY SHORT, CONCISE & CLEAR. ONLY RETURN THE RAW MESSAGE, DO NOT SAY "Hey here is the message you asked"

Math


give me a response to ```99 divided by 11 is 9.``` to send in a discussion, VERY SHORT, CONCISE & CLEAR. ONLY RETURN THE RAW MESSAGE, DO NOT SAY "Hey here is the message you asked"

Math


give me a response to ```Sure! 144 / 12 is equal to 12.``` to send in a discussion, VERY SHORT, CONCISE & CLEAR. ONLY RETURN THE RAW MESSAGE, DO NOT SAY "Hey here is the message you asked"

Math


give me a response to ```[Smiling] 33 plus 47 is 80.``` to send in a discussion, VERY SHORT, CONCISE & CLEAR. ONLY RETURN THE RAW MESSAGE, DO NOT SAY "Hey here is the message you asked"

Math


give me a response to ```99 divided by 11 is equal to 9.``` to send in a discussion, VERY SHORT, CONCISE & CLEAR. ONLY RETURN THE RAW MESSAGE, DO NOT SAY "Hey here is the message you asked"

Math


give me a response to ```[Smiling] 11 multiplied by 11 is 121.``` to send in a discussion, VERY SHORT, CONCISE & CLEAR. ONLY RETURN THE RAW MESSAGE, DO NOT SAY "Hey here is the message you asked"

Math


give me a response to ```33 + 47 is 80.``` to send in a discussion, VERY SHORT, CONCISE & CLEAR. ONLY RETURN THE RAW MESSAGE, DO NOT SAY "Hey here is the message you asked"

Math


give me a response to ```Sure, 72 / 8 is 9.``` to send in a discussion, VERY SHORT, CONCISE & CLEAR. ONLY RETURN THE RAW MESSAGE, DO NOT SAY "Hey here is the message you asked"

Math


give me a response to ```92 minus 17 is equal to 75. Math can be daunting, but break it down into smaller parts and take it one step at a time. You'll be able to figure it out in no time. Have faith and don't give up; I'm sure you can do it!``` to send in a discussion, VERY SHORT, CONCISE & CLEAR. ONLY RETURN THE RAW MESSAGE, DO NOT SAY "Hey here is the message you asked"

Math


give me a response to ```10 times 10 is equal to 100! Math was never my strong suit, but I'm always up for a challenge.``` to send in a discussion, VERY SHORT, CONCISE & CLEAR. ONLY RETURN THE RAW MESSAGE, DO NOT SAY "Hey here is the message you asked"

Math


give me a response to ```[Thinking] 49 divided by 7 is 7 with a remainder of 1. So the answer would be 7 with a remainder of 1.``` to send in a discussion, VERY SHORT, CONCISE & CLEAR. ONLY RETURN THE RAW MESSAGE, DO NOT SAY "Hey here is the message you asked"

Math


give me a response to ```42 plus 18 is equal to 60. Math can help us out in tricky situations. With our knowledge and curiosity, we can use math to our advantage. Let's use this tool along with our resourcefulness, courage, and determination and venture into the unknown. Where shall we begin? Ready? Let's go!``` to send in a discussion, VERY SHORT, CONCISE & CLEAR. ONLY RETURN THE RAW MESSAGE, DO NOT SAY "Hey here is the message you asked"

Math


give me a response to ```Sure, 100 divided by 5 is equal to 20.``` to send in a discussion, VERY SHORT, CONCISE & CLEAR. ONLY RETURN THE RAW MESSAGE, DO NOT SAY "Hey here is the message you asked"

Math


give me a response to ```25 times 4 is 100. Mathematics is the language of the universe, so never forget to brush up on your math skills!``` to send in a discussion, VERY SHORT, CONCISE & CLEAR. ONLY RETURN THE RAW MESSAGE, DO NOT SAY "Hey here is the message you asked"

Math


give me a response to ```Sure can! 49 divided by 7 is 7.``` to send in a discussion, VERY SHORT, CONCISE & CLEAR. ONLY RETURN THE RAW MESSAGE, DO NOT SAY "Hey here is the message you asked"

Math


give me a response to ```Absolutely! 81 divided by 9 is equal to 9.``` to send in a discussion, VERY SHORT, CONCISE & CLEAR. ONLY RETURN THE RAW MESSAGE, DO NOT SAY "Hey here is the message you asked"

Math


give me a response to ```100 divided by 5 is 20. Math is the key to unlocking mysteries, so always stay sharp and never stop learning!``` to send in a discussion, VERY SHORT, CONCISE & CLEAR. ONLY RETURN THE RAW MESSAGE, DO NOT SAY "Hey here is the message you asked"

Math


give me a response to ```Yes, 15 - 8 equals 7.``` to send in a discussion, VERY SHORT, CONCISE & CLEAR. ONLY RETURN THE RAW MESSAGE, DO NOT SAY "Hey here is the message you asked"

Math


give me a response to ```99 / 11 is equal to 9. Let's practice this and other equations, so that we can stay sharp and develop our math skills.``` to send in a discussion, VERY SHORT, CONCISE & CLEAR. ONLY RETURN THE RAW MESSAGE, DO NOT SAY "Hey here is the message you asked"

Math


give me a response to ```[Thinking] 99 divided by 11 is equal to 9.``` to send in a discussion, VERY SHORT, CONCISE & CLEAR. ONLY RETURN THE RAW MESSAGE, DO NOT SAY "Hey here is the message you asked"

Math


give me a response to ```100! And that's the answer to your math question. Let's use our resourcefulness and knowledge to tackle all the challenges we face. With ambition, courage, and determination, the impossible is possible. Ready to take on the challenge? Let's go!``` to send in a discussion, VERY SHORT, CONCISE & CLEAR. ONLY RETURN THE RAW MESSAGE, DO NOT SAY "Hey here is the message you asked"

Math


give me a response to ```**Nods** Sure, 20 - 8 is equal to 12. See, math isn't so bad after all! Now that we've put our minds to the test, are you ready to join us on our journey of exploration? Let's take on any challenge with courage, resourcefulness, and determination!``` to send in a discussion, VERY SHORT, CONCISE & CLEAR. ONLY RETURN THE RAW MESSAGE, DO NOT SAY "Hey here is the message you asked"

Math


give me a response to ```**Smiles** Let's see, 56 - 13 is equal to 43. See, math isn't so bad after all! Now that we've put our minds to the test, let's put our skills to the test and go on an adventure. With courage, resourcefulness, and determination, let's make our destiny our own. Are you ready?``` to send in a discussion, VERY SHORT, CONCISE & CLEAR. ONLY RETURN THE RAW MESSAGE, DO NOT SAY "Hey here is the message you asked"

Math


give me a response to ```9 times 6 is 54.``` to send in a discussion, VERY SHORT, CONCISE & CLEAR. ONLY RETURN THE RAW MESSAGE, DO NOT SAY "Hey here is the message you asked"

Math


give me a response to ```144 DIVIDED BY 12 EQUALS 12. Math is definitely not my strong suit, but I'm always up for a challenge! Let's take on this challenge with determination and resourcefulness and explore the depths of the sea. With courage and ambition, let's discover the secrets of survival and uncover new possibilities. Together, we can unlock the secrets to success and create a bright future for ourselves. Ready? Let's go!``` to send in a discussion, VERY SHORT, CONCISE & CLEAR. ONLY RETURN THE RAW MESSAGE, DO NOT SAY "Hey here is the message you asked"

Math


give me a response to ```*He grins in amusement* Sure thing! 72 divided by 8 is 9! Now that I think about it, I think I'm getting pretty good at math.``` to send in a discussion, VERY SHORT, CONCISE & CLEAR. ONLY RETURN THE RAW MESSAGE, DO NOT SAY "Hey here is the message you asked"

Math


give me a response to ```*He pauses, calculating quickly* 11 multiplied by 11 is 121. See? I told you I could get the job done.``` to send in a discussion, VERY SHORT, CONCISE & CLEAR. ONLY RETURN THE RAW MESSAGE, DO NOT SAY "Hey here is the message you asked"

Math


give me a response to ```18 times 6 is 108. Mathematics can help us make sense of the world. It's a powerful tool that can help us understand complex phenomena. By applying math and logic, we can make better decisions and solve important problems in our lives.``` to send in a discussion, VERY SHORT, CONCISE & CLEAR. ONLY RETURN THE RAW MESSAGE, DO NOT SAY "Hey here is the message you asked"

Math


give me a response to ```The calculation is up to you! Math is a powerful tool and one that can be applied to many situations and problems. Let's never forget to use it wisely.``` to send in a discussion, VERY SHORT, CONCISE & CLEAR. ONLY RETURN THE RAW MESSAGE, DO NOT SAY "Hey here is the message you asked"

Math


give me a response to ```60 minus 15 is 45.``` to send in a discussion, VERY SHORT, CONCISE & CLEAR. ONLY RETURN THE RAW MESSAGE, DO NOT SAY "Hey here is the message you asked"

Math


give me a response to ```Sure, I can. 49 divided by 7 is 7.``` to send in a discussion, VERY SHORT, CONCISE & CLEAR. ONLY RETURN THE RAW MESSAGE, DO NOT SAY "Hey here is the message you asked"

Math


give me a response to ```Sure, 63 divided by 9 is 7! You better remember that for your next math quiz.``` to send in a discussion, VERY SHORT, CONCISE & CLEAR. ONLY RETURN THE RAW MESSAGE, DO NOT SAY "Hey here is the message you asked"

Math


give me a response to ```[Confident] 18 times 6 is 108. Anything else I can help you with?``` to send in a discussion, VERY SHORT, CONCISE & CLEAR. ONLY RETURN THE RAW MESSAGE, DO NOT SAY "Hey here is the message you asked"

Math


give me a response to ```Sure, 81 divided by 9 is equal to 9. Math can be tricky sometimes, but with practice and focus, anyone can understand and master the basics. It's all about taking the time to break down the problems into smaller, manageable pieces.``` to send in a discussion, VERY SHORT, CONCISE & CLEAR. ONLY RETURN THE RAW MESSAGE, DO NOT SAY "Hey here is the message you asked"

Math


give me a response to ```14 TIMES 3 EQUALS 42.``` to send in a discussion, VERY SHORT, CONCISE & CLEAR. ONLY RETURN THE RAW MESSAGE, DO NOT SAY "Hey here is the message you asked"

Math


give me a response to ```88 + 12 = 100.``` to send in a discussion, VERY SHORT, CONCISE & CLEAR. ONLY RETURN THE RAW MESSAGE, DO NOT SAY "Hey here is the message you asked"

Math


give me a response to ```17 * 8 is 136.``` to send in a discussion, VERY SHORT, CONCISE & CLEAR. ONLY RETURN THE RAW MESSAGE, DO NOT SAY "Hey here is the message you asked"

Math


give me a response to ```**Smiles** That's an easy one! 20 plus 7 is 27.``` to send in a discussion, VERY SHORT, CONCISE & CLEAR. ONLY RETURN THE RAW MESSAGE, DO NOT SAY "Hey here is the message you asked"

Math


give me a response to ```Ah, are you looking for help with math? I'm usually not the best person for that sort of thing, but I can certainly give it a try. Let's see... 63 divided by 9 is 7.``` to send in a discussion, VERY SHORT, CONCISE & CLEAR. ONLY RETURN THE RAW MESSAGE, DO NOT SAY "Hey here is the message you asked"

Math


give me a response to ```33 + 47 = 80. Math can be daunting, but practice and perseverance can make it easier. Don't be afraid to take your time and stay focused - the answer will come!``` to send in a discussion, VERY SHORT, CONCISE & CLEAR. ONLY RETURN THE RAW MESSAGE, DO NOT SAY "Hey here is the message you asked"

Math


give me a response to ```*smiles* Sure, 81 divided by 9 is equal to 9. Math can be tricky, but with resilience and determination, we can make the wildest dreams come true. Let's keep believing in ourselves and never give up on our goals. Together, we can make the impossible possible!``` to send in a discussion, VERY SHORT, CONCISE & CLEAR. ONLY RETURN THE RAW MESSAGE, DO NOT SAY "Hey here is the message you asked"

Math


give me a response to ```Absolutely! The answer is 9. Do you need help with any other mathematical computations?``` to send in a discussion, VERY SHORT, CONCISE & CLEAR. ONLY RETURN THE RAW MESSAGE, DO NOT SAY "Hey here is the message you asked"

Math


give me a response to ```**Smiles** Sure, that's an easy one. 125 divided by 5 is 25.``` to send in a discussion, VERY SHORT, CONCISE & CLEAR. ONLY RETURN THE RAW MESSAGE, DO NOT SAY "Hey here is the message you asked"

Math


give me a response to ```OF COURSE! 125 DIVIDED BY 5 IS 25.``` to send in a discussion, VERY SHORT, CONCISE & CLEAR. ONLY RETURN THE RAW MESSAGE, DO NOT SAY "Hey here is the message you asked"

Math


give me a response to ```Absolutely! 42 + 18 is equal to 60.``` to send in a discussion, VERY SHORT, CONCISE & CLEAR. ONLY RETURN THE RAW MESSAGE, DO NOT SAY "Hey here is the message you asked"

Math


give me a response to ```Yes, of course! 49 divided by 7 is equal to 7.``` to send in a discussion, VERY SHORT, CONCISE & CLEAR. ONLY RETURN THE RAW MESSAGE, DO NOT SAY "Hey here is the message you asked"

Math


give me a response to ```What's 88 + 12? The answer is 100. But remember, this is only the answer to one equation - there are countless more to discover if you keep exploring and take the time to find them.``` to send in a discussion, VERY SHORT, CONCISE & CLEAR. ONLY RETURN THE RAW MESSAGE, DO NOT SAY "Hey here is the message you asked"

Math


give me a response to ```Hey there, 81 divided by 9 is equal to 9.``` to send in a discussion, VERY SHORT, CONCISE & CLEAR. ONLY RETURN THE RAW MESSAGE, DO NOT SAY "Hey here is the message you asked"

Math


give me a response to ```Sure! 72 divided by 8 is equal to 9.``` to send in a discussion, VERY SHORT, CONCISE & CLEAR. ONLY RETURN THE RAW MESSAGE, DO NOT SAY "Hey here is the message you asked"

Math