problem stringlengths 10 5.15k | answer stringlengths 0 1.23k |
|---|---|
The numbers $1447$, $1005$ and $1231$ have something in common: each is a $4$-digit number beginning with $1$ that has exactly two identical digits. How many such numbers are there?
| 432 |
Miss Aisha's legs are 1/3 of her total height. If her head is also 1/4 of her total height, and she is 60 inches tall, calculate the length of the rest of her body. | Miss Aisha's legs are 1/3*60 = <<1/3*60=20>>20 inches.
The length of her head is 1/4*60 = <<1/4*60=15>>15 inches.
Together, her head and legs are 15+20 = <<15+20=35>>35 inches.
If her total height is 60, the rest of her body has a length of 60-35 = <<60-35=25>>25 inches.
#### 25 |
We are given that $$54+(98\div14)+(23\cdot 17)-200-(312\div 6)=200.$$Now, let's remove the parentheses: $$54+98\div14+23\cdot 17-200-312\div 6.$$What does this expression equal? | 200 |
Homer scored 400 points on the first try in a Candy crush game, 70 points fewer on the second try, and twice the number of points she scored on the second try on the third try. What's the total number of points that she scored in all tries? | If Homer scored 400 points on the first try, he scored 400-70 = <<400-70=330>>330 points on the second try.
The total number of points that Homer scored in the game after two tries are 400+330 = <<400+330=730>>730
On the third try of the Candy crush game, Homer scored twice the number of points she scored on the second... |
Given three integers \( x, y, z \) satisfying \( x + y + z = 100 \) and \( x < y < 2z \), what is the minimum value of \( z \)? | 21 |
The absolute value of -9 is ; the reciprocal of -3 is . | -\frac{1}{3} |
How many even divisors does $9!$ have? | 140 |
Find the number of integer points that satisfy the system of inequalities:
\[
\begin{cases}
y \leqslant 3x \\
y \geqslant \frac{1}{3}x \\
x + y \leqslant 100
\end{cases}
\] | 2551 |
Socorro is preparing for a math contest. She needs to train for a total of 5 hours. Each day, she answers problems about multiplication for 10 minutes and then division problems for 20 minutes. How many days will it take for her to complete her training? | Socorro trains for a total of 10 + 20 = <<10+20=30>>30 minutes each day.
She needs to train for a total of 5 x 60 = <<5*60=300>>300 minutes since an hour has 60 minutes.
Therefore, she will complete her training in 300/30 = <<300/30=10>>10 days.
#### 10 |
How many integers are there from 1 to 16500 that
a) are not divisible by 5;
b) are not divisible by either 5 or 3;
c) are not divisible by 5, 3, or 11? | 8000 |
Given that $\{a_n\}$ is an arithmetic sequence, if $a_3 + a_5 + a_{12} - a_2 = 12$, calculate the value of $a_7 + a_{11}$. | 12 |
You flip a fair coin which results in heads ( $\text{H}$ ) or tails ( $\text{T}$ ) with equal probability. What is the probability that you see the consecutive sequence $\text{THH}$ before the sequence $\text{HHH}$ ? | \frac{7}{8} |
We inscribed a regular hexagon $ABCDEF$ in a circle and then drew semicircles outward over the chords $AB$, $BD$, $DE$, and $EA$. Calculate the ratio of the combined area of the resulting 4 crescent-shaped regions (bounded by two arcs each) to the area of the hexagon. | 2:3 |
Christine must buy at least $45$ fluid ounces of milk at the store. The store only sells milk in $200$ milliliter bottles. If there are $33.8$ fluid ounces in $1$ liter, then what is the smallest number of bottles that Christine could buy? (You may use a calculator on this problem.) | 7 |
What is the result of subtracting $7.305$ from $-3.219$? | -10.524 |
There are 101 natural numbers written in a circle. It is known that among any three consecutive numbers, there is at least one even number. What is the minimum number of even numbers that can be among the written numbers? | 34 |
What is the value of $x$ if $x=\frac{2009^2-2009}{2009}$? | 2008 |
How many square units are in the area of the triangle whose vertices are the $x$ and $y$ intercepts of the curve $y = (x-3)^2 (x+2)$? | 45 |
A triangle has vertices $P=(-8,5)$, $Q=(-15,-19)$, and $R=(1,-7)$. The equation of the bisector of $\angle P$ can be written in the form $ax+2y+c=0$. Find $a+c$.
[asy] import graph; pointpen=black;pathpen=black+linewidth(0.7);pen f = fontsize(10); pair P=(-8,5),Q=(-15,-19),R=(1,-7),S=(7,-15),T=(-4,-17); MP("P",P,N,f);M... | 89 |
A factory received a task to process 6000 pieces of part P and 2000 pieces of part Q. The factory has 214 workers. Each worker spends the same amount of time processing 5 pieces of part P as they do processing 3 pieces of part Q. The workers are divided into two groups to work simultaneously on different parts. In orde... | 137 |
The coefficient sum of the expansion of the binomial ${{\left(\frac{1}{x}-2x^2\right)}^9}$, excluding the constant term, is $671$. | 671 |
Spencer is making burritos, each of which consists of one wrap and one filling. He has enough filling for up to four beef burritos and three chicken burritos. However, he only has five wraps for the burritos; in how many orders can he make exactly five burritos? | 25 |
Given a geometric sequence $\{a_n\}$ with the first term $\frac{3}{2}$ and common ratio $- \frac{1}{2}$, the sum of the first $n$ terms is $S_n$. If for any $n \in N^*$, it holds that $S_n - \frac{1}{S_n} \in [s, t]$, then the minimum value of $t-s$ is \_\_\_\_\_\_. | \frac{17}{12} |
Given that $\tan\alpha=3$, calculate the following:
(1) $\frac{\sin\alpha+\cos\alpha}{2\sin\alpha-\cos\alpha}$
(2) $\sin^2\alpha+\sin\alpha\cos\alpha+3\cos^2\alpha$ | 15 |
What is the smallest positive integer with exactly 12 positive integer divisors? | 96 |
Roll a die twice. Let $X$ be the maximum of the two numbers rolled. Which of the following numbers is closest to the expected value $E(X)$? | 4.5 |
A right triangle has an area of 120 square units, and a leg length of 24 units. What is the perimeter of the triangle, in units? | 60 |
Let $a$, $b$, and $c$ be the 3 roots of the polynomial $x^3 - 2x + 4 = 0$. Find $\frac{1}{a-2} + \frac{1}{b-2} + \frac{1}{c-2}$. | -\frac{5}{4} |
Let $ABCD$ be a square with side length $16$ and center $O$ . Let $\mathcal S$ be the semicircle with diameter $AB$ that lies outside of $ABCD$ , and let $P$ be a point on $\mathcal S$ so that $OP = 12$ . Compute the area of triangle $CDP$ .
*Proposed by Brandon Wang* | 120 |
Given that $α \in (0, \frac{π}{2})$, and $\sin (\frac{π}{6} - α) = -\frac{1}{3}$, find the value of $\cos α$. | \frac{2\sqrt{6} - 1}{6} |
Find the value of $a$ such that the maximum value of the function $y=-x^{2}-2x+3$ in the interval $[a,2]$ is $\frac{15}{4}$. | -\frac{1}{2} |
Let $a, b$, and $c$ be the roots of the cubic polynomial $2x^3 - 3x^2 + 165x - 4$. Compute \[(a+b-1)^3 + (b+c-1)^3 + (c+a-1)^3.\] | 117 |
The solutions to the equations $z^2=4+4\sqrt{15}i$ and $z^2=2+2\sqrt 3i,$ where $i=\sqrt{-1},$ form the vertices of a parallelogram in the complex plane. The area of this parallelogram can be written in the form $p\sqrt q-r\sqrt s,$ where $p,$ $q,$ $r,$ and $s$ are positive integers and neither $q$ nor $s$ is divisible... | 20 |
The three-digit positive integer $N$ has a ones digit of 3. What is the probability that $N$ is divisible by 3? Express your answer as a common fraction. | \frac{1}{3} |
An employee makes 30 dollars an hour for the first 40 hours in the workweek and an additional 50% for every hour above 40 in the week. If he works 6 hours for the first 3 days in the workweek and twice as many hours per day for the remaining 2 days, how much money did he make? | His overtime pay per hour is 30*1.5=$<<30*1.5=45>>45 per hour
He works 6*2=<<6*2=12>>12 hours per day for the last two days.
He works 6+6+6+12+12=<<6+6+6+12+12=42>>42 hours
He gets 42-40=<<42-40=2>>2 hours of overtime.
He makes 40*30+2*45=$<<40*30+2*45=1290>>1290 for the week
#### 1290 |
Let $\omega$ be a nonreal root of $z^3 = 1.$ Find the number of ordered pairs $(a,b)$ of integers such that $|a \omega + b| = 1.$ | 6 |
Ryan's party was 4 times as huge as Taylor's birthday party. If both parties combined had 240 people, how many people were there at Ryan's party? | To get the number of people at Taylor's party, we'll assume there were n people at his party.
The total number of people at Ryan's party is 4*n, four times the number of attendees at Taylor's party.
Combined, there were 4n+n = 240 people at both parties.
This translates to 5n=240.
The total number of people at Taylor's... |
Given a quadrilateral formed by the two foci and the two endpoints of the conjugate axis of a hyperbola $C$, one of its internal angles is $60^{\circ}$. Determine the eccentricity of the hyperbola $C$. | \frac{\sqrt{6}}{2} |
Let \(ABCD\) be an isosceles trapezoid such that \(AD = BC\), \(AB = 3\), and \(CD = 8\). Let \(E\) be a point in the plane such that \(BC = EC\) and \(AE \perp EC\). Compute \(AE\). | 2\sqrt{6} |
Find the difference between $1234_8$ and $765_8$ in base $8$. | 225_8 |
The minimum value of the function \( y = |\cos x| + |\cos 2x| \) (for \( x \in \mathbf{R} \)) is ______. | \frac{\sqrt{2}}{2} |
A certain brand specialty store is preparing to hold a promotional event during New Year's Day. Based on market research, the store decides to select 4 different models of products from 2 different models of washing machines, 2 different models of televisions, and 3 different models of air conditioners (different model... | 100 |
Given $\overrightarrow{a}=(1,2)$ and $\overrightarrow{b}=(-3,2)$, for what value of $k$ does
(1) $k \overrightarrow{a}+ \overrightarrow{b}$ and $\overrightarrow{a}-3 \overrightarrow{b}$ are perpendicular?
(2) $k \overrightarrow{a}+ \overrightarrow{b}$ and $\overrightarrow{a}-3 \overrightarrow{b}$ are parallel? When the... | -\frac{1}{3} |
The function $y = \frac{2}{x}$ is defined on the interval $[1, 2]$, and its graph has endpoints $A(1, 2)$ and $B(2, 1)$. Find the linear approximation threshold of the function. | 3 - 2\sqrt{2} |
Given the function $f(x)=2\ln x - ax^2 + 3$,
(1) Discuss the monotonicity of the function $y=f(x)$;
(2) If there exist real numbers $m, n \in [1, 5]$ such that $f(m)=f(n)$ holds when $n-m \geq 2$, find the maximum value of the real number $a$. | \frac{\ln 3}{4} |
If $4 \in \{a^2-3a, a\}$, then the value of $a$ equals ____. | -1 |
In convex quadrilateral \(EFGH\), \(\angle E = \angle G\), \(EF = GH = 150\), and \(EH \neq FG\). The perimeter of \(EFGH\) is 580. Find \(\cos E\). | \frac{14}{15} |
At a birthday party, 30% of the guests are married, 50% are single, and the rest are children. If there are 1000 guests, how many more married people are there than children? | There are 1000 x 30/100 = <<1000*30/100=300>>300 people who are married.
There are 1000 x 50/100 = <<1000*50/100=500>>500 people who are single.
So, there are a total of 300 + 500 = <<300+500=800>>800 that are either married or single.
This means, 1000 - 800 = <<1000-800=200>>200 are children.
Therefore, there are 300 ... |
Susie has $200 in her piggy bank. If she puts 20% more money into her piggy bank, how much money she will have? | If Susie puts 20% more money into her piggy bank, she'll have 20/100*200 = $<<20/100*200=40>>40 more in her piggy bank.
The total amount of money in Susie's piggy bank will increase to $200+$40=$<<200+40=240>>240
#### 240 |
Three builders build a single floor of a house in 30 days. If each builder is paid $100 for a single day’s work, how much would it cost to hire 6 builders to build 5 houses with 6 floors each? | 6 builders can build a single floor 6 builders / 3 builders = <<6/3=2>>2 times as fast as 3 builders.
Thus 6 builders would build a single floor in 30 days / 2 = 15 days
There are 5 hours x 6 floors/house = <<5*6=30>>30 floors in total in 5 houses with 6 floors each.
Therefore 6 builders would complete the project in 1... |
What is the least five-digit positive integer which is congruent to 7 (mod 12)? | 10,003 |
Given the function $f(x)=-\cos^2 x + \sqrt{3}\sin x\sin\left(x + \frac{\pi}{2}\right)$, find the sum of the minimum and maximum values of $f(x)$ when $x \in \left[0, \frac{\pi}{2}\right]$. | -\frac{1}{2} |
For how many ordered pairs of positive integers $(x, y)$ with $x < y$ is the harmonic mean of $x$ and $y$ equal to $12^{10}$? | 409 |
Real numbers \(a, b, c\) and a positive number \(\lambda\) such that \(f(x)=x^3 + ax^2 + bx + c\) has three real roots \(x_1, x_2, x_3\), satisfying
1. \(x_2 - x_1 = \lambda\);
2. \(x_3 > \frac{1}{2}(x_1 + x_2)\).
Find the maximum value of \(\frac{2a^3 + 27c - 9ab}{\lambda^3}\). | \frac{3 \sqrt{3}}{2} |
What is $1254_6 - 432_6 + 221_6$? Express your answer in base $6$. | 1043_6 |
What is the last digit of the decimal expansion of $\frac{1}{2^{10}}$? | 5 |
The function $f(x)$ satisfies
\[xf(y) = yf(x)\]for all real numbers $x$ and $y.$ If $f(15) = 20,$ find $f(3).$ | 4 |
On the $x O y$ coordinate plane, there is a Chinese chess "knight" at the origin $(0,0)$. The "knight" needs to be moved to the point $P(1991,1991)$ using the movement rules of the chess piece. Calculate the minimum number of moves required. | 1328 |
Tim's car goes down in value by $1000 a year. He bought it for $20,000. How much is it worth after 6 years? | It went down in value 1000*6=$<<1000*6=6000>>6000
So the car is worth 20000-6000=$<<20000-6000=14000>>14,000
#### 14000 |
Let numbers $x$ and $y$ be chosen independently at random from the intervals $[0, \pi]$ and $[-\frac{\pi}{2}, \frac{\pi}{2}]$, respectively. Define $P(\alpha)$ as the probability that
\[\cos^2{x} + \cos^2{y} < \alpha\]
where $\alpha$ is a constant with $1 < \alpha \leq 2$. Find the maximum value of $P(\alpha)$.
A) $\fr... | \frac{\pi}{2} |
The triangle $\triangle ABC$ is an isosceles triangle where $AB = 4\sqrt{2}$ and $\angle B$ is a right angle. If $I$ is the incenter of $\triangle ABC,$ then what is $BI$?
Express your answer in the form $a + b\sqrt{c},$ where $a,$ $b,$ and $c$ are integers, and $c$ is not divisible by any perfect square other than $1... | 8 - 4\sqrt{2} |
How many ways are there to put 5 balls in 3 boxes if the balls are not distinguishable and neither are the boxes? | 5 |
Let $O$ be the origin. A variable plane has a distance of 1 from the origin, and intersects the $x$-axis, $y$-axis, and $z$-axis at $A,$ $B,$ and $C,$ respectively, all distinct from $O.$ Let $(p,q,r)$ be the centroid of triangle $ABC.$ Find
\[\frac{1}{p^2} + \frac{1}{q^2} + \frac{1}{r^2}.\] | 9 |
In the Cartesian coordinate plane, point $P$ is a moving point on the line $x=-1$, point $F(1,0)$, point $Q$ is the midpoint of $PF$, point $M$ satisfies $MQ \perp PF$ and $\overrightarrow{MP}=\lambda \overrightarrow{OF}$, and the tangent line is drawn through point $M$ on the circle $(x-3)^{2}+y^{2}=2$ with tangent po... | \sqrt{6} |
Real numbers \(a, b, c\) and positive number \(\lambda\) make the function \(f(x) = x^3 + ax^2 + bx + c\) have three real roots \(x_1, x_2, x_3\), such that (1) \(x_2 - x_1 = \lambda\); (2) \(x_3 > \frac{1}{2}(x_1 + x_2)\). Find the maximum value of \(\frac{2a^3 + 27c + 9ab}{\lambda^3}\). | \frac{3\sqrt{3}}{2} |
Given the origin of the rectangular coordinate system xOy as the pole and the positive semi-axis of the x-axis as the polar axis, establish a polar coordinate system with the same unit length. The parametric equation of the line l is $$\begin{cases} \overset{x=2+t}{y=1+t}\end{cases}$$ (t is the parameter), and the pola... | \sqrt{2} |
James wants to build a ladder to climb a very tall tree. Each rung of the ladder is 18 inches long and they are 6 inches apart. If he needs to climb 50 feet how many feet of wood will he need for the rungs? | He needs 12/6=<<12/6=2>>2 rungs per foot
So he needs 50*2=<<50*2=100>>100 rungs
Each rung is 18/12=<<18/12=1.5>>1.5 feet
So he needs 1.5*100=<<1.5*100=150>>150 feet
#### 150 |
A high school's second-year students are studying the relationship between students' math and Chinese scores. They conducted a simple random sampling with replacement and obtained a sample of size $200$ from the second-year students. The sample observation data of math scores and Chinese scores are organized as follows... | \frac{15}{7} |
Given the function $f(x)=2\ln x+8x$, find the value of $\lim_{n\to\infty} \frac{f(1-2\Delta x)-f(1)}{\Delta x}$ ( ). | -20 |
Given vectors $\overrightarrow{m}=(\cos \frac {x}{2},-1)$ and $\overrightarrow{n}=( \sqrt {3}\sin \frac {x}{2},\cos ^{2} \frac {x}{2})$, and the function $f(x)= \overrightarrow{m} \cdot \overrightarrow{n}+1$.
(I) If $x \in [\frac{\pi}{2}, \pi]$, find the minimum value of $f(x)$ and the corresponding value of $x$.
(II) ... | \frac{3\sqrt{3}+4}{10} |
The area of the shaded region BEDC in parallelogram ABCD is to be found, where BC = 15, ED = 9, and the total area of ABCD is 150. If BE is the height of parallelogram ABCD from base BC and is shared with ABE, both of which overlap over BE, calculate the area of the shaded region BEDC. | 120 |
Let $f(x) = |\lg(x+1)|$, where $a$ and $b$ are real numbers, and $a < b$ satisfies $f(a) = f(- \frac{b+1}{b+2})$ and $f(10a + 6b + 21) = 4\lg2$. Find the value of $a + b$. | - \frac{11}{15} |
Let $S = (1+i)^{17} - (1-i)^{17}$, where $i=\sqrt{-1}$. Find $|S|$.
| 512 |
Calvin and Phoebe each have 8 more pastries than Frank but only five less than Grace. If Grace has 30 pastries, calculate the total number of pastries that the four have? | If Grace has 30 pastries, then both Phoebe and Calvin each have 30-5 = <<30-5=25>>25 pastries.
The total number of pastries that Phoebe and Calvin have is 25+25 = <<25+25=50>>50
Together, Phoebe, Calvin, and Grace have 50+30 = <<50+30=80>>80 pastries.
Since Calvin and Phoebe each have 8 more pastries than Frank, then F... |
How many orderings $(a_{1}, \ldots, a_{8})$ of $(1,2, \ldots, 8)$ exist such that $a_{1}-a_{2}+a_{3}-a_{4}+a_{5}-a_{6}+a_{7}-a_{8}=0$ ? | 4608 |
Randy has $200 in his piggy bank. He spends 2 dollars every time he goes to the store. He makes 4 trips to the store every month. How much money, in dollars, will be in his piggy bank after a year? | Randy spends 2*4=<<2*4=8>>8 dollars every month.
Randy spends 8*12=<<8*12=96>>96 dollars in a year.
Randy will have 200-96=<<200-96=104>>104 dollars in his piggy bank after a year.
#### 104 |
Jennifer wants to go to a museum. There is one 5 miles away from her home and one 15 miles away. If Jennifer goes to both museums on two separate days, how many miles total will she travel? | Jennifer's home is 5 miles away from the first museum, so the round trip back and forth is 5 miles there + 5 miles back = <<5+5=10>>10 miles altogether.
On another day Jennifer goes to a museum 15 miles away + 15 miles to return home = <<15+15=30>>30 miles total.
Combined, Jennifer travels 10 miles on the first day + 3... |
What is the smallest solution of the equation $x^4-34x^2+225=0$? | -5 |
What is the sum of all of the positive even factors of $504$? | 1456 |
Compute
\[\sum_{k = 1}^\infty \frac{6^k}{(3^k - 2^k)(3^{k + 1} - 2^{k + 1})}.\] | 2 |
Find the units digit of $7 \cdot 17 \cdot 1977 - 7^3$ | 0 |
Let $A,$ $B,$ $C$ be the angles of a triangle. Evaluate
\[\begin{vmatrix} \sin^2 A & \cot A & 1 \\ \sin^2 B & \cot B & 1 \\ \sin^2 C & \cot C & 1 \end{vmatrix}.\] | 0 |
Two distinct natural numbers end in 5 zeros and have exactly 42 divisors. Find their sum. | 700000 |
Samantha bought a crate of 30 eggs for $5. If she decides to sell each egg for 20 cents, how many eggs will she have left by the time she recovers her capital from the sales? | There are 100 cents in each $1 so $5 gives 5*100 cents = <<5*100=500>>500 cents
To recover her capital of 500 cents from a selling price of 20 cents per egg she has to sell 500/20 = <<500/20=25>>25 eggs
There were 30 eggs in the crate to start with so she will have 30-25 = <<30-25=5>>5 eggs left
#### 5 |
Keisha's basketball team must decide on a new uniform. The seventh-graders will pick the color of the shorts (black, gold, or red) and the eighth-graders will pick the color of the jersey (black, white, gold, or blue), and each group will not confer with the other. Additionally, the ninth-graders will choose whether to... | \frac{5}{6} |
Let $P$ and $Q$ be points on line $l$ with $P Q=12$. Two circles, $\omega$ and $\Omega$, are both tangent to $l$ at $P$ and are externally tangent to each other. A line through $Q$ intersects $\omega$ at $A$ and $B$, with $A$ closer to $Q$ than $B$, such that $A B=10$. Similarly, another line through $Q$ intersects $\O... | \frac{8}{9} |
The area of rectangle $ABCD$ with vertices $A$(0, 0), $B$(0, 4), $C$($x$, 4) and $D$($x$, 0) is 28 square units. If $x > 0$, what is the value of $x$? | 7 |
Among the following propositions, the true one is numbered \_\_\_\_\_\_.
(1) The negation of the proposition "For all $x>0$, $x^2-x\leq0$" is "There exists an $x>0$ such that $x^2-x>0$."
(2) If $A>B$, then $\sin A > \sin B$.
(3) Given a sequence $\{a_n\}$, "The sequence $a_n, a_{n+1}, a_{n+2}$ forms a geometric s... | (1) |
Determine the number of ordered pairs of positive integers \((a, b)\) satisfying the equation
\[ 100(a + b) = ab - 100. \] | 18 |
Find the equation of the directrix of the parabola \( y = \frac{x^2 - 8x + 12}{16} \). | y = -\frac{1}{2} |
Let $S$ be the set of 10-tuples $(a_0, a_1, \dots, a_9),$ where each entry is 0 or 1, so $S$ contains $2^{10}$ 10-tuples. For each 10-tuple $s = (a_0, a_1, \dots, a_9)$ in $S,$ let $p_s(x)$ be the polynomial of degree at most 9 such that
\[p_s(n) = a_n\]for $0 \le n \le 9.$ For example, $p(x) = p_{(0,1,0,0,1,0,1,0,0,... | 512 |
A delicious circular pie with diameter $12\text{ cm}$ is cut into three equal-sized sector-shaped pieces. Let $l$ be the number of centimeters in the length of the longest line segment that may be drawn in one of these pieces. What is $l^2$? | 108 |
Let $P(x) = (x-1)(x-2)(x-3)$. For how many polynomials $Q(x)$ does there exist a polynomial $R(x)$ of degree 3 such that $P\left(Q(x)\right) = P(x)\cdot R(x)$? | 22 |
Find the distance between the points $(-5,-2)$ and $(7,3)$. | 13 |
Consider a modified octahedron with an additional ring of vertices. There are 4 vertices on the top ring, 8 on the middle ring, and 4 on the bottom ring. An ant starts at the highest top vertex and walks down to one of four vertices on the next level down (the middle ring). From there, without returning to the previous... | \frac{1}{3} |
A right pyramid has a square base with perimeter 24 inches. Its apex is 9 inches from each of the other vertices. What is the height of the pyramid from its peak to the center of its square base, in inches? | 3\sqrt{7} |
Tom decides to renovate a house. There are 3 bedrooms and each bedroom takes 4 hours to renovate. The kitchen takes 50% longer than each bedroom. The living room took twice as much time as everything else combined. How long did everything take? | The kitchen took 4 * .5 = <<4*.5=2>>2 hours longer than the bedrooms
So the kitchen took 4 + 2 = <<4+2=6>>6 hours
The bedrooms took 3 * 4 = <<3*4=12>>12 hours
So the kitchen and bedrooms combined took 12 + 6 = <<12+6=18>>18 hours
The living room took 18 * 2 = <<18*2=36>>36 hours
So everything took a total of 18 + 36 = ... |
Dr. Harry wants to know how many candies Susan consumed during the week. Susan tells him she bought 3 on Tuesday, 5 on Thursday, 2 on Friday. If she has only 4 of them left, how many did she eat? | She had bought 3+5+2 = <<3+5+2=10>>10 candies over the week
She has only 4 left which means she ate 10-4 = <<10-4=6>>6 candies during the week
#### 6 |
Find the smallest positive integer whose cube ends in $888$.
| 192 |
Stacy just bought a 6 month prescription of flea & tick medicine for her dog for $150.00 online. Her cashback app was offering 10% cashback and she has a mail-in rebate for $25.00 on a 6-month prescription. How much will the medicine cost after cash back and rebate offers? | Her cash back app gave her 10% back on $150.00 so that's .10*150 = $<<10*.01*150=15.00>>15.00 cash back
She received $15.00 from the cashback app and has a $25.00 mail-in rebate for a total of 15+25 = $<<15+25=40.00>>40.00 discounts
She spent $150.00 for the medicine and has $40.00 worth of discounts so the medicine wi... |
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