problem stringlengths 10 5.15k | answer stringlengths 0 1.23k |
|---|---|
Chip has a $50.00 balance on his credit card. Since he didn't pay it off, he will be charged a 20% interest fee. He puts $20.00 on his credit card the following month and doesn't make any payments to his debt. He is hit with another 20% interest fee. What's the current balance on his credit card? | He has a balance of $50.00 and is charged 20% interest so that's 50*.20 = $<<50*.20=10.00>>10.00
He had a balance of $50.00 and now has a $10.00 interest fee making his balance 50+10 = $<<50+10=60.00>>60.00
His balance is $60.00 and he puts another $20.00 on his card for a total of 60+20 = $<<60+20=80.00>>80.00
He didn... |
180 grams of 920 purity gold was alloyed with 100 grams of 752 purity gold. What is the purity of the resulting alloy? | 860 |
If the line \(x=\frac{\pi}{4}\) intersects the curve \(C: (x-\arcsin a)(x-\arccos a) + (y-\arcsin a)(y+\arccos a)=0\), determine the minimum value of the chord length as \(a\) varies. | \frac{\pi}{2} |
Let \( z \) be a complex number. If \( \frac{z-2}{z-\mathrm{i}} \) (where \( \mathrm{i} \) is the imaginary unit) is a real number, then the minimum value of \( |z+3| \) is \(\quad\). | \sqrt{5} |
For a positive integer \( n \), consider the function
\[
f(n)=\frac{4n+\sqrt{4n^2-1}}{\sqrt{2n+1}+\sqrt{2n-1}}
\]
Calculate the value of
\[
f(1)+f(2)+f(3)+\cdots+f(40)
\] | 364 |
In the Cartesian coordinate system $xOy$, there is a curve $C_{1}: x+y=4$, and another curve $C_{2}$ defined by the parametric equations $\begin{cases} x=1+\cos \theta, \\ y=\sin \theta \end{cases}$ (with $\theta$ as the parameter). A polar coordinate system is established with the origin $O$ as the pole and the non-ne... | \dfrac{1}{4}(\sqrt{2}+1) |
Given an angle α with its vertex at the origin of coordinates, its initial side coinciding with the non-negative half-axis of the x-axis, and two points on its terminal side A(1,a), B(2,b), and cos(2α) = 2/3, determine the value of |a-b|. | \dfrac{\sqrt{5}}{5} |
There are 10 horizontal roads and 10 vertical roads in a city, and they intersect at 100 crossings. Bob drives from one crossing, passes every crossing exactly once, and return to the original crossing. At every crossing, there is no wait to turn right, 1 minute wait to go straight, and 2 minutes wait to turn left. Let... | 90 \leq S<100 |
Stacy, Steve and Sylar have 1100 berries total. Stacy has 4 times as many berries as Steve, and Steve has double the number of berries that Skylar has. How many berries does Stacy have? | Let x be the number of berries Skylar has.
Steve has 2x berries
Stacy has 4(2x)=8x berries
1100=x+2x+8x
1100=11x
x = <<100=100>>100 berries
Stacy has 8(100)=<<8*100=800>>800 berries
#### 800 |
In the triangular pyramid $A-BCD$, where $AB=AC=BD=CD=BC=4$, the plane $\alpha$ passes through the midpoint $E$ of $AC$ and is perpendicular to $BC$, calculate the maximum value of the area of the section cut by plane $\alpha$. | \frac{3}{2} |
Vinny weighed 300 pounds then lost 20 pounds in the first month of his diet. He continued his diet but each month, he lost half as much weight as he had lost in the previous month. At the start of the fifth month of his diet, he worked harder to lose extra weight then decided to end his diet. If Vinny weighed 250.5 pou... | In the second month, Vinny lost half as much as he had the first month, so he lost 20 pounds / 2 = <<20/2=10>>10 pounds.
In the third month, he again lost half as much which was 10 pounds / 2 = <<10/2=5>>5 pounds.
And in the fourth month, he lost 5 pounds / 2 = <<5/2=2.5>>2.5 pounds.
So in total, Vinny lost 20 + 10 + 5... |
The cost of building a certain house in an area is 100,000 more than the construction cost of each of the houses in the area. But it sells for 1.5 times as much as the other houses, which sell at $320,000 each. How much more profit is made by spending the extra money to build? | The house cost 320,000*1.5=$<<320000*1.5=480000>>480,000
So it is worth 480,000-320,000=$<<480000-320000=160000>>160,000 more than other houses
So the profit is 160,000-100,000=$<<160000-100000=60000>>60,000 more
#### 60,000 |
A circle has an area of $M\text{ cm}^2$ and a circumference of $N\text{ cm}$. If $\dfrac{M}{N}=20$, what is the radius of the circle, in cm? | 40 |
Find the sum of all positive rational numbers that are less than 10 and that have denominator 30 when written in lowest terms. | 400 |
If $y = \displaystyle\frac{1}{3x+1}$, what is the value of $x$ when $y = 1$? | 0 |
What is the value of $\displaystyle\frac{235^2-221^2}{14}$? | 456 |
Compute $\tan \left(\operatorname{arccot} \frac{3}{5}\right)$ and verify if $\sin \left(\operatorname{arccot} \frac{3}{5}\right) > \frac{1}{2}$. | \frac{5}{3} |
Four-digit "progressive numbers" are arranged in ascending order, determine the 30th number. | 1359 |
Natasha has more than $\$1$ but less than $\$10$ worth of dimes. When she puts her dimes in stacks of 3, she has 1 left over. When she puts them in stacks of 4, she has 1 left over. When she puts them in stacks of 5, she also has 1 left over. How many dimes does Natasha have? | 61 |
In writing the integers from 20 through 199 inclusive, how many times is the digit 7 written? | 38 |
There are 8 white balls and 2 red balls in a bag. Each time a ball is randomly taken out, a white ball is put back in. What is the probability that all red balls are taken out exactly by the 4th draw? | 353/5000 |
Tricia buys large bottles of iced coffee that have 6 servings per container. She drinks half a container a day. The coffee is currently on sale for $3.00 a bottle. How much will it cost her to buy enough bottles to last for 2 weeks? | She drinks half a container of a 6 serving bottle of iced coffee a day so she drinks 6/2 = <<6/2=3>>3 servings a day
There are 7 days in a week and she needs enough bottles to last for 2 weeks so that's 7*2 = <<7*2=14>>14 days
She drinks 3 servings a day for 14 days so that's 3*14 = <<3*14=42>>42 servings
Each bottle h... |
Compute \[
\left\lfloor \frac{2007! + 2004!}{2006! + 2005!}\right\rfloor.
\](Note that $\lfloor x \rfloor$ denotes the greatest integer less than or equal to $x$.) | 2006 |
Given a set of data $x_1, x_2, x_3, x_4, x_5$ with a mean of 8 and variance of 2, find the mean and variance of a new set of data: $4x_1+1, 4x_2+1, 4x_3+1, 4x_4+1, 4x_5+1$. | 32 |
Integers $x$ and $y$ with $x>y>0$ satisfy $x+y+xy=80$. What is $x$? | 26 |
The minute hand on a clock points at the 12. After rotating $120^{\circ}$ clockwise, which number will it point at? | 4 |
Nancy has a bag containing 22 tortilla chips. She gives 7 tortilla chips to her brother and 5 tortilla chips to her sister, keeping the rest for herself. How many did Nancy keep for herself? | She gave away 7+5=<<7+5=12>>12 chips.
Then she kept 22-12=<<22-12=10>>10.
#### 10 |
A circle with center $O$ has area $156\pi$. Triangle $ABC$ is equilateral, $\overline{BC}$ is a chord on the circle, $OA = 4\sqrt{3}$, and point $O$ is outside $\triangle ABC$. What is the side length of $\triangle ABC$? | $6$ |
Given the function $f(x)=4\sin x\cos \left(x- \frac {\pi}{3}\right)- \sqrt {3}$.
(I) Find the smallest positive period and zeros of $f(x)$.
(II) Find the maximum and minimum values of $f(x)$ in the interval $\left[ \frac {\pi}{24}, \frac {3\pi}{4}\right]$. | - \sqrt {2} |
In quadrilateral \( \square ABCD \), point \( M \) lies on diagonal \( BD \) with \( MD = 3BM \). Let \( AM \) intersect \( BC \) at point \( N \). Find the value of \( \frac{S_{\triangle MND}}{S_{\square ABCD}} \). | 1/8 |
How many ways are there to arrange the letters of the word $\text{CA}_1\text{N}_1\text{A}_2\text{N}_2\text{A}_3\text{T}_1\text{T}_2$, where there are three A's, two N's, and two T's, with each A, N, and T considered distinct? | 5040 |
Joel collected a bin of old toys to donate. By asking his friends, he was able to collect 18 stuffed animals, 42 action figures, 2 board games, and 13 puzzles. His sister gave him some of her old toys from her closet, and then Joel added twice as many toys from his own closet as his sister did from hers. In all, Joel w... | Let T be the number of toys Joel’s sister donated.
Joel donated twice as many toys, so he donated 2T toys.
Joel’s friends donated 18 + 42 + 2 + 13 = <<18+42+2+13=75>>75 toys.
In all, Joel collected T + 2T + 75 = 3T + 75 = 108 toys.
Joel and his sister donated 3T = 108 - 75 = 33 toys together.
Therefore, T = 33 / 3 = <<... |
Jenna is making a costume for her role in Oliver Twist. She needs to make an overskirt and two petticoats. Each skirt uses a rectangle of material that measures 12 feet by 4 feet. She also needs to make a bodice that uses 2 square feet of material for the shirt and 5 square feet of fabric for each of the sleeves. If th... | First find the amount of material needed for one skirt: 12 feet * 4 feet = <<12*4=48>>48 square feet
Then multiply that number by the number of skirts to find the total material used on the skirts: 48 square feet/skirt * 3 skirts = 144 square feet
Then find the total amount of material she uses for the sleeves: 5 squar... |
A straight line passing through the point $(0,4)$ is perpendicular to the line $x-3y-7=0$. Its equation is: | y+3x-4=0 |
What is the area of the polygon whose vertices are the points of intersection of the curves $x^2 + y^2 = 16$ and $(x-5)^2 + 4y^2 = 64$?
A) $\frac{5\sqrt{110}}{6}$
B) $\frac{5\sqrt{119}}{6}$
C) $\frac{10\sqrt{119}}{6}$
D) $\frac{5\sqrt{125}}{6}$ | \frac{5\sqrt{119}}{6} |
Mona bikes 30 miles each week to stay fit. This week, she biked on Monday, Wednesday, and Saturday. On Wednesday, she biked 12 miles. On Saturday, she biked twice as far as on Monday. How many miles did she bike on Monday? | Let M be the number of miles Mona biked on Monday.
Thus, Mona biked 2M miles on Saturday.
In all, Mona biked M + 2M + 12 = 30 miles.
Thus, on Monday and Saturday, she biked M + 2M = 3M = 30 - 12 = 18 miles.
Therefore, on Monday, Mona biked M = 18 / 3 = <<18/3=6>>6 miles.
#### 6 |
Twelve tiles numbered $1$ through $12$ are turned up at random, and an 8-sided die (sides numbered from 1 to 8) is rolled. Calculate the probability that the product of the numbers on the tile and the die will be a square. | \frac{7}{48} |
John uses 5 liters of fuel per km to travel. How many liters of fuel should John plan to use if he plans to travel on two trips of 30 km and 20 km? | The first trip will use 30*5=<<30*5=150>>150 liters of fuel.
The second trip will use 20*5=<<20*5=100>>100 liters of fuel.
The total liters of fuel are 150+100=<<150+100=250>>250 liters.
#### 250 |
Point A is a fixed point on a circle with a circumference of 3. If a point B is randomly selected on the circumference of the circle, the probability that the length of the minor arc is less than 1 is ______. | \frac{2}{3} |
Determine the value of $x$ that satisfies $\sqrt[5]{x\sqrt{x^3}}=3$. | 9 |
How many positive divisors do 8400 and 7560 have in common? | 32 |
Marie has 4 notebooks with 20 stamps each. She also has two binders with 50 stamps each. If she decides to only keep 1/4 of the stamps, how many stamps can she give away? | Marie has 4 x 20 = <<4*20=80>>80 stamps from her notebooks.
And she has 2 x 50 = <<2*50=100>>100 stamps from her binders.
So she has a total of 80 + 100 = <<80+100=180>>180 stamps.
Marie decided to keep 180 x 1/4 = <<180*1/4=45>>45 stamps only.
Therefore, she can give away 180 - 45 = <<180-45=135>>135 stamps.
#### 135 |
Let $m$ be the largest real solution to the equation
\[\dfrac{3}{x-3} + \dfrac{5}{x-5} + \dfrac{17}{x-17} + \dfrac{19}{x-19} = x^2 - 11x - 4\]There are positive integers $a, b,$ and $c$ such that $m = a + \sqrt{b + \sqrt{c}}$. Find $a+b+c$. | 263 |
Given integer $n\geq 2$. Find the minimum value of $\lambda {}$, satisfy that for any real numbers $a_1$, $a_2$, $\cdots$, ${a_n}$ and ${b}$,
$$\lambda\sum\limits_{i=1}^n\sqrt{|a_i-b|}+\sqrt{n\left|\sum\limits_{i=1}^na_i\right|}\geqslant\sum\limits_{i=1}^n\sqrt{|a_i|}.$$ | \frac{n-1 + \sqrt{n-1}}{\sqrt{n}} |
Jenna works as a truck driver. She gets paid $0.40 cents per mile. If she drives 400 miles one way, how much does she get paid for a round trip? | First find the total number of miles Jenna drives: 400 miles/way * 2 ways = 800 miles
Then multiply that number by her pay per mile to find her total pay: 800 miles * $0.40/mile = $<<800*0.4=320>>320
#### 320 |
Stock investor Li Jin bought shares of a certain company last Saturday for $27 per share. The table below shows the price changes of the stock within the week.
| Day of the Week | Monday | Tuesday | Wednesday | Thursday | Friday | Saturday |
|-----------------|--------|---------|-----------|----------|--------|-------... | 24.5 |
Given that the moving point $P$ satisfies $|\frac{PA}{PO}|=2$ with two fixed points $O(0,0)$ and $A(3,0)$, let the locus of point $P$ be curve $\Gamma$. The equation of $\Gamma$ is ______; the line $l$ passing through $A$ is tangent to $\Gamma$ at points $M$, where $B$ and $C$ are two points on $\Gamma$ with $|BC|=2\sq... | 3\sqrt{3} |
What is the base ten equivalent of $54321_6$? | 7465 |
Given a regular triangular prism $ABC-A_1B_1C_1$ with side edges equal to the edges of the base, the sine of the angle formed by $AB_1$ and the lateral face $ACCA_1$ is equal to _______. | \frac{\sqrt{6}}{4} |
Acute-angled $\triangle ABC$ is inscribed in a circle with center at $O$; $\stackrel \frown {AB} = 100^\circ$ and $\stackrel \frown {BC} = 80^\circ$.
A point $E$ is taken in minor arc $AC$ such that $OE$ is perpendicular to $AC$. The task is to determine the ratio of the magnitudes of $\angle OBE$ and $\angle BAC$. | \frac{1}{2} |
A positive integer $n$ is loose if it has six positive divisors and satisfies the property that any two positive divisors $a<b$ of $n$ satisfy $b \geq 2 a$. Compute the sum of all loose positive integers less than 100. | 512 |
Given \\(-\pi < x < 0\\), \\(\sin x + \cos x = \frac{1}{5}\\).
\\((1)\\) Find the value of \\(\sin x - \cos x\\);
\\((2)\\) Find the value of \\(\frac{3\sin^2 \frac{x}{2} - 2\sin \frac{x}{2}\cos \frac{x}{2} + \cos^2 \frac{x}{2}}{\tan x + \frac{1}{\tan x}}\\). | -\frac{108}{125} |
What is the minimum number of participants that could have been in the school drama club if fifth-graders constituted more than $25\%$, but less than $35\%$; sixth-graders more than $30\%$, but less than $40\%$; and seventh-graders more than $35\%$, but less than $45\%$ (there were no participants from other grades)? | 11 |
Brady will make $450 more in a year than Dwayne. If Dwayne makes $1,500 in a year, how much will Brady and Dwayne make combined in a year? | Brady will make $450 + $1500 = $<<450+1500=1950>>1950.
Combined, Brady and Dwayne will make $1950 + $1500 = $<<1950+1500=3450>>3450 in a year.
#### 3450 |
You have 5 identical buckets, each with a maximum capacity of some integer number of liters, and a 30-liter barrel containing an integer number of liters of water. All the water from the barrel was poured into the buckets, with the first bucket being half full, the second one-third full, the third one-quarter full, the... | 29 |
Given two unit vectors \\( \overrightarrow{a} \\) and \\( \overrightarrow{b} \\). If \\( |3 \overrightarrow{a} - 2 \overrightarrow{b}| = 3 \\), find the value of \\( |3 \overrightarrow{a} + \overrightarrow{b}| \\). | 2 \sqrt {3} |
Given that a bin contains 10 kg of peanuts, 2 kg of peanuts are removed and 2 kg of raisins are added and thoroughly mixed in, and then 2 kg of this mixture are removed and 2 kg of raisins are added and thoroughly mixed in again, determine the ratio of the mass of peanuts to the mass of raisins in the final mixture. | \frac{16}{9} |
Using toothpicks of equal length, a rectangular grid is constructed. The grid measures 25 toothpicks in height and 15 toothpicks in width. Additionally, there is an internal horizontal partition at every fifth horizontal line starting from the bottom. Calculate the total number of toothpicks used. | 850 |
What is the greatest integer less than or equal to \[\frac{5^{105} + 4^{105}}{5^{99} + 4^{99}}?\] | 15624 |
Tom went to the store to buy fruit. Lemons cost $2, papayas cost $1, and mangos cost $4. For every 4 fruits that customers buy, the store offers a $1 discount. Tom buys 6 lemons, 4 papayas, and 2 mangos. How much will he pay? | For 6 lemons, Tom will pay 6 * 2 = $<<6*2=12>>12.
For 3 papayas, he will pay 3 * 1 = $<<3*1=3>>3
For 2 mangos, he will pay 2 * 4 = $<<2*4=8>>8.
In total, the cost of the fruits before discount is 12 + 4 + 8 = $<<12+4+8=24>>24.
The total number of fruits is 6 + 4 + 2 = <<6+4+2=12>>12 fruits.
For 12 fruits, Tom gets a di... |
Read the following material: The overall idea is a common thinking method in mathematical problem solving: Here is a process of a student factorizing the polynomial $(x^{2}+2x)(x^{2}+2x+2)+1$. Regard "$x^{2}+2x$" as a whole, let $x^{2}+2x=y$, then the original expression $=y^{2}+2y+1=\left(y+1\right)^{2}$, and then res... | 2021 |
The digits of 2021 can be rearranged to form other four-digit whole numbers between 1000 and 3000. Find the largest possible difference between two such four-digit whole numbers. | 1188 |
Given the parametric equation of line $l$ as $\begin{cases} x = \frac{\sqrt{2}}{2}t \\ y = \frac{\sqrt{2}}{2}t + 4\sqrt{2} \end{cases}$ (where $t$ is the parameter) and the polar equation of circle $C$ as $\rho = 2\cos (\theta + \frac{\pi}{4})$,
(I) Find the rectangular coordinates of the center of circle $C$.
(II) F... | 2\sqrt {6} |
A person is waiting at the $A$ HÉV station. They get bored of waiting and start moving towards the next $B$ HÉV station. When they have traveled $1 / 3$ of the distance between $A$ and $B$, they see a train approaching $A$ station at a speed of $30 \mathrm{~km/h}$. If they run at full speed either towards $A$ or $B$ st... | 10 |
In isosceles triangle $\triangle ABC$ we have $AB=AC=4$. The altitude from $B$ meets $\overline{AC}$ at $H$. If $AH=3(HC)$ then determine $BC$. | 2\sqrt{2} |
In trapezoid \(ABCD\), the bases \(AD\) and \(BC\) are equal to 8 and 18, respectively. It is known that the circumcircle of triangle \(ABD\) is tangent to lines \(BC\) and \(CD\). Find the perimeter of the trapezoid. | 56 |
Given that the broad money supply $\left(M2\right)$ balance was 2912000 billion yuan, express this number in scientific notation. | 2.912 \times 10^{6} |
Given the angle $\frac {19\pi}{5}$, express it in the form of $2k\pi+\alpha$ ($k\in\mathbb{Z}$), then determine the angle $\alpha$ that makes $|\alpha|$ the smallest. | -\frac {\pi}{5} |
A rectangle having integer length and width has a perimeter of 100 units. What is the number of square units in the least possible area? | 49 |
Given $α-β=\frac{π}{3}$ and $tanα-tanβ=3\sqrt{3}$, calculate the value of $\cos \left(\alpha +\beta \right)$. | -\frac{1}{6} |
Andy and Bethany have a rectangular array of numbers with $40$ rows and $75$ columns. Andy adds the numbers in each row. The average of his $40$ sums is $A$. Bethany adds the numbers in each column. The average of her $75$ sums is $B$. What is the value of $\frac{A}{B}$? | \frac{15}{8} |
The formula $N=8 \times 10^{8} \times x^{-3/2}$ gives, for a certain group, the number of individuals whose income exceeds $x$ dollars.
The lowest income, in dollars, of the wealthiest $800$ individuals is at least: | 10^4 |
In the trapezoid \(ABCD\) with bases \(AD \parallel BC\), the diagonals intersect at point \(E\). Given the areas \(S(\triangle ADE) = 12\) and \(S(\triangle BCE) = 3\), find the area of the trapezoid. | 27 |
Jeremy made a Venn diagram showing the number of students in his class who own types of pets. There are 32 students in his class. In addition to the information in the Venn diagram, Jeremy knows half of the students have a dog, $\frac{3}{8}$ have a cat, six have some other pet and five have no pet at all. How many stud... | 1 |
Given a triangle $\triangle ABC$ with sides $a$, $b$, and $c$ opposite to angles $A$, $B$, and $C$ respectively. If $\cos A= \frac {3}{4}$, $\cos C= \frac {1}{8}$,
(I) find the ratio $a:b:c$;
(II) if $| \overrightarrow{AC}+ \overrightarrow{BC}|= \sqrt {46}$, find the area of $\triangle ABC$. | \frac {15 \sqrt {7}}{4} |
A circle with a radius of 3 units has its center at $(0, 0)$. Another circle with a radius of 8 units has its center at $(20, 0)$. A line tangent to both circles intersects the $x$-axis at $(x, 0)$ to the right of the origin. Determine the value of $x$. Express your answer as a common fraction. | \frac{60}{11} |
Given a positive integer $n,$ let $s(n)$ denote the sum of the digits of $n.$ Compute the largest positive integer $n$ such that $n = s(n)^2 + 2s(n) - 2.$ | 397 |
Given is a regular tetrahedron of volume 1. We obtain a second regular tetrahedron by reflecting the given one through its center. What is the volume of their intersection? | \frac{1}{2} |
Given any two positive real numbers $x$ and $y$, then $x \, \Diamond \, y$ is a positive real number defined in terms of $x$ and $y$ by some fixed rule. Suppose the operation $x \, \Diamond \, y$ satisfies the equations $(xy) \, \Diamond \, y=x(y \, \Diamond \, y)$ and $(x \, \Diamond \, 1) \, \Diamond \, x = x \, \Di... | 19 |
Graeme is weighing cookies to see how many he can fit in his box. His box can only hold 40 pounds of cookies. If each cookie weighs 2 ounces, how many cookies can he fit in the box? | First find how many cookies are in a pound. 16 ounces per pound / 2 ounces/cookie = 8 cookies per pound
The box can hold 40 pounds, so 40 pounds * 8 cookies per pound = <<40*8=320>>320 cookies.
#### 320 |
Find the sum of the rational roots of $g(x)=x^3-9x^2+16x-4$. | 2 |
Roger had a 6-hour drive planned out. He didn't want to listen to music so he downloaded several podcasts. The first podcast was 45 minutes long. The second podcast was twice as long as that. The third podcast was 1 hour and 45 minutes long. His fourth podcast is 1 hour long. How many hours will his next podcast ... | The second podcast was twice as long as the first so 2*45 = <<2*45=90>>90
1 hour is 60 mins. So his 1 hour and 45 min podcast is 60+45 = <<1*60+45=105>>105 minutes long
So far he has downloaded 45+90+105+60 = <<45+90+105+60=300>>300 min
If he converts 300 min to hours then he has 300/60 = <<300/60=5>>5 hours of podcast... |
The line $y = 3x - 11$ is parameterized by the form
\[\begin{pmatrix} x \\ y \end{pmatrix} = \begin{pmatrix} r \\ 1 \end{pmatrix} + t \begin{pmatrix} 4 \\ k \end{pmatrix}.\]Enter the ordered pair $(r,k).$ | (4,12) |
Five coaster vans are used to transport students for their field trip. Each van carries 28 students, 60 of which are boys. How many are girls? | There are a total of 5 vans x 28 students = <<5*28=140>>140 students.
If 60 are boys, then 140 - 60 = <<140-60=80>>80 of these students are girls.
#### 80 |
Frank needs to meet a quota at work for his sales. It’s the beginning of the month and in 30 days he needs to have 50 cars sold. The first three days he sold 5 cars each day. Then the next 4 days he sold 3 cars each day. If the month is 30 days long how many cars does he need to sell for the remaining days to meet his ... | On days one, two, and three he sold 5 cars each day so, 5 cars + 5 cars + 5 cars = <<5+5+5=15>>15 cars that he sold on those days.
On days 4,5,6 and 7 he sold 3 cars each day so, 3 cars + 3 cars + 3 cars + 3 cars = <<3+3+3+3=12>>12 cars that he sold on those days.
Now we combine the cars he has already sold, which is 1... |
Compute $\sin 60^\circ$. | \frac{\sqrt{3}}{2} |
If $\frac{1}{x} - \frac{1}{y} = \frac{1}{z}$, then $z$ equals: | \frac{xy}{y - x} |
Let $m$ be the product of all positive integers less than $4!$ which are invertible modulo $4!$. Find the remainder when $m$ is divided by $4!$.
(Here $n!$ denotes $1\times\cdots\times n$ for each positive integer $n$.) | 1 |
What percent of the positive integers less than or equal to $150$ have no remainders when divided by $6$? | 16.\overline{6}\% |
Find one-fourth of 6 times 8. | 12 |
What is the maximum number of rooks one can place on a chessboard such that any rook attacks exactly two other rooks? (We say that two rooks attack each other if they are on the same line or on the same column and between them there are no other rooks.)
Alexandru Mihalcu | 16 |
The square of $a$ and the square root of $b$ vary inversely. If $a=2$ when $b=81$, then find $b$ when $ab=48$. | 16 |
A tree had 1000 leaves before the onset of the dry season, when it sheds all its leaves. In the first week of the dry season, the tree shed 2/5 of the leaves. In the second week, it shed 40% of the remaining leaves. In the third week, the tree shed 3/4 times as many leaves as it shed on the second week. Calculate the ... | In the first week, the tree shed 2/5*1000 = <<2/5*1000=400>>400 leaves.
The number of leaves remaining on the tree at the end of the first week is 1000-400 = <<1000-400=600>>600
In the second week, the tree shed 40/100*600 = <<40/100*600=240>>240 leaves.
The number of leaves remaining on the tree is 600-240 = <<600-240... |
Find the value of $b$ that satisfies the equation $161_{b}+134_{b}=315_{b}$. | 8 |
What is the degree measure of the smaller angle between the hour hand and the minute hand of a clock at exactly 2:30 p.m. on a 12-hour analog clock? | 105^\circ |
What is the 5th term of an arithmetic sequence of 20 terms with first and last terms of 2 and 59, respectively? | 14 |
The value of $\log_{10}{17}$ is between the consecutive integers $a$ and $b$. Find $a+b$. | 3 |
Given the power function $f(x)=kx^{\alpha}$, its graph passes through the point $(\frac{1}{2}, \frac{\sqrt{2}}{2})$. Find the value of $k+\alpha$. | \frac{3}{2} |
$O K R A$ is a trapezoid with $O K$ parallel to $R A$. If $O K=12$ and $R A$ is a positive integer, how many integer values can be taken on by the length of the segment in the trapezoid, parallel to $O K$, through the intersection of the diagonals? | 10 |
How many distinct four-digit numbers are divisible by 3 and have 47 as their last two digits? | 30 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.