Practice (EndingDigits,TheDivideByNineMethod,MODBasic)
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The endpoints of a diameter of a circle are (-1, -4) and (-7, 6). We must find the coordinates of the center of the circle.
The mean of {1, 2, 4, 8, 9, 10, 14, 16,17} is 9. If one number is removed and the mean decreases by 1, what is the value of the number that was removed?
Line $l$ is perpendicular to the line with equation $6y$ = $kx +24$. The slope of line $l$ is $-2$. Find the value of $k$.
Sam's monthly commission is $C = 270g + 3g^2$, where $g$ is the number of cars that Sam sells. Sam sold 30 cars so how much commission did Sam earn?
There is a shallow fish pond in the shape of a square. The perimeter of the pond is 24 ft and the water is 6 in deep. We must find the volume of the water in the pond.
The cube shown has a side length of $s$. Points $A$, $B$, $C$ and $D$ are vertices of the cube. We need to find the area of rectangle $ABCD$.
It rained on exactly 10 days during Tricia's vacation. It rained either in the morning or in the afternoon on each rainy day. There were 13 mornings when it didn't rain and 17 afternoons when it didn't rain. So how many days did Tricia's vacation last?
If the letters of the word ELEMENT are randomly arranged, what is the probability that the three E's are consecutive?
The diagram shows 8 congruent squares inside a circle. Find the ratio of the shaded area to the area of the circle.
Matt has a twenty dollar bill and buys two items worth $7.99 each. How much change does he receive, in dollars?
The sum of two distinct numbers is equal to the positive difference of the two numbers. What is the product of the two numbers?
Evaluate $\frac{1 + 2 + 3 + 4 + 5 + 6 + 7}{8 + 9 + 10 + 11 + 12 + 13 + 14}$.
A sphere with radius $r$ has volume $2\pi$. Find the volume of a sphere with diameter $r$.
Yannick ran 100 meters in 14.22 seconds. Compute his average speed in meters per second, rounded to the nearest integer.
The mean of the numbers 2, 0, 1, 5, and $x$ is an integer. Find the smallest possible positive integer value for $x$.
Let $f(x) = \sqrt{2^2-x^2}$. Find the value of $f(f(f(f(f(-1)))))$.
Find the smallest positive integer $n$ such that 20 divides $15n$ and 15 divides $20n$.
A circle is inscribed in equilateral triangle $ABC$. Let $M$ be the point where the circle touches side $AB$ and let $N$ be the second intersection of segment $CM$ and the circle. Compute the ratio $\frac{MN}{CN}$ .
Four boys and four girls line up in a random order. What is the probability that both the first and last person in line is a girl?
Let $k$ be a positive integer. After making $k$ consecutive shots successfully, Andy's overall shooting accuracy increased from 65% to 70%. Determine the minimum possible value of $k$.
In square $ABCD$, $M$ is the midpoint of side $CD$. Points $N$ and $P$ are on segments $BC$ and $AB$ respectively such that $\angle AMN = \angle MNP = 90^{\circ}$. Compute the ratio $\frac{AP}{PB}$ .
Meena writes the numbers $1$, $2$, $3$, and $4$ in some order on a blackboard, such that she cannot swap two numbers and obtain the sequence $1$, $2$, $3$, $4$. How many sequences could she have written?
Find the smallest positive integer $N$ such that $2N$ is a perfect square and $3N$ is a perfect cube.
A polyhedron has $60$ vertices, $150$ edges, and $92$ faces. If all of the faces are either regular pentagons or equilateral triangles, how many of the $92$ faces are pentagons?
All positive integers relatively prime to 2015 are written in increasing order. Let the twentieth number be $p$. The value of $\frac{2015}{p}\u2212 1$ can be expressed as $\frac{a}{b}$, where $a$ and $b$ are relatively prime positive integers. Compute $a + b$.