Practice (90/1000)
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Carol, Jane, Kim, Nancy and Vicky competed in a 400-meter race. Nancy beat Jane by 6 seconds. Carol finished 11 seconds behind Vicky. Nancy finished 2 seconds ahead of Kim, but 3 seconds behind Vicky. We are asked to find by how many seconds Kim finished ahead of Carol.
$S$ and $T$ are both two-digit integers less than 80. Each number is divisible by 3. $T$ is also divisible by 7. $S$ is a perfect square. $S + T$ is a multiple of 11, so what is the value of $T$?
In a stack of six cards, each card is labeled with a different integer from $0$ to $5$. Two cards are selected at random without replacement. So what is the probability that their sum will be $3$?
Okta stays in the sun for $16$ minutes before getting sunburned. Using a sunscreen, he can stay in the sun $20$ times as long before getting sunburned (or $320$ minutes). If he stays in the sun for $9$ minutes and then applies the sunscreen, how much longer can he remain in the sun?
A bag contains ten each of red and yellow balls. The balls of each color are numbered from 1 to 10. If two balls are drawn at random, without replacement, then what is the probability that the yellow ball numbered 3 is drawn followed by a red ball?
In trapezoid $ABCD$, $AB = BC = 2AD$ and $AD= 5$. We are asked to find the area of trapezoid $ABCD$.
One line has a slope of \u22121/3 and contains the point (3, 6). Another line has a slope of 5/3 and contains the point (3, 0). We are asked to find the product of the coordinates of the point at which the two lines intersect.
Consider all integer values of $a$ and $b$ for which $a < 2$ and $b \ge -2$. We are asked to find the minimum value of $b -a$.
In the figure shown, the diagonals of a square are drawn and then two additional segments from each vertex to a diagonal. How many triangles are in the figure?
Six circles of radius, $r = 1$ unit are drawn in the hexagon as shown. We must find the perimeter of the hexagon.
If $x^2+\frac{1}{x^2}= 3$, then what is the value of $\frac{x^2}{(x^2+1)^2}$?
A circle is inscribed in a rhombus with sides of length 4cm. The two acute angles each measure $60^{\circ}$. We are asked to find the length of the circle'9s radius.
A line containing the points (-8, 9) and (-12, 12) intersects the $x$-axis at point $P$. Find the $x$-coordinate of point $P$.
Mike wrote a list of 6 positive integers on his paper. The first two are chosen randomly. Each of the remaining integers is the sum of the two previous integers. We are asked to find the ratio of the fifth integer to the sum of all 6 integers.
How many positive integers not exceeding $2000$ have an odd number of factors?
A $5 \times 5 \times 5$ cube is painted on 5 of its 6 faces. It is then cut into 125 unit cubes. One unit cube is randomly selected and rolled. We are asked to find the probability that the top face of the cube that is rolled is painted.
Circle O has diameter AE and AE = 8. Point C is on the circumference of the circle such that segments AC and CE are congruent. Segment AC is a diameter of semicircle ABC and segment CE is a diameter semicircle CDE. What is the total combined area of the shaded regions?
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.
Line $l$ is perpendicular to the line with equation $6y$ = $kx +24$. The slope of line $l$ is $-2$. Find the value of $k$.
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 $ABCD$.
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.
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 $r$.