Practice (TheColoringMethod)
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A cylindrical container has a diameter of 8 cm (i.e., a radius of 4 cm) and a volume of 754 $cm^2$. Another container also has a diameter of 8 cm, but is twice as tall as the original container. We are asked to find the volume of the second container.
The angles of a triangle are in the ratio 1:3:5. What is the degree measure of the largest angle in the triangle?
Four numbers are written in a row. The mean of the first two is 10 and the mean of the last two is 20. We are asked to find the mean of all four numbers.
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.
A car traveled a certain distance at 20 mph. Then it traveled twice the distance at 40 mph. The entire trip lasted for four hours and we must find the total number of miles driven.
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.
Tawana purchases 3 CDs for \$6.98, \$7.49 and \$15.63. If the three prices sum to less than \$30, then shipping is \$3; otherwise it's 10% of the total price. What is the total cost of Tawana's merchandise?
Three and one half hours ago it was 10:15 am. We must find how many more minutes it is from now until the next noon.
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.
Sonia has 5 more pairs of shoes than Danielle. Imelda has twice as many pairs as Sonia. The girls have a total of 39 pairs of shoes. We are asked to find how many more pairs of shoes Imelda has than Sonia and Danielle combined.
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 first third of tickets for the play sell for \$8 each. Remaining tickets sell for \$10 each. There are 27 rows of seats with 44 seats in each row. We are asked to find out how much will be collected from selling all the tickets.