If a rectangle measures 20 meters by 48 meters, what is the length, in meters, of the diagonal of the rectangle?

Solution
To find the length of the diagonal, apply the Pythagorean Theorem; the sides of the rectangle are the legs of a right triangle and the diagonal of the rectangle is the hypotenuse of the right triangle.
Thus c^{2} = 20^{2} + 48^{2}, and c = 52.
At a bottling plant, 10,000 liters of carbonated water are needed to produce 3,000 bottles of soda. How many liters of carbonated water are needed to produce 750 bottles of soda?

Solution
To find the number of liters of carbonated water needed to produce 750 bottles of soda, set up a proportion with ratios of liters of carbonated water to bottles of soda, as follows:
\(\frac{10,000}{3,000}=\frac{x(liters\: carbonated\: water)}{750}\)
Crossmultiply and solve for x.
3, 000x = 7, 500, 000
x = 2, 500
Reggie knows how to make 5 different entrees, 4 different side dishes, and 6 different desserts. How many distinct complete meals, each consisting of an entrée, a side dish, and a dessert, can Reggie make?

Solution
To find the number of distinct complete meals that Reggie can make from 5 different entrees, 4 different sides, and 6 different desserts, multiply the quantities in the 3 different groups together. Thus, there are (5)(4)(6), or 120 distinct meals that Reggie can make. The figure below shows that for each meal, there are 4 sides,and for each side there are 6 desserts.
Point A is to be graphed in a quadrant, not on an axis, of the standard (x, y) coordinate plane below. If the xcoordinate and the ycoordinate of point A are to have the same signs, then point A must be located in:

Solution
The xcoordinate is positive if A is to the right of the yaxis. The ycoordinate is positive if y is above the xaxis. The table below shows the sign of x and the sign of y in the four quadrants.
Thus the signs are the same in Quadrants I and III only
What expression must the center cell of the table below contain so that the sums of each row and each column are equivalent?

Solution
Because the sum of each row is equivalent, the sum of row 1 is the same as the sum of row 2.
Row 1: (−4x) + 9x + 2x = 7x
Row 2: 7x + ? + (−3x) = 4x + ?
The question mark must represent 3x, because 7x = 4x + 3x. You could also perform these calculations using the sum values in column 1 and column 2.
If you selected answer choice K, you may have thought that each sum must be 0 and found that −4x would make the sums of row 2 and column 2 equal 0.
The following chart shows the current enrollment in all social studies classes—Geography, US History, World Cultures, and Government—at Iron Mountain High School.
The school wants to have all of the students enrolled in social studies classes read the same book at the same
time so that the author of the book can speak to the students at an assembly. The school originally purchased
two classroom sets of 30 books each, but now one set is missing 3 books and the other is missing 5. For which
of the following class periods, if any, are there NOT enough books available for each student to have one book?

Solution
The total number of books available is (30 − 3) + (30 − 5), or 27 + 25, which is 52. To find the class periods for which there are not enough books, find the total number of books needed for each period, as given in the table below.
The only entry in the table with more than 52 is 56 for period 3.
If you selected answer choice E, you probably used 60 as the number of available books and did not take into account the 8 missing books.
The following chart shows the current enrollment in all social studies classes—Geography, US History, World Cultures, and Government—at Iron Mountain High School.
What is the average number of students enrolled per section in US History?

Solution
To find the average number of students per section enrolled in US History, find the total number of students in all sections and divide by the number of sections. Add 25+29+24 to get 78, then divide by 3. This results in an average of 26 students enrolled per section in US History.
If you selected answer choice F, you found the median, or middle number (which is not always the average), of 24, 25, and 29.
The number of students participating in fall sports at a certain high school can be shown with the following matrix:
The athletic director estimates the ratio of the number of sports awards that will be earned to the number of students participating with the following matrix:
Given these matrices, what is the athletic director’s estimate for the number of sports awards that will be earned for these fall sports?

Solution
To find the number of sports awards earned, multiply the number of participants in each sport by the ratio for that sport, and then add these 4 products. This is a matrix multiplication, as shown below:
\([25\: 30\: 50\: 80]\begin{bmatrix} 0.2\\ 0.5\\ 0.3\\ 0.4 \end{bmatrix}\)
= 25(0.2) + 30(0.5) + 50(0.3) + 80(0.4)
= 5 + 15 + 15 + 32 = 67
If a gumball is randomly chosen from a bag that contains exactly 6 yellow gumballs, 5 green gumballs, and 4 red gumballs, what is the probability that the gumball chosen is NOT green?

Solution
The probability that the gumball chosen will NOT be green when there are 6 yellow gumballs, 5 green gumballs, and 4 red gumballs is the number of favorable outcomes (the number of times a yellow or red gumball can be chosen) divided by the number of total outcomes (the total number of gumballs). The number of favorable outcomes is 10 because there are 6 yellow gumballs and 4 red gumballs. The total number of outcomes is 6+5+4, or 15. Thus the probability of the gumball NOT being green is ^{10}⁄_{15}, which can be reduced to ^{2}⁄_{3}.
Answer choice G is incorrect because it is the probability that a chosen gumball will be green.
The formula for the volume, V, of a sphere with radius r is V = (^{4}⁄_{3})πr^{3}. If the radius of a baseball is 1^{1}⁄_{3} inches, what is the volume to the nearest cubic inch?

Solution
To find the volume, substitute ^{4}⁄_{3} for r in the equation V = (^{4}⁄_{3})πr^{3} as follows:
(^{4}⁄_{3})π(^{4}⁄_{3})^{3}
= (^{4}⁄_{3})π\(\left ( \frac{64}{27} \right )\)
= \(\left ( \frac{256}{81} \right )\pi\)
Recall that π = approx. 3.14, so \(\left ( \frac{256}{81} \right )\)(3.14) is about 9.92, or 10 when rounded to the nearest cubic inch.