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 c² = 20² + 48², and c = 52.

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:

\(\frac{10,000}{3,000}=\frac{x(liters\: carbonated\: water)}{750}\)

Cross-multiply and solve for x.
3, 000x = 7, 500, 000
x = 2, 500

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.

The x-coordinate is positive if A is to the right of the y-axis. The y-coordinate is positive if y is above the x-axis. 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

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 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.

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.

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

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.

To find the volume, substitute ⁴⁄₃ for r in the equation V = (⁴⁄₃)πr³ 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.