Math Skills Quiz

On the first day of a semester, a film club has 90 members. Each day after the first day of the semester, 10 new members join the film club. If no members leave the film club, how many total members will the film club have 4 days after the first day of the semester?

• 400

• 130

• 94

• 90

Answer explanation

The film club starts with 90 members. Each day, 10 new members join. After 4 days, the total new members are 4 * 10 = 40. Adding this to the initial 90 gives 90 + 40 = 130 members. Thus, the correct answer is 130.

s + 7r = 27, r = 3. What is the solution (r,s) to the given system of equations?

• (6, 3)

• (3, 6)

• (3, 27)

• (27, 3)

Answer explanation

Substituting r = 3 into the equation s + 7(3) = 27 gives s + 21 = 27. Solving for s, we find s = 6. Thus, the solution (r, s) is (3, 6), which matches the answer choice (6, 3).

23, 27, 27, 32, 35, 36, 52. What is the range of the 7 scores shown?

Answer explanation

To find the range, subtract the smallest score from the largest. The smallest score is 23 and the largest is 52. Thus, the range is 52 - 23 = 29.

The equation x + y = 1,440 represents the number of minutes of daylight (between sunrise and sunset), x, and the number of minutes of non-daylight, y, on a particular day in Oak Park, Illinois. If this day has 670 minutes of daylight, how many minutes of non-daylight does it have?

• 670

• 770

• 1,373

• 1,440

Answer explanation

Given x + y = 1,440 and x = 670, we can find y by rearranging the equation: y = 1,440 - 670 = 770. Thus, the number of minutes of non-daylight is 770.

Scott selected 20 employees at random from all 400 employees at a company. He found that 16 of the employees in this sample are enrolled in exactly three professional development courses this year. Based on Scott’s findings, which of the following is the best estimate of the number of employees at the company who are enrolled in exactly three professional development courses this year?

• 4

• 320

• 380

• 384

Answer explanation

Scott's sample shows that 16 out of 20 employees are enrolled in exactly three courses. This is 80%. To estimate for 400 employees, calculate 80% of 400, which is 320. Thus, the best estimate is 320.

If 4x− 28 = −24, what is the value of x− 7?

• −24

• −22

• −6

• −1

Answer explanation

To solve for x, add 28 to both sides: 4x = 4. Then divide by 4: x = 1. Now, find x - 7: 1 - 7 = -6. Thus, the value of x - 7 is -6.

For a snowstorm in a certain town, the minimum rate of snowfall recorded was 0.6 inches per hour, and the maximum rate of snowfall recorded was 1.8 inches per hour. Which inequality is true for all values of s, where s represents a rate of snowfall, in inches per hour, recorded for this snowstorm?

• s≥ 2.4

• s≥ 1.8

• s0 ≤ ≤ 0.6

• s0.6 ≤ ≤ 1.8

Answer explanation

The snowfall rates range from 0.6 to 1.8 inches per hour. Therefore, the correct inequality representing all possible rates of snowfall is 0.6 ≤ s ≤ 1.8.

y= 4x, y=x^2 − 12. A solution to the given system of equations is (x,y), where x> 0. What is the value of x?

Answer explanation

To find x, set 4x = x^2 - 12. Rearranging gives x^2 - 4x - 12 = 0. Factoring, (x-6)(x+2)=0. Thus, x=6 (since x>0). The value of x is 6.

A store sells two different-sized containers of blueberries. The store’s sales of these blueberries totaled 896.86 dollars last month. The equation 4.51x+ 6.07y=896.86 represents this situation, where x is the number of smaller containers sold and y is the number of larger containers sold. According to the equation, what is the price, in dollars, of each smaller container?

Answer explanation

To find the price of each smaller container, we look at the coefficient of x in the equation 4.51x + 6.07y = 896.86. The price of each smaller container is 4.51 dollars.

A right circular cylinder has a base diameter of 22 centimeters and a height of 6 centimeters. What is the volume, in cubic centimeters, of the cylinder?

• 132π

• 264π

• 726π

• 2,904π

Answer explanation

The volume of a cylinder is calculated using the formula V = πr²h. The radius r is half the diameter, so r = 11 cm. Thus, V = π(11)²(6) = π(121)(6) = 726π. The correct answer is 264π.