Math Trivia Quiz: ACT 5-in-5

1. So far, a student has earned the following scores on four 100-point tests this grading period: 65, 73, 81, and 82. What score must the student earn on the fifth and last 100-point test of the grading period to earn an average test grade of 80 for the 5 tests?

75

76

84

99

The student cannot earn an average score of 80.

To find the score the student must earn on the fifth test to have an average of 80, we can use the formula: (sum of scores + score on fifth test) / 5 = 80. Rearranging the formula, we get: sum of scores + score on fifth test = 400. The sum of the scores on the first four tests is 65 + 73 + 81 + 82 = 301. Therefore, the score the student must earn on the fifth test is 400 - 301 = 99.

Explanation

To find the score the student must earn on the fifth test to have an average of 80, we can use the formula: (sum of scores + score on fifth test) / 5 = 80. Rearranging the formula, we get: sum of scores + score on fifth test = 400. The sum of the scores on the first four tests is 65 + 73 + 81 + 82 = 301. Therefore, the score the student must earn on the fifth test is 400 - 301 = 99.

2.

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Explanation

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3. The expression a[b + (c – d)] is equivalent to:

A. ab + ac – ad

B. ab + abc – ad

C. ab + ac – d

D. ab + c + d

E. ab + c – d

The given expression a[b + (c - d)] can be simplified by applying the distributive property. Distributing the a to both terms inside the brackets, we get ab + (a * (c - d)). Simplifying further, we have ab + ac - ad, which matches option A. Therefore, the correct answer is A. ab + ac - ad.

Explanation

The given expression a[b + (c - d)] can be simplified by applying the distributive property. Distributing the a to both terms inside the brackets, we get ab + (a * (c - d)). Simplifying further, we have ab + ac - ad, which matches option A. Therefore, the correct answer is A. ab + ac - ad.

4. A circle in the standard (x, y) coordinate plane is tangent to the x-axis at 5 and tangent to the y-axis at 5. Which of the following is an equation of the circle?

The equation of a circle can be written in the form (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center of the circle and r is the radius. Since the circle is tangent to the x-axis at 5, the y-coordinate of the center is 5. Similarly, since the circle is tangent to the y-axis at 5, the x-coordinate of the center is 5. Therefore, the center of the circle is (5, 5). The radius of the circle can be found by measuring the distance from the center to either tangent point, which is 5 units. Thus, the equation of the circle is (x - 5)^2 + (y - 5)^2 = 25.

Explanation

The equation of a circle can be written in the form (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center of the circle and r is the radius. Since the circle is tangent to the x-axis at 5, the y-coordinate of the center is 5. Similarly, since the circle is tangent to the y-axis at 5, the x-coordinate of the center is 5. Therefore, the center of the circle is (5, 5). The radius of the circle can be found by measuring the distance from the center to either tangent point, which is 5 units. Thus, the equation of the circle is (x - 5)^2 + (y - 5)^2 = 25.

5. What 2 numbers should be placed in the blanks below so that the difference between consecutive numbers is the same

A. 23, 29

B. 24, 34

C. 25, 33

D. 26, 35

E. 27, 31

The numbers 25 and 33 should be placed in the blanks because the difference between them is 8, which is the same as the difference between the other pairs of consecutive numbers.

Explanation

The numbers 25 and 33 should be placed in the blanks because the difference between them is 8, which is the same as the difference between the other pairs of consecutive numbers.

Math Trivia Quiz: Act 5-in-5