Question

1. critical thinking find values for x, y, and z so that all of the following statements are true.

• ( y > x ), ( z < y ), and ( x < 0 )
• ( x + 2 ) and ( z + 3 ) are integers.
• ( x + z = -2 )
• ( x + y = z )

1. critical thinking addition and multiplication are said to be closed for whole numbers, but subtraction and division are not. that is, when you add or multiply any two whole numbers, the result is a whole number. which operations are closed for integers?

1. writing in math answer the question that was posed at the beginning of the lesson.

how is dividing integers related to multiplying integers?
include the following in your answer:

• two related multiplication and division sentences, and
• an example of each case (same signs, different signs) of dividing integers.

1. on saturday, the temperature fell ( 10^circ ) in 2 hours. which expresses the temperature change per hour?

options: a ( 5^circ ), b ( -2^circ ), c ( -5^circ ), d ( -10^circ )

1. mark has quiz scores of 8, 7, 6, and 9. what is the lowest score he can get on the remaining quiz to have a final average (mean) score of at least 8?

options: a 7, b 8, c 9, d 10

Explanation:

Question 40

Step1: Understand the problem

The temperature fell \(10^\circ\) in 2 hours. We need to find the temperature change per hour. A fall in temperature means a negative change.

Step2: Calculate the rate of change

To find the change per hour, we divide the total change in temperature by the number of hours. So we calculate \(\frac{-10}{2}\) (negative because it's a fall).
\(\frac{-10}{2}=-5\)

Step1: Recall the formula for the mean

The mean (average) of a set of numbers is the sum of the numbers divided by the count of numbers. Let the score on the remaining quiz be \(x\). There are 5 quizzes in total (4 existing + 1 remaining). The sum of the existing scores is \(8 + 7+6 + 9\).

Step2: Calculate the sum of existing scores

\(8 + 7+6 + 9 = 30\)

Step3: Set up the inequality for the mean

We want the mean to be at least 8. So \(\frac{30 + x}{5}\geq8\)

Step4: Solve the inequality

Multiply both sides by 5: \(30 + x\geq40\)
Subtract 30 from both sides: \(x\geq10\)? Wait, no, wait. Wait, 4 quizzes? Wait, no, the problem says "quiz scores of 8, 7, 6, and 9" – that's 4 scores, and then "the remaining quiz" – so total of 5 quizzes. Wait, let's recalculate. Wait, 8 + 7 is 15, 15 + 6 is 21, 21 + 9 is 30. So sum of 4 scores is 30. Let \(x\) be the fifth score. The mean is \(\frac{30 + x}{5}\geq8\). Multiply both sides by 5: \(30 + x\geq40\). Then \(x\geq10\)? But the options are 7,8,9,10. Wait, maybe I made a mistake. Wait, the problem says "at least 8" for the mean. Let's check again. Wait, 8 (mean) times 5 (number of quizzes) is 40. So total sum needed is 40. Existing sum is 8 + 7 + 6 + 9 = 30. So 40 - 30 = 10. So he needs at least 10? But option D is 10. Wait, but let's check the options. Wait, maybe I miscounted the number of quizzes. Wait, the problem says "quiz scores of 8, 7, 6, and 9" – that's 4 quizzes, and "the remaining quiz" – so 5 quizzes. So mean is (8 + 7 + 6 + 9 + x)/5 ≥ 8. So (30 + x)/5 ≥ 8 → 30 + x ≥ 40 → x ≥ 10. So the lowest score he can get is 10.

Answer:

C. \(-5^\circ\)

Question 41