Question

1. sandras scores on the first 4 tests were 87%, 92%, 76%, and 89%. what is the minimum score she needs to make on the fifth test so that her average is at least an 80%? 11. make a list of 5 numbers with a mean of 12 and a mode of 15.

Explanation:

Step1: Set up the average formula for question 10

Let the score on the fifth test be $x$. The average of the five - test scores is $\frac{87 + 92+76 + 89+x}{5}$. We want this average to be at least 80, so we set up the inequality $\frac{87 + 92+76 + 89+x}{5}\geq80$.

Step2: Simplify the numerator of the left - hand side

$87+92 + 76+89=344$. So the inequality becomes $\frac{344 + x}{5}\geq80$.

Step3: Solve the inequality for $x$

Multiply both sides of the inequality by 5: $344 + x\geq400$. Then subtract 344 from both sides: $x\geq400 - 344$, so $x\geq56$.

Step4: Solve question 11

Let the five numbers be $a,b,c,d,e$. We know that the mean $\frac{a + b + c + d+e}{5}=12$, so $a + b + c + d+e=60$. We also know that the mode is 15, which means 15 appears more frequently than any other number. Let's assume two of the numbers are 15. So $15+15+a + b + c=60$, or $a + b + c=30$. We can choose $a = 9$, $b = 10$, $c = 11$.

Answer:

1. 56%
2. 9, 10, 11, 15, 15