A sample of midterm grades for five students showed the following results: 72, 65, 82, 90, 76. Which of the following statements are correct, and which should be challenged as being too generalized?

a. The average midterm grade for the sample of five students is 77.

b. The average midterm grade for all students who took the exam is 77.

c. An estimate of the average midterm grade for all students who took the exam is 77.

d. More than half of the students who take this exam will score between 70 and 85.

e. If five other students are included in the sample, their grades will be between 65 and 90.

a. The average midterm grade for the sample of five students is 77.

c. An estimate of the average midterm grade for all students who took the exam is 77.

Step-by-step explanation:

a. Average is the sum of all five students divided by 5 which gives us 77 thus statement a is correct.

b. Statement b is too generalized because the average is only base on a sample of 5 students and not all students.

c. Statement c is correct  because the average of 77 is referred to as an estimate.

d. Statement d is too generalized because because it is possible that the population deviates from the given sample.

e.  Statement d is too generalized because it is possible that the population deviates from the given sample and therefore the five newly included students could have different grades which could be lower than 65 or higher than 90.

simplifying

5(x + -6) = 2(x + 3)

reorder the terms:

5(-6 + x) = 2(x + 3)

(-6 * 5 + x * 5) = 2(x + 3)

(-30 + 5x) = 2(x + 3)

reorder the terms:

-30 + 5x = 2(3 + x)

-30 + 5x = (3 * 2 + x * 2)

-30 + 5x = (6 + 2x)

solving

-30 + 5x = 6 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-30 + 5x + -2x = 6 + 2x + -2x

combine like terms: 5x + -2x = 3x

-30 + 3x = 6 + 2x + -2x

combine like terms: 2x + -2x = 0

-30 + 3x = 6 + 0

-30 + 3x = 6

add '30' to each side of the equation.

-30 + 30 + 3x = 6 + 30

combine like terms: -30 + 30 = 0

0 + 3x = 6 + 30

3x = 6 + 30

combine like terms: 6 + 30 = 36

3x = 36

divide each side by '3'.

x = 12

simplifying

x = 12

this should .