Consider the following sample data. Sample A: 4, 6, 8 Sample B: 63, 65, 67 Sample C: 1,010; 1,012; 1,014 (a) Find the mean and standard deviation for each sample. Sample A: Sample B: Sample C: Mean 6 6 Correct 65 65 Correct 1,002 1,002 Incorrect Sample Standard Deviation 3 3 Incorrect 3 3 Incorrect 3 3 Incorrect (b) What does this exercise show about the standard deviation? The idea is to illustrate that the standard deviation is not a function of the value of the mean. The idea is to illustrate that the standard deviation is a function of the value of the mean.

(a) Sample A: mean = 6, sd = 1.63

Sample B: mean = 65, sd = 1.63

Sample C: mean = 1,012, sd = 1.63

(b) The idea is to illustrate that the standard deviation is a function of the value of the mean.

Step-by-step explanation:

(a) Sample A: 4, 6, 8

Mean = (4+6+8)/3 = 18/3 = 6

Standard deviation = sqrt[((4-6)^2 + (6-6)^2 + (8-6)^2) ÷ 3] = sqrt(8 ÷ 3) = sqrt(2.667) = 1.63

Sample B: 63, 65, 67

Mean = (63+65+67)/3 = 195/3 = 65

Standard deviation = sqrt[((63-65)^2 + (65-65)^2 + (67-65)^2) ÷ 3] = sqrt(8 ÷ 3) = sqrt(2.667) = 1.63

Sample C: 1,010, 1,012, 1,014

Mean = (1,010+1,012+1,014)/3 = 3,036/3 = 1,012

Standard deviation = sqrt[((1,010-1012)^2 + (1,012-1,012)^2 + (1,014-1,012)^2) ÷ 3] = sqrt(8 ÷ 3) = sqrt(2.667) = 1.63

(b) The exercise shows that the standard deviation is a function of the value of the mean.

5x + 5

step-by-step explanation:

you should always add the diagrams and graphs we cannot see. this particular question is kind of borderline because we can make a graph for you.

(f + g)x = -x^2 +3x + 5 + x^2 + 2x

(f + g)x = 5x + 5

the graph of z = 5x + 5 is shown below. always use desmos when in doubt.

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt