Question

nehemiah wants to create a function to represent the change in his income over the past few months. nehemiah estimates that the best fit linear function for the change in his income is ( y = 2310 + 220x ), where ( x ) is the number of months. complete the statements. the predicted value of nehemiah’s income in month 6 is (\boxed{quad}). if the actual value of nehemiah’s income was $3750 in month 6, the residual value for month 6 would be (\boxed{quad}). 27) karen wants to prove ( sqrt{8} = 8^{\frac{1}{2}} ). which of the following expressions could she use to help her show the two expressions are equivalent? select all that apply. ( 2^{\frac{1}{2}} + \frac{1}{2} + \frac{1}{2} ) ( 8^{\frac{1}{3}} + \frac{1}{3} + \frac{1}{3} ) ( (2 cdot 2 cdot 2)^{\frac{1}{2}} ) ( 8^{\frac{1}{3}} + 8^{\frac{1}{3}} + 8^{\frac{1}{3}} ) ( (2 + 2 + 2 + 2)^{\frac{1}{2}} )

Explanation:

Part 1: Predicted Income in Month 6

Step 1: Identify the function and x-value

The function is \( y = 2310 + 220x \), and we need to find the predicted value when \( x = 6 \) (month 6).

Step 2: Substitute x = 6 into the function

Substitute \( x = 6 \) into \( y = 2310 + 220x \):
\( y = 2310 + 220(6) \)

Step 3: Calculate the multiplication

First, calculate \( 220(6) \):
\( 220 \times 6 = 1320 \)

Step 4: Calculate the sum

Then, add 2310 and 1320:
\( y = 2310 + 1320 = 3630 \)

Step 1: Recall the formula for residual

Residual = Actual value - Predicted value.

Step 2: Identify actual and predicted values

Actual value = \( \$3750 \), Predicted value = \( \$3630 \) (from part 1).

Step 3: Calculate the residual

Residual = \( 3750 - 3630 = 120 \)

Answer:

The predicted value of Nehemiah's income in month 6 is \( \$3630 \).

Part 2: Residual Value for Month 6