High school math worksheet on scatter plots, correlation, and linear regression.

I'll solve the problem presented in this image. The image shows a worksheet on "Scatter Plot, Correlation, and Line of Best Fit" for High School Common Core: Interpret Linear Models.

Let me analyze the questions one by one:

Question 1: A baseball coach graphs some data and finds the line of best fit. The equation for the line is y = 0.32x + 105.15, where x is the number of times at bat and y is the number of hits. How many hits should he expect from a player who is at bat 375 times?

To solve this, I need to substitute x = 375 into the equation:
y = 0.32(375) + 105.15
y = 120 + 105.15
y = 225.15

Since we're talking about hits (which must be whole numbers), we would round to the nearest whole number: 225 hits.

Question 2: Below is the table of data regarding the cherry blossom trees in Washington D.C. Make a scatter plot of the given data.

This is an instruction to create a scatter plot, not a question that requires a numerical answer.

Question 3: Chang wants to know if he is improving his skill on the cello. He recorded a summer goal and drew a line of best fit.

The question asks which equation would represent the line of best fit, with options:
A) y = 2.1x + 12.3
B) y = 2.1x + 3.77
C) y = 0.48x + 12.3
D) y = 2.1x - 9.39

Looking at the graph, I can see that the line passes through approximately (0, 12.3) and has a positive slope. The y-intercept appears to be around 12.3, and the slope looks to be about 2.1 (for every 1 unit increase in x, y increases by about 2.1 units). So option A seems correct.

Question 4: The graph shows the relationship between the distance in miles a delivery truck traveled and the number of hours each delivery took. Which of the two given points would be the best to use to calculate the line of best fit?

The options are:
A) (300, 11) and (400, 1)
B) (300, 11) and (400, 5)
C) (300, 1) and (400, 5)
D) (300, 7) and (400, 1)

Looking at the graph, I can see that when x=300, y is approximately 11, and when x=400, y is approximately 5. So option B seems correct.

Question 5: Jared collected data on the ages and heights of a random sample of elementary school students. When relationship was most likely to be shown as a positive, negative, or no correlation?

For age vs. height in elementary school students, we would expect a positive correlation - as children get older, they generally get taller.

Therefore, the answers are:
1. 225 hits
3. A) y = 2.1x + 12.3
4. B) (300, 11) and (400, 5)
5. A) Positive correlation