Question

1. the table shows the monthly high temperature for austin, texas, in degrees fahrenheit over a 12 - month period.

what does the correlation coefficient for the data indicate about the strength of the linear association between the month and the temperature in austin?
a. weak negative correlation
b. strong negative correlation
c. weak positive correlation
d. strong positive correlation

1. the daily cost of hiring a lawn service, y, to work x hours mowing the grounds on a golf course can be modeled using a linear function. the lawn service charges a fixed cost of $100, plus an additional cost of $25 per hour. the lawn service works a maximum of 6 hours per day. for one day of work, what is the range of the function for this situation?

a. ( 25 leq y leq 400 )
b. ( 100 leq y leq 250 )
c. ( 0 leq x leq 6 )
d. ( 0 leq x leq 8 )

1. what are the equation and slope of the line shown on the grid?

a. ( x = 10 ); slope is 10
b. ( y = 10 ); slope is zero
c. ( x = 10 ); slope is zero
d. ( y = 10 ); slope is undefined

Explanation:

Question 5

• First, analyze the trend of the data. As the month number (from 1 - 12) increases, the temperature first increases (from month 1 - 9: 90 - 112) and then decreases (from month 9 - 12: 112 - 90).
• A correlation coefficient close to \(0\) (in absolute value) indicates a weak correlation. Since the overall pattern is not a strong - upward or strong - downward linear trend.

• The linear function is \(y=25x + 100\), where \(x\) (the number of hours) satisfies \(0\leq x\leq6\).
• When \(x = 0\), \(y=25\times0+100=100\).
• When \(x = 6\), \(y=25\times6+100=150 + 100=250\).
• The range of a function \(y = f(x)\) is the set of all possible \(y\) - values.

• For a horizontal line, the equation is of the form \(y = k\) (where \(k\) is a constant). In this case, the line passes through \(y = 10\) for all \(x\) - values.
• The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). For a horizontal line, \(y_2=y_1\), so \(m = 0\).

Answer:

A. Weak negative correlation

Question 6