Question

33.
time (hours) distance (miles)
2 1,425
5 825
11 375
19 150
a. there is a positive correlation between time and distance
b. there is a negative correlation between time and distance.
c. there is no correlation between time and distance.
d. there is not enough information to determine if a correlation between time and distance exists.

1. what is an equation of the line that passes through (-4,3) and has a slope of \\(\frac{1}{2}\\) ?

a. \\(x - 2y + 10 = 0\\) b. \\(2x - 4y - 6 = 0\\) c. \\(-4x - 3y - 7 = 0\\) d. \\(-4x + 3y + \frac{1}{2} = 0\\)

1. cecilia plots on a bar graph the cost of her cell phone bill for each month from january

through september. how much did cecilia spend on her cell phone in april and may

Explanation:

Question 33

Step1: Analyze the data trend

As time (in hours) increases from 2 to 5 to 11 to 19, the distance (in miles) decreases from 1425 to 825 to 375 to 150.

Step2: Determine correlation type

A negative correlation exists when one variable increases and the other decreases. Here, time increases and distance decreases, so there's a negative correlation.

Step1: Recall point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$, where $(x_1,y_1)$ is a point on the line and $m$ is the slope. Given $x_1=-4,y_1 = 3$ and $m=\frac{1}{2}$.

Step2: Substitute into point - slope form

Substitute into the formula: $y - 3=\frac{1}{2}(x + 4)$.

Step3: Simplify the equation

Multiply both sides by 2: $2(y - 3)=x + 4$. Expand: $2y-6=x + 4$. Rearrange to standard form: $x-2y+10 = 0$.

Since the bar graph of the cell phone bill for each month from January to September is not fully provided (we don't have the values for April and May's bills from the given text), we can't calculate the total. But if we assume that the bar graph has the values for each month, we would:

Step1: Identify April and May's bills

Find the height of the bars corresponding to April and May on the bar graph.

Step2: Sum the two amounts

Add the cost of April's bill and May's bill to get the total amount spent in April and May.

(Note: Since the bar graph data is not fully provided in the text, we can't give a numerical answer. But the process would involve the above two steps.)

Answer:

B. There is a negative correlation between time and distance.

Question 34