1. the correlation coefficient for a set of linear data is r = - 0.6. what does this mean?
2. which equations have no solution? a. - 5.2x + 2 = 8.1 b. 5x = 0 c. x + 3 = x + 1 d. x = x + 10
3. write a sentence to describe the association. then draw a trend line to represent the data.
4. name the obvious point on the line y - 6 = 2(x + 13).
5. graph 8x - 6y = - 24
6. solve for x. 3 - 2(x - 7)+1 = 4x
7. create a graph that: is exponential, is decreasing, is discrete, contains (4,2)
8. evaluate the expression b² - 4ac if a = - 1, b = 6, and c = 8.

Question

Accepted Answer

### 1.
# Explanation:
## Step1: Interpret correlation coefficient
The correlation coefficient $r$ measures the strength and direction of a linear relationship. A value of $r = - 0.6$ indicates a moderate negative linear relationship. That is, as one variable increases, the other variable tends to decrease, and the linear - association is not very weak nor very strong.
# Answer:
There is a moderate negative linear relationship between the variables in the data - set.

### 2.
# Explanation:
## Step1: Analyze option A
Solve $-5.2x + 2=8.1$. Subtract 2 from both sides: $-5.2x=8.1 - 2=6.1$. Then $x =-\frac{6.1}{5.2}$, so it has a solution.
## Step2: Analyze option B
Solve $5x = 0$. Divide both sides by 5, we get $x = 0$, so it has a solution.
## Step3: Analyze option C
Solve $x + 3=x + 1$. Subtract $x$ from both sides, we get $3 = 1$, which is a contradiction. So it has no solution.
## Step4: Analyze option D
Solve $x=x + 10$. Subtract $x$ from both sides, we get $0 = 10$, which is a contradiction. So it has no solution.
# Answer:
C. $x + 3=x + 1$, D. $x=x + 10$

### 3.
# Explanation:
## Step1: Describe association
Looking at the scatter - plot, as the value on the x - axis (Car Cost) increases, the value on the y - axis (Miles per Gallon) seems to decrease. So, there is a negative association between car cost and miles per gallon.
## Step2: Draw trend line
To draw a trend line, try to draw a straight line that best fits the data points. Place the line so that approximately half of the data points are above the line and half are below the line.
# Answer:
There is a negative association between car cost and miles per gallon. (Trend - line drawing is a manual process and cannot be fully represented in text)

### 4.
# Explanation:
## Step1: Rewrite the equation in point - slope form
The equation of a line in point - slope form is $y - y_1=m(x - x_1)$. The given equation $y - 6=2(x + 13)$ is in point - slope form, where the point $(x_1,y_1)$ is $(-13,6)$.
# Answer:
The point $(-13,6)$ is on the line.

### 5.
# Explanation:
## Step1: Rewrite the equation in slope - intercept form
Start with $8x-6y=-24$. Subtract $8x$ from both sides: $-6y=-8x - 24$. Divide by $-6$: $y=\frac{4}{3}x + 4$.
## Step2: Find the y - intercept
When $x = 0$, $y = 4$. So the y - intercept is $(0,4)$.
## Step3: Find the x - intercept
When $y = 0$, $0=\frac{4}{3}x + 4$. Subtract 4 from both sides: $-4=\frac{4}{3}x$. Multiply both sides by $\frac{3}{4}$, we get $x=-3$. So the x - intercept is $(-3,0)$. Plot the points $(0,4)$ and $(-3,0)$ and draw a straight line through them.
# Answer:
Graph with x - intercept $(-3,0)$ and y - intercept $(0,4)$ and a line passing through them.

### 6.
# Explanation:
## Step1: Expand the left - hand side
Expand $3-2(x - 7)+1$: $3-2x + 14+1=-2x+18$.
## Step2: Solve the equation
The equation becomes $-2x + 18=4x$. Add $2x$ to both sides: $18 = 6x$. Divide both sides by 6: $x = 3$.
# Answer:
$x = 3$

### 7.
# Explanation:
## Step1: Write a general exponential function
A general exponential function is $y = a\cdot b^x$. Since it is decreasing, $0\lt b\lt1$. Let's assume $y=a\cdot(\frac{1}{2})^x$.
## Step2: Find the value of a
Since the graph contains the point $(4,2)$, substitute $x = 4$ and $y = 2$ into $y=a\cdot(\frac{1}{2})^x$. We get $2=a\cdot(\frac{1}{2})^4$. Then $2=a\cdot\frac{1}{16}$, and $a = 32$. So the function is $y = 32\cdot(\frac{1}{2})^x$. Plot points for discrete values of $x$ (e.g., $x = 0,1,2,\cdots$) and connect them with non - connected points (since it is discrete).
# Answer:
Graph of the discrete exponential function $y = 32\cdot(\frac{1}{2})^x$ with points plotted for integer values of $x$.

### 8.
# Explanation:
## Step1: Substitute the values of a, b, and c
Given $a=-1$, $b = 6$, and $c = 8$, substitute into the expression $b^2-4ac$. We get $(6)^2-4	imes(-1)	imes8$.
## Step2: Calculate the result
First, calculate $(6)^2=36$, and $4	imes(-1)	imes8=-32$. Then $36-(-32)=36 + 32=68$.
# Answer:
$68$

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QUESTION IMAGE

Question

Explanation:

1.

Step1: Interpret correlation coefficient

Step1: Analyze option A

Step2: Analyze option B

Step3: Analyze option C

Step4: Analyze option D

Step1: Describe association

Step2: Draw trend line

Answer:

2.