Marla owes her sister $15. She pays her $6 today. Which integer represents the amount of debt she has remaining?

Find the slope of every line that is parallel to the line on the graph.

melamori03 [73]

Answer:

-1/5

Step-by-step explanation:

What are parallel lines?

Lines that are parallel never touch. They can extend infinitely and they will still never touch. In order for this to happen the slope of the two lines must be the same. So if we want to find the slope of every line that is parallel to the line on the graph, we simply find the slope of the line of the graph.

Finding the slope

We can find the slope using the following formula:

$Slope=\frac{y_2-y_1}{x_2-x_1}$

Where the x and y values are derived from any given points on the line (x1,y1) and (x2,y2)

Here the given points are (-5,-1) and (0,-2)

So we have (x1,y1) = (-5,-1) meaning x1 = -5 and y1 = -1

We also have (x2,y2) = (0,-2) meaning x2 = 0 and y2 = -2

Now we plug these values into the formula

Recall formula : $Slope=\frac{y_2-y_1}{x_2-x_1}$

==> Plug in x1 = -5 , y1 = -1 , x2 = 0 and y2 = -2

$Slope=\frac{-2-(-1)}{0-5}$

==> simplify numerator and denominator

$slope = \frac{1}{-5}$

So the slope of the line is -1/5

This means the slope of any parallel line to that line would also have a slope of -1/5

8 0

3 years ago

A random sample of 150recent donations at a certain

gtnhenbr [62]

Answer:

Null hypothesis: $p\geq 0.4$

Alternative hypothesis: $p < 0.4$

$z=\frac{0.3 -0.4}{\sqrt{\frac{0.4(1-0.4)}{150}}}=-2.5$

$p_v =2*P(Z$

If we compare the p value obtained and the significance level given $\alpha=0.01$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that the true proportion is not significantly lower than 0.4 or 40% at 1% of significance.

Step-by-step explanation:

1) Data given and notation

n=150 represent the random sample taken

X=45 represent the people with type A blood

$\hat p=\frac{45}{150}=0.3$ estimated proportion of people with type A blood

$p_o=0.4$ is the value that we want to test

$\alpha=0.01$ represent the significance level

Confidence=99% or 0.99

z would represent the statistic (variable of interest)

$p_v$ represent the p value (variable of interest)

2) Concepts and formulas to use

We need to conduct a hypothesis in order to test the claim that the true proportion of people type A blood is less than 0.4:

Null hypothesis: $p\geq 0.4$

Alternative hypothesis: $p < 0.4$

When we conduct a proportion test we need to use the z statisitc, and the is given by:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

The One-Sample Proportion Test is used to assess whether a population proportion $\hat p$ is significantly different from a hypothesized value $p_o$ .

3) Calculate the statistic

Since we have all the info requires we can replace in formula (1) like this:

$z=\frac{0.3 -0.4}{\sqrt{\frac{0.4(1-0.4)}{150}}}=-2.5$

4) Statistical decision

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.

The significance level provided $\alpha=0.01$ . The next step would be calculate the p value for this test.

Since is a bilateral test the p value would be:

$p_v =2*P(Z$

If we compare the p value obtained and the significance level given $\alpha=0.01$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that the true proportion is not significantly lower than 0.4 or 40% at 1% of significance.

7 0

3 years ago

Need help with this

likoan [24]

Answer:

The answer is h = 2A/(b+c) .

Step-by-step explanation:

You have to move all the unrelated terms to the other side by making h the subject :

$A = \frac{1}{2} (b + c)h$