The slope of the line that passes through the points (8, y) and (-4, 10) is 4.

Kobotan [32]

For number 2, you set up a proportion, which in this case, is 17/1 = w/6.

To get w by itself you need to get rid of the 6 in the denominator by canceling it out buy multiplying by the reciprocal.

Your new equation should be 6/1 = 17/1 or 17.

You then multiply 6 and 17 to get a total of 102

Hope this helps!

4 0

3 years ago

A coin is tossed,and a four-section spinner is spun once.The tree diagram shows the possible outcomes for the Two events. What i

Llana [10]

I believe that the answer is 1/8. I hope this helps

8 0

3 years ago

Read 2 more answers

Which represents the inverse of the function f(x) = 4x?

irga5000 [103]

Answer:

y = x/4

Step-by-step explanation:

First, replace f(x) with y, so it's easier to find the inverse:

y = 4x

To find the inverse of this function, you would replace all the y's with x's and all the x's with y's, and then solve for y. That would be:

x = 4y

y = x/4

Therefore, the inverse function of y = 4x is y = x/4.

4 0

3 years ago

What two numbers multiply to -50 and add up to -23

umka2103 [35]

Answer:

-25 and 2

Step-by-step explanation:

x + y = -23

xy = 50, so y = 50 /x

.

x + 50/x =-23, x^2 +23x - 50 = (x-2)(x+25)

so 2 and -25

4 0

3 years ago

Health insurance benefits vary by the size of the company (the Henry J. Kaiser Family Foundation website, June 23, 2016). The sa

xxMikexx [17]

Answer:

$\chi^2 = \frac{(32-42)^2}{42}+\frac{(18-8)^2}{8}+\frac{(68-63)^2}{63}+\frac{(7-12)^2}{12}+\frac{(89-84)^2}{84}+\frac{(11-16)^2}{16}=19.221$

Now we can calculate the degrees of freedom for the statistic given by:

$df=(rows-1)(cols-1)=(3-1)(2-1)=2$

And we can calculate the p value given by:

$p_v = P(\chi^2_{2} >19.221)=0.000067$

And we can find the p value using the following excel code:

"=1-CHISQ.DIST(19.221,2,TRUE)"

Since the p values is higher than a significance level for example $\alpha=0.05$ , we can reject the null hypothesis at 5% of significance, and we can conclude that the two variables are dependent at 5% of significance.

Step-by-step explanation:

Previous concepts

A chi-square goodness of fit test "determines if a sample data matches a population".

A chi-square test for independence "compares two variables in a contingency table to see if they are related. In a more general sense, it tests to see whether distributions of categorical variables differ from each another".

Solution to the problem

Assume the following dataset:

Size Company/ Heal. Ins. Yes No Total

Small 32 18 50

Medium 68 7 75

Large 89 11 100

_____________________________________

Total 189 36 225

We need to conduct a chi square test in order to check the following hypothesis:

H0: independence between heath insurance coverage and size of the company

H1: NO independence between heath insurance coverage and size of the company

The statistic to check the hypothesis is given by:

$\sum_{i=1}^n \frac{(O_i -E_i)^2}{E_i}$

The table given represent the observed values, we just need to calculate the expected values with the following formula $E_i = \frac{total col * total row}{grand total}$

And the calculations are given by:

$E_{1} =\frac{50*189}{225}=42$

$E_{2} =\frac{50*36}{225}=8$

$E_{3} =\frac{75*189}{225}=63$

$E_{4} =\frac{75*36}{225}=12$

$E_{5} =\frac{100*189}{225}=84$

$E_{6} =\frac{100*36}{225}=16$

And the expected values are given by:

Size Company/ Heal. Ins. Yes No Total

Small 42 8 50

Medium 63 12 75

Large 84 16 100

_____________________________________

Total 189 36 225

And now we can calculate the statistic:

$\chi^2 = \frac{(32-42)^2}{42}+\frac{(18-8)^2}{8}+\frac{(68-63)^2}{63}+\frac{(7-12)^2}{12}+\frac{(89-84)^2}{84}+\frac{(11-16)^2}{16}=19.221$

Now we can calculate the degrees of freedom for the statistic given by:

$df=(rows-1)(cols-1)=(3-1)(2-1)=2$

And we can calculate the p value given by:

$p_v = P(\chi^2_{2} >19.221)=0.000067$

And we can find the p value using the following excel code:

"=1-CHISQ.DIST(19.221,2,TRUE)"

Since the p values is higher than a significance level for example $\alpha=0.05$ , we can reject the null hypothesis at 5% of significance, and we can conclude that the two variables are dependent at 5% of significance.

3 0

4 years ago