What is the value of (-4) to the power of 4

The length of the rectangular garden is 4 meters longer than the width. If the garden area is 60 square

rusak2 [61]

Step-by-step explanation:

Let x be the Width, and x+4 be the Length of the rectangle ; =>

Area = x*(x+4) = 60 ; =>

x^2 +4x - 60 = 0 ; Now solve the Quadratic equation using factoring to find x;

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5 0

2 years ago

What is the volume of the prism that can be constructed from this net? units3

kirza4 [7]

3×9=27
27×7=189 units³

I hope this helped!!!:)

4 0

3 years ago

Read 2 more answers

Luda [366]

Answer:

a) H0: There is no association between level of education and TV station preference (Independence)

H1: There is association between level of education and TV station preference (No independence)

b) $\chi^2 = \frac{(15-10)^2}{10}+\frac{(15-20)^2}{20}+\frac{(10-10)^2}{10}+\frac{(5-10)^2}{10}+\frac{(25-10)^2}{10}+\frac{(10-20)^2}{20} =33.75$

c) $\chi^2_{crit}=5.991$

d) Since the p value is lower than the significance level we enough evidence to reject the null hypothesis at 5% of significance, and we can conclude that we have dependence between the two variables analyzed.

Step-by-step explanation:

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".

Assume the following dataset:

High school Some College Bachelor or higher Total

Public Broadcasting 15 15 10 40

Commercial stations 5 25 10 40

Total 20 40 20 80

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

Part a

H0: There is no association between level of education and TV station preference (Independence)

H1: There is association between level of education and TV station preference (No independence)

The level os significance assumed for this case is $\alpha=0.05$

The statistic to check the hypothesis is given by:

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

Part b

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:

$E_{1} =\frac{20*40}{80}=10$

$E_{2} =\frac{40*40}{80}=20$

$E_{3} =\frac{20*40}{80}=10$

$E_{4} =\frac{20*40}{80}=10$

$E_{5} =\frac{40*40}{80}=20$

$E_{6} =\frac{20*40}{80}=10$

And the expected values are given by:

High school Some College Bachelor or higher Total

Public Broadcasting 10 20 10 40

Commercial stations 10 10 20 40

Total 20 30 30 80

Part b

And now we can calculate the statistic:

$\chi^2 = \frac{(15-10)^2}{10}+\frac{(15-20)^2}{20}+\frac{(10-10)^2}{10}+\frac{(5-10)^2}{10}+\frac{(25-10)^2}{10}+\frac{(10-20)^2}{20} =33.75$

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

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

Part c

In order to find the critical value we need to look on the right tail of the chi square distribution with 2 degrees of freedom a value that accumulates 0.05 of the area. And this value is $\chi^2_{crit}=5.991$

Part d

And we can calculate the p value given by:

$p_v = P(\chi^2_{3} >33.75)=2.23x10^{-7}$

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

"=1-CHISQ.DIST(33.75,2,TRUE)"

Since the p value is lower than the significance level we enough evidence to reject the null hypothesis at 5% of significance, and we can conclude that we have dependence between the two variables analyzed.

7 0

3 years ago

This drawing would be a step in finding which point of concurrency in a triangle?

ad-work [718]

Answer:

A. Orthocenter

Step-by-step explanation:

In the given triangle, ΔWKS, the drawing shown the construction of a perpendicular line to the side KS that pass through the vertex W of ΔWKS. Therefore, the completed construction gives an altitude of the triangle ΔWKS

Repeating the same procedure from the vertex S to construct the perpendicular line (altitude) to the side WK, and from the vertex K the perpendicular line (altitude) to the side WS gives the three altitudes of the triangle

The point of intersection (the point of concurrency) of the three altitudes is the orthocenter of the triangle and the drawing would therefore be a step in finding the orthocenter of a triangle.

3 0

3 years ago

Write the number below (81) as a power with a base of 3 and a base of 9

likoan [24]

Answer:

base of 3 --> 3^4 (three to the fourth); base of 9 --> 9^2 (nine squared)

Step-by-step explanation:

3 x 3 = 9 x 3 = 27 x 3 = 81 = 3^4

You multiply 3 by itself 4 times.

9 x 9 = 81 = 9^2

You multiply 9 by itself 2 times.

5 0

1 year ago