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3 years ago

Find the area of an equilateral triangle with a side of 6 inches.

Mathematics

1 answer:

sweet-ann [11.9K]3 years ago

6 0

Answer:

9 $\sqrt{3}$ in²

Step-by-step explanation:

The area (A) of an equilateral triangle is calculated as

A = $\frac{s^2\sqrt{3} }{4}$ ( s is the length of a side )

Here s = 6, thus

A = $\frac{6^2\sqrt{3} }{4}$ = $\frac{36\sqrt{3} }{4}$ = 9 $\sqrt{3}$ in²

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The candy jar has 251 pieces of candy. Sophia adds 31 pieces of candy to it. If the candy is divided equally between 6 campers,

NeTakaya

Answer:

Step-by-step explanation:

251+31= 282

282 divided by six = 47

4 0

3 years ago

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Let f(x) = x2- 3x - 7. Find f(-3)

Alexxx [7]

F(x) = x^2 - 3x - 7
f(-3) = (-3)^ 2 - 3(-3) - 7
f(-3) = 9 + 9 - 7
f(-3) = 18 - 7
f(-3) = 11

6 0

3 years ago

4.5 - 17 - X 8 I need help! 10 pts

sesenic [268]

Answer:

x = -1.5625

Step-by-step explanation:

Solve for x:

-8 x - 12.5 = 0

Add 12.5` to both sides:

(12.5 - 12.5) - 8 x = 12.5

12.5 - 12.5 = 0:

-8 x = 12.5

Divide both sides of -8 x = 12.5 by -8:

(-8 x)/(-8) = 12.5/(-8)

(-8)/(-8) = 1:

x = 12.5/(-8)

12.5/(-8) = -1.5625:

Answer: x = -1.5625

7 0

3 years ago

Helpp fast will name brainliest5. A worker drives 2 hours each day to work. Write an algebraic expression to represent the numbe

Alchen [17]

The first question is d

i think the second one is c

8 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