Consider the right triangle below. Solve for x. Label the sides in the image as opposite, adjacent, or hypotenuse, then show your work

Using the t-distribution, it is found that:

a) Since the test statistic is greater than the critical value for the right-tailed test, it is found that there is enough evidence to conclude that significantly more electricity is used at the student center, on average, on weekdays than weekend days.

b) The 95% confidence interval for the difference in mean electricity use at the student center between weekdays and weekend days is (3.56, 33.18).

Item a:

At the null hypothesis, it is tested if there is no difference, that is, the subtraction is at most 0, hence:

[tex]H_0: \mu_1 - \mu_2 \leq 0[/tex]

At the alternative hypothesis, it is tested if there is difference, that is, the subtraction is positive, hence:

[tex]H_1: \mu_1 - \mu_2 > 0[/tex]

The standard errors are given by:

[tex]s_1 = \frac{32.07}{\sqrt{60}} = 4.14[/tex]

[tex]s_2 = \frac{43.29}{\sqrt{30}} = 7.9[/tex]

The distribution of the difference has mean and standard deviation given by:

[tex]\overline{x} = \mu_1 - \mu_2 = 112.63 - 94.26 = 18.37[/tex]

[tex]s = \sqrt{s_1^2 + s_2^2} = \sqrt{4.14^2 + 7.9^2} = 8.92[/tex]

The standard deviation are given for the samples, hence, the t-distribution is used.

The test statistic is given by:

[tex]t = \frac{\overline{x} - \mu}{s}[/tex]

In which [tex]\mu = 0[/tex] is the value tested at the hypothesis.

Hence:

[tex]t = \frac{\overline{x} - \mu}{s}[/tex]

[tex]t = \frac{18.37 - 0}{8.92}[/tex]

[tex]t = 2.06[/tex]

The critical value for a right-tailed test, as we are testing if the mean is greater than a value, with a significance level of 0.05 and 30 + 60 - 2 = 88 df is [tex]t^{\ast} = 1.66[/tex]

Since the test statistic is greater than the critical value for the right-tailed test, it is found that there is enough evidence to conclude that significantly more electricity is used at the student center, on average, on weekdays than weekend days.

Item b:

The interval is:

[tex]\overline{x} \pm t^{\ast}s[/tex]

Hence:

[tex]\overline{x} - t^{\ast}s = 18.37 - 1.66(8.92) = 3.56[/tex]

[tex]\overline{x} + t^{\ast}s = 18.37 + 1.66(8.92) = 33.18[/tex]

The 95% confidence interval for the difference in mean electricity use at the student center between weekdays and weekend days is (3.56, 33.18).

A similar problem is given at https://brainly.com/question/25812826

Answer:

84mm

Step-by-step explanation:

square = LxW = 6x6 =36

triangle = bxh/2 = 6x8/2 =24

add together 24x2+36=84

Answer:

A

Step-by-step explanation:

Answer:

Step-by-step explanation:

- BRAINLIEST answerer

Answer:

-40/8= -5

Step-by-step explanation:

Multiply the top to get -40 then the bottom to get 8. When you simplify, you get -5.

Answer:

-5.625

Step-by-step explanation:

5/4 × (-9/2)

=5×(-9)/4×2

=-45/8

=-5.625

The value of given expression when x=-4 and y=4 is 1250.

The expression is missing in the question which is [tex]\dfrac{x^6-x}{4y}[/tex].

We have to solve it for x= -4 and y = 4.

Now putting the value of x and y we get,

[tex]\dfrac{x^6-x}{4y}=\dfrac{(-4)^6-(-4)}{4}[/tex]

[tex]\dfrac{x^6-x}{4y}=\dfrac{4096+4}{4}[/tex]

[tex]\dfrac{x^6-x}{4y}=1250[/tex]

Hence the value of given expression when x=-4 and y=4 is 1250.

For more details follow the link:

https://brainly.com/question/11897796

Answer:

The third option, 1/2..

Answer:

Divide the no. by three

Step-by-step explanation:

153÷3 = 51

so, 51+51+51 = 153

Answer:

an odd number can be expressed as 2n+1 (2n would be even, add 1 = odd)

first number = 2n+1

second number = 2n+3 -> skip + 2 because it would make it even

third number = 2n+5

2n+1+2n+3+2n+5=153

6n+9=153

6n=144

n=24

24*2+1=48+1=49

24*2+3=48+3=51

24*2+5=48+5=53

the numbers are 49, 51, and 53.

Answer:your mom

Step-by-step explanation:

[tex]\huge \bf༆ Answer ༄[/tex]

Any value multiplied by Zero gives Zero, therefore ~

the domain is the x value (first number) and the range is the y value (second number)

(if a number appears more than once in the domain or range, like in number 1 you don't have to write it again.)

to graph the domain and range you just plot the points,

and to map them you have to put the x values in the first oval and the y values in the second, usually in order from smallest to largest.

then you have to draw arrows connecting each x value to the y value that was in the same pair. just like when writing down the domain/range, if a number comes up again you don't have to write it down again. instead, you might have two or more arrows connecting to the same  number.

Answer:

B. 2/5

Step-by-step explanation:

I hope this helps!

Answer:

B 2/5

Step-by-step explanation:

Answer:

5:36

Step-by-step explanation:

12 inches = 1 foot, so 6 feet = 72 inches

10:72, reduces to 5:36

Answer: the operation can be said as x( 576-68)t-5= x

Step-by-step explanation:

You can see this because I am smart and just am

Answer:

A 20

Step-by-step explanation:

yeah-ya....... right?

Answer:

okkkkkkkkkkkkkkkkkkkkkkkkkkk

[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]

Sum of angles of a pentagon is ~ 540°

Therefore,

Value of x = 95°

Answer:

96

Step-by-step explanation:

C=πd

C=?

π=3

d=32

C=3×32

Therefore C=96

Answer:

Step-by-step explanation:

The sum of the square of the constants is 3/4

Given the equation [tex]\frac{1}{a+1} +\frac{1}{b+1} +\frac{1}{c+1} =2[/tex]

The partial form of the equation is given as:

Solve for the constant "a"

[tex]\frac{1}{a +1} = 2\\a+1 = \frac{1}{2} \\a = \frac{1}{2} - 1\\a =-\frac{1}{2}[/tex]

Hence [tex]a=b=c=-\frac{1}{2} \\[/tex]

Taking the square of the constant, we will have:

[tex]a^2 + b^2 + c^2 =(-1/2)^2 +(-1/2)^2+(-1/2)^2\\a^2 + b^2 + c^2 =1/4 + 1/4 + 1/4\\a^2 + b^2 + c^2 =3/4[/tex]

Hence the sum of the square of the constants is 3/4

Learn more on partial fraction here: https://brainly.com/question/24594390

Answer -the sum of the square of the consonants is 3/4

Answer:

Axis interception points of -52 :

Y intercepts : (0,-52 )

The approximate value of q in the equation is [tex]0.774[/tex]

The equation is given as:

[tex]q\log_2(6) = 2[/tex]

Divide both sides of the equation by [tex]\log_2(6)[/tex].

So, we have:

[tex]q= \frac{2}{\log_2(6) }[/tex]

Determine log(6) base 2

[tex]q= \frac{2}{2.585}[/tex]

Divide 2 by 2.585

[tex]q= 0.774[/tex]

Hence, the approximate value of q in the equation is [tex]0.774[/tex]

Read more about logarithmic equations at:

https://brainly.com/question/11897620

I think its the third one but im not completly sure

Answer:

-t-5>-1.5

Step-by-step explanation:

Just ask.

Hope this helps! :)

Answer:

7

Step-by-step explanation:

basically just subtract 10-3=7 then to check 3+7=10

Answer:

x = 7

Step-by-step explanation:

3 + x = 10

-3         -3

x = 7

you subtract by 3 on both sides (because the opposite property of addition is subtraction) to cancel it out and isolate the x.

Answer:

30

Step-by-step explanation:

15x30 = 450

Answer:

She purchased 30 shirts.

Step-by-step explanation:

She paid only $400 Dollars, because she got a discount of $50.

So the total before getting the discount was $450.

If you divide $450 by $15 (the price for 1 shirt) you come up with 30.

450/15 = 30

Answer:

A

Step-by-step explanation:

In a function, each x value must have a singular y value. This means that one x-value (the values on the left) may not have a line pointing to 2 different y-values (the values on the right). In the first relation, the x-value of 6 points to both 4 and 6. This means that the value repeats, and in a function x-values cannot repeat.

However, y-values can repeat. So, situations like that seen in D, where both the x-values of 2 and 4 equal the y-value of 6 are fine.

Answer:

It's A

Step-by-step explanation:

Answer:

well, we know it is

y = -4 x + b

so all we need is b

5 = -4(9) + b

5 = -36 + b

b = 41

so

y = -4 x + 41

Answer:

y = -1/2x - 1/2

Step-by-step explanation:

lmk if you want an explanation