Please answer this question.

Arlen already established that ΔRST and ΔUTS has two pairs of congruent angles and a pair of congruent included sides, which meet the ASA Congruence Criterion. Therefore:

The ASA Congruence Criterion states that for two triangles to be considered congruent to each other, both triangles must have a pair of congruent included sides and two pairs of congruent angles.

Thus, the two-column proof that shows that RS ≅ TU that Arlen is trying to write, has already established that ΔRST and ΔUTS has the following:

Two pairs of congruent angles - ∠RST ≅ ∠UTS and ∠RTS ≅ ∠UST.

A pair of congruent included sides - ST ≅ S.

These satisfy the ASA Congruence Criterion. Therefore:

Learn more about the ASA Congruence Criterion on:

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Step-by-step explanation:

given, ¾-½= ¼gallon milk.

hope this helps you.

Answer: The quotient is 4 52/185, which rounds to 4.

Explanation is in the image.

Answer:

a - 4/11

b - 11/30

c - 9/25

Step-by-step explanation:

have a lovely day <3

Answer:

a b c

Step-by-step explanation:

hope it helps

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:

5km

Step-by-step explanation:

The formula for hypotenuse is

a squared + b squared = c squared,

4 squared is 16, and 3 squared is 9.

16+9 = c squared

25 = c squared

However, you don't want it to be squared, so you have to find the square root of 25, which is 5.

Answer:

  50 miles

Step-by-step explanation:

Multiply the given scale numbers by 1/2 to find your answer:

  1/2 in = 100 mi

  (1/2)(1/2 in) = (1/2)(100 mi) . . . . multiply the ratio values by 1/2

  1/4 in = 50 mi

Answer:

There is one solution to this system of equations

Step-by-step explanation:

When solving, there is a specific point of intersection which is (7/6,-7/6), making the answer one solution.

The amount that should deposit monthly is $164.98

The formula for calculating the compound amount is expressed as:

[tex]A=P(1+\frac{r}{n} )^{nt}[/tex]

Substitute the given values into the formula to have:

[tex]75000=P(1+\frac{0.075}{12} )^{12(18)}\\75000 = P(1.00625)^{216}\\75000 =P(3.84125)\\P = \frac{75000}{3.84125}\\P= \$19,524.89[/tex]

Hence the amount of money they started with is $19,524.89.

Amount to deposit monthly = 19,524.89/120

Amount to deposit monthly = $164.98

Hence the amount that should deposit monthly is $164.98

Learn more on compound interest here: https://brainly.com/question/24274034

Answer:

See below

Step-by-step explanation:

As x approaches negative infinity, h(x) approaches negative infinity

As x approaches positive infinity, h(x) approaches negative infinity

I've attached a graph to show why these two are true. Remember that in an absolute value function, the result is always positive. However, because there's a negative constant multiplying the absolute value function, this flips the graph over the x-axis and the result is now always negative. In other words, no matter how big or small x is, y will always get smaller.

Answer:

Cuando tenga problemas con una pregunta, venga aquí y también lo ayudaremos si no recibe la pregunta, intente omitirla.

Step-by-step explanation:

Answer:

Letter C.

Step-by-step explanation:

Lap 1 be x

Lap 2 be y

Line graph: plot the values, and will get C.

Answer:

Hope this helps

Step-by-step explanation:

first question --> area of circle ---> [tex]\pi r^{2}[/tex] ---> [tex]1.5^{2} \pi[/tex] ---> [tex]2.25\pi[/tex]

second question --> unclear quetion but I assume 4?

third question --> area of cylinder --> [tex]r^{2} \pi h[/tex] --> [tex]2.25\pi h[/tex] --> [tex]2.25\pi 4[/tex] --> [tex]9\pi[/tex]

h --> height

r --> Radius

[tex]\pi[/tex] --> pi

The total surface area of the can is 61.23 square inches

The formula for calculating the total surface area of a can is expressed as:

S = 2πr(r+h)

where:

h is the height

r is the radius

Given the following parameters

h = 5in

r = 1.5in

S = 2(3.14)(1.5)(1.5 + 5)

S = 6.28(1.5)(6.5)

S = 61.23 square inches

Hence the total surface area of the can is 61.23 square inches

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Answer:

look it up thats what i do

Step-by-step explanation:

Answer:

Therefore, |x-1|>0

=> (x-1)>0 or - (x-1)>0

=> x > 1 or x < 1

=> (- infinity, 1) U (1, infinity)

Answer:

I think it's a Box Plot, hope this helps

Answer:

x = -5/2, (5+5i√3)/4, (5-5i√3)/4

Answer:

[tex](x+2)(3x^3-5x-10)[/tex]

Step-by-step explanation:

If you don't know how to divide polynomials then I can help with that too or you can just search it up

Answer:

the third one

Step-by-step explanation:

iiiieeeeew edgeuinty

Answer:

15 inch. By 27 inch.

Step-by-step explanation:

Answer:a grocery worker is checking in for broken eggs in a cartoons 12 x 4 c 9

Step-by-step explanation:

Answer: R= 7

Step-by-step explanation:

Answer:

[tex]\huge\boxed{\sf t = 7}[/tex]

Step-by-step explanation:

-8 (4 - t) = 24

-32 + 8t = 24

Add 32 to both sides

8t = 24 + 32

8t = 56

Divide both sides by 8

t = 7

[tex]\rule[225]{225}{2}[/tex]

Hope this helped!

Step-by-step explanation:

this is a strange rental company charging no daily fees.

but ok.

so, we have a fixed part of the cost : $24

we have to pay that no matter how many miles we drive. even for 0 miles, just to get the keys to the car.

and then we pay $0.35 for every mile driven.

that makes our function

C(x) = 0.35x + 24

and if we drive 40 miles, that makes x = 40.

C(24) = 0.35×40 + 24 = 14 + 24 = $38

it would cost us $38.

Answer:

B(if the option is 10^7 instead of  107

Step-by-step explanation:

no. of people in New York=19000000

no. of people in Vermont =626,000

difference in populations = 19000000-626,000 =18374000

therefore, the difference in populations is 18374000

(which can also be written as 1.8374x10^7)

Answer:

Look at photo for answer, I have not done a piecewise function for a long time... so double check my work.

Step-by-step explanation:

The true statement about the group of 120 seventh-and eighth-grade students is (c) twenty-four seventh-grade students chose a non-sports activity

The entries are given as:

                           Sports       Non Sports          Total

Seventh Grade:     39              24                    63

Eighth Grade:        29              28                    57

Total                       68              52                   120

From the above entries, we have the following highlights:

From the above highlights, we can conclude that the following statement from the options is true

(c) twenty-four seventh-grade students chose a non-sports activity

Read more about data representation at:

https://brainly.com/question/1592223

Answer:

c)

Step-by-step explanation:

Answer:

y=6+8

y=14

Step-by-step explanation:

y=14 is the answer to this question