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dezoksy [38]
3 years ago
8

A researcher is interested in determining the mean energy consumption of a new

Mathematics
1 answer:
Nana76 [90]3 years ago
7 0

Answer:

The most appropriate  value of the critical value is 2.289.

Step-by-step explanation:

We are given that a researcher takes a random sample of 41 bulbs and determines  that the mean consumption is 1.3 watts per hour with a standard deviation of 0.7.

We have to find that when constructing a 97% confidence interval, which would be the most appropriate  value of the critical value.

Firstly, as we know that the test statistics that would be used here is t-test statistics because we don't know about the population standard deviation.

So, for finding the critical value we will look for t table at (41 - 1 = 40) degrees of freedom at the level of significance will be \frac{1 - 0.97}{2} = 0.015 .

Now, as we can see that in the t table the critical values for P = 1.5% are not given, so we will interpolate between P = 2.5% and P = 1%, i.e;

     \frac{0.015 - 0.025}{0.025-0.01}= \frac{\text{Critcal value}-2.021}{2.021-2.423}

So, the critical value at a 1.5% significance level is 2.289.

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Drag a statement or reason to each box to complete this proof.
alukav5142 [94]

The table to complete the proof is as follows

Equation                                                              statement

1. m∠ABD = 60°, m∠DBC=40°                               Given

2. m∠ABD + m∠DBC = m∠ABC               Angle Addition Postulate

3. 60° +  40° = m∠ABC                           Substitution Property of Equality

4. 100° = m∠ABC                                                  Simplifying

5. ∠ABC is an obtuse angle.                       greater than 90 degrees

6. △ABC is an obtuse triangle.                Definition of obtuse triangle

<h3>What is obtuse angles?</h3>

When an angel is greater than 90 degrees the angle is said to be an obtuse angle.

For the question solved here m∠ABC is greater than 90 degrees hence an obtuse angle.

Read more on angles here: brainly.com/question/25716982

#SPJ1

8 0
10 months ago
What is the length of BC in the right triangle below?
Neko [114]

Answer and Step-by-step explanation:

<u>How to solve:</u>

Use the Pythagorean Theorem to find the length of side <em>BC</em>.

<u>Pythagorean Theorem Formula:</u>

<u />A^2+B^2=C^2<u />

<u />

Side AB will be A, side AC will be B, and side BC will be C.

<u>Plug in values.</u>

8^2+15^2 = C^2\\\\\\64 + 225 = C^2\\\\289 = C^2\\Square.root.both.sides.\\\\\sqrt{289} = C\\17 = C\\\\\\

<u>This means the answer is A. 17.</u>

<u></u>

<u>I hope this helps!</u>

<em><u>#teamtrees #PAW (Plant And Water)</u></em>

5 0
3 years ago
Select each of the following experiments that are binomial experiments:
Vinvika [58]

Answer:

a) No.

b) Yes.

c) Yes.

Step-by-step explanation:

a) No.

As being without replacement, the probabilities of each color in each draw change depending on the previous draws.

This is best modeled by an hypergeometric distribution.

b) Yes.

As being with replacement, the probabilities for each color is constant.

Also, there are only two colors, so the "success", with probability p, can be associated with the color red, and the "failure", with probability (1-p), with the color blue, for example.

(With more than two colors, it should be "red" and "not red", allowing only two possibilities).

c) Yes.

The answer is binary (Yes or No) and the probabilities are constant, so it can be represented as a binomial experiment.

8 0
2 years ago
Triangle RST has the vertices R(2, 3), S(-2, 1), and T(-1, 5). What are the coordinates after the two transformations: Translati
igor_vitrenko [27]

Given :

Triangle RST has the vertices R(2, 3), S(-2, 1), and T(-1, 5).

To Find :

The coordinates after the two transformations:

a) Translation (x, y) --> (x - 2, y - 1) .

b)  Rotation: 90 degrees counterclockwise at the origin.

Solution :

Applying transition a) , we get :

R'(2-2,3-1) , S'(-2-2,1-1) , T'(-1-2,5-1)

R'( 0, 2) , S'( -4 , 0), T'( -3, 4)

Now , When any point ( h , k ) is rotated 90° counterclockwise about the origin, the new points are (-k , h) .

So , R''( -2, 0) , S''( 0, -4 ) , T''( -4 , -3 ) .

Therefore , the coordinates after transformations are

( -2, 0) ,( 0, -4 ) , ( -4 ,-3 ) .

Hence , this is the required solution .

6 0
2 years ago
A scaled factor of 2 is used to increase the triangle. What is the new area?
lesya [120]

Answer:b

Step-by-step explanation:b

8 0
3 years ago
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