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chubhunter [2.5K]
3 years ago
13

Find the sum of the interior angle measures of a convex octagon

Mathematics
1 answer:
muminat3 years ago
8 0


The sum of the interior angles of any polygon is always . . .

     (180 degrees ) times (2 less than the number of sides in the polygon) .

It doesn't matter whether the polygon is regular, haphazard, convex,
or all mangled and squashed etc.  The only thing that matters is
how many sides it has.

The octagon has 8 sides.  So the sum of interior angles is . . .

     (180 degrees) times (8 - 2) = (180 x 6) = <em>1,080 degrees</em>


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fluorescent light factory that manufactures fluorescent lights that have a lifetime that is approximately normally distributed w
EastWind [94]

Answer:

The p-value obtained is greater than the significance level at which the test was performed, hence, we fail to reject the null hypothesis & say that there is enough evidence to conclude that the mean life of the fluorescent lights is 700 hours

Step-by-step explanation:

Complete Question

fluorescent light factory that manufactures fluorescent lights that have a lifetime that is approximately normally distributed with a mean of 700 hours and a standard deviation of 45 hours. Test the hypothesis that mean is 700 hours against the alternative hypothesis that the mean is not equal to 700 hours, if a random sample of 30 bulbs has an average life of 688 hours. Use a P-value in your answer.

Solution

For hypothesis testing, the first thing to define is the null and alternative hypothesis.

The null hypothesis plays the devil's advocate and usually takes the form of the opposite of the theory to be tested. It usually contains the signs =, ≤ and ≥ depending on the directions of the test.

While, the alternative hypothesis usually confirms the the theory being tested by the experimental setup. It usually contains the signs ≠, < and > depending on the directions of the test.

For this question, the null hypothesis is that the mean life of the fluorescent lights is 700 hours.

The alternative hypothesis will now be that the mean life of the fluorescent lights is significantly different from 700 hours.

Mathematically,

The null hypothesis is represented as

H₀: μ = 700

The alternative hypothesis is represented as

Hₐ: μ ≠ 700

To do this test, we will use the z-distribution because no information on the population standard deviation is known

So, we compute the z-test statistic

z = (x - μ₀)/σₓ

x = sample mean = 688 hours

μ₀ = 700 hours

σₓ = standard error = (σ/√n)

σ = standard deviation = 45 hours

n = Sample size = 30

σₓ = (45/√30) = 8.2158383626 = 8.216

z = (688 - 700) ÷ 8.216

z = 1.46

checking the tables for the p-value of this z-statistic

Significance level = 0.05 (This is used when significance level isn't given)

The hypothesis test uses a two-tailed condition because we're testing in two directions.

p-value (for z = 1.46, at 0.05 significance level, with a two tailed condition) = 0.14429

The interpretation of p-values is that

When the (p-value > significance level), we fail to reject the null hypothesis and when the (p-value < significance level), we reject the null hypothesis and accept the alternative hypothesis.

So, for this question, significance level = 0.05

p-value = 0.14429

0.14429 > 0.05

Hence,

p-value > significance level

This means that we fail to reject the null hypothesis & say that there is enough evidence to conclude that the mean life of the fluorescent lights is 700 hours.

Hope this Helps!!

6 0
3 years ago
Which properties must you use to add or subtract complex numbers?
Leno4ka [110]
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(0.5n+0.3)-(0.75n-0.45) find answer
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I believe your answer is -0.25n+0.75
8 0
3 years ago
Erin has 5 cookies, and Adlynn has 8. If Mallory has half the number of cookies as Adlynn, how many
Dimas [21]

Answer:

17

Step-by-step explanation:

8*2=4

4+8+5= 17

4 0
3 years ago
Read 2 more answers
Please &amp; thankssssss
malfutka [58]
Multiply both sides of the equation by 28 4y+7=10
Then move constants to the right side and change its sign 4y=10-7
Now subtract the numbers 4y=3 divide both sides by 4 so your answer is y=3/4
8 0
3 years ago
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