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Rus_ich [418]
3 years ago
15

Find the length of an arc made by a 180-degree central angle in a circle with a 10ft radius

Mathematics
1 answer:
mixas84 [53]3 years ago
8 0

Answer:

the length of an arc = 10π ft.

Step-by-step explanation:

The length of an arc with angle Θ and radius r will be equal r * Θ

note the angle must be in radian

Given: Θ = 180° = π  and radius = r = 10 ft.

<u>So, the length of the arc = π * 10 = 10π ft.</u>

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Solve the following compound inequality.<br><br> 5x+7&lt;=-3 or 3x-4&gt;=11
Kobotan [32]

Answer:

x\leq -2 or x\geq 5

Step-by-step explanation:

5x+7\leq -3          or    3x-4\geq 11\\

     

5x+7\leq -3\\5x\leq -10\\x\leq -2

3x-4\geq 11\\3x\geq 15\\ x\geq 5

4 0
3 years ago
Easy question :)
bulgar [2K]
C. because 2.25 X 3 = 6.75 and 6.75 X 3 is 20.25
3 0
3 years ago
Suppose a random sample of 100 observations from a binomial population gives a value of pˆ = .63 and you wish to test the null h
irakobra [83]

Answer:

We conclude that the population proportion is equal to 0.70.

Step-by-step explanation:

We are given that a random sample of 100 observations from a binomial population gives a value of pˆ = 0.63 and you wish to test the null hypothesis that the population parameter p is equal to 0.70 against the alternative hypothesis that p is less than 0.70.

Let p = <u><em>population proportion.</em></u>

(1) The intuition tells us that the population parameter p may be less than 0.70 as the sample proportion comes out to be less than 0.70 and also the sample is large enough.

(2) So, Null Hypothesis, H_0 : p = 0.70      {means that the population proportion is equal to 0.70}

Alternate Hypothesis, H_A : p < 0.70      {means that the population proportion is less than 0.70}

The test statistics that would be used here <u>One-sample z-test</u> for proportions;

                           T.S. =  \frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n} } }  ~  N(0,1)

where, \hat p = sample proportion = 0.63

            n = sample of observations = 100

So, <u><em>the test statistics</em></u>  =  \frac{0.63-0.70}{\sqrt{\frac{0.70(1-0.70)}{100} } }

                                     =  -1.528

The value of z-test statistics is -1.528.

<u>Now at 0.05 level of significance, the z table gives a critical value of -1.645 for the left-tailed test.</u>

Since our test statistics is more than the critical value of z as -1.528 > -1.645, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which <u><em>we fail to reject our null hypothesis</em></u>.

Therefore, we conclude that the population proportion is equal to 0.70.

(c) The observed level of significance in part B is 0.05 on the basis of which we find our critical value of z.

4 0
3 years ago
This is hard i need help
taurus [48]

Answer:

a. 6  b. -2

Step-by-step explanation:

a. x^3 = 216

x = ³√216

x = 6

b. -n^3/4 = 2

-n^3 = 8

-n = ³√8

- n = 2

n = -2

3 0
3 years ago
Read 2 more answers
Which equality represents the proportion $10 is to 15 cans as $30 is to $45 cans?
Sladkaya [172]

Answer:

I'm guessing it's C because it's the only one that looks right

5 0
3 years ago
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