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2 years ago

Find the value of r.

Mathematics

1 answer:

fgiga [73]2 years ago

6 0

Answer:

r = 10.5

Step-by-step explanation:

using the Pythagorean theorem:

(7 + r)² = 14² + r²

49 + 14r + r² = 196 + r²

subtract r² from both sides of the equation:

14r + 49 = 196

subtract 49 from both sides:

14r = 147

divide both sides by 14:

r = 10.5

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Round 2.127 to the nearest hundredths, tenths and tens

Svetach [21]

Tenths: 2.1 hundredths:2.13 Tens:2

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3 years ago

A simple random sample of size nequals81 is obtained from a population with mu equals 83 and sigma equals 27. (a) Describe the

Ivanshal [37]

Answer:

a) $\bar X \sim N (\mu, \frac{\sigma}{\sqrt{n}})$

With:

$\mu_{\bar X}= 83$

$\sigma_{\bar X}=\frac{27}{\sqrt{81}}= 3$

b) $z= \frac{89-83}{\frac{27}{\sqrt{81}}}= 2$

$P(Z>2) = 1-P(Z$

c) $z= \frac{75.65-83}{\frac{27}{\sqrt{81}}}= -2.45$

$P(Z$

d) $z= \frac{89.3-83}{\frac{27}{\sqrt{81}}}= 2.1$

$z= \frac{79.4-83}{\frac{27}{\sqrt{81}}}= -1.2$

$P(-1.2$

Step-by-step explanation:

For this case we know the following propoertis for the random variable X

$\mu = 83, \sigma = 27$

We select a sample size of n = 81

Part a

Since the sample size is large enough we can use the central limit distribution and the distribution for the sampel mean on this case would be:

$\bar X \sim N (\mu, \frac{\sigma}{\sqrt{n}})$

With:

$\mu_{\bar X}= 83$

$\sigma_{\bar X}=\frac{27}{\sqrt{81}}= 3$

Part b

We want this probability:

$P(\bar X>89)$

We can use the z score formula given by:

$z = \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}$

And if we find the z score for 89 we got:

$z= \frac{89-83}{\frac{27}{\sqrt{81}}}= 2$

$P(Z>2) = 1-P(Z$

Part c

$P(\bar X$

We can use the z score formula given by:

$z = \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}$

And if we find the z score for 75.65 we got:

$z= \frac{75.65-83}{\frac{27}{\sqrt{81}}}= -2.45$

$P(Z$

Part d

We want this probability:

$P(79.4 < \bar X < 89.3)$

We find the z scores:

$z= \frac{89.3-83}{\frac{27}{\sqrt{81}}}= 2.1$

$z= \frac{79.4-83}{\frac{27}{\sqrt{81}}}= -1.2$

$P(-1.2$

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3 years ago

Round to the nearest hundreth

n200080 [17]

Answer:

∠ B ≈ 66.42°

Step-by-step explanation:

Using the cosine ratio in the right triangle

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B = $cos^{-1}$ ( $\frac{2}{5}$ ) ≈ 66.42° ( to the nearest hundredth )

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3 years ago

Please help asap!! BRAINLIEST to best/right answer!

deff fn [24]

Q: What is the value of the upper quartile?

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Read 2 more answers

You are considering developing a regression equation relating a dependent variable to two independent variables. One of the vari

lys-0071 [83]

Answer:

Step-by-step explanation:

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categorical variable has 2 outcomes

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Answer: 1

Note: If our categorical variable had 5 outcomes, we would need 5-1 = 4 dummy variables.

b. Write the multiple regression equation relating the dependent variable to the independent variables.

Note: Depending your your professor, this can be written one of the following ways...

yhat = a + b1 x1 + bx2

yhat = b0 + b1 x1 + b2 x2

yhat = beta0hat + beta1hat x1 + betahat2 x2

where x1 is the ratio variable

and x2 is the dummy variable

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b0 = the predicted value of y when x1 and x2 both equal 0.

b1 = the change in y when x1 increases by 1 unit holding x2 constant.

b2 = the predicted difference in y between the two possible outcomes of the categorical variable holding x1 constant.

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