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3 years ago

14

Which of the following is the solution to the equation 25^(z - 4) = 125 ? Select one: A. z = 5.5. B. z = 3.5. C. z = -2.5. D. z

= -0.5.

2 answers:

Bogdan [553]3 years ago

8 0

A. z=5.5
25^(5.5-4)=125
25^(1.5)=125
125 = 125
z=5.5

cestrela7 [59]3 years ago

7 0

<span>
given
25^(z - 4) = 125
ln(</span>25^(z - 4)) = ln (125)
(z-4)ln(25) = ln(125)
z = ln(125)/ln(25) + 4
z = 5.5

which means that the answer is A.

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<u>Step-by-step explanation:</u>

Here we have , Dwight and Walt are building model cars. Dwight builds 7 fewer models than 4 times the number Walt builds.Dwight builds at most 9 models. We need to find Which inequality could be used to find the number of models Walt builds . Let's find out:

Let the the number Walt builds is x , So Dwight builds 7 fewer models than 4 times the number Walt builds i.e.

⇒ $4x-7$

But , according to question Dwight builds at most 9 models i.e.

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Answer:

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With:

$\mu_{\bar X}= 83$

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

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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:

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

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

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