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3 years ago

11. Calculate the following logarithms. a. log5(25)

Mathematics

1 answer:

Mama L [17]3 years ago

8 0

Answer:

the logarithmic solution of log₅(25) is equal to 2

Step-by-step explanation:

given,

log₅(25)

now using logarithmic identity

log ₓ (x) = 1 and

log (aˣ) = x log (a)

now,

log₅(25)

=log₅(5²)

=2 log₅(5)

hence, the logarithmic solution of log₅(25) is equal to 2

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If A = 30° and r = 12, find x. (Round your answer to the nearest whole number.)

Margaret [11]

Answer:

$\boxed{12}$

Step-by-step explanation:

A = 30° and r = 12

$\sin A = \frac{r}{r + x}$

$\sin 30 = \frac{12}{12 + x}$

$\frac{1}{2} = \frac{12}{12 + x}$

$1(12 + x) = 2(12)$

$12 + x = 24$

$x = 24 - 12$

$x = 12$

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Answer:

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Step-by-step explanation:

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3 years ago

Suppose that a market research firm is hired to estimate the percent of adults living in a large city who have cell phones. 500

Alborosie

Answer:

The 95% confidence interval estimate for the true proportion of adults residents of this city who have cell phones is (0.81, 0.874).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

For this problem, we have that:

$n = 500, \pi = \frac{421}{500} = 0.842$

95% confidence level

So $\alpha = 0.05$ , z is the value of Z that has a pvalue of $1 - \frac{0.05}{2} = 0.975$ , so $Z = 1.96$ .

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.842 - 1.96\sqrt{\frac{0.842*0.158}{500}} = 0.81$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.842 + 1.96\sqrt{\frac{0.842*0.158}{500}} = 0.874$

The 95% confidence interval estimate for the true proportion of adults residents of this city who have cell phones is (0.81, 0.874).

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3 years ago

What is the value of z?

UNO [17]

Answer:

z =23

Step-by-step explanation:

The three angles in a triangle add to 180 degrees.

62+95+z = 180

Combine like terms

157 +z = 180

Subtract 157 from each side

157-157 +z = 180-157

z =23

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3 years ago