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2 years ago

Solve log x = 2. 100 1,000 2 20

Mathematics

1 answer:

dybincka [34]2 years ago

5 0

keeping in mind that when the logarithm base is omitted, the base 10 is assumed.

$\textit{exponential form of a logarithm} \\\\ \log_a(b)=y \qquad \implies \qquad a^y= b \\\\[-0.35em] ~\dotfill\\\\ \log(x)=2\implies \log_{10}(x)=2\implies 10^2=x\implies 100=x$

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Hot dogs come in packs of 6, and buns come in packs of 8. What is the LEAST number of packs of each product that can be purchase

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Answer:

2 packs of buns and 3 pakcs of hot dogs

Step-by-step explanation:

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3 years ago

A hiker is walking down a mountain. She walked 5,978 feet in 17 minutes. In that time, she descended 1,024 feet from the top

olya-2409 [2.1K]

Answer:

63.5 feet/minute

Step-by-step explanation:

She first descended 1,024 feet in 17 minutes

Then she descended 500 feet in 7 minutes

The total feet descended is 1,024 + 500 = 1,524 feet

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4 years ago

In a study of government financial aid for college students, it becomes necessary to estimate the percentage of full-time coll

algol13

Answer:

(a) The sample size required is 2401.

(b) The sample size required is 2377.

Step-by-step explanation:

The confidence interval for population proportion p is:

$CI=\hat p\pm z_{\alpha/2}\sqrt{\frac{\hatp(1-\hat p)}{n}}$

The margin of error in this interval is:

$MOE=z_{\alpha/2}\sqrt{\frac{\hatp(1-\hat p)}{n}}$

The information provided is:

MOE = 0.02

$z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.96$

(a)

Assume that the proportion value is 0.50.

Compute the value of n as follows:

$MOE=z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}\\0.02=1.96\times \sqrt{\frac{0.50(1-0.50)}{n}}\\n=\frac{1.96^{2}\times0.50(1-0.50)}{0.02^{2}}\\=2401$

Thus, the sample size required is 2401.

(b)

Given that the proportion value is 0.55.

Compute the value of n as follows:

$MOE=z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}\\0.02=1.96\times \sqrt{\frac{0.55(1-0.55)}{n}}\\n=\frac{1.96^{2}\times0.55(1-0.55)}{0.02^{2}}\\=2376.99\\\approx2377$