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2 years ago

8

A miner for gold digs at a constant rate. They were able to dig -90 feet in 6 hours. How long have they been digging if they dug

-225 feet?

1 answer:

Pachacha [2.7K]2 years ago

7 0

Answer:

he will dig for 15 hours

Step-by-step explanation:

if a miner digs —90 feets in 6 hours

then he will dig –225 feet in x hours

—225 feet x 6 hours /—90 feet = 15 hours

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The following results come from two independent random samples taken of two populations.

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Answer:

$(a)\ \bar x_1 - \bar x_2 = 2.0$

$(b)\ CI =(1.0542,2.9458)$

$(c)\ CI = (0.8730,2.1270)$

Step-by-step explanation:

Given

$n_1 = 60$ $n_2 = 35$

$\bar x_1 = 13.6$ $\bar x_2 = 11.6$

$\sigma_1 = 2.1$ $\sigma_2 = 3$

Solving (a): Point estimate of difference of mean

This is calculated as: $\bar x_1 - \bar x_2$

$\bar x_1 - \bar x_2 = 13.6 - 11.6$

$\bar x_1 - \bar x_2 = 2.0$

Solving (b): 90% confidence interval

We have:

$c = 90\%$

$c = 0.90$

Confidence level is: $1 - \alpha$

$1 - \alpha = c$

$1 - \alpha = 0.90$

$\alpha = 0.10$

Calculate $z_{\alpha/2}$

$z_{\alpha/2} = z_{0.10/2}$

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

The z score is:

$z_{\alpha/2} = z_{0.05} =1.645$

The endpoints of the confidence level is:

$(\bar x_1 - \bar x_2) \± z_{\alpha/2} * \sqrt{\frac{\sigma_1^2}{n_1}+\frac{\sigma_2^2}{n_2}}$

$2.0 \± 1.645 * \sqrt{\frac{2.1^2}{60}+\frac{3^2}{35}}$

$2.0 \± 1.645 * \sqrt{\frac{4.41}{60}+\frac{9}{35}}$

$2.0 \± 1.645 * \sqrt{0.0735+0.2571}$

$2.0 \± 1.645 * \sqrt{0.3306}$

$2.0 \± 0.9458$

Split

$(2.0 - 0.9458) \to (2.0 + 0.9458)$

$(1.0542) \to (2.9458)$

Hence, the 90% confidence interval is:

$CI =(1.0542,2.9458)$

Solving (c): 95% confidence interval

We have:

$c = 95\%$

$c = 0.95$

Confidence level is: $1 - \alpha$

$1 - \alpha = c$

$1 - \alpha = 0.95$

$\alpha = 0.05$

Calculate $z_{\alpha/2}$

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

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

The z score is:

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

The endpoints of the confidence level is:

$(\bar x_1 - \bar x_2) \± z_{\alpha/2} * \sqrt{\frac{\sigma_1^2}{n_1}+\frac{\sigma_2^2}{n_2}}$

$2.0 \± 1.96 * \sqrt{\frac{2.1^2}{60}+\frac{3^2}{35}}$

$2.0 \± 1.96* \sqrt{\frac{4.41}{60}+\frac{9}{35}}$

$2.0 \± 1.96 * \sqrt{0.0735+0.2571}$

$2.0 \± 1.96* \sqrt{0.3306}$

$2.0 \± 1.1270$

Split

$(2.0 - 1.1270) \to (2.0 + 1.1270)$

$(0.8730) \to (2.1270)$

Hence, the 95% confidence interval is:

$CI = (0.8730,2.1270)$

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3 years ago

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Answer:

x = 29

Step-by-step explanation:

If the equation is :

4.2(9-x)+36=102-2.5(2x+2)

→distribute 4.2 and -2.5 in parenthesis

4.2(9 - x) + 36 = 102 -2.5(2x + 2)

37.8 - 4.2x +36 = 102 -5x -5

→ have terms with x = terms without x

Keep the terms you need the way they are, and move the terms you need on the other side of equal sign with changed sign.

4.2(9 - x) + 36 = 102 -2.5(2x + 2)

37.8 - 4.2x +36 = 102 -5x -5

- 4.2x +5 x = - 37.8 - 36 + 102 - 5

→ Combine like terms

0.8x = 23.2

→ Divide both sides by 0.8

x = 29

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2 years ago

The following equation is a linear equation that has a slope of 3 and a y-intercept of positive 2:

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The y intercept in the equation is -2. What is your question?

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2 years ago