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3 years ago

A cylinder has a radius of 30 ft and a height of 19 ft. What is the exact surface area of the cylinder?

2 answers:

5 0

$SA=2(pi)rh+2(pi)r^2$

$SA=2(pi)(30)(19)+2(pi)(30^2)$

$SA=2(pi)(30)(19)+2(pi)(900)$

$SA=3581.3+5654.7$

$SA=9236$

9236 square feet

Ad libitum [116K]3 years ago

4 0

$A=2\pi r(r+h)\\
A=2\pi\cdot30\cdot(30+19)\\
A=60\pi\cdot49\\
A=2940\pi\hbox{ ft}^2$

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3 years ago

A population has mean 187 and standard deviation 32. If a random sample of 64 observations is selected at random from this popul

Zina [86]

Answer:

11.51% probability that the sample average will be less than 182

Step-by-step explanation:

To solve this question, we have to understand the normal probability distribution and the central limit theorem.

Normal probability distribution:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit theorem:

The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$ , a large sample size can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$

In this problem, we have that:

$\mu = 187, \sigma = 32, n = 64, s = \frac{32}{\sqrt{64}} = 4$

What is the probability that the sample average will be less than 182

This is the pvalue of Z when X = 182. So

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$

$Z = \frac{182 - 187}{4}$

$Z = -1.2$

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11.51% probability that the sample average will be less than 182

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2 years ago

Jim worked 40 hours last week, plus 8 overtime hours at the time-and-a-half rate. His gross pay was $884. A. What was his hourly

marishachu [46]

Answer:

Hourly rate: $17.

Hourly overtime rate: $25.5.

Step-by-step explanation:

Let x represent Jim's hourly pay.

We have been given that Jim worked 40 hours last week. So amount paid in 40 hours would be $40x$ .

We are also told that his over time pay is time-and-a-half rate that is $1.5x$ .

The amount earned for working 8 overtime hours would be $8\cdot 1.5x=12x$ .

Since Jim's gross pay was $884, so we will equate amount earned in 40 hours and 8 hours of overtime with 884 as:

$40x+12x=884$

$52x=884$

$\frac{52x}{52}=\frac{884}{52}$

$x=17$

Therefore, Jim's hourly rate is $17.

Overtime rate would be $1.5x\Rightarrow1.5(17)=25.5$

Therefore, Jim's hourly overtime rate is $25.5.

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3 years ago

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iris [78.8K]

Answer: Pick an x value like x = 2

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1 year ago