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3 years ago

Choose the equation below that represents the line passing though the point(-5, 1) with a slope of 2/3

Mathematics

1 answer:

neonofarm [45]3 years ago

3 0

Y=2/3x+7/3 is an equation that passes through the point (-5,1) with a slope of 2/3

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3 years ago

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What is 0.216 (26 recurring) as a fraction?

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4 years ago

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The circumference of a standard bowling ball is about 27 in. To the nearest unit, how many square inches is the surface area of

Sidana [21]

The surface area of a sphere is $S=4 \pi r^{2}$ where r is the radius;
The circumference is $2 \pi r=27 in$ so that $r= \frac{27}{2 \pi }=4.5 in$ using this value we can evaluate the surface area of 1 ball as:
$S=4 \pi r^{2} =4 \pi (4.5)^{2} =254.3 in^{2}$
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3 years ago

Question 15 of 43

Andrews [41]

Answer:

Option A

Step-by-step explanation:

$\frac{12}{25} \times \frac{11}{24} \times \frac{10}{23} \times \frac{9}{22}$

we start with 12 red marbles out of 25 marbles, that's the probability for the first.

in the second step we have one red marble less, wich also means one marble less overall

and so on

$\frac{12 \times 11 \times 10 \times 9}{25 \times 24 \times 23 \times 22}$

$= \frac{11880}{303600}$

can be reduced by 1320 (step by step) to

$\frac{9}{230}$

6 0

3 years ago

The head of maintenance at XYZ Rent-A-Car believes that the mean number of miles between services is 3639 3639 miles, with a var

Andrei [34K]

Answer:

96.6% probability that the mean of a sample would differ from the population mean by less than 126 miles

Step-by-step explanation:

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

A reminder is that the standard deviation is the square root of the variance.

Normal probability distribution

When the distribution is normal, we use 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 normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question:

$\mu = 3639, \sigma = \sqrt{145161} = 381, n = 41, s = \frac{381}{\sqrt{41}} = 59.5$

Probability that the mean of the sample would differ from the population mean by less than 126 miles

This is the pvalue of Z when X = 3639 + 126 = 3765 subtracted by the pvalue of Z when X = 3639 - 126 = 3513. So

X = 3765

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

By the Central Limit Theorem

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

$Z = \frac{3765 - 3639}{59.5}$

$Z = 2.12$

$Z = 2.12$ has a pvalue of 0.983

X = 3513

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

$Z = \frac{3513 - 3639}{59.5}$

$Z = -2.12$

$Z = -2.12$ has a pvalue of 0.017

0.983 - 0.017 = 0.966

96.6% probability that the mean of a sample would differ from the population mean by less than 126 miles

3 0

3 years ago