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3 years ago

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Use the inequality to answer Parts 1-3. -3(x - 2) Part 1: Solve the inequality. Leave answer in terms of a whole number or reduc

ed improper fraction. Part 2: Write a verbal statement describing the solution to the inequality. Part 3: Verify your solution to the inequality using two elements of the solution set. Use a word processing program or handwrite your responses to Parts 1-3. Turn in all three responses.

1 answer:

SOVA2 [1]3 years ago

5 0

Answer:

Part 1: x ≥ 17/9

Part 2: x is greater than or equal to seventeen ninths.

Part 3: using x= 3 and 4 respectively, the solution was verified

The complete statement related to this found on brainly (ID: 2020133) is stated below:

Use the inequality to answer Parts 1-3.

-3(x - 2) ≤ one third

Part 1: Solve the inequality. Leave answer in terms of a whole number or reduced improper fraction.

Part 2: Write a verbal statement describing the solution to the inequality.

Part 3: Verify your solution to the inequality using two elements of the solution set.

Use a word processing program or handwrite your responses to Parts 1-3. Turn in all three responses.

Step-by-step explanation:

Part 1) The inequality: -3(x - 2) ≤ one third

-3(x - 2) ≤ ⅓

Multiply through by 3

-3(3)(x-2) ≤ 3(⅓)

-9(x-2) ≤ 1

Expand the bracket

-9x + 18 ≤ 1

Collect like terms

-9x ≤ 1-18

-9x ≤ -17

Divide through by coefficient of x (-9)

-9x/-9 ≤ -17/-9

When you divide an expression in inequality by a negative sign, the inequality sign changes

x ≥ 17/9

Part 2) the verbal statement of the solution:

x is greater than or equal to seventeen ninths.

Part 3) We would verify the solution to the inequality using two elements of the solution set greater than 17/9.

17/9 = 1.89

Let's use x= 3 and x = 4. As they are greater than 17/9

-3(x - 2) ≤ ⅓

When x= 3

-3(3 - 2) ≤ ⅓

-3(1) ≤ ⅓

-3 ≤ ⅓

This satisfies the solution of the inequality

When x= 4

-3(4 - 2) ≤ ⅓

-3(2) ≤ ⅓

-6 ≤ ⅓

This satisfies the solution of the inequality

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If the right side of the equation dy dx = f(x, y) can be expressed as a function of the ratio y/x only, then the equation is sai

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Answer:

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Step-by-step explanation:

Given:

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Solution:

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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

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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

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

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

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$Z = 2.12$ 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

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Answer:

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Step-by-step explanation:

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