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Tems11 [23]
4 years ago
8

Evaluate the replacement set for the following equation 2n - 3 < 9. replacement set : n = {2, 5, 0}

Mathematics
1 answer:
ad-work [718]4 years ago
7 0

n = {2, 5, 0} holds true for 2n - 3 < 9

<em><u>Solution:</u></em>

Replacement set is the set of values that may be substituted for the variable.

Plug in each value from the replacement set and evaluate both sides of the inequality

If the inequality is true for a certain value, that value belongs in the solution set.

<em><u>Given equation is:</u></em>

2n - 3 < 9

<em><u>Substitute n = 2</u></em>

2(2) - 3 < 9

4 - 3 < 9

1 < 9

1 is less than 9 is true

Thus n = 2 is a solution to equation

<em><u>Substitute n = 5</u></em>

2(5) - 3 < 9

10 - 3 < 9

7 < 9

7 is less than 9 is true

Thus n = 5 is a solution to equation

<em><u>Substitute n = 0</u></em>

2(0) - 3 < 9

0 - 3 < 9

-3 < 9

-3 is less than 9 is true

Thus n = -3 is a solution to equation

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Katarina [22]
Just multiply 3 and 16 and that gives you 48 days.
8 0
3 years ago
Carpenters refer to the slope of a roof as the pitch of the roof. Find the pitch of the roof.
KiRa [710]

Answer: Approximately 13 ft

Step-by-step explanation: For this, you have to do the Pythagorean Theorem. First set up an equation. That equation is a squared+b squared=c squared. Next, plug in values. A=12 and b=4. The equation becomes 12 squared+4 squared=c squared. Do the math and you'll get 144+16=c squared. Add and get 160=c squared. Then do the square root of both sides and you'll get 12.649=c. Round to nearest whole number to get approximately 13 ft. You can also represent it as the square root symbol with 160 inside, like this(√160).

3 0
3 years ago
Suppose 46% of politicians are lawyers. If a random sample of size 662 is selected, what is the probability that the proportion
Svet_ta [14]

Answer:

0.9606 = 96.06% probability that the proportion of politicians who are lawyers will differ from the total politicians proportion by less than 4%

Step-by-step explanation:

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

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes 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.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean \mu = p and standard deviation s = \sqrt{\frac{p(1-p)}{n}}

Suppose 46% of politicians are lawyers.

This means that p = 0.46

Sample of size 662

This means that n = 662

Mean and standard deviation:

\mu = p = 0.46

s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.46*0.54}{662}} = 0.0194

What is the probability that the proportion of politicians who are lawyers will differ from the total politicians proportion by less than 4%?

p-value of Z when X = 0.46 + 0.04 = 0.5 subtracted by the p-value of Z when X = 0.46 - 0.04 = 0.42. So

X = 0.5

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

By the Central Limit Theorem

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

Z = \frac{0.5 - 0.46}{0.0194}

Z = 2.06

Z = 2.06 has a p-value of 0.9803

X = 0.42

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

Z = \frac{0.42 - 0.46}{0.0194}

Z = -2.06

Z = -2.06 has a p-value of 0.0197

0.9803 - 0.0197 = 0.9606

0.9606 = 96.06% probability that the proportion of politicians who are lawyers will differ from the total politicians proportion by less than 4%

8 0
3 years ago
Simple interest rate earned after 12 years on 1350 at an interest rate of 8%
Mademuasel [1]

Answer:

1296

Step-by-step explanation:

Simple interest is

I = PRT where I is the interest P is the principle, r is the rate and t is the time

I = 1350 * .08 * 12

I = 1296

8 0
4 years ago
Mikey's family is taking a road trip. Their car can travel no more than 260 miles without needing to refill the gas tank. They h
Assoli18 [71]

The solution to the inequality is that Mikey's family can drive at most 148

Inequality shows the non equal comparison of numbers or expressions.

Given that Mikey situation can be represented by the inequality:

112 + x ≤ 260

Solving the inequality:

112 + x ≤ 260

Subtract 112 from both sides of the equation:

112 + x - 112 ≤ 260 - 112

x ≤ 148

Hence from the inequality, we can see that Mikey's family can drive

at most 148

Find out more at: brainly.com/question/25285332

6 0
2 years ago
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