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3 years ago

-2 < 3x+4 < 31 find x

Mathematics

1 answer:

Eva8 [605]3 years ago

8 0

First rewrite into 2 inequalities,

$-2\lt3x+4$

$3x+4\lt31$

Solve each of the inequalities,

$-2\lt3x+4\implies3x\gt-6\implies x\gt-2$

$3x+4\lt31\implies 3x\lt27\implies x\lt9$

So our x is between -2 and 9 which can be written as,

$-2\lt x\lt9$

or as an interval,

$x\in(-2,9)$

Hope this helps :)

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kupik [55]

They had the same quotient because both of those equations are equal

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3 years ago

The College Boards, which are administered each year to many thousands of high school students, are scored so as to yield a mean

Marysya12 [62]

Answer:

a) 15.87% of the scores are expected to be greater than 600.

b) 2.28% of the scores are expected to be greater than 700.

c) 30.85% of the scores are expected to be less than 450.

d) 53.28% of the scores are expected to be between 450 and 600.

Step-by-step explanation:

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.

In this problem, we have that:

$\mu = 500, \sigma = 100$

a. Greater than 600

This is 1 subtracted by the pvalue of Z when X = 600. So

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

$Z = \frac{600 - 500}{100}$

$Z = 1$

$Z = 1$ has a pvalue of 0.8413.

1 - 0.8413 = 0.1587

15.87% of the scores are expected to be greater than 600.

b. Greater than 700

This is 1 subtracted by the pvalue of Z when X = 700. So

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

$Z = \frac{700 - 500}{100}$

$Z = 2$

$Z = 2$ has a pvalue of 0.9772

1 - 0.9772 = 0.0228

2.28% of the scores are expected to be greater than 700.

c. Less than 450

Pvalue of Z when X = 450. So

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

$Z = \frac{450 - 500}{100}$

$Z = -0.5$

$Z = -0.5$ has a pvalue of 0.3085.

30.85% of the scores are expected to be less than 450.

d. Between 450 and 600

pvalue of Z when X = 600 subtracted by the pvalue of Z when X = 450. So

X = 600

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

$Z = \frac{600 - 500}{100}$

$Z = 1$

$Z = 1$ has a pvalue of 0.8413.

X = 450

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

$Z = \frac{450 - 500}{100}$

$Z = -0.5$

$Z = -0.5$ has a pvalue of 0.3085.

0.8413 - 0.3085 = 0.5328

53.28% of the scores are expected to be between 450 and 600.

6 0

3 years ago

nevsk [136]

#Personal computer:-

Total=480

Percent

$\\ \bull\sf\dashrightarrow \dfrac{480}{1500}\times 100$

$\\ \bull\sf\dashrightarrow 32\%$

#Pacemaker:-

$\\ \bull\sf\dashrightarrow 0.26(1500)$

$\\ \bull\sf\dashrightarrow 390$

#Wireless communication:-

$\\ \bull\sf\dashrightarrow 0.18(1500)$

$\\ \bull\sf\dashrightarrow 270$

#Television:-

Percent

$\\ \bull\sf\dashrightarrow \dfrac{150}{1500}\times 100$

$\\ \bull\sf\dashrightarrow 10\%$

#Others

100-(10+18+26+32)=100-86=14%

$\\ \bull\sf\dashrightarrow 0.14(1500)$

$\\ \bull\sf\dashrightarrow 225$

4 0

3 years ago

Read 2 more answers

evelyn drinks 8 glasses of water a day , which is 56 glasses of water a week.how many glasses of water does she drink in a year?

MissTica

If you would like to know how many glasses of water does Evelyn drink in a year (1 year = 52 weeks), you can calculate this using the following steps:

8 glasses of water per day
56 glasses of water per week
x glasses of water per year = ?

x = 56 * 52 = 2912 glasses of water per year

Result: Evelyn drinks 2912 glasses of water per year.

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3 years ago

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What is 0.8637 rounded to the nearest hundredth

umka21 [38]

<h3>Answer:</h3>

0.86

<h3>Step-by-step explanation:</h3>

The hundredths place is the second digit after the decimal point. It is the 6 in this case.

Since the next digit (3) is 4 or less, the hundredths place stays the same and the rest is basically just cut off, leaving 0.86.

If the next digit (3) were 5 or more, the hundredths place would have gone up 1 (to 7) and the rest would have been cut off, giving a final result of 0.87

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3 years ago