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marin [14]
3 years ago
10

The length of a rectangle is 5 inches less than three times its width. The perimeter is 86 inches. Find the dimensions, in inche

s, of the rectangle.
Mathematics
1 answer:
Arte-miy333 [17]3 years ago
5 0

8x - 10 = 86 {combined like terms}

8x = 96 {added 10 to both sides}

x = 12 {divided both sides by 8}

3x - 5 = 31 {substituted 12, in for x, into 3x - 5}


width = 12 in.

length = 31 in.

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An art museum had 275,760 visitors last year. The museum was open every day of the year except for 5 holidays. How many visitors
satela [25.4K]

Answer:766 people on average because 275,760 divided 360 because 365=1 year 365-5=360 and 275760/360=766

Step-by-step explanation:

7 0
3 years ago
A company considers buying a machine to manufacture a certain item. When tested, 28 out of 600 items produccd by the machine wer
weqwewe [10]

Answer:

The p-value of the test is 0.9918 > 0.05, which means that we fail to reject H_0, as we do not have enough evidence to say that defect rate of machine is smaller than 3%.

Step-by-step explanation:

The null and alternate hypothesis are:

H0:p≥0.03

Ha:p<0.03

The test statistic is:

z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}

In which X is the sample mean, \mu is the value tested at the null hypothesis, \sigma is the standard deviation and n is the size of the sample.

0.03 is tested at the null hypothesis:

This means that \mu = 0.03, \sigma = \sqrt{0.03*0.97}

28 out of 600 items produced by the machine were found defective.

This means that n = 600, X = \frac{28}{600} = 0.0467

Value of the test-statistic:

z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}

z = \frac{0.0467 - 0.03}{\frac{\sqrt{0.03*0.97}}{\sqrt{600}}}

z = 2.4

P-value of the test:

The p-value of the test is the probability of finding a sample proportion below 0.0467, which is the p-value of z = 2.4.

Looking at the z-table, z = 2.4 has a p-value of 0.9918.

The p-value of the test is 0.9918 > 0.05, which means that we fail to reject H_0, as we do not have enough evidence to say that defect rate of machine is smaller than 3%.

7 0
2 years ago
What is the solution set of the equation<br> x + 6 = 2(x + 3) - x?
Svetach [21]

Answer:

<em>x</em> = all real numbers

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right  

Distributive Property

Equality Properties

  • Multiplication Property of Equality
  • Division Property of Equality
  • Addition Property of Equality
  • Subtraction Property of Equality<u> </u>

<u>Algebra I</u>

  • Terms/Coefficients

Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify</em>

x + 6 = 2(x + 3) - x

<u>Step 2: Solve for </u><em><u>x</u></em>

  1. [Addition Property of Equality] Add <em>x</em> on both sides:                                     2x + 6 = 2(x + 3)
  2. [Distributive Property] Distribute 2:                                                                 2x + 6 = 2x + 6

Here we see that both sides are identical.

∴ our solution is all real numbers.

6 0
3 years ago
Suppose we are testing the null hypothesis H 0 mu=20 and the alternative H iu =20 , normal population with sigma=6 A random samp
cupoosta [38]

Answer:

The value of the test statistic is z = -1.5

Step-by-step explanation:

The formula for the test statistic is:

z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}

In which X is the statistic, \mu is the mean, \sigma is the standard deviation and n is the number of observations.

In this problem, we have that:

\mu = 20, X = 17, \sigma = 6, n = 9

So

z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}

z = \frac{17 - 20}{\frac{6}{\sqrt{3}}}

z = -1.5

The value of the test statistic is z = -1.5

8 0
3 years ago
I have no clue what it is
Orlov [11]
13.95+2.25+2.25+2.25+2.75+2.75+2.75= 28.95

6 0
2 years ago
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