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3 years ago

How would you solve a inequality like: 15-13(2x+6)< 15-3(6x-7)

2 answers:

7 0

Hello!

You can solve this algebraically

15 - 13(2x + 6) < 15 - 3(6x - 7)

Subtract 15 from both sides

-13(2x + 6) < -3(6x - 7)

Distribute the -13

-26x + -78 < -3(6x - 7)

Distribute the -2

-26x - 78 < -18x + 21

Add 18x to both sides

-8x - 78 < 21

Add 78 to both sides

-8x < 99

Divide both sides by -8

x < -12.375

The answer is -12.375

Hope this helps!

Arturiano [62]3 years ago

3 0

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A manufacturer of paper coffee cups would like to estimate the proportion of cups that are defective (tears, broken seems, etc.)

Maksim231197 [3]

Answer:

The 95% confidence interval is $0.0503 < p < 0.1297$

The sample proportion is $\r p = 0.09$

The critical value is $Z_{\frac{\alpha }{2} } = 1.96$

The standard error is $SE =0.020$

Step-by-step explanation:

From the question we are told that

The sample size is n = 200

The number of defective is k = 18

The null hypothesis is $H_o : p = 0.08$

The alternative hypothesis is $H_a : p > 0.08$

Generally the sample proportion is mathematically evaluated as

$\r p = \frac{18}{200}$

$\r p = 0.09$

Given that the confidence level is 95% then the level of significance is mathematically evaluated as

$\alpha = 100 - 95$

$\alpha = 5\%$

$\alpha = 0.05$

Next we obtain the critical value of $\frac{ \alpha }{2}$ from the normal distribution table, the value is

$Z_{\frac{\alpha }{2} } = 1.96$

Generally the standard of error is mathematically represented as

$SE = \sqrt{\frac{\r p (1 - \r p)}{n} }$

substituting values

$SE = \sqrt{\frac{0.09 (1 - 0.09)}{200} }$

$SE =0.020$

The margin of error is

$E = Z_{\frac{ \alpha }{2} } * SE$

=> $E = 1.96 * 0.020$

=> $E = 0.0397$

The 95% confidence interval is mathematically represented as

$\r p - E < \mu < p < \r p + E$

=> $0.09 - 0.0397 < \mu < p < 0.09 + 0.0397$

=> $0.0503 < p < 0.1297$

7 0

3 years ago

If f(x) = 3x + 2, what is f(5)?

Minchanka [31]

Answer:

Step-by-step explanation:

1. 3(5) + 2

2. 15 + 2

3. 17

5 0

3 years ago

Read 2 more answers

If a person ran 32 kilometers at a rate of 8 kilometers/hr, how long did he run?

Alchen [17]

Answer:

u use speed triangle so 32/8=4

so he travelled 4 hours

MARK AS BRAINLIEST

8 0

3 years ago

Read 2 more answers

Find the value of x. Give your answer in simplest radical forms

REY [17]

Use the Pythagorean theorem:

$x^2=5^2+6^2\\\\x^2=25+36\\\\x^2=61\to x=\sqrt{61}$

8 0

4 years ago

Daniel needs 65 feet of oak boards and 100 feet of pine boards for a building project. Each board will be cut into 5 ft lengths.

olchik [2.2K]

Each piece of board is being cut into 5, so therefore for every one piece of board there will be 5 pieces.
So for pine you would do 100x5 and oak you would do 65x5
That would be your step 1 and 2 which eliminates C and D.
The question asks to find the difference between the two. Which means you need to subtract them to find the difference between the two numbers.

Option A would be correct.
Hope this helps! :)

5 0

4 years ago