If 3n=3a-6,which inequality below will make n a positive number?

Kisachek [45]

76 rounded to the nearest 10 is 80.

Since 6 is greater than 5, it rounds 7 to 8.

5 0

3 years ago

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

Maksim231197 [3]

Answer:

a

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

b

The sample proportion is $\r p = 0.09$

c

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

d

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

The length of a rectangle is twice the width. The area is 50 square inches. Find the

Airida [17]

Answer:

The dimensions are 5 and 10 inches

Step-by-step explanation:

The area is 50 square inches and the length is twice the width. 10 is the length, which is two times 5. 10 times 5 is 50.

The length is 10 and the width is 5.

4 0

3 years ago

If ΔLMN ≅ ΔOPR, m∠L = (x^2 - x)°, m∠P = 16°, m∠N = (4x+160)°. Find m∠R.

Marizza181 [45]

Answer:

mZR = (4x + 160)°

Step-by-step explanation:

cause, mZR = mZN

;-))

8 0

3 years ago

A rectangular swimming pool that is 10 ft wide by 16 ft long is surrounded by a cement sidewalk of uniform width. If the area of

Alchen [17]

We are asked to solve for the width "x" in the given problem. To visualize the problem, see attached drawing.
We have the area of the swimming pool such as:
Area SP = l x w
Area SP = 10 * 16
Area SP = 160 feet2
Area of the swimming pool plus the sidewalk with uniform width:
Area SP + SW = (10 + x) * (16 + x)
160 + 155 = 160 + 10x + 16x + x2
160 -160 + 155 = 26x + x2
155 = 26 x + x2
x2 + 26x -155= 0
Solving for x, we need to use quadratic formula and the answer is 5 feet.

The value of x is <span>5 feet. </span>

5 0

3 years ago