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skelet666 [1.2K]

2 years ago

6

Which equation is the same as “f of x equals the quantity one-fourth x plus nine all over ten”

1 answer:

Sergio [31]2 years ago

4 0

F(x)=((1/4)x+9)/10 Because f of x = f(x), equals the quantity means =, one-fourth x is just (1/4)x, plus 9 is + 9, and all over ten means take everything previously said over ten.

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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:

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 figure is a circle with center O.

STatiana [176]

<u>Given</u>:

Given that the circle with center O.

The radius of the circle is OB.

The chord of the circle O is PQ and the length of PQ is 12 cm.

We need to determine the length of the segment PA.

<u>Length of the segment PA:</u>

We know that, "if a radius is perpendicular to the chord, then it bisects the chord and its arc".

Thus, we have;

$PA=\frac{PQ}{2}$

Substituting the value PQ = 12, we get;

$PA=\frac{12}{2}$

$PA=6 \ cm$

Thus, the length of the segment PA is 6 cm.

Hence, Option d is the correct answer.

3 0

2 years ago

I did 4 more problems than Manuel how many problems did I do

Aleksandr-060686 [28]

4 more than Manuel did

5 0

3 years ago

The number of square feet per house are normally distributed with a population standard deviation of 137 square feet and an unkn

pshichka [43]

Answer:

Step-by-step explanation:

Given that X, the number of square feet per house is N(mean, 137)

Sample size = 19

Sample mean x bar =1350 sq ft

Since population std dev is given,

std error of sample = $\frac{137}{\sqrt{19} } \\=31.43$

Since sample size is small, t critical value can be used

df = 18

t value for 80% two tailed = 1.333

Margin of error = ±1.333(std error) = ± $1.333*31.43\\=41.896$

Confidence interval = sample mean ±margin of error

= $1350-41.896,1350+41.896\\=(1308.104,1391.896)$

7 0

3 years ago

What is the value of 5^3i^9?

Yakvenalex [24]

Answer:

$\displaystyle 125^i$

Step-by-step explanation:

<u>Extended Information </u><u>on</u><u> </u><u>the</u><u> Complex Number System</u>

$\displaystyle \sqrt{-1} = i \\ -1 = i^2 \\ -i = i^3 \\ 1 = i^4\:[all\:multiples\:of\:four]$

I am joyous to assist you at any time.

All work is shown above. ↑

4 0

3 years ago