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lorasvet [3.4K]

3 years ago

14

Pvc pipe is manufactured with a mean diameter of 1.01 inch and a standard deviation of 0.003 inch. the diameters are known to be

normally distributed. find the probability that a random sample of n = 9 sections of pipe will have a sample mean diameter greater than 1.009 inch and less than 1.012 inch.

1 answer:

serious [3.7K]3 years ago

5 0

Answer:

about 82%

Step-by-step explanation:

The distribution of sample means has a standard deviation that is the pipe standard deviation divided by the square root of the sample size. Thus, the standard deviation of the sample mean is 0.003/√9 = 0.001.

Then the limits on sample mean are 1.010 - 1×0.001 = 1.009 and 1.010 +2×0.001 = 1.012. The proportion of the normal distribution that lies between -1 and +2 standard deviations is about 81.9%.

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Fudgin [204]

subtract 1/4 from 7/8

find common denominator, in this case 8

1/4 = 2/8

now you have 7/8 - 2/8 = 5/8 hour left

3 0

3 years ago

The population of fish in a certain lake follows the logistic growth function , where t is the time in years.

Murrr4er [49]

Answer:

46 years

Step-by-step explanation:

We have the logistic growth function $f(t)=\frac{25,000}{1+8.25e^{-0.076t}}$ and we want to find the time when the population will reach 20,000, to do it we just need to replace $f(x)$ with 20,000 and solve for $t$ :

$f(t)=\frac{25,000}{1+8.25e^{-0.076t}}$

$20,000=\frac{25,000}{1+8.25e^{-0.076t}}$

Divide both sides by 25,000

$\frac{20,000}{25,000} =\frac{1}{1+8.25e^{-0.076t}}$

$0.8=\frac{1}{1+8.25e^{-0.076t}}$

Multiply both sides by $1+8.25e^{-0.076t}$ and divide them by 0.8

$1+8.25e^{-0.076t}=1.25$

Subtract 1 from both sides

$8.25e^{-0.076t}=0.25$

Divide both sides by 8.25

$e^{-0.076t}=\frac{0.25}{8.25}$

$e^{-0.076t}=\frac{1}{33}$

Take natural logarithm to both sides

$ln(e^{-0.076t})=ln(\frac{1}{33} )$

$-0.076t=ln(\frac{1}{33} )$

Divide both sides by -0.076

$t=\frac{ln(\frac{1}{33} )}{-0.076}$

$t$ ≈ 46

We can conclude that the population will reach 20,000 after 46 years.

5 0

3 years ago

The length of overline CD is 12 units. C^ prime D^ prime is the image of overline CD under a dilation with a scale factor of n.

Rufina [12.5K]

Answer:

A, D , and E

Step-by-step explanation:

We have that:

$\overline{CD} = 12 \: units$

$\overline{C'D'}$

is the image of CD after a dilation of scale factor n.

We use the relation between the image length and object length:

$\overline{C'D'} = n \times \overline{CD}$

Option A

If n=3/2, then

$\overline{C'D'} = \frac{3}{2} \times 12 = 3 \times 6 = 18 \: units$

This is true.

Option B

If n=4, then

$\overline{C'D'} = 4 \times 12 = 36 \: units$

This is false.

Option C

If n=8, then

$\overline{C'D'} = 8 \times 12 = 96 \: units$

This too is false.

Option D

If n=2, then

$\overline{C'D'} = 2 \times 12 = 24 \: units$

This is true

Option E

If n=3/4, then

$\overline{C'D'} = \frac{3}{4} \times 12$

$\overline{C'D'} = 3 \times 3 = 9 \: units$

This is also true.

4 0

3 years ago

What is the slope of the line that passes through the points (10,-6) and (8, -16)?

gulaghasi [49]

Answer:

y = 5x -56

Step-by-step explanation:

Delta y over Delta x for slope. Plug in x = 0 for y int.

y = 5(0) -56

y = -56

8 0

3 years ago

Simplify 6(x + 2) + 7.<br><br> 6x + 9<br> 6x + 15<br> 6x + 19

salantis [7]

Answer:

6x +19

Step-by-step explanation:

6(x +2) +7

distribute the 6 (multiply 6*x and 6*2)

6x + 12

add the 7 to the 12

=6x + 19

4 0

2 years ago

Read 2 more answers