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3 years ago

the area of the base of a triangular prism is 4.5 and the lenght of the prism is 5. what is the volume of the prism

1 answer:

3 0

Hi! I need to know the height of the prism to solve the volume. Please describe that and I will surely be able to help you. Have a nice day!

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An article in The Engineer (Redesign for Suspect Wiring," June 1990) reported the results of an investigation into wiring errors

GarryVolchara [31]

Answer:

a) The 99% confidence interval on the proportion of aircraft that have such wiring errors is (0.0005, 0.0095).

b) A sample of 408 is required.

c) A sample of 20465 is required.

Step-by-step explanation:

Question a:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

Of 1600 randomly selected aircraft, eight were found to have wiring errors that could display incorrect information to the flight crew.

This means that $n = 1600, \pi = \frac{8}{1600} = 0.005$

99% confidence level

So $\alpha = 0.01$ , z is the value of Z that has a pvalue of $1 - \frac{0.01}{2} = 0.995$ , so $Z = 2.575$ .

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.005 - 2.575\sqrt{\frac{0.005*0.995}{1600}} = 0.0005$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.005 + 2.575\sqrt{\frac{0.005*0.995}{1600}} = 0.0095$

The 99% confidence interval on the proportion of aircraft that have such wiring errors is (0.0005, 0.0095).

b. Suppose we use the information in this example to provide a preliminary estimate of p. How large a sample would be required to produce an estimate of p that we are 99% confident differs from the true value by at most 0.009?

The margin of error is of:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

A sample of n is required, and n is found for M = 0.009. So

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$0.009 = 2.575\sqrt{\frac{0.005*0.995}{n}}$

$0.009\sqrt{n} = 2.575\sqrt{0.005*0.995}$

$\sqrt{n} = \frac{2.575\sqrt{0.005*0.995}}{0.009}$

$(\sqrt{n})^2 = (\frac{2.575\sqrt{0.005*0.995}}{0.009})^2$

$n = 407.3$

Rounding up:

A sample of 408 is required.

c. Suppose we did not have a preliminary estimate of p. How large a sample would be required if we wanted to be at least 99% confident that the sample proportion differs from the true proportion by at most 0.009 regardless of the true value of p?

Since we have no estimate, we use $\pi = 0.5$

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$0.009 = 2.575\sqrt{\frac{0.5*0.5}{n}}$

$0.009\sqrt{n} = 2.575*0.5$

$\sqrt{n} = \frac{2.575*0.5}{0.009}$

$(\sqrt{n})^2 = (\frac{2.575*0.5}{0.009})^2$

$n = 20464.9$

Rounding up:

A sample of 20465 is required.

8 0

2 years ago

A certain scale has an uncertainty of 4 g and a bias of 2 g. A single measurement is made on this scale. What are the bias and u

Fed [463]

Answer: 0.8

Step-by-step explanation:

given data:

uncertainity = 4g

bias = 2g

solution:

σX =0.2 and σY = 0.4

σcX

= 3σX

= 4(0.2)

= 0.8

6 0

3 years ago

A sphere has center (0,0,0) and a radius of 5. Which of the following points lie on the sphere?

Colt1911 [192]

Since the sphere is located at the center and has radius 5.
Out of the following given points,
(5,5,-5) will lie on the sphere, where x and y coordinates will be positive and z coordinate will be negative.
This is because the radius of the circle is 5 units.

7 0

3 years ago

Rewrite the expression ln(33^3)+ln(9^4) so that it includes the expressions ln(3) and 33 and 9 do not appear inside a natural lo

krok68 [10]

Answer:

In Section 6.1, we introduced the logarithmic functions as inverses of exponential functions and

discussed a few of their functional properties from that perspective. In this section, we explore

the algebraic properties of logarithms. Historically, these have played a huge role in the scientific

development of our society since, among other things, they were used to develop analog computing

devices called slide rules which enabled scientists and engineers to perform accurate calculations

leading to such things as space travel and the moon landing. As we shall see shortly, logs inherit

analogs of all of the properties of exponents you learned in Elementary and Intermediate Algebra.

We first extract two properties from Theorem 6.2 to remind us of the definition of a logarithm as

the inverse of an exponential function.

Step-by-step explanation:

Hope this helps

4 0

3 years ago

This is flipping an image over the y-axis. The coordinates change from (x, y) to (-x, y).

raketka [301]

I think that is a reflection

4 0

3 years ago