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3 years ago

How do you find surface area of a triangular prism ?

1 answer:

5 0

The formula to find the surface area of a triangular prism is basically finding out the area of one of the faces of a traingle, which is:

 $(base)*(height)/2$

So, basically you take the face of the triangle that your trying to find the surface area of and plug in your values for the base length and height, multiply them together, hen divide that product by 2 to find your surface area :)

Thank you for the question! I hope this helped! Have an amazing day!! :D

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A quality control expert at LIFE batteries wants to test their new batteries. The design engineer claims they have a variance of

yan [13]

Answer:

"The probability that the mean battery life would be greater than 948.8 minutes" is 0.1446.

Step-by-step explanation:

In this case, the quality control expert takes a sample of batteries. From these batteries, we want to find "the probability that the mean battery life would be greater than 948.8 minutes".

Different concepts needed to take into account to solve this question

Sampling Distribution of the Means

For doing this, we need to use the sampling distribution of the means, which results from taking the mean for each possible sample coming from a random variable $\\ x$ . Roughly speaking, each sample will have a different mean, $\\ \overline{x}$ , and the probability distribution for any of these means is called the sampling distribution of the means.

The sampling distribution of the means has a mean that equals the population's mean for the random variable $\\ x$ , i.e., $\\ \mu$ , and its standard deviation is $\\ \frac{\sigma}{\sqrt{n}}$ . We can express this mathematically as:

$\\ \overline{x} \sim N(\mu, \frac{\sigma}{\sqrt{n}})$ [1]

Standardized Values for $\\ \overline{x}$

We can standardized the values for $\\ \overline{x}$ using z-scores:

$\\ Z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}$ [2]

This random variable $\\ Z$ follows a standard normal distribution, that is, $\\ Z \sim N(0,1)$ , and it is easier to find probabilities since the values for them are tabulated in the standard normal table (available in any Statistics book or on the Internet.)

What type of distribution follows the sampling distribution of the means?

A general rule of thumb is that this distribution (the sampling distribution of the means) follows a normal distribution if the sample size, $\\ n$ , is bigger than or equal to 30 observations, or $\\ n \geq 30$ . In this case, $\\ n = 109$ batteries. This is a result from the Central Limit Theorem, fundamental in Statistical Inference.

Standard Deviation

We have to remember that the standard deviation is the square root of the variance $\\ \sigma^2$ , or $\\ \sqrt{\sigma^2}$ .

$\\ \sigma^{2} =5929$
$\\ \sigma = \sqrt{5929} = 77$

Therefore, the standard deviation in this case is $\\ \sigma = 77$ minutes.

In sum, we have the following information to answer this question:

$\\ \sigma = 77$ minutes.
$\\ \mu = 941$ minutes.
$\\ n = 109$ batteries (the sample size is large enough to assume that the sampling distribution of the means follows a normal distribution).
$\\ \overline{x} = 948.8$ minutes.

What is the probability that the mean battery life would be greater than 948.8 minutes?

Well, having all the previous information, we can use [2] to solve this question (without using units):

$\\ z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}$

$\\ z = \frac{948.8 - 941}{\frac{77}{\sqrt{109}}}$

$\\ z = \frac{7.8}{\frac{77}{\sqrt{109}}}$

$\\ z = \frac{7.8}{7.37526}$

$\\ z = 1.05758 \approx 1.06$

This result is the standardized value or z-score for $\\ \overline{x}$ , considering $\\ \mu = 941$ and $\\ \sigma = 77$ .

We round z to two decimals digits since standard normal table only uses it as an entry to find probabilities.

With $\\ z = 1.06$ , we can consult the cumulative standard normal table. First, we need to find with $\\ z = 1.0$ in the first column in the table. Then, in its first raw, we need to find +0.06. The intersection for these two values determines the cumulative probability for $\\ P(z$ .

It is important to recall that $\\ P(z$ because $\\ z = 1.06$ is the standardized value for $\\ \overline{x} = 948.8$ minutes.

Then, $\\ P(z$

However, the question is about $\\ P(\overline{x} > 948.8) = P(z>1.06)$

And

$\\ P(\overline{x} > 948.8) + P(\overline{x} < 948.8) = 1$

$\\ P(z>1.06) + P(z$

Then

$\\ P(z>1.06) = 1 - P(z$

$\\ P(z>1.06) = 1 - 0.8554$

$\\ P(z>1.06) = 0.1446$

Therefore, "the probability that the mean battery life would be greater than 948.8 minutes" is 0.1446.

6 0

4 years ago

Simplify to create an equivalent expression -4(-11 + 4n) -3(-2n + 9)

Marizza181 [45]

Answer:

-71 + 22n is the equivalent expression.

This is the simplified expression.

Step-by-step explanation:

4(-11 + 4n) -3(-2n + 9)

= -44 + 16n + 6n - 27

= -44 + 22n - 27

= -71 + 22n

7 0

3 years ago

Read 2 more answers

Question 20 read the question and type your response in the box below the question. your response will be saved automatically. w

grandymaker [24]

You're looking for something like y=2x+3 and 2y=4x+6?

3 0

3 years ago

I don’t know how to answer this so look at the pic

MA_775_DIABLO [31]

Answer:

a = 4 and b = 1/2

Step-by-step explanation:

7 0

3 years ago

What is the number nearest to 10000 which is exactly divisible by 3, 4, 5, 6, 7, and 8?.

Luba_88 [7]

The nearest number is 10080 if the number is nearest to 10000 which is exactly divisible by 3, 4, 5, 6, 7, and 8.

It is defined as the common number of two integers, which is the lowest number that is a multiple of two or more numbers. The full name of LCM is the least common multiple.

It is given that:

The number nearest to 10000 is exactly divisible by 3, 4, 5, 6, 7, and 8.

TO find the number:

Find the LCM of 3, 4, 5, 6, 7, and 8:

LCM = 760

= 10000/760

There are two possibilities:

= 10000 - 760 = 9240

or 10000 + (840 - 760) = 10080

The nearest number = 10080

Thus, the nearest number is 10080 if the number is nearest to 10000 which is exactly divisible by 3, 4, 5, 6, 7, and 8.

Learn more about the LCM here:

brainly.com/question/20739723

#SPJ4

3 0

2 years ago