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Korolek [52]
3 years ago
9

Answer ASAP What is the volume of the triangular prism below?

Mathematics
1 answer:
natita [175]3 years ago
5 0

Answer: 18- Hope this helps :)

(re-do with explanation)

Step-by-step explanation: The volume formula for a triangular prism is (height x base x length) / 2

All you must do is calculate it which is 4 x 3 x 3 = 36 and than you divide it by half and you get your answer- 18

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A population has a mean of 200 and a standard deviation of 50. Suppose a sample of size 100 is selected and x is used to estimat
zmey [24]

Answer:

a) 0.6426 = 64.26% probability that the sample mean will be within +/- 5 of the population mean.

b) 0.9544 = 95.44% probability that the sample mean will be within +/- 10 of the population mean.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question, we have that:

\mu = 200, \sigma = 50, n = 100, s = \frac{50}{\sqrt{100}} = 5

a. What is the probability that the sample mean will be within +/- 5 of the population mean (to 4 decimals)?

This is the pvalue of Z when X = 200 + 5 = 205 subtracted by the pvalue of Z when X = 200 - 5 = 195.

Due to the Central Limit Theorem, Z is:

Z = \frac{X - \mu}{s}

X = 205

Z = \frac{X - \mu}{s}

Z = \frac{205 - 200}{5}

Z = 1

Z = 1 has a pvalue of 0.8413.

X = 195

Z = \frac{X - \mu}{s}

Z = \frac{195 - 200}{5}

Z = -1

Z = -1 has a pvalue of 0.1587.

0.8413 - 0.1587 = 0.6426

0.6426 = 64.26% probability that the sample mean will be within +/- 5 of the population mean.

b. What is the probability that the sample mean will be within +/- 10 of the population mean (to 4 decimals)?

This is the pvalue of Z when X = 210 subtracted by the pvalue of Z when X = 190.

X = 210

Z = \frac{X - \mu}{s}

Z = \frac{210 - 200}{5}

Z = 2

Z = 2 has a pvalue of 0.9772.

X = 195

Z = \frac{X - \mu}{s}

Z = \frac{190 - 200}{5}

Z = -2

Z = -2 has a pvalue of 0.0228.

0.9772 - 0.0228 = 0.9544

0.9544 = 95.44% probability that the sample mean will be within +/- 10 of the population mean.

7 0
3 years ago
In 5 OR MORE SENTENCES, write a short story explaining the graph OR write about the key features of the graph.
rewona [7]

The graph illustrated is divided into three seperate sections namely <em>A, B and C,</em> the short story culled from the graph is described thus:

Rate of change or slope = (Rise/ Run)

  • <em>Rise = y2 - y1 </em>
  • <em>Run = x2 - x1 </em>

<u>SECTION A:</u><u> </u>

Slope = (40 - 0) ÷ (20 - 0) = 40/20 = 2

Distance traveled = 50 meters

<u>SECTION B</u> :

This section gives an horizontal line, hence, the slope is 0.

Distance covered = 0 ; as there was no change in the distance over the period of time.

<u>SECTION</u><u> </u><u>C</u><u>:</u>

Slope = (80 - 50) ÷ (70 - 60) = 30/10 = 3

The total distance traveled = 80 - 50 = 30 meters

<u>The total </u><u>distance</u><u> </u><u>and</u><u> </u><u>time spent traveling</u> :

Total distance traveled = (50 + 30) = 80 meters

Total time spent = 70 seconds (<em>time at the 80 meter mark</em>)

Hence, the story.

Learn more : brainly.com/question/25309609

6 0
3 years ago
Hardcover book sales for $24 at the bookmark men days of total of $25.02 for the book what is the sales tax rate
Ber [7]
25.02-24=1.02
1.02/24=0.0425
The sales tax rate is 4.25%.
3 0
3 years ago
Please solve these questions with the equations. Will give 80 points and mark brainliest to the person with the answers.
I am Lyosha [343]

1]

8(x-7)=128 \ \ /:8\\\\x-7=16 \ \ /+7\\\\\huge\boxed{x=23}

2]

16=2(x+7) \ \ /:2\\\\x+7=8 \ \ /-7\\\\\huge\boxed{x=1}

3]

\frac{7y}{7}=20\\\\\huge\boxed{y=20}

4]

2x-1=9 \ \ /+1\\\\2x=10 \ \ /:2\\\\\huge\boxed{x=5}

5]

2(x-8)=20 \ \ /:2\\\\x-8=10 \ \ /+8\\\\\huge\boxed{x=18}

5 0
3 years ago
Who the hell gave conan gray the right to looke this fine like i- anyways look at hiiiiiim
Marrrta [24]

Answer:

very cute

Step-by-step explanation:

7 0
2 years ago
Read 2 more answers
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