MATHEMATICS COLLEGE

Which sequence is geometric?1, 5, 9, 13,
2. 6, 8, 10,
5, 7, 9, 11,
ОО
4. 3. 16. 32

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Answer 1
Answer: 4.3.16.32 is geometric

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Suppose that the US plans to send a shipment of "rovers" to Mars. These are mobile robots, programmed to collect rock and soil samples, and then return to the landing site. The rovers operate independently of each other. The mean weight a rover is programmed to collect is 50 pounds, and the standard deviation of weights is 5 pounds. Weights collected by rovers are approximately normally distributed. If the US sends 10 rovers, what is the probability that the average weight of rock and soil brought back by these rovers will be between 48 pounds and 52 pounds? What sampling distribution should we use to compute this probability?

Answers

Answer:

79.24% probability that the average weight of rock and soil brought back by these rovers will be between 48 pounds and 52 pounds

We use the sampling distribution of the sample means of size 10 to solve this question, by the Central Limit Theorem. They are normally distributed with mean 50 and standard deviation 1.58.

Step-by-step explanation:

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

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

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

Z = (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 = (\sigma)/(√(n)).

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

In this problem, we have that:

\mu = 50, \sigma = 5, n = 10, s = (5)/(√(10)) = 1.58

What is the probability that the average weight of rock and soil brought back by these rovers will be between 48 pounds and 52 pounds?

This is the pvalue of Z when X = 52 subtracted by the pvalue of Z when X = 48. So

X = 52

Z = (X - \mu)/(\sigma)

By the Central Limit Theorem

Z = (X - \mu)/(s)

Z = (52 - 50)/(1.58)

Z = 1.26

Z = 1.26 has a pvalue of 0.8962

X = 48

Z = (X - \mu)/(s)

Z = (48 - 50)/(1.58)

Z = -1.26

Z = -1.26 has a pvalue of 0.1038

0.8962 - 0.1038 = 0.7924

79.24% probability that the average weight of rock and soil brought back by these rovers will be between 48 pounds and 52 pounds

What sampling distribution should we use to compute this probability?

We use the sampling distribution of the sample means of size 10 to solve this question, by the Central Limit Theorem. They are normally distributed with mean 50 and standard deviation 1.58.

Hotdogs are sold in packages The graph below shows the total number of hotdogs sold relative to the number of packages what does the point (4,2) mean in the context of the situation

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Answer:

do you still need help

Step-by-step explanation:

to this question

Answer:

C

Step-by-step explanation:

A rectangular deck is 12 ft by 14 ft. When the length and width are increased by the same amount, the area becomes 288 sq. Ft. How much were the dimensions increased?

Answers

The dimensions increased by 4 feet.

What is the area of the rectangle?

The area of the rectangle is the product of the length and width of a given rectangle.

The area of the rectangle = length × Width

Given;

Dimensions of rectangle = 12 + x and 14 + x

The area of the rectangle= (12 + x) (14 + x) = 288

x² + 26x + 168 = 288

x² + 26x - 120 = 0

(x + 30) (x - 4) = 0

x=-30, x =4

Hence, The dimensions increased by 4 feet.

Learn more about the area;

brainly.com/question/1658516

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Answer:

4 ft

Step-by-step explanation:

288=16 * 18

12+4=16

14+4=18

ind the area of the shaded regions below. Give your answer as a completely simplified exact value in terms of π (no approximations).

Answers

Step by Step Explanation:
First find the area of the circle
Area = πr^2
=3.14 x 16
50.24 cm^2
But here we need the area of the semicircle
so 50.24/2 = 25.12 cm^2

Now we find the area of the triangle
Area = 1/2bh
= 1/2 x 8 x 4
16 cm^2

The area of the shaded region = 25.12-16
= 9.12 cm^2

Hope this helps you!

I need this FAST please help!!!

Answers

Answer:

the answer is   9.879

In the 2020 Super Bowl, San Francisco lost by 11 points. Develop a playbook for the team to use to win the game if there were 5 minutes on the clock.

Answers

Answer:

do better and kick butt ( lol) srry not helpful but just what I thought

Step-by-step explanation:
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