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alexandr402 [8]
3 years ago
7

The plot line shows the number of miles the individual members in a group of runners run each day

Mathematics
1 answer:
Wittaler [7]3 years ago
6 0

Answer: 13

Step-by-step explanation:

2 miles = 6

3 miles = 4

4 miles = 2

5 miles = 1

Add them together to get 13 miles, the only people who don’t run at least 2 miles are the people who ran only 1 mile.

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Simplify (3x − 8) + (2x + 5) − (4x − 8).<br> A) x − 11 <br> B) x + 5 <br> C) x + 21 <br> D) 9x + 5
lozanna [386]

Answer:

B

Step-by-step explanation:

3x-8+2x+5-4x+8

3x+2x-4x    -8+5+8

     x        +        5      

x+5

6 0
3 years ago
Read 2 more answers
The taxi and takeoff time for commercial jets is a random variable x with a mean of 8.9 minutes and a standard deviation of 2.9
Eva8 [605]

Answer:

a) 0.2981 = 29.81% probability that for 37 jets on a given runway, total taxi and takeoff time will be less than 320 minutes.

b) 0.999 = 99.9% probability that for 37 jets on a given runway, total taxi and takeoff time will be more than 275 minutes

c) 0.2971 = 29.71% probability that for 37 jets on a given runway, total taxi and takeoff time will be between 275 and 320 minutes

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 normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes 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.

Mean of 8.9 minutes and a standard deviation of 2.9 minutes.

This means that \mu = 8.9, \sigma = 2.9

Sample of 37:

This means that n = 37, s = \frac{2.9}{\sqrt{37}}

(a) What is the probability that for 37 jets on a given runway, total taxi and takeoff time will be less than 320 minutes?

320/37 = 8.64865

Sample mean below 8.64865, which is the p-value of Z when X = 8.64865. So

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

By the Central Limit Theorem

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

Z = \frac{8.64865 - 8.9}{\frac{2.9}{\sqrt{37}}}

Z = -0.53

Z = -0.53 has a p-value of 0.2981

0.2981 = 29.81% probability that for 37 jets on a given runway, total taxi and takeoff time will be less than 320 minutes.

(b) What is the probability that for 37 jets on a given runway, total taxi and takeoff time will be more than 275 minutes?

275/37 = 7.4324

Sample mean above 7.4324, which is 1 subtracted by the p-value of Z when X = 7.4324. So

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

Z = \frac{7.4324 - 8.9}{\frac{2.9}{\sqrt{37}}}

Z = -3.08

Z = -3.08 has a p-value of 0.001

1 - 0.001 = 0.999

0.999 = 99.9% probability that for 37 jets on a given runway, total taxi and takeoff time will be more than 275 minutes.

(c) What is the probability that for 37 jets on a given runway, total taxi and takeoff time will be between 275 and 320 minutes?

Sample mean between 7.4324 minutes and 8.64865 minutes, which is the p-value of Z when X = 8.64865 subtracted by the p-value of Z when X = 7.4324. So

0.2981 - 0.0010 = 0.2971

0.2971 = 29.71% probability that for 37 jets on a given runway, total taxi and takeoff time will be between 275 and 320 minutes

7 0
2 years ago
You are planning a movie marathon. Each movie lasts 3/2 hours. You want to watch 4 movies nonstop. How many hours will your movi
Citrus2011 [14]

Answer:

Your movie marathon will last 6 hours.

Step-by-step explanation:

This question can be solved using a rule of three.

Each movie lasts \frac{3}{2} = 1.5 hours. How much do 4 movies last?

So

1 movie - 1.5 hours

4 movies - x hours

x = 4*1.5 = 6

Your movie marathon will last 6 hours.

5 0
3 years ago
Use the dropdown menus to write an equation with infinitely many solutions.
nika2105 [10]

Answer:

4(2x + 3) - x = 7x + 12

Explanation:

That's what T4L/Edge said

8 0
2 years ago
What is the annual wage for a person who works 2,000 hours and earns $12.00 an hour?
daser333 [38]
$24,000 per year!! Hope it helps :) goodluck
3 0
2 years ago
Read 2 more answers
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