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serious [3.7K]
3 years ago
14

Solve for X with an equation

Mathematics
2 answers:
vredina [299]3 years ago
8 0
The sum of the interior angels is 180(n-2). In this case 180(5-2)= 540. So the equation is 540=100+103+4x+(3x+3)+(5x-2). Then solve for x. X=28
loris [4]3 years ago
8 0

Answer:

Equation: 540=(4x)+(3x+3)+100+103+(5x-2)

x=28

Step-by-step explanation:

540° in a 5 sided polygon

so knowing that

540=(4x)+(3x+3)+100+103+(5x-2)

Combine Like Terms

540=(4x+3x+5x)+(3+100+103+−2)

540=12x+204

flip equation

12x+204=540

subtract 204 from both sides

12x=336

divide both sides by 12

x=28

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A spinner is divided into 8 equal sections, and each section contains a number from 1 to 8. What is the probability of the spinn
nexus9112 [7]

Answer:

b

Step-by-step explanation:

5 is one of the numbers in 1,2,3,4,5,6,7,8

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6 0
3 years ago
A total of 691 tickets were sold for the school play they were either adult tickets or student tickets there were fifty nine few
garri49 [273]
691 = A+ S
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5 0
3 years ago
Which lengths could be the sides of a triangle?
galina1969 [7]
345,354,354,341,098cm
5 0
3 years ago
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
On a map of the United States, the distance between New York City and Nashville, TN is 2.5 inches. In real life, the distance is
Natalka [10]

Answer: Rounded: 350 miles/inch

Exactly 352 miles per inch.

Step-by-step explanation: Divide the miles by the inches to find miles per inch.

880/2.5 = 352.

It would make sense to round that to say the scale is 350 miles per inch.

One inch represents 350 miles

3 0
2 years ago
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