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kifflom [539]
3 years ago
11

How does kinetic energy affect the stopping distance of a vehicle traveling at 30 mph compared to the same vehicle traveling at

60 mph?
Mathematics
1 answer:
Aleks04 [339]3 years ago
8 0
The vehicle traveling 60 mph is going 4 times as fast. the brakes must do an amount of work that's equal to the original kinetic energy. the brakes exert the same amount of force no matter what the case is, so the stopping distance will be four times as long for the car going 60 mph compared to the car going 30 mph.
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The inside diameter of a randomly selected piston ring is a random variable with mean value 8 cm and standard deviation 0.03 cm.
S_A_V [24]

Answer:

a) P(7.99 ≤ X ≤ 8.01) = 0.8164

b) P(X ≥ 8.01) = 0.0475.

Step-by-step explanation:

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

Normal probability distribution:

Problems of normally distributed samples can be 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 = \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 random variable X, with mean \mu and standard deviation \sigma, the sample means with size n can be approximated to a normal distribution with mean

In this problem, we have that:

\mu = 8, \sigma = 0.03

(a) Calculate P(7.99 ≤ X ≤ 8.01) when n = 16.

n = 16, so s = \frac{0.03}{4} = 0.0075

This probability is the pvalue of Z when X = 8.01 subtracted by the pvalue of Z when X = 7.99. So

X = 8.01

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

Applying the Central Limit Theorem

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

Z = \frac{8.01 - 8}{0.0075}

Z = 1.33

Z = 1.33 has a pvalue of 0.9082

X = 7.99

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

Z = \frac{7.99 - 8}{0.0075}

Z = -1.33

Z = -1.33 has a pvalue of 0.0918

0.9082 - 0.0918 = 0.8164

P(7.99 ≤ X ≤ 8.01) = 0.8164

(b) How likely is it that the sample mean diameter exceeds 8.01 when n = 25? P(X ≥ 8.01) =

n = 25, so s = \frac{0.03}{5} = 0.006

This is 1 subtracted by the pvalue of Z when X = 8.01. So

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

Z = \frac{8.01 - 8}{0.006}

Z = 1.67

Z = 1.67 has a pvalue of 0.9525

1 - 0.9525 = 0.0475

P(X ≥ 8.01) = 0.0475.

4 0
3 years ago
AHHHHH HELP IM NOT A MATH KID
sergij07 [2.7K]

Answer:

y = 6

x = 200

Quick Explanation:

The horizontal arrowed line labeled <em>t</em> would be the <em>y </em>axis, and according to the dot on the graph, it's on the 6. The vertical arrowed line labeled <em>h </em>would be the <em>x </em>axis, and the dot tells you the number is 200. Easy peasy, just remember the <em>x </em>axis is vertical and the <em>y</em> axis is horizontal and it'll help you find the location of any dot.

8 0
2 years ago
Read 2 more answers
How many feet are there in 23 yards?
kvasek [131]
The answer is 75 foot
7 0
3 years ago
Read 2 more answers
HELP PLEASE!!!!!BRAINLIEST
Greeley [361]
That is false because you have to subtract the exponents not divide
4 0
3 years ago
Read 2 more answers
Find the value of 151 - 4(32 - 2).<br> -11<br> -33<br> 7<br> -23
egoroff_w [7]

Steps to solve:

151 - 4(32 - 2)

~Distribute

151 - 128 - 8

~Subtract

23 - 8

15

Best of Luck!

3 0
3 years ago
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