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Murljashka [212]
3 years ago
11

The sum of the speeds of two trains is 723.1 miles per hour. If the speed of the first train is 10.9 mph faster than that of the

second train, find the speeds of each.
What is the speed of the first train?
Mathematics
1 answer:
Komok [63]3 years ago
8 0

9514 1404 393

Answer:

  367 miles per hour

Step-by-step explanation:

The speed of the faster train is half the total plus half the difference:

  s1 = (723.1 +10.9)/2 = 367 . . . . miles per hour

_____

<em>Check</em>

The slower train is 367-10.9 = 356.1, and the total is 723.1 mph, as required.

_____

If you want an equation, you can let x represent the faster speed. Then the total is ...

  x + (x -10.9) = 723.1

  2x = 723.1 +10.9

  x = (723.1 +10.9)/2 = 367

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In 2001 polls indicated that 74% of Americans favored mandatory testing of students in public schools as a way to rate the schoo
Kryger [21]

Answer:

The right answer is:

"If 74% of Americans still favor mandatory testing this year, then there is a 1.5% chance that poll results will show 71% or fewer with this opinion."

Step-by-step explanation:

The P-value represents the probability of getting the sample we got, given that the null hypothesis is true. For this reason, it the P-value is lower than the significance level, it means that the sample result is unlikely due to chance, but due to a false null hypothesis.

In this case, the P-value represents a probability P=0.015 of having a sample with proportion p=0.71, given that the population has a proportion π=0.74.

The right answer is:

"If 74% of Americans still favor mandatory testing this year, then there is a 1.5% chance that poll results will show 71% or fewer with this opinion."

8 0
3 years ago
A charity receives 2025 contributions. Contributions are assumed to be mutually independent and identically distributed with mea
uysha [10]

Answer:

The 90th percentile for the distribution of the total contributions is $6,342,525.

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 = \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.

For sums of size n, the mean is \mu*n and the standard deviation is s = \sqrt{n}*\sigma

In this question:

n = 2025, \mu = 3125*2025 = 6328125, \sigma = \sqrt{2025}*250 = 11250

The 90th percentile for the distribution of the total contributions

This is X when Z has a pvalue of 0.9. So it is X when Z = 1.28. Then

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

By the Central Limit Theorem

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

1.28 = \frac{X - 6328125}{11250}

X - 6328125 = 1.28*11250

X = 6342525

The 90th percentile for the distribution of the total contributions is $6,342,525.

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Answer:

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Step-by-step explanation:

Add 1+2=3

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Out it back in the ratio

6:12

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Step-by-step explanation:

the answer is

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