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Varvara68 [4.7K]

3 years ago

12

Jackie's dad drives her to a friend's house at the speed 30 mph. The friend's mom drives her back using the same route at the sp

eed 25 mph. If the way back takes 6 minutes longer how far away is the friend's house?

1 answer:

kvv77 [185]3 years ago

5 0

Answer:

The distance to Jackie's friend house is 15 miles

Step-by-step explanation:

The given parameters are outlined as follows;

1) The speed with which Jackie's dad drove her to her friends house = 30 mph

2) The speed Jackie's fiend mom drove her back home on the same route = 25 mph

The time it takes Jackie's friend mom to drive her back home = 6 minutes + The time it took Jackie's dad drove her to her friends house

Let the time, in minutes, it took Jackie's dad drove her to her friends house = t

Therefore;

The time it takes Jackie's friend mom to drive her back home = 6 + t

We have that speed = Distance/Time

∴ For Jackie's friend mom, her speed of 25 mph = (The distance of Jackie's friend house)/(6 + t)

Which gives;

The distance of Jackie's friend house = 25 × (6 + t)

Similarly, for Jackie's dad, his speed of 25 mph = (The distance of Jackie's friend house)/t

Which gives;

The distance of Jackie's friend house = 30 × t

By substitution, we have;

The distance of Jackie's friend house = 25 × (6 + t) = 30 × t

By the distributive property, we have;

150 + 25·t = 30·t

150 = 30·t - 25·t = 5·t

150 = 5·t

t = 150/5 = 30 minutes

t = 30 = 0.5 Hours

Using the equation for the distance to Jackie's friend house derived with the speed of motion of Jackie's dad, we have

The distance to Jackie's friend house = 30 × t = 30 mi/h × 0.5 h = 15 mi

The distance to Jackie's friend house = 15 miles

Similarly, from the equation derived from the speed of motion of Jackie's friend mom, we have;

The distance to Jackie's friend house = 25 × (6 + t) = 25 × (6 + 30)

The distance to Jackie's friend house = 25 mph × 36 minutes

The distance to Jackie's friend house = 25 miles per hour × 0.6 hours = 15 miles

The distance to Jackie's friend house = 15 miles.

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Margarita [4]

Answer:

a) P(X < 99) = 0.2033.

b) P(98 < X < 100) = 0.4525

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 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.

Mean of 100 and variance of 36.

This means that $\mu = 100, \sigma = \sqrt{36} = 6$

Sample of 25:

This means that $n = 25, s = \frac{6}{\sqrt{25}} = 1.2$

(a) P(X<99)

This is the pvalue of Z when X = 99. So

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

By the Central Limit Theorem

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

$Z = \frac{99 - 100}{1.2}$

$Z = -0.83$

$Z = -0.83$ has a pvalue of 0.2033. So

P(X < 99) = 0.2033.

b) P(98 < X < 100)

This is the pvalue of Z when X = 100 subtracted by the pvalue of Z when X = 98. So

X = 100

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

$Z = \frac{100 - 100}{1.2}$

$Z = 0$

$Z = 0$ has a pvalue of 0.5

X = 98

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

$Z = \frac{98 - 100}{1.2}$

$Z = -1.67$

$Z = -1.67$ has a pvalue of 0.0475

0.5 - 0.0475 = 0.4525

So

P(98 < X < 100) = 0.4525

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3 years ago

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Troyanec [42]

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</span>

<span>Thank you for posting your question. I hope you found what you were after. Please feel free to ask me more.</span>

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3 years ago

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slamgirl [31]

Step-by-step explanation:

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To solve for x-intercept , Arrange the values in

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3 years ago

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Can you relly much help me do this

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Hey!
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3 years ago

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maks197457 [2]

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3 years ago