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2 years ago

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A stream is flowing down a slope into a larger river. The elevation of the head of the stream is 2,200 feet above sea level. The

elevation of the mouth of the stream is 1,000 feet. The horizontal distance along the stream between those two points is 63,360 feet. What is the gradient of the slope the stream is flowing over in ft/mi

1 answer:

Trava [24]2 years ago

7 0

Answer:

$100\ \text{ft/mi}$

Step-by-step explanation:

Elevation of the head of the stream is 2,200 feet above sea level

Elevation of the mouth of the stream is 1,000 feet

Rise = $2200-1000=1200\ \text{ft}$

Distance between the two points = $63360\ \text{ft}=\dfrac{63360}{5280}=12\ \text{mi}$ = Run

Gradient is given by

$\dfrac{\text{Rise}}{\text{Run}}=\dfrac{1200}{12}\\ =100\ \text{ft/mi}$

The gradient of the slope the stream is flowing over is $100\ \text{ft/mi}$ .

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Write the equation of the graph in slope-intercept form (y = mx + b).

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Student records suggest that the population of students spends an average of 6.30 hours per week playing organized sports. The p

Ymorist [56]

Answer:

a) 99.24% chance HLI will find a sample mean between 5.5 and 7.1 hours.

b) 81.64% probability that the sample mean will be between 5.9 and 6.7 hours.

Step-by-step explanation:

To solve this question, it is important to know 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 $\sigma$ , a large sample size can be approximated to a normal distribution with mean $\mu$ and standard deviation $\frac{\sigma}{\sqrt{n}}$ .

In this problem, we have that:

$\mu = 6.3, \sigma = 2.1, n = 49, s = \frac{2.1}{\sqrt{49}} = 0.3$

A) What is the chance HLI will find a sample mean between 5.5 and 7.1 hours?

This is the pvalue of Z when X = 7.1 subtracted by the pvalue of Z when X = 5.5.

By the Central Limit Theorem, the formula for Z is:

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

X = 7.1

$Z = \frac{7.1 - 6.3}{0.3}$

$Z = 2.67$

$Z = 2.67$ has a pvalue of 0.9962

X = 5.5

$Z = \frac{5.5 - 6.3}{0.3}$

$Z = -2.67$

$Z = -2.67$ has a pvalue of 0.0038

So there is a 0.9962 - 0.0038 = 0.9924 = 99.24% chance HLI will find a sample mean between 5.5 and 7.1 hours.

B) Calculate the probability that the sample mean will be between 5.9 and 6.7 hours.

This is the pvalue of Z when X = 6.7 subtracted by the pvalue of Z when X = 5.9

X = 6.7

$Z = \frac{6.7 - 6.3}{0.3}$

$Z = 1.33$

$Z = 1.33$ has a pvalue of 0.9082

X = 5.9

$Z = \frac{5.9 - 6.3}{0.3}$

$Z = -1.33$

$Z = -1.33$ has a pvalue of 0.0918.

So there is a 0.9082 - 0.0918 = 0.8164 = 81.64% probability that the sample mean will be between 5.9 and 6.7 hours.

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Step-by-step explanation:

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Citrus2011 [14]

<u>ANSWER</u>

$p(x)=-3+6(x+2)^2$

<u>EXPLANATION</u>

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$p(x)=21+6(4x+x^2)$

We now add and subtract half the coefficient of $x$ multiplied by a factor of 6 to obtain;

$p(x)=21-6(2)^2+6(2)^2+6(4x+x^2)$

We now factor 6 out of the last two terms to get;

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The quadratic trinomial in the parenthesis is now a perfect square.

$p(x)=-3+6(x+2)^2$

Hence the vertex form of the polynomial is

$p(x)=6(x+2)^2-3$

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2 years ago

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