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3 years ago

A palm tree casts a shadow that is 28 feet long. A 6-foot sign casts a shadow 8 feet long.

Mathematics

1 answer:

s2008m [1.1K]3 years ago

3 0

Answer: The height of the palm tree is 21 feet.

Step-by-step explanation:

We can use a ratio to solve this:

Actual height to shadow for both objects. The fraction equivalents must be equal.

6/8 = x/28 . Cross multiply

6(28) = 8x

168 = 8x Divide both sides by 8 (8's "cancel" on the right)

168/8 =8x/8

21 = x . This gives us the tree's height as 21 feet.

Another way to solve this is to use the ratios, but simplify the first fraction

6/8 = 3/4

Then multiply the length of the shadow by 3/4

3/4 × 28 = height

28÷4 = 7 7 × 3 = 21

21 feet= the height of the palm tree.

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3 years ago

Suppose a 90% confidence interval for the mean salary of college graduates in a town in Mississippi is given by [$38,737, $50,46

JulsSmile [24]

Answer:

a. The point estimate was of $44,600.

b. The sample size was of 16.

Step-by-step explanation:

Confidence interval concepts:

A confidence interval has two bounds, a lower bound and an upper bound.

A confidence interval is symmetric, which means that the point estimate used is the mid point between these two bounds, that is, the mean of the two bounds.

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(38737+50463)/2 = 44600.

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b. Determine the sample size used for the analysis.

First we need to find the margin of error, so:

$M = \frac{50463-38737}{2} = 5863$

Relating the margin of error with the sample size:

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1 - 0.9}{2} = 0.05$

Now, we have to find z in the Z-table as such z has a p-value of $1 - \alpha$ .

That is z with a pvalue of $1 - 0.05 = 0.95$ , so Z = 1.64.

Now, find the margin of error M as such

$M = z\frac{\sigma}{\sqrt{n}}$

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

For this problem, we have that $\sigma = 14300, M = 5863$ . So

$M = z\frac{\sigma}{\sqrt{n}}$

$5863 = 1.645\frac{14300}{\sqrt{n}}$

$5863\sqrt{n} = 1.645*14300$

$\sqrt{n} = \frac{1.645*14300}{5863}$

$(\sqrt{n})^2 = (\frac{1.645*14300}{5863})^2$

$n = 16$

The sample size was of 16.

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3 years ago

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patriot [66]

Answer:

I am a little late but here is the answer

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Non-proportional linear relationships can be expressed in the form y = m x + b

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Step-by-step explanation:

From Graph :

The graph of a non-proportional linear relationship is a straight line that does not pass through the origin.

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From Table:

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3 years ago

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wariber [46]

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Step-by-step explanation:

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3 years ago

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Answer:

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Step-by-step explanation:

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