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Law Incorporation [45]
2 years ago
15

Henry walked on a flat field 9 meters due north from a tree. He then turned due east and walked 24 feet. He then turned due sout

h and walked 9 meters plus 32 feet. How many feet away from his original starting point is Henry
Mathematics
1 answer:
soldi70 [24.7K]2 years ago
7 0

Henry was 40 feet away from his original starting point. Using Pythagorean's theorem it is calculated.

<h3>What is the Pythagorean theorem?</h3>

The theorem says that,

In a right-angled triangle, the sum of squares of the lengths of two arms (opposite and adjacent sides) is equal to the square of the hypotenuse.

I.e, Consider a right-angled triangle ΔABC, where AC is the hypotenuse side of the triangle. So, according to the theory,

AC² = AB² + BC²

<h3>Calculation:</h3>

It is given that,

Henry walked on a flat field,

9 meters - towards the north

24 feet - towards the east

9 meters + 32 feet - towards the south

This can be shown in the diagram below.

In the diagram, the distance from the starting point is X, and the last point is  S.

To find the distance between these two points, a line is joined as shown in the diagram. Thus, it is formed as a right-angled triangle.

So, according to the Pythagorean theorem,

XS² = (24)² + (32)²

(here 32 feet is the only distance from the assumed point to the endpoint)

⇒ XS² = 1600 = 40²

∴ XS = 40 feet

So, Henry is 40 feet away from the original starting point.

Learn more about the Pythagorean theorem here:

brainly.com/question/343682

#SPJ4

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The linear speed of one of the cars is 7.75 feet per second

The cars (seats) of a Ferris wheel are positioned 74 feet from its center.

The radius, r = 74 feet

The Ferris wheel makes 4 revolutions every 4 minutes

Number of revolutions per minute = 1

Angular speed, w = 1 rev/min

Angular speed, w = 0.10472 rad/sec

The relationship between the linear speed (v), and the angular speed (w) is:

v  =  wr

Substitute w = 0.10472  and r = 74 feet into the formula:

v  =  0.10472  x  74

v  =  7.75 feet per second

The linear speed of one of the cars is 7.75 feet per second

Learn more on linear speed here: brainly.com/question/4357151

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3 years ago
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Assume that a sample is used to estimate a population proportion p. Find the 98% confidence interval for a
Vikki [24]

Answer:

0.81 - 2.326 \sqrt{\frac{0.81(1-0.81)}{131}}=0.730

0.81 + 2.326 \sqrt{\frac{0.81(1-0.81)}{131}}=0.890

And the confidence interval would be:

0.730 \leq \p \leq 0.890

Step-by-step explanation:

Information given:

n=131 represent the sample size

\hat p=0.81 represent the estimated proportion

The confidence interval would be given by this formula

\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}

For the 98% confidence interval the value of \alpha=1-0.98=0.02 and \alpha/2=0.01, with that value we can find the quantile required for the interval in the normal standard distribution.

z_{\alpha/2}=2.326

And replacing into the confidence interval formula we got:

0.81 - 2.326 \sqrt{\frac{0.81(1-0.81)}{131}}=0.730

0.81 + 2.326 \sqrt{\frac{0.81(1-0.81)}{131}}=0.890

And the confidence interval would be:

0.730 \leq \p \leq 0.890

6 0
3 years ago
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