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1 year ago

Circle E has a radius of 40 inches with = 324°. Find the exact length of

2 answers:

8 0

Let the arc is ABC with angle 324 degree, to find the length of that arc follow the steps;
The circumference of the circle E is :C = 2 r π
C = 2 * 40 π = 80 π cm.
Also 324° / 360° = 0.9m Arc (ABC ) = 0.9 * 80 π = 72 π cm
There is also formula for calculating the measure of an arc:
m Arc = r π α / 180°
m Arc = 40 π * 324 / 180
= 40π * 1.8 = 72 π
Now we have to find the exact length ( π ≈ 3.14 )
m Arc ( ABC ) = 72 * 3.14 = 226.08 cm

Maksim231197 [3]1 year ago

5 0

Answer:

72 π inches

Step-by-step explanation:

1) Set up a ratio: 324/360. Simplify it: 9/10.

2) Then do: 9/10 x 2 π r --> 9/10 x 2 π 40. You should get: 72 π.

3) So, the exact length of arc ABC = 72 π inches.

(The reason you are supposed to leave it 72 π inches is because only if the question asks you to find the approximate length of the arc, then you can use 3.14 instead of π. But if the question asks you to find the exact length of the arc, you have to leave it as said above because you would still have to round the answer (if you multiply 72 by pi), which makes it an approximate answer, not an exact answer.)

pi (π) = 3.14159265359......................

Pi is an endless number.

Hope this helps! :)

You might be interested in

What is the exponential notation for 262,144

7nadin3 [17]

since there is always a decimal at the end of every value so :

= 262144.0

you move the decimal backwards if there is no decimal between the value. you place the decimal after the 1st digit, you will also count the digits you have passed :

= 2.62144 X 10^5

you passed 5 values so you put 5 in exponent form.

7 0

1 year ago

Read 2 more answers

A television station plans to ask a random sample of 400 city residents if they can name the news anchor on the evening news at

hodyreva [135]

Answer:

There is an 8.38% probability that the anchor will be fired.

Step-by-step explanation:

For each resident, there is only two possible outcomes. Either they can name the news anchor on the evening news at their station, or they cannot.

This means that the binomial probability distribution will be used in our solution.

However, we are working with samples that are considerably big. So i am going to aaproximate this binomial distribution to the normal.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

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.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X), \sigma = \sqrt{V(X)}$ .

In this problem, we have that:

400 city residents are going to be asked. So $n = 400$ .

Suppose that in fact 12% of city residents could name the anchor if asked. This means that $p = 0.12$ .

So,

$\mu = E(X) = 400*0.12 = 48$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{400*0.12*0.88} = 6.5$ .

They plan to fire the news anchor if fewer than 10% of the residents in the sample can do so.

What is the approximate probability that the anchor will be fired?

10% of the residents is 0.10*400 = 40 residents.

Fewer than 10% is 39 residents. So the probability that the anchor will be fired is the pvalue of Z when $X = 39$ .

So:

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

$Z = \frac{39 - 48}{6.5}$

$Z = -1.38$

$Z = -1.38$ has a pvalue of 0.0838. This means that there is an 8.38% probability that the anchor will be fired.

5 0

2 years ago

A commercial jet can fly 868 miles in 2 hours with a tailwind but only 792 miles in 2 hours into a headwind. Find the speed of t

erik [133]

Answer:

The speed of the jet in still air is 415 mph and the speed of the wind is 19 mph

Step-by-step explanation:

we know that

The speed is equal to divide the distance by the time

Let

x -----> the speed of the wind in miles per hour

y ----> the speed of the jet in still air in miles per hour

we know that

With a tailwind

$y+x=\frac{868}{2}$

$y+x=434$ ----> equation A

With a headwind

$y-x=\frac{792}{2}$

$y-x=396$ ----> equation B

solve the system of equations A and B by elimination

Adds equation A and equation B

$y+x=434\\y-x=396\\------\\y+y=434+396\\2y=830\\y=415$

Find the value of x

$y+x=434$

$415+x=434$

$x=434-415$

$x=19$

therefore

The speed of the jet in still air is 415 mph and the speed of the wind is 19 mph

6 0

1 year ago

Read 2 more answers

A railroad crew can lay 7 miles of track each day. They need to lay 203 miles of track. The length, L (in miles), that is left t

swat32

Answer:

It will take 29 days to lay the track

After 18 days the crew still has 77 miles of track left to lay

Step-by-step explanation:

203÷7

=29 days

L= 203 - 7(18)

L= 203 - 126

L= 77

7 0

1 year ago

Personnel tests are designed to test a job applicant's cognitive and/or physical abilities. A particular dexterity test is adm

Elza [17]

Answer:

26.11% of the test scores during the past year exceeded 83.

Step-by-step explanation:

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

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

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.

In this problem, we have that:

It is known that for all tests administered last year, the distribution of scores was approximately normal with mean 78 and standard deviation 7.8. This means that $\mu = 78, \sigma = 7.8$ .

Approximately what percentatge of the test scores during the past year exceeded 83?

This is 1 subtracted by the pvalue of Z when $X = 83$ . So:

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

$Z = \frac{83 - 78}{7.8}$

$Z = 0.64$

$Z = 0.64$ has a pvalue of 0.7389.

This means that 1-0.7389 = 0.2611 = 26.11% of the test scores during the past year exceeded 83.

3 0

2 years ago