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3 years ago

9

50 POINTSS!!!!- The figure below shows the ideal pattern of movement of a herd of cattle, with the arrows showing the movement o

f the handler as he moves the herd. The arc the handler makes from the starting point to the return point should be a quarter of a circle:
Based on this theory, what distance will the handler move from the starting point to the return point if he creates an arc of a circle of radius 80 feet? (6 points)

125.6 feet
502.4 feet
83.73 feet
62.8 feet

2 answers:

Rudiy273 years ago

6 0

Answer:

125.6 feet

Step-by-step explanation:

I took the test and got it correct.

olga_2 [115]3 years ago

5 0

Answer:

the first option

Step-by-step explanation:

solution:

distance: d=1/4 lc (because is a quarter of a circle)

length of the circumference: lc=2 pi r

pi: constant=3.14

radius of the circle: r=80 feet

replacing pi and r in the formula of lc:

lc=2 pi r

lc=2 (3.14) (80 feet)

lc=502.4 feet

replacing lc in the formula of d:

d=1/4 lc

d=1/4 (502.4 feet)

d=502.4/4 feet

d=125.6 feet

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In the following problem, check that it is appropriate to use the normal approximation to the binomial. Then use the normal dist

frosja888 [35]

Answer:

a) 0.9920 = 99.20% probability that 15 or more will live beyond their 90th birthday

b) 0.2946 = 29.46% probability that 30 or more will live beyond their 90th birthday

c) 0.6273 = 62.73% probability that between 25 and 35 will live beyond their 90th birthday

d) 0.0034 = 0.34% probability that more than 40 will live beyond their 90th birthday

Step-by-step explanation:

We solve this question using the normal approximation to the binomial distribution.

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 distributions 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:

Sample of 723, 3.7% will live past their 90th birthday.

This means that $n = 723, p = 0.037$ .

So for the approximation, we will have:

$\mu = E(X) = np = 723*0.037 = 26.751$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{723*0.037*0.963} = 5.08$

(a) 15 or more will live beyond their 90th birthday

This is, using continuity correction, $P(X \geq 15 - 0.5) = P(X \geq 14.5)$ , which is 1 subtracted by the pvalue of Z when X = 14.5. So

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

$Z = \frac{14.5 - 26.751}{5.08}$

$Z = -2.41$

$Z = -2.41$ has a pvalue of 0.0080

1 - 0.0080 = 0.9920

0.9920 = 99.20% probability that 15 or more will live beyond their 90th birthday

(b) 30 or more will live beyond their 90th birthday

This is, using continuity correction, $P(X \geq 30 - 0.5) = P(X \geq 29.5)$ , which is 1 subtracted by the pvalue of Z when X = 29.5. So

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

$Z = \frac{29.5 - 26.751}{5.08}$

$Z = 0.54$

$Z = 0.54$ has a pvalue of 0.7054

1 - 0.7054 = 0.2946

0.2946 = 29.46% probability that 30 or more will live beyond their 90th birthday

(c) between 25 and 35 will live beyond their 90th birthday

This is, using continuity correction, $P(25 - 0.5 \leq X \leq 35 + 0.5) = P(X 24.5 \leq X \leq 35.5)$ , which is the pvalue of Z when X = 35.5 subtracted by the pvalue of Z when X = 24.5. So

X = 35.5

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

$Z = \frac{35.5 - 26.751}{5.08}$

$Z = 1.72$

$Z = 1.72$ has a pvalue of 0.9573

X = 24.5

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

$Z = \frac{24.5 - 26.751}{5.08}$

$Z = -0.44$

$Z = -0.44$ has a pvalue of 0.3300

0.9573 - 0.3300 = 0.6273

0.6273 = 62.73% probability that between 25 and 35 will live beyond their 90th birthday.

(d) more than 40 will live beyond their 90th birthday

This is, using continuity correction, P(X > 40+0.5) = P(X > 40.5), which is 1 subtracted by the pvalue of Z when X = 40.5. So

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

$Z = \frac{40.5 - 26.751}{5.08}$

$Z = 2.71$

$Z = 2.71$ has a pvalue of 0.9966

1 - 0.9966 = 0.0034

0.0034 = 0.34% probability that more than 40 will live beyond their 90th birthday

6 0

3 years ago

Which relation represents a function ?

yKpoI14uk [10]

Answer:

The third choice

Step-by-step explanation:

a relation is a function if an input has at most one output for a given input

Choices 1, 2 and 4 are not functions as they have two different outputs for the same input. (See the red ovals)

7 0

3 years ago

PLEASE HELP !! WILL MARK THE BRAINLIEST <br><br> Solve the system y = -x + 7 and y = 0.5(x - 3)2

Leno4ka [110]

Y = -X + 7
Y = .5(X-3)2

Alright check it out. Substitute the Y in the second equation for the first equation so...

-X + 7 = .5(X-3)2

After this, you have to get rid of the .5 and the 2 which is easy peasy because they just cancel out. If you were to multiply by half and then multiply by 2 then you'd be back to where you started. So...

-X + 7 = X - 3

Move the X to combine them on one side, I moved the -X to the opposite side by adding X to each side so you get...

7 = 2X - 3

You then add 3 to both side so...

10 = 2X

Divide by 2

X = 5

So...

Y = -5 + 7
Y = 2

Y = .5(5-3)2
Cancel out the .5 and the 2
Y = 5-3
Y = 2

(5,2) is your answer

6 0

3 years ago

Can someone help me pls?

Aleks [24]

The answer is number two

8 0

3 years ago

Read 2 more answers

Which simplified choice??

jek_recluse [69]

Answer:

Its the first choice

Step-by-step explanation:

because 2^3 is 8 and 5^2 is 25. you can just multiply both and that is the only option that give you 200.

8 0

3 years ago