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3 years ago

7

the completion times for three runner in a 100-yard dash are 9.75 seconds,9.7seconds,and 9.675 seconds. which is the winning tim

e?

1 answer:

siniylev [52]3 years ago

7 0

Its comparing least times, so 9.675 would be the winning time.why?you ask.well, change all the decimals to the thousandths(9.750,9.700,9.675). now you could see which is the least.

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Find the area of the attached figure

Alex17521 [72]

Answer:

15

Step-by-step explanation:

7 0

3 years ago

Evaluate p(x)=-3+4x when x=-2,0,and 5

Luden [163]

Answer: -11, -3, 17

Step-by-step explanation:

There are three answers depending on what x equals. In this case, x can equal: -2, 0, or 5.

Part 1:

Step 1: Substitute -2 for x

-3 + 4(2)

Step 2: Solve

-3 + 8 = 5

This is the first answer

Part 2:

Step 1: Substitute 0 for x

-3 + 4(0)

Step 2: Solve

-3 + 0 = -3

This is the second answer

Part 3:

Step 1: Substitue 5 for x

-3 + 4(5)

Step 2: Solve

-3 + 20 = 17

This is the third answer

3 0

3 years ago

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

(ASAP LOTS OF POINTS)

shusha [124]

Answer:

52 inches by 29 inches

Step-by-step explanation:

Let one side by 16x and the other side be 9x

We know the diameter is 60 inches

Using the Pythagorean theorem

a^2 + b^2 = c^2

(16x) ^2 + ( 9x) ^2 = 60 ^2

256 x^2 + 81x^2 = 3600

Combine like terms

337 x^2 = 3600

Divide each side by 337

337x^2 /337 = 3600/337

x^2 =10.68249258

Take the square root of each side

sqrt(x^2) =sqrt(10.68249258)

x =3.268408264

The sides are 16x by 9x

16*(3.268408264) =52.29453223 or 52

9 *(3.268408264)= 29.41567438 or 29

5 0

3 years ago

Please help thank you

Cerrena [4.2K]

Answer:

the first one maybe?

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers