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asambeis [7]
2 years ago
7

Find the distance between the given points. Round to the nearest tenth.

Mathematics
1 answer:
sashaice [31]2 years ago
4 0

Answer:

B and is (-2, 3)...........

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The annual rainfall (in inches) in a certain region is normally distributed with mean 43.2 and variance 20.8. Assume rainfall in
Wittaler [7]

Answer:

92.24% probability that out of 15 years, at most 2 have rainfall of more than 50 inches.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the binomial probability distribution.

Normal probability distribution:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean \mu and standard deviation(which is the square root of the variance) \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.

Binomial probability distribution:

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

In this problem, we have that:

\mu = 43.2, \sigma = \sqrt{20.8} = 4.56

Probability that a year has rainfall of more than 50 inches.

pvalue of Z when X = 50. So

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

Z = \frac{50 - 43.2}{4.56}

Z = 1.49

Z = 1.49 has a pvalue of 0.9319

1 - 0.9319 = 0.0681

Find the probability that out of 15 years, at most 2 have rainfall of more than 50 inches.

This is P(X \leq 2) when n = 15, p = 0.0681. So

P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 0) = C_{15,0}.(0.0681)^{0}.(0.9319)^{15} = 0.3472

P(X = 1) = C_{15,1}.(0.0681)^{1}.(0.9319)^{14} = 0.3805

P(X = 2) = C_{15,2}.(0.0681)^{2}.(0.9319)^{13} = 0.1947

P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.3472 + 0.3805 + 0.1947 = 0.9224

92.24% probability that out of 15 years, at most 2 have rainfall of more than 50 inches.

8 0
3 years ago
Read 2 more answers
For which value of c is the line y=3x+c a tangent to the parabola with equation y=x^2-5x+7
Alik [6]
Equating the y's:-

3x + c = x^2 - 5x + 7

x^2  - 8x +7 - c = 0

If y = 3x + c is a tangent then there  will be duplicate solutions to this equation 
That is the discriminant b^2 - 4ac = 0. So we have:-

(-8)^2 - 4 * 1 * (7 -c)  = 0
64 -28 + 4c = 0
4c  = - 36

so c = -9  answer
6 0
3 years ago
What is total surface area of the rectangular prism shown 10m 10m 8m​
Dahasolnce [82]

Answer:

equals 800

Step-by-step explanation:

10 x 10 x 8

you would multiply

6 0
3 years ago
Read 2 more answers
Write an<br> equation of the line that passes through each pair of points.<br> (-3,9), (-3,-5)
Fantom [35]

Answer:

x = -3

Step-by-step explanation:

x is -3 in all values so we just write an equation.

6 0
3 years ago
Read 2 more answers
If $190 is invested at an interest rate of 11% per year and is compounded continuously, how much will the investment be worth in
dangina [55]

Answer:

$295.01

Step-by-step explanation:

Using the compounding continuously formula, we are looking for A.  We have that P = 190; r = .11 (always use the decimal form of the rate!); and t = 4.  Filling in we have:

A=190e^{(.11)(4)}

Simplifying that multiplication:

A=190e^{.44}.

On your calculator, raise e to the .44 power to get

A = 190(1.552707219) and

A = $295.01

5 0
3 years ago
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