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3 years ago

Just a quick math problem that I forgot how to do.

Mathematics

2 answers:

Hunter-Best [27]3 years ago

6 0

Answer:

Step-by-step explanation:

If they are parallel then the 2 angles are congruent, so

8x + 14 = 12x - 50

64 = 4x

16 = x

Firlakuza [10]3 years ago

3 0

Answer:

x = 16

Step-by-step explanation:

For the 2 lines to be parallel, then

12x - 50 and 8x + 14 would be corresponding angles and congruent , so

12x - 50 = 8x + 14 ( subtract 8x from both sides )

4x - 50 = 14 ( add 50 to both sides )

4x = 64 ( divide both sides by 4 )

x = 16

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For a certain river, suppose the drought length Y is the number of consecutive time intervals in which the water supply remains

AnnZ [28]

Answer:

a) There is a 9% probability that a drought lasts exactly 3 intervals.

There is an 85.5% probability that a drought lasts at most 3 intervals.

b)There is a 14.5% probability that the length of a drought exceeds its mean value by at least one standard deviation

Step-by-step explanation:

The geometric distribution is the number of failures expected before you get a success in a series of Bernoulli trials.

It has the following probability density formula:

$f(x) = (1-p)^{x}p$

In which p is the probability of a success.

The mean of the geometric distribution is given by the following formula:

$\mu = \frac{1-p}{p}$

The standard deviation of the geometric distribution is given by the following formula:

$\sigma = \sqrt{\frac{1-p}{p^{2}}$

In this problem, we have that:

$p = 0.383$

$\mu = \frac{1-p}{p} = \frac{1-0.383}{0.383} = 1.61$

$\sigma = \sqrt{\frac{1-p}{p^{2}}} = \sqrt{\frac{1-0.383}{(0.383)^{2}}} = 2.05$

(a) What is the probability that a drought lasts exactly 3 intervals?

This is $f(3)$

$f(x) = (1-p)^{x}p$

$f(3) = (1-0.383)^{3}*(0.383)$

$f(3) = 0.09$

There is a 9% probability that a drought lasts exactly 3 intervals.

At most 3 intervals?

This is $P = f(0) + f(1) + f(2) + f(3)$

$f(x) = (1-p)^{x}p$

$f(0) = (1-0.383)^{0}*(0.383) = 0.383$

$f(1) = (1-0.383)^{1}*(0.383) = 0.236$

$f(2) = (1-0.383)^{2}*(0.383) = 0.146$

Previously in this exercise, we found that $f(3) = 0.09$

$P = f(0) + f(1) + f(2) + f(3) = 0.383 + 0.236 + 0.146 + 0.09 = 0.855$

There is an 85.5% probability that a drought lasts at most 3 intervals.

(b) What is the probability that the length of a drought exceeds its mean value by at least one standard deviation?

This is $P(X \geq \mu+\sigma) = P(X \geq 1.61 + 2.05) = P(X \geq 3.66) = P(X \geq 4)$ .

We are working with discrete data, so 3.66 is rounded up to 4.

Either a drought lasts at least four months, or it lasts at most thee. In a), we found that the probability that it lasts at most 3 months is 0.855. The sum of these probabilities is decimal 1. So:

$P(X \leq 3) + P(X \geq 4) = 1$

$0.855 + P(X \geq 4) = 1$

$P(X \geq 4) = 0.145$

There is a 14.5% probability that the length of a drought exceeds its mean value by at least one standard deviation

8 0

3 years ago

Question 14 of 25

Naily [24]

Answer:

Step-by-step explanation:

perpendicular lines are the negative reciprocals of each other, and a pair of these lines intersects at 90 degrees.

5 0

3 years ago

Read 2 more answers

Dylan made $45,765 and Orlando made $34,715. Both boys worked for 6 months. How much more money did Dylan earn than Orlando per

Ymorist [56]

Answer:

$425

Step-by-step explanation:

45,765 divided by 26 equals 1,760.192307692308

34,715 divided by 26 equals 1,335.192307692308

1,760.192307692308-1,335.192307692308=425

5 0

3 years ago

Midpoint is the center point on the line segment <br> True or false?

Mariana [72]

Your Answer should be True

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3 years ago

You get a student loan from the Educational Assistance Foundation to pay for your educational expenses as you earn your associat

Dahasolnce [82]

Answer:

$2880

Step-by-step explanation:

I = Prt

= $3600·8%·10 = 0.80·$3600 = $2880

The simple interest on $3600 over a 10-year period is $2880.

3 0

4 years ago