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kvasek [131]
3 years ago
5

Write a sentence that describes the relationship between the dependent variable and the independent variable. (Hint: Ratio langu

age can help.)
Mathematics
1 answer:
BartSMP [9]3 years ago
5 0
An Independent variable can change the dependent variable because the independent variable can be changed alone while a dependent variable can also be changed by another variable.

correct me if I am wrong.
You might be interested in
A complex electronic system is built with a certain number of backup components in its subsystems. One subsystem has eight ident
Fudgin [204]

Answer:

a) 0.0486 = 4.86% probability that exactly two of the four components last longer than 1000 hours.

b) 0.9996 = 99.96% probability that the subsystem operates longer than 1000 hours.

Step-by-step explanation:

For each component, there are only two possible outcomes. Either they last more than 1,000 hours, or they do not. Components operate independently, which means that the binomial probability distribution is used to solve this question.

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.

One subsystem has eight identical components, each with a probability of 0.1 of failing in less than 1,000 hours.

So 1 - 0.1 = 0.9 probability of working for more, which means that p = 0.9

a. exactly two of the four components last longer than 1000 hours.

This is P(X = 2) when n = 4. So

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

P(X = 2) = C_{4,2}.(0.9)^{2}.(0.1)^{2} = 0.0486

0.0486 = 4.86% probability that exactly two of the four components last longer than 1000 hours.

b. the subsystem operates longer than 1000 hours.

The subsystem has 8 components, which means that n = 8

It will operate if at least 4 components are working correctly, so we want:

P(X \geq 4) = 1 - P(X < 4)

In which

P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)

So

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

P(X = 0) = C_{8,0}.(0.9)^{0}.(0.1)^{8} \approx 0

P(X = 1) = C_{8,1}.(0.9)^{1}.(0.1)^{7} \approx 0tex][tex]P(X = 2) = C_{8,2}.(0.9)^{2}.(0.1)^{6} \approx 0

P(X = 3) = C_{8,3}.(0.9)^{3}.(0.1)^{5} = 0.0004

Then

P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0 + 0 + 0 + 0.0004 = 0.0004

P(X \geq 4) = 1 - P(X < 4) = 1 - 0.0004 = 0.9996

0.9996 = 99.96% probability that the subsystem operates longer than 1000 hours.

5 0
3 years ago
Write the coordinates​
Ilia_Sergeevich [38]
What kind of coordinates?
6 0
3 years ago
Find the exact value of cos (1140)°.
slamgirl [31]

now let's recall that a full circle has 360°, so then 1140 = 360 + 360 + 360 + 60.

namely, 1140 is 3 full-go-around the circle and then it lands on the I Quadrant at 60°.  Thus cos(1140°) = cos(60°).

what's that cosine of 60°?  Check the picture below.

8 0
2 years ago
What is the slope of a line parallel to y = 4/3x-2
den301095 [7]

I'm not that sure but I want to help

Step-by-step explanation:

y=4/3×-2

y=2/3×

Divide 2/3×

4 0
2 years ago
How much money would a person have 8 years after they invested $2,000 into an account that has an annual interest rate of 3% tha
madam [21]

The amount of money the person would have in 8 years s $2541.74.

<h3>How much would the person have in 8 years? </h3>

The formula for calculating future value is:

FV = P (1 + r)^nm]

Where:

FV = Future value
  • P = Present value = $2000
  • R = interest rate = 3% / 12 = 0.25%
  • m = number of compounding = 12
  • N = number of years = 8 years

Value of the account in 8 years with monthly compounding = $2000(1.0025)^(12 x 8) = $2541.74

To learn more about future value, please check: brainly.com/question/18760477

4 0
2 years ago
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