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2 years ago

I will give BRAINlIEST if u explain how to solve these plz!!!

Mathematics

2 answers:

AURORKA [14]2 years ago

7 0

<h2>Answer:</h2>

Question 4: $\frac{8}{1}$

Question 5: $\frac{4}{5}$

Question 6: $\frac{2.5}{1}$

Question 7: $\frac{1}{1}$

<h2>Step-by-step explanation:</h2>

The way to solve these types of questions, also know as "<em>slope</em>" is solved in the format $\frac{y-y}{x-x}$ (y minus y over x minus x) which also can be known as $\frac{rise-rise}{run-run}$ (rise minus rise over rune minus run). To solve this you can choose any two sets of numbers (the top and the bottom of a chart is 1 set) and you use its numbers to find the slope. One important rule when solving for slope is to never write your answer in decimal form and rarely write your answer as a whole number always answer questions in fraction form!!!! Anyway, the y and the x are already given so no need to find those as well. Here's the solving of all questions:

for this question I choose the number sets: $\frac{24}{3} and, \frac{32}{4} in. ..equation... written... as, \frac{24-32}{3-4}$

so, now the easy part, 24-32=-8

Next we solve the bottom, 3-4=-1

so we end up with $\frac{-8}{-1}$ and when we simplify it can be written as $\frac{8}{1}$ or just 8 (I recommend to always write in fraction form because some teachers will remove points if its not in fraction form).

Now, for the rest of the problems I wont explain the solving process.

$\frac{60}{185} and\frac{100}{235} written...as,\frac{60-100}{185-235}$

60-100=-40

185-235=-50

$\frac{-40}{-50} simplify...to,\frac{4}{5}$

$\frac{12.5}{5} and\frac{25}{10} written...as,\frac{12.5-25}{5-10}$

12.5-25=-12.5

5-10=-5

$\frac{-12.5}{-5}simplify...to,\frac{2.5}{1}$ or 2.5 (I recommend to always write in fraction form because some teachers will remove points if its not in fraction form).

$\frac{4}{2} and\frac{5}{3} written...as,\frac{4-5}{2-3}$

4-5=-1

2-3=-1

$\frac{-1}{-1}simplify...to,\frac{1}{1}$ or 1 (I recommend to always write in fraction form because some teachers will remove points if its not in fraction form).

Hope this helped, please give mw brainiest I spent half an hour on this :D

-Thanks for your time.

alexandr402 [8]2 years ago

5 0

Answer:

i dont have any idea.....my brain is full of BTS

Step-by-step explanation:

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The question is incomplete. Here is the complete question.

The probability density function of the time to failure of an electronic component in a copier (in hours) is

$f(x)=\frac{e^{\frac{-x}{1000} }}{1000}$

for x > 0. Determine the probability that

a. A component lasts more than 3000 hours before failure.

b. A componenet fails in the interval from 1000 to 2000 hours.

c. A component fails before 1000 hours.

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Step-by-step explanation: <em>Probability Density Function</em> is a function defining the probability of an outcome for a discrete random variable and is mathematically defined as the derivative of the distribution function.

So, probability function is given by:

P(a<x<b) = $\int\limits^b_a {P(x)} \, dx$

Then, for the electronic component, probability will be:

P(a<x<b) = $\int\limits^b_a {\frac{e^{\frac{-x}{1000} }}{1000} } \, dx$

P(a<x<b) = $\frac{1000}{1000}.e^{\frac{-x}{1000} }$

P(a<x<b) = $e^{\frac{-b}{1000} }-e^\frac{-a}{1000}$

a. For a component to last more than 3000 hours:

P(3000<x<∞) = $e^{\frac{-3000}{1000} }-e^\frac{-a}{1000}$

Exponential equation to the infinity tends to zero, so:

P(3000<x<∞) = $e^{-3}$

P(3000<x<∞) = 0.05

There is a probability of 5% of a component to last more than 3000 hours.

b. Probability between 1000 and 2000 hours:

P(1000<x<2000) = $e^{\frac{-2000}{1000} }-e^\frac{-1000}{1000}$

P(1000<x<2000) = $e^{-2}-e^{-1}$

P(1000<x<2000) = 0.2325

There is a probability of 23.25% of failure in that interval.

c. Probability of failing between 0 and 1000 hours:

P(0<x<1000) = $e^{\frac{-1000}{1000} }-e^\frac{-0}{1000}$

P(0<x<1000) = $e^{-1}-1$

P(0<x<1000) = 0.6321

There is a probability of 63.21% of failing before 1000 hours.

d. P(x) = $e^{\frac{-b}{1000} }-e^\frac{-a}{1000}$

0.1 = $1-e^\frac{-x}{1000}$

$-e^{\frac{-x}{1000} }=-0.9$

${\frac{-x}{1000} }=ln0.9$

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x = 105.4

10% of the components will have failed at 105.4 hours.

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