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murzikaleks [220]
3 years ago
9

Which expression is equivalent to (x+2)(3x-3)?

Mathematics
1 answer:
trapecia [35]3 years ago
8 0

Answer:D

Step-by-step explanation:Multiply x and 3x to get 3x^2 which is the first part, then multiply x and -3 to get -3x then and that to 2 times 3x which get you 3x bc -3x + 6x is 3x, and for the last part, multiply 2 and -3 to get -6 so your answer will be 3x^2+3x-6

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The probability density function of the time to failure of an electronic component in a copier (in hours) is f(x) for Determine
salantis [7]

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.

d. Determine the number of hours at which 10% of all components have failed.

Answer: a. P(x>3000) = 0.5

              b. P(1000<x<2000) = 0.2325

              c. P(x<1000) = 0.6321

              d. 105.4 hours

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

-x = -1000.ln(0.9)

x = 105.4

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

5 0
3 years ago
What is (c+1) +9 in simplified form plz help
Afina-wow [57]
=(c+1)+9
=C+1+9
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3 years ago
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Elan is painting the outside of a rectangular barn door. It is
UkoKoshka [18]

Answer:

9600

Step-by-step explanation:

80 times 60 times 2

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3 years ago
A farmer is selling apples from his orchard. He uses the equation c = 1.6p to calculate the total cost, c, for every pound of ap
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A) a customer would pay $1.60 for 1 pound of apples. (To solve, plug in “1” for “p” and find c))

B) 8.5 pounds of apples would cost $13.60. (To solve, plug in 8.5 for p and find c)

C) If a customer pays $5.20, they will have purchased 3.25 pounds of apples. (To solve, plug in 5.2 for c and solve for p)

Have a great day!
3 0
3 years ago
I need some help on this
andrew-mc [135]

Answer:

b, k = -4

Step-by-step explanation:

3/2 = k + 11/2

=> 3/2 - 11/2 = k

=> -8/2 = k

=> k = -4

6 0
2 years ago
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