How do you do this? It’s factoring polynomials by the way.

Mathematics

1 answer:

galben [10]3 years ago

8 0

You find the GCF of 10x³ and - 12x² and the GFC of 5x and - 6.

10x³ and - 12x² share a GCF of 2x². 5x and - 6 share a GCF of 1

So factoring 10x³ - 12x² + 5x - 6 becomes:

2x²(5x - 6) + 1(5x - 6).

Your factored equation and answer is (2x² + 1)(5x - 6)

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Our faucet is broken, and a plumber has been called. The arrival time of the plumber is uniformly distributed between 1pm and 7p

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Answer:

$E(A+B) = E(A)+E(B)=4+0.5 =4.5 hours$

$Var(A+B)= Var(A)+Var(B)=3+0.25 hours^2=3.25 hours^2$

Step-by-step explanation:

Let A the random variable that represent "The arrival time of the plumber ". And we know that the distribution of A is given by:

$A\sim Uniform(1 ,7)$

And let B the random variable that represent "The time required to fix the broken faucet". And we know the distribution of B, given by:

$B\sim Exp(\lambda=\frac{1}{30 min})$

Supposing that the two times are independent, find the expected value and the variance of the time at which the plumber completes the project.

So we are interested on the expected value of A+B, like this

$E(A +B)$

Since the two random variables are assumed independent, then we have this

$E(A+B) = E(A)+E(B)$

So we can find the individual expected values for each distribution and then we can add it.

For ths uniform distribution the expected value is given by $E(X) =\frac{a+b}{2}$ where X is the random variable, and a,b represent the limits for the distribution. If we apply this for our case we got: