Factor the following:
12 x^4 - 42 x^3 - 90 x^2
Factor 6 x^2 out of 12 x^4 - 42 x^3 - 90 x^2:
6 x^2 (2 x^2 - 7 x - 15)
Factor the quadratic 2 x^2 - 7 x - 15. The coefficient of x^2 is 2 and the constant term is -15. The product of 2 and -15 is -30. The factors of -30 which sum to -7 are 3 and -10. So 2 x^2 - 7 x - 15 = 2 x^2 - 10 x + 3 x - 15 = x (2 x + 3) - 5 (2 x + 3):
6 x^2 x (2 x + 3) - 5 (2 x + 3)
Factor 2 x + 3 from x (2 x + 3) - 5 (2 x + 3):
Answer: 6 x^2 (2 x + 3) (x - 5)
Answer:
The mean of W is 55 ounces.
The standard deviation of W is 4.33 ounces.
Step-by-step explanation:
Let X: weight of a red delicious apple, and B: the weight of the box and packing material.
The distribution that will represent W: the total weight of the packaged 5 randomly selected apples will be also normally distributed.
Applying the property of the mean:
, the mean of W will be:

Applying the property of the variance:
, the variance of W will be:

The mean standard deviation of W will be the squared root of V(W):

The mean of W is 55 ounces.
The standard deviation of W is 4.33 ounces.
2(3t - 1) - 5(t - 1)
2(3t) - 2(1) - 5(t) + 5(1)
6t - 2 - 5t + 5
6t - 5t - 2 + 5
t + 3