Answer:
x³ - 8x² - 11x + 148
Step-by-step explanation:
Given that x = 6 + i is a root then x = 6 - i is also a root
Complex roots occur as conjugate pairs.
The factors are therefore (x - (6 + i)) and(x - (6 - i))
Given x = - 4 is a root then (x + 4) is a factor
The polynomial is the product of the factors, that is
p(x) = (x + 4)(x - (6 + i))(x - (6 - i))
= (x + 4)(x - 6 - i)(x - 6 + i)
= (x + 4)((x - 6)² - i²)
= (x + 4)(x² - 12x + 36 + 1)
= (x + 4)(x² - 12x + 37) ← distribute
= x³ + 4x² - 12x² - 48x + 37x + 148
= x³ - 8x² - 11x + 148
Hi,
Let's solve the equation step-by-step.
x−3x=2(4+x)
Step 1: Simplify both sides of the equation.
x−3x=2(4+x)
x+−3x=(2)(4)+(2)(x)(Distribute)
x+−3x=8+2x
(x+−3x)=2x+8(Combine Like Terms)
−2x=2x+8
−2x=2x+8
Step 2: Subtract 2x from both sides.
−2x−2x=2x+8−2x
−4x=8
Step 3: Divide both sides by -4.
−4x/−4 = 8/−4
x=−2
Answer:
x=−2
Have a great day!
Gloria is neglecting the concept of portfolio diversification. Gloria's method suggests to only invest in Blue Chip companies, which are companies which have been long established and ensured. Gloria also suggests putting all of her friend's money directly in the stock market without looking into the other financial instruments like bonds, mutual funds and variable universal life insurance.
Answer:
Probability that the average mileage of the fleet is greater than 30.7 mpg is 0.7454.
Step-by-step explanation:
We are given that a certain car model has a mean gas mileage of 31 miles per gallon (mpg) with a standard deviation 3 mpg.
A pizza delivery company buys 43 of these cars.
<em>Let </em>
<em> = sample average mileage of the fleet </em>
<em />
The z-score probability distribution of sample average is given by;
Z = 
~ N(0,1)
where, 
= mean gas mileage = 31 miles per gallon (mpg)
= standard deviation = 3 mpg
n = sample of cars = 43
So, probability that the average mileage of the fleet is greater than 30.7 mpg is given by = P(<em> </em>> 30.7 mpg)
P(<em> </em>> 30.7 mpg) = P( > 
) = P(Z > -0.66) = P(Z < 0.66)
= 0.7454
<em>Because in z table area of P(Z > -x) is same as area of P(Z < x). Also, the above probability is calculated using z table by looking at value of x = 0.66 in the z table which have an area of 0.7454.
</em>
Therefore, probability that the average mileage of the fleet is greater than 30.7 mpg is 0.7454.
