What is the difference between the probability of five heads and the probability of exactly five heads?

Find a third-degree polynomial equation with rational coefficients that has roots -4 and 6 + i.

dolphi86 [110]

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

3 0

2 years ago

X=4y,2x+y=18 solve by substitution show all work

Mkey [24]

Here is the math, did it on paper, sorry it’s blue. just add parenthesis around the x in the second equation and add what x equals. then solve as PEMDAS.

7 0

1 year ago

Solve each equation 3m-3/5=2m-1/2

Kazeer [188]

Answer:

m= 1/10

Step-by-step explanation:

1. Move the terms so that will be 3m - 2m=-1/2 + 3/5

2. Subtract the m values so that will be 3m - 2m= 1 or m

3. Calculate the sum.

4. So the answer will be m= 1/10. M because we subtracted 2 from 3 which make us 1 so we say it m and 1/10 by doing 1/2 + 3/5.

3 0

2 years ago

Read 2 more answers

A human resource manager wants to see if there is a difference in the proportion of minority applicants who get the job and the

mash [69]

Answer:

Error Bound = 0.04

Step-by-step explanation:

Whenever we want to estimate parameter from a subset (or sample) of the population, we need to considerate that your estimation won't be a 100% precise, in other words, the process will have a random component that prevents us from always making the exact decision.

With that in mind, the objective of a confidence interval is to give us a better insight of where we expect to find the "true" value of the parameter with a certain degree of certainty.

The estivamative of the true difference between proportions was -0.19 and the confidence interval was [-0.23 ; -0.15].

The question also defines the error bound, as the right endpoint of the confidence interval minus the sample mean difference, so it's pretty straight foward:

Error Bound = $-0.15 -(-0.19) = -0.15 + 0.19 = 0.04$

The interpretation of this would be that we expect that the estimative for the difference of proportions would deviate from the "true" difference about $\pm 0.04$ or 4%.