Select the better deal in the pair. Then give the unit rate for the better deal.

Given that 2y^3+by-cy+d,where b,c and d are constants,leaves a remainder R when divided by (y+1) , (y-2) and (2y-1). Find the va

Eddi Din [679]

The polynomial remainder theorem says that a polynomial p(x) leaves a remainder of p(k) when it's divided by x - k.

We're given that dividing p(y) = 2y³ + by² - cy + d leaves the same remainder R after dividing it by y + 1, y - 2, and 2y - 1. So we have

p(-1) = 2(-1)³ + b(-1)² - c(-1) + d = R

==> R = -2 + b + c + d

p(2) = 2(2)³ + b(2)² - c(2) + d = R

==> R = 16 + 4b - 2c + d

p(1/2) = 2(1/2)³ + b(1/2)² - c(1/2) + d = R

==> R = 1/4 + b/4 - c/2 + d

We're also given that y + 2 is a factor, which means dividing p(y) by it leaves no remainder, and so

p(-2) = 2(-2)³ + b(-2)² - c(-2) + d = 0

==> 0 = -16 + 4b + 2c + d

Solve the system of equations in boldface. You can eliminate d from the first 3 to first solve for b and c, then solve for d :

(-2 + b + c + d) - (16 + 4b - 2c + d) = R - R

-18 - 3b + 3c = 0

b - c = -6

(-2 + b + c + d) - (1/4 + b/4 - c/2 + d) = R - R

-9/4 + 3b/4 + 3c/2 = 0

b + 2c = 3

(b - c) - (b + 2c) = -6 - 3

-3c = -9

c = 3

b - 3 = -6

b = -3

-16 + 4(-3) + 2(3) + d = 0

d = 22

7 0

3 years ago

Suppose 12% of students are veterans. From a sample of 263 students, how unusual would it be to have less than 22 veterans?

kkurt [141]

Answer:

Yes, both np and n(1-p) are ≥ 10

Mean = 0.12 ; Standard deviation = 0.02004

Yes. There is a less than 5% chance of this happening by random variation. 0.034839

Step-by-step explanation:

Given that :

p = 12% = 0.12 ;

Sample size, n = 263

np = 263 * 0.12 = 31.56

n(1 - p) = 263(1 - 0.12) = 263 * 0.88 = 231.44

According to the central limit theorem, distribution of sample proportion approximately follow normal distribution with mean of p = 0.12 and standard deviation sqrt(p*(1 - p)/n) = sqrt (0.12 *0.88)/n = sqrt(0.0004015) = 0.02004

Z = (x - mean) / standard deviation

x = 22 / 263 = 0.08365

Z = (0.08365 - 0.12) / 0.02004

Z = −1.813872

Z = - 1.814

P(Z < −1.814) = 0.034839 (Z probability calculator)

Yes, it is unusual

0.034 < 0.05 (Hence, There is a less than 5% chance of this happening by random variation.

7 0

3 years ago

2 X. - 144 (Type your answer in factor

tresset_1 [31]

Answer:

(x+12) (x-12)

Step-by-step explanation:

12x12=144

6 0

3 years ago

What is x and y 2x-3y=-1,y=x-1?

kenny6666 [7]

Answer:

1x

Step-by-step explanation:

2x-3x[x-1]

=2x-3x+1

=-x+1

=0

7 0

3 years ago

Scarlett took a taxi from her house to the airport. The taxi company charged a pick-up fee of $2.80 plus $1.25 per mile. The tot

Alexxandr [17]

Answer:

x ≤ 17

Step-by-step explanation:

Pick up fee = 2.80

Cost per mile = 1.25

Total cost = $24.05

Number of miles ride, x

Pickup fee + mile per ride * number of ride ≤ total cost

2.80 + 1.25x ≤ 24.05

1.25x ≤ 24.05 - 2.80

1.25x ≤ 21.25

x ≤ 17

Number one of miles ride x ≤ 17

4 0

3 years ago