What is the GCF of 1683t, 4085, and 68t?? O 4 O 483t O 8 O 8837

Mekhanik [1.2K]

$\frac{ - 3}{8} \times \frac{8}{15} \\ \\ = \frac{ \cancel{- 3}}{ \cancel8} \times \frac{ \cancel8}{ \cancel{15}} \\ \\ = - \frac{1}{5}$

Hope This Helps ~

8 0

2 years ago

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

Profit, P(x), is the difference between revenue, R(x), and cost, C(x), so P(x) = R(x) - CC). Which

aleksklad [387]

Answer:

Step-by-step explanation:

Profit, P(x), is the difference between revenue, R(x), and cost, C(x)

R(x) = 2x^4 - 3x^3 + 2x - 1

C(x) = x^4 -x^2 + 2x + 3

Substituting into the equation

P(x) = R(x) - C(x)

= (2x^4 - 3x^3 + 2x - 1) - (x^4 -x^2 + 2x + 3)

= x^4 - 3x^3 + x^2 - 4

The answer is the lower left option.

7 0

3 years ago

Read 2 more answers

Someone help lolz..

Mkey [24]

The answer is y =-4 !

6 0

3 years ago

Roll the number cube to find the observed frequency. Which statements are true? Check all that apply

ch4aika [34]

Answer:

(a) and (c)

Step-by-step explanation:

Given

See attachment for complete question

Required

Select all true statements

First, calculate the total observed frequency;

$Total = 11 + 16 + 14 + 20 + 12 + 17$

$Total = 90$

(a): Relative frequency of 4 is 2/9

Relative frequency is calculated by:

$RF= \frac{Observed\ Frequency}{Total}$

For roll 4

$Observed\ frequency = 20$

So, the relative frequency is:

$RF = \frac{20}{90}$

Simplify

$RF = \frac{2}{9}$

(a) is true

(b): Experimental probability of 3 greater than its theoretical probability

The experimental probability is its relative frequency;

For roll 3

$Observed\ frequency = 14$

The experimental probability is:

$Pr = \frac{14}{90}$

Simplify

$Pr = \frac{7}{45} = 0.156$

To calculate the theoretical probability, w have:

$S = \{1,2,3,4,5,6\}$ ---- sample space

$n(S)= 6$

$n(3) = 1$ --- number of times 3 occur

The theoretical probability is:

$Pr = \frac{1}{6} = 0.167$

The theoretical probability is $greater\ than\ the$ experimental probability.

(b) is false

(c): Experimental probability of 2 greater than its theoretical probability

Using the explanations in (b), we have:

For roll 2

$Observed\ frequency = 16$

The experimental probability is:

$Pr = \frac{16}{90}$

Simplify

$Pr = \frac{8}{45} = 0.178$

To calculate the theoretical probability, we have:

$n(S)= 6$

$n(2) = 1$

The theoretical probability is:

$Pr = \frac{1}{6} = 0.167$

The experimental probability is $greater\ than\ the$ theoretical probability.

(c) is true

(d): Relative frequency of 5 is 2/13

For roll 5

$Observed\ frequency = 12$

The relative frequency is:

$RF = \frac{12}{90}$

Simplify

$RF = \frac{2}{15}$

(d) is true

7 0

3 years ago