Which would be the better value? A) 12 pens for $2.70 B) 16 pens for $3.40

Joshua has a bag of marbles. In the bag are 5 white marbles, 3 blue marbles, and 7 green marbles. Peter randomly draws one marbl

Step2247 [10]

Answer:

1 / 5

Step-by-step explanation:

Given that:

Number of white marbles = 5

Number of blue marbles = 3

Number of green marbles = 7

Required is the approximate probability of drawing 2 green marbles, Note that drawing is done without replacement :

Probability = required outcome / Total possible outcomes

Total possible outcomes = sum of all marbles = (5 + 3 + 7) = 15 marbles

First draw:

P(Green) = 7 / 15

Second draw:

Required outcome = 7 - 1 = 6

Possible outcomes = 15 - 1 = 14

P(green) = 6 / 14

Probability of drawing out two green marbles :

(7/15 * 6/14) = 42 / 210 = 1 / 5

6 0

3 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

The volume of a cube is V= S^3 where V is the volume and s is the length of one side what is the volume of a cube if the length

sammy [17]

The volume of cube is 1000 cubic feet

Solution:

Given that,

The volume of cube is given by formula:

$V = s^3$

Where,

V is the volume of cube

"s" is the length of one side

What is the volume of a cube if the length of a side s is 10 feet

Given, s = 10 feet

Substitute s = 10 in given formula,

$V = 10^3\\\\V = 10 \times 10 \times 10\\\\V = 1000$

Thus volume of cube is 1000 cubic feet

7 0

3 years ago

Write a unit rate for the situation. 1080 miles on 15 gallons

Masja [62]

72 miles=1 gallon

Step by step Explanation:
Divide 1080 by 15 and divide 15 by 15. You get 72 and one.
Hope me helped!

4 0

3 years ago

Read 2 more answers

Write and expression equal to 7x8

Lubov Fominskaja [6]

(4+3)x(4+4) this should be the answer

3 0

4 years ago

Read 2 more answers