8.1 divided into 81 problem

A point $(x, y)$ with integer coordinates is randomly selected such that $0 \le x \le 8$ and $0 \le y \le 4$. what is the probab

ahrayia [7]

Answer:

$\frac{1}{3}$

Step-by-step explanation:

A point (x, y) with integer coordinates is randomly selected such that $0 \le x \le 8 \:and\: $0 \le y \le 4$.$

The possible pairs of (x,y) are:

(0,0),(0,1),(0,2),(0,3),(0,4)

(1,0),(1,1),(1,2),(1,3),(1,4)

(2,0),(2,1),(2,2),(2,3),(2,4)

(3,0),(3,1),(3,2),(3,3),(3,4)

(4,0),(4,1),(4,2),(4,3),(4,4)

(5,0),(5,1),(5,2),(5,3),(5,4)

(6,0),(6,1),(6,2),(6,3),(6,4)

(7,0),(7,1),(7,2),(7,3),(7,4)

(8,0),(8,1),(8,2),(8,3),(8,4)

The Total Possible Outcomes n(S)= 45

The pair (x, y) that satisfies the given condition (say event A: $x + y \le 4$ ) are:

$(0,0),(0,1),(0,2),(0,3),(0,4)\\(1,0),(1,1),(1,2),(1,3)\\(2,0),(2,1),(2,2)\\(3,0),(3,1)\\(4,0)$

n(A)=15

Therefore:

$P(A)=\frac{n(A)}{n(S)} =\frac{15}{45} =\frac{1}{3}$

5 0

3 years ago

The hourly cost of renting office space in Manhattan is shown by the graph below. The hourly cost of renting office space in Bro

Liula [17]

Answer:

Brooklyn is more expensive

Step-by-step explanation:

4 0

2 years ago

Read 2 more answers

<img src="https://tex.z-dn.net/?f=%20%5Cfrac%7Bx%20%2B%201%20%7D%7B2%7D%20%20%3D%20%20%5Cfrac%7B7x%20-%203%7D%7B2%7D%20" id="Tex

MAVERICK [17]

Answer:

$\sf x =\dfrac{2}{3}$

Explanation:

$\sf \rightarrow \dfrac{x+1}{2} = \dfrac{7x-3}{2}$

cross multiply

$\sf \rightarrow 2(x+1) = 2(7x-3)$

divide both sides by 2

$\sf \rightarrow x + 1 = 7x-3$

isolate variables

$\sf \rightarrow x -7x = -3-1$

simplify

$\sf \rightarrow -6x = -4$

divide both sides by -6

$\sf \rightarrow \dfrac{-6x}{-6} = \dfrac{-4}{-6}$

simplify

$\sf \rightarrow x =\dfrac{2}{3}$

4 0

1 year ago

Read 2 more answers

Help with my homework pls<br> Solve the compound inequality y + 7 ≥ –1 and y∕4 + 3 ≤ 5.

Marianna [84]

Answer:

-8 ≤ y ≤ 8

Step-by-step explanation:

Subtract 7 from the first one:

y ≥ -8

Subtract 3 from the second one, then multiply by 4.

y/4 ≤ 2

y ≤ 8

Now, you can write these as a compound inequality:

-8 ≤ y ≤ 8

_____

<em>Additional comment</em>

You basically solve these the same way you would an equation. The only difference is that multiplying or dividing by a negative number will reverse the inequality symbol:

2 > 1

-2 < -1 . . . . . multiplied above by -1.

8 0

1 year ago

PLEASE HELP ANSWER THIS ASAP!!! :)

PilotLPTM [1.2K]

Answer:

C, 42 degrees

Step-by-step explanation:

Considering angle BAD is 60 degrees, that makes angle BCD also 60 degrees. Since parallelograms have 360 degrees in total, we're still missing 240 degrees. Since angles BAD and BCD are congruent (equal), that means that angles ABC and ADC also have to be congruent. To find their angles, we do 240 divided by 2, which equals 120. Now that we know all of the angles, lets focus on angle ADC. Since angle 1 has been given to us, all we need to do is subtract 78 from 120 which turns out to be 42 degrees, which is the answer.

5 0

2 years ago