An item is regularly priced at $45. Josh bought it on sale for 15% off the regular price.

One satellite is scheduled to be launched from Cape Canaveral in Florida, and another launching is scheduled for Vandenberg Air

Lisa [10]

Answer:

$P(A) = 0.45$

$P(B) = 0.32$

Step-by-step explanation:

Given

$P(A) > P(B)$

$P(A\ u\ B) = 0.626$

$P(A\ n\ B) = 0.144$

Required

Find P(A) and P(B)

We have that:

$P(A\ u\ B) = P(A) + P(B) - P(A\ n\ B)$ --- (1)

and

$P(A\ n\ B) = P(A) * P(B)$ --- (2)

The equations become:

$P(A\ u\ B) = P(A) + P(B) - P(A\ n\ B)$ --- (1)

$0.626 = P(A) + P(B) - 0.144$

Collect like terms

$P(A) + P(B) = 0.626 + 0.144$

$P(A) + P(B) = 0.770$

Make P(A) the subject

$P(A) = 0.770 - P(B)$

$P(A\ n\ B) = P(A) * P(B)$ --- (2)

$0.144 = P(A) * P(B)$

$P(A) * P(B) = 0.144$

Substitute: $P(A) = 0.770 - P(B)$

$[0.770 - P(B)] * P(B) = 0.144$

Open bracket

$0.770P(B) - P(B)^2 = 0.144$

Represent P(B) with x

$0.770x - x^2 = 0.144$

Rewrite as:

$x^2 - 0.770x + 0.144 = 0$

Expand

$x^2 - 0.45x - 0.32x + 0.144 = 0$

Factorize:

$x[x - 0.45] - 0.32[x - 0.45]= 0$

Factor out x - 0.45

$[x - 0.32][x - 0.45]= 0$

Split

$x - 0.32= 0 \ or\ x - 0.45= 0$

Solve for x

$x = 0.32\ or\ x = 0.45$

Recall that:

$P(B) = x$

So, we have:

$P(B) = 0.32 \ or \ P(B) = 0.45$

Recall that:

$P(A) = 0.770 - P(B)$

So, we have:

$P(A) = 0.770 - 0.32 \ or\ P(A) =0.770 - 0.45$

$P(A) = 0.45 \ or\ P(A) =0.32$

Since:

$P(A) > P(B)$

Then:

$P(A) = 0.45$

$P(B) = 0.32$

6 0

3 years ago

if you’re good with set theory and this sudoko puzzle in math 30 please help with question 33!! real answers only !!

Sidana [21]

Answer: A) 2, 7, 9

Step-by-step explanation:

In a sudoku puzzle, there are three rules:

Each vertical line must contain the numbers 1 - 9, with no duplicates
Each horizontal line must contain the numbers 1 - 9, with no duplicates
Each 3 x 3 box must contain the numbers 1 - 9, with no duplicates.

Using logic:

2 must go in the 1st box. It cannot go in the 2nd or 3rd shaded square because 2 is already in that 3 x 3 box.

That leaves the 2nd and 3rd shaded square.

9 cannot go in the 2nd shaded square because 9 is already in that vertical line.

Therefore, 9 must go in the 3rd shaded square.

That leaves the 2nd shaded square.

7 must go in the 2nd shaded square because it is the only number remaining (2 and 9 have already been placed in the other squares).

6 0

3 years ago

The mass of a cylinder made of barium with a height of 2 inches depends on the radius of the cylinder as defined by the

irina [24]

Answer:

Y=7.188 pieR^2 and Y=11,000; r=22.07 inches

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

For question 1, find the x- and y-intercept of the line. -10x +5y=40

katen-ka-za [31]

Answer:

D. x-intercept is -4; y-intercept is 8

Step-by-step explanation:

Given line:

- 10x + 5y = 40

Find x- intercept, when y = 0:

- 10x = 40
x = - 4

Find y- intercept, when x = 0:

5y = 40
y = 8

Correct choice is D

5 0

3 years ago

PLEASE HELPPPPP rsm hw pls help

Masteriza [31]

Answer:

-12

Please mark as brainliest if answer is right

Have a great day, be safe and healthy

Thank u

XD

6 0

3 years ago