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3 years ago

Use the system of equations to answer the questions.

Mathematics

1 answer:

kap26 [50]3 years ago

4 0

The value of x is 16/7

the value of y is 8/7

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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

2 years ago

Whats the volume of the pyramid shown

adell [148]

Answer:

Volume of the Pyramid = 40 cubic centimeters

Step-by-step explanation:

The volume of a pyramid is given by the formula:

$V=\frac{lwh}{3}$

Where

l is the length

w is the width

h is the height

In the figure shown, the length is 5, width is 4, and height is 6 (in cm). We just substitute and find the answer. Shown below:

$V=\frac{lwh}{3}\\V=\frac{5*4*6}{3}\\V=40$

So, we can say:

Volume of the Pyramid = 40 cubic centimeters

7 0

3 years ago

How can the vertical number line be used to add or subtract

deff fn [24]

A vertical number line resembles a thermometer. It emphasizes that we count up in the number system. Vertical number lines are just alternative way to look at the numbers.

This is commonly used in adding or subtracting

For example: 5 – 3

5 is the start, the sign determines whether you go down or go up, the minus sign denotes down then so the last number denotes how many steps you are going down where you land is the answer. The same goes with addition but instead of down, the plus sign denotes going up.

8 0

3 years ago

Theta is an acute angle and sin theta and cos theta are given. Use identities to find tan, csc, sec, and cot. Where necessary, r

dimulka [17.4K]

Answer: C. sec theta

5 0

3 years ago

920,026-535,722 what is the sum!??!! help!!!

kow [346]

920026
535722 -
-----------
<span>384304</span>

4 0

3 years ago

Read 2 more answers