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3 years ago

15

Using the following triangle, what is the cosine of angle B?

1 answer:

stealth61 [152]3 years ago

3 0

Hello!

To find cosine, use the formula cos = adjacent / hypotenuse.

According to angle B, adjacent of angle B is side A, and the hypotenuse is side c because the hypotenuse is always opposite the right angle.

Therefore, the cosine of angle B is a/c.

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(Anderson, 1.14) Assume that P(A) = 0.4 and P(B) = 0.7. Making no further assumptions on A and B, show that P(A ∩ B) satisfies 0

Goshia [24]

Answer with Step-by-step explanation:

We are given that

P(A)=0.4 and P(B)=0.7

We know that

$P(A)+P(B)+P(A\cap B)=P(A\cup B)$

We know that

Maximum value of $P(A\cup B)$ =1 and minimum value of $P(A\cup B)$ =0

$0\leq P(A\cup B )\leq 1$

$0\leq P(A)+P(B)-P(A\cap B)\leq 1$

$0\leq 0.4+0.7-P(A\cap B)\leq 1$

$0\leq 1.1-P(A\cap B)\leq 1$

$0\leq 1.1-P(A\cap B)$

$P(A\cap B)\leq 1.1$

It is not possible that $P(A\cap B)$ is equal to 1.1

$1.1-P(A\cap B)\leq 1$

$-P(A\cap B)\leq 1-1.1=-0.1$

Multiply by (-1) on both sides

$P(A\cap B)\geq 0.1$

Again, $P(A\cup B)\geq P(B)$

$0.4+0.7-P(A\cap B)\geq 0.7$

$1.1-P(A\cap B)\geq 0.7$

$-P(A\cap B)\geq -1.1+0.7=-0.4$

Multiply by (-1) on both sides

$P(A\cap B)\leq 0.4$

Hence, $0.1\leq P(A\cap B)\leq 0.4$

3 0

3 years ago

Create an equivalent trinomial for 2 (3x + 5)(2x - 6)

emmainna [20.7K]

Answer:

24x^2+112x+120

Step-by-step explanation:

distribute the 2

(6x+10)(4x+12)

foil it

24x^2+112x+120

5 0

3 years ago

Help!!! 10 PTS!!!

Crank

Answer:

This is actually pretty easy just find the intersecting points from the lines

Number of solutions: 2

What are the solutions: (4,5) and (0,-3)

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3 years ago

What is the probability that the first card is a kingking and the second card is a kingking if the sampling is done with replac

IRINA_888 [86]

You want to draw 2 kings from a 52 card deck. And you do it with replacement.
There are 4 kings in a standard deck. The probability of getting one of them is
4/52 on the first draw.

For the second draw the probability is the same.
4/52

The probability for both happening is
(4/52)*(4/52) = (1/13)*(1/13) = 1/169 = 0.001597

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3 years ago

How do you solve<br> -6n-20=-2n+4 (1-3n)

DedPeter [7]

-6n-20=-2n+4-12n
-6n-20=-14n+4
+6n +6n
-20=-8n+4
-4 -4
-24=-8n
/8 /8
n=-3
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3 0

3 years ago