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Maurinko [17]
2 years ago
7

If VW≅VY, WX = s + 69, and XY = 4s, what is the value of s?

Mathematics
1 answer:
Katen [24]2 years ago
7 0

Answer:

s = 23

Step-by-step explanation:

1. VW ≅ VY is given.

2. XV ≅ VX as it is the same side.

3. ∠WVX ≅ ∠YVX as they are both 90°. ∠WVY is 180° as it is a straight line, so both ∠WVX and ∠YVX are exactly half of that.

Given those three things, you can say that ΔWVX ≅ ΔYVX. Because all corresponding parts of congruent triangles are also congruent, you can be sure that WX ≅ XY. Finally, using that information, you can write an equation and solve for s.

s+69=4s\\s-s+69=4s-s\\69=3s\\\frac{69}{3}=\frac{3s}{3}\\s=23

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The one-time fling! Have you ever purchased an article of clothing (dress, sports jacket, etc.), worn the item once to a party,
rjkz [21]

Answer:

a)  0.2725

b)  0.7275

c)  0.8948

Step-by-step explanation:

This is a binomial distribution probability problem. The formula is:

P(x)=\frac{n!}{(n-x)!x!}p^{x}q^{n-x}

Where

n is the number of trials [here we are taking 8 person, so n = 8]

x is what we are looking for [in the problem]

p is the probability of success [ 15%, so p = 0.15

q is the probability of failure [q = 1-p = 0.85]

Now,

a)

We are looking for "no one" did fling, so x = 0

Let's put into formula and find out the probability:

P(x=0)=\frac{8!}{(8-0)!0!}(0.15)^{0}(0.85)^{8}\\P(x=0)=0.2725

So, the probability that no one has done a one-time fling is 0.2725

b)

Atleast 1 person means P(x ≥ 1).

This can be found by:

P(x ≥ 1) = 1 - P(x=0) = 1 - 0.2725 = 0.7275

THus, Probability that at least one person has done a one-time fling is 0.7275

c)

No more than 2 people means P (x≤2).

This is essentially

P ( x ≤ 2 ) = P(x=0) + P(x=1) + P(x=2)

P ( x = 0 ) is found in part (a), which is 0.2725

P (x = 1 ) and P(x=2) can be found using formula:

P(x=1)=\frac{8!}{(8-1)!1!}(0.15)^{1}(0.85)^{7}\\P(x=1)=0.3847

and

P(x=2)=\frac{8!}{(8-2)!2!}(0.15)^{2}(0.85)^{6}\\P(x=2)=0.2376

Thus,

P ( x ≤ 2 ) = P(x=0) + P(x=1) + P(x=2) = 0.2725 + 0.3847 + 0.2376 = 0.8948

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