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4 years ago

Which value of y would make OP || LN ?

Mathematics

1 answer:

guajiro [1.7K]4 years ago

3 0

Remark
All you need do is assume the small triangle is similar to the large one. MO:ML :: MP:MN must be solved.

Givens
MO = 28
ML = 28 + 14
MP = y
MN = y + 18

Equation
28:28+14 :: y: y + 18

Solve
28/42 = y / (y + 18)
28*(y + 18) = 42y Remove the brackets
28y + 18*28 = 42y
28y + 504 = 42y Subtract 28y from both sides.
504 = 42y - 28y
504 = 14y Divide by 14
504/14 = y
y = 36

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Write y+4=2/3(x+7) ...?

iragen [17]

y+4=2/3(x+7)

Multiplying both sides by the denominator which is 3:
3(y+4) = 3(2/3) * (x+7)
3y+12=2x+14

Subtract 3y:
12 = 2x - 3y + 14

Subtract 14
-2 = 2x - 3y

8 0

3 years ago

A study found that 1% of Social Security recipients are too young to vote. If 800 social security recipients are randomly select

GalinKa [24]

Answer:

8, 7.92, 2.81

Step-by-step explanation:

For each Social Security recipient, there are only two possible outcomes. Either they are too young to vote, or they are not. The probability of a Social Security recipient is independent of any other Social Security recipient. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

The expected value of the binomial distribution is:

$E(X) = np$

The variance of the binomial distribution is:

$V(X) = np(1-p)$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

In this problem, we have that:

$n = 800, p = 0.01$

Mean:

$E(X) = np = 800*0.01 = 8$

The variance of the binomial distribution is:

$V(X) = np(1-p) = 800*0.01*0.99 = 7.92$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{800*0.01*0.99} = 2.81$

Formatted answer: 8, 7.92, 2.81

6 0

4 years ago

1 If a = p^1/3-p^-1/3 prove that: a^3 + 3a = p - 1/p

alexandr402 [8]

Hello, please consider the following.

We know that

$a = p^{\frac{1}{3}}-p^{-\frac{1}{3}}\\\\=p^{\frac{1}{3}}-\dfrac{1}{p^{\frac{1}{3}}}$

And we can write that.

$(p-\dfrac{1}{p})^3=(p-\dfrac{1}{p})(p^2-2+\dfrac{1}{p^2})\\\\=p^3-2p+\dfrac{1}{p}-p+\dfrac{2}{p}-\dfrac{1}{p^3}\\\\=p^3-\dfrac{1}{p^3}-3(p-\dfrac{1}{p})$

It means that, by replacing p by $p^{1/3}$

$(p^{1/3}-\dfrac{1}{p^{1/3}})^3=p-\dfrac{1}{p}-3(p^{1/3}-\dfrac{1}{p^{1/3}})\\\\\\\text{ So }\\\\a^3=p-\dfrac{1}{p}-3a\\\\\boxed{ a^3+3a=p-\dfrac{1}{p} }$

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

4 0

3 years ago

7x+2y=z if x=3 and y=2 what is the value of z

Masteriza [31]

Answer:

z=25

Step-by-step explanation:

7x+2y=z

7(3)+2(2)=z

21+4=z

25=z

Hope this helps! :)

6 0

3 years ago

One half of negative five eighths

evablogger [386]

-0.3125 is the answer, but you probably have to round

6 0

4 years ago

Read 2 more answers