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3 years ago

Which of the following are best described as lines that meet to form a right angle

1 answer:

8 0

Perpendicular- meeting to form a right angle.
Perpendicular bisector- a line,Ray, or line segment that bisects a line segment at a right angle.
Perpendicular lines- if perpendicular lines are graphed on a Cartesian coordinate system.

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Let Y1 and Y2 be independent exponentially distributed random variables, each with mean 7. Find P(Y1 > Y2 | Y1 < 2Y2). (En

ArbitrLikvidat [17]

Y₁ and Y₂ are independent, so their joint density is

$f_{Y_1,Y_2}(y_1,y_2)=f_{Y_1}(y_1)f_{Y_2}(y_2)=\begin{cases}\frac1{49}e^{-\frac{y_1+y_2}7}&\text{for }y_1\ge0,y_2\ge0\\0&\text{otherwise}\end{cases}$

By definition of conditional probability,

P(Y₁ > Y₂ | Y₁ < 2 Y₂) = P((Y₁ > Y₂) and (Y₁ < 2 Y₂)) / P(Y₁ < 2 Y₂)

Use the joint density to compute the component probabilities:

• numerator:

$P((Y_1>Y_2)\text{ and }(Y_1$

$=\displaystyle\frac1{49}\int_0^\infty\int_{\frac{y_1}2}^{y_1}e^{-\frac{y_1+y_2}7}\,\mathrm dy_2\,\mathrm dy_1$

$=\displaystyle-\frac17\int_0^\infty\int_{-\frac{3y_1}{14}}^{-\frac{2y_1}7}e^u\,\mathrm du\,\mathrm dy_1$

$=\displaystyle-\frac17\int_0^\infty\left(e^{-\frac{2y_1}7} - e^{-\frac{3y_1}{14}}\right)\,\mathrm dy_1$

$=\displaystyle-\frac17\left(-\frac72e^{-\frac{2y_1}7} + \frac{14}3 e^{-\frac{3y_1}{14}}\right)\bigg|_0^\infty$

$=\displaystyle-\frac17\left(\frac72 - \frac{14}3\right)=\frac16$

• denominator:

$P(Y_1$

(I leave the details of the second integral to you)

Then you should end up with

P(Y₁ > Y₂ | Y₁ < 2 Y₂) = (1/6) / (2/3) = 1/4

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2 years ago

Suppose that the times it takes adult women to run a mile are normally distributed with an unknown mean and standard deviation.

Inga [223]

Answer:

Step-by-step explanation:

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2 years ago

Kevin and Joaquim had a total of $620. Joaquim had $100 more than Kevin. How much money did Kevin have?

Fantom [35]

Answer:

$260

Step-by-step explanation:

620-100=520 ( to make both of them equal)

520÷2=$260

Hope this helps! Thanks.

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2 years ago

What is -1/19,7/4,-4/7 in least to greatest

r-ruslan [8.4K]

Answer:

-4/7 is the smallest. then it's -1/19 and then finally it's 7/4

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3 years ago

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Convert 5 2/5 into an improper fraction

ss7ja [257]

Step-by-step explanation:

To write 5 as a fraction with a common denominator, multiply by 55 . Combine 5 and 55 . Combine the numerators over the common denominator. Simplify the numerator.

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3 years ago

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