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3 years ago

52.5% of what number is 25.83?

1 answer:

6 0

Given:
25.83 - part
52.5% percentage of the part against the whole

To get the whole number, we need to divide the part by its corresponding percentage.

25.83 ÷ 52.50% = 49.20

49.20 is the whole number wherein 25.83 represents 52.50% of it.

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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

5 0

2 years ago

1)Se considera un cerc si un punct oarecare. Expresiile punct interior cercului, punct pe cerc sau punct exterior textului descr

BaLLatris [955]

Explanation:

Unclear question. But I inferred this to be clear rendering of your question;

1) It is considered a circle and a certain point. The expressions dot inside the circle, dot on circle, or dot outside the text describe the position of a dot relative to a circle. In figure 2 are drawn: a circle C of center O, points on the circle, points outside the circle and points inside the circle. a) Name the points inside the circle; b) Name the points that belong to the circle; c) Name the points outside the circle.

2) Consider any point P and a circle C of center O and radius r. Compare the distance OP with the radius of the circle if: a) The point is inside the circle; b) The point is on the circle; c) The point is outside the circle.

3 0

3 years ago

In 2018, there were about 32 million teenagers (aged 13–17) in the United States. They each sent an average of 1200 text message

Alja [10]

Answer:3.84x10^10

Step-by-step explanation:

32,000,000 teenagers

1200 text messages per month

32,000,000 * 1,200= 38,400,000,000----(scientific notation)-----> 3.84x10^10

3 0

3 years ago

He fourth-grade students at Curtis Estabrook make up 0.3 of all students at the school. What fraction is equivalent to 0.3?

BartSMP [9]

Answer:

3/10

Step-by-step explanation:

fouth grade students at Estrabook make up 0.3 percents of the students at school

The fraction is therefore equivalent to

= 3/10

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3 years ago

Select the equation that is the inverse of the function: f(x)= x-3/5

andrezito [222]

-1(x)= 5x+15inverse of the function

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3 years ago