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3 years ago

Round each number to the nearest tenth!

Mathematics

1 answer:

belka [17]3 years ago

3 0

#1-824.1

#2-10,386.1

#3-585.1

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Solve the following exponential equation: 4ˣ - 2ˣ⁺¹ - 8 = 0

aliya0001 [1]

Exponential eqation solution

6 0

3 years ago

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

What is the equation of a line that has an x-intercept of -4 and a y-intercept of 8 ?

podryga [215]

Answer:

y=2/-1+8

Step-by-step explanation:

-4= (-4,0) -4=x1 0=y1, 8= (0,8) 0=x2 8=y2
formula is, y2-y1/x2-x1
8-0/0-4=8/-4=4/-2= 2/-1
2/-1 is the slope or (m), use (-4,0) or (0,8) i used (0,8) because its easier.
(0,8), 0=x1 8=y1
formula is y-y1=m(x-x1)
y-8=2/-1(x-0) ---->distribute
y-8=2/-1x-0 --->get y alone

+8 +8

so the answer is y=2/-1+8

7 0

3 years ago

Based on the line plot, how many batteries lasted more than 5 1/2 hours? *

babunello [35]

Answer:

5 batteries.

Explanation:

"How many batteries lasted more than 5 1/2 hours?" which means it's counting not only 5 1/2, but 5 3/4 and 6 1/4

3 0

3 years ago

Read 2 more answers

3/5 = 12/x find the missing numbers in the equivalent ratios

pogonyaev

Answer:

x=20

Step-by-step explanation:

Well just cross multiply if its easier

x(3)=3x

12*5=60

60=3x

x=20

4 0

2 years ago

Read 2 more answers