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3 years ago

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Cathryn went on a 3 day round trip hike at Matterhorn Peak Mountain. The first day she hiked 3 miles. The second day she hiked 2

1⁄2 miles and the last day she hiked 3 miles. How many feet did she hike?

1 answer:

Nitella [24]3 years ago

7 0

44,880 feet because there are 5280ft in a mile so you do: 5280(3) + 5280(2.5) + 5280(3) = 44,880

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Luke bought 256 ounces of strawberries. he divided them evenly between 8 different pies.

pychu [463]

Answer:

2 pounds.

Step-by-step explanation:

We have been given that Luke bought 256 ounces of strawberries. He divided them evenly between 8 different pies. We are asked to find the pounds of strawberries that Luke put on each pie.

First of all, we will convert 256 ounces into pounds.

We know that 1 pound equals 16 ounces. To convert 256 ounces into pounds, we need to divide 256 by 16.

$256$ $ounces=\frac{256}{16}$ $pounds=16$ $pounds$

Now we will divide 16 pounds by 8 to find number of strawberries put on each pie.

$Pounds$ $of$ $strawberries$ $on$ $each$ $pie=\frac{16}{8}$

$Pounds$ $of$ $strawberries$ $on$ $each$ $pie=2$

Therefore, Luke put 2 pounds strawberries on each pie.

3 0

3 years ago

When 60% of a number is added to the number, the result is 208<br>

NNADVOKAT [17]

Answer:

x=120

CK

0.60*120=72

120+72=192

192=192

Hope this helps

Step-by-step explanation:

THE ANSWER IS 192

6 0

3 years ago

John buys a computer with a 20% discount. If he paid $760 for the computer, how much was the discount?

Mumz [18]

If there was 20% taken off you add 20% back on and that is how you will get your answer. So take 760 plus the 20% which gives you 912 dollars

8 0

3 years ago

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The lifetime X (in hundreds of hours) of a certain type of vacuum tube has a Weibull distribution with parameters α = 2 and β =

stich3 [128]

I'm assuming $\alpha$ is the shape parameter and $\beta$ is the scale parameter. Then the PDF is

$f_X(x)=\begin{cases}\dfrac29xe^{-x^2/9}&\text{for }x\ge0\\\\0&\text{otherwise}\end{cases}$

a. The expectation is

$E[X]=\displaystyle\int_{-\infty}^\infty xf_X(x)\,\mathrm dx=\frac29\int_0^\infty x^2e^{-x^2/9}\,\mathrm dx$

To compute this integral, recall the definition of the Gamma function,

$\Gamma(x)=\displaystyle\int_0^\infty t^{x-1}e^{-t}\,\mathrm dt$

For this particular integral, first integrate by parts, taking

$u=x\implies\mathrm du=\mathrm dx$

$\mathrm dv=xe^{-x^2/9}\,\mathrm dx\implies v=-\dfrac92e^{-x^2/9}$

$E[X]=\displaystyle-xe^{-x^2/9}\bigg|_0^\infty+\int_0^\infty e^{-x^2/9}\,\mathrm x$

$E[X]=\displaystyle\int_0^\infty e^{-x^2/9}\,\mathrm dx$

Substitute $x=3y^{1/2}$ , so that $\mathrm dx=\dfrac32y^{-1/2}\,\mathrm dy$ :

$E[X]=\displaystyle\frac32\int_0^\infty y^{-1/2}e^{-y}\,\mathrm dy$

$\boxed{E[X]=\dfrac32\Gamma\left(\dfrac12\right)=\dfrac{3\sqrt\pi}2\approx2.659}$

The variance is

$\mathrm{Var}[X]=E[(X-E[X])^2]=E[X^2-2XE[X]+E[X]^2]=E[X^2]-E[X]^2$

The second moment is

$E[X^2]=\displaystyle\int_{-\infty}^\infty x^2f_X(x)\,\mathrm dx=\frac29\int_0^\infty x^3e^{-x^2/9}\,\mathrm dx$

Integrate by parts, taking

$u=x^2\implies\mathrm du=2x\,\mathrm dx$

$\mathrm dv=xe^{-x^2/9}\,\mathrm dx\implies v=-\dfrac92e^{-x^2/9}$

$E[X^2]=\displaystyle-x^2e^{-x^2/9}\bigg|_0^\infty+2\int_0^\infty xe^{-x^2/9}\,\mathrm dx$

$E[X^2]=\displaystyle2\int_0^\infty xe^{-x^2/9}\,\mathrm dx$

Substitute $x=3y^{1/2}$ again to get

$E[X^2]=\displaystyle9\int_0^\infty e^{-y}\,\mathrm dy=9$

Then the variance is

$\mathrm{Var}[X]=9-E[X]^2$

$\boxed{\mathrm{Var}[X]=9-\dfrac94\pi\approx1.931}$

b. The probability that $X\le3$ is

$P(X\le 3)=\displaystyle\int_{-\infty}^3f_X(x)\,\mathrm dx=\frac29\int_0^3xe^{-x^2/9}\,\mathrm dx$

which can be handled with the same substitution used in part (a). We get

$\boxed{P(X\le 3)=\dfrac{e-1}e\approx0.632}$

c. Same procedure as in (b). We have

$P(1\le X\le3)=P(X\le3)-P(X\le1)$

and

$P(X\le1)=\displaystyle\int_{-\infty}^1f_X(x)\,\mathrm dx=\frac29\int_0^1xe^{-x^2/9}\,\mathrm dx=\frac{e^{1/9}-1}{e^{1/9}}$

Then

$\boxed{P(1\le X\le3)=\dfrac{e^{8/9}-1}e\approx0.527}$

7 0

3 years ago

What is the measure of angle BJL

Harrizon [31]

Its f ok i hope it helps

6 0

3 years ago

Read 2 more answers