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strojnjashka [21]

3 years ago

14

Jon borrows $6.50 from his friends to pay for snacks, and $11.75 from his sister to go to the movies. how much money does he nee

d to repay

2 answers:

insens350 [35]3 years ago

5 0

That’s easy you add 11.75 + 6.50 first do 5 + 0=5 then 5 + 7 = 12 regroup 6 +1 = 7 +1= 8 and nothing plus 1 is 1 so the answer is $ 18.25

Alex777 [14]3 years ago

3 0

Answer:

Step-by-step explanation:

You need to add $6.50 and $11.75 and you get $18.25.

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Solve for the missing side in the following right triangle: hypotenuse = 17, leg = 8, leg = ?.

krek1111 [17]

Hyp^2 = leg1^2 + leg2^2
hyp^2 -leg1^2 = leg2^2
17^2 - 8^2 = leg2^2
leg2^2 = 289 -64
leg2^2 = 225
leg2 = 15

7 0

3 years ago

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

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

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3 years ago

Ben is making math manipulatives to sell. He wants to make at least $450. Each manipulative costs $18 to make. He is selling the

lys-0071 [83]

7 is the answer because 7 is great and is always the answer

6 0

3 years ago

You win an online auction for a toy. Your winning bid of $52 is 65% of your maximum bid. How much more were you willing to pay f

SpyIntel [72]

Answer:

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Step-by-step explanation:

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3 years ago

Solve the system of linear equations by substitution.<br><br> 4x−2y=14<br> y=12x−1

Alexus [3.1K]

Answer:

The answer is (-0.7, -9.4)

Step-by-step explanation:

1) Since we are using the substitution method, and we know that y = 2x-1, in the first equation, plug that into y. It should look like this:

4x-2(12x-1) = 14

4x -24x + 2 = 14

2) Combine like terms and continue to simplify until you get a direct answer for each variable.

-20x + 2 = 14.

-20x = 12.

x = -7/10 (or -0.7)

3) Now we know what x equals, so to find our y-coordinate, we will plug this into either equation.

y = 12(-7/10) -1

y= -84/10 -1

y= -9.4

4) Now that we have our x value and y value, we know our point. The solution is (-0.7, -9.4).

3 0

3 years ago