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3 years ago

9

bone-shaped treats are five for 3:50 at Shelly store in Sarah wants to buy 12 she set up and solve this proportion to find how m

uch they would cost describe her error and find the correct solution

2 answers:

Travka [436]3 years ago

4 0

Sarah multiplied the denominator by the denominator and the numerator by the numerator instead of finding the cross products. The equation should be 5x = 42, so the cost should be $8.40.

Valentin [98]3 years ago

3 0

Answer:

8.4 dollars

Step-by-step explanation:

The error is in the resolution of the proportion. In fact, the initial proportion is correct:

$\frac{5}{3.5}=\frac{12}{x}$

where x is the total cost. However, the following step of the resolution is wrong. In fact, the correct resolution is the following:

- Multiplying by x on both sides:

$\frac{5x}{3.5}=12$

- Multiplying by 3.5 no both sides:

$5 x = 12 \cdot 3.5 \\5x = 42$

And now we can find x:

$x=\frac{42}{5}=8.4$

So, the total cost is 8.4 dollars.

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

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

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

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

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

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

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

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

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

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

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Answer:

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Step-by-step explanation:

It's very simple actually!

<u>All you need to do is subtract 32:</u>

58 - 32 = 26

<u>Then divide:</u>

<u />

26 ÷ 2 = 13

13 is Rudy's age. Let's find her father's age!

<u>We then add 32 back to 13:</u>

32 + 13 = 45

And there you have it!

Hope this helped! :)

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