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borishaifa [10]
2 years ago
9

What is the unit price of a quart of milk for $0.89?

Mathematics
1 answer:
astraxan [27]2 years ago
7 0

Answer:

$3.65/gallon APEX

Step-by-step explanation:

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Suppose that Y has density function
zvonat [6]

I'm assuming

f(y)=\begin{cases}ky(1-y)&\text{for }0\le y\le1\\0&\text{otherwise}\end{cases}

(a) <em>f(x)</em> is a valid probability density function if its integral over the support is 1:

\displaystyle\int_{-\infty}^\infty f(x)\,\mathrm dx=k\int_0^1 y(1-y)\,\mathrm dy=k\int_0^1(y-y^2)\,\mathrm dy=1

Compute the integral:

\displaystyle\int_0^1(y-y^2)\,\mathrm dy=\left(\frac{y^2}2-\frac{y^3}3\right)\bigg|_0^1=\frac12-\frac13=\frac16

So we have

<em>k</em> / 6 = 1   →   <em>k</em> = 6

(b) By definition of conditional probability,

P(<em>Y</em> ≤ 0.4 | <em>Y</em> ≤ 0.8) = P(<em>Y</em> ≤ 0.4 and <em>Y</em> ≤ 0.8) / P(<em>Y</em> ≤ 0.8)

P(<em>Y</em> ≤ 0.4 | <em>Y</em> ≤ 0.8) = P(<em>Y</em> ≤ 0.4) / P(<em>Y</em> ≤ 0.8)

It makes sense to derive the cumulative distribution function (CDF) for the rest of the problem, since <em>F(y)</em> = P(<em>Y</em> ≤ <em>y</em>).

We have

\displaystyle F(y)=\int_{-\infty}^y f(t)\,\mathrm dt=\int_0^y6t(1-t)\,\mathrm dt=\begin{cases}0&\text{for }y

Then

P(<em>Y</em> ≤ 0.4) = <em>F</em> (0.4) = 0.352

P(<em>Y</em> ≤ 0.8) = <em>F</em> (0.8) = 0.896

and so

P(<em>Y</em> ≤ 0.4 | <em>Y</em> ≤ 0.8) = 0.352 / 0.896 ≈ 0.393

(c) The 0.95 quantile is the value <em>φ</em> such that

P(<em>Y</em> ≤ <em>φ</em>) = 0.95

In terms of the integral definition of the CDF, we have solve for <em>φ</em> such that

\displaystyle\int_{-\infty}^\varphi f(y)\,\mathrm dy=0.95

We have

\displaystyle\int_{-\infty}^\varphi f(y)\,\mathrm dy=\int_0^\varphi 6y(1-y)\,\mathrm dy=(3y^2-2y^3)\bigg|_0^\varphi = 0.95

which reduces to the cubic

3<em>φ</em>² - 2<em>φ</em>³ = 0.95

Use a calculator to solve this and find that <em>φ</em> ≈ 0.865.

8 0
3 years ago
What is the surface area of the cylinder with height 7 ft and radius 3 ft? Round your answer to the nearest thousandth.​
Vlada [557]
Area = 2 π r 2 + 2 π r h
where:
π is Pi, approximately 3.142
r is the radius of the cylinder
h height of the cylinder
3 0
3 years ago
How much longer do the turkey need to cook
Alenkasestr [34]
1 hour!!!!!!!!!!! Well the full amount a turkey needs to cook is 15minutes per pound
4 0
3 years ago
Read 2 more answers
Plz help me .. I am really stumped!!!!!!! part of the set for a play is a big triangular piece of plywood. the area of the trian
saul85 [17]
The way to find the area of a triangle is A=\frac{B*H}{2}
if the base is 3 feet longer then the height we can write it like this B=H+3

now we can add it to our area equation
20=\frac{H(H+3)}{2}
20=\frac{ h^{2} +3h}{2}
40=H^{2}+3H
10\frac{1}{3}=H^{2}
h=3.2ft

3 0
3 years ago
10 to the zero power times 0.23=
Lana71 [14]
The answer is 0.23. Ned an explanation
5 0
3 years ago
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