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iVinArrow [24]
2 years ago
5

N example 5.4 and exercise 5.5, we considered the joint density of y1, the proportion of the capacity of the tank that is stocke

d at the beginning of the week, and y2, the proportion of the capacity sold during the week, given by f(y1,y2)= 3y1, 0≤y2≤y1≤1, 0, elsewhere. a find the marginal density function for y2. b for what values of y2 is the conditional density f ( y1 | y2 ) defined? c what is the probability that more than half a tank is sold given that three-fourths of a tank is stocked?

Mathematics
1 answer:
Snowcat [4.5K]2 years ago
5 0
See complete work in the attached picture.

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Water is poured into a conical paper cup at the rate of 3/2 in3/sec (similar to Example 4 in Section 3.7). If the cup is 6 inche
aliya0001 [1]

Answer:

The water level rising when the water is 4 inches deep is \frac{3}{8\times \pi} inch/s.

Step-by-step explanation:

Rate of water pouring out in the cone = R=\frac{3}{2} inch^3/s

Height of the cup = h = 6 inches

Radius of the cup = r = 3 inches

\frac{r}{h}=\frac{3 inch}{6 inch}=\frac{1}{2}

r = h/2

Volume of the cone = V=\frac{1}{3}\pi r^2h

V=\frac{1}{3}\pi r^2h

\frac{dV}{dt}=\frac{d(\frac{1}{3}\pi r^2h)}{dt}

\frac{dV}{dt}=\frac{d(\frac{1}{3}\pi (\frac{h}{2})^2h)}{dt}

\frac{dV}{dt}=\frac{1}{3\times 4}\pi \times \frac{d(h^3)}{dt}

\frac{dV}{dt}=\frac{1\pi }{12}\times 3h^2\times \frac{dh}{dt}

\frac{3}{2} inch^3/s=\frac{1\pi }{12}\times 3h^2\times \frac{dh}{dt}

h = 4 inches

\frac{3}{2} inch^3/s=\frac{1\pi }{12}\times 3\times (4inches )^2\times \frac{dh}{dt}

\frac{3}{2} inch^3/s=\pi\times 4\times \frac{dh}{dt} inches^2

\frac{dh}{dt}=\frac{3}{8\times \pi} inch/s

The water level rising when the water is 4 inches deep is \frac{3}{8\times \pi} inch/s.

6 0
2 years ago
Caleb started with 50 bacteria for his science experiment and they doubled in one day. Jenna also started with 50 bacteria for h
MrRa [10]

Answer: B

Step-by-step explanation:

The second power basically means that you multiply the number by itself that many times depending on the power, and since it's 50^2, the answer is Caleb - 100 | Jenna - 2,500. (Tip: Just multiply 50 x 50)

4 0
2 years ago
The parent function f(x) = x3 is transformed to g(x) = (x – 1)3 + 4. Identify the graph of g(x).
Dominik [7]

we have f(x)=x^3 which is a cubic function.

and =(x-1)^3+4.

from f(x) and g(x) we know that both are cubic and g(x) has shrink of 1 and up by 4 units in x axis .

4 0
2 years ago
Read 2 more answers
It is known that 70% of the customers in a sporting goods store purchase a pair of running shoes. a random sample of 25 customer
NikAS [45]

Let x be the discrete random variable whose value is the number of successes in n trials.

The probability distribution function for x of the binomial distribution B(n,p) is defined as

B(n,p)= nC_xp^x(1-p)^{n-x}

Given that the random sample size is n=25

let x represent number of customers who purchase running shoes

Let "p" be the probability of customers in a sporting goods store purchase a pair of running shoes.

It is given that 70% of the customers in a sporting goods store purchase a pair of running shoes.

Thus p=\frac{70}{100}=0.7

Thus the Probability distribution of x is given by

P(X=x)= 25C_x(0.7)^x(1-0.7)^{25-x}, where x=0,1,2,3,...,25.

8 0
2 years ago
Jada invests $590 in a money market account her account pays 7.2% simple interest if she does not add or withdraw any money how
denis-greek [22]

Answer:

$169.92

Step-by-step explanation:

<em>Multiply Yearly Interest By How Many Years</em>

7.2 * 4 = 28.8

<em>Take 28.8 Percent Of Amount Of Money In The Account</em>

28.8 percent of 590 = 169.92

3 0
2 years ago
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