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3 years ago

A cylinder has a diameter of 24 inches. If its height is half its radlus, what is the volume of the cylinder in cubic Inches?

Mathematics

1 answer:

ella [17]3 years ago

4 0

Answer:

about 2714.34 in^3

Step-by-step explanation:

24/2=12--radius

12/2=6--height

formula is V=(pi)(r^2)(h)

r is for radius and h is for height

V=(pi)(12*12)(6)

V=(pi)(144)(6)

V=(pi)(864)

V= about 2714.34 in^3

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Re-write the quadratic function below in Standard Form<br> y=5(x + 1)^2+9

omeli [17]

Answer:

y = 5x^2+10x +14

Step-by-step explanation:

y = 5(x+1)^2+9

= 5(x^2+2x+1)+9

= 5x^2+10x +14

4 0

3 years ago

Please help me. math.

KiRa [710]

Answer:

y =293(1.06) ^x

y = 370 after 4 years

Step-by-step explanation:

If we are using the model for growth

y = a ( 1+b)^x

a is the initial population

b is the increase rate

We can substitute the values into the equation

y =293 (1+.06) ^ x

y =293(1.06) ^x

Let x equal 4 for the 4 years

y = 293(1.06)^4

y=369.9

3 0

3 years ago

Find the average range. Round the mean and the average range to the nearest tenth. (Show all your work on scratch paper, then en

NISA [10]

3, 12, 15, 25, 30, 40The range is the difference between the greatest and smallest values:
range = 40 - 3 = 37

Thee average is the sum of elements divided by the number of elements:
average = (<span>3 + 12 + 15 + 25 + 30 + 40</span>)/6
average = 125/6 = 20.83

4 0

2 years ago

Suppose X, Y, and Z are random variables with the joint density function f(x, y, z) = Ce−(0.5x + 0.2y + 0.1z) if x ≥ 0, y ≥ 0, z

kompoz [17]

$f_{X,Y,Z}(x,y,z)=\begin{cases}Ce^{-(0.5x+0.2y+0.1z)}&\text{for }x\ge0,y\ge0,z\ge0\\0&\text{otherwise}\end{cases}$

is a proper joint density function if, over its support, $f$ is non-negative and the integral of $f$ is 1. The first condition is easily met as long as $C\ge0$ . To meet the second condition, we require

$\displaystyle\int_0^\infty\int_0^\infty\int_0^\infty f_{X,Y,Z}(x,y,z)\,\mathrm dx\,\mathrm dy\,\mathrm dz=100C=1\implies \boxed{C=0.01}$

b. Find the marginal joint density of $X$ and $Y$ by integrating the joint density with respect to $z$ :

$f_{X,Y}(x,y)=\displaystyle\int_0^\infty f_{X,Y,Z}(x,y,z)\,\mathrm dz=0.01e^{-(0.5x+0.2y)}\int_0^\infty e^{-0.1z}\,\mathrm dz$

$\implies f_{X,Y}(x,y)=\begin{cases}0.1e^{-(0.5x+0.2y)}&\text{for }x\ge0,y\ge0\\0&\text{otherwise}\end{cases}$

Then

$\displaystyle P(X\le1.375,Y\le1.5)=\int_0^{1.5}\int_0^{1.375}f_{X,Y}(x,y)\,\mathrm dx\,\mathrm dy$

$\approx\boxed{0.12886}$

c. This probability can be found by simply integrating the joint density:

$\displaystyle P(X\le1.375,Y\le1.5,Z\le1)=\int_0^1\int_0^{1.5}\int_0^{1.375}f_{X,Y,Z}(x,y,z)\,\mathrm dx\,\mathrm dy\,\mathrm dz$

$\approx\boxed{0.012262}$

7 0

3 years ago

a recipe includes 8 cups of flour and two third cups of shortening. write the ratio to the amount of flour to the amount of shor

Paul [167]

8:2/3 because you can't go lower than 2/3

8 0

2 years ago