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3 years ago

Mr. popper needs to build an icebox for his penguin. the length is 7 ft and the width is 5 ft. what is the area of the icebox?

1 answer:

6 0

Assuming he is constructing a rectangular icebox base, the formula for the area is length times width.

area = 7 ft x 5 ft = 35 ft²

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A carousel horse travels on a circular path with a radius of 15 ft. How many feet does the horse travel over an angle of 2π3 rad

aleksandr82 [10.1K]

Answer:

The horse travels 31 feet over an angle of $\frac{2\pi }{3}$ radians

Step-by-step explanation:

The formula of the length of an arc is L = $\frac{x}{360}$ × 2πr, where x is the central angle subtended by this arc and r is the radius of the circle
To change the angle from radian measure to degree measure multiply it by $\frac{180}{\pi }$

∵ A carousel horse travels on a circular path

- That means the distance that the horse travels is the length

of an arc of the circular path

∵ The radius of the circular path is 15 feet

∴ r = 15 ft

∵ The horse travel over an angle of $\frac{2\pi }{3}$ radians

- Let us change it to degree by multiply it by $\frac{180}{\pi }$

∵ $\frac{2\pi }{3}$ × $\frac{180}{\pi }$ = $\frac{360}{3}$ = 120°

- use the formula above to find the distance

∵ d = $\frac{x}{360}$ × 2πr

∵ x = 120°

∴ d = $\frac{120}{360}$ × 2π × 15

∴ d = 10π

∴ d = 31.41592654 feet

- Round it to the nearest foot

∴ d = 31 feet

The horse travels 31 feet over an angle of $\frac{2\pi }{3}$ radians

4 0

4 years ago

:Phil’s age decreased by 9 years is 14 years ?

Crank

Answer:

Phil is 23

Step-by-step explanation:

Add 14 to 9 and you get 23. So then you subtract 9 from 23

8 0

3 years ago

What integer multiplied by negative 4 gives negative 32

Salsk061 [2.6K]

8
8 multiplied by -4 gives -32

8 0

3 years ago

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Helpppp asapppppppppppppp 15 points

Marizza181 [45]

Answer:

Last one

Step-by-step explanation:

17 times 3 is 51

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3 years ago

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Let X have the uniform distribution U(0, 2) and let the conditional distribution of Y , given that X = x, be U(0, x). Find the j

Elina [12.6K]

Answer:

$f(x,y) = \frac{1}{x} \frac{1}{2}= \frac{1}{2x} , 0\leq x \leq 2 , 0\leq y \leq x$

$E(Y|x) = \int_{x=y}^2 y \frac{1}{x} dx= y ln x \Big|_{x=y}^2 =y ln 2 -y ln y = y(1-lny) \$

Step-by-step explanation:

We have two random variables X and Y. $X \sim Unif(0,2)$ and given that X=x, Y has uniform distribution (0,x)

From the definition of the uniform distribution we have the densities for each random variable given by:

$f_X (x) =\frac{1}{2} , 0\leq x\leq 2$

$f_{Y|X} (y|x) = \frac{1}{x}, 0\leq y \leq x$

And on this case we can find the joint density with the following formula:

$f(x,y) = f_{Y|X}(y|x) f_X (x)$

And multiplying the densities we got this:

$f(x,y) = \frac{1}{x} \frac{1}{2}= \frac{1}{2x} , 0\leq x \leq 2 , 0\leq y \leq x$

Now with the joint density we can find the expected value E(Y|x) with the following formula:

$E(Y|x) = \int y f_{Y|X}(y|x)dx$

And replacing we got:

$E(Y|x) = \int_{x=y}^2 y \frac{1}{x} dx= y ln x \Big|_{x=y}^2 =y ln 2 -y ln y = y(1-lny) \$

5 0

4 years ago