Answer:
B
Step-by-step explanation:
The number of basketball that will fill up the entire office is <u>approximately 16,615.</u>
<em><u>Recall:</u></em>
Volume of a spherical shape = ![\frac{4}{3} \pi r^3](https://tex.z-dn.net/?f=%5Cfrac%7B4%7D%7B3%7D%20%5Cpi%20r%5E3)
Volume of a rectangular prism = ![l \times w \times h](https://tex.z-dn.net/?f=l%20%5Ctimes%20w%20%5Ctimes%20h)
<em><u>Given:</u></em>
Diameter of basketball = 9.5 in.
Radius of the ball = 1/2 of 9.5 = 4.75 in.
Radius of the ball in ft = 0.4 ft (12 inches = 1 ft)
Dimension of the office (rectangular prism) = 20 ft by 18 ft by 12 ft
- First, find the volume of the basketball:
Volume of ball = ![\frac{4}{3} \pi r^3 = \frac{4}{3} \times \pi \times 4.75^3\\](https://tex.z-dn.net/?f=%5Cfrac%7B4%7D%7B3%7D%20%5Cpi%20r%5E3%20%3D%20%5Cfrac%7B4%7D%7B3%7D%20%5Ctimes%20%5Cpi%20%5Ctimes%204.75%5E3%5C%5C)
Volume of basketball = ![448.92 $ in^3](https://tex.z-dn.net/?f=448.92%20%24%20in%5E3)
- Convert to
![ft^3](https://tex.z-dn.net/?f=ft%5E3)
![1728 $ in.^3 = 1 $ ft^3](https://tex.z-dn.net/?f=1728%20%24%20in.%5E3%20%3D%201%20%24%20ft%5E3)
<em>Therefore,</em>
- Volume of basketball =
![\frac{448.92}{1728} = 0.26 $ ft^3](https://tex.z-dn.net/?f=%5Cfrac%7B448.92%7D%7B1728%7D%20%3D%200.26%20%24%20ft%5E3)
- Find the volume of the office (rectangular prism):
Volume of the office = ![20 \times 18 \times 12 = 4,320 $ ft^3](https://tex.z-dn.net/?f=20%20%5Ctimes%2018%20%5Ctimes%2012%20%3D%204%2C320%20%24%20ft%5E3)
- Number of basket ball that will fill the office = Volume of office / volume of basketball
Number of basket ball that will fill the office = ![\frac{4,320}{0.26} = 16,615](https://tex.z-dn.net/?f=%5Cfrac%7B4%2C320%7D%7B0.26%7D%20%3D%2016%2C615)
Therefore, it will take approximately <u>16,615 balls</u><u> to fill up the entire office</u>.
Learn more here:
brainly.com/question/16098833
Answer:
379.56ft²
Step-by-step explanation:
Oh lordy why, okay we got this:
So we're going to start with the area of the square, this is easy because all of the sides are 25ft, so we just have to plug into our formula for squares (base x height):
25 x 25 = 625
Now we have to do the semicircle, remember that the formula for the area of a circle is pi x radius², we're using 3.14 for pi, so we have to find the radius (half the diameter):
25 ÷ 2 = 12.5
12.5² = 156.25
3.14 x 156.25 = 490.625
Normally we would stop here, but because this is only a semicircle, we have to divide by two:
490.625 ÷ 2 = 245.3125
So, now that we have our two areas, we have to subtract the semicircle from the square:
625 - 245.3125 = 379.6875
Now, I realize that his answer isn't in your cute little word bank, but that because I rounded pi, so the closest is 379.56
So, the area of the figure is 379.56ft²
if this is wrong let me know so I can fix it
hope this helps:)
By definition of conditional probability,
![P(B\mid A)=\dfrac{P(B\cap A)}{P(A)}\implies P(B\cap A)=0.2\cdot0.9=0.18](https://tex.z-dn.net/?f=P%28B%5Cmid%20A%29%3D%5Cdfrac%7BP%28B%5Ccap%20A%29%7D%7BP%28A%29%7D%5Cimplies%20P%28B%5Ccap%20A%29%3D0.2%5Ccdot0.9%3D0.18)
Similarly,
![P(A\mid B)=\dfrac{P(A\cap B)}{P(B)}=\dfrac{0.18}{0.3}=0.6](https://tex.z-dn.net/?f=P%28A%5Cmid%20B%29%3D%5Cdfrac%7BP%28A%5Ccap%20B%29%7D%7BP%28B%29%7D%3D%5Cdfrac%7B0.18%7D%7B0.3%7D%3D0.6)
Answer:
3951>3519>3191
Step-by-step explanation:
hope you understood how