Answer:
A natural history museum surveyed the people visiting the museum for one month and created a circle graph to show the age of the visitors for that month.
Plzz I need the answers for A
a. Find the number of degrees for each part of the museum visitors graph. (8 points)
Age 18 and under:
Age 19 – 44:
Age 45 – 64:
Age 65 and over:
b. If 5000 people visited the museum during the month the survey was taken, how many visitors were there for each age group? (8 points)
Age 18 and under:
Age 19 – 44:
Age 45 – 64:
Age 65 and over:
Step-by-step explanation:
Answer:
Option B. 0.783 pounds
Step-by-step explanation:
step 1
Find the area of a a 36 inch piece of PVC pipe with an outside diameter of 0.82 inches and an inside diameter of 0.75 inches
The area of a circle is equal to
![A=\pi r^{2}](https://tex.z-dn.net/?f=A%3D%5Cpi%20r%5E%7B2%7D)
we have
![r2=0.82\ in](https://tex.z-dn.net/?f=r2%3D0.82%5C%20in)
![r1=0.75\ in](https://tex.z-dn.net/?f=r1%3D0.75%5C%20in)
assume
![\pi =3.14](https://tex.z-dn.net/?f=%5Cpi%20%3D3.14)
![A=\pi (r2^2-r1^2)](https://tex.z-dn.net/?f=A%3D%5Cpi%20%28r2%5E2-r1%5E2%29)
substitute the values
![A=(3.14)(0.82^2-0.75^2)](https://tex.z-dn.net/?f=A%3D%283.14%29%280.82%5E2-0.75%5E2%29)
![A=0.345086\ in^2](https://tex.z-dn.net/?f=A%3D0.345086%5C%20in%5E2)
step 2
Find the volume of the piece of PVC
Multiply the area by its length
![V=0.345086(36)=12.42\ in^3](https://tex.z-dn.net/?f=V%3D0.345086%2836%29%3D12.42%5C%20in%5E3)
step 3
Find the weight of the piece of PVC
Multiply the volume by its density
The density is ![0.063\frac{lb}{in^3}](https://tex.z-dn.net/?f=0.063%5Cfrac%7Blb%7D%7Bin%5E3%7D)
so
![W=12.42(0.063)=0.783\ lb](https://tex.z-dn.net/?f=W%3D12.42%280.063%29%3D0.783%5C%20lb)
The driver has to drive 20 miles to come back to the starting point directly
Step-by-step explanation:
The driver has driven in the form of two legs on a right-angled triangle where the vertical side (perpendicular) is 12 miles and the horizontal side (base) is 16 miles.
Now as the driver has to return back to the starting point directly, it will form a right-angled triangle making the direct path a hypotenuse
So,
B = 16
P = 12
H = ?
we have to find the hypotenuse
As the triangle is a right angled triangle, we can use the Pythagoras theorem to find the length of hypotenuse So,
![H^2 = B^2 + P^2\\H^2 = (16)^2 + (12)^2\\H^2 = 256+144\\H^2 = 400](https://tex.z-dn.net/?f=H%5E2%20%3D%20B%5E2%20%2B%20P%5E2%5C%5CH%5E2%20%3D%20%2816%29%5E2%20%2B%20%2812%29%5E2%5C%5CH%5E2%20%3D%20256%2B144%5C%5CH%5E2%20%3D%20400)
taking Square root on both sides
![\sqrt{H^2} = \sqrt{400}\\H = 20](https://tex.z-dn.net/?f=%5Csqrt%7BH%5E2%7D%20%3D%20%5Csqrt%7B400%7D%5C%5CH%20%3D%2020)
So
The driver has to drive 20 miles to come back to the starting point directly
Keywords: Pythagoras theorem, Right angled triangle
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