It helps immensely if you know the formula for the area of a sphere.
Area of a sphere = (4 π) (radius)² . . . . . for ANY sphere.
If the radius is 5-ft, then Area = (4 π) (5)² = 100 π = 314.16... square feet (rounded)
The length of the field is 48 yard while the width of the field is 16 yards.
My Work/Reasoning:
Say that the width is "x" yards.
![x](https://tex.z-dn.net/?f=x)
The length of the field is three times longer than the width.
![3x](https://tex.z-dn.net/?f=3x)
The perimeter of the rectangle is 128 yards.
![128](https://tex.z-dn.net/?f=128)
To get the perimeter of a rectangle you multiply the sum of the length and the width by two.
![2(x+3x)=128](https://tex.z-dn.net/?f=2%28x%2B3x%29%3D128)
Then you follow order of operations and add x and 3x.
![2*4x=128](https://tex.z-dn.net/?f=2%2A4x%3D128)
Then you multiply.
![8x=128](https://tex.z-dn.net/?f=8x%3D128)
After that, you divide 8 on both sides to get the width (total) in yards.
![x=32](https://tex.z-dn.net/?f=x%3D32)
Then you divide that to get the width.
![32/2=16](https://tex.z-dn.net/?f=32%2F2%3D16)
Finally, to get the length of the field, you multiply the width of the field by three to get its length.
Answer: (x^2+20)(x-4)
Step-by-step explanation:
See attached picture
Answer:
![x = 5](https://tex.z-dn.net/?f=x%20%3D%205)
Step-by-step explanation:
25 - 3x = -5(1 - x) - 2x
<u></u>
<u>We have to first get rid of the parenthesis:</u>
==> -5
==> 5x
<u>So now you should have:</u>
25 - 3x = -5 + 5x - 2x
<u>Combine like terms:</u>
25 - 3x = -5 + 5x - 2x
25 - 3x = -5 + 3x
<u>Add 3x to both sides:</u>
25 - 3x = -5 + 3x
+ 3x = + 3x
<u>And you should have:</u>
25 = -5 + 6x
<u></u>
<u>Add 5 to both sides:</u>
25 = -5 + 6x
+5 = +5
30 = 6x
<u>Divide 6 to both sides:</u>
= ![\frac{6x}{6}](https://tex.z-dn.net/?f=%5Cfrac%7B6x%7D%7B6%7D)
5 = x
Answer:
The probability of getting a black pen from the bag is 13.5%.
Step-by-step explanation:
To determine the percentage probability that a black pen will be obtained from the bag, the following calculation must be performed:
12 + 20 + 5 = 37
37 = 100%
5 = X
(5 x 100) / 37 = X
500/37 = X
13.5 = X
Thus, it is determined that the totality of pens is 100%, and through a cross multiplication the percentage of the 5 black pens with respect to the total of pens is obtained.
Therefore, the probability of getting a black pen from the bag is 13.5%.