Hey guys, I'm really stuck with this problem. A dozen golf balls fit inside a box in the shape of a rectangular prism. The golf balls are packed tightly together and they touch the top, bottom and sides of the box. What percentage of the volume within the box is air? Please show work.
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split the box into 12 cubes around each golf ball
nnow find the wasted space that each golf ball wastes around itself since the ratio of the total percent must be the same as the total
so lets say the height of the cubes=2 so therefor volume of each cube=2^3=8
now find the volume of each apere
volume=4/3pir^3
the height=diameter
diameter/2=radius
2/2=1=radius
volumeofsphere=4/3pi1^3
vs=4/3pi1
vs=4/3pi
aprox pi to 3.14
vs=12.56/3
vs=4.18666
so now we have
total space=8
area of ball=4.186666
percent lost=total-areauseed=8-4.18666=3.81333333
so percent lost=lost/total=3.81333/8=0.397/1
percent means parts out of 100
0.397/1 times 100/100=39.7/100=39.7%
so the answer is 39.7% wasted space (aprox 40%)
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Answers
The range of the data set {33.4, 31.7 ,31.3, 35.6, 33.4, 33.5, 38.8, 39.2, 38.8, 33.4, 37.8} is R = 7.9
Given details in the problem :
The data set : 33.4, 31.7 ,31.3, 35.6, 33.4, 33.5, 38.8, 39.2, 38.8, 33.4, 37.8
In statistics, The range is the spread of your data from the lowest to the highest value in the distribution. It is a commonly used measure of variability.
The range is calculated by subtracting the lowest value from the highest value. While a large range means high variability, a small range means low variability in a distribution.
Rearrange the given Data Set : 31.3, , 31.7 , 33.4, 33.4, 33.4, 33.5, 35.6, , 37.8 , 38.8, 38.8, 39.2,
The lowest Value of the data set is 31.3
The Highest value of the data set is 39.2
The formula to calculate the range is:
R =H- L
R = range
H = highest value
L = lowest value
R = 39.2-31.3
R = 7.9
The range of the data set {33.4, 31.7 ,31.3, 35.6, 33.4, 33.5, 38.8, 39.2, 38.8, 33.4, 37.8} is R = 7.9
Learn more about Data Set: brainly.com/question/22210584
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Answers
5x - 5x = 6x² - 5x - 3
0 = 6x² - 5x - 3
x = -(-5) ± √((-5)² - 4(6)(-3))
2(6)
x = 5 ± √(25 + 72)
12
x = 5 ± √(97)
12
x = 5 + √(97) U x = 5 - √(97)
12 12
The value of x are; x = 5 + √(97)/12 and x = 5 - √(97)/12.
What is a quadratic equation?
A quadratic equation is the second-order degree algebraic expression in a variable.
The standard form of this expression is ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.
Given;
5x = 6x² - 3
Subtract 5x on both sides
5x - 5x = 6x² - 5x - 3
0 = 6x² - 5x - 3
x = -(-5) ± √((-5)² - 4(6)(-3)) / 2(6)
x = 5 ± √(25 + 72)/ 12
x = 5 ± √(97)/ 12
The value of x are;
x = 5 + √(97)/12
x = 5 - √(97)/12
Learn more about quadratic equations;
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8y = 6
13y = 13
5y = 13
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8y+6=7+5y
3y+6=7
3y=1
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A=4(3.14)4²
A=(12.56) (16)
A=200.96
You mught want to check over it so you will be able to solve it for yourself the next time you have this question.
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Answer:
Added 19 to each side
Step-by-step explanation:
15x-19=4x+11
Add 19 to each side
5x-19+19=4x+11+19
5x = 4x+30
Answer:
added 19 and 11