<h3>
Answer: 210/216</h3>
This reduces to 35/36
I didn't reduce because the given fraction 6/216 wasn't fully reduced either.
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Explanation:
There are 6 faces to one cube. So that's where the first 6 in 6/216 comes from.
The 216 is from the fact that 6*6*6 = 216 representing all the ways to roll 3 dice.
6 of those 216 ways have all three numbers match up, so the remaining 216-6 = 210 ways have the numbers not matching up. We could have all three numbers different, or only two match but the third doesn't match.
So that's why the answer is 210/216. To reduce this, you would divide each part by the GCF 6 to get 35/36. The original fraction 6/216 reduces to 1/36. Notice how 35/36 and 1/36 combine to 36/36 = 1.
<h3>
Answer: 14</h3>
Explanation:
Pick two columns from the table to form the (x,y) points.
I'll pick the last two columns, since everything is positive here. So we have the points (2, 17) and (4, 45)
Apply the slope formula to those points
m = (y2 - y1)/(x2 - x1)
m = (45 - 17)/(4 - 2)
m = (28)/(2)
m = 14
The rate of change is 14.
For this you're going to want to whip out your calculator.
make sure it is in degrees instead of radians
plug in tan^-1(-3.4141)
it should equal about -73.674
to change that to be between 0 and 360
360 - 73.674 ≈ 286.325
Volume of the 1st package : 8.5x11x2 =187 in³
Volume of the 2nd package = 17.5x12x10 = 2,100 in³
Number of packages that fit = V₂/V₁ = 2100/187 = 11.23 Packages