A.) Since there are no restrictions as to the dimensions of the candle except that their volumes must equal 1 cubic foot and that each must be a cylinder, we have the freedom to decide the candles' dimensions.
I decided to have the candles equal in volume. So, 1 cubic foot divided by 8 gives us 0.125 cubic foot, 216 in cubic inches.
With each candle having a volume of 216 cubic inches, I assign a radius to each: 0.5 in, 1.0 in, 1.5 in, 2.0 in, 2.5 in, 3.0 in, 3.5 in, and 4.0 in. Then, using the formula of the volume of a cylinder, which is:
V=pi(r^2)(h)
we then solve the corresponding height per candle. Let us let the value of pi be 3.14.
Hence, we will have the following heights (expressed to the nearest hundredths) for each of the radius: for
r=2.5 in: h=11.01 in
r=3.0 in: h= 7.64 in
r=3.5 in: h= 5.62 in
r=4.0 in: h= 4.30 in
r=4.5 in: h= 3.40 in
r=5.0 in: h= 2.75 in
r=5.5 in: h= 2.27 in
r=6.0 in: h= 1.91 in
b. each candle should sell for $15.00 each
($20+$100)/8=$15.00
c. yes, because the candles are priced according to the volume of wax used to make them, which in this case, is just the same for all sizes
The method of successive differences uses subtraction to the one number to the next and the process goes on until the difference settles constant which is not equal to zero. In this case, the constant difference reaches 25. Reversing the process to get the next term, the answer is 2509.
There would be 8 ones, 4 fives, 12 tens, and 4 twenties. That together would be about $228
So average is of the first 6 tests is 82 well that means
(test1 + test2+ test3+ test4 + test5+test6)/6 = 82
so now let do some cross multiplliying
test1 + test2 + test3 + test 4 + test5 +test6 = 82*6
test1 + test2 + test3 + test 4 + test5 +test6 = 492
now lets see if we can find that 7th test score
(test1 + test2 + test3 + test4 + test5 +test6 + test7)/7 = 80.5
So look we found test1 + test2 + test3 + test4 + test5 +test6 to be 492 so lets substitute.
(492 + test7 )/7 = 80.5
test7 = (80.5*7)-492 = 71.5
