Answer:
Step-by-step explanation:
Let be the volumes of the smaller and bigger cylinder.
The formula for the volume of a cylinder is given by :
As the two triangles are similar, the cube of their ratio would equal the ratio of their volume i.e.
So, the volume of the smaller cylinder is equal to .
a) Let n represent the number of 1 7/8 ft pieces. Then we have ...
... 16 1/2 ft = n × (1 7/8 ft)
We can find n by dividing this equation by 1 7/8.
... (16 1/2)/(1 7/8) = n = (132/8)/(15/8) = 132/15
... n = 8 12/15 = 8 4/5
The integer number of pieces that can be cut is 8 pieces.
b) The length of the left-over piece is 4/5 of the full length of a piece, so is ...
... (4/5) × (15/8 ft) = 12/8 ft
We want to divide this into 4 equal lengths, so each of those lengths will be 1/4 of the length of the left-over:
... (1/4) × (12/8 ft) = 3/8 ft
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<em>Comment on arithmetic with fractions</em>
This problem is easier if you <em>convert the mixed numbers to improper fractions</em>. This is done by expressing the integer as a number of fractional parts, then adding the fraction part of the mixed number:
... a + b/c = (a×c/c) + b/c = (ac +b)/c
Division with fractions is taught a couple of different ways. One way you can do it is to "invert and multiply". That is, you multiply the numerator fraction by the reciprocal of the denominator fraction:
... (a/b)/(c/d) = (a/b)×(d/c)
Another way you can do the division is to express each of the numerator and denominator fractions over the same denominator. Then the quotient is the ratio of numerators.
... (a/c)/(b/c) = a/b
This is the method we used here. Effectively, we converted 16 1/2 to 16 4/8 then to (16×8 +4)/8 = 132/8. Then the numerator and denominator fractions both had denominators of 8, so (132/8)/(15/8) = 132/15. This fraction can be reduced by removing a factor of 3 from numerator and denominator to give ...
... 132/15 = 44/5 = 8 4/5
Answer:
a. 4.33.
Step-by-step explanation:
If there is only one correct answer out of four alternatives, the expected proportion of correct answers is p =0.25
Sample size (n) = 100 questions
The standard deviation of a proportion 'p' is given by:
Applying the given data:
If X is the number of correct responses in 100 guesses, the standard deviation of X is:
The standard deviation of X is 4.33 questions.