Answer
A ratio is a comparison of two quantities by division. Ratios describe a part-to-part comparison or a part-to-whole comparison. Ratios are written three ways: as a fraction, with a colon, and with the word “to.” The ratio for quantity a to quantity b is : a to b, a over b, and a:b
Since A = bh
and A = 198 and b = 18?
h = A/b
= 198/18
= 11
Answer:
A. see below for a graph
B. f(x, y) = f(0, 15) = 90 is the maximum point
Step-by-step explanation:
A. See below for a graph. The vertices are those defined by the second inequality, since it is completely enclosed by the first inequality: (0, 0), (0, 15), (10, 0)
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B. For f(x, y) = 4x +6y, we have ...
f(0, 0) = 0
f(0, 15) = 6·15 = 90 . . . . . the maximum point
f(10, 0) = 4·10 = 40
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<em>Comment on evaluating the objective function</em>
I find it convenient to draw the line f(x, y) = 0 on the graph and then visually choose the vertex point that will put that line as far as possible from the origin. Here, the objective function is less steep than the feasible region boundary, so vertices toward the top of the graph will maximize the objective function.
Answer:
49
Step-by-step explanation:
2 quarters
1 quarter, 2 dimes, 1 nickel
1 quarter, 1 dime, 3 nickels
1 quarter, 5 nickels
5 dimes
4 dimes, 2 nickels
3 dimes, 4 nickels
2 dimes, 6 nickels
1 dime, 8 nickels
10 nickels
10 ways without pennies. Pennies can be substituted for any quarter, dime, or nickel, so ...
8 ways to have 5 pennies
7 ways to have 10 pennies
6 ways to have 15 pennies
5 ways to have 20 pennies
4 ways to have 25 pennies
3 ways to have 30 pennies
2 ways to have 35 pennies
2 ways to have 40 pennies
1 way to have 45 pennies
1 way to have 50 pennies
For an additional 39 ways with pennies.
There are a total of 10 +39 = 49 ways to make change for 50¢.
1. They are tje only common factor
