The product of two numbers is the same as one of the factors. How can you use properties of multiplication to determine what the
1 answer:
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Answer:
The rectangles that have exactly 100 squares are 1 by 100 4 by 11 and 5 by 8
Step-by-step explanation:
The given parameters are;
A 2 by 3 rectangle contains 8 squares
A 3 by 4 rectangle contains 20 squares
A 4 by 6 rectangle contains 50 squares
We note that the number of squares varies proportionately to the increase in the dimension of the rectangle, that is we have;
2 by 3 rectangle contains 8 squares
3 by 4 rectangle contains 20 squares increase by 12 = 3 × 4
4 by 5 rectangle contains 40 squares increase by 20 = 4 × 5
The number of squares formed can therefore be arranged in a matrix as follows(please see attached matrix);
Column, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11
Row
1
2
3
4
5
6
7
8
9
10
11
It will be observed that after reaching a point where the row and column are equal, (x, x) the rate of increase in the number of squares become constant and equal to x × ((x - 1) × 0.5) + 1) = x × (x + 1)/2
From the matrix, the rectangles that have exactly 100 squares are 1 by 100 4 by 11 and 5 by 8 and there are no more as presented in the attached matrix, the number of squares formed keeps increasing for each column and row added.
There are 19 people total, and groups of four are being asked of us. We can use the formula for permutations or combinations.
Permutations:
Combinations:
Where in both scenarios, there are <em>n</em> objects being chosen at <em>r</em> times.
19 P 4 is 93024
19 C 4 is 3876
It all depends on whether order matters with group placement; if it does, your answer is 93024, if not, then your answer is 3876.
:)
Permutations:
Combinations:
Where in both scenarios, there are <em>n</em> objects being chosen at <em>r</em> times.
19 P 4 is 93024
19 C 4 is 3876
It all depends on whether order matters with group placement; if it does, your answer is 93024, if not, then your answer is 3876.
:)