In this item, we are informed that the order of the entries does not matter in determination the number of ways in which the Archie can choose for his party. Because the arrangement or order is not important, this type of problem uses the concept of COMBINATION.
The equation for combination is,
nCr = n!/((n - r)!(r!))
nCr is read as "combination of n taken r".
Substituting the known values to the equation,
15C6 = 15! / ((15 - 6)!(6!))
= 5005
Hence, there are 5005 ways in which Archee can choose the 6 entrees for his party.
<h3>
Answer: Choice C) 40 </h3>
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Work Shown:
Plug in x = 0
This indicates that (0,1) is on the curve. This is the y intercept.
Do the same for x = 2
So we know that (2,81) is another point on this curve.
We need to find the slope of the line through (0,1) and (2,81) to get the slope of the secant line we want.
The slope of the line through (0,1) and (2,81) is m = 40. This value of m is exactly the slope of the secant line your teacher is asking for. This is why the answer is choice C.
As the variation is direct we have:
We must find the value of k.
For this, we use the following data:
y = 200 when x = 5
Substituting values we have:
Clearing k:
Then, the function is:
We evaluate the function for x = -3
Answer:
the value of y when x = -3 is:
c.
72
A nice riddle, mathematical riddle.
Assuming a turtle winning means the declared winner is the weaker one actually won over the stronger one. In this context, the turtle winner is the one who has a lesser number of favourable votes.
The given rules for the points are as follows:
1. Point for the first choice must be greater than or equal to that of the second choice.
2. All points must be positive whole numbers.
Let's suppose we have Henry against Tim.
Henry is favourite of the voters and is the leading candidate, according to popular polls.
Tim is an excellent manipulator, sly, and everybody knows this.
On polling day, the vote count came out as follows (in point counts)
Henry Tim
2 1
2 1
2 1
2 1
2 1
2 1
10 1 (Henry's own vote)
1 100 (Tim's own vote)
------------------
17 107 TOTAL POINTS
So Tim the turtle was declared winner of the race, and since everything was according to rule, even a recount of the votes did not change the results.
Be aware, voting by districts (instead of popular votes) also exhibits a similar problem.
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