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kati45 [8]
3 years ago
11

Based on the first two questions, which is larger.. f(n) or f(n-1)?

Mathematics
1 answer:
Darina [25.2K]3 years ago
7 0

i would go with f(n)

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Jasper is giving four non-collinear points. How many different triangles can he draw using these points?
kotegsom [21]

Answer:

4

Step-by-step explanation:

There are 4 ways to ignore one of the points. The other 3 can be connected to form a triangle.

_____

More formally, the number of ways that 4 items can be chosen 3 at a time is given by ...

... C(4, 3) = 4!/(3!(4-3)!) = 4/1 = 4

8 0
3 years ago
The only contents of a container are 10 disks that are each numbered with a different positive integer from 1 through 10, inclus
allsm [11]

First we calculate for the total number of possibilities (permutation) to select 4 disks from the container:

Total number of possibilities = 10 * 9 * 8 * 7

Total number of possibilities = 5040

<span>
Now let us find the 4 disks that will result in a range of 7. </span>

Range = highest number – lowest number

The pair of highest and lowest number that will result in range of 7 is: (1 & 8), (2 & 9), (3 & 10)

 

As a basis of calculation, let us use the pair 1 & 8.

There are four possible ways to select 1 and three for 8.

Arrangements of maximum and minimum pair = 4 * 3

Arrangements of maximum and minimum pair=12

Now we need to calculate for the remaining 2 disk. There are 6 numbers between 1 & 8. The total possibilities for selecting 2 disk from the remaining 6 is:

Possibilities of selecting 2 disk from remaining 6 = 6 * 5

Possibilities of selecting 2 disk from remaining 6 = 30

Therefore, the total possibility to get a range of 7 from a pair of 1 & 8 is:

Total possibility for a pair = 12 * 30

Total possibility for a pair = 360

 

Since there are a total of three pairs (1 & 8), (2 & 9), (3 & 10):

Total possibilities of the 3 pairs = 360 * 3

Total possibilities of the 3 pairs = 1080

 

Therefore:

Probability = Total possibilities of the 3 pairs / Total number of possibilities

<span>Probability = 1080 / 5040 = 3 / 14                      (FINAL ANSWER)</span>

6 0
3 years ago
Prove by contradiction that the interval (a,<br> b.has no minimum element.
Snowcat [4.5K]

Assume (a,b) has a minimum element m.


m is in the interval so a < m < b.


a < m


Adding a to both sides,


2a < a + m


Adding m to both sides of the first inequality,


a + m < 2m


So


2a < a+m < 2m


a < (a+m)/2 < m < b


Since the average (a+m)/2 is in the range (a,b) and less than m, that contradicts our assumption that m is the minimum. So we conclude there is no minimum since given any purported minimum we can always compute something smaller in the range.


8 0
3 years ago
Factor the expression x^4+6x-7 completely
melisa1 [442]
(x-1)(x^3+x^2+x+7) is your answer.
5 0
3 years ago
laura deposits $2000 into an account that pays simple interest at a rate of 2% per year. How much interest will she be paid in t
vladimir2022 [97]
She will be paid $2,240.

The equation to use for this is: A=P(1+rt)

More specifically:
A = 2000(1 + (0.02 × 6)) = 2240
A = $2,240.00
5 0
3 years ago
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