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GarryVolchara [31]
3 years ago
6

Find the number of permutations on the first 12 letters taken 3 at a time

Mathematics
1 answer:
Flura [38]3 years ago
6 0
Slot method
12 in 1st slot
11 in 2nd slot
10 in 3rd slot

12*11*10=1210 possible permutations
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What is x? 6x-18+14x+38
evablogger [386]

Answer:

x= -1

Step-by-step explanation:

6x-18+14x+38

group= 20x+20

set equal to 0

20x+20=0

       -20  -20

20x/20= -20/20

x= -1

8 0
3 years ago
How many pounds in an oz
givi [52]
1 oz = 0.0625 lbs or 1/16 lbs

1 lb = 16 oz

Hope I helped!
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3 years ago
Javier shared his post with 4 friends, who each shared it with 4 more friends. They continued sharing at the same rate
Fittoniya [83]

First, 4 people know the post

Then, those 4 people share it each with 4 people (4 * 4 = 16)

Then, each of those people share it with another 4 people (16 * 4 = 64)

And so on. the function is as simple as: 4^x (4 to the power of x)

4 0
3 years ago
3. Let A, B, C be sets and let ????: ???? → ???? and ????: ???? → ????be two functions. Prove or find a counterexample to each o
Fiesta28 [93]

Answer / Explanation

The question is incomplete. It can be found in search engines. However, kindly find the complete question below.

Question

(1) Give an example of functions f : A −→ B and g : B −→ C such that g ◦ f is injective but g is not  injective.

(2) Suppose that f : A −→ B and g : B −→ C are functions and that g ◦ f is surjective. Is it true  that f must be surjective? Is it true that g must be surjective? Justify your answers with either a  counterexample or a proof

Answer

(1) There are lots of correct answers. You can set A = {1}, B = {2, 3} and C = {4}. Then define f : A −→ B by f(1) = 2 and g : B −→ C by g(2) = 4 and g(3) = 4. Then g is not  injective (since both 2, 3 7→ 4) but g ◦ f is injective.  Here’s another correct answer using more familiar functions.

Let f : R≥0 −→ R be given by f(x) = √

x. Let g : R −→ R be given by g(x) = x , 2  . Then g is not  injective (since g(1) = g(−1)) but g ◦ f : R≥0 −→ R is injective since it sends x 7→ x.

NOTE: Lots of groups did some variant of the second example. I took off points if they didn’t  specify the domain and codomain though. Note that the codomain of f must equal the domain of

g for g ◦ f to make sense.

(2) Answer

Solution: There are two questions in this problem.

Must f be surjective? The answer is no. Indeed, let A = {1}, B = {2, 3} and C = {4}.  Then define f : A −→ B by f(1) = 2 and g : B −→ C by g(2) = 4 and g(3) = 4. We see that  g ◦ f : {1} −→ {4} is surjective (since 1 7→ 4) but f is certainly not surjective.  Must g be surjective? The answer is yes, here’s the proof. Suppose that c ∈ C is arbitrary (we  must find b ∈ B so that g(b) = c, at which point we will be done). Since g ◦ f is surjective, for the  c we have already fixed, there exists some a ∈ A such that c = (g ◦ f)(a) = g(f(a)). Let b := f(a).

Then g(b) = g(f(a)) = c and we have found our desired b.  Remark: It is good to compare the answer to this problem to the answer to the two problems

on the previous page.  The part of this problem most groups had the most issue with was the second. Everyone should  be comfortable with carefully proving a function is surjective by the time we get to the midterm.

3 0
3 years ago
PLEASE HELP ASAP PLEASE ANSWER CORRECTLY WILL GET BRAINLIEST
Xelga [282]

Answer:

True

Step-by-step explanation:

Each x input has 1 y output

5 0
3 years ago
Read 2 more answers
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