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Alla [95]
3 years ago
14

Change 1/4 to a decimal, then a percent. 0.25, 2.5% 2.5, 25% 0.25, 0.25% 0.25, 25%

Mathematics
2 answers:
777dan777 [17]3 years ago
6 0
1/4 to a decimal 0.25
to a percent is 25%
Viefleur [7K]3 years ago
4 0

Answer:  The correct option is (D) 0.25, 25%.

Step-by-step explanation:  We are given to change \dfrac{1}{4} to a decimal and then to a percent.

We have

\dfrac{1}{4}=0.25.

And, to convert into percent, we must multiply a number by 100%.

Therefore, the percent form of the given number is

\dfrac{1}{4}=\dfrac{1}{4}\times 100\%=25\%.

Thus, the decimal form is 0.25 and the percent form is 25%.

Option (D) is CORRECT.

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Step-by-step explanation:

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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
A huge Ping-Pong tournament is held in Beijing with 65,536 participants at the start of the tournament. Each round of
lisabon 2012 [21]

Answer:

After 16 rounds the champion of Ping-Pong player can be determined.

Step-by-step explanation:

This is an example of geometric progression,

First term = 65,536

\texttt{Common ratio = }\frac{1}{2}

Now we need to find which term is 1 in this GP.

N th term of GP is given by

             t_n=ar^{n-1}

Substituting

               1=65536\times \left ( \frac{1}{2}\right )^{n-1}\\\\\frac{1}{65536}=\left ( \frac{1}{2}\right )^{n-1}\\\\2^{n-1}=65536\\\\2^{n-1}=2^{16}\\\\n=17

Seventeenth term of this GP is 1.

That is after 16 rounds the champion of Ping-Pong player can be determined.

3 0
3 years ago
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