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7nadin3 [17]
3 years ago
12

Can somebody check to see if these are right? THANK YOU!!

Mathematics
2 answers:
PIT_PIT [208]3 years ago
8 0
The first one should be x - y <= 25. Since there are 25 OR fewer available, depending on who is out sick or on vacation.
Fed [463]3 years ago
3 0
Those answers are correct cause i did that before.

Hope this Helped!

;D
Brainliest??
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Iodine-125 has a half-life of about 60 days. How many milligrams of a 1000 mg sample will remain after 240 days?
Tomtit [17]

240 days is 4 times the half-life, which means that a sample of 1000 mg will decay to

\dfrac{1000}{2^4}=\dfrac{125}2=62.5\,\mathrm{mg}

after 240 days.

3 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 ILL GIVE BRAINLIEST!!!! AND WORTH MORE THEN 10 POINTS
Tanzania [10]

Answer: 27 ft

Step-by-step explanation:

Given

the angle of elevation is \theta =4^{\circ}

Length of track is L=387\ ft

Vertical rise is given by

\Rightarrow \sin (4^{\circ})=\dfrac{H}{387}\\\\\Rightarrow H=387\sin (4^{\circ})=26.99\approx 27\ ft

4 0
3 years ago
Circle S is shown. Line segment R T is a diameter. The length of S T is 4. Sector R S T is shaded. The measure of central angle
ad-work [718]

Answer: 8π (Option B)

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
What is 0.12 with12 repeating
Ilya [14]

Answer:

4/33

Step-by-step explanation:

We seek to find the repeating decimal 0.121212... in the form of a fraction.

First, set x equal to this decimal:

x = 0.121212...

Multiply both sides by 100:

100x = 12.121212....

Now, let's subtract the original equation from this new one:

    100x = 12.121212....

-    x = 0.121212....

We realize that since the repeating decimal part goes on forever, we can simply cancel it out when we subtract. So we're left with:

100x - x = 12 - 0

99x = 12

Divide both sides by 99:

x = 12/99 = 4/33

The answer is 4/33.

<em>~ an aesthetics lover</em>

7 0
3 years ago
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