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brilliants [131]
3 years ago
5

Picture attached. help plz :)

Mathematics
2 answers:
Oksana_A [137]3 years ago
6 0
The answer is B. I need points plsss
dlinn [17]3 years ago
5 0

Answer:

B

Step-by-step explanation:

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The base of a rectangular fish tank measures 18 inches long by 10 inches wide. If it is filled with 1,080 cubic inches of water,
Elena-2011 [213]
V = 18 x 8 x 12 = 1728 cm3 = 1728 ml = 1.729 liters
6 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
Find the original price of a pair of shoes if the sale price is $20 after a 50% discount.
MrMuchimi
The Original Price is $40

Explanation:
50 1 20
—- = — Which means ——
100 2 40

7 0
3 years ago
Circumference (Level 2)
DENIUS [597]

Answer:

d=4.14

Step-by-step explanation:

use the equation d=2r

d=C/π=13/π≈4.13803

4.13803≈4.14

7 0
3 years ago
Read 2 more answers
Please help :(<br> [math]
sergij07 [2.7K]

Hey!

------------------------------------------------

First Equation:

2x + 3 = -7

2x + 3 - 3 = -7 - 3 (Subtract 7 to both sides)

2x = -10

2x/2 = -10/2 (Divide 2 to both sides)

x = -5

------------------------------------------------

Second Equation:

4.5x - 7 = 20

4.5x + (-7) + 7 = 20 + 7 (Add 7 to both sides)

4.5x = 27

4.5x/4.5 = 27/4.5 (Divide 4.5 to both sides)

x = 6

------------------------------------------------

Third Equation:

-3x + 7 = 28

-3x + 7 - 7 = 28 - 7 (Subtract 7 to both sides)

-3x/-3 = 21/-3 (Divide -3 to both sides)

x = -7

------------------------------------------------

Answers:

2x + 3 = -7 → x = -5

4.5x - 7 = 20 → x = 6

-3x + 7 = 28 → x = -7

------------------------------------------------

Hope This Helped! Good Luck!

8 0
3 years ago
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