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mafiozo [28]
3 years ago
13

Monica deposits $100 into a savings account that pays a simple interest rate of 4.5%, Paul

Mathematics
2 answers:
elixir [45]3 years ago
7 0
Yes she is correct!

Hope this helps!
victus00 [196]3 years ago
4 0

Answer:

yes she is correct

Step-by-step explanation:

because in 1 year it will go up 4.5%

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Nostrana [21]
1)5 2)6 3)17 because h(x)+k(x)=3x-1
6 0
3 years ago
Read 2 more answers
Diego is thinking of two positive numbers. He says, 'If we triple the first number and double the second number, the sum is 34.'
UNO [17]

1st number: 0

2nd number: 17

Answer

Step-by-step explanation:

3x+2y=34 x is the first number, y is the second.

1/2x+2y=34 multiply each number by two to get rid of the integer by the variable x.

x+4y=68 solve for x.

x=68-4y add this into the first equation to solve for variable y.

3(68-4y)+2y=34 solve for y.

204-10y=34

-10y= -170

y=17

now to solve for x

x= 68-4(17)

x= 0

8 0
3 years ago
A flower bed has the shape of a rectangle 5 yards long and 4 yards wide. What is its area in square feet?
aalyn [17]
To find the area, use A= bh (base x height), or A = lw (length x width)

There are 3 feet in 1 yard

3 x 5 = 15
4 x 3 = 12

15 x 12 = 180

The flower bed is 180 ft² 

hope this helps
3 0
3 years ago
You have a bag of marbles. 4 are blue, 3 are red, 2 are green, 2 are yellow are 4 are purple. What is the probability that you p
valkas [14]

Answer:

2/35

Step-by-step explanation:

There are 15 marbles in total.

\frac{4\\}{15} ×\frac{3}{14}

The answer would be \frac{2}{35}.

6 0
2 years ago
Read 2 more answers
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
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