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Alchen [17]
3 years ago
13

Rena evaluated 3/4 ÷ 2/5 and got an answer of 1 7/8. Which statement is true about her answer

Mathematics
1 answer:
hammer [34]3 years ago
3 0

Rena's answer is correct.

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Determine whether each of these sets is finite, countably infinite, or uncountable. For those that are countably infinite, exhib
anzhelika [568]

Answer:

a) Countably infinite

b) Countably infinite

c) Finite

d) Uncountable

e) Countably infinite

Step-by-step explanation:

a) Let S the set of integers grater than 10.

Consider the following correspondence:

f: S\rightarrow \mathbb{Z}^+ defined by f(10+k)=k-1 for k\in\mathbb{Z}^+/\{0\}.

Let's see that the function is one-to-one.

Suppose that f(10+k)=f(10+j) for k≠j. Then k-1=j-1. Thus k-j=1-1=0. Then k=j. This implies that 10+k=10+j. Then the correspondence is injective.

b) Let S the set of odd negative integers

Consider the following correspondence:

f: S\rightarrow \mathbb{Z}^+ defined by f(-(2k+1))=k.

Let's see that the function is one-to-one.

Suppose that f(-(2k+1))=f(-(2j+1)) for k≠j. By definition, k=j. This implies that the correspondence is injective.

c) The integers with absolute value less than 1,000,000 are in the intervals A=(-1.000.000, 0) B=[0, 1.000.000). Then there is 998.000 integers in A that satisfies the condition and 999.000 integers in B that satifies the condition.

d) The set of real number between 0 and 2 is the interval (0,2) and you can prove that the interval (0,2) is equipotent to the reals. Then the set is uncountable.

e) Let S the set A×Z+ where A={2,3}

Consider the following correspondence:

f: S\rightarrow \mathbb{Z}^+ defined by f(2,k)=2k, \;f(3,j)= 2j+1

Let's see that the function is one-to-one.

Consider three cases:

1. f(2,k)=f(2,j), then 2k=2j, thus k=j.

2. f(3,k)=f(3,j), then 2k+1=2j+1, then 2k=2j, thus k=j.

3.  f(2,k)=f(3,j), then 2k=2j+1. But this is impossible because 2k is an even number and 2j+1 is an odd number.

Then we conclude that the correspondence is one-to-one.

6 0
3 years ago
Gcf of 18m x 18m and 7m
IrinaVladis [17]
The Gcf of 18m x 18m and 7m is 1
6 0
3 years ago
How to divide different bases with same exponents.
Svetllana [295]
How to Divide Exponents With Different Bases:

Different Bases and Same Exponent. In this case, you can group the two bases into a quotient and apply the exponent. ...


Different Bases and Different Exponents. The expression b^4 / a^2 is equivalent to (b * b * b * b) / (a * a). ...

Order of Operations
7 0
2 years ago
What is the answer to -3/4+1/8 in simplest form?
Over [174]
Here are the steps. I hope I do them easy enough for you to understand it 

-3/4+1/8
=-3/4+1/8
=-6/8+1/8
=6+1
 -------
    8

And the answer  is -5/8 (The decimal is -0.625)

I hoped I helped :)
5 0
3 years ago
Please help me branniest <br><br><br> Any answer without proof will be reported
Ghella [55]

There Is one solution because there only one point of the line that intercept.

4 0
3 years ago
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