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3 years ago

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4 roommates share the cost of $108 of the electric bill evenly. What is the fraction to represent the division and classify each

result by indicating the set or sets to which it belongs.

1 answer:

GrogVix [38]3 years ago

8 0

108/4 = 27 so $27 is what each roommate needs to pay for the electric bill

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Daniel [21]

Answer:

Step-by-step explanation:

As the statement is ‘‘if and only if’’ we need to prove two implications

$f : X \rightarrow Y$ is surjective implies there exists a function $h : Y \rightarrow X$ such that $f\circ h = 1_Y$ .
If there exists a function $h : Y \rightarrow X$ such that $f\circ h = 1_Y$ , then $f : X \rightarrow Y$ is surjective

Let us start by the first implication.

Our hypothesis is that the function $f : X \rightarrow Y$ is surjective. From this we know that for every $y\in Y$ there exist, at least, one $x\in X$ such that $y=f(x)$ .

Now, define the sets $X_y = \{x\in X: y=f(x)\}$ . Notice that the set $X_y$ is the pre-image of the element $y$ . Also, from the fact that $f$ is a function we deduce that $X_{y_1}\cap X_{y_2}=\emptyset$ , and because $f$ the sets $X_y$ are no empty.

From each set $X_y$ choose only one element $x_y$ , and notice that $f(x_y)=y$ .

So, we can define the function $h:Y\rightarrow X$ as $h(y)=x_y$ . It is no difficult to conclude that $f\circ h(y) = f(x_y)=y$ . With this we have that $f\circ h=1_Y$ , and the prove is complete.

Now, let us prove the second implication.

We have that there exists a function $h:Y\rightarrow X$ such that $f\circ h=1_Y$ .

Take an element $y\in Y$ , then $f\circ h(y)=y$ . Now, write $x=h(y)$ and notice that $x\in X$ . Also, with this we have that $f(x)=y$ .

So, for every element $y\in Y$ we have found that an element $x\in X$ (recall that $x=h(y)$ ) such that $y=f(x)$ , which is equivalent to the fact that $f$ is surjective. Therefore, the prove is complete.

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2 years ago

Write the product in standard form.<br>(2 - 3i)(2 + i)

Stels [109]

Answer:

Brainelist?

Step-by-step explanation:

7-4i

just use a online calculator

8 0

3 years ago

Read 2 more answers

Jacob receives $15 per week for his allowance. His parents have asked him to put $5 in his savings account and the rest of his a

drek231 [11]

Answer:

5:10

Step-by-step explanation:

$5-money he saves

$10-money he can spend

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2 years ago

PLS TO GOD HELP ME I GOTTA GET ALL OF THIS TURNED IN BY 11:59 IM PANICKING AND TIRED!!!!

nirvana33 [79]

It might be the first one or the second one. i said MIGHT!!

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2 years ago

Given the graph, which coordinate point is NOT a solution?

Natasha2012 [34]

Answer: (1, 2) (The third option)

Step-by-step explanation: A solution has to be on the line. (1, 2) is the only point that isn't on the line.

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1 year ago