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alexgriva [62]
3 years ago
14

HELP! ITS ABOUT SURVEYSSS EXPLANATION NEEDED

Mathematics
1 answer:
dimaraw [331]3 years ago
3 0

Answer:

B is the correct answer (Check the explanation below)

Step-by-step explanation:

Probability of boys who do play = 1593/2451 = 0.6499 or 64.99% (if you times by 100 to change to percentage)

Probability of boys who do not play =858/2451 = 0.35 or 35%

Probability of girls who do play = 1361/2996 = 0.4542 or 45.42%

Probability of girls who do not play = 1635/2996 = 0.5457 or 54.57%

Probability of boys and girls who play = 2954/5447 = 0.5423 or 54.23%

Probability of boys and girls who do not play = 2493/5447 =0.4577 or 45.77%

you can see the correct statement is

Probability of girls who do play = 1361/2996 = 0.4542 or 45.42%

total number of girls is 2996 and we found out almost 54% do not play and almost 45% play

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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

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