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3 years ago

7

Seetha drove to work at 30 miles per hour. How fast would she need to drive home for the average speed for her round trip commut

e to be 60 miles per hour

1 answer:

Sophie [7]3 years ago

8 0

Answer:

40

Step-by-step explanation: Total distance = 60 miles

Total time = 30 / 30 + 30/60 = 3/2

Avg. speed = 40.

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In addition sentence 7 + 4=11 the 7 is the addend the 11 is the sum what is the name of the 4

romanna [79]

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3 years ago

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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3 years ago

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dmitriy555 [2]

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Step-by-step explanation:

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Plz help!! A jar contained 6 red marbles, 10 green marbles, and 8 blue marbles. A marble was selected at random, the color was r

Inessa [10]

Answer:

To calculate the relative frequency, first we need to know what exactly is and how to calculate it.

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13redmarble Fr = -------------------------

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