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2 years ago

A bakery has 245 dozen cupcakes. How many individual cupcakes are there?

Mathematics

2 answers:

Irina18 [472]2 years ago

7 0

2,940
12x245=2,940
Because a dozen=12
So you multiply 12x245=2,940

balu736 [363]2 years ago

4 0

Answer: 2,940

Step-by-step explanation: 245 x 12= 2,940

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3 years ago

DIscrete Math

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

The sum of three numbers is 72. One number is two times 10 and another number is three times 10. What is the third number?

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The third number is 20

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2 years ago

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IgorC [24]

Least to greatest is r, t, k, h<span />

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3 years ago

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Find the mean absolute deviation of the set of data 3,8,10,12,15

inn [45]

Answer:

3.28

Step-by-step explanation:

find the mean of all the numbers

3 + 8 + 10 + 12 + 15 = 48

48/5=9.6

so the mean of all the numbers is 9.6

now subtract 9.6 from all the numbers

|3 - 9.6| = 6.6

|8 - 9.6| = 1.6

|10 - 9.6| = .4

|12 - 9.6| = 2.4

|15 - 9.6| = 5.4

Find the mean/average of the new values

6.6 + 1.6 + .4 + 2.4 + 5.4 = 16.4

16.4/5 = 3.28

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3 years ago