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2 years ago

Let U = {1, 2, 3, 4, 5, 6), A = {1, 2, 3, 4), and B = {1, 2, 4). Find the set A n B.

Mathematics

1 answer:

PSYCHO15rus [73]2 years ago

3 0

Step-by-step explanation:

(A n b) = this means that we need d value that is in a and b only

ans= (1,2,4)

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You buy milk that contains 180 calories per 2 cups. Use a ratio table to find the number of calories in 5.5 cups.

Ludmilka [50]

Answer:

The number of calories in 5.5 cups are 495.

Step-by-step explanation:

Given:

You buy milk that contains 180 calories per 2 cups.

Now, to find the number of calories in 5.5 cups.

Let the number of calories in 5.5 cups be $x.$

As, in 2 cups there are 180 calories.

2 cups is equivalent to 180 calories.

Thus, the ratio would be $2:180.$

So, in 5.5 cups there are $x$ calories.

5.5 cups is equivalent to $x$ calories.

Thus, the ratio would be $5.5:x.$

Now, we set proportion to get the number of calories in 5.5 cups:

$2:180::5.5:x$

$\frac{2}{180} =\frac{5.5}{x}$

By cross multiplying we get:

$2x=990$

Dividing both sides by 2 we get:

$x=495$ .

Therefore, the number of calories in 5.5 cups are 495.

4 0

3 years ago

A teacher can spend as much as $95.00 to take students to a movie. A movie theater charges a $10.00 group fee and a $5.50 per ti

Pachacha [2.7K]

Answer:

Step-by-step explanation:

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2 years ago

Which of the following functions are homomorphisms?

Vikentia [17]

Part A:

Given $f:Z \rightarrow Z,$ defined by $f(x)=-x$

$f(x+y)=-(x+y)=-x-y \\ \\ f(x)+f(y)=-x+(-y)=-x-y$

but

$f(xy)=-xy \\ \\ f(x)\cdot f(y)=-x\cdot-y=xy$

Since, f(xy) ≠ f(x)f(y)

Therefore, the function is not a homomorphism.

Part B:

Given $f:Z_2 \rightarrow Z_2,$ defined by $f(x)=-x$

Note that in $Z_2$ , -1 = 1 and f(0) = 0 and f(1) = -1 = 1, so we can also use the formular $f(x)=x$

$f(x+y)=x+y \\ \\ f(x)+f(y)=x+y$

and

$f(xy)=xy \\ \\ f(x)\cdot f(y)=xy$

Therefore, the function is a homomorphism.

Part C:

Given $g:Q\rightarrow Q$ , defined by $g(x)= \frac{1}{x^2+1}$

$g(x+y)= \frac{1}{(x+y)^2+1} = \frac{1}{x^2+2xy+y^2+1} \\ \\ g(x)+g(y)= \frac{1}{x^2+1} + \frac{1}{y^2+1} = \frac{y^2+1+x^2+1}{(x^2+1)(y^2+1)} = \frac{x^2+y^2+2}{x^2y^2+x^2+y^2+1}$

Since, f(x+y) ≠ f(x) + f(y), therefore, the function is not a homomorphism.

Part D:

Given $h:R\rightarrow M(R)$ , defined by $h(a)= \left(\begin{array}{cc}-a&0\\a&0\end{array}\right)$

$h(a+b)= \left(\begin{array}{cc}-(a+b)&0\\a+b&0\end{array}\right)= \left(\begin{array}{cc}-a-b&0\\a+b&0\end{array}\right) \\ \\ h(a)+h(b)= \left(\begin{array}{cc}-a&0\\a&0\end{array}\right)+ \left(\begin{array}{cc}-b&0\\b&0\end{array}\right)=\left(\begin{array}{cc}-a-b&0\\a+b&0\end{array}\right)$

but

$h(ab)= \left(\begin{array}{cc}-ab&0\\ab&0\end{array}\right) \\ \\ h(a)\cdot h(b)= \left(\begin{array}{cc}-a&0\\a&0\end{array}\right)\cdot \left(\begin{array}{cc}-b&0\\b&0\end{array}\right)= \left(\begin{array}{cc}ab&0\\-ab&0\end{array}\right)$

Since, h(ab) ≠ h(a)h(b), therefore, the funtion is not a homomorphism.

Part E:

Given $f:Z_{12}\rightarrow Z_4$ , defined by $\left([x_{12}]\right)=[x_4]$ , where $[u_n]$ denotes the lass of the integer $u$ in $Z_n$ .

Then, for any $[a_{12}],[b_{12}]\in Z_{12}$ , we have

$f\left([a_{12}]+[b_{12}]\right)=f\left([a+b]_{12}\right) \\ \\ =[a+b]_4=[a]_4+[b]_4=f\left([a]_{12}\right)+f\left([b]_{12}\right)$

and

$f\left([a_{12}][b_{12}]\right)=f\left([ab]_{12}\right) \\ \\ =[ab]_4=[a]_4[b]_4=f\left([a]_{12}\right)f\left([b]_{12}\right)$

Therefore, the function is a homomorphism.

7 0

3 years ago

can you simplify 183/100 to fraction (it is improper fraction and i need to know if it can be simplified or not)

NikAS [45]

You can turn it into a mixed number 1 83
--
100

7 0

3 years ago

Read 2 more answers

Help pleaseeeeee!

marin [14]

Answer:

Horizontal shift of 1 unit to the right, a vertical shift upward of 6 units, and a vertical stretch by a factor of 3 ..

Step-by-step explanation:

Given function is:

3[|x-1|+2]

Can also be written as:

3|x-1|+6

As we can see that the -1 is grouped with x which means it is a horizontal shift of 1 unit to the right.

Now, 6 is added to the function and it is not grouped with x which means that there is a vertical shift of 6 units upward.

Lastly, 3 is multiplied with the term containing x which means that there is a vertical stretch of 3 units.

Hence, the correct option is:

Horizontal shift of 1 unit to the right, a vertical shift upward of 6 units, and a vertical stretch by a factor of 3 ..

4 0

3 years ago

Read 2 more answers