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3 years ago

The bar graph shows the z-score results of four employees for two different work weeks.

Mathematics

2 answers:

MrRissso [65]3 years ago

6 0

Hello!

You look at the graph and see the the blue bars are week one

You look and see who has the lowest

The answer is Oberto

Hope this helps!

zvonat [6]3 years ago

3 0

Hello!

You look at the graph and see the the blue bars are week one

You look and see who has the lowest

The answer is Oberto

Hope this helps!

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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

Given gif and GHF, write three proportions involving geometric mean.<br>

almond37 [142]

Answer:

$\frac{z}{h}=\frac{h}{y}\\\\\frac{a}{x}=\frac{x}{z}\\\\\frac{a}{w}=\frac{w}{y}$

Step-by-step explanation:

For this exercise it is important to remember that a Right triangle is a triangle that has an angle that measures 90 degrees.

According to the Altitude Rule, given a Right triangle, if you draw an altitude from the vertex of the angle that measures 90 degrees (The right angle) to the hypotenuse, the measure of that altitude is the geometric mean between the measures of the two segments of the hypotenuse.

In this case, you can identify that the altitude that goes from the vertex of the right angle ( $\angle G=90\°$ ) to the hypotenuse of the triangle, is:

$GF=h$

Then, based on the Altitude Rule, you can set up the following proportion:

$\frac{z}{h}=\frac{h}{y}$

According to the Leg Rule, each leg is the mean proportional between the hypotenuse and the portion of the hypotenuse that is located directly below that leg of the triangle.

Knowing this, you can set up the following proportions:

$\frac{a}{x}=\frac{x}{z}\\\\\frac{a}{w}=\frac{w}{y}$

6 0

3 years ago

Read 2 more answers

On Friday,65% of the students at Plainview Middle School bought a hot lunch and the rest of the students packed their lunch. Wha

oksano4ka [1.4K]

35% packed their lunch. 65/100 bought hot lunch. 100-65=35.

7 0

3 years ago

Find the perimeter of a square with a side length of 10 meters

Vlad [161]

side length of square=10

Now,

perimeter of square =4l

=4×10

=40m

6 0

2 years ago

When Albert was born, he was 19.5 inches "tall". Today, on his 13th birthday, Albert is four feet, nine inches.

Ivanshal [37]

Answer: 76.5in or 6.37ft

Step-by-step explanation:

You would convert the 4 feet into inches which would be 48in. You would add the 9in and the 19.5in and come up with 76.5in. Then you just convert the 76.5in to 6.375ft

7 0

2 years ago