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Serga [27]
3 years ago
11

Fill in the information in the table. The first is done for you

Mathematics
1 answer:
lisov135 [29]3 years ago
8 0

Answer:

≥                                         closed dot

<                                           open dot

≤     less than or equal to   closed dot

There are the missing blanks

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The graph shows the absolute value parent function. Which statement best describes the function?
Lubov Fominskaja [6]

Answer:

b. the function is always positive

8 0
3 years ago
Determine,in each of the following cases, whether the described system is or not a group. Explain your answers. Determine what i
zheka24 [161]

Answer:

(a) Not a group

(b) Not a group

(c) Abelian group

Step-by-step explanation:

<em>In order for a system <G,*> to be a group, the following must be satisfied </em>

<em> (1) The binary operation is associative, i.e., (a*b)*c = a*(b*c) for all a,b,c in G </em>

<em>(2) There is an identity element, i.e., there is an element e such that a*e = e*a = a for all a in G </em>

<em> (3) For each a in G, there is an inverse, i.e, another element a' in G such that a*a' = a'*a = e (the identity) </em>

<em> </em>

If in addition the operation * is commutative (a*b = b*a for every a,b in G), then the group is said to be Abelian

(a)  

The system <G,*> is not a group since there are no identity.  

To see this, suppose there is an element e such that  

a*e = a

then  

a-e = a which implies e=0

It is easy to see that 0 cannot be an identity.

For example  

2*0 = 2-0 = 2

Whereas

0*2 = 0-2 = -2

So 2*0 is not equal to 0*2

(b)

The system <G,*> is not a group either.

If A is a matrix 2x2 and the determinant of A det(A)=0, then the inverse of A does not exist.

(c)

The table of the operation G is showed in the attachment.

It is evident that this system is isomorphic under the identity map, to the cyclic group

\mathbb{Z}_{5}

the system formed by the subset of Z, {0,1,2,3,4} with the operation of addition module 5, which is an Abelian cyclic group

We conclude that the system <G,*> is Abelian.

Attachment: Table for the operation * in (c)

4 0
3 years ago
Find and simplify the difference quotient of the form<img src="https://tex.z-dn.net/?f=%5Cfra%5Cfrac%7Bf%28x%29-f%28a%29%7D%7Bx-
Ilia_Sergeevich [38]

Answer: 3x + 13

Step-by-step explanation:

f(x)=3x^2+x\\f(a)=3a^2+a\\f(4)=3*4^2+4=52\\\\f(x)-f(4)=3x^2+x-52=(x-4)(3x+13)\\\\\dfrac{f(x)-f(4)}{x-4} =\dfrac{3x^2+x-52}{x-4} \\\\if\ x \neq 4\ then \\\\\dfrac{f(x)-f(4)}{x-4} =\dfrac{(x-4)(3x+13)}{x-4} \\\\=3x+13\\

6 0
3 years ago
Read 2 more answers
ASAP NO WORK JUST ANSWER
Hunter-Best [27]

Answer:

c

Step-by-step explanation:

8 0
3 years ago
The article "Occurrence and Distribution of Ammonium in Iowa Groundwater" (K. Schilling, Water Environment Research, 2002:177–18
Papessa [141]

Answer: 95% confidence interval for the difference between the proportions would be (1.31, 1.39).

Step-by-step explanation:

Since we have given that

Number of alluvial wells = 349

Number of quaternary wells = 143

Number of alluvial wells that had concentrations above 0.1 = 182

Number of quaternary wells that had concentrations above 0.1 = 112

Average of alluvial wells = 0.27

Standard deviation = 0.4

Average of quaternary wells = 1.62

Standard deviation =1.70

So, 95% confidence interval gives

alpha = 5% level of significance.

\dfrac{\alpha}{2}=2.5\%\\\\z_{\frac{\alpha}{2}}=1.96

So, 95% confidence interval becomes,

(1.62-0.27)\pm 1.96\sqrt{\dfrac{0.4^2}{349}+\dfrac{1.7^2}{143}}\\\\=1.35\pm 1.96\times 0.020\\\\=(1.35-0.040,1.35+0.040)\\\\=(1.31,1.39)

Hence, 95% confidence interval for the difference between the proportions would be (1.31, 1.39).

6 0
3 years ago
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