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777dan777 [17]
2 years ago
10

BOWLING A bowling alley charges a flat fee to rent shoes. There is an additional fee for each game played. The function y=2.5x+3

Mathematics
1 answer:
liq [111]2 years ago
7 0
The answer is x= -1.2
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(a) If G is a finite group of even order, show that there must be an element a = e, such that a−1 = a (b) Give an example to sho
Dahasolnce [82]

Answer:

See proof below

Step-by-step explanation:

First, notice that if a≠e and a^-1=a, then a²=e (this is an equivalent way of formulating the problem).

a) Since G has even order, |G|=2n for some positive number n. Let e be the identity element of G. Then A=G\{e} is a set with 2n-1 elements.

Now reason inductively with A by "pairing elements with its inverses":

List A as A={a1,a2,a3,...,a_(2n-1)}. If a1²=e, then we have proved the theorem.

If not, then a1^(-1)≠a1, hence a1^(-1)=aj for some j>1 (it is impossible that a^(-1)=e, since e is the only element in G such that e^(-1)=e). Reorder the elements of A in such a way that a2=a^(-1), therefore a2^(-1)=a1.

Now consider the set A\{a1,a2}={a3,a4,...,a_(2n-1)}. If a3²=e, then we have proved the theorem.

If not, then a3^(-1)≠a1, hence we can reorder this set to get a3^(-1)=a4 (it is impossible that a^(-1)∈{e,a1,a2} because inverses are unique and e^(-1)=e, a1^(-1)=a2, a2^(-1)=a1 and a3∉{e,a1,a2}.

Again, consider A\{a1,a2,a3,a4}={a5,a6,...,a_(2n-1)} and repeat this reasoning. In the k-th step, either we proved the theorem, or obtained that a_(2k-1)^(-1)=a_(2k)

After n-1 steps, if the theorem has not been proven, we end up with the set A\{a1,a2,a3,a4,...,a_(2n-3), a_(2n-2)}={a_(2n-1)}. By process of elimination, we must have that a_(2n-1)^(-1)=a_(2n-1), since this last element was not chosen from any of the previous inverses. Additionally, a_(2n1)≠e by construction. Hence, in any case, the statement holds true.

b) Consider the group (Z3,+), the integers modulo 3 with addition modulo 3. (Z3={0,1,2}). Z3 has odd order, namely |Z3|=3.

Here, e=0. Note that 1²=1+1=2≠e, and 2²=2+2=4mod3=1≠e. Therefore the conclusion of part a) does not hold

7 0
3 years ago
Help me on this math problem?
shusha [124]

Answer:

just add them

Step-by-step explanation:

4 0
3 years ago
Place decimal points in 431 and 205 so that the difference of the two numbers is 16.19
Gnoma [55]

Answer:

Step-by-step explanation:

Note that 20 (an approximation for 205) less 4 (an approx. for 431) comes out to 16.

This tells us that the proper placement of the decimals is

20.50

-   4.31

----------

and this comes out to 16.19.

7 0
3 years ago
The expression on the left side of an equation is shown below. 3x+9= []
kozerog [31]

Answer:

C. 3x

Step-by-step explanation:

The first two choices give 1 solution each.

The last choice gives an infinite number of solutions.

Choice C. gives no solution.

3x + 9 = 3x

Subtract 3x from both sides.

9 = 0

Since 9 = 0 is false, equation 3x + 9 = 3x has no solution.

4 0
3 years ago
Read 2 more answers
Wil has a coin collection and is currently adding 9 coins per day to his existing number of coins in his collection.After 22 day
ira [324]

Answer:

344

Step-by-step explanation:

Number of coins added per day in the collection = 9

Number of coins in the collection after 22 days = 218

To find:

Number of coins in the collection after 36 days.

Solution:

First of all, let us find how many coins did he have initially.

Let the number of coins present initially with Wil = x

Number of coins added per day = 9

Number of coins added after 22 days = 22 \times 9 = 198

Therefore,

x + 198 = 218\\\Rightarrow x = \bold{20}

Number of coins present with Wil initially = 20

Number of coins added after 36 days = 36 \times 9 = 324

Total number of coins after 36 days = Number of coins present initially with Will + Number of coins added = 324 + 20 = <em>344</em>

7 0
2 years ago
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