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k0ka [10]
3 years ago
13

Janie and Jasmine are playing three games at an arcade. Each of the games requires either 2, 3, or 4 tokens. The girls plan to p

lay as many games as they can before running out of tokens. Let m represent the number of games that require 2 tokens; n represent the number of games that require 3 tokens; and p represent the number of games that require 4 tokens.
Janie plays the 3-token game four times. Write two equivalent expressions to represent the number of tokens that Janie will need to play each of the three games at least one time.
Mathematics
1 answer:
DENIUS [597]3 years ago
3 0
I think the answer would be -12 maybe
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Suppose that five ones and four zeros are arranged around a circle. Between any two equal bits you insert a 0 and between any tw
PolarNik [594]

Answer:

Using <u>backward reasoning</u> we want to show that <em>"We can never get nine 0's"</em>.

Step-by-step explanation:

Basically in order to create nine 0's, the previous step had to have all 0's or all 1's. There is no other way possible, because between any two equal bits you insert a 0.

If we consider two cases for the second-to-last step:

<u>There were 9 </u><u>0's</u><u>:</u>

We obtain nine 0's if all bits in the previous step were the same, thus all bit were 0's or all bits were 1's. If the previous step contained all 0's, then we have the same case as the current iteration step. Since initially the circle did not contain only 0's, the circle had to contain something else than only 0's at some point and thus there exists a point where the circle contained only 1's.

<u>There were 9 </u><u>1's</u><u>:</u>

A circle contains only 1's, if every pair of the consecutive nine digits is different. However this is impossible, because there are five 1's and four 0's (we have an odd number of bits!), thus if the 1's and 0's alternate, then we obtain that 1's that will be next to each other (which would result in a 1 in the next step). Thus, we obtained a contradiction and thus assumption that the circle contains nine 0's after iteratins the procedure is false. This then means that you can never get nine 0's.

To summarize, in order to create nine 0's, the previous step had to have all 0's or al 1's. As we didn't start the arrange with all 0's, the only way is having all 1's, but having all 1's will not be possible in our case since we have an odd number of bits.

<u />

5 0
3 years ago
Which of these properties is enough to prove that a given parallelogram is also a Rectangle?
lozanna [386]

we are supposed to find

Which of these properties is enough to prove that a given parallelogram is also a Rectangle?

As we know from the theorem, if the diagonals of a parallelogram are congruent then the parallelogram is a rectangle.

The other options The diagonals bisect each other is not sufficient because in parallelogram diagonals always gets bisected , parallelogram becomes rectangles only if both the diagonals are of same length.

In a parallelogram The opposite angles and opposite sides are always equal.

Hence the correct option is

The diagonals are congruent.

3 0
3 years ago
Read 2 more answers
Claire and her partner, Grace, are throwing for the javelin event as a team. Claire threw the javelin 42 feet and Grace threw it
stepan [7]
The team throw the javelin 81 feet
39+42=81
3 0
2 years ago
Read 2 more answers
a magazine is offering a special subscription rate of $30 per year for 12 issues the regular price for the magazine is $4 per is
katrin2010 [14]

Answer:

Step-by-step explanation:

c

3 0
3 years ago
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What is the expression 4(3+2) called
Anna71 [15]
An Algebraic Expression

Hope you have a great day!
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3 years ago
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