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Galina-37 [17]
3 years ago
15

Representatives running for office are handing out items to voters. Every 8th voter gets a button. Every 10th voter gets a stick

er.
Which voter is the first to receive both items?

Drag and drop the answer into the box to complete the statement.


The th voter receives both items.

a 4th
b 5th
c 8th
d 9th
e 10th
f 24th
g 40th
h 48th
i 80th
Mathematics
1 answer:
seropon [69]3 years ago
3 0
I)
Every 8.th voter gets a button:

so a sequence of the voters who receive a button is:

8, 16, 24, 32, ....   that is  8*1, 8*2, 8*3, 8*4, .... in general: 8k for some integer k  

ii)

Every 10.th voter gets a sticker, so the voters who receive stickers are the :

10, 20, 30, 40, .... voters    that is 10*1, 10*2, 10*3, 10*4... in general 10t

for some integer t


iii) what we are looking for is the first number which is 8k and 10t at the same time.

8k=2*2*2k, 
10t=2*5t

Thus this number must be divisible by 2*2*2*5*{some positive integer}

the smallest number is when the positive integer is 1, thus the number is 

2*2*2*5=8*5=40


Answer: g. the 40th
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[T]EE=\left[\begin{array}{ccc}2&3&3\\6&4&4\\-2&3&4\end{array}\right]

Step-by-step explanation:

First we start by finding the dimension of the matrix [T]EE

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To find [T]EE we must transform the vectors of the basis E and then that result express it in terms of basis E using coordinates and putting them into columns. The order in which we transform the vectors of basis E is very important.

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The second vector of basis E is e2(t) = t

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T[e3(t)]=T(t^{2})

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Then

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Let's write our matrix

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Applying the coordinates 2,6 and -2 to the basis E we obtain

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