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VMariaS [17]
3 years ago
5

A radio station had 205 tickets to a concert. They gave away 4 times as many tickets to listeners as to employees. How many tick

ets did they give away to employees?
Mathematics
1 answer:
Citrus2011 [14]3 years ago
7 0

Answer:

As per the statement: A radio station had 205 tickets to a concert. They gave away 4 times as many tickets to listeners as to employees.

⇒Let number of tickets Employees have x and Number of ticket Listeners  have 4x

It is also, given that a radio station had 205 ticket to a concert.

⇒ \text{Number of ticket Employees have} +\text{Number of ticket Listeners have} = 205

Then, substitute the given values we have;

4x + x = 205

Combine like terms, we have;

5x = 205

Divide both sides by 5 we have;

x = 41

Therefore, number of tickets did they give away to employees have 41 tickets



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Answer:

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Step-by-step explanation:

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15(5)^2(-\frac{1}{2})^4

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Substitute 6 for n

(a+b)^6 = ......+15(5)^2(-\frac{1}{2})^4+.......

[Next is to solve for a and b]

<em>From the above expression, the power of (5) is 2</em>

<em>Express 2 as 6 - 4</em>

(a+b)^6 = ......+15(5)^{6-4}(-\frac{1}{2})^4+.......

By direct comparison of

(a+b)^n = ......+ ^nC_ra^{n-r}b^r+.......

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We have;

^nC_ra^{n-r}b^r= 15(5)^{6-4}(-\frac{1}{2})^4

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^nC_r = 15

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By direct comparison of a^{n-r} =(5)^{6-4}

a = 5

n = 6

r = 4

[Solving for b]

By direct comparison of b^r= (-\frac{1}{2})^4

r = 4

b = \frac{-1}{2}

Substitute values for a, b, n and r in

(a+b)^n = ......+ ^nC_ra^{n-r}b^r+.......

(5+\frac{-1}{2})^6 = ......+ ^6C_4(5)^{6-4}(\frac{-1}{2})^4+.......

(5-\frac{1}{2})^6 = ......+ ^6C_4(5)^{6-4}(\frac{-1}{2})^4+.......

Solve for ^6C_4

(5-\frac{1}{2})^6 = ......+ \frac{6!}{(6-4)!4!)}*(5)^{6-4}(\frac{-1}{2})^4+.......

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(5-\frac{1}{2})^6 = ......+ \frac{6*5}{2*1}*(5)^{6-4}(\frac{-1}{2})^4+.......

(5-\frac{1}{2})^6 = ......+ \frac{30}{2}*(5)^{6-4}(\frac{-1}{2})^4+.......

(5-\frac{1}{2})^6 = ......+15*(5)^{6-4}(\frac{-1}{2})^4+.......

(5-\frac{1}{2})^6 = ......+15(5)^{6-4}(\frac{-1}{2})^4+.......

(5-\frac{1}{2})^6 = ......+15(5)^2(\frac{-1}{2})^4+.......

<em>Check the list of options for the expression on the left hand side</em>

<em>The correct answer is </em>(5-\frac{1}{2})^6<em />

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