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Naily [24]
1 year ago
11

Ralph is paid twice per month. His work offers a flexible-spending account to be used for medical expenses. This plan allows Ral

ph to put a specific amount of money from each check into a savings fund so that he can pay for big bills a little at a time. If his son Billy needs new glasses that will cost $1,200, how much should Ralph have taken out of each check so the glasses can be paid for by the end of the year, with nothing left over in the account?
A.$50

B.$100

C.$30

D.$60
Mathematics
1 answer:
slava [35]1 year ago
6 0
In this question, we're assuming Ralph had 0 in his saving funds to start with.

The glasses cost 1200 dollars.

There are 12 months in a year.

Each month, Ralph is given his check two times, that means that Ralph receives his check 2(12), or 24, times per year.

Divide 1200 (the cost of the glasses) by 24 (the amount of times Ralph is given his check)

1200 / 24
Divide both numerator and denominator by 12
100 / 2
Simplify
50

Ralph should have put 50 dollars per pay check to pay for the glasses.

A is your answer.

Have an awesome day! :)
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Answer:

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Step-by-step explanation:

The given system of equations is:

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From (1): x + y = xy

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y = x(y - 1)

x = y/(y - 1).......................................(4)

From (2): 2(x + z) = xz

=> 2x + 2z = xz

2x = xz - 2z

2x = z(x - 2)

z = 2x/(x - 2) ....................................(5)

From (3): 3(y + z) = yz

=> 3y + 3z = yz

3y = yz - 3z

3y = z(y - 3)

z = 3y/(y - 3)....................................(6)

Comparing (5) and (6)

2x/(x - 2) = 3y/(y - 3)

2x(y - 3) = 3y(x - 2)

2xy - 6x = 3xy - 6y

6(y - x) = xy .................................(7)

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Using this in (7), we have

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5y = 7x

x = 5y/7................................................(8)

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(y - 1) = 7/5

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Using this in (8)

x = 5(12/5)/7 = 12/7 .......................(10)

Using (10) in (5)

z = 2x/(x - 2)

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Answer:

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Step-by-step explanation:

From the question we are told that

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    The  sample mean is  \= x  =  68 \ hr

     The  standard deviation is  \sigma  =  20 \ hr

The  null hypothesis is  H_o  :  \mu  =  60

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Here we would assume the level of significance of this test to be  

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Next we will obtain the critical value of the level of significance from the normal distribution table, the value is    Z_{0.05} =  1.645

  Generally the test statistics  is mathematically represented as

           t =  \frac{ \= x  - \mu}{  \frac{ \sigma }{\sqrt{n} } }

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Answer:

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Step-by-step explanation:

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Or, 4 x -  \dfrac{3 x}{4}  = \dfrac{5}{4}

Or, \dfrac{16 x - 3 x}{4}  = \dfrac{5}{4}

Or, \dfrac{13 x}{4}  = \dfrac{5}{4}

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Answer:

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