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Sloan [31]
3 years ago
5

James did not get the PlayStation that he wanted for his birthday, but instead, he got $80. He decided that he will save the $80

and save his $20 allowance every week, for the next few weeks, until he has exactly $360 to buy the PlayStation himself. Write an equation that models the story. Use w to represent the number of weeks.
Mathematics
1 answer:
Vika [28.1K]3 years ago
6 0
W=14 that’s because 360-80=280 then you have to divide that by 20. And you get 14 weeks.
You might be interested in
in a game using two dice, a person wins if the outcome is a prime number. Find the probability of winning.
AlexFokin [52]

Answer:

45% I think because prime numbers are 5/ the 11 possible numbers when rolling two die

7 0
3 years ago
You borrow $5,000 from your parents to purchase a used car. The arrangements of the loan are such that you make payments of $250
AfilCa [17]
Part A:
1st month: Interest payable = 1% of $5,000 = $50.00
Amount paid in first month = $250 + $50.00 = $300
Unpaid balance = $5,000 - $250 = $4,750

2nd month: Interest payable = 1% of $4,750 = $47.50
Amount paid in second month = $250 + $47.50 = $297.50
Unpaid balance = $4,750 - $250 = $4,500

3rd month: Interest payable = 1% of $4,500 = $45.00
Amount paid in third month = $250 + $45.00 = $295.00
Unpaid balance = $4,500 - $250 = $4,250

4th month: Interest payable = 1% of $4,250 = $42.50
Amount paid in fouth month = $250 + $42.50 = $292.50
Unpaid balance = $4,250 - $250 = $4,000

5th month: Interest payable = 1% of $4,000 = $40.00
Amount paid in fifth month = $250 + $40.00 = $290.00
Unpaid balance = $4,000 - $250 = $3,750

6th month: Interest payable = 1% of $3,750 = $37.50
Amount paid in sixth month = $250 + $37.50 = $287.50
Unpaid balance = $3,750 - $250 = $3,500

7th month: Interest payable = 1% of $3,500 = $35.00
Amount paid in seventh month = $250 + $35.00 = $285.00
Unpaid balance = $3,500 - $250 = $3,250

8th month: Interest payable = 1% of $3,250 = $32.50
Amount paid in eighth month = $250 + $32.50 = $282.50
Unpaid balance = $3,250 - $250 = $3,000

9th month: Interest payable = 1% of $3,000 = $30.00
Amount paid in ninth month = $250 + $30.00 = $280.00
Unpaid balance = $3,000 - $250 = $2,750

10th month: Interest payable = 1% of $2,750 = $27.50
Amount paid in fouth month = $250 + $27.50 = $277.50
Unpaid balance = $2,750 - $250 = $2,500

11th month: Interest payable = 1% of $2,500 = $25.00
Amount paid in seventh month = $250 + $25.00 = $275.00
Unpaid balance = $2,500 - $250 = $2,250

12th month: Interest payable = 1% of $2,250 = $22.50
Amount paid in eighth month = $250 + $22.50 = $272.50
Unpaid balance = $2,250 - $250 = $2,000



Part B:
Number of payments = 5000 / 250 = 20
Total amount of interest = 50 + 47.5 + 45 + . . . + upto the 20th payment.
This is an arithmetic sequence with the first term as 50, common difference as -2.5 and number of terms = 20.

Sum of the first 20th term of the GP is given by
S_n= \frac{20}{2}[2(50)+(20-1)(-2.5)] \\  \\ =10(100-2.5(19))=10(100-47.5) \\  \\ =10(52.5)=\$525.00

Therefore, the <span>total amount of interest paid over the term of the loan is $525.00</span>
8 0
3 years ago
Find a particular solution to y" - y + y = 2 sin(3x)
leonid [27]

Answer with explanation:

The given differential equation is

y" -y'+y=2 sin 3x------(1)

Let, y'=z

y"=z'

\frac{dy}{dx}=z\\\\d y=zdx\\\\y=z x

Substituting the value of , y, y' and y" in equation (1)

z'-z+zx=2 sin 3 x

z'+z(x-1)=2 sin 3 x-----------(1)

This is a type of linear differential equation.

Integrating factor

     =e^{\int (x-1) dx}\\\\=e^{\frac{x^2}{2}-x}

Multiplying both sides of equation (1) by integrating factor and integrating we get

\rightarrow z\times e^{\frac{x^2}{2}-x}=\int 2 sin 3 x \times e^{\frac{x^2}{2}-x} dx=I

I=\frac{-2\cos 3x e^{\fra{x^2}{2}-x}}{3}+\int\frac{2x\cos 3x e^{\fra{x^2}{2}-x}}{3} dx -\int \frac{2\cos 3x e^{\fra{x^2}{2}-x}}{3} dx\\\\I=\frac{-2\cos 3x e^{\fra{x^2}{2}-x}}{3}+\int\frac{2x\cos 3x e^{\fra{x^2}{2}-x}}{3} dx-\frac{2I}{3}\\\\\frac{5I}{3}=\frac{-2\cos 3x e^{\fra{x^2}{2}-x}}{3}+\int\frac{2x\cos 3x e^{\fra{x^2}{2}-x}}{3} dx\\\\I=\frac{-2\cos 3x e^{\fra{x^2}{2}-x}}{5}+\int\frac{2x\cos 3x e^{\fra{x^2}{2}-x}}{5} dx

8 0
3 years ago
Please help me gotta pass
Rudik [331]
Answer:

Y=59 Z=93

Explanation:

To find Z, you have to know the line is equal to 180 degrees. You then subtract 180-87=93 that’s how you get Z. Then with that you know that 34+Y is going to equal 93 because they are across from each other. I forgot what that property is called, but yeah. Then you subtract 93-34=59 there you go hope that helps :)
4 0
3 years ago
2.5 kg of potatoes cost £1.40<br> Work out the cost of 4.25 kg of potatoes.<br> 5.95
kvasek [131]

Answer:

£2.38

Step-by-step explanation:

Write and solve an equation of ratios:

 £1.40       2.5 kg

----------- = ------------

     c          4.25 kg

Cross multiplying, we get:

(£1.40)(4.25 kg) = (2.5 kg*c), or

       (£1.40)(4.25 kg)

c = -------------------------- =  £2.38

             2.5 kg

4 0
3 years ago
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