Jessica purchased a DVD that was on sale for 12% off.
The sales tax in her county is 3%.
Let, y represent the original price of the DVD.
We can simply solve this mathematical problem by using the following mathematical process.
Here, we will form an algebraic expression, according to the given data.
So,
The original price of the DVD = y
Discount on the original price :
y * 12/100
=3y/25
Price after discount :
y - 3y/25
=25y - 3y/25
=22y/25
Sales tax amount :
22y/25 * 3/100
11y/25 * 3/50
=33y/1250
Final price including the sales tax :
22y/25 + 33y/1250
1100y + 33y/1250
1133y/1250
(This will be considered as the final result.)
Learn more about sales tax here:brainly.com/question/9437038
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Answer:
Step-by-step explanation:
<u>Given</u>
- A costs 5$
- B costs $0.25
- C costs $0.05
- A + B + C = 100
- 5A + 0.25B + 0.05C = 100 ⇒ 100A + 5B + C = 2000
<u>Subtract the first equation from the second:</u>
<u>We have a restriction in numbers:</u>
<u>Since 4B can be max 400, we get 99A > 1500 and 99A < 1900 so:</u>
and
A can be 16 or 18 as it should be even number to get B the whole number.
<u>If A = 16:</u>
- 99*16 + 4B = 1900
- 4B = 1900 - 1584
- 4B = 316
- B = 316/4 = 79
<u>If A = 18:</u>
- 99*18 + 4B = 1900
- 4B = 1900 - 1782
- 4B = 118
- B = 118/4 = 29.5, discarded as decimal
<u>So we get:</u>
- A = 16, B = 79 and C = 100 - (16 + 79) = 5
<u>Let's proof the numbers:</u>
- 16*5 + 79*0.25 + 5*0.05 = 100, confirmed
The variance of a constant is zero. Rule 2. Adding a constant value, c, to a random variable does not change the variance, because the expectation (mean) increases by the same amount. ... Multiplying a random variable by a constant increases the variance by the square of the constant.
