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miskamm [114]
3 years ago
12

Stores X, Y, and Z each sell a certain item that has a given list price. Stores X and Y are located in a state with a 5 percent

sales tax, and both sell the item at a 5 percent discount off list price, while Store Z is located in a state with no sales tax and gives no discounts. Store X applies its discount first and then charges tax on the discounted price, while Store Y adds the tax first and then applies the discount to the price with tax. If x and y are the prices, with tax and discount, charged by Stores X and Y, respectively, and z is the price charged by Store Z, which of the following statements correctly describes the relationship among x, y, and z ? A. x=y=zB. x=y
Mathematics
1 answer:
hram777 [196]3 years ago
5 0

Answer:

B. x=y

Step-by-step explanation:

A 5% tax charge is equivalent to multiply the current price by 1.05. On the other hand, a 5% discount is equivalent to substrace the current the 5% of it, so in the end, you multiply the current price by 0.95.

For X we should multiply first by 0.95, then by 1.05

For Y we multiply first by 1.05, then by 0.95

Hence, if L = price list, we have

  • x = L*0.95*1.05 = 0.9975L
  • y = L*1.05*0.95 = 0.9975L
  • z = L

As a result, x=y<z. Option B is correct.

Note that applying discount first or charging taxes first doesnt matter because the order of the factors doesnt ater the product.

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Write an equation in slope-intercept from the line with slope 3/5 and y-intercept 1 . Then graph the line.
never [62]

Answer:

y=(3/5)x+1

Step-by-step explanation:

Slope-intercept form of a line is as follows

y=mx+c, where m is the slope of the line and c is the y intercept.

Hence the equation of the line is y=(3/5)x+1

3 0
2 years ago
Marc has 45 Cds in his collection, and Corinna has 61. If Marc buys 4 new CDs each month and Corinna buys 2 new CDs each month,
Mkey [24]

After 8 months they both will have 77 CD's

4 0
3 years ago
How to find the volume of a cone?<br> Height- 8 in.<br> Diameter- 7 in.
mestny [16]
The formula for the volume of a cone is V = \pi r^{2} \frac{h}{3}

So the answer is 102.63
4 0
3 years ago
Tim bought some 25 cent and some 29 cent stamps. He paid 7.60 dollars for 28 stamps. How many of each type of stamp did he buy?
Citrus2011 [14]

Answer:

25 cent stamps = 13 and 29 cent stamps = 15

Step-by-step explanation:

x = 25 cent stamps and y = 29 cent stamps

x + y = 28......x = 28 - y

0.25x + 0.29y = 7.60

0.25(28 - y) + 0.29y = 7.60

7 - 0.25y + 0.29y = 7.60

-0.25y + 0.29y = 7.60 - 7

0.04y = 0.60

y = 0.60 / 0.04

y = 15 <===== 29 cent stamps

x + y = 28

x + 15 = 28

x = 28 - 15

x = 13 <===== 25 cent stamps

lets check it...

0.25x + 0.29y = 7.60

0.25(13) + 0.29(15) = 7.60

3.25 + 4.35 = 7.60

7.60 = 7.60 (correct..it checks out)

8 0
3 years ago
businessText message users receive or send an average of 62.7 text messages per day. How many text messages does a text message
KiRa [710]

Answer:

(a) The probability that a text message user receives or sends three messages per hour is 0.2180.

(b) The probability that a text message user receives or sends more than three messages per hour is 0.2667.

Step-by-step explanation:

Let <em>X</em> = number of text messages receive or send in an hour.

The random variable <em>X</em> follows a Poisson distribution with parameter <em>λ</em>.

It is provided that users receive or send 62.7 text messages in 24 hours.

Then the average number of text messages received or sent in an hour is: \lambda=\frac{62.7}{24}= 2.6125.

The probability of a random variable can be computed using the formula:

P(X=x)=\frac{e^{-\lambda}\lambda^{x}}{x!} ;\ x=0, 1, 2, 3, ...

(a)

Compute the probability that a text message user receives or sends three messages per hour as follows:

P(X=3)=\frac{e^{-2.6125}(2.6125)^{3}}{3!} =0.21798\approx0.2180

Thus, the probability that a text message user receives or sends three messages per hour is 0.2180.

(b)

Compute the probability that a text message user receives or sends more than three messages per hour as follows:

P (X > 3) = 1 - P (X ≤ 3)

              = 1 - P (X = 0) - P (X = 1) - P (X = 2) - P (X = 3)

             =1-\frac{e^{-2.6125}(2.6125)^{0}}{0!}-\frac{e^{-2.6125}(2.6125)^{1}}{1!}-\frac{e^{-2.6125}(2.6125)^{2}}{2!}-\frac{e^{-2.6125}(2.6125)^{3}}{3!}\\=1-0.0734-0.1916-0.2503-0.2180\\=0.2667

Thus, the probability that a text message user receives or sends more than three messages per hour is 0.2667.

6 0
2 years ago
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