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Inessa [10]
3 years ago
11

Three business associates are at their favorite local café for lunch. They have finished their meals and just received their bil

ls. Each bill is labeled at the top as Customer #1, Customer #2, or Customer #3. Note: Sales tax is 6%, and tips are rounded to the nearest $0.25. Customer #1: The bill, before sales tax has been added, is $12.95. This customer plans to leave a 15% tip, calculated after the tax has been added. Customer #2: The bill, after sales tax has been added, is $11.65. This customer plans to leave a 20% tip, calculated before the tax was added. Customer #3: The bill, before sales tax has been added, is $11.50. This customer plans to leave an 18% tip, calculated before the tax is added.
1. Which customer has the smallest total bill, including tax and tip?
2. Which of the following expressions best represents the following scenario?
The total bill, b, at a restaurant is first recalculated to include 6% sales tax and then recalculated to include a 16% tip.

a) 1.06b + 0.16(1.06b)
b) b + 0.16(1.06b)
c) 1.06b + 0.16b
d) 1.06(0.16b) + 0.16b

3. Customer #3's total bill is approximately
13%, 11%, 10% 12%
less or more than Customer #1's total bill.

4. Which customer will leave the largest tip?
Mathematics
1 answer:
telo118 [61]3 years ago
4 0
Customer #2 has the smallest total bill, including tax and tip.
Choice A, 1.06b + 0.16(1.06b), is correct.
Customer 3's bill is approximately 10% less than customer 1's bill.
Customer 2 leaves the bigger tip.

For customer #1:
(1.06(12.95))(1.15) = 15.79; the tip is 0.15(1.06(12.95)) = 2.06.
For customer #2:
1.06x = 11.65; x = 10.99; 20% tip = 0.2(10.99) = 2.20; total = 11.65+2.20 = 13.85.
For customer #3:
1.06(11.50) + 0.18(11.50) = 14.26; the tip is (0.18)(11.50) = 2.07.

Customer 3 spends 15.79-14.26 = 1.53 less than customer #1, which is 1.53/15.79 = 0.097 ≈ 10% less.
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IceJOKER [234]

Answer:

for the 1st one the answer is x= 3 y=1 and the second one is x= 5 and y = 3 and 1/3

Step-by-step explanation: so basically for the first one -5 times x which is 3 is -15 right? and then 5 times y which is 1 is 5 right so -15 plus 5 = -10

second one is x = 5 and y = 3 and 1/3 because 5*x which is 5 is = to 15 right? and then 3 times y which is equal to 3 and 1/3 is equal to 10 which when you do 15-10 in pretty sure it equals 5 correct me if im wrong

Hope this helps xD ;)

7 0
3 years ago
The Distributive Property allows you to say that 3(x − 1) = 3x −
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Answer:

3x - 3

Step-by-step explanation:

In the distributive property each value inside the parenthesis will be multiplied by the value outside the parenthesis.

In the expression 3(x - 1) it will look like:

(3 . x) - (3 . 1)

Then we multiply both value separately giving us:

3x - 3

So in conclusion it would be right to assume that.

3(x - 1) = 3x - 3

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3 years ago
A radioactive substance decreases in the amount of grams by one-third each year. If the starting amount of the
katovenus [111]

Answer:

The sequence is geometric. The recursive formula is a_{n}=2/3a_{n-1}

Step-by-step explanation:

In order to solve this problem, you have to calculate the amount of the substance left after the end of each year to obtain a sequence and then you have to determine if the sequence is arithmetic or geometric.

The substance decreases by one-third each year, therefore:

After 1 year:

1452-\frac{1}{3}(1452)

Using 1452 as a common factor and solving the fraction:

1452(1-\frac{1}{3})=1452(\frac{2}{3})=968

You can notice that in general, after each year the amount of grams is the initial amount of the year multiplied by 2/3

After 2 years:

968(\frac{2}{3})=\frac{1936}{3}

After 3 years:

\frac{1936}{3}(\frac{2}{3})=\frac{3872}{9}

The sequence is:

1452,968,1936/3,3872/9....

In order to determine if the sequence is geometric, you have to calculate the ratio of two consecutive terms and see if the ratio is the same for all two consecutive terms. The ratio is obtained by dividing a term by the previous term.

The sequence is arithmetic if the difference of two consecutive terms is the same for all two consecutive terms.

-Calculating the ratio:

For the first and second terms:

968/1452=2/3

For the second and third terms:

1936/3 ÷ 968 = 2/3

In conclussion, the sequence is geometric because the ratio is common.

The recursive formula of a geometric sequence is given by:

a_{n}=ra_{n-1}

where an is the nth term, r is the common ratio and an-1 is the previous term.

In this case, r=2/3

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3 years ago
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First we need to find out the time it took for the truck to reach town B.

Speed= \frac{Distance}{Time}

40= \frac{200}{T}
T=5hours

Now, because the van left 1.5 hours earlier and reached the destination 2.5 hours before, it took 1 hour less the the truck to arrive.

5hours-1hour=4hours which is the time it took for the van to arrive.

Now we use the speed equation again to work out speed.

Speed= \frac{200}{4}

Speed=50mph = speed of van

Hope this helped :)

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UkoKoshka [18]
I assume you happen to mean, what is the formula for a circle.

The formula is:

A=\pi  r^{2}
5 0
3 years ago
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