Ask question

Ask question

All categories

3 years ago

14

Anna enjoys having dinner at a restaurant in a town where the sales tax on meals is 10%. She leaves 15% tip before the sales tax

is applied, and the tax is calculated on the pre-tip amount. She spends a total of $27.50 on her dinner. What was the cost of her dinner without tax or tip?

1 answer:

vitfil [10]3 years ago

5 0

Answer:

The cost of her dinner without tax or tip is <u>$22</u>.

Step-by-step explanation:

Given:

Anna enjoys having dinner at a restaurant in a town where the sales tax on meals is 10%.

She leaves 15% tip before the sales tax is applied, and the tax is calculated on the pre-tip amount.

She spends a total of $27.50 on her dinner.

Now, to find the cost of her dinner without tax or tip.

Let the cost of dinner without tax or tip be $x.$

So, the tax is:

$10\%\ of\ x.$

$=\frac{10}{100} \times x$

$=0.10\times x$

$=0.10x.$

And, the tip is:

$15\%\ of \ x.$

$=\frac{15}{100} \times x$

$=0.15\times x$

$=0.15x.$

<u><em>As given, she spends a total $27.50 on her dinner.</em></u>

Now, to get the cost of her dinner without tax or tip:

$x+0.15x+0.10x=27.50$

$x+0.25x=27.50$

$1.25x=27.50$

<em>Dividing both sides by 1.25 we get:</em>

$x=22$

$x=\$22.$

Therefore, the cost of her dinner without tax or tip is <u>$22</u>.

You might be interested in

Assume that X is normally distributed with a mean of 20 and a standard deviation of 2. Determine the following. (a) P(X 24) (b)

Tems11 [23]

Answer:

a) P( X < 24 ) = 0.9772

b) P ( X > 18 ) =0.8413

c) P ( 14 < X < 26) = 0.9973

d) P ( 14 < X < 26) = 0.9973

e) P ( 16 < X < 20) = 0.4772

f) P ( 20 < X < 26) = 0.4987

Step-by-step explanation:

Given:

- Mean of the distribution u = 20

- standard deviation sigma = 2

Find:

a. P ( X < 24 )

b. P ( X > 18 )

c. P ( 18 < X < 22 )

d. P ( 14 < X < 26 )

e. P ( 16 < X < 20 )

f. P ( 20 < X < 26 )

Solution:

- We will declare a random variable X that follows a normal distribution

X ~ N ( 20 , 2 )

- After defining our variable X follows a normal distribution. We can compute the probabilities as follows:

a) P ( X < 24 ) ?

- Compute the Z-score value as follows:

Z = (24 - 20) / 2 = 2

- Now use the Z-score tables and look for z = 2:

P( X < 24 ) = P ( Z < 2) = 0.9772

b) P ( X > 18 ) ?

- Compute the Z-score values as follows:

Z = (18 - 20) / 2 = -1

- Now use the Z-score tables and look for Z = -1:

P ( X > 18 ) = P ( Z > -1) = 0.8413

c) P ( 18 < X < 22) ?

- Compute the Z-score values as follows:

Z = (18 - 20) / 2 = -1

Z = (22 - 20) / 2 = 1

- Now use the Z-score tables and look for z = -1 and z = 1:

P ( 18 < X < 22) = P ( -1 < Z < 1) = 0.6827

d) P ( 14 < X < 26) ?

- Compute the Z-score values as follows:

Z = (14 - 20) / 2 = -3

Z = (26 - 20) / 2 = 3

- Now use the Z-score tables and look for z = -3 and z = 3:

P ( 14 < X < 26) = P ( -3 < Z < 3) = 0.9973

e) P ( 16 < X < 20) ?

- Compute the Z-score values as follows:

Z = (16 - 20) / 2 = -2

Z = (20 - 20) / 2 = 0

- Now use the Z-score tables and look for z = -2 and z = 0:

P ( 16 < X < 20) = P ( -2 < Z < 0) = 0.4772

f) P ( 20 < X < 26) ?

- Compute the Z-score values as follows:

Z = (26 - 20) / 2 = 3

Z = (20 - 20) / 2 = 0

- Now use the Z-score tables and look for z = 0 and z = 3:

P ( 20 < X < 26) = P ( 0 < Z < 3) = 0.4987

8 0

3 years ago

What is the volume of the right prism 8 mm 18 mm 12 mm

lisabon 2012 [21]

It will be clearly B.38mm3

7 0

3 years ago

Rename 200 tens into hundreds

Arlecino [84]

2 hundreds be cause there are 2, and you are trying to find hundreths so take the first number

4 0

3 years ago

Psychologist Michael Cunningham conducted a survey of university women to see whether, upon graduation, they would prefer to mar

bagirrra123 [75]

Answer:

A.The probability that exactly six of Nate's dates are women who prefer surgeons is 0.183.

B. The probability that at least 10 of Nate's dates are women who prefer surgeons is 0.0713.

C. The expected value of X is 6.75, and the standard deviation of X is 2.17.

Step-by-step explanation:

The appropiate distribution to us in this model is the binomial distribution, as there is a sample size of n=25 "trials" with probability p=0.25 of success.

With these parameters, the probability that exactly k dates are women who prefer surgeons can be calculated as:

$P(x=k) = \dbinom{n}{k} p^{k}(1-p)^{n-k}\\\\\\P(x=k) = \dbinom{25}{k} 0.25^{k} 0.75^{25-k}\\\\\\$

A. P(x=6)

$P(x=6) = \dbinom{25}{6} p^{6}(1-p)^{19}=177100*0.00024*0.00423=0.183\\\\\\$

B. P(x≥10)

$P(x\geq10)=1-P(x$

$P(x=0) = \dbinom{25}{0} p^{0}(1-p)^{25}=1*1*0.0008=0.0008\\\\\\P(x=1) = \dbinom{25}{1} p^{1}(1-p)^{24}=25*0.25*0.001=0.0063\\\\\\P(x=2) = \dbinom{25}{2} p^{2}(1-p)^{23}=300*0.0625*0.0013=0.0251\\\\\\P(x=3) = \dbinom{25}{3} p^{3}(1-p)^{22}=2300*0.0156*0.0018=0.0641\\\\\\P(x=4) = \dbinom{25}{4} p^{4}(1-p)^{21}=12650*0.0039*0.0024=0.1175\\\\\\P(x=5) = \dbinom{25}{5} p^{5}(1-p)^{20}=53130*0.001*0.0032=0.1645\\\\\\P(x=6) = \dbinom{25}{6} p^{6}(1-p)^{19}=177100*0.0002*0.0042=0.1828\\\\\\$

$P(x=7) = \dbinom{25}{7} p^{7}(1-p)^{18}=480700*0.000061*0.005638=0.1654\\\\\\P(x=8) = \dbinom{25}{8} p^{8}(1-p)^{17}=1081575*0.000015*0.007517=0.1241\\\\\\P(x=9) = \dbinom{25}{9} p^{9}(1-p)^{16}=2042975*0.000004*0.010023=0.0781\\\\\\$

$P(x\geq10)=1-(0.0008+0.0063+0.0251+0.0641+0.1175+0.1645+0.1828+0.1654+0.1241+0.0781)\\\\P(x\geq10)=1-0.9287=0.0713$

C. The expected value (mean) and standard deviation of this binomial distribution can be calculated as:

$E(x)=\mu=n\cdot p=25\cdot 0.25=6.25\\\\\sigma=\sqrt{np(1-p)}=\sqrt{25\cdot 0.25\cdot 0.75}=\sqrt{4.69}\approx2.17$

4 0

3 years ago

The figure consists of a quarter circle and a parallelogram. What is the area of the composite figure? Use 3.14 for n 76, Round

asambeis [7]

A is the answer i think

3 0

2 years ago