A restaurant has tables that seat 6 people and booths that seat 4 people. If the restaurant a total of 37 tables and booths that
2 answers:
Answer:
21 Booths
Step-by-step explanation:
Let there are T tables and B boots in the restaurant.
For equation 1.
Each table can accommodate 6 people and each booth seat 4 people and total persons accommodated = 180
Therefore, equation will be 6T + 4B = 180 -------(1)
For equation 2.
Total seats and booths in the restaurant are 37.
T + B = 37---------(2)
Now we will multiply equation 2 by 6 and then subtract the new equation from equation (1)
(6T + 4B) - 6(T + B) = 180 - 6×37
6T + 4B - 6T - 6B = 180 - 222
-2B = - 42
2B = 42
B = 21
Therefore, there are 21 booths in the restaurant.
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This question is incomplete, the complete question is;
Customers arrive at a movie theater at the advertised movie time only to find that they have to sit through several previews and preview ads before the movie starts. Many complain that the time devoted to previews is too long (The Wall Street Journal, October 12, 2012). A preliminary sample conducted by The Wall Street Journal showed that the standard deviation of the amount of time devoted to previews was 4 minutes. Use that as a planning value for the standard deviation in answering the following questions. Round your answer to next whole number,
a) If we want to estimate the population mean time for previews at movie theaters with a margin of error of 75 seconds, what sample size should be used? Assume 95% confidence.
b) If we want to estimate the population mean time for previews at movie theaters with a margin of error of 1 minute, what sample size should be used? Assume 95% confidence.
Answer:
a) the required Sample Size is 40
b) the required Sample Size is 62
Step-by-step explanation:
Given the data in the question;
standard deviation σ = 4 minutes
a)
margin of error E = 75 seconds = ( 75 / 60 )minutes = 1.25 minutes
And 95% confidence.
Now, Critical Value of z for 0.95 confidence interval;
∝ = 1 - 0.95 = 0.05
= 1.96
so, sample size n will be;
n = [ × σ/E ]²
we substitute;
n = [ 1.96 × (4/1.25) ]²
n = [ 1.96 × 3.2 ]²
n = [ 6.272 ]²
n = 39.338
Since we referring to a number of sample, its approximately becomes 40
Therefore, the required Sample Size is 40
b)
margin of error E = 1 minutes
And 95% confidence.
Now, Critical Value of z for 0.95 confidence interval;
∝ = 1 - 0.95 = 0.05
= 1.96
so, sample size n will be;
n = [ × σ/E ]²
we substitute;
n = [ 1.96 × (4/1) ]²
n = [ 1.96 × 4 ]²
n = [ 7.84 ]²
n = 61.466
Since we referring to a number of sample, its approximately becomes 62
Therefore, the required Sample Size is 62