A local library manager randomly surveys 80 patrons about the type of book they borrow when they visit the library. The manager finds that 3 patrons borrow novels. If the local library has 345 patrons, approximately how many of them borrow novels when they visit the library? Round your answer to the nearest whole number.
? patrons
We can set up a proportion to solve for the approximate number of patrons who borrow novels:
3/80 = x/345
To solve for x, we can cross-multiply and simplify:
80x = 3*345
80x = 1035
x = 1035/80
x ≈ 12.94
Rounded to the nearest whole number, approximately 13 patrons borrow novels when they visit the library.
Group A 18 20 46 34 58 31 41
Group B 15 21 32 42 29 57 39
The table shows the times, in minutes, spent shopping by two different groups. First find the mean times each group spent shopping. Then determine the difference in the mean times. Round your answers to one decimal place.
The mean time Group A spent shopping is ? minutes.
The mean time Group B spent shopping is ? minutes.
The mean times Group A and Group B spent shopping differ by
minutes.
To find the mean time each group spent shopping, we can use the formula:
mean = sum of data values / number of data values
For Group A:
mean = (18 + 20 + 46 + 34 + 58 + 31 + 41) / 7
mean = 248 / 7
mean ≈ 35.4
For Group B:
mean = (15 + 21 + 32 + 42 + 29 + 57 + 39) / 7
mean = 235 / 7
mean ≈ 33.6
The mean time Group A spent shopping is approximately 35.4 minutes.
The mean time Group B spent shopping is approximately 33.6 minutes.
To determine the difference in the mean times, we can subtract the mean time for Group B from the mean time for Group A:
35.4 - 33.6 ≈ 1.8
The mean times Group A and Group B spent shopping differ by approximately 1.8 minutes.
To find the approximate number of patrons who borrow novels when they visit the library, we can use proportions.
Given:
- Number of patrons surveyed = 80
- Number of patrons who borrow novels = 3
Let's set up a proportion:
(Number of patrons who borrow novels) / (Number of surveyed patrons) = (Number of total patrons who borrow novels) / (Number of total patrons)
Using the known values:
3 / 80 = (Number of total patrons who borrow novels) / 345
Now, cross multiplying:
(3 * 345) = (80 * Number of total patrons who borrow novels)
Dividing both sides by 80:
(3 * 345) / 80 = Number of total patrons who borrow novels
Simplifying:
1035 / 80 = Number of total patrons who borrow novels
Rounding the result to the nearest whole number:
Number of total patrons who borrow novels ≈ 12
Therefore, approximately 12 patrons borrow novels when they visit the library.
To estimate the number of patrons who borrow novels when they visit the library, we can use proportions.
Step 1: Find the proportion of patrons in the survey who borrow novels.
We know that out of the 80 patrons surveyed, 3 patrons borrow novels. So, the proportion of patrons that borrow novels can be calculated by dividing the number of patrons who borrow novels by the total number of patrons surveyed:
Proportion of patrons borrowing novels = Number of patrons borrowing novels / Total number of patrons surveyed
Proportion of patrons borrowing novels = 3 / 80
Step 2: Use the proportion to estimate the number of patrons who borrow novels in the entire library.
To estimate the number of patrons who borrow novels in the entire library, we can multiply the proportion calculated in step 1 by the total number of patrons in the library:
Estimated number of patrons borrowing novels = Proportion of patrons borrowing novels * Total number of patrons in the library
Estimated number of patrons borrowing novels = (3 / 80) * 345
Step 3: Round the answer to the nearest whole number.
After performing the above calculation, you can round the result to the nearest whole number to get the approximate number of patrons who borrow novels when they visit the library.