22. Karla's credit card bill is $420.90. Part of the bill is from the previous month's balance, part is in new charges, and part is from a late fee of $35. The previous balance is $176.20 less than the new charges. How much is the previous balance and how much is in new charges? ______________________________________________________
Let's assume the previous balance is x and the new charges are y.
The previous balance is $176.20 less than the new charges:
x = y - $176.20
The total bill includes the previous balance, new charges, and a late fee:
$420.90 = x + y + $35
Substituting the value of x from the first equation into the second equation:
$420.90 = (y - $176.20) + y + $35
Combining like terms:
$420.90 = 2y - $176.20 + $35
Simplifying the expression:
$420.90 = 2y - $141.20
Adding $141.20 to both sides of the equation:
$562.10 = 2y
Dividing both sides of the equation by 2:
y = $281.05
Substituting the value of y back into the first equation:
x = $281.05 - $176.20
x = $104.85
Therefore, the previous balance is $104.85 and the new charges are $281.05.
23. The two-night attendance for a Friday/Saturday basketball tournament at the University of Connecticut was 2571. There were 535 more people on Saturday for the finals than on Friday. How many people attended each night?
Let's assume the number of people attending on Friday is x.
According to the given information, there were 535 more people attending on Saturday than on Friday. Therefore, the number of people attending on Saturday is x + 535.
The total attendance for the two nights is 2571. Therefore, we can write the equation:
x + (x + 535) = 2571
Simplifying the equation:
2x + 535 = 2571
Subtracting 535 from both sides of the equation:
2x = 2571 - 535
2x = 2036
Dividing both sides of the equation by 2:
x = 2036 / 2
x = 1018
Therefore, the number of people attending on Friday is 1018, and the number of people attending on Saturday is 1018 + 535 = 1553.
Mean Median Mode
a. 9, 7, 5, 10, 8, 3, 8, 6, 0 ________ ________ ________
b. −21, −15, −12, −16, −17 ________ ________ ________
a. To find the mean, we sum up all the numbers and divide by the total count.
Mean: (9 + 7 + 5 + 10 + 8 + 3 + 8 + 6 + 0) / 9 = 56 / 9 = 6.22
To find the median, we arrange the numbers in ascending order and find the middle value.
Arranged in ascending order: 0, 3, 5, 6, 7, 8, 8, 9, 10
Median: 7
There is no mode in this dataset because no number repeats more than once.
b. To find the mean, we sum up all the numbers and divide by the total count.
Mean: (-21 + -15 + -12 + -16 + -17) / 5 = -81 / 5 = -16.2
To find the median, we arrange the numbers in ascending order and find the middle value.
Arranged in ascending order: -21, -17, -16, -15, -12
Median: -16
There is no mode in this dataset because no number repeats more than once.
25. The salaries for seven Associate Professors at a university in the Midwest are listed. These are salaries for 9-month contracts for a recent year. Find the mean, median, and mode (if one exists). Round to the nearest dollar. $104,250, $107,000, $67,750, $82,500, $75,000, $88,300, $104,250
To find the mean, we need to sum up all the salaries and divide by the total count:
Mean: ($104,250 + $107,000 + $67,750 + $82,500 + $75,000 + $88,300 + $104,250) / 7 = $628,050 / 7 = $89,721.43
To find the median, we need to arrange the salaries in ascending order and find the middle value.
Arranged in ascending order: $67,750, $75,000, $82,500, $88,300, $104,250, $104,250, $107,000
Median: $88,300
To find the mode, we need to determine if there is a value that appears more than once. In this case, the salaries $104,250 appear twice, making it the mode.
Mean: $89,721.43
Median: $88,300
Mode: $104,250
solve
f. −1.5m + 14.65 = 0.2(18 − m)
To solve the equation -1.5m + 14.65 = 0.2(18 - m), we will first simplify the equation and then isolate the variable.
Starting with the given equation:
-1.5m + 14.65 = 0.2(18 - m)
Distribute 0.2 to both terms inside the parentheses:
-1.5m + 14.65 = 3.6 - 0.2m
Now, let's gather the m terms on one side of the equation:
-1.5m + 0.2m = 3.6 - 14.65
Combine like terms on both sides:
-1.3m = -11.05
Next, divide both sides of the equation by -1.3 to isolate m:
(-1.3m) / -1.3 = (-11.05) / -1.3
Simplifying:
m = 8.5
Therefore, the solution to the equation -1.5m + 14.65 = 0.2(18 - m) is m = 8.5.