The sum of the ages of Arturo, Benny, and Carlos is 41 years. Twice Arturo's age exceeds the sum of Benny and Carlos's ages by one year. Five years ago, Benny was 2 years more than twice as old as Carlos. Find their ages now
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Answer: Arturo is 14 years
Benny is 17 years
Carlos is 10 years
Step-by-step explanation:
Let x represent the age of Arturo.
Let y represent the age of Benny.
Let z represent the age of Carlos.
The sum of the ages of Arturo, Benny, and Carlos is 41 years. It means that
x + y + z = 41- - - - - - - - - - - - -1
Twice Arturo's age exceeds the sum of Benny and Carlos's ages by one year. It means that
2x = y + z + 1- - - - - - - - - 2
Five years ago, Benny was 2 years more than twice as old as Carlos. It means that
y - 5 = 2(z - 5) + 2
y - 5 = 2z - 10 + 2
y = 2z - 8 + 5
y = 2z - 3
Substituting y = 2z - 3 into equation 2, it becomes
2x = 2z - 3 + z + 1
2x = 2z + z - 3 + 1
2x = 3z - 2
x = 3z/2 - 1
Substituting y = 2z - 3 and
x = 3z/2 - 1 into equation 1, it becomes
3z/2 - 1 + 2z - 3 + z = 41
Multiplying through by 2, it becomes
3z - 2 + 4z - 6 + 2z = 82
3z + 4z + 2z - 2 - 6 = 82
9z - 8 = 82
9z = 82 + 8 = 90
z = 90/9
z = 10
x = 3z/2 - 1 = (3 × 10)/2 - 1
x = 14
y = 2z - 3 = 2 × 10 - 3
y = 17
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Final answer:
Manuel gets paid $460 for the first 40 hours of work, and an additional $103.50 for the 6 hours of overtime, making his total weekly pay $563.50 if he works 46 hours per week.
Explanation:
To calculate Manuel's weekly wage based on his hourly rate, we first need to consider his regular work hours and his overtime hours separately.
For his regular work hours, which are the first 40 hours, Manuel is paid at his regular hourly rate of $11.50. Therefore, his earnings for the 40 hours are: 40 hours * $11.50/hour = $460.
If he works more than 40 hours in a week, the additional hours are considered overtime.
For these extra hours, he is paid 1.5 times his regular pay. In this case, Manuel worked 46 hours, so he had 6 hours of overtime. His overtime earnings are: 6 hours * 1.5 * $11.50/hour = $103.50.
Adding these together, in a 46-hour week, Manuel's total earnings would be $460 + $103.50 = $563.50.
Learn more about overtime pay here:
#SPJ2
b. the line that minimizes the vertical distances of the data points from the line.
c. the line such that half of the data points fall above the line and half fall below the line.
d. All of the choices are correct.
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Answer:
a. the line that passes through the most data points.
Step-by-step explanation:
Regression analysis, is used to draw the line of‘ best fit’ through co-ordinates on a graph. The techniques used enable a mathematical equation of the straight line form y=mx+c to be deduced for a given set of co-ordinate values, the line being such that the sum of the deviations of the co-ordinate values from the line is a minimum, i.e.
The least-squares regression lines is the line of best fit
b. Suppose Darnell creates another model and decides to use a different scale. An actual length of 42 feet is shown on the new model as 12
inches. Complete the ratio for the new scale.
1 inch = feet
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Answer:
A. 432 feet.
(I'll let somebody else answer B cause im to dum for dat)
Step-by-step explanation:
I did the math and checked :)