Answer:
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144. Prime factorization: 144 = 2 x 2 x 2 x 2 x 3 x 3, which can also be written 144 = (2^4) x (3^2)
Step-by-step explanation:
Answer: Gender = categorical ; Age = quantitative ; Household income = quantitative ; Automobile preference = Categorical
Step-by-step explanation:
Distinction between quantitative and categorical variables are based made on whether the variables are represented with a numeric or non-numeric value. Categorical variables usually takes in strings such as in the scenario above, the appropriate input for gender will be either 'Male' or 'Female' and Automobile preference will be a string of the type of automobile which the user prefers. On the other hand, quantitative variables will accept numeric values such as age and household income.
Answer:
The first mechanic $90/hour and the second charged $70/hour
Step-by-step explanation:
Lets start off by letting x be the first mechanics rate and y being the second mechanics rate. We know that the first mechanic worked 5 hours and that the second mechanic worked 10 hours and together they charged 1150. An equation to express this would be:
5x+10y = 1150
We also know that together they charged 160/per hour. An equation to express this would be:
x+y = 160
Now we can solve the second equation for x or the first mechanics rate.
x+y = 160
x = 160 - y
Now that we have an expression for x we can plug that back into the first equation and solve for y or how much the second mechanic charged.
5x+10y=1150 plug in x =160-y
5(160-y)+10y=1150 Distribute
800 -5y+10y = 1150 Combine like terms
800 +5y = 1150 Subtract 800 from both sides
5y = 350 divide by 5
y = 70
So we know that the second mechanic charged $70/hour. We also know that(from our work before) that the first mechanic charges $160 - the rate the second mechanic charged. We know that's $70/hour so we can plug in and solve for the first rate.
x = 160-y
x = 160-70
x = 90
So we know that the first mechanic charged $90/hour and the second mechanic charged $70/hour.
