Answer:
Step-by-step explanation:
A direct variation equation is of the form
y = kx,
where, in words, it reads "y varies directly with x" or "y varies directly as x". In order to use this as a model, we have to have enough information to solve for k, the constant of variation. The constant of variation is kind of like the slope in a straight line. It rises or falls at a steady level; it is the rate of change.
We have that a vet gives a dose of three-fifths mg to a 30 pound dog. If the dose varies directly with the weight of the dog, then our equation is
d = kw and we need to find k in order to have the model for dosing the animals.

Divide both sides by 1/30 to get k alone.
and

Our model then is

This means that for every pound of weight, the dog will get one-fiftieth of a mg of medicine.
Bottom left corner quadrant number 3
Answer:
Step-by-step explanation:
I like to work problems involving repetitive calculations using a spreadsheet. The sort function can easily put the results in the appropriate order.
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Here, we need to compute minutes and kilometers remaining for each cyclist, and then divide the former by the latter to find the required timing.
Minutes remaining will be the difference between the qualifying time and the time used so far.
Km remaining will be the difference between the race length and the distance traveled so far.
Required minutes per km will be the ratio of minutes remaining to km remaining.
Levi has the least allowed minutes per km for his remaining distance. Roberto has the most.
_____
Christopher only has to increase his average speed by about 5% in order to qualify; Levi has the greatest challenge, as he needs about 18% more speed for the rest of the race.