Question

question 16 (5 points)
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a veterinarian will prescribe an antibiotic to a dog based on its weight. the effective dosage of the antibiotic is given by d ≥ 1/5w², where d is dosage in milligrams and w is the dogs weight in pounds. which of the following ordered pairs gives an effective dosage of antibiotics for a 35 - pound dog?
a) (240, 35)
b) (260, 35)
c) (35, 260)
d) (35, 240)

Explanation:

Step1: Identify the variables

In the ordered - pair $(x,y)$, $x$ represents the dosage $d$ and $y$ represents the weight $w$. Here $w = 35$ pounds.

Step2: Calculate the minimum dosage

Substitute $w = 35$ into the formula $d\geq\frac{1}{5}w^{2}$. Then $d\geq\frac{1}{5}\times35^{2}=\frac{1}{5}\times1225 = 245$.

Step3: Check the ordered - pairs

We need to find an ordered - pair where the first value (dosage $d$) is greater than or equal to 245 and the second value (weight $w$) is 35.
For option A: $(240,35)$, since $240<245$, it is not valid.
For option B: $(260,35)$, since $260\geq245$ and $w = 35$, it is valid.
For option C: $(35,260)$, here the first value 35 is the weight and the second value 260 is the dosage, which is in the wrong order.
For option D: $(35,240)$, the first value 35 is the weight and the second value 240 is the dosage, which is in the wrong order and $240<245$.

Answer:

B. $(260,35)$