At Lake Clay, marine biologists catch, tag, and release 50 smallmouth bass. Over the next few days, they catch 175 smallmouth bass, of which 7 have the original tags. What is the estimated population of smallmouth bass in Lake Clay?

The $x$-intercepts of the parabola $y = x^2 + bx + c$ are $(-3,0)$ and $(5,0).$ find the equation of the parabola, and submit your answer in $y = ax^2 + bx + c$ form.

Adoctor administers a drug to a 38-kg patient, using a dosage formula of 50 mg/kg/day. assume that the drug is available in a 100 mg per 5 ml suspension or in 500 mg tablets. a. how many tablets should a 38-kg patient take every four hours? b. the suspension with a drop factor of 10 ggt/ml delivers the drug intravenously to the patient over a twelve-hour period. what flow rate should be used in units of ggt/hr? a. the patient should take nothing pills every four hours. (type an integer or decimal rounded to the nearest hundredth as needed.)

Explain in a minimum of 2 sentences how to graph the equation of the absolute value function given a vertex of (-1,3) and a value of “a” equal to ½.