Let x represent the number of hours that Gordon spends tutoring math, and let y represent the number of hours that he spends tutoring English. For parts (a)-(d), write an inequality to represent the given statement. a. Gordon has at most 12 hr to tutor per week. b. The amount of time that Gordon spends tutoring English is at least twice the amount of time he spends tutoring math. c. The number of hours spent tutoring math cannot be negative. d. The number of hours spent tutoring English cannot be negative. e. Graph the solution set to the system of inequalities from parts (a)-(d).
Let x represent the number of hours that Gordon spends tutoring math, and let y represent the number of hours that he spends tutoring English. For parts (a)-(d), write an inequality to represent the given statement. a. Gordon has at most 12 hr to tutor per week. b. The amount of time that Gordon spends tutoring English is at least twice the amount of time he spends tutoring math. c. The number of hours spent tutoring math cannot be negative. d. The number of hours spent tutoring English cannot be negative. e. Graph the solution set to the system of inequalities from parts (a)-(d).
Solution Summary: The author explains that Gordon has at most 12 hours to tutor per week and the required inequality is x+yle 12.
Let
x
represent the number of hours that Gordon spends tutoring math, and let
y
represent the number of hours that he spends tutoring English. For parts (a)-(d), write an inequality to represent the given statement.
a. Gordon has at most
12
hr
to tutor per week.
b. The amount of time that Gordon spends tutoring English is at least twice the amount of time he spends tutoring math.
c. The number of hours spent tutoring math cannot be negative.
d. The number of hours spent tutoring English cannot be negative.
e. Graph the solution set to the system of inequalities from parts (a)-(d).
Can you answer this question and give step by step and why and how to get it. Can you write it (numerical method)
Can you answer this question and give step by step and why and how to get it. Can you write it (numerical method)
There are three options for investing $1150. The first earns 10% compounded annually, the second earns 10% compounded quarterly, and the third earns 10% compounded continuously. Find equations that model each investment growth and
use a graphing utility to graph each model in the same viewing window over a 20-year period. Use the graph to determine which investment yields the highest return after 20 years. What are the differences in earnings among the three
investment?
STEP 1: The formula for compound interest is
A =
nt
= P(1 + − − ) n²,
where n is the number of compoundings per year, t is the number of years, r is the interest rate, P is the principal, and A is the amount (balance) after t years. For continuous compounding, the formula reduces to
A = Pert
Find r and n for each model, and use these values to write A in terms of t for each case.
Annual Model
r=0.10
A = Y(t) = 1150 (1.10)*
n = 1
Quarterly Model
r = 0.10
n = 4
A = Q(t) = 1150(1.025) 4t
Continuous Model
r=0.10
A = C(t) =…
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