Solve the problem.The size P of a certain insect population at time t (in days) obeys the function 
After how many days will the population reach 1500?
Fill in the blank(s) with the appropriate word(s).
26 days
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P(E) is the probability of an event E occurring, and O(E) is the odds of an event E occurring. Solve the following problem.If P(E)=
, find O(E).
A. 1:6 B. 4:5 C. 1:4 D. 1:5
Factor completely using the grouping method to factor trinomials. If unfactorable, indicate that the polynomial is prime.7x2 - 27x + 4
A. (7x - 1)(x + 4) B. (7x + 1)(x - 4) C. (7x - 4)(x + 1) D. prime
Find the center, transverse axis, vertices, foci, and asymptotes of the hyperbola.
- 
= 1
A. center at (0, 0)
transverse axis is x-axis
vertices at (-5, 0) and (5, 0)
foci at (-12, 0) and (12, 0)
asymptotes of y = - 
and y = 
B. center at (0, 0)
transverse axis is y-axis
vertices at (0, -5) and (0, 5)
foci at (- 13, 0) and (13, 0)
asymptotes of y = - 
and y = 
C. center at (0, 0)
transverse axis is x-axis
vertices at (-12, 0) and (12, 0)
foci at (- 13, 0) and (13, 0)
asymptotes of y = - 
and y = 
D. center at (0, 0)
transverse axis is x-axis
vertices at (-5, 0) and (5, 0)
foci at (- 13, 0) and (13, 0)
asymptotes of y = - 
and y = 
Solve the problem.Suppose the supply function of a certain item is given by 
and the demand function is given by 
Find the producers' surplus. (Hint: The equilibrium quantity q0 is a perfect cube.)
A. 64
B. 
C. 
D. 32