E3AP - Math 01

Find the area under the curve y = 1/x between the limits y = 2 and y = 10.

Let A and B be events with P(A) = 3/8, P(B) = 5/8 and P(AUB) = ¾. Find P(A|B).

Suppose a flu-like virus is spreading through a population of 50,000 at a rate proportional both to the number of people already infected and to number of still uninfected. If 100 people were infected yesterday and 130 are infected today, how many will be infected a week from today?

If the discrete random variable X has a geometric distribution parameter P and smallest mass point 0, what is the expected value of X?

The area bounded by y = x², x = 2 and y = 0 is rotated about the y–axis. Find the volume generated.

A box contains 5 green balls and 4 red balls. The probability of selecting 2 green balls and 1 red ball with a random sample of 3 balls without replacement is:

What are the coordinates of the point of inflection on the graph of y = x³ – 15x² + 33x + 100?

The standard deviation of 5, 6, 7, 8, 10, 12 is:

A charter bus company advertises a trip for a group as follows: At least 20 people must sign up. The cost when 20 participate is P80 per person. The price will drop by P2 per ticket for each member of the traveling group in excess of 20. If the bus can accommodate 28 people, how many participants will maximize the company’s revenue?

What type of curve is generated by a point that moves in uniform circular motion about an axis, while traveling with a constant speed, v, parallel to the axis?

Lˉ¹ {a/[S(S + a)]} =

From a stationary point directly in front of the center of a bull’s eye, Kim aims two arrows at the bull’s eye. The first arrow nicks one point on the edge of the bull’s eye; the second strikes the center of the bull’s eye. Kim knows the second arrow traveled 20 meters since she knows how far she is from the target. If the bull’s eye is 4 meters wide, how far did the first arrow travel? You may assume that the arrows traveled in straight-line paths and that the bull’s eye is circular. Round answer to the nearest tenth.

Find the equation of the normal to the curve y = 2x² at the point (2, 8).

Find the equation of the tangent to the circle defined by the equation x² + y² = 25 at the point (3,4).

The point of concurrency where the three altitudes of a triangle intersect.

The point of concurrency where the three medians of a triangle intersect.

The point of concurrency where the three angle bisectors of a triangle intersect.