Alan

See https://web2.0calc.com/questions/geometry-question_70#r4 

Solution as follows:

Note that O is the centre of the circle.

I'm with Zekken on this. 

Normally if you write a number as abc_p, for example, you mean that the number is already in base p, so that a, b and c are all less than p itself. 

For the question to make sense, we are presumably supposed to interpret each number as a base ten number, then convert it to various bases, p, and work out which values of p are possible.  So for 6_p, for example, we could have 110₂, or 20₃, or 11₅ etc.  However, without this sort of explanation accompanying the question I consider it to be poorly phrased.

As follows:

The three vertices of the triangle are (-15/2, 0), (k, 0) and (k, 2k/3+5)

Hence base length b = k + 15/2 and height h = 2k/3 + 5

Calculate area from (1/2)bh and set equal to 20 to find the highest possible k.  Take the floor value of the result as k is an integer. The lowest value of k is -7 since k must be greater than -15/2.

Hence determine the possible integer values of k and sum them.

See https://web2.0calc.com/questions/find-the-sum_5#r2

See https://web2.0calc.com/questions/please-help-asap_111#r1

For -1 < x < 1 the two functions result in the same magnitude but have opposite sign.  For example: f(-0.5) = 0.577i and g(-0.5) = -0.577i.

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From symmetry, if it contains the point (2,0), which is (5-3, 0), then it also contains the point (5+3, 0) or (8, 0).  Hence you have three equations:

From (2, 0):    0 = a*2² + b*2 + c

From (5,3):     3 = a*5² + b*5 + c

From (8, 0):    0 = a*8² + b*8 + c

Use these three equations to find a, b and c.

"Because not all airline passengers show up for their reserved seat, an airline sells 125 tickets for a flight that holds only 115 passengers. The probability that a passenger does not show up is 0.05, and the passengers behave independently. Round your answers to four decimal places (e.g. 98.7654).

a) What is the probability that every passenger who shows up can take the flight?

b) What is the probability that the flight departs with at least one empty seat?"