Michael finds that 35 customers at his grandfather's grocery store use a coupon. to simulate the behavior of the next 5 customers, he writes the numbers 1, 2, 3, 4, and 5 on cards and mixes them up. he writes down that 1, 2, and 3 represent someone using a coupon and 4 and 5 represent someone not using a coupon. michael then randomly selects a card, puts it back, and records the number. he repeats this 5 times to represent 5 customers or 1 trial. he repeats this experiment for a total of 15 trials. the results are shown in the table. 43454 24511 55555 43453 55315 25215 32235 43311 11154 13342 42514 13223 44215 45313 13324 using this simulation, what is the probability that, out of the next 5 customers, 4 or more will use a coupon? enter your answer, as a fraction in simplified form, in the box.

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for

d 25 pi/6

step-by-step explanation:

the diameter is 10 inches

the radius is 1/2 of the diameter or 5 inches

the area of the circle is

a = pi r^2

  = pi 5^2

  = 25 pi

the slice is 60 degrees of the entire circle.

60 degrees out of 360   60/360 = 1/6

the area of the slice is 1/6 of the circle

a slice = 1/6 a circle

a slice = 1/6 * 25 pi