Aspinner labeled 1 to 7 gives each of the numbers 3, 5, and 7 a 3
10
chance of being landed upon. the chance of landing on each of the
other four numbers is equal.
a) if the spinner is spun 1,300 times, how many times do you
expect it to land on the 5? show all work.
b) knowing the probability of landing on a 3, 5, or 7, you can find
the probability of landing on the 1, 2, 4, or 6. find the
probability of not landing on a 3, 5, or 7. divide this by number
of numbers remaining to find the probability of landing on a 1, 2,
4, or 6. show all work finding the probability of landing on one
of these numbers.
c) if the spinner is spun 1,500 times, how many times do you
expect it to land on the 2?

geometric series converge the common ratio r has magnitude less than one.

which is equivalent to

for the example we need

|2-x| < 1

-1 < 2-x   and 2-x < 1

x < 3 and x > 1

we can write that

answer: 1 < x < 3

1a. common ratio r=250/25=10 > 1     diverges

1b.   r=50/100=1/2 converges

when these converge they converge to

where a is the first term.

answer: 200

1c. r=-1   so it's not the case that |r| < 1.     diverges

2a. x is the common ratio so we converge when |x|< 1

2b.   r=-10x / -2 = 5x.

we converge when

|5x| < 1

|x| < 1/5

2c.   r=3-2x

-1 < 3-2x and 3-2x < 1

-4 < -2x and 2 < 2x

x < 2 and 1 < x

1 < x < 2

2d. [/tex] r=-48x^3/12 = 4x^3[/tex]

|4x^3| < 1

|x^3| < \frac 1 4

|x| < 4^{-1/3}

answer: evaluate the objective function at each vertex to determine which - and -values, if any, maximize or minimize the function. example: find the minimum value and maximum value of the objective function f ( x , y ) = 4 x + 5 y , subject to the following constraints

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step-by-step explanation: