Answer:
k = 16/33
Step-by-step explanation:
Determine k so that 2/3,k and 5/8k are the three consecutive terms of an a.p
k - 2/3 = 5/8k - k
3k-2/3 = 5k-8k/8
Cross product
(3k-2)(8) = (3)(5k-8k)
24k - 16 = 15k - 24k
24k - 16 = -9k
24k + 9k = 16
33k = 16
k = 16/33
Answer:
y intercept = 4
x intercept = 1/3
<u>x - intercept</u>
To find the x intercept, substitute 0 for y and solve for x.
0 = -12x + 4
0 = -12 (1/3) + 4
0 = -4 + 4
0 = 0
The x - intercept is 1/3
<u>y - intercept</u>
To find the y intercept, substitute 0 for x and solve for y.
y = -12 (0) + 4
y = 0 + 4
y = 4
The y - intercept is 4.
Answer:
Most people found the probability of just stopping at the first light and the probability of just stopping at the second light and added them together. I'm just going to show another valid way to solve this problem. You can solve these kinds of problems whichever way you prefer.
There are three possibilities we need to consider:
Being stopped at both lights
Being stopped at neither light
Being stopped at exactly one light
The sum of the probabilities of all of the events has to be 1 because there is a 100% chance that one of these possibilities has to occur, so the probability of being stopped at exactly one light is 1 minus the probability of being stopped at both lights minus the probability of being stopped at neither.
Because the lights are independent, the probability of being stopped at both lights is just the probability of being stopped at the first light times the probability of being stopped at the second light. (0.4)(0.7) = 0.28
The probability of being stopped at neither is the probability of not being stopped at the first light, which is 1-0.4 or 0.6, times the probability of not being stopped at the second light, which is 1-0.7 or 0.3. (0.6)(0.3) = 0.18
The probability at being stopped at exactly one light is 1-0.18-0.28=.54 or 54%.
I believe you are asking in how many ways they can sit. If so:
The 1st can sit anywhere: he has only 1 way to sit
The 2nd can sit in 11 ways, since one seat is already occupied
The 3rd can sit in 10 ways, since 2 seat are already occupied
The 4th can sit in 9 ways, since 3 seat are already occupied
The 5th can sit in 8 ways, since 4 seat are already occupied
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The 12th can sit in 1 way, since11 seat are already occupied
General formula for a circular table:
Number of ways they n persons can be seated: (n-1)!
and the 12 can be seated in (12-1)! = 11! = 39,916,800 ways.
This is called circular permutation
