Divide 2x^4 - 4x^3 - 11x^2 + 3x - 6 by x + 2
1 answer:
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Let's start by visualising this concept.
Number of grains on square:
1 2 4 8 16 ...
We can see that it starts to form a geometric sequence, with the common ratio being 2.
For the first question, we simply want the fifteenth term, so we just use the nth term geometric form:
Thus, there are 16, 384 grains on the fifteenth square.
The second question begs the same process, only this time, it's a summation. Using our sum to n terms of geometric sequence, we get:
Thus, there are 32, 767 total grains on the first 15 squares, and you should be able to work the rest from here.
Number of grains on square:
1 2 4 8 16 ...
We can see that it starts to form a geometric sequence, with the common ratio being 2.
For the first question, we simply want the fifteenth term, so we just use the nth term geometric form:
Thus, there are 16, 384 grains on the fifteenth square.
The second question begs the same process, only this time, it's a summation. Using our sum to n terms of geometric sequence, we get:
Thus, there are 32, 767 total grains on the first 15 squares, and you should be able to work the rest from here.
Answer:
0.0023 = 0.23% probability that all 5 balls selected will be the same color
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
The order in which the balls are selected is not important, which means that the combinations formula is used to solve this question.
Combinations formula:
is the number of different combinations of x objects from a set of n elements, given by the following formula.
Desired outcomes:
Either 5 amber from a set of 6, or 5 blue from a set of 5. So
Total outcomes:
5 balls selected from a set of 6 + 5 + 4 = 15. So
Probability:
0.0023 = 0.23% probability that all 5 balls selected will be the same color