__,__, 8.16,32,64 what is the arithmetic sequence?
1 answer:
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Answer:
a. 0.5 or 50%
b. 5 rolls.
Step-by-step explanation:
a. There are 30 possible outcomes for this experiment, the sample space for the outcomes in which the six-sided die produces a value larger than the roll of the five-sided die is:
S={6,1; 6,2; 6,3; 6,4; 6,5; 5,1; 5,2; 5,3; 5,4; 4,1; 4,2; 4,3; 3,2; 3,1; 2,1}
There are five outcomes when rolling a 6, four when rolling a 5, three when rolling a 4, two when rolling a 3 and one when rolling a two.
The probability is:
b. The probability of rolling a 3 on the five-sided die is 1 in 5 or 0.20. The expected number of rolls until a fair five-sided die rolls a 3 is:
Answer:
Step-by-step explanation:
If we have a linear function and we multiply the input of the function, we aren't really <em>changing</em> the values of the function, we're changing the rate at which those values are reached.
E.g. if you look at the attached picture, we have and
, which is just
. The value when the red line is x = 1 is half that of the value of the blue line when x = 1.
The values of the f(2x) line are reaching the values of f(x) twice as fast, meaning it has a slope of twice as much. However, it still grows through the same intercept.
If you're interested in the calculus behind this, look up the chain rule of derivatives.
However, when you start changing the output of the function, you're changing the entire equation. It's not the same line anymore.
