It’s the third one, if not I’m sorry
If you graph it, it looks linear.
Answer:P(BBR) = 1/2 × 25/51 × 26/50 = 13/102 if cards are not replaced.
P(RBB) = 1/2 × 26/51 × 25/50 (simplified 1/2) = 13/102
P(BRB) = 1/2 × 26/51 ×25/50 (simplified 1/2) = 13/102
Step-by-step explanation: P(B) at first step is 26 cards out of a possible 52 therefore 26/52 (or simplified 1/2). We then have 25 black cards left out of a possible 51 therefore 25/51. The final card then has to be red to meet the criteria, we have 26 red cards still out of a possible 50 therefore 26/50.
This would be an example of binomial probability as at each step there are only 2 options R or B.
Bundle (31 , 40) has 40 bananas.
So 40 - 28 = 12 bananas
These 12 banana give the consumer negative utility which will be balance one for one apple.
So we have to need 12 apple to balance it.
So the final utility of apples and banana is 28 + (31 - 12) = 28 + 19 = 43
In second bundle (X , 23) has 23 bananas. We need to get the same utility 43.
Which we will get from 43 - 23 = 20 apples.
So X equal to 23.
See the attached image for the graph. The piecewise function is simply a collection of functions glued together to form a sort of "frankenstein function" of sorts. Here's how it works. If x is between 0 and 1 (including 0 but excluding 1), then f(x) = -2 for all x values mentioned. This is exactly what the first row of the piecewise function says. Then the second line says "if x is between 1 and 2, including both endpoints, then f(x) = 3-x". Finally the last line says f(x) = 1 as long as x is larger than 1 but smaller than 4. The value x = 4 is allowed for this piece but x = 1 is not allowed.
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Now onto function evaluation. We want to evaluate f(1) so we need to find f(x) when x = 1. If x = 1, then we'll use the second piece because the first piece excludes x = 1. So
f(x) = 3-x
f(1) = 3-1
f(1) = 2
is the first answer for the function evaluation section.
The value of f(3) is equal to 1 since we resort to using the third piece of the piecewise function (x = 3 is in the range from x = 2 to x = 4)
The value of f(-5) is undefined simply because we're out of the range defined by the piecewise function. The smallest x can get is x = 0.
Finally, f(2) is equal to 1 since...
f(x) = 3-x
f(2) = 3-2
f(2) = 1
again we use the second piece of the piecewise function because x = 2 is in the range 1 <= x <= 2
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In summary:
f(1) = 2
f(3) = 1
f(-5) = undefined
f(2) = 1
Once again have a look at the graph to see how the points match up. I've color-coded the graph so that each piece is a different color. The first piece is in red, the second in blue, the third in green. Note the open hole at point B to indicate "don't include this point as part of the graph".