Help I'm stuck on this problem
2 answers:
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Answer:
f(x) = {x-3 for x ≤ -1; -3x+14 for x > 5}
Step-by-step explanation:
To write the piecewise function, we can consider the pieces one at a time. For each, we need to define the domain, and the functional relation.
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<h3>Left Piece</h3>The domain is the horizontal extent. It is shown as -∞ to -1, with -1 included.
The relation has a slope (rise/run) of +1, and would intersect the y-axis at -3 if it were extended.
The first piece can be written ...
f(x) = x-3 for x ≤ -1
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<h3>Right Piece</h3>The domain is shown as 5 to ∞, with 5<em> not included</em>.
The relation is shown as having a slope (rise/run) of (-3)/(1) = -3. If extended, it would intersect the point (5, -1), so we can write the point-slope equation as ...
y -(-1) = -3(x -5)
y = -3x +15 -1 = -3x +14
The second piece can be written ...
f(x) = -3x +14 for x > 5
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<h3>Whole function</h3>Putting these pieces together, we have ...
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<em>Additional comment</em>
Sometimes it is convenient to write inequalities in number-line order (using < or ≤ symbols). This gives a visual indication of where the variable stands in relation to the limit(s). Perhaps a more conventional way to write the domain for the second piece is, <em>x > 5</em>.
Answer:
The expected value of the proposition is of -0.29.
Step-by-step explanation:
For each free throw, there are only two possible outcomes. Either the player will make it, or he will miss it. The probability of a player making a free throw is independent of any other free throw, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
In which is the number of different combinations of x objects from a set of n elements, given by the following formula.
And p is the probability of X happening.
Suppose a basketball player has made 231 out of 361 free throws.
This means that
Probability of the player making the next 2 free throws:
This is P(X = 2) when n = 2. So
Find the expected value of the proposition:
0.4095 probability of you paying $31(losing $31), which is when the player makes the next 2 free throws.
1 - 0.4059 = 0.5905 probability of you being paid $21(earning $21), which is when the player does not make the next 2 free throws. So
The expected value of the proposition is of -0.29.