Answer: - 0.28
Explanation:
1) Expected value: is the weighted average of the values, being the probabilities the weight.
That is: ∑ of prbability of event i × value of event i.
In this case: (probability of getting 2 or 12) × (+6) + (probability of gettin 3 or 11) × (+2) + (probability of any other sum) × (-1).
2) Sample space:
Sum Points awarded
1+ 1 = 2 +6
1 + 2 = 3 +2
1 + 3 = 4 -1
1 + 4 = 5 -1
1 + 5 = 6 -1
1 + 6 = 7 -1
2 + 1 = 3 +2
2 + 2 = 4 -1
2 + 3 = 5 -1
2 + 4 = 6 -1
2 + 5 = 7 -1
2 + 6 = 8 -1
3 + 1 = 4 -1
3 + 2 = 5 -1
3 + 3 = 6 -1
3 + 4 = 7 -1
3 + 5 = 8 -1
3 + 6 = 9 -1
4 + 1 = 5 -1
4 + 2 = 6 -1
4 + 3 = 7 -1
4 + 4 = 8 -1
4 + 5 = 9 -1
4 + 6 = 10 -1
5 + 1 = 6 -1
5 + 2 = 7 -1
5 + 3 = 8 -1
5 + 4 = 9 -1
5 + 5 = 10 -1
5 + 6 = 11 +2
6 + 1 = 7 -1
6 + 2 = 8 -1
6 + 3 = 9 -1
6 + 4 = 10 -1
6 + 5 = 11 +2
6 + 6 = 12 +6
2) Probabilities
From that, there is:
- 2/36 probabilities to earn + 6 points.
- 4/36 probabilites to earn + 2 points
- the rest, 30/36 probabilities to earn - 1 points
3) Expected value = (2/36)(+6) + (4/36) (+2) + (30/36) (-1) = - 0.28
A.) Integers are positive and negative counting numbers. So, in order to find the integer coefficients, round off the coefficients in the equation to the nearest whole number. The function for g(x) is:
g(x) = 3x²+3x
B.) Substitute x=4 to the two functions.
f(x) = 2.912345x²<span>+3.131579x-0.099999
</span>f(4) = 2.912345(4)²+3.131579(4)-0.099999
f(4) = 59.023837
g(x) = 3x²+3x
g(4) = 3(4)²+3(4)
g(4) = 60
C.) The percentage error is equal to:
Percentage error = |g(4) - f(4)|/f(4) * 100
Percentage error = |60 - 59.023837|/59.023837 * 100
Percentage error = 1.65%
D.) If x is a large number, for example x=10 or x=20, then g(x) would be an overestimate. This is because the value of x is raised to the power of 2. So, as the x increases, the corresponding function would increase exponentially. Even at x=4, g(x) is already an overestimate. What more for larger values of x? That means that the gap from the true answer f(x) would increase.
Answer:
Slope = 1
Step-by-step explanation:
Answer:
a and b
Step-by-step explanation:
Answer:
h = 60 ; x = 25
Step-by-step explanation:
You are going to want to use Pythagorean Theorem to solve these.
Pythagorean Theorem: a² + b² = c²
h² + 144² = 156²
h² + 20736 = 24336
h² = 3600
h = 60
x² + 60² = 65²
x² + 3600 = 4225
x² = 625
x = 25
