Sample space is the set of possible outcomes of an experiment.
1. <span>Tossing a coin three times
There are possible outcomes.
Tossing the coin for the first time it can be a haid (H) or a tail (T). So, we can have this outcomes:
HHH
HHT
HTH
THH
TTH
THT
TTT
total: 6 outcomes
2. </span><span>The order that the top 5 students will receive their diplomas.
Here we need to find the number of permutations: 5!=5*4*3*2*1=120
3. </span><span>Tossing a pair of dice
The possible outcomes are the following: (a,b), where a is the first dice and b is the second dice
</span>(1,1)(1,2)(1,3)(1,4)(1,5)(1,6)(2,1)(2,2)(2,3)(2,4)(2,5)(2,6)(3,1)(3,2)(3,3)(3,4)(3,5)(3,6)(4,1)(4,2)(4,3)(4,4)(4,5)(4,6)(5,1)(5,2)(5,3)(5,4)(5,5)(5,6)(6,1)(6,2)(6,3)(6,4)(6,5)(6,6) , total 36 possible outcomes.
Answer:
Expected revenue = $400
Step-by-step explanation:
Expected revenue is given by the formula;
Expected revenue = Sum of x * p(x)
x = 200
x = 600
p(x) = 1/2
p(x) = 1/2
Substituting, we have;
Expected revenue = 200*1/2 + 600*1/2
= 100 + 300
= $400
Therefore, expected revenue = $400
Answer:
The answer to your question is below
Step-by-step explanation:
See the graph below
Process
1.- Find the distance from A to B, B to C, C to D, A to D
Formula
d = ![\sqrt{(x2 - x1)^{2} + (y2 - y1)^{2}}](https://tex.z-dn.net/?f=%5Csqrt%7B%28x2%20-%20x1%29%5E%7B2%7D%20%2B%20%28y2%20-%20y1%29%5E%7B2%7D%7D)
d AB = ![\sqrt{(1 + 3)^{2} + (6 - 5)^{2}} = \sqrt{17}](https://tex.z-dn.net/?f=%5Csqrt%7B%281%20%2B%203%29%5E%7B2%7D%20%2B%20%286%20-%205%29%5E%7B2%7D%7D%20%20%3D%20%5Csqrt%7B17%7D)
dBC = ![\sqrt{(-2 -6)^{2} + (3 - 1)^{2}} = \sqrt{68}](https://tex.z-dn.net/?f=%5Csqrt%7B%28-2%20-6%29%5E%7B2%7D%20%2B%20%283%20-%201%29%5E%7B2%7D%7D%20%20%3D%20%5Csqrt%7B68%7D)
dCD = ![\sqrt{(-1 - 3)^{2} + (-3 +2)^{2}} = \sqrt{17}](https://tex.z-dn.net/?f=%5Csqrt%7B%28-1%20-%203%29%5E%7B2%7D%20%2B%20%28-3%20%2B2%29%5E%7B2%7D%7D%20%20%3D%20%5Csqrt%7B17%7D)
dAD = ![\sqrt{(-1 + 3)^{2} + (-3 - 5)^{2}} = \sqrt{68}](https://tex.z-dn.net/?f=%5Csqrt%7B%28-1%20%2B%203%29%5E%7B2%7D%20%2B%20%28-3%20-%205%29%5E%7B2%7D%7D%20%20%3D%20%5Csqrt%7B68%7D)
2.- Find the perimeter
Perimeter = 2
=
u
3.- Find the area
Area = ![\sqrt{17} x \sqrt{68}](https://tex.z-dn.net/?f=%5Csqrt%7B17%7D%20x%20%5Csqrt%7B68%7D)
Area = ![\sqrt{17x68} = \sqrt{1156} = 34 u^{2}](https://tex.z-dn.net/?f=%5Csqrt%7B17x68%7D%20%3D%20%5Csqrt%7B1156%7D%20%3D%2034%20u%5E%7B2%7D)