Jasmine completed an obstacle course in 3 minutes, Masao completed it in 3.4 minutes, and Alex completed it in 3 minutes. Order
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Answer:
Step-by-step explanation:
(a)
The number of receivers is 5.
The number of CD players is 4.
The number of speakers is 3.
The number of cassettes is 4.
Select one receiver out of 5 receivers in ways.
Select one CD player out of 4 CD players in ways.
Select one speaker out of 3 speakers in ways.
Select one cassette out of 4 cassettes in ways.
Find the number of ways can one component of each type be selected.
By the multiplication rule, the number of possible ways can one component of each type be selected is,
The number of ways can one component of each type be selected is
Part a
Therefore, the number of possible ways can one component of each type be selected is 240.
(b)
The number of Sony receivers is 1.
The number of Sony CD players is 1.
The number of speakers is 3.
The number of cassettes is 4.
Select one Sony receiver out of 1 Sony receivers in ways.
Select one Sony CD player out of 1 Sony CD players in ways.
Select one speaker out of 3 speakers in ways.
Select one cassette out of 4 cassettes in ways.
Find the number of ways can components be selected if both the receiver and the CD player are to be Sony.
By the multiplication rule, the number of possible ways can components be selected if both the receiver and the CD player are to be Sony is,
Number of ways can one components of each type be selected
Therefore, the number of possible ways can components be selected if both the receiver and the CD player are to be Sony is 12.
(c)
The number of receivers without Sony is 4.
The number of CD players without Sony is 3.
The number of speakers without Sony is 3.
The number of cassettes without Sony is 3.
Select one receiver out of 4 receivers in 4C_1 ways.
Select one CD player out of 3 CD players in 3C_1 ways.
Select one speaker out of 3 speakers in 3C_1 ways.
Select one cassette out of 3 cassettes in 3C_1 ways.
Find the number of ways can components be selected if none is to be Sony.
By the multiplication rule, the number of ways can components be selected if none is to be Sony is,
[excluding sony from each of the component]
Therefore, the number of ways can components be selected if none is to be Sony is 108.
(d)
The number of ways can a selection be made if at least one Sony component is to be included is,
= Total possible selections -Total possible selections without Sony
= 240-108
= 132
Therefore, the number of ways can a selection be made if at least one Sony component is to be included is 132.
(e)
If someone flips the switches on the selection in a completely random fashion, the probability that the system selected contains at least one Sony component is,
= 132 / 240
= 0.55
The probability that the system selected contains exactly one Sony component is,
Therefore, if someone flips the switches on the selection in a completely random fashion, then is the probability that the system selected contains at least one Sony component is 0.55.
If someone flips the switches on the selection in a completely random fashion, then is the probability that the system selected contains exactly one Sony component is 0.4125.
Step-by-step explanation:
There are certain methods for solving a system of equations. Some of which are:
- Substitution Method
- Elimination Method
- Graphing Method
<em>Substitution Method</em>
Substitution method to solve a system of equations is suitable if a variable of a any equation seems isolated or could comfortably be isolated without any ration/fraction resulting.
For example, for the following system of equations
x - 2y = 11....[A]
x = 5 - y....[B]
substituting the value of x = 5 - y from equation [B] into equation [A], so that
(5 - y) - 2y = 11
5 - y - 2y = 11
3y = -6
y = -2
<em>Elimination Method</em>
Elimination method to solve a system of equations is suitable if both equation are in standard form, and just adding or subtracting the equations to determine an equation in one variable.
For example, for the following system of equations
2x + 7y = -5....[C]
5x - 7y = 12....[D]
Adding Equation [C] and Equation [D].
7x + 0 = 7
x = 1
<em>Graphing Method</em>
Sometimes graphing method may be used to solve the system of the equation and visualize the solution.
For example,
y = -2....[E]
y = 3x + 1....[F]
The solution for this system of equation is the point of intersection of both the lines, which is shown in attached figure. The point of intersection is (-1, -2).
Hence, the solution of this system of equations is (-1, -2), as shown in attached figure.
<em>Keywords: system of equations, elimination method, substitution method, graphing method</em>
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