The following equation represents the function g in function notation,
g(x) = 3x - 14 [Option (A)]
Definition of a Function
A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. A function, in general, represents the idealized relationship between two changing quantities.
Given equation is,
y -3x = -14
⇒ y = -14 + 3x
or y = 3x - 14
Here, y stands for or represents the function g(x) which is a function of independent variable x.
Thus, the correct function notation is as follows,
g(x) = 3x - 14
Learn more about a function here:
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Answer:
<em>The age at which both companies charge the same premium is 44 years</em>
Step-by-step explanation:
<u>Graph Solution to System of Equations</u>
One approach to solving systems of equations of two variables is the graph method.
Both equations are plotted in the same grid and we find the intersection point(s) of both graphs. Those are the feasible solutions.
The annual premium p as a function of the client's age a for two companies are given as:
Company A: p= 2a+24
Company B: p= 2.25a+13
The graphs of both functions are shown in the image below.
The red line indicates the formula for Company A and the blue line indicates the formula for Company B.
It can be seen that both lines intersect in the point with approximate coordinates of (44,112).
The age at which both companies charge the same premium is 44 years
Answer:
32760 ways
Step-by-step explanation:
Given
Number of Candidates = 15
Job Positions = 4
Required:
Number of outcomes
This question represent selection; i.e. selecting candidates for job positions;
This question can be solved in any of the following two ways
Method 1.
The first candidate can be chosen from any of the 15 candidates
The second candidate can be chosen from any of the remaining 14 candidates
The third candidate can be chosen from any of the remaining 13 candidates
The fourth candidate can be chosen from any of the remaining 12 candidates
Total Possible Selection = 15 * 14 * 13 * 12
<em>Total Possible Selection = 32760 ways</em>
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Method 2:
This can be solved using permutation method which goes thus;

Where n = 15 and r = 4
So;
becomes





<em>Hence, there are 32760 ways</em>
To solve for f, you need to isolate/get the variable by itself in the equation:
4(0.5f - 0.25) = 6 + f Distribute 4 into (0.5f - 0.25)
(4)0.5f + (4)(-0.25) = 6 + f
2f - 1 = 6 + f Subtract f on both sides to get "f" on one side of the equation
2f - f - 1 = 6 + f - f
f - 1 = 6 Add 1 on both sides to get "f" by itself
f - 1 + 1 = 6 + 1
f = 7
PROOF
4(0.5f - 0.25) = 6 + f Substitute/plug in 7 into "f" since f = 7
4(0.5(7) - 0.25) = 6 + 7
4(3.5 - 0.25) = 13
4(3.25) = 13
13 = 13