The mathematical model representing the scenarios described can be expressed as follows :
- If n ≤ 8 ; A(n) = 31.25n
- If n > 8 ; A(n) = 31.25 + 46.875(n - 8)
1.)
Amount paid per 8 hours at summer job = 250
Additional hours beyond, 8 hours = 1.5 × hourly rate
Let:
- hourly rate = p
- Number of hours worked = n
- Amount earned as a function of n, A(n)
Hourly rate, p = (250 ÷ 8) = 31.25
Therefore, the hourly rate, p at the summer job = $31.25
Overtime pay = 1.5 × 31.25 = $46.875
Therefore,
If n ≤ 8 ; A(n) = 31.25n
If n > 8 ; A(n) = 31.25 + 46.875(n - 8)
2.)
Let :
- Number of playing hours = n
- Total amount charged as a function of n ; T(n)
Therefore,
T(n) = First hour fee + (charge per additional hour × number of additional hours)
T(n) = 15 + 5(n - 1)
Therefore, the models can be used to calculate the total earning and amount charged for any given hour value.
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Answer:
32
Step-by-step explanation:
34 = -62 + 3x
34+62 = 3x
96 = 3x
x = 32
Answer:
Step-by-step explanation:
The formula of a slope:
We have two points (-6, -8) and (-14, 4).
Substitute
Answer:
x1 = 0.16203454
x2= 0.04843273+0.06766624j
x3= 0.04843273-0.06766624j
Step-by-step explanation:
The better way to obtain roots of a polynomial when is not easy to analytically factorize is to use software as Matlab or Python. Use the following code in Python
import numpy as np
pol=np.array([1,-0.2589, 0.02262,-0.001122])
roots=np.roots(pol)
print(roots)
Answer:
The arrangement of the given equation in the slope - intercept form are
1. 
Step-by-step explanation:
Given:
Let A ≡ ( x1 , y1 ) ≡ (-12 , 70)
B ≡ ( x2 , y2 ) ≡ (-4 , 78)
Slope - intercept form :
Where,
m is the slope of the line.
c is the y-intercept.
When two points are given say ( x1 , y1 ) and ( x2 , y2) we can remove slope by
Slope,
∴ 
Now equation of a line for a point ( x1 , y1 ) and having slope m is given as,
Which is in the required form
y = 1x + 82
Intercepts: Where the line cut X axis called X- intercept and where cut Y axis is called Y- intercept.
