Answer:
z=2
Step-by-step explanation:
The colored one would be a 1 in 4 and the b&w is a 1 in 5 :1
Part A)
f(x) = 5^x
f(0) = 5^0
f(0) = 1
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f(x) = 5^x
f(1) = 5^1
f(1) = 5
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f(x) = 5^x
f(2) = 5^2
f(2) = 5*5
f(2) = 25
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f(x) = 5^x
f(3) = 5^3
f(3) = 5*5*5
f(3) = 125
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Rate of change for section A = (f(1) - f(0))/(1 - 0)
Rate of change for section A = (5 - 1)/(1 - 0)
Rate of change for section A = 4/1
Rate of change for section A = 4
Rate of change for section B = (f(3) - f(2))/(3 - 2)
Rate of change for section B = (125 - 25)/(3 - 2)
Rate of change for section B = 100/1
Rate of change for section B = 100
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Part B)
From part A) above, we found,
Rate of change for section A = 4
Rate of change for section B = 100
Which means that section B's rate of change is 25 times greater (since 100/4 = 25, or 25*4 = 100)
Answer for part B: 25
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Extra: Explain why one rate of change is greater than the other.
The rate of change for section B is larger because the exponential function is growing faster as x increases. This is shown visually by the sharper and steeper incline as the function curve goes upward. The function starts off with relatively slower growth but it accelerates in speed.
Answer:
1/80 of the agency's employees have PhDs.
Step-by-step explanation:
Given that:
Total number of employees = 4000
Number of employees with bachelors degree = 1000
Fraction of employees with graduate degree = 1/4 of 1000 = 250
1/5 of the employees with graduate degrees have PhD.
Number of employees with PhDs = 1/5 of 250 = 50
Now,
Fraction of PhD employees to total employees = 
Hence,
1/80 of the agency's employees have PhDs.
Let x = cups of 11% wheat, and y = cups of 63% wheat
He wants 12 cups in total, so we need:
x + y = 12
These 12 cups need to have 50% wheat, which means we are looking at 12*.5 = 6 cups of wheat in total, so our second equation is:
.11x + .63y = 6
We have two equations and two variables. So we can solve by using any means you want. I used substitution:
x = 12 - y
.11(12-y) + .63y = 6
1.32 -.11y + .63y = 6
.52y = 4.68
y = 9
Which means x = 3
Thus, 3 cups of 11% and 9 cups of 63%.
