Answer:
12 2/3 km/hour or 12.666 km/hour
Step-by-step explanation:
Because 3 1/6 is the rate for every quarter hour, simply multiply that rate by 4 in order to get the average speed over the course of an hour.
Answer: x=-10
Step-by-step explanation:
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.
To find the probability of landing on a triangle, you will want find the combined areas of the triangles and the total area of the square target.
Divide the area of the combined areas and the total area to find the probability of landing on a triangle.
A = 1/2bh
1/2 x 8 x 8
A = 32 square inches
32 x 4
128 square inches (areas of triangles)
A = bh
26 x 26
A = 676 square inches
128/676 = 0.189
There is an approximate probability of 0.19 of hitting a triangle.
It would be C. 13.6 because
A=1/2bh
A=1/2 (6.8) 4
A= 1/2 (27.2)
A= 13.6 cm
