Answer:
-17 ft/s
Step-by-step explanation:
The average rate of change is the difference in height on the interval, divided by the difference in time.
m = (h(4.5) -h(2))/(4.5 -2) . . . . . . . . definition of rate of change on [2, 4.5]
h(4.5) = (-16·4.5 +87)(4.5) = 67.5
h(2) = (-16·2 +87)(2) = 110
Then ...
m = (67.5 -110)/(2.5) = -17
The average rate of change on the interval from 2 to 4.5 seconds is -17 ft/s.
_____
<em>Check</em>
The slope of the curve is given by its derivative:
h'(t) = -32t +87
The midpoint of the interval is (2+4.5)/2 = 3.25.
The slope at the midpoint is ...
h'(3.25) = -32(3.25) +87 = -17 . . . . average rate of change on [2, 4.5]
For a quadratic function. the average rate of change on an interval is the slope of the function at the midpoint of the interval. This calculation confirms that.
Let n = required random sample size.
Assume that the population standard deviation is known as σ.
Let m = sample mean.
At the 95% confidence level, the expected range is
(m - k(σ/√n), m + k(σ/√n))
where k = 1.96.
Therefore the error margin is 1.96(σ/√n).
Because the error margin is specified as 3% or 0.03, therefore
(1.96σ)/√n = 0.03
√n = (1.96σ)/0.03
n = 128.05σ²
This means that the sample size is about 128 times the population variance.
Answer:
Smallest sample size = 128.05σ², where σ = population standard deviation.
Answer
28 committees
Explanation:
The total number of members = 8
We want to make a committee of 2 members
We will be applying the combination concept
Therefore, 28 committees can be formed
Given :
Insurance cost , $693.00 .
Gas cost , $452.00 .
Average charge per fare , $7.00 .
Tuition fee , $3280.00 .
To Find :
The fare he have to get to pay his fee .
Solution :
Let , number of fair required is n .
Therefore , total profit is :
Now , to pay his fee this profit must be equal to his fee because he don't have other expenditure .
So ,
But number of rides cannot be in decimal so minimum rides he must get is
632+1 = 633 .
Hence, this is the required solution .
Part (a)
<h3>Answer:
2(2.4+w) = 14.2</h3>
--------------
Explanation:
L = 2.4 = length
W = unknown width
The perimeter of any rectangle is P = 2(L+W)
We replace L with 2.4, and replace P with 14.2 to get 14.2 = 2(2.4+w) which is equivalent to 2(2.4+w) = 14.2
========================================================
Part (b)
<h3>Answer:
w = 4.7</h3>
--------------
Explanation:
We'll solve the equation we set up in part (a)
2(2.4+w) = 14.2
2(2.4)+2(w) = 14.2
4.8+2w = 14.2
2w = 14.2-4.8
2w = 9.4
w = 9.4/2
w = 4.7
The width must be 4.7 cm.