Answer:
volume of the tank be when the sensor turns on = 92.316 ft³
Step-by-step explanation:
Volume of a cylinder = πr²h
Pi = π = 3.14
Radius = r = 7 ft
Height = h = 3 ft
Volume of a cylinder = πr²h
= 3.14 × 7² × 3
= 3.14 × 49 × 3
= 461.58 ft³
The tank comes equipped with a sensor to alert the farmer to fill it up when the water falls to 20% capacity.
volume of the tank be when the sensor turns on = 20% of Volume of a cylinder
= 0.20 * 461.58 ft³
= 92.316 ft³
volume of the tank be when the sensor turns on = 92.316 ft³
If inspection department wants to estimate the mean amount with 95% confidence level with standard deviation 0.05 then it needed a sample size of 97.
Given 95% confidence level, standard deviation=0.05.
We know that margin of error is the range of values below and above the sample statistic in a confidence interval.
We assume that the values follow normal distribution. Normal distribution is a probability that is symmetric about the mean showing the data near the mean are more frequent in occurence than data far from mean.
We know that margin of error for a confidence interval is given by:
Me=
α=1-0.95=0.05
α/2=0.025
z with α/2=1.96 (using normal distribution table)
Solving for n using formula of margin of error.

n=
=96.4
By rounding off we will get 97.
Hence the sample size required will be 97.
Learn more about standard deviation at brainly.com/question/475676
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The given question is incomplete and the full question is as under:
If the inspection division of a county weights and measures department wants to estimate the mean amount of soft drink fill in 2 liters bottles to within (0.01 liter with 95% confidence and also assumes that standard deviation is 0.05 liter. What is the sample size needed?
The increasing and decreasing intervals are marked on the graph and attached below.
The red arrow mark shows the part where graph is decreasing
The green arrow mark shows the part where graph is increasing
There is no end point or starting point for the graph
The graph starts decreasing at -∞ and it decreases till it reaches -2.5
Also the graph start decreasing at 0 and goes to +∞
So we have two decreasing intervals
(-∞ , -2.5) U (0, ∞)
The graph starts increasing at -2.5 and it increases till it reaches 0
So increasing interval is
(-2.5, 0)
g(x) =
or g(x) is 3/4 times of f(x) , F(x) and g(x) have common solution or intersecting point in the graph parabola at x=0 i.e. in origin and x =
.
<u>Step-by-step explanation:</u>
We have a function f(x) =
and another function , g(x) =
. In the graph of y =
, the point (0, 0) is called the vertex. The vertex is the minimum point in a parabola that opens upward. In a parabola that opens downward, the vertex is the maximum point.
Graphing y = (x - h)2 + k , where h = 0 & k = 0
Function g(x) can be formed with compression in function f(x) by a factor of 3/4 , i.e. g(x) =
or g(x) is 3/4 times of f(x).Domain and range of f(x) and g(x) are same ! Although structure of both functions is same the only difference is g(x) is compressed vertically by a factor 3/4. Both are graph of a parabola with vertex at (0,0). Also, F(x) and g(x) have common solution or intersecting point at x=0 i.e. in origin.