Answer:
a. t
b. a (or x = a)
c. r
d.
1) c
2) t
3) a
4) p
Step-by-step explanation:
a. Draw vertical line passing through the point (c,0). This line intersects the graph at point L. Point L has coordinates (c,t), so

b. If
draw the horizontal line passing through the point (0,p). This line intersects the graph at point K with coordinates (a,p), so 
c. Note that
then

d. Coordinates of point L are (c,t), coordinates of point K are (a,p)
The standard deviation of the population function is 2
<h3>How to determine the standard deviation?</h3>
The given parameters are:
M(x) = 2
M(x²)=8
The standard deviation is calculated using:

Substitute known values

Evaluate the expression

Hence, the standard deviation of the population function is 2
Read more about standard deviation at:
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Answer:
Radius = 11.85yd
Step-by-step explanation:
Volume of a Cone formula: V = πr²(h/3)
We know that;
V = Volume
r = radius
π = pi (this is a sign located on your calculator)
h = height
We are given that;
V = 4,410
r = unknown
h = 30
Let's substitute the values in:
=> V = πr²(h/3)
=> 4,410 = πr²(30/3)
=> 4,410 = πr²(10)
=> 4,410 / 10 = πr²
=> 441 = πr²
=> 441 / π = r²
=> 140.37 = r²
=>
= r
=> 11.85 = r
Therefore, <u>the radius of the cone = 11.85yd</u>
Hope this helps!
The population Pa of insect A after t years is given by the equation
Pa = 1.3(1-0.038)^t
while the population Pb of insect B after t years is
Pb = 2.1(1-0.046)^t
We equate the above expressions to find the number of years t it will take the two populations to be equal:
Pa = Pb
1.3(1-0.038)^t = 2.1(1-0.046)^t
1.3(0.962)^t = 2.1(0.954)^t
These are the equations that can be used to determine how long it will be before the populations of the two species are equal.
We can now solve for t:
(0.962)^t / (0.954)^t = 2.1/1.3
(0.962/0.954)^t = 2.1/1.3
After taking the log of both sides of our equation, number of years t is
t = log (2.1/1.3) / log (0.962/0.954)
t = 57 years
Therefore, it will take 57 years for the population of insect A to equal the population of insect B.