Answer:
The population density is 0.364 fish per gallon.
Step-by-step explanation:
The population density can be defined as the number of individuals (in this case, small tropical fish) per unit of area or volume. In this case, the volume of the aquarium (55 gallon).
The density can be calculated then as:
The population density is 0.364 fish per gallon.
Answer:
45.40
Step-by-step explanation:
First of all, the shape of rope is not a parabola but a catenary, and all catenaries are similar, defined by:
y=acoshxa
You just have to figure out where the origin is (see picture). The hight of the lowest point on the rope is 20 and the pole is 50 meters high. So the end point must be a+(50−20) above the x-axis. In other words (d/2,a+30) must be a point on the catenary:
a+30=acoshd2a(1)
The lenght of the catenary is given by the following formula (which can be proved easily):
s=asinhx2a−asinhx1a
where x1,x2 are x-cooridanates of ending points. In our case:
80=2asinhd2a
40=asinhd2a(2)
You have to solve the system of two equations, (1) and (2), with two unknowns (a,d). It's fairly straightforward.
Square (1) and (2) and subtract. You will get:
(a+30)2−402=a2
Calculate a from this equation, replace that value into (1) or (2) to evaluate d.
My calculation:
a=353≈11.67
d=703arccosh257≈45.40
Answer:
P(Spinner lands on purple section) = 0.6 = 60%
Step-by-step explanation:
We are given the following in the question:
Number of sections = 10
Number of purple sections = 6
a) probability that the spinner will land on purple purple
P(purple) =
0.6 is the probability that the spinner will land on purple purple.
b) Interpretation of probability
There is a 60% chance that the spinner will land on purple color.
