Answer:
Step-by-step explanation:
The table shows the results of randomly selecting colored marbles from a bag 40 times. The marble was returned to the bag after
each selection. Based on the results, what is the expected probability of randomly selecting a green marble from the bag in one attempt?
A: 0.125
B:0.20
C: 0.80
D:1.0
A: 0.125
B:0.20
C: 0.80
D:1.0
1 answer:
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Answer:
Step-by-step explanation:
Hello!
The variable of interest is
X: The number of emergency service calls made by the volunteer ambulance service of Walterboro, South Carolina for 50 days.
a)
In the first column, you have the possible number of emergency calls made, in the second column, you have the observed absolute frequency (fi) for each value of the variable.
To establish the probability distribution you have to calculate the relative frequency (hi) for each value of X.
The formula for the relative frequency is
hi= fi*n where i= 0, 1, 2, 3, 4
X₁= 0
f₁= 8
h₁= 8/50= 0.16
X₂= 1
f₂= 10
h₂= 0.20
X₃= 2
f₃= 22
h₃= 22/50= 0.44
X₄= 3
f₄= 9
h₄= 9/50= 0.18
X₅= 4
f₅= 1
h₅= 1/50= 0.02
(See attachment)
b)
The variable of interest is a cuantitative discrete variable, so this is an example of a driscrete distribution.
Discrete variables are numerical and take certain numbers within its range of definition, contrary to the continuous variables that can take any value within the range of definition of the variable.
Another example of a discrete variable is "the money", If the variable is "I have at most 10 dollars in my wallet", the range of definition goes from 0 dollars to 10 dollars.
c) To calculate the mean when the data is arranged in a frequency table you have to use the following formula:
X[bar]= ∑Xihi= (0*0.16)+(1*0.2)+(2*0.44)+(3*0.18)+(4*0.02)= 1.7
This means that they expect an average of 1.7 calls per day.
d) The formula for the standard deviation is:
∑X²fi= (0²*8)+(1²*10)+(2²*22)+(3²*9)+(4²*1)= 195
∑Xfi= (0*8)+(1*10)+(2*22)+(3*9)+(4*1)= 85
I hope this helps!
Answer:
a) (dy/dt) = 2 - [3y/(100 + 2t)]
b) The solved differential equation gives
y(t) = 0.4 (100 + 2t) - 40000 (100 + 2t)⁻¹•⁵
c) Concentration of salt in the tank after 20 minutes = 0.2275 kg/L
Step-by-step explanation:
First of, we take the overall balance for the system,
Let V = volume of solution in the tank at any time
The rate of change of the volume of solution in the tank = (Rate of flow into the tank) - (Rate of flow out of the tank)
The rate of change of the volume of solution = dV/dt
Rate of flow into the tank = Fᵢ = 5 L/min
Rate of flow out of the tank = F = 3 L/min
(dV/dt) = Fᵢ - F
(dV/dt) = (Fᵢ - F)
dV = (Fᵢ - F) dt
∫ dV = ∫ (Fᵢ - F) dt
Integrating the left hand side from 100 litres (initial volume) to V and the right hand side from 0 to t
V - 100 = (Fᵢ - F)t
V = 100 + (5 - 3)t
V = 100 + (2) t
V = (100 + 2t) L
Component balance for the amount of salt in the tank.
Let the initial amount of salt in the tank be y₀ = 0 kg
Let the rate of flow of the amount of salt coming into the tank = yᵢ = 0.4 kg/L × 5 L/min = 2 kg/min
Amount of salt in the tank, at any time = y kg
Concentration of salt in the tank at any time = (y/V) kg/L
Recall that V is the volume of water in the tank. V = 100 + 2t
Rate at which that amount of salt is leaving the tank = 3 L/min × (y/V) kg/L = (3y/V) kg/min
Rate of Change in the amount of salt in the tank = (Rate of flow of salt into the tank) - (Rate of flow of salt out of the tank)
(dy/dt) = 2 - (3y/V)
(dy/dt) = 2 - [3y/(100 + 2t)]
To solve this differential equation, it is done in the attached image to this question.
The solution of the differential equation is
y(t) = 0.4 (100 + 2t) - 40000 (100 + 2t)⁻¹•⁵
c) Concentration after 20 minutes.
After 20 minutes, volume of water in tank will be
V(t) = 100 + 2t
V(20) = 100 + 2(20) = 140 L
Amount of salt in the tank after 20 minutes gives
y(t) = 0.4 (100 + 2t) - 40000 (100 + 2t)⁻¹•⁵
y(20) = 0.4 [100 + 2(20)] - 40000 [100 + 2(20)]⁻¹•⁵
y(20) = 0.4 [100 + 40] - 40000 [100 + 40]⁻¹•⁵
y(20) = 0.4 [140] - 40000 [140]⁻¹•⁵
y(20) = 56 - 24.15 = 31.85 kg
Amount of salt in the tank after 20 minutes = 31.85 kg
Volume of water in the tank after 20 minutes = 140 L
Concentration of salt in the tank after 20 minutes = (31.85/140) = 0.2275 kg/L
Hope this Helps!!!
