Step-by-step explanation:
In statistics, the empirical rule states that for a normally distributed random variable,
- 68.27% of the data lies within one standard deviation of the mean.
- 95.45% of the data lies within two standard deviations of the mean.
- 99.73% of the data lies within three standard deviations of the mean.
In mathematical notation, as shown in the figure below (for a standard normal distribution), the empirical rule is described as
where the symbol 
(the uppercase greek alphabet phi) is the cumulative density function of the normal distribution, 
is the mean and 
is the standard deviation of the normal distribution defined as 
.
According to the empirical rule stated above, the interval that contains the prices of 99.7% of college textbooks for a normal distribution 
,
Therefore, the price of 99.7% of college textbooks falls inclusively between $77 and $149.
Answers:
a. £2,090
b. My answer would be less because my total in euros would be divided by a greater number when converting euros to pounds.
Work for part a:
Apartment: 560•3= 1680 euros
Car: 20.16•15= 302.4 euros
1680+302.4=1982.4
1982.4/1.12 = £x/1
1982.4 / 1.12= £1,770
£1,770 + £320 = £2,090 total
Work for part b:
Example:
(instead of 1.12 I put 2 to see what would happen with a greater number)
1982.4 / 2 = 991.2
991.2 is less than 1,770 (the answer I got with 1.12)
Let me know if you need any clarification! :)
Answer:
Time,t that it will elapse before the concerntration of the dye in the tank reaches1% of its original value is 460.52 seconds
Step-by-step explanation:
Let Q(t) = amount of dye for all time,t.
Let Q'= rate in - rate out.
But Q/200 = concerntration of dye
Therefore rate out= Q/200 ×2.
Q'/Q = - 1/100
Dividing by Q gives
Ln/Q/ + c = -1/100t + c1
Integrating both sides with respect to t
Ln/Q/ = -1/100t + c2.
c1 and c1 are just another constants
Q= c3e^-t/100
Exponentiating both sides will cause the absolute values to get absorbed into the constants giving rise to a new constant c3
200= c3-0/100
c3= 200
2= 200e^-t/100
Ln1/100= - t/100
Ln0.01 = - t/ 100
Cross multiply
t= Ln0.01 × 100
t = 4.6052 ×100
t = 460.52seconds
The 1st graph is the answer.
