Answer:
The longest day of the year is day 172
Step-by-step explanation:
Since the length of day is L(t)=727+22sin[2π(t−80.75)/365], the maximum length of day is obtained when sin[2π(t−80.75)/365] is at its maximum value which is 1. So. sin[2π(t−80.75)/365] = 1
We now solve this to find the day at which this maximum value occurs.
sin[2π(t−80.75)/365] = 1
[2π(t−80.75)/365] = sin⁻¹(1)
[2π(t−80.75)/365] = π/2
dividing both sides by 2π/365, we have
[2π(t−80.75)/365] ÷ 2π/365 = π/2 ÷ 2π/365
t−80.75 = 365/4
t−80.75 = 91.25
t = 91.25 + 80.75
t = 172
The longest day of the year is day 172
Answer: Probability = 0.2
Step-by-step explanation:
Given data:
Mean production time = 32.20 seconds
Standard deviation = 1,05seconds
probability that a full production run will take less than 32 seconds on average to produce
= P(Xbar<32)
= P(Z<-0.8518)
= 0.2
Answer:
Step-by-step explanation:
Rate of leakage, R(t) = 1400 e^0.06t gallons/h
fraction remains , S(t) = e^(-0.32t)
initial contaminant = 1000 gallon
gallons contaminant present after t hour is S(t) R(t)
G(t) = S(t) R(t)
Put t = 18 hours
Taking log on both the sides
ln G = ln 1400 - 0.26 x 18
ln G = 7.244 - 4.68
ln G = 2.564
G = 13 gallons
Answer:
One sample t-test for population mean would be the most appropriate method.
Step-by-step explanation:
Following is the data which botanist collected and can use:
- Sample mean
- Sample Standard Deviation
- Sample size (Which is 10)
- Distribution is normal
We have to find the best approach to construct the confidence interval for one-sample population mean. Two tests are used for constructing the confidence interval for one-sample population mean. These are:
- One-sample z test for population mean
- One-sample t test for population mean
One sample z test is used when the distribution is normal and the population standard deviation is known to us. One sample t test is used when the distribution is normal, population standard deviation is unknown and sample standard deviation is known.
Considering the data botanist collected, One-sample t test would be the most appropriate method as we have all the required data for this test. Using any other test will result in flawed intervals and hence flawed conclusions.
Therefore, One-sample t-test for population mean would be the most appropriate method.
Answer:
c
Step-by-step explanation:
since the axis of symmetry is 0, and the y intercept is 2, the answer should be c
