Here's my work shown for question 1 and 2
Y = 3/4x - 3/10 to standard form
2 answers:
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Answer:
The mean of the sampling distribution of x is 0.5 and the standard deviation is 0.083.
Step-by-step explanation:
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean and standard deviation
, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
and standard deviation
.
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For the population, we have that:
Mean = 0.5
Standard deviaiton = 0.289
Sample of 12
By the Central Limit Theorem
Mean = 0.5
Standard deviation
The mean of the sampling distribution of x is 0.5 and the standard deviation is 0.083.
The function represents exponential growth with the initial value equal to 1, the decay factor equal to 0.3, and the rate equal to 0.7.
<h3>Population Growth Equation</h3>
The formula for the Population Growth Equation is:
Pf= future population
Po=initial population
r=growth rate
t= time (years)
growth or decay factor = (1 ±r)
When 1+R > 1, the equation represents growth, while 1+R < 1 the equation represents decay.
The question gives:
, then
Pf=y
Po= 1
, thus
r= -70%= -0.7
decay factor= (1-0.7)=0.3
Therefore,
1+R will be = 1+(-0.7)=1 - 0.7 =0.3
When 1+R >1, the function represents exponential growth.
Read more about the exponential function here:
Using the method of Lagrange multipliers, we have the Lagrangian
with partial derivatives (set equal to 0)
From
and 
, we find that 
. Then substituting into 
, we find
and substituting these into
, we get
So we have two possible critical points,
, which give extreme values of 
and 
, respectively.
with partial derivatives (set equal to 0)
From
and substituting these into
So we have two possible critical points,