1,300
4 is less than five so you round it down
Answer:
The sample mean would most likely be 50 centimeters.
Step-by-step explanation:
Central Limit Theorem
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 a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean and standard deviation
In this question:
The mean of the population is 50 centimers.
So, by the Central Limit Theorem, the sample mean would most likely be also 50 centimeters.
Answer:
y = (11x + 13)e^(-4x-4)
Step-by-step explanation:
Given y'' + 8y' + 16 = 0
The auxiliary equation to the differential equation is:
m² + 8m + 16 = 0
Factorizing this, we have
(m + 4)² = 0
m = -4 twice
The complimentary solution is
y_c = (C1 + C2x)e^(-4x)
Using the initial conditions
y(-1) = 2
2 = (C1 -C2) e^4
C1 - C2 = 2e^(-4).................................(1)
y'(-1) = 3
y'_c = -4(C1 + C2x)e^(-4x) + C2e^(-4x)
3 = -4(C1 - C2)e^4 + C2e^4
-4C1 + 5C2 = 3e^(-4)..............................(2)
Solving (1) and (2) simultaneously, we have
From (1)
C1 = 2e^(-4) + C2
Using this in (2)
-4[2e^(-4) + C2] + 5C2 = 3e^(-4)
C2 = 11e^(-4)
C1 = 2e^(-4) + 11e^(-4)
= 13e^(-4)
The general solution is now
y = [13e^(-4) + 11xe^(-4)]e^(-4x)
= (11x + 13)e^(-4x-4)
Answer:
Answer is x = -24/13, y = 3/13
Step-by-step explanation:
The vector equation of line is;
(x,y) = () + t (v) ............... 1
we know that;
() = (2,1)
and
v = 5i + 1j
put in equation 1
The parametric equation becomes;
by comparison we get;
multiply equation 3 by -5 and add it to equation 2
we know that;
so, m = 5
we can find the family of lines that are perpendicular to the above line by swapping the coefficients and change the sign of one of them:
So, the equation of other line is
multiply equation 5 by -5
put this value of y in equation 5.
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