An=a1+d(n-1)
an=nth term
a1=first term, when n=1
d=common differnce=amount each term increases by
n=which one
so
when n=1, an=40
so a1=40
it seems to increas by 7 each time
an=40+7(n-1)
explicit formula is expanded
an=40+7n-7
an=33+7n is the formula
the domain is natural numbers because you can't have the -3rd term or the 0th term or the 3.24th term
domain is natural numbers
the formula is
or
The answer is C. 1 lb 14 oz.
Answer:
Bias for the estimator = -0.56
Mean Square Error for the estimator = 6.6311
Step-by-step explanation:
Given - A normally distributed random variable with mean 4.5 and standard deviation 7.6 is sampled to get two independent values, X1 and X2. The mean is estimated using the formula (3X1 + 4X2)/8.
To find - Determine the bias and the mean squared error for this estimator of the mean.
Proof -
Let us denote
X be a random variable such that X ~ N(mean = 4.5, SD = 7.6)
Now,
An estimate of mean, μ is suggested as
Now
Bias for the estimator = E(μ bar) - μ
= 
= 
= 
= 
= 
= 3.9375 - 4.5
= - 0.5625 ≈ -0.56
∴ we get
Bias for the estimator = -0.56
Now,
Mean Square Error for the estimator = E[(μ bar - μ)²]
= Var(μ bar) + [Bias(μ bar, μ)]²
= 
= 
= ![\frac{1}{64} ( [{3Var(X_{1}) + 4Var(X_{2})] }) + 0.3136](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B64%7D%20%28%20%5B%7B3Var%28X_%7B1%7D%29%20%2B%204Var%28X_%7B2%7D%29%5D%20%20%7D%29%20%2B%200.3136)
= ![\frac{1}{64} [{3(57.76) + 4(57.76)}] } + 0.3136](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B64%7D%20%5B%7B3%2857.76%29%20%2B%204%2857.76%29%7D%5D%20%20%7D%20%2B%200.3136)
= ![\frac{1}{64} [7(57.76)}] } + 0.3136](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B64%7D%20%5B7%2857.76%29%7D%5D%20%20%7D%20%2B%200.3136)
= ![\frac{1}{64} [404.32] } + 0.3136](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B64%7D%20%5B404.32%5D%20%20%7D%20%2B%200.3136)
= 
= 6.6311
∴ we get
Mean Square Error for the estimator = 6.6311
Answer:
Part A: x0.50 + 3 = 18.50
Part B: x0.75 + 3 - x0.10 = 21
Part C: The equations from Part A and Part B differ because of the cost of plastic cup.
Step-by-step explanation:
Let x represent the number of cup of lemonade sold. Therefore, we have:
Part A:
This situation can be represented by the following equation:
x0.50 + 3 = 18.50
Part B:
This situation can be represented by the following equation:
x0.75 + 3 - x0.10 = 21
Part C:
The equations from Part A and Part B differ because of the cost of plastic cup.
For equation from Part A, revenue is the same as profit as Sydney does incur any cost to buy plastic cup before selling her lemonade.
For equation from Part B, revenue is different from profit because Daria has to incur the cost of plastic cup which $0.10 per cup of lemonade before selling her lemonade.
Answer:
14 miles per hour
Step-by-step explanation:
Convert 270 minutes to hours first= 4.5hrs
Then divide 63 by 4.5= 14
