Answer:
<u>Total Cost (in dollars) = a + c</u>
Step-by-step explanation:
<u>Algebra</u>
When mathematics quantities are generalized into letters or variables, then we are dealing with algebra.
We are said the cost of an adult's ticket into a theme park is $a and a child's ticket costs $c. Since both quantities are unknown, we must treat them as variables and use the same logic procedure to solve the problem as if they were numbers.
The total cost for an adult and a child is the sum of both individual costs, thus
Total Cost (in dollars) = a + c
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:
4,099 and 5,011
Step-by-step explanation:
This problem can be solved by taking options one by one.
Option (1) : 4,099
Digit in ones place = 9
The value of the digit in tens place = 90
. It is correct.
Option (2) : 4,110
Digit in one places = 0
The value of the digit in tens place = 10
It is incorrect.
Option (3) : 5,909
Digit in one places = 9
The value of the digit in tens place = 0
It is again incorrect.
Option (4) : 5,011
Digit in one places = 1
The value of the digit in tens place = 10
. It is correct.
Hence, in option (a) and (d), the he ones place is 1/10 the value of the digit in the tens place.
Answer: 2/5
Step-by-step explanation:
Since there are 5 marbles and 3 aren't yellow, you have a 2/5 chance to choose the other two yellow marbles
Hope this helps:)
Answer:
Exponential functions!
Step-by-step explanation:
I think what you are dealing with is an exponential function!
So, to solve this, we need to first understand the main form of an exponential function:

Where a is the number we start off with, and b is the constant thing(forgot what it was called).
Now, 150 is our starting number, so it is a, and b is our constant at which the initial term is multiplied, which is 3!
Also, defining variables:
Let f(x)= # of Bees
Let x= # of years
Thus, here is our equation:

So, that's it!
Now, some of my answers have been recently deleted because they violated community guidelines for recommending something that shall not be named, so if you do really need help on the subject, look online! It is the largest source of information humanity has created! (also I cannot explain Exponential Functions in a single paragraph)
Stay Safe!