Answer:
781250 
Step-by-step explanation:
Let y is the length of the farm field
Let x is the width of the farm field
Given that, no fencing is necessary along the rock wall, so we can find the perimeter of the farm is:
2x + y = 2500 feet
<=> y = 2500 -2x
The are of the farm has the following formula:
A = x*y
<=> A = x(2500 - 2x)
<=> A = 2500x -2
To have the maximum area of field in square feet, we need to use differentials to estimate:
= 2500 - 4x
Set = 0, we have:
2500 - 4x = 0
<=> x = 625 feet.
=> y = 2500 - 2*625 = 1250 feet
So the maximum area of field is:
A = x*y = 625*1250 = 781250
Answer:
No solution
Step-by-step explanation:
Note how "2x" shows up in both equations. This suggests doing a substitution to solve the system.
Focus first on the first equation. Solving 2x - y = 7 for 2x, we get:
2x = y + 7.
Next, we substitute y + 7 for 2x in the second equation:
y = (y + 7) + 3.
Simplifying this produces:
0 = 10
This is not true and can never be true. Thus, this system has no solution.
The two angles are verticals angles so they are congruent, so you can solve for x by writing and solving an equation
6x-82=3x-23
Combine like terms
3x=105
And simplify to get x=35
Answer:
- In a cluster sample, every sample of size n has an equal chance of being included.
- In a stratified sample, random samples from each strata are included.
- In a cluster sample, the clusters to be included are selected at random and then all members of each selected cluster are included.
- In a stratified sample, every sample of size n has an equal chance of being included
Step-by-step explanation:
In a stratified sample the population is divided into different segments and then we take random elements from each segment.
In a cluster sample, the sample is divided into segments (or clusters) and then the sample is taken by selecting different clusters.
Therefore, in the cluster sample we take ALL elements from different clusters while in a stratified sample we take SOME elements from the different sections.
Now let's take a look at the options given:
- In a cluster sample, the only samples possible are those including every kth item from the random starting position: FALSE. In the cluster sample we select all items from the cluster.
- In a cluster sample, every sample of size n has an equal chance of being included: TRUE. if we divide the sample into clusters of size n then every cluster has an equal chance of being selected (since we select them at random).
- In a stratified sample, random samples from each strata are included: TRUE. We already said that we take a random sample from each segment (strata).
- In a stratified sample, the only samples possible are those including every kth item from the random starting position: FALSE. We can apply different methods to select our sample from each strata.
- In a cluster sample, the clusters to be included are selected at random and then all members of each selected cluster are included. TRUE. This is the definition of cluster sample we wrote at first.
- In a stratified sample, every sample of size n has an equal chance of being included: TRUE, we take samples from elements, not from stratas.
- In a cluster sample, random samples from each strata are included: FALSE. This is the definition of stratified sample.
- In a stratified sample, the clusters to be included are selected at random and then all members of each selected cluster are included: FALSE. This is the definition of cluster sample.
