Answer:
The selections are dependent.
Yes, they can be treated as independent (less than 5% of the population).
Step-by-step explanation:
Since the selections are made without replacement, each selection affects the outcome of the next selection and, therefore, the selections are dependent.
Although they are dependent, the selections can be treated as independent if the sample size is no more than 5% of the total population. In this case, the sample size is 1235 adults out of a population of 15,958,866 adults. The percentage represented by the sample is:
Thus the selections can be treated as independent for the purposes of calculations.
All you have to do is substitute the y value from the 1st equation into the second equation and solve...
a) y= 2-x
5x + 4y = 5
Substitute (2-x) into the second equation anywhere there is a y...
5x + 4y = 5
5x + 4(2-x) = 5
Now solve
5x + 8 - 4x = 5
5x - 4x + 8 = 5
x + 8 = 5
x = -3
Now that you have a solution for x, substitute -3 into either of the original equations anywhere there is an x then solve for y...
y = 2 - x
y = 2 - (-3)
y = 2+3 = 5
You solved for x and got -3 and solved for y and got 5, so your solution set is
(-3, 5).
Now check it by substituting both numbers into one of the original equations and you should have a true statement if it is correct...
y = 2 - x
5 = 2 - (-3)
5 = 2+3
5 = 5
True statement... it checks!
note* during the check, if the equation would have worked out to something like 2 = 5, then that is a false statement therefore the solution set would be wrong and you'd have to go back and find the mistake.
Answer:
4 cm
Step-by-step explanation:
The perimeter of the original rectangle is ...
P = 2(L+W) = 2(4x + x) = 10x
The perimeter of the larger rectangle after we add "a" to each side is ...
P = 2(L +W)
= 2((4x+a) +(x+a))
= 10x +4a = 10x +16
4a = 16 . . . . . subtract 10x from both sides
a = 4 . . . . . . . divide by 4
The length added to each side is 4 cm.
