Answer:
1) C
2) C
3) A
Step-by-step explanation:
1) The right answer is C.
Each volunteer is a pair, consisting of the test of each chair. The difference can be compared for each individual and treated as a paired t-test.
2) The right answer is C.
There is no paired relation between the houses of each sample. There are two independent samples with the same sample size.
3) The right answer is A.
The hours are selected at random, so there is no relation between the hours picked for each worker. There are two indpendent samples with the same sample size.
The equation to represent the area of the triangle would be:
y = 1/2(x²) - (7/2)x
The equation to represent the perimeter of the triangle would be:
y = 3x - 6
The solutions to the system would be (12, 30) or (1, -3). The only viable solution is (12, 30).
Explanation
The area of a triangle is found using the formula
A = 1/2bh
For our triangle, b = x and h = x-7, so we have:
A = 1/2(x)(x-7)
A = 1/2(x²-7x)
A = 1/2(x²) - (7/2)x
We will replace A with y, so we have:
y = 1/2(x²) - (7/2)x
The perimeter of a triangle is found by adding together all sides, so we have:
P = (x-7) + x + (x+1)
Combining like terms we get:
P = 3x - 6
We will replace P with y, so we have:
y = 3x - 6
Since both equations have y isolated on one side, it will be easy to use substitution to solve the system:
3x - 6 = 1/2(x²) - (7/2)x
It's easier to work with whole numbers, so we will multiply everything by 2:
6x - 12 = x² - 7x
We want all of the variables on one side, so we will subtract 6x:
6x - 12 - 6x = x² - 7x - 6x
-12 = x² - 13x
When solving quadratics, we want the equation equal to 0, so we will add 12:
-12+12 = x² - 13x + 12
0 = x² - 13x + 12
This is easy to factor, as there are factors of 12 that sum to -13; -12(-1) = 12 and -12+-1 = -13:
0 = (x-12)(x-1)
Using the zero product property, we know that either x-12=0 or x-1=0; therefore x=12 or x=1.
Putting these back into our equation for perimeter (the simplest one) we have:
y = 3(12)-6 = 36-6 = 30; (12, 30);
y = 3(1) - 6 = 3 - 6 = -3; (1, -3)
We cannot have a negative perimeter, so the only viable solution is (12, 30).
Sorry I know this late, but the answer is 40 MPH, I don't know if this helps! I HOPE SO THO!! <3
Answer:
B = (3, 3)
Step-by-step explanation:
Since the line segment is fifteen units long, from the looks of it, chopping ⅓ of A's side, led to the ordered pair of (3, 3).
I hope this helps you out alot, and as always, I am joyous to assist anyone at any time.
11.
(87+91+86+x)/4=90.
x=96.
13.
50×y > 130.
the lowest number could be 3, because 50×2=120, which is less than 130.
