Answer:
Option B is correct.
The average and median levels of control found in her sample are 4 and 3.5 respectively.
Step-by-step explanation:
The average is given as
Average = (Σx)/N
The average is the sum of variables divided by the number of variables
x = each variable
N = number of variables = 6
Average = (4 + 2 + 5 + 3 + 3 + 7)/6
Average = (24/6) = 4.
The median is described as the number in the middle when the variables are arranged in ascending or descending order.
For variables whose number is odd, the median is just the variable in the middle of the ordered distribution.
For variables whose number is even, the median is just the average of the two variables in the middle of the ordered distribution.
Arranging the levels of control, we have
2, 3, 3, 4, 5, 7 (number of variables is even; 6)
The middle numbers are 3 and 4.
The average of these 2 = (3+4)/2 = 3.5
Answer:
2
Step-by-step explanation:
<span>1. X = -2 or 3
2. X = -5 or 3
3. X = -2.5 or 3
4. X = -4 or 2
5. X = 3 or -3
6. X = -4 or 2
I am assuming that you're looking for the intersections between the two equations for each problem. The general approach to each of the given problems is to solve both equations for y (only need to do this with problems 4 through 6 since you've already been given the equations solved for y with problems 1 through 3). After you have two equations solved for y, simply set them equal to each other and then manipulate until you have a quadratic equation of the form:
Ax^2 + Bx + C = 0
After you've gotten your quadratic equation, just find the roots to the equation and you'll know both X values that will result in the same Y value as the equations you've been given for each problem. I'm personally using the quadratic formula for getting the desired roots, but you can also factor manually. So let's do it.
1. y = x+2, y = x^2 - 4
Set the equations equal to each other
x + 2 = x^2 - 4
2 = x^2 - x - 4
0 = x^2 - x - 6
Using the quadratic formula with A=1, B=-1, C=-6, you get the solutions -2 and 3.
2. y = x^2 + 3x - 1, y = x+14
Same thing, set the equations equal to each other.
x^2 + 3x - 1 = x + 14
x^2 + 2x - 1 = 14
x^2 + 2x - 15 = 0
Use the quadratic formula with A=1, B=2, C=-15. Roots are -5 and 3.
3. y = 2x^2 + x - 7, y = 2x + 8
Set the equations equal to each other again.
2x^2 + x - 7 = 2x + 8
2x^2 - x - 7 = 8
2x^2 - x - 15 = 0
Quadratic formula with A=2, B=-1, C=-15, gives you the roots of -2.5 and 3
4. y = x(x + 3), y - x = 8
A little more complicated. Solve the second equation for y
y - x = 8
y = x + 8
Multiply out the 1st equation
y = x(x + 3)
y = x^2 + 3x
Now set the equations equal to each other
x + 8 = x^2 + 3x
8 = x^2 + 2x
0 = x^2 + 2x - 8
And use the quadratic formula with A=1, B=2, C=-8. Roots are -4, 2
5. y = -3x^2 - 2x + 5, y + 2x + 22 = 0
Solve the 2nd equation for y
y + 2x + 22 = 0
y + 22 = -2x
y = -2x - 22
Set equal to 1st equation
-2x - 22 = -3x^2 - 2x + 5
-22 = -3x^2 + 5
0 = -3x^2 + 27
Use the quadratic formula with A=-3, B=0, C=27, giving roots of 3 and -3
6. y + 6 = 2x^2 + x, y + 3x = 10
Solve the 1st equation for y
y + 6 = 2x^2 + x
y = 2x^2 + x - 6
Solve the 2nd equation for y
y + 3x = 10
y = -3x + 10
Set the solved equations equal to each other
2x^2 + x - 6 = -3x + 10
2x^2 + 4x - 6 = + 10
2x^2 + 4x - 16 = 0
Use the quadratic formula with A=2, B=4, C=-16, getting roots of -4 and 2.</span>
I know how to do it but I caint explain (sorry:( )
Answer:
Yes.
Step-by-step explanation:
It is given that, A sponge can filter 8 liters of water in 10 hours or 12 liters in 15 hours.
8 L = 10 h
1 h = = 1.25 h
or
12 L = 15 h
1 h = = 1.25 h
Hence, this relationship is proportional.