Answer:
a) M =82
Step-by-step explanation:
Let´s study this as a Normal distribution.
As we know in a normal distribution the z score is = (X-μ)/(sd/sqrt(n))
where
X = mean for the taken sample = What we want to know in this problem
μ = Total population mean =80
sd= standard deviation= 12
n = sample size=9
So in this case z=( X-80)/(12/sqr(9))= (X-80)/4
also we know that the effect size taken by the machine is 0.5, which is the same as the z-score
so...
0.5 = (X-80)/4 => 0.5*4 = X-80
2+80 = X
X = 82
Answer:
60%
Step-by-step explanation:
Divide the amount of people who showed up by the total invited...
39/65 = 0.6
To convert a decimal to a percent, multiply the decimal by 100%...
0.6(100%) = 60%
Answer:
The value of h'(7) = 44 .
Step-by-step explanation:
Given:
f'(7)=9 and g(7)= 5
We have to find : h'(7)
Also,
⇔ 
...equation (i)
Plugging the value of 'x' = 7 in equation (i) the equation can be re-framed as:
⇔ 
⇔
Now plugging the value of f'=(7)=9 and g(7)=5 in the above equation:
⇔ 
⇔ 
⇔ 
So the value of h=(7) = 44 .
Answer:
y = 3x - 16
Step-by-step explanation:
We are asked to find the equation of the line perpendicular to 2x + 6y = 30
We can use two formulas for this question, either
y = mx + c. Or
y - y_1 = m(x - x_1)
Step 1: calculate the slope
From the equation given
2x + 6y = 30
Make y the subject of the formula
6y = 30 - 2x
Or
6y = -2x + 30
Divide both sides by 6, to get y
6y/6 = ( -2x + 30)/6
y = (-2x + 30)/6
Separate them in order to get the slope
y = -2x/6 + 30/6
y = -1x/3 + 5
y = -x/3 + 5
Slope = -1/3
Step 2:
Note: if two lines are perpendicular to the other, both are negative reciprocal of each other
Perpendicular slope = 3/1
Substitute the slope into the equation
y = mx + c
y = 3x + c
Step 3: substitute the point into the equation
( 6,2)
x = 6
y = 2
2 = 3(6) + c
2 = 18 + c
Make the c the subject
2 - 18 =c
c = 2 - 18
c = -16
Step 4: sub the value of c into the equation
y = 3x + c
y = 3x - 16
The equation of the line is
y = 3x - 16
If you try out the other formula, u will get the same answer
