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
y=2
Step-by-step explanation:
Make an equation of straight line by using the formula :y= mx+c
put the x-value of point (2,4) which is 2 and the gradient,m which is 2 into the straight line equation:
y=2x +c
So you need to find the y-intercept to complete the equation, therefore:
when y=0,
0=2(2)+c
c=-4
next the question ask to find the y-coordinate when x =3, therefore you just need to replace x in the equation with 3:
y=2(3)-4
y=4
Answer:
3x
Step-by-step explanation:
3 . x is 3x
1) Given binomials:
First binomial 7r - 5
Second binomial 5r + 8
2) To pass from 7r to 5r you have to subtract 2r, so the first term of the binomial to be subtracted is 2r
3) To pass form - 5 to + 8, you have fo subtract - 13
4) So the answer is 2r - 13, option b.
Answer:
or
units.
Step-by-step explanation:
To find the <em>distance between two points</em>, we can use the Distance Formula.
Distance Formula: 
<u />
<u>Given:</u>
P (10, -7) ⇒ x₁ = 10, y₁ = -7
Q (7, -10) ⇒ x₂ = 7, y₂ = -10
Substitute the given values into the formula and simplify.

The distance between points P and Q is
or
units.
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