the first step Andre made was
2x+6=3x-8
or, -x+6=-8
And the first step Diego made was
2x+6=3x-8
or, +6=3x-2x
or, 6=x-8
...
Answer:
a) ρ (X,Y) = 0.125
b) The linear relationship is weak because ρ (X,Y) is almost 0
c) There is a positive linear relationship because ρ (X,Y) > 0
Step-by-step explanation:
The Pearson correlation coefficient is calculate as :
ρ (X,Y) = (σXY) / (σX)(σY)
-1 ≤ ρ ≤ 1
When ρ = 0 there is no linear relationship between the variables. This does not mean that the variables are independent.
When ρ = 1 the linear relationship is perfect positive. ρ = 1 means a direct relation between X and Y : When X increases also Y increases in constant proportion. When Y increases also X increases in constant proportion.
When ρ = -1 the linear relationship is perfect negative. ρ = -1 means a inverse relation between X and Y : When X increases Y decreases in constant proportion. When Y increases X decreases in constant proportion.
In our exercise ρ (X,Y) = 13.44 / (15.57)(6.90) = 0.125
a) ρ (X,Y) = 0.125
b) The linear relationship is weak because ρ (X,Y) is almost 0
c) There is a positive linear relationship because ρ (X,Y) > 0
The midpoint of the range of frequencies given is:
midpoint = (82.4 +
659.2) / 2 = 370.8 Hertz
Then the difference from midpoint to the other end is:
370.8 - 83.4 = 288.4 Hertz
Therefore the inequality formula is
|f - 370.8| <= 288.4
Answer: BC is 9 units long
==============================================================
Work Shown:
Let x be the length of segment BC.
BC is parallel to DE, so this means that triangle ABC is similar to triangle ADE.
Side AB pairs with side AD (both are horizontal sides of triangle ABC and triangle ADE respectively)
Side BC pairs with side DE (both are vertical sides of triangle ABC and triangle ADE respectively)
Because of those facts above, we can end up with this proportion
AB/AD = BC/DE
-------------------
Let's plug in the given values and isolate x
AB/AD = BC/DE
12/20 = x/15
12*15 = 20*x ... cross multiply
180 = 20x
20x = 180
20x/20 = 180/20 ... divide both sides by 20
x = 9
Segment BC is 9 units long.
note: There is no need to calculate the length of segment AE. Though you are correct in stating that AE = 25.
I would download the photomath app. you can take a picture of the graph and it will solve it for you and show you the steps