Answer:
The mean is 8.
Step-by-step explanation:
The mean is the sum of a set of numbers divided by the number of numbers in a set. In this case, you add up all the numbers to get 56, and divide by 7 to get 8.
First you need to know the definition of a complementary angle. That means that two angles add up to 90 degrees, or a right angle.
To find an angle complementary to a 78 degree angle, you need to subtract 78 from 90.
90 - 78 = 12
Answer:
34.134%
68.268%
Step-by-step explanation:
Given that:
Mean (m) = 500
Standard deviation (s) = 100
Percentage between 500 and 600
P(500 < x < 600)
P(x < 600) - P(x < 500)
Z = (x - m) / s
P(x < 600)
Z = (600 - 500) /100 = 1
P(x < 500)
Z = (500 - 500) / 500 = 0
P(Z< 1) - P(Z < 0)
0.84134 - 0.5
= 0.34134
= 0.34134 * 100%
= 34.134%
B.) Between 400 and 600
P(x < 400)
Z = (400 - 500) /100 = - 1
P(x < 600)
Z = (600 - 500) / 500 = 1
P(Z< 1 ) - P(Z < - 1)
0.84134 - 0.15866
= 0.68268
= 0.68268 * 100%
= 68.268%
Intersection of the first two lines:
Multiply the first equation by 4 and the second by 5:
Subtract the two equations:
Plug this value for y in one of the equation, for example the first:
So, the first point of intersection is 
We can find the intersection of the other two lines in the same way: we start with
Use the fact that x and y are the same to rewrite the second equation as
And since x and y are the same, the second point is 
So, we're looking for a line passing through and . We may use the formula to find the equation of a line knowing two of its points, but in this case it is very clear that both points have the same coordinates, so the line must be 
In the attached figure, line 
is light green, line 
is dark green, and their intersection is point A.
Simiarly, line 
is red, line 
is orange, and their intersection is B.
As you can see, the line connecting A and B is the red line itself.
This is a well known joke:
Why six afraid of seven? Because seven ate nine!
It is supposed to be a "word game" where instead of writing eight, the authour wrote ate, which sound the same but means something different.
Hope it helped,
Happy homework/ study/ exam!
