Answer:
Note that we need calculate the scores between the mean (
) and the mean plus 3 times the standard deviation. It is 3 times since the distance between the values given (513 and 759) divided by the standard deviation is 3 (
)
So the rule say that 99.7% of data is between
and
, as it is a normal distribution half of 99.7% is between
and
. Hence 49.85% of people score between 513 and 759.
Answer:
(5,6)
Step-by-step explanation:
<em>Generally, is the coordinate (x,y) is translated right by a units and up by b units, the resulting coordinate wil be;</em>
g(X, Y) = (x+a, y+b)
To the right is along the positive x axis while up is along the positive y axis
Given a = 3 and b = 4
g(X,Y) = (2 + 3, 2 + 4)
g(X, Y) = (5, 6)
Hence the resulting coordinate of g is (5,6)
Find the unit rate which is 260/12 which is 21 and 2/3 now divide 286 by 21 and 2/3.
The parent function is : f ( x ) = x³
f ( x + 3 ) = ( x + 3 )³
It is B ) shift to the left 3 units.
Answer:
![f(x)=2x^{3}+24x^{2}+82x+60](https://tex.z-dn.net/?f=f%28x%29%3D2x%5E%7B3%7D%2B24x%5E%7B2%7D%2B82x%2B60)
Step-by-step explanation:
we know that
The roots of the polynomial are the values of x when the value of the polynomial f(x) is equal to zero
The roots of the polynomial function are
x=-6 -----> (x+6)=0
x=-5 -----> (x+5)=0
x=-1 -----> (x+1)=0
The equation of the cubic polynomial is
![f(x)=a(x+6)(x+5)(x+1)](https://tex.z-dn.net/?f=f%28x%29%3Da%28x%2B6%29%28x%2B5%29%28x%2B1%29)
where
a is the leading coefficient
Remember that
f(0)=60
That means ------> For x=0 the value of f(x) is equal to 60
substitute the value of x and the value of y in the function and solve for a
![60=a(0+6)(0+5)(0+1)](https://tex.z-dn.net/?f=60%3Da%280%2B6%29%280%2B5%29%280%2B1%29)
![60=a(6)(5)(1)](https://tex.z-dn.net/?f=60%3Da%286%29%285%29%281%29)
![60=30a](https://tex.z-dn.net/?f=60%3D30a)
![a=2](https://tex.z-dn.net/?f=a%3D2)
so
![f(x)=2(x+6)(x+5)(x+1)](https://tex.z-dn.net/?f=f%28x%29%3D2%28x%2B6%29%28x%2B5%29%28x%2B1%29)
Applying the distributive property
Convert to expanded form
![f(x)=2(x+6)(x+5)(x+1)\\\\f(x)=2(x+6)(x^{2}+x+5x+5)\\\\f(x)=2(x+6)(x^{2}+6x+5)\\\\f(x)=2(x^{3}+6x^{2}+5x+6x^{2}+36x+30)\\\\f(x)=2x^{3}+24x^{2}+82x+60](https://tex.z-dn.net/?f=f%28x%29%3D2%28x%2B6%29%28x%2B5%29%28x%2B1%29%5C%5C%5C%5Cf%28x%29%3D2%28x%2B6%29%28x%5E%7B2%7D%2Bx%2B5x%2B5%29%5C%5C%5C%5Cf%28x%29%3D2%28x%2B6%29%28x%5E%7B2%7D%2B6x%2B5%29%5C%5C%5C%5Cf%28x%29%3D2%28x%5E%7B3%7D%2B6x%5E%7B2%7D%2B5x%2B6x%5E%7B2%7D%2B36x%2B30%29%5C%5C%5C%5Cf%28x%29%3D2x%5E%7B3%7D%2B24x%5E%7B2%7D%2B82x%2B60)