Answer:
180
Step-by-step explanation:
total ratio is 15
gallons of red =

gallons of yellow

gallons of blue

total =144+30+6
=180
Answer:
See picture and explanation below.
Step-by-step explanation:
With this information, the matrix A that you can find is the transformation matrix of T. The matrix A is useful because T(x)=Av for all v in the domain of T.
A is defined as
denotes the vector of coordinates of
respect to the basis
(we can apply this definition because
forms a basis for the domain of T).
The vector of coordinates can be computed in the following way: if
then
.
Note that we have all the required information:
then
hence
The matrix A is on the picture attached, with the multiplication A(1,1,1).
Finally, to obtain the output required at the end, use the properties of a linear transformation and the outputs given:
In this last case, we can either use the linearity of T or multiply by A.
3x + y = -3
-2x + y = 7
Use elimination method
Subtract both equations
5x = -10, x = -2
Plug in -2 for x (any equation)
3(-2) + y = -3
-6 + y = -3
y = 3
Solution: x = -2, y = 3
Or as a coordinate: (-2, 3)
Answer:
P(0) = 7,917
Step-by-step explanation:
The population of the community is given by the following formula:

In which P(0) is the initial population and r is the growth rate.
The initial population P0 has doubled in 5 years.
This means that

Which lets us find r.



Applying the 5th root to both sides


So

Suppose it is known that the population is 12,000 after 3 years.
With this, we find P(0)





Answer:
60% of the students wanted hamburgers
Step-by-step explanation:
just multiply