Consider a homogeneous machine of four linear equations in five unknowns are all multiples of 1 non-0 solution. Objective is to give an explanation for the gadget have an answer for each viable preference of constants on the proper facets of the equations.
Yes, it's miles true.
Consider the machine as Ax = 0. in which A is 4x5 matrix.
From given dim Nul A=1. Since, the rank theorem states that
The dimensions of the column space and the row space of a mxn matrix A are equal. This not unusual size, the rank of matrix A, additionally equals the number of pivot positions in A and satisfies the equation
rank A+ dim NulA = n
dim NulA =n- rank A
Rank A = 5 - dim Nul A
Rank A = 4
Thus, the measurement of dim Col A = rank A = five
And since Col A is a subspace of R^4, Col A = R^4.
So, every vector b in R^4 also in Col A, and Ax = b, has an answer for all b. Hence, the structures have an answer for every viable preference of constants on the right aspects of the equations.
For given sample of salaries of four employees, the variance of their salaries is: 26 thousands of dollars
The formula for the variance is,
where,
= sample variance
= the value of the one observation
= the mean value of all observations
n = the number of observations
For given question,
n = 4
First we find the mean of their salaries.
(33 + 31 + 24 + 36 ) / 4 = 31
So, 
Using the formula for variance ,
Therefore, for given sample of salaries of four employees, the variance of their salaries is: 26 thousands of dollars
Learn more about the variance here:
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Answer:
Step-by-step explanation:
g(x)= -x-1 or g(x) = x+1
if g(x) = -x-1
-x-1=2x+4
-x=2x+5
-x/2=x+5
-x/2 -x=5
-x/2-2x/2=5
-x-2x=5
-3x=5
x=5/-3
if g(x) = x+1
x+1=2x+4
x=2x+3
x/2=x+3
x/2-x=3
x/2-2x/2=3
x-2x=3
-x=3
x=3
Answer:
Step-by-step explanation:
is the given line 3x - 4y = -17?
then,
- 4y = -3x -17
y=(3/4)x+17/4
it is parallel, so slope of our line is 3/4 or 0.75
y=0.75x+b
next, lets plug in the given point to get the y-int
2=0.75*(-3)+b
2=-2.25+b
b-2.25=2
b=4.25
the equation is y=0.75x+4.25
does this clear anything, or am I off topic? please tell me I will help you
Answer:
- difference: -4 cubic inches
- % change: -10%
Step-by-step explanation:
The difference between the new volume and the original volume is ...
(new volume) - (original volume) = (36 in³) - (40 in³) = -4 in²
__
The percentage change is figured with respect to the original volume:
% change = (difference)/(original volume) × 100% = (-4 in³)/(40 in³) × 100%
= -1/10 × 100% = -10%
