Find the x- and y-intercepts of the line x - 3y= -9
2 answers:
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Let's consider an arbitrary 2x2 matrix as an example,
The columns of
are linearly independent if and only if the column vectors 
are linearly independent.
This is the case if the only way we can make a linear combination of reduce to the zero vector is to multiply the vectors by 0; that is,
only by letting
.
A more concrete example: suppose
Here,
and 
. Notice that we can get the zero vector by taking 
and 
:
so the columns of are not linearly independent, or linearly dependent.
The columns of
This is the case if the only way we can make a linear combination of
only by letting
A more concrete example: suppose
Here,
so the columns of
Answer:
A) Between 388 and 450
B) Between 357 and 481
C) Between 326 and 512
D) 99.995%
E) 72.907%
Step-by-step explanation:
We are given;
Mean; x¯ = 419 minutes
Standard deviation; σ = 31 minutes
A) From the empirical rule, 68% falls within 1 standard deviation.
Thus, it will be between;
419 - 1(31) and 419 + 1(31)
Thus gives;
Between 388 and 450
B) From the empirical rule, 95% falls within 2 standard deviation.
Thus, it will be between;
419 - 2(31) and 419 + 2(31)
Thus gives;
Between 357 and 481
C) From the empirical rule, 99.7% falls within 2 standard deviations.
Thus, it will be between;
419 - 3(31) and 419 + 3(31)
Thus;
Between 326 and 512
D)between 359 and 479 minutes, we will use z-s roe formula;
z = (479 - 359)/31
z = 3.871
From the z-table attached, we see that the probability is 0.99995 and as such, the percentage is 99.995%
E) worker spent 400 minutes on the job.
Thus;
z = (419 - 400)/31
z = 0.613
From z-tables, p = 0.72907
In percentage, we have; 72.907%
