Answer:
See below for answers and explanations
Step-by-step explanation:
<u>Part A</u>
10x - 12x - 3 does not equal -5x. Looks like what she did wrong was treating -3 as -3x and got her incorrect result that way
<u>Part B</u>
10x - 12x - 3 = (10-12)x - 3 = -2x - 3
Answer:
a) 51.4
b) answer attached
c) 48.59% female
Step-by-step explanation:
a) Male driver = 100-48.6 = 51.4%
b) answer attached below
c) probability that out of 20-64 group a randomly selected sample is female
( 39.54 ÷ 81.36 ) x 100
= 48.59% chance of her being a female
Answer:
D
Step-by-step explanation:
Answer:
Net Profit after tax Rs 15,000
Step-by-step explanation:
The computation of the net profit after tax is shown below:
Gross profit Rs. 1,25,000
Less:
Selling and distribution expenses Rs. 21,000
General and administrative expenses Rs. 75,000
Interest on loan Rs. 5,000
Gain on sale of plant Rs. 4,000
Profit before tax Rs 20,000
Less: income tax expense at 25% of Rs 20,000 Rs 5000
Net Profit after tax Rs 15,000
Answer:
(A) Set A is linearly independent and spans
. Set is a basis for
.
Step-by-Step Explanation
<u>Definition (Linear Independence)</u>
A set of vectors is said to be linearly independent if at least one of the vectors can be written as a linear combination of the others. The identity matrix is linearly independent.
<u>Definition (Span of a Set of Vectors)</u>
The Span of a set of vectors is the set of all linear combinations of the vectors.
<u>Definition (A Basis of a Subspace).</u>
A subset B of a vector space V is called a basis if: (1)B is linearly independent, and; (2) B is a spanning set of V.
Given the set of vectors
, we are to decide which of the given statements is true:
In Matrix
, the circled numbers are the pivots. There are 3 pivots in this case. By the theorem that The Row Rank=Column Rank of a Matrix, the column rank of A is 3. Thus there are 3 linearly independent columns of A and one linearly dependent column.
has a dimension of 3, thus any 3 linearly independent vectors will span it. We conclude thus that the columns of A spans
.
Therefore Set A is linearly independent and spans
. Thus it is basis for
.