1998=2×33×37
Too many questions! Submit each as a separate question.
(4.1.1) VENN DIAGRAM
In this diagram the red circle represents everyone surveyed, the green circle those with a driving licence, and the blue circle those with a parking ticket.
The letters are regions defined here:
A Licence, no ticket
B Licence and ticket
C No licence, but a ticket
D Neither a licence nor a ticket
We can assign numbers:
A+B=15% of 300=45 with a driving licence (green circle)
B+C=10% of 300=30 with a parking ticket (blue circle)
D=78% of 300=234 with neither
A+B+C+D=300 all surveyed
A+B+C=300-234=66,
A=66-(B+C)=66-30=36,
B=45-A=45-36=9; C=30-B=30-9=21.
(4.1.2) B (licence and ticket)=9
(4.1.3) C (ticket but no licence)=21
See how the diagram makes the problem easy to solve!
(1.2) -⅓p=
⎛ 17 ⎞
⎝ 9 ⎠
Divide each component of the vector by -3.
(1.3) 8(k-1)-(-4(2k-3))=8k-8+8k-12=16k-20.
(2.1) (4x+5)+7=-2(3x+23)-4, expand and distribute:
4x+5+7=-6x-46-4, simplify:
4x+12=-6x-50, group variables and constants, (add 6x-12 to both sides):
4x+6x=-50-12, simplify:
10x=-62, divide both sides by 10:
x=-62/10=-31/5 or -6.2 (reduced to fraction or decimal).
(2.2) Create equations according to the positions of the matrix elements:
2x+4=-10, 2x=-14, x=-7; 2+z=5, z=3;
x+y=3, -7+y=3, y=10; 3+y+z=16, 3+10+z=16, 13+z=16, z=3.
(x,y,z)=(-7,10,3).
(2.3) Simple interest formula is I=PTR/100. P=N$350000, T=10 years, R=annual %ge.
I=350000×10×15/100=N$525000. This is the interest to be added to the capital (principal).
Total after 10 years=350000+525000=N$875000.