Answer:
5B; 7B; 1,024; see answer
Step-by-step explanation:
5.
We can see from the table that
a1 = 5
a2= 5·2 = 10
a3= 5·2·2 = 5·2² = 20
a4 = 5·2·2·2 = 5·2³ = 40
...
[tex]a_{n} = 5*2^{n-1}[/tex]
7.
Is given that the filter removes 90% of contaminated air
after run 1 :
100% air
90% contamination removed for 100% air
100% is 10%+10%+10%+10%+10%+10%+10%+10%+10%+10%
10% is still contaminated air
after run 2:
10% air
90% contamination removed for 10% air
10% is 1%+1%+1%+1%+1%+1%+1%+1%+1%+1%
1% is still contaminated air
after run 3:
1% air
90% contamination removed for 1% air
1% is .1%+.1%+.1%+.1%+.1%+.1%+.1%+.1%+.1%+.1%
.1% is still contaminated air
11.
Figure 1 = 1 piece
Figure 2 = 4 pieces
Figure 3 = 4² = 16
...
[tex]Figure 6 = 4^{(6-1)} = 4^{5} = 1024[/tex]
12.
[tex](c+d)^{6} \\[/tex]
-we know that the coefficients should be 1, 6, 15, 20, 15, 6, 1
-we start with c to the lowest power 0 and d to the highest power 6 and end with d to the lowest power 0 and c to the highest power 6
[tex](c+d)^{6} = 1*c^{0} d^{6} +6*c^{1} d^{5} +15*c^{2} d^{4} +20*c^{3} d^{3} +15*c^{4} d^{2} +6*c^{5} d^{1} +1*c^{6} d^{0}[/tex]
-we simplify to have the final answer:
[tex](c+d)^{6 } = d^{6} +6cd^{5} +15c^{2} d^{4} +20c^{3} d^{3} +15c^{4} d^{2} +6c^{5} d+c^{6}[/tex]
