Math Project Essay

Section 1.1
16) 5 [19 + (5² - 16)²]
5 [19 + (9)²]²
5 [19 + 81]²
5 [100]²
5 [10,000]
= 50,000

18) $200 / 1 + 0.09 x 4 / 12
$200 / 1 + 0.09 x 0.33
$200 / 1 + 0.03
$200 / 1.03
= $194.17

20) $1,000 (1 + 0.02)³
$1,000 (1.02)³
$1,000 (1.06)
= $1,061.21

22) $300[1-1/〖□(((1+0.03))/(0.03))〗^2 ]
$300[1-1/〖□(((1.03))/0.03)〗^2 ]
$300[1-1/〖□(1.0609/0.03)〗^ ]
$300[1- 0.942595909/0.03]
$300[1-31.41986364]
$300[ (1-0.942595909)/0.03]
$300[ 0.057404091/0.03]
$300[ 1.913469696]
= $574.04

Section 1.2
10) -1 11/32
-1 + 0.34375
= -0.65625 = -65.62500%

18) -4/900
-0.004 ̅= -0.4 ̅%

26) 0.030405
0.03041

34) 15/365
0.041096 = 4.1096%

42) ($10,000)/(1-0.10 * □(182/365))
$10,000/(1-0.10*0.498630137)
$10,000/0.950136986
= $10,524.80

44) $950.75(1- 〖(0.095)/4)〗^2
$950.75(1-0.02375 )^2
$950.75(0.953064063)
= $906.13

Section 1.3
30) $1.25 is 3/4% of what amount?
1.25/0.75=$1.6 ̅

36) $99,736.41/(5.7%)
= $1,749,761.579
$1,749,761.579/$0.99
= 1,767,435.94 Songs

38)
31.16 * 1,000 = 31,160 milligrams
0.05% impurities (100% – 99.95%)
31,160 * 0.05% = 15.58mg
44)
$210,000/2.5=$84,000 Original Selling Price

Section 1.4
8)
500g per can
$8.25 / HR
$0.18 / KG in excess of 500KG in 7.5 HR Shift
250 cans per HR
1,000g = 1KG

250 cans * 7.5 hrs = 1,875 cans per shift
$8.25 * 7.5 hrs = $61.875
500g * 1,875 cans = 937,500g
937,500g/1,000 = 937.5KG per shift

937.50KG – 500KG = 437.50KG * $0.18
= $78.75 + $61.875
Total per day = $140.63
14)
Monthly $2,000 plus 2.2% commission on sales exceeding $150,000 / Month $227,000 sales - $150,000 quota = $77,000 * 2.2% = $1,694 + $2,000 salary = $3,694 $235,000 sales - $150,000 quota = $85,000 * 2.2% = $1,870 + $2,000 salary = $3,870
To earn $3,870 monthly Sharon would need to earn a straight commission rate of 1.6468%
$3,870/$235,000=1.6468% which would generate the same average monthly earnings
Section 1.5
6)
Grade: C+ B- B+ C- B C
Credit: 5 3 4 2 3 4 total: 21
GP: 2.3 2.7 3.3 1.7 3.0 2.0
GPxCR: 11.5 8.1 13.2 3.4 9 8 total: 53.2

GPA = 53.2/21=2.53 ̅ Margot`s GPA

10)
Security Proportion invested (%) Rate of return for the year (%) PIxROR
Company A shares .15 14 2.1%
Province B bonds .20 10 2%
Company C shares .10 -13 -1.3%
Units in Fund D .35 12 4.2%
Company E shares .20 27 5.4% 1.00 12.4%

Overall rate of return on portfolio was: (12.4%)/1.00 = 12.4%

12)
Disposable Income Consumers Spend (%) Average Change (%) CSxAC
Food .30 10 3%
Clothes .20 -5 -1%
Rent .50 15 7.5% 9.5%

Average Price Increase experienced: (9.5%)/1.00 = 9.5%

Section 1.6
10)
a) $298,000/$100=$2,980*$1.52193=$4,535.35 Current year property tax
$285,000/$100=$2,850*$1.56324=$4,455.23 Prior year property tax
Change from Prior to Current = $4,535.35 - $4,455.23 = $80.12
b) $4,455.23/$2,980=$1.495043624 prop.tax rate which would have no $ change from Prior to Current

Section 2.1
8) 4(a^2-3a-4) -2(5a^2-a-6)
= 4a^2-12a-16-10a^2+2a+12
= (4a^2-10a^2)+(-12a+2a)+(-16+12)
= (-6a^2)+(-10a)+(-4)

14) 2x/(1.045)-(2.016x)/3+x/2
1.91x – 0.672x + 0.5x
X=1.7419

24) (3p^2-5p) (-4p+2)
= 3p^2(-4p+2) -5p(-4p+2)
= (-12p^3)+(6p^2+20p^2)+(-10p)
= (-12p^3)+(26p^2)+(-10p)

26) 5(2x-y)(y+3x)-6x(x-5y)
= 10x-5y+y+3x-6x^2+30xy
= 10x-5y+y+3x-6x^2+30xy
= x(10+3+30) = 43x
= y(-5+1+1) = -3y
= -6x^2 + 43x -3y

28) (6a^2 b)/(-2ab^2 )
=(3(2)(a)(a)(b))/(-1 (2)(a)(b)(b))
=3(a)/(-1(b) )

32) (32a^2-8ab+14ab^2)/2ab
=(32a^2 b)/2ab-8ab/2ab+(14ab^2)/2ab
= 16a -4 + 7b

34) (120(1+〖i)〗^2+180(1+〖i)〗^3)/(360 (1+i))
=(2(60)(1+i)(1+i)+3(60)(1+i)(1+i)(1+i))/(6(60)(1+i))
=(2(1+〖i)〗^2+3(1+〖i)〗^2)/6
=(5(1+〖i)〗^2)/6
=5/6

48) R[((1+〖i)〗^n-1)/i](1+i)
R=$910 i=0.1038129 n=4

=$910[((1.1038129)^4-1)/0.1038129](1+0.1038129)

=$910[0.484505671/0.1038129](1.1038129)

=$910[4.667104677](1.1038129)

=

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