Mathematical Models
Personal Finance
Geometry and Trigonometry
Data Management
100
What makes this equation Quadratic? 5x2-3x+3=0
The 2 makes this equation Quadratic.
100
What would be the yearly earnings for a person with $6,000 in savings at an annual interest rate of 3.5 percent?
$6,000 × 0.035 = $210
100
If you were designing a diamond necklace, the most important factor would be?
Best Aesthetics
100
Data describing your favorite type of music is?
Qualitative
200
What is the maximum/minimum value of this graph?
The value is a minimum: y = –1
200
The maximum amount of money the credit card company has allowed you to borrow using your card is the?
Credit Limit
200
What scale is Pentagon B?
1:3 OR 1 to 3
200
Calculate the mean, median, and mode for the following data set: 12, 54, 34, 63, 23, 54, 65, 37, 82, 83, 11.
Mean - 47.09
Median - 54
Mode - 54 (appears twice)
300
How has y=0.25x2 been transformed from the parent function y=x2?
A vertical compression by a factor of 0.25.
300
You take out a bank loan for the amount of the purchase at 5.5%, compounded monthly. (Compare the cost of borrowing $2200 for four months)
Principal (P)=$2222 - Interest rate (i)=0.055 - Number of compounding periods per year (n)=12 - Total number of compounding periods (nt)=4
A=P(1+i/n)nt
A=2200 (1+0.055/12)4
A=2200 (1.0045833)4
A=2240.61
I=A-P
I=2240.61-2200=40.61
The bank loan will cost $40.61 in interest.
300
Calculate the size of the unknown angle, to the nearest degree.
Angle C = tan-1(15.7/21.8)
Angle C =35.76°
Therefore, Angle C is approximately 36°.
300
Determine the range and standard deviation for the list of shoe sizes you collected in your store this week.
The largest size shoe is 10 and the smallest is 5.
The range is 10 - 5 which equals 5.
Standard Deviation = 1.174
400
A culture of Lactobacillus bacteria doubles every two hours. The initial number of bacteria is 20. How many bacteria are there after 16 hours?
A=I(2)t/b
A=20(2)16/2
A=20(2)8
A=5120
There are 5120 bacteria after 16 hours.
400
Calculate the amount of simple interest paid on a loan of $8000, at a rate of 5.2% per year for six years.
I=PRT
I=80000.0526
I=2496
The total interest paid on the loan is $2496.
400
Which law would you use to calculate the unknown required? Solve for the unknown side or angle.
Cosine Law. Solving for side b:
b2=(262)2+(175)2-2 (262) (175) cos(42°)
b2=31 122.619
b=176.4 km
400
A dream-home lottery is valued at $800 000 in prizes and sells a maximum of 12 500 tickets. You have decided to buy five tickets. What is your probability of winning? Show your solution as a fraction, decimal, and percent.
Fraction: 512/500 = 1/2500
Decimal: 5/12 500 = 5 ÷12 500 = 0.0004
Percent: 0.0004 x 100= 0.04%
500
A stamp collection worth $2500 appreciates at a rate of 10% per year. How much will it be worth after 30 years? Round your answer to two decimal places.
A=I(1+i)t
A=2500(1+0.10)30
A=2500(1.10)30
A=43 623.51
The stamp collection will be worth $ 43 623.51 after 30 years.
500
You take out the money as a cash advance at 21.99%, compounded daily. Your creditor charges a flat fee of $3, plus 2% of the transaction. (Compare the cost of borrowing $2200 for four months.)
Fees:$47 - Principal:$2247 - Interest rate: 0.2199 - number of compounding periods per year: 365 - total number of compounding periods: 120.
A= p(1 i/n)nt
A= 2247(1+0.2199/12)120
A=2247(1.0006025)120
A=2415.41
I=A-P
I=2415.41-2200=215.41
The cash advance will cost $215.41 in interest and fees.
500
Which law would you use to calculate the unknown required? Solve for the unknown side or angle.
Sine Law. Solving for∠Y :
sin(∠Y)/12.5=sin(50°)/16.5
sin(∠Y)= sin(50°)/16.5 x 12.5
∠Y=sin-1(sin(50°)/16.5 x 12.5)
∠A=35.5°
500
John has won 6 out of the last 10 races he has entered. He will be running a 2 km race tomorrow. Based on his record of winning races, what are the odds he will win the race tomorrow?
If John has won 6 out of 10 races, the experimental probability of John winning a race is 6/10. If he has won 6 out of 10 races, he has lost 4 out of 10.
Number of lost races: 10 - 6 = 4
His odds of winning tomorrow are 6:4 or 3:2.