Category ‘7th Grade’

Solution:

The APR is 4%, so the semi-annual interest rate is 2%. If you deposit $10,000 in the bank after every six months, you will have $85,829.69 in the bank at the end of 4 years:

1. After six months you will have $10,000
2. After one year you will have 10,000×1.02+10,000 = $20,200
3. After 1.5 years you will have $20,200×1.02+10,000 = $30,604
4. After 2 years you will have $30,604×1.02+10,000 = $41,216.08
5. After 2.5 years you will have $41,216.08×1.02+10,000 = $52,040.40
6. After 3 years you will have $52,040.40×1.02+10,000 = $63,081.21
7. After 3.5 years you will have $63,081.21×1.02+10,000 = $74,342.83
8. After 4 years you will have $74,342.83×1.02+10,000 = $85,829.69

The present value of that $85,829.69, discounting at 2% is $73,254.81 (i.e. $85,829.69/(1.02^8)), so if you put this amount in the bank now, and make the payments every six months, there will be nothing left in the account after four years.

Solution:

A scientific experiment has three types of variables: independent, dependent and controlled. Please click on this link to get details: http://www.sciencebuddies.org/mentoring/project_variables.shtml.

Solution:

Scientific experiment has three types of variables: independent, dependent and controlled.

Please click on this link to get details:

http://www.sciencebuddies.org/mentoring/project_variables.shtml

Solution:

This is a well known “trick question”. It’s simply a series of squares with the digits reversed:

1² = 1   => 1

2² = 4   => 4

3² = 9   => 9

4² = 16 => 61

5² = 25 => 52

6² = 36 => 63

7² = 49 => 94

8² = 64 => 46

9² = 81 => 18

Solution:

1. (15/45) / 60/75)
2. (1/3) / 4/5)
3. (1/3) x 5/4)
4. 5/12

Solution:

Specific heat capacity for water = 4.18 Joules/(gram*degree Celcius)
(how much energy is required per gram per change in degrees C)

mass = 4g
Change in temperature = 6 deg C

energy required = mass * change in temperature * specific heat capacity
= 4g * 6 deg C * 4.18 J/(g*deg C)
= 100.32 Joules