I have all these questions to work out the answer to for homework and we are allowed to get any sort of help as long as we get the right answer.

There are a lot. but help me out if you can answer any of the questions. Please show working out so i understand what you are doing to calculate the answers.

1) a packing carton is to be constructed the square face = X by X and the side length is = 9-X

i) show that the surface area (SA) of the carton is SA= 36X-2X squared

ii) explain why the formula is only valid for values of X from X=0 to X=9

2)a lamp on a desk is 90cm from a book and stands 25cm vertically (the lamp)

i) calculate the angle of elevation( to the nearest degree) of the light from the book

ii) determine the length (L) of the light beam (to one decimal place)

iii) when the lamp is moved closer to the book, the new angle of elevation is 20 degrees. How far ( correct to one decimal place ) was the lamp moved toward the book.

3) this is simpson's rule.... find the value of h

11070= h/3(0+(4 x 19)+110) + 5/3(110+(96 x 4) + 58 )

4) a large group of people undertook a survey regarding the number of hours of sleep per week they generally have.

The results of the survey were normally distributed with 95% of the people indicating that they had between 42 and 54 hours of sleep per week.

i) determine the mean number of hours of sleep per week from the group.

ii) what was the standard deviation ?

iii) how many hours of sleep per week would a person from the group have who recorded a Z-score of -2.5 ?

iv) determine the probability (as a percentage) that a person selected from the group at random, would have indicated that they had between 51 and 57 hours of sleep per week.

5) A plastic container for 3 tennis balls is designed with a hemisherical base and a cylindrical body. three balls are fit snuggly inside the container. each ball has a diameter of 6cm. If a lid is placed on top of the container it will just touch the top tennis ball.

find the total Surface Area (SA) of plastic which will be required to make the container (without the lid). Give your answer correct to 1 decimal place.

6) A company is selling a car the terms are indicated below.

cash price = $22 000 terms = 15% deposit plus 36 monthly repayments of $770

calcuate the interest charged

7) an investor decide to purchase 1000 shares in telstra at a price of $3.98 per share. There is a brokerage fee of 1% of the value of any purchase or sale of shares.

i) find the total cost of purchasing these shares.

ii) the company releases its dividend at $0.20 per share. how much will this investor recieve in dividends ?

iii) calculate the dividend yeild. express your answer as a percentage, correct to 2 decimal places.