hidden questions in math problems

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Question:consider the following pattern of digits... 5,3,8,6,11,9,14,12,17,15,20... part a: what is the 500th term in the sequence? part b:what is the 999th term in the sequence? part c: name the first 5 prime numbers that are not terms in this sequence. part d: what is the largest 2-digit prime number that is not a term in this sequence? any and all help is greatly appreciated how did u figure that out?

Answers:a. 735 b. 1497 c. 2, 7, 13, 19, 31 d. 97

Question:Lydia paints a room that has 400 square feet of wall space in 2 1/2 hours. At the same rate, how long will it take her to paint a room with 720 square feet of wall space?

Answers:Four and one half hours.

Question:the side of a square sheet of metal is 6 metres. Four equal squares of side x metres are cut out, one from each corner. The edges left are then turned up perpendicular to the base to form an open tank find the greatest volume that the tank could hold? i dont even know where to start here any help would be great thanks

Answers:you can start as from one side and remove 2x from each side ,then height is x if it is made into a box . volume = (6-2x)^2 *x.then continue with the differentiation formulae. I has a short cut for problems like these: An open box of max volume is made from a square piece of side 'a' by cutting four equal square pieces from four cornersand folding up the tin.Then The length of square cut is "a/6". If the box is an rectangle oflength'a' &breadth 'b' then squarecut length is {(a+b)-sqrt(a^2+b^2-ab)}/6 For this problem max volume is 25 m^3.

Question:I bought a plant that grew at a rate of doubling it's size everyday. 60 days later it filled the room, how many days did it take to fill half the room?? 3 friends were drinking one night in a Hotel Bar. It was snowing pretty good and the roads were bad so they decieded to get a room and spend the night. They went to the desk and got a room, the clerk said 30 dollars so they all put in ten each. When the manager came on he saw the 30 dollars and said he should have charged the regular rate of 25 dollars. So he sent 5 dollars back to the room with the bell captain. The bell captain knew 3 people couldn't split 5 dollars so he gave them 3 dollars and kept the other $2.. Now it only cost the 3 men 9 dollars each, so that equals $27.00 and the Bell Captain kept $2.00 so $27.00 & $2.00= $29.00. What happened to the 30th dollar??

Answers:1. The size of the plant doubles everyday. So the size of the plant on the 60th day is double than the size on the 59th day. Thus the room is half-full on the 59th day. 2.The manager has $25+$2. The 3 people have $3. On adding we get $30. According to the question, we should not add $2 to $27. We should subtract it. And this gives the amount after discount. Now we should add the discount i.e., $5. Then we get $30.

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