subject: Math

solve the following questions ( handwritten solution only neatly and clean box final answer) thankyou!

1. Consider a number. Multiply it by 4. Add 10 to it. Divide the sum by 2. Subtract 5. What can you conjecture about the final result compared to the starting number? Use deductive reasoning to prove this conjecture. (2 points for the conjecture, 3 points for the proof) Use Polya's 4 steps to answer the following. No need to show each step, but show your thought process as to how you solved it. (5 points) 2. How many perfect squares are there between 1,000,000 and 9,000,0007 (Hint: 1,000,000 and 9,000,000 are both perfect squares.) 1. The current population of the Philippines is approximately 115,000,000. If this is the population of our study, and we want to have a margin of error of about 2%, what should our sample size be according to Slovn's formula? (2 pts) We want to know what proportion of the population watches anime using a sample data set. From a previous study, we know that the past proportion was 30%. We want to be 99% confident with 3% precision. The population we are dealing with numbers 2000. What should our sample size be? (Note: Zq0s= 2.58, Z50:s= 1.96) (4 points) Given the following data set, find the mean, median, mode, range, POPULATION variance and POPULATION standard deviation. Show your solution. (9 points) 2,2,2,3,4,4,5,7,8,9,10,10,11, 11,15