Consider the weighted voting system 10 10 5 3 1 Identify

1 Consider the following grammar ScScc A AaaaAbb aaaDbb DddD d a Describe the language produced by this grammar in set notation i e L ie th same format used in other problems e g 2 below Briefly explain your reasoning b Come up with a PDA that accepts the same language

The National Transportation Safety Board collected data showing that 70 of all licensed drivers are older than age 25 Information on the age of n 50 individuals who recently received speeding tickets was sourced by a team of researchers interested in examining whether the age distribution of individuals who receive speeding tickets is different from the age distribution of licensed drivers Question What is the appropriate analysis to answer this research question and why

If you are trying to build credit by using a credit card each time you make a purchase with the credit card deduct that amount from your checking account That way when your credit card bill is due you will have enough to pay the credit card off in full Kathy Lehner is going to start doing this She plans on paying her credit card bill in full this month How much does she owe with a 9 APR and the following transactions Note Round your answer to the nearest cent 31 day billing cycle 10 1 10 3 Previous balance 1 175 Credit 68 Credit 10 12 Charge King Soopers 159 10 15 Payment 420 Credit 10 25 Charge Delta 332 10 30 Charge Holiday Fun 72

2 Suppose 1000 raffle tickets are sold at a price of 5 each Two first place tickets will be drawn with a prize worth 200 Five second place tickets will be drawn at a prize valued at 100 and ten third place tickets will be drawn at prize valued at 50 Find the expected value of the net gain to the consumer Note In this example X represents the net gain You have to be careful because this is a game you pay to play In other words if you win first prize you do not gain 200 you gain 195 because you paid for a ticket

There are some excellent free personal finance apps available Mint com Good Budget Mvelopes BillGuard PocketExpense HomeBudget and Expensify After using Mint com you realize you need to pay off one of your high interest loans to reduce your interest expense You decide to discount a 6 250 340 day note at 3 to your bank at a discount rate of 4 0 on day 220 What ar your proceeds Note Round your final answer to the nearest whole number Proceeds

Four candidates running for a vacant seat on the town council receive votes as follows Levan 219 Edelson 1617 Borowski 991 Callow 417 Determine whether any candidate earns a majority and determine who wins using the plurality method Is there a candidate who earns a majority Yes No Who wins the election using the plurality method OA Levan OB Callow OC Edelson OD Borowski

A researcher wishes to estimate with 95 confidence the population proportion of adults who think the president of their country can control the price of gasoline Her estimate must be accurate within 3 of the true proportion a No preliminary estimate is available Find the minimum sample size needed b Find the minimum sample size needed using a prior study that found that 34 of the respondents said they think their president can control the price of gasoline c Compare the results from parts a and b a What is the minimum sample size needed assuming that no prior information is available n Round up to the nearest whole number as needed b What is the minimum sample size needed using a prior study that found that 34 of the respondents said they think their president can control the price of gasoline n Round up to the nearest whole number as needed c How do the results from a and b compare OA Having an estimate of the population proportion reduces the minimum sample size needed B Having an estimate of the population proportion has no effect on the minimum sample size needed OC Having an estimate of the population proportion raises the minimum sample size needed

You randomly select and measure the contents of 10 bottles of cough syrup The results in fluid ounces are shown to the 4 216 4 297 4 253 4 245 4 188 right 4 201 4 262 4 242 4 227 4 237 Assume the sample is taken from a normally distributed population Construct 80 confidence intervals for a the population variance o and b the population standard deviation o Interpret the results a The confidence interval for the population variance is Round to six decimal places as needed Interpret the results Select the correct choice below and fill in the answer box es to complete your choice Round to six decimal place as needed 0 OA With 20 confidence it can be said that the population variance is less than OC With 20 confidence it can be said that the population variance is between and OB With 80 confidence it can be said that the population variance is between OD With 80 confidence it can be said that the population variance is greater than and b The confidence interval for the population standard deviation is D Round to four decimal places as needed Interpret the results Select the correct choice below and fill in the answer box es to complete your choice Round to four decimal place as needed OA With 80 confidence you can say that the population standard deviation is between and OB With 80 confidence you can say that the population standard deviation is less than inches inches OC With 20 confidence you can say that the population standard deviation is greater than OD With 20 confidence you can say that the population standard deviation is between and inches inches

An outcome is Pareto efficient Pareto optimal only if everyone prefers it to every other feasible outcome or is indifferent True or False

Let A 1 1 1 2 11 ER 4 1 a 4 marks For each ER find Cartesian equations for Col A and Null A