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Homework Helper, Page 302

Homework Helper, Page 302. 1.) Mr. Nelson’s class recently took a test. He made a list of the scores. 66, 79, 76, 95, 55, 82, 60, 85, 93, 76, 63, 96, 75, 82, 71 Find all three measures of central tendency for the test scores.

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Homework Helper, Page 302

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  1. Homework Helper, Page 302 1.) Mr. Nelson’s class recently took a test. He made a list of the scores. 66, 79, 76, 95, 55, 82, 60, 85, 93, 76, 63, 96, 75, 82, 71 Find all three measures of central tendency for the test scores. Start by putting all the scores in numerical order from least to greatest. 55, 60, 63, 66, 71, 75, 76, 76, 79, 82, 82, 85, 93, 95, 96 Range (The difference between the largest and smallest numbers in the set.) 96 – 55 = 41 Median (The middle number in the set) = 76 Mode (the number(s) that appear the most) = 76 and 82 Both of these numbers appear twice.

  2. Homework Helper, Page 302 2.) Create a stem plot from the test score data in number 1. 66, 79, 76, 95, 55, 82, 60, 85, 93, 76, 63, 96, 75, 82, 71 5 5 6 0 3 6 7 1 5 6 6 9 8 2 2 5 9 3 5 6 Tens digit Ones digit

  3. Homework Helper, Page 62 1.) It costs Tia $450 to purchase food to cater a picnic. She gets paid $725. a.) How much money did she make as profit? Money made – Costs to cater = Profit $725 – $450 = $275 b.) What percent of profit is this? $275 - Profit made after costs $725 - Total amount of money made $275 ÷ $725 = 0.379 x 100 = 37.9% Approximately 38% of profit

  4. Homework Helper, Page 62 2.) Noah wants to buy a laptop that he sees for $799. By the time he goes to buy it, the price has increased to $1050. a.) Find the percent of increase of the laptop. Final amount –Original amount = $1050 - $799 = $251 Original amount $799 $799 $251 ÷ $799 = 0.31 x 100 = 31% of increase b.) If the price increases by another 5%, what will be the additional markup and final sale price? $1050 x 5% = $1050 x 0.05 $52.50 - Additional Markup $1050 + $52.50 = $1102.50 - Final Sale Price

  5. Homework Helper, Page 62 3.) A video game originally priced at $65.50 is on sale at a 15% discount. a.) What is the amount of the discount and the final sale price? Original price x percent discount = Discount $65.50 x 15% = $65.50 x 0.15 $9.825 (round up) = $9.83 -> This is the discount Original price – Discount = Sale price $65.50 - $9.83 = $55.67 -> This is the final sale price b.) Would it be a better or worse deal if the store had simply lowered the original price to $55.95? Use percent of decrease to explain. Percent of decrease = Final price – Original price Original price Percent of decrease = $55.95 – $65.50 = -$9.55 $65.50 $65.50 Percent of decrease = -0.1458 = -14.6%

  6. Homework Helper, Page 62 4.) Convert each number to the specified form. a.) 107 (percent)Since it’s over 100, the numerator is your percent =107% 100 b.) 345% (fraction) Put the percent over 100 = 345 100 c.) 225% (decimal) Divide by 100 = 2.25 d.) 1.42 (percent) Multiply by 100 = 142% e.) 0.0047 (percent) Multiply by 100 = 0.47% f.) 0.3% (decimal) Divide by 100 = 0.003 g.) 0.08% (fraction) Put the percent over 100 = 0.08 100 h.) 3 (percent) Divide the numerator and denominator by 10 to get 100 as your 1000 denominator = 0.3%

  7. Homework Helper, Page 62 5.) A realtor sells a house for $460,000. If her commission is 3%, how much money does she make as commission? Commission is a form of payment rendered to an agent for services rendered. It is generally a set percentage of how much money is exchanged during these services. Amount of money exchanged x Commission percent = Commission earned $460,000 x 3% = $460,000 x 0.03 $13,800

  8. Homework Helper, Page 62 6.) Maria takes out a loan for $30,000 to buy a car. If her bank charges 5.4% simple interest, how much total interest will she pay in 3 years? Use the formula I = prt p = principal ($30,000) r = rate (5.4% or 0.054) t = time in years (3) I = $30,000 x 0.054 x 3 I = $4,860

  9. Homework Helper, Page 62 7.) Gage must choose between two banks for investing his money that both offer compound interest. Bank 1 offers a 3.9% interest compounded quarterly, and Bank 2 offers 4.3% interest compounded semi-annually. a.) Show how much money Gage would have in his account after 2 years at each bank if he invests $1,200. First we have to know the difference between simple interest and compound interest and what quarterly and semi-annually mean. Simple interest – Interest that is paid on the principal alone. Compound interest – Interest calculated on the total principal plus the interest earned or owed during the previous time period. This interest is not going to be multiplied by the same amount in the account/loan every time. Interest that is compounded quarterly means that it is calculated 4 times each year. Interest that is compounded semi-annually means it is calculated 2 times each year. Let’s take one bank at a time, using the I = prtformula.

  10. Homework Helper, Page 62 7.) Gage must choose between two banks for investing his money that both offer compound interest. Bank 1 offers a 3.9% interest (Rate) compounded quarterly (Time in months, 3/12 or 0.25). a.) Show how much money Gage would have in his account after 2 years at each bank if he invests $1,200 (Principal). 1st Year 2nd Year 1st Quarter I = $1,200 x 0.039 x 0.25 I = $11.70 $1,200 + $11.70 = $1,211.70 1st Quarter I = $1,247.49 x 0.039 x 0.25 I = $12.16 $1,247.49 + $12.16 = $1,259.65 2nd Quarter I = $1,259.65 x 0.039 x 0.25 I = $12.28 $1,259.65 + $12.28 = $1,271.93 2nd Quarter I = $1,211.70 x 0.039 x 0.25 I = $11.81 $1,211.70 + $11.81 = $1,223.51 3rd Quarter I = $1,271.93 x 0.039 x 0.25 I = $12.40 $1,271.93 + $12.40 = $1,284.33 3rd Quarter I = $1,223.51 x 0.039 x 0.25 I = $11.93 $1,223.51 + $11.93 = $1,235.44 Now let’s look at Bank 2. 4th Quarter I = $1,235.44 x 0.039 x 0.25 I = $12.05 $1,235.44 + $12.05 = $1,247.49 4th Quarter I = $1,284.33 x 0.039 x 0.25 I = $12.52 $1,284.33 + $12.52 = $1,296.85

  11. Homework Helper, Page 62 7.) Gage must choose between two banks for investing his money that both offer compound interest. Bank 2 offers 4.3% interest (Rate) compounded semi-annually (Time in months, 6/12 or 0.5). a.) Show how much money Gage would have in his account after 2 years at each bank if he invests $1,200 (Principal). 1st Year 2nd Year 1st half of the year I = $1,252.15 x 0.043 x 0.5 I = $26.92 $1,252.15 + $26.92 = $1,279.07 1st half of the year I = $1,200 x 0.043 x 0.5 I = $25.80 $1,200 + $25.80 = $1,225.80 2nd half of the year I = $1,225.80 x 0.043 x 0.5 I = $26.35 $1,225.80 + $26.35 = $1,252.15 2nd half of the year I = $1,279.07 x 0.043 x 0.5 I = $27.50 $1,279.07 + $27.50 = $1,306.57

  12. Homework Helper, Page 62 7.) Gage must choose between two banks for investing his money that both offer compound interest. Bank 1 offers a 3.9% interest compounded quarterly, and Bank 2 offers 4.3% interest compounded semi-annually. b.) Which bank should Gage use and why? Look at the totals from the two banks side-by-side. Which bank do you think he should choose?

  13. Percent Estimations Remember, when the directions say to estimate, you should round the numbers to nicer numbers, that are easier to work with, before you get started. (Think multiples of 5 or 10.) Original problem Rounded numbers Estimated answer 1.) 24% of 36 25% of 40 10 2.) 81% of 25 80% of 25 20 3.) 11% of 67 10% of 70 7 4.) 150% of 179 150% of 180 120 5.) 67% of 450 70% of 450 315 6.) 79% of 590 80% of 600 480

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