Mathematics for Elementary Educators II QUESTION AND CORRECT ANSWER 2023/2024

Mathematics for Elementary Educators II QUESTION AND CORRECT ANSWER 2023/2024 There are approximately 2 lbs of muscle for every 3 lbs of body weight of a certain animal. For a 66-lb animal, how much of the weight is muscle? - CORRECT ANSWER-66 Divided by 3 x 2 = 44 Robert weighs 160 lb on Earth and 352lbs on another planet. Find Jeremy's weight on that planet if he weights 180lbs on Earth. - CORRECT ANSWER-Times 180 x 352 = 63360 then divide by 160 the answer is 396 There are six adult divers to each teenage driver in a city. If there are 14,832 adult drivers how many teenage drivers are there? - CORRECT ANSWER-14,832 divided by 6 = 2472 On a city map a rectangular park has a length of 2 in. If the actual length and width of the part are 400 ft and 100 ft, respectively how wide is the park on the map? - CORRECT ANSWER-2 times 100 = 200 divide 200 by 400 = 1/2 On a map 1/2 in represents 4 miles if two cities are 18 inches apart on the map what is the actual distance between them? - CORRECT ANSWER-8 miles = 1 inch 8 miles times 18 inches = 144 If a certain recipe takes 1 1/4 c sugar and 4 c milk how much milk should be added if the cook only has 1 cup sugar? - CORRECT ANSWER-4 divided by 1 1/4 = 3 1/5 Vonna scored 48 goals in her soccer practice. If her success to failure rate was 3:2 how many times did she attempt a goal? - CORRECT ANSWER-Times the failure rate of 2 x 48 goals kicked = 96 then divide by the number of successes 96/3 = 32 then add total goals kicked 32 +48 = 80 Subtract when dividing - CORRECT ANSWER-Square roots top and bottom higher number on top, lower number on bottom 2 1/2 is to 6 as x is to 18 - CORRECT ANSWER-2 1/2 x 18 = 45 then divide by 6 = 7 1/2 6 over 7 = 3x over 42 - CORRECT ANSWER-7x3x = 21x then 6x42 = 252 then divide by 21 = 12 rational number - CORRECT ANSWER-any number that can be written as a fraction irrational numbers - CORRECT ANSWER-numbers that cannot be expressed in the form a/b, where a and b are integers and b =0. Intergers - CORRECT ANSWER-whole numbers and their opposites terminating decimal - CORRECT ANSWER-a decimal whose digits end and the prime factorization of the denominator contains no primes other then 2 or 5 Decimals from Greatest to Least - CORRECT ANSWER-write them all out in a row add 0's to make them all have the same decimal places, put them in order by decimal places. Negatives are backwards Fraction to a Decimal - CORRECT ANSWER-Use F-D key on the calculator 3.36 with line over the 36 - CORRECT ANSWER-convert to 336.36 then subtract 3.36 from that and place it over 99 so = 333 over 99, then reduce to lowest terms Order from greatest to least with line over the repeating numbers - CORRECT ANSWER-no line, one line over last number, line over 3 numbers, line over 2 numbers Order from greatest to least negative numbers with line over repeating numbers - CORRECT ANSWER-Same order as when they are positive numbers no line, one line over last number, line over 3 numbers, line over 2 numbers 522.16 Rounded to the nearest hundred - CORRECT ANSWER-500 522.16 Rounded to the nearest tenth - CORRECT ANSWER-522.2 522.16 rounded to the nearest unit - CORRECT ANSWER-522 Rounding numbers - CORRECT ANSWER-left side is dreds, right side is dths A baseball player gets 14 hits in 40 at bats, what percent of the at bats are hits? - CORRECT ANSWER-Divide 14 by 40 = 35% 102 is 60% of what number? - CORRECT ANSWER-Change the 60% to 0.6 and divide 102 by 0.6 = 170 98.0 is what percent of 24.5? - CORRECT ANSWER-98 divided by 24.5 = 4 then 4 times 100 = 400% 68 is 40% of what number? - CORRECT ANSWER-change 40% to a decimal .4 then divide 68 by 4 = 170 A person collected $2,800 on a loan of $2,400 they made 5 years ago, if the person charged simple interest what was the rate of interest? - CORRECT ANSWER-400- 2,400xrx5 400= 2400 x 5 = 12000 Divide both sides by 400 x 12,000 = 0.0333 Change to a percent 0.0333 x 100 = 3.33 What is the square root of 28? - CORRECT ANSWER-find common denominators then leave the 2 on the right to find the answer 2 to the square root of 7 is the answer. Square root power of 3 no number next to 54 - CORRECT ANSWER-answer is 3^3 = 27 with the number 2 inside the square root. because 2x27 = 54. For a particular event 916 tickets were sold for a total of 5915. Students paid $5 per ticket and non students paid $8 how many student tickets were sold? - CORRECT ANSWER-8 x 916 = 7328 then subtract 7328 from the total tickets sold of 5915 = 1413 then divide by the difference between the cost of the tickets which is 1413/3 = 471 A box contains 95 coins only dimes and nickels . The amount of money in the box is $7.05 how many dimes and nickels are in the box? - CORRECT ANSWER-5 x 95 = 475 subtract 475 from 705 = 230. Divide 230 x 5 = 46. Number of dimes is 46 number of nickels is 49. = $7.05 A Farmer has 725 yd of fencing to enclose a rectangular pasture for her goats. Since one side of the pasture borders a river that side does not need to be fenced side b must be 3 times as log as side a find the dimensions of the rectangular pasture. - CORRECT ANSWER-take 725 and divide by 5 = 145. Then take 145 x 3 = 435. so side a and a are both 145 and side b = 435. a + a + 3b = 5 that is how you get the 5 In a college there are 11 times as many students as professors. If together the students and professors number 36,000 how many students are in the college? - CORRECT ANSWER-You take the number 11 + 1 for P and divide it by 36,000 divided by 12. = 3,000. Then times 3,000 x 11 = 33,000 students A 17 ft board is cut into three pieces. Two are equal length and the 3 is 3 inches shorter than each of the other two, how long are the pieces? - CORRECT ANSWER-change the ft into inches so it = 204 inches add 3 inches = 207 then divided 207 by 3 = 69 for the longer pieces and the shorter piece is 69-3 = 66 Matt has 10 times as many stickers as David. How many stickers must Matt give David so that they will each have 220 stickers? - CORRECT ANSWER-If they each have 220 stickers then the total number of stickers between them is 440. Then divide 440 by 11 (the amount plus one for David = 40. Ten times 40 = 400 then subtract the original amount of 220. So Matt needs to give David 180 stickers so they will both have 220. Function - CORRECT ANSWER-A function from set A to set B is a correspondence from A to B in which each element of A is paired with one and only one element of B. Every domain must be used only once. A cannot be used more then once. Or if there is no match from A to B. But if there is a match left in B but all of A is paired then it is a function. Relations - CORRECT ANSWER-A relation from set A to set B is a correspondence between elements of A and elements of B but nlike functions we do not require that each element of A be paired with one and only one element of B. Transitive Property - CORRECT ANSWER-If a=b and b=c, then a=c Reflexive Property - CORRECT ANSWER-a=a Symmetric Property - CORRECT ANSWER-if a=b, then b=a Input/Output - CORRECT ANSWER-f(x) = 2 f(x) = g((x)=x+3. For this the key is the last function +3 and the first of 2x so the output for 0 = 3 the output for 5 is 5x2+3= 13 and the output for 12 is 12x2+3 = 27 It is a function - CORRECT ANSWER-to be a function it is only necessary for each input to be paired with one and only one output. It is not necessary for each output to be paired with one and only one input. Slope of a line - CORRECT ANSWER-rate of change in y (vertical) compared to change in x (horizontal) which is constant in a line ordered pair - CORRECT ANSWER-The first number is the x-coordinate, and the second number is the y-coordinate Graph the equation by plotting points y=2x+4 - CORRECT ANSWER-Make a table x 2x+4 0 2(0)+4=4 plot is 0,4 1 2(1)+4=6 plot is 1,6 2 2(2)+4=8 plot is 2,8 3 2(3)+4=10 plot is 3,10 Find the slope of the line through the pair of points by using the slope formula (-9,-5) and (8,-8) - CORRECT ANSWER--5 subtract -8 = 3 and 8- -9 = 17 = -3 over 17 Find the slope of the line through the pair of points by using the slope formula 1, -2 and 3, 4 - CORRECT ANSWER-subtract -2 from 4 = -6 and subtract 1 from 3 = 2. Then reduce from 6 over 2 to 3. So the answer is 3 Write the following equation in slope intercept from and identify the slope and y intercept. 4x+5y=20 - CORRECT ANSWER-The equation is y=-4 over 5x+4 The slope of the line is -4 over 5 The y intercept of the line is (0,4) 65 men and 55 women are enrolled in calculus. There are 20 business majors, 50 biology majors, 35 computer science majors, and 15 mathematics majors. No person has a double major. If a single calculus student is chosen, find the following probabilities - CORRECT ANSWER-65 over 120 = 13 over 24. The probability that the student is a business major is 20 so 20 over 120 or 1/6. There are 15 mathematics majors enrolled in calculus, so the probability of selecting a mathematics major is 15 Over 120. The probability of selecting a non mathematics major is 105 over 120 0r 7/8. Since there are no double majors, majoring in business and majoring in mathematics are mutually exclusive events. The probability of selecting either a business major or a mathematics major is represented as P(business union∪mathematics). 20 + 15 over 120 = 7/24. Remember to use calculator to reduce! When a particular type of thumbtack is dropped, it will land point up (A flat-top thumbtack resting on its flat top) or point down (A flat-top thumbtack resting on the edge of its flat top and the tip of its needle). This experiment was repeated 100 times with the following results: point up: 58 times; point down: 42 times. a. What is the experimental probability that a particular type of thumbtack will land point up? b. What is the experimental probability that a p - CORRECT ANSWER-Point up and point down are just the number over 100. If the experiment was tried another 100 times would the same results occur? NO Is it expected that nearly the same results will occur on a second trial: YES In the game of "Between," two cards are dealt from a standard deck and not replaced. You then pick a third card from the deck. To win, you must pick a card that has a value between the other two cards. The order of values is 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K, A, where the letters represent a jack, queen, king, and ace, respectively. Determine the probability of your winning if the first two cards dealt are a 7 and a queen. - CORRECT ANSWER-between 7 and a queen there are 4 spots. so 4 x 4(suites for each value) = 16. There are 52 cards and 2 have been taken out so 16 over 50 is 8/25.