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Mathematics for Elementary Educators II
Questions and Answers Already Passed
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? ✔✔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. ✔✔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? ✔✔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? ✔✔2 times 100 = 200 divide 200 by 400 = 1/
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? ✔✔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? ✔✔4 divided by 1 1/4 = 3 1/
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? ✔✔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 ✔✔Square roots top and bottom higher number on top, lower number on bottom
2 1/2 is to 6 as x is to 18 ✔✔2 1/2 x 18 = 45 then divide by 6 = 7 1/
6 over 7 = 3x over 42 ✔✔7x3x = 21x then 6x42 = 252 then divide by 21 = 12
rational number ✔✔any number that can be written as a fraction
Order from greatest to least negative numbers with line over repeating numbers ✔✔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 ✔✔ 500
522.16 Rounded to the nearest tenth ✔✔522.
522.16 rounded to the nearest unit ✔✔ 522
Rounding numbers ✔✔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? ✔✔Divide 14 by 40 = 35%
102 is 60% of what number? ✔✔Change the 60% to 0.6 and divide 102 by 0.6 = 170
98.0 is what percent of 24.5? ✔✔98 divided by 24.5 = 4 then 4 times 100 = 400%
68 is 40% of what number? ✔✔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? ✔✔400-2,400xrx5 400=
2400 x 5 = 12000
Divide both sides by 400 x 12,000 = 0.
Change to a percent 0.0333 x 100 = 3.
What is the square root of 28? ✔✔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 ✔✔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? ✔✔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
Matt has 10 times as many stickers as David. How many stickers must Matt give David so that they will each have 220 stickers? ✔✔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 ✔✔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 ✔✔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 ✔✔If a=b and b=c, then a=c
Reflexive Property ✔✔a=a
Symmetric Property ✔✔if a=b, then b=a
Input/Output ✔✔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 ✔✔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 ✔✔rate of change in y (vertical) compared to change in x (horizontal) which is constant in a line
ordered pair ✔✔The first number is the x-coordinate, and the second number is the y-coordinate
Graph the equation by plotting points y=2x+4 ✔✔Make a table
x 2x+
0 2(0)+4=4 plot is 0,
1 2(1)+4=6 plot is 1,
2 2(2)+4=8 plot is 2,
3 2(3)+4=10 plot is 3,
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 ✔✔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 particular type of thumbtack will land point down?
c. If the experiment was tried another 100100 times would the same results occur? Why?
d. Is it expected that nearly the same results occur on a second trial? Why ✔✔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. ✔✔between 7 and a queen there are 4 spots. so 4 x 4(suites for each value) =
- There are 52 cards and 2 have been taken out so 16 over 50 is 8/25.
A Executive committee consists of 12 members 4 men and 8 women, 3 members are slected at randome to attend a meeting, what is the probability that all 3 selected are women? ✔✔8/12 x 7/11 x 6/10 = 336/1320 = 14/
So just decrease the numbers by the amount drew from the hat and time it by themselves.
Assume that the probability is 1/2 that a child born at any time is a girl and births are independent. What is the probability of the even that if a family of 4 children and none of them are girls? ✔✔1/2 x 1/2 x 1/2 x 1/2 = 1/
Just times the fraction by the amount given.
tree diagram ✔✔A diagram used to show the total number of possible outcomes.
If it is a black and white ball you multiply the number of outcomes at the end of the tree. Then add the WW and the BB outcomes to get the probability of the same color.
When a ball is drawn at random from the box its color is recorded then the ball is put back in the box. Then a second ball is drawn at random from the box. Make a tree for this then multiply the outcomes at the end of the tree and add the 2 sums together to get the answer.
The 8th grade class has 11 girls and 13 boys, how many boy + girls dates can be arranged? ✔✔11 x 13 = 143
A company wants to have a 3 digit phone extension with the first digit not being zero. ✔✔ 9 outcomes
10 if it is 2nd digit
9 x 10 x 10 = 900
Pizza House offers
5
different salads,
4
different kinds of pizza, and
5
different desserts. How many different three-course meals can be ordered? ✔✔5 x 4 x 5 = 100
If a fair coin is tossed 3 times, in how many different ways can the sequence of heads and tails appear? ✔✔There are 2 possible outcomes
2 x 2 x 2 = 2^3 = 8
How many permutations are there of the letters in the word CHARGES if all the letters are used without repetition? ✔✔7 letters in the word
7 x 6 x 5 x 4 x 3 x 2 x 1 = 5040
How many 7 person committees can be formed out of a class of 25 students? ✔✔7 spots to fill
7 x 6 x 5 x 4 x 3 x 2 x 1 = 5040
25 x 24 x 23 x 22 x 21 x 20 x 19 = 242272800
Divide 5040 into 242272800 = 480,
y - 2 = 1/2x -1/2 (subtract 2 from both sides)
y=1/2x+1 1/
mixed number y= 1/2x+3/
Find the equation of the line containing the given parts 1, 3 and 3, 4 ✔✔
CH. 1 Simplest form 2500u^5y^2 over 80^3y^5 ✔✔divide the numbers by 10 (for lowest fraction) then subtract the U's and the Y's. U's on top, Y's on bottom = 125u^2 4y^
In Rae's Algebra Class 13 of the 30 students received an A's on the test. The same test was given to Sam's class and 11 of the 23 students received A's. What class had a higher rate of A's? ✔✔Dived 13/30 and 11/
A scale on a map is 90 miles to the inch what is the airline mileage between two cities that are 2/3 inches apart on the map? ✔✔Multiply 90 x 2/3 = 60
Find 3 Fractions Equal to a/5 ✔✔1/5 = 2a/10 Because 5 is multiplied twice to get 10.
a/5 = 14a/70 because 5 is multiplied 14 times to get 70. a/5 = 22a/110 because 5 is multiplied 22 times to get 110.
find a value so that x = 35/30 = -7/x ✔✔The cross products are -210 (30 x -7) and 35. Then divide both sides by 35 = -
Suppose a large pizza is divided into 3 equal size pieces and a small pizza is divided into 4 equal size pizzas does 1/3 + 1/4 represent what you got? ✔✔No, because they are not the same size
Multiplicative Inverse of 1 1/4 is: ✔✔When you do the math on the calculator it come out to 5/ to inverse it you just flip it so it = 4/
Multiplication principal 4/5x = -4/3 so x= ✔✔Divide both sides by 4/5 and the calculator will show -3/5 to get the principal you flip it so = -5/
Perform the proper calculations 16x3 1/4 = ✔✔change 3 1/4 to improper fraction and divide 16/ divided by 13/4 = 52
Metro train had a route reduction of 1/10 of its routes. 198 routes were left after the reduction, how many routes were there originally? ✔✔Take 198 dived by what was left 9 = 22 add that to 198 = 220
Thousand = 1000
Hundredths = 684.
Left is Ands
Right is Enths
17 over 2^2x55 is this a terminating decimal ✔✔No because 17 does not go into 5 or 2
Nathan received a 5% raise last year, if his salary is now $17,535 what was his salary last year? ✔✔100% + 5% = 105% Divide 17535 by 1.05 = 16700
There are 140 coins in a piggy bank of which 40% are dimes. what is the least possible amount of money that could be in the piggy bank? ✔✔140 x 40% = 56 (5.60 in dimes) subtract 56 from 140 = 84 the least is .84 cents so add 5.60 + .84 = $6.
67.5 is _________% of 22.5 ✔✔300%
Arrange the following real numbers in order from greatest to least ✔✔.996 (line over the 96)
.96 (line over the 96)
.966 (line over the 66)
square root of .93,
0.9,
0.8 (line over the 8) and
0.797 (line over the 797)
Watch the line
A student wants to get some T-shirts made. The company that the student chooses to print the T- Shirts charges a flat overhead of $39 plus the cost to make each shirt. It will cost $78 to make 3 and $130 to make 7.
How do you write this equation? ✔✔C=13t+
A Number M is equal to 3 times the sum of the square of another number k and 15. How do you write the equation? ✔✔m=(k^2+15)
