GRE QUANT
Square roots What is another way to write negative square root of 81?
keep - on the outside. -9
X^a times X^a.
multiply X. Add a+a
How do you change decimal values to %? How do you change fractions to %?
multiply by 100 or just move the decimal point two to the right. get decimal via calculator and move decimal
Factoring Binomials - What is your approach? Practice the 3 problems.
Take out the GCF.
Square roots Solve 3 sr of 18 + 5 sr of 72 - 4 sr of 32.
To +/-, make sure sr match. To do this, find the GCF. in this case, it is 2. Answer: 23 sr of 2.
Box Line and Whisker Plot Consists of: Max, Min (not always correct at first glance), Q1, Q2, Q3, and IQR - How do you spot the outliers?
(Q1-1.5 IQR, Q3 +1.5 IQR)
Absolute Value Inequalities - How to solve Practice. - I 3X -4I </ 17 - 3 I 7x -4 I +5 > 7
- x </ 7 and x >/ -13/3 - x > 8/7 or x < 0.
Square roots How do you find a square root of a non perfect square? Practice with sr of 18 and 12.
1. Factor. Use the factor that is a perfect square. Write multiples in their own sr. 2. sr the perfect square. this stays on the outside. sr of 18 = 3 sr of 2. / sr of 12 = 2 sr of 3
Solving Quadratic formula What is the formula? When can it be used?
Look it up. Standard form (all to the left) quadratic formulas. If factoring gets too difficult, use this.
Percent Increase and Decrease Changes. Formula? - Price of gas changes from 2.24 to 2.56. Calc % of change. - 500 students enrolled in class. After first exam, 140 dropped out. % of change? - If New is less than original, expect what?
(New - Original / Original) times 100 - 14.29 % - -28% - negative answer.
Expected Value - Lisa plays a game in which are only two outcomes. The cost to play the game is $100. If she wins, she gets $500. The probability of winning is 20%. What is the expected value for winning a single game on average ? - Company XYZ generates a profit of $40 for each laptop they sell. The company loses $500 for every laptop that is returned due to some defect. If 3 out of every 100 laptops is defective, what is the expected value of profit per laptop?
- $ 20 per game - $ 23.8 per laptop.
Probability Strategy first then answer. A bag contains 5 red & 10 blue. Two are selected w/o replacement. - % of selecting two red marbles? - % of selecting a red & blue marble?
- (1/3) (2/7). Multiply each other but make sure to subtract necessary marble. ; 9.5% - ORDER DOES NOT MATTER: this is a OR scenario : (RB) + (BR) make sure to subtract both scenarios. = 47%
Basics of Algebra - (24x^9 y^5) / (8x^3 y^12) solve. Note this is __. - (12x^5 y^-3 z^4) / (36x^8 y^-4 z^-8) - (2^3 x^4 y^5) ^2 - what is the answer if something is raised to the power of 0?
- (3x^6)/y^7 ... monomial - (y^7z^12 )/ (3x^3) - 64 x^8 y^10 - always 1 .. even if it's a crazy looking equation
Basics of Algebra - -2^3 - (-2)^3 - -(-2)^3
- -8 - -8 Note: this is negative bc raised to the third power. If it were even, it would have been positive. - 8
Converting Decimals to Fractions - .433333 -> - .63232323
- 13/30. First: subtract the .3 from .4. This leaves .1 as an "actual" number. You are left with .33333 and .4 to convert as a fraction. Do each and add them. Make sure denominators are the same. - 313/495: First: subtract .23 from .63. This leaves .4 as an "actual" number. You are left with .23232323 and .4 to convert as a fraction. Do each and add them. Make sure denominators are the same.
Permutations and Combinations Starting questions but still need more practice. - In how many diff ways can you arrange 3 books from a group of 7? - how many ways can we arrange 5 books on a shelf? - how many teams of 4 can be produced from a pool of 12? - how many different ways can you arrange the letters in a word like ALABAMA?
- 210 ; permutation - 120 ; permutation - 495 ; combination - 7!/ 4! (4 being the repeating factor) = 210
Scientific Notation Exponent Positive - 2.7 x 10^5 - 8.36 x 10^7 Exponent Negative - 4.5 x 10^-3 - 3.746 x 10^-4 Convert to proper notation - 37.4 x 10^5 - 426.8 x 10^7
- 270k - 83,600,000 - .0045 - .0003746 - 3.74 x 10^6 - 4.268 x^9
Scientific Notation Square root - sr of 4x10^6 - sr of 36x10^-6 - cube root of 8x10^9 - not sr but reverse. (4x 10^-3) ^2
- 2x10^3 or 2k - .006 - 2k - 1.6x10^-5
Consecutive Integer Word Problems - sum of consecutive odd integers is 105. What is the lowest #? - sum of four consecutive even integers is 116. What is the sum of the first two integers? - sum of 5 consecutive even integers is 250. Product of first and last? - sum of 4 consecutive even integers is Y. What represents sum of first two integers in terms of Y if first is equal to X?
- 33 - 54 - 2484 - 1/2Y -4
Basics of Algebra For practice - (3x-4)(x^2 +3x -5) - (x^2 + 3x -2) (2x^2 +4x -5)
- 3x^3 +5x^2 -27x +20 - 2x^4 +10x^3 +3x^2 -23x +10
Ratio and Proportion Word Problems - 540 cats and 675 dogs. What is their ratio? - Ratio of boys and girls is 8:7. 40 boys total. What is the total for girls? Explain how to solve this. - Ratio of nickles, dimes, and quarters in a jar is 3:4:7. Total of coins is 112. How many nickles are there? Explain how to solve this.
- 4:5 NOTE: cats came first bc was worded like that in teh question. - 35. when ratios are given, you can cross multiply to find X. Make sure to have labels in columns and not rows when creating fractions. - 24 nickles. ^ same concept. add ratios together to get total ratio and put it over 112. Cross multilpy to get nickles. To check, cross mul. to get others and add to see if you get 112.
Converting Decimals to Fractions - .24 - .9 - .218 - 0.22222 -> - 0.232323 -> - .126126 ->
- 6/25. Since there two decimal points, multipy (0.24/1) (100/100) then reduce. Each 0 in the 10,100,1000 accounts for decimal point. - 9/10. Since ther is one decimal point, multiply (.9/1) (10/10). - 109/500. Since theres three decimal points, multilpy (.218/1) (1000/1000). Reduce. - 2/9 - 23/99 - 126/999 NOTE: for infinite, 9 per each diff number.
Scientific Notation Multiplying and dividing. - (3x10^5) (2x10^-3) - (3x 10^4)(3x10^5) - (50x10^4)(30x 10^-3) - (12x10^6) / (3x10^-4) - (96x10^-5)/ (6x10^2)
- 6x10^2 - 9x 10^9 - 1.5x10^4 - 4 x 10^10 - 1.6x10^-6
Scientific Notation Adding and subtracting - 8x10^4 + 2x10^3 - 3.6x10^7 - 9.1x10^5
- 8.2x 10^4 - 3.509x10^7
Absolute Value Inequalities - How to solve These, you basically solve the same as normal linear inequalities. Just a few more rule of thumbs to keep in mind: - what does > and < mean? - when creating the second negative equation, what do you have to do? - starting equation is I 3X +5 I < -3. What can you tell about this equation? - starting equation is I 4X -3 I > -4. What can you tell about this equation?
- > is or and < is and - switch the > or < and make the after number negative per usual. - this is the same as saying 0 < -3. Not sure. The answer is NO solution. - same as 0 > -4. True statement. The answer is all real numbers (- infinity, + infinity)
Factoring Factoring sums and differences of cubes - what is the formula for the sum? - what is the formula for the differences? Solve the 4 problems.
- A^3 + B^3 = (A+B) (A^2-AB +B^2) - A^3 - B^3 = (A-B) (A^2+AB +B^2)
- How do you add mixed numbers? 4 (3/4) + 3 (1/5) - How do you subtract mixed numbers? What if the final fraction is negative? 5 (2/7) - 3 (3/4)
- Add coefficents. Add remaining fractions by getting den to be the same. 7 (19/20) - Sub coefficients. Sub remaining fractions by getting den to be the same. If there is a negative fraction, "borrow" a one from the coefficient, subtract from final fraction to get a positive one. 1 (15/28)
Factoring - Trinomials when leading coefficient is 1. - what is your approach? - Trinomials when leading coefficient is still divisible, ex: 2- what is your approach? Practice the 5 problems.
- Calculate what two numbers multiply the 3rd number and add to the second number. - Take our the GCF then ^ approach.
Basics of Algebra - How would you solve (5x^2 -6x -12) - (7x^2 +4x -13) - Solve x^4/x^7 - y^-4 - (4x y^2)(8x^2 y^3) is the same as (4x y^2)(8x^2 y^3) - strategy wise. Why?
- Distribute the - then add. I get confused bc I sometimes interpret this is as a multiplication problem. Would've been foil bc trinomial but not the case. Answer: -2x^2 -10x+1 - 1/x^3 - 1/y^4 - both are monomials. You will simply multiply like terms.
Basics of Algebra Factoring binomials - what are the two strategies? - 8x+12 - (x^2-9) - 12ab^2 +18a^2b^3 - 81x^4 - 16y^8
- Factor out the GCF or if perfect square, (A -B) (A+B) is the answer. - 4(2x+3) - (x-3)(x+3) - 6ab^2 (2 +3ab) - see answer on number 10 bottom.
Simple interest - formula? - Sally invest 8k w/ 8.7% annual interest. How many years will it take for her to earn 4,872 in interest? - James invests 25k w/ 8% interest. How many years will it take to get to 43k? - Marie invests 3k. In 4 years, earns 768 in interest. What is the annual interest rate?
- I = Prt - 7 years - 9 years - 6.4%
Quartiles, Deciles, and Percentiles. - What is a formula that can help me quickly find Q1? EX: 2,3,5,7,8,10,11,13,15,16,19. - what is a interquartile range?
- Location of percentile (ex: 25%) = k/100 times (n+1). Answer is 5. Same applies for 50%, and 75%, etc. NOTE: the answer you get is the amount of numbers you should count from left to right. - Q3-Q1.
Midpoint formula - what is it? - find midpoint w (-4, 2) (8, -6) - find midpoint w (1/5 , -2/3) (4/3, 3/4)
- M = ( x1 + x2 /2 , Y1 + y2 /2) - 2, -2 - 23/30 , 1/24
Probability Bag: 3 blue marbles & 7 red. Megan selects 3 w/ replacement. Strategy first then answer. - % at least 1 red - % at most two blue - % no red? - exactly 2 blue marbles?
- P (at least 1 red) = 1 - P (BBB) = 97% -At most = 0, 1, and 2. Strategy is the same as first answer because you don't want BBB as it exceeds. = 97% - BBB (3/10)^3 = 2.7% - think of the options: BBR, RBB, BRB. This is an or statement. = 18.9%
Permutations and Combinations What is the main difference? - Key words for combination questions? (4) - Key words for permutations questions? (3)
- Permutations: order matters ; Combination: order does not matter (ex: teams AB and BA are the same) - select, choose, pick, and combination. - Arrangements, ordered ways, and unique. (This is where AB and BA are different)
Linear Functions - graph equation 2X-3y =6 using x and y int. - Write EQ of line passing (2,5) w/ slope of 3. - Write EQ of line passing ( -3,1) and (2,-4) - Write EQ passing (3, -2) and parallel to 2X +5y -3=0 - Write EQ passing (-4, -3) and perpendicular to 3x -4 y +5 =0
- can solve this by simply substituting each letter by 0 so you know the others intercept. Y= -2, X= 3 - use point-slope EQ. Y=3x -1 - You have two points: can use the Y=MX+B substitution after getting the slope. — just use any points. OR the point slope equation. Answer: y= -x-2 - use point slope. Y= - (2/5) X - (4/5) - use point slope. Y = -(4/3)x - (25/3)
Graphing. Quadratic Transformations - which values is an x-int on graph y= 2x^2 +10x -28? - what is an x value solution to 35x^2-3x-54=0? - what equation contains solution 3+5i and 3-5i? - The revenue generated by company xyz due to textbooks can be modeled by R (x) = 1500 +80x -0.01 ^2. A) How many books should the company sell to maximize their revenue? B) what is the maximum revenue of the company?
- factor and solve as y=0. Answer: -7, and 2 - this problem would take long to factor. Use quad formula. Answer= 6/5. - squared equation. +/- 5i. Answer: x^2 -6x+34 - looking for X vector A) 4000 B) 161,500
Basics of Algebra Factoring Polynomials. - what is the approach? - x^3 -4x^2 +3x -12 - 2x^3 -6x^2 +4x -12 - 3x^3 + 8x^2 -6x -16
- factor by grouping if the first two coefficients divided by each other and the second two coefficients divided by each other are the same number. This means to take out both GCF from each pairs and eliminate the repeating - (x^2+3) (x-4) - (X-3) (2x^2+4) - (x^2 -2) (3x +8)
Order of operations: - What is an important rule of thumb with M and D? - Does the order matter for A and S?
- if M is first on the equation, order does not matter with both. if D is first on equation, DO THIS BEFORE M!!. - no.
Factoring - Trinomials but leading coefficient is not divisible, what is your approach? - What is your new formula? - what do you do w this? Solve the two problems .
- multiply the leading coefficient with the last number. With this new number, calculate what two numbers multiply to get it and add to the second number from original formula. - first and last are the same but middle number is replaced by the two calculated numbers. — not the answer but gives you a new solvable formula — YOU have a polynomial! - Get GCF from first two sets (separate) solve as poly factoring.
Permutations and Combinations - formula for permutation? - combination?
- nPr = n! / (n-r)! -nCr = n! / (n-r)! (r)!
Unit Rates, Ratios, and Proportions - what does unit rate mean? - quarter pound of sugar costs .85 cents. How much would a 5 pound bag cost? what is the unit rate?
- one. like if someone types 346 in 8. min. finding the unit rate would be WMP. - 5 pounds cost 17 dollars - 1 pound aka unit rate costs 3.4 dollars
Linear Equations - Parallel lines: what is their slope relationship on a graph? - Perpendicular lines: what is their slope relationship on a graph?
- same slope. - each correspond by (-) reciprocal of the other
Two points -> linear equations - Write slope intercept, point slope, and standard from (-2,1) (3,16) - Write in standard (0,3) (5,0)
- slope int: y= 3x+7 Others: google. Good practice. - 3x+5y = 15 (prettier version)
Histogram - when the highest levels are on the right. How would you describe the skew?
- to the left. You have to look at the "tail" = lowest , to define a skew NOTE: left skew = negative. Right skew = positive
- How do you multiply mixed numbers? 6 (4/5) 7 (2/3) - How do you dividde mixed numbers? 5 (2/7) / 3 (1/4)
- turn into improper. mulitply accross like reg fractions 782/15 - turn into improper. KCF accorss like reg fractions. 148/91
Graphing Quadratic Transformations Describe trends - y = x^2 - y = -x^2 - y = (x - 1)^2 - y = - (x -3) ^2 +2 You have an equation in standard form and don't know the vertex. What is the equation to get the X point ? How do you get Y after this ? How do you get if it's U or downward U?
- upward U - downward U - upward U, right 1 - vertex: on (3, 2) facing downward Use -b/2a . Once you get X vertex value, plug into formula and solve for Y vertex value. Plug in two more x values to see right and left of vertex to see if it is up or down U
- What is an improper fraction? - how do you turn an improper fraction to a mixed? EX: 29/7 - how do you turn a mixed into a improper? 2 (4/5)
- when num > den - see how much the den fits to num. that amount is the coefficient, den stays the same, and num is the left over. 4(1/7) - multiply the den w/ the coefficient. add the num. this is the new num. den stays the same. 14/5
Absolute Value - I x I = 9 - I 5x +7 I =42 - I x+3 I = -4 - 2 I 3x -4 I +5 = 27 - I x -4 I + 8 = 3 - I 7x+2 I = 4x +11 - I x + 3 I = I x - 11 I
- x = 9 and -9 - x = 7 and -49/5 - no solution ; you have to be the one that "tests" out the negative in the second made up equation. - x = 5 and 7/3 - no solution bc you have to be the one that "tests" out the negative in the second made up equation. And 9 - 3 and -13/11 ; since there are no numbers next to the I I then it is okay to carry on as usual. On the right side, distribute the -. - no solution ; x = 4 . Same idea, distribute the - on right side.
Inverse Functions - what is the inverse of f(x) =3x+9 - what is the inverse of f(x) =x^2 -4 - How can you know if f(x) = 3x+9 is inverse w g(x) =x-9/3? - How can you tell if f(x) is a function? - f (x) passes horizontal test. What does this mean?
- y= x-9/3 = y= +/- Square root of x+4 - plug both in for the others x. Solve and the answer should be x for EACH. This shows they are inversed. - do a vertical line test. If passes, then it is a function. - means f'(x) is inverse and will pass vertical line test. If f (x) does not pass horizontal, no inverse.
Evaluate the function F(x,y) =3x^2 -4xy +5y^2, f (4,y) =100, y?
-2
Algebra word problems. 1) the sum of 5 times a # and 12 is 32. 2) 3 more than twice a number is 5 less than the square of the #. 3) sum of two #'2 is 33. The difference of them is 3. What are they? 4) the sum of a # and 6 times its reciprocal is 5. #? 5) the sum of two #'s is 14. If the product is 48, what is the diff of both? 6) two times the difference of a # and six is three more than the square root of the #.
1) 4 2) 4, -2 3) 18, 15 4) 3, 2 5) 2 6) 9
Linear Equations What are the 3 kinds of Linear Equations? Name their formula. + What is the M formula?
1) Slope- Int : Y = mx+b 2) Standard Form: Ax +By = C 3) Point- Slope Form: Y-Y1 = m(x -x1) M: rise over run. Just need two points: (Y2-Y1) / (X2-X1)
Two points and parallel/perp line —> other linear eq 1) write EQ of the line that passes (2,3) and is parallel to line y=4x-3 2) Write the EQ of the line that passes (3, -4) and is parallel to 2X-3y =6 3) passes through (1,2) and is perpendicular to Y= (3/5)X -2
1) Use point slope to get the formula and check by plugging in point to see if it equals Y. For all. Answer: Y=4x -5 2) Y= (2/3) x -6 3) Y = -(5/3) x + 11/3
How do you find the LCM using prime factorization? (3)
1. Factor all the way and box prime numbers 2. If duplicates, only count the factored number that has the most frequency in it. EX: 12 has 2 2s as primes and 8 has 3 2s prime. In this case, ONLY account for the 3 2s from the 8. 3. Multiply ALL of the highest freq numberes. This gives the LCM. NOTE: does not matter if one factored number does not have a matched prime. think of it as only multiplying the "best" qualities out of " factored contestants"
How do you find the GCF using prime factorization?
1. Factor all the way. 2. If duplicates, only pay attention if the other factored numbers have a SAME amount. ONLY take this into account. EX: 24 has 3 as a prime and 40 has 5 as a prime. Don't take into account both when multiplying final primes. 3. Multiply all of the matched primes. This gives the GCF. Think of it as splitting the bill equally. CROSS MATCH
Square roots What is another way to write square root of -25?
1. Take out the negative from inside the sr. this will leave you with sr of -1. multiplies by sr of 25. 2. since 25 is a perfect sr, answer is 5i. NOTE: i = square root of -1
Square roots What is another way to write negative square root of -64?
1. transfer inside sr to i form. This would've been positive but 2. since negative on outside still, makes -8i as the answer.
Compound Interest What is the formula? - Luke puts 1k in an account that pays annual interest of 9%. What will be the value after A) 10 years B) 20 years - Sam invests 5k in an account that pays an annual interest of 10%. The funds are invested for 20 years. What will be the value if interest is credited A) quarterly B) monthly? - Megan invests 10k in an annuity that pays a fixed interest of 6% annually. How many years will it take for her investment to double in value?
A = P (1 + r/n) ^nt - A) 2,367.36 B) 5,604.41 - A) 36,047 B) 36,640 - use the 72 method to get an estimate. 12 years
Probability 8 red marbles & 12 blue. 2 are selected w/ replacement. Strategy first then answer. A) what is the % of selecting 2 blue? B) % of selecting at least 1 red? C) % of selecting a red first then a blue? D) % a red and blue?
A) (12/20) (12/20) = 36% B) This is the same as saying everything BUT two blue. If you were to write down all of the combinations except this ^, you would have at least one red. So, P(at least one red) = 1 - P (BB). 64% C) Because ORDER MATTERS, "and" then: (8/20) (12/20) = 24% D) Because ORDER DOES NOT matter: P (RB) + P (BR) = 48%
Interest compounded continuously What is the formula What does E stand for? - Kim invests 10k in mutual fund that grows continuously. By 9% per year. What will the value of the account be after 10 years? - how long will it take for Kim's mutual investments to double if her mutual fund continuous to grow by 9% per year?
A=Pe^rt E: 2. 7182818 - 24596. 03 - use the 72 method, about 8 years.
Factoring What is the perfect square on trinomial formula? Solve the 4 problems
A^2 + 2AB + B^2 = (A +B) (A+B)
Factoring What is the perfect square binomial formula? - how do you solve non-perfect square binomials? - how do you solve a non-perfect square binomial that does not have a GCF? Solve the 10 problems
A^2 -B^2 = (A+B)(A-B) - by getting out the GCF then solving the perfect square that results. - get each their own square and putting them in (A+B) (A-B) form and getting the perfect square of (A-B) form.
Finding Point of intersection of two linear EQ What is the point of intersection for equations Y= (3/2) X -5 and 3 X -4Y =8? - How do you solve? What does this mean? How can you check?
Answer: (4, 1) - solve as system of equations ; this means to sub a "Y= THIS PART" into another Y. Or other way if you have an X =. Solving for the other coordianate by plugging in the answer you get. ; check by graphing equations in slope int form.
How can you get a X % of Y whole number? ex: 18% of 39
By converting the % to a decimal / moving decimal 2x to left. THEN multiplying it by whole number. ex: 7.02 OR can just break it down and add .
How can you compare fractions to see which is larger when den is different and w/o calc?
Cross multiply. The top is associated w side. EX: (5/10) (2/3). 15 goes with first and 20 goes with second.
-x-(-x). Positive or negative?
Depends on the first #. First convert the middle as a positive + and add from there.
Expected Value What is the formula and what is important to note about this? (2)
E (x) = x1 p1 + x2 p2 NOTE: P has to be in percent —> decimal. This equation gets the value appropriate for one trial so make sure you can talk that into the equation. Ex: a part two or the actual question might ask per 100. So whatever you get will be times 100.
(8x^3 + 5x^2 - 9) - (5x^3 -7x -5). Approach?
First spread the -. Then combine like terms.
Factoring Solving by factoring - approach?
Fully factor: then put remaking in = 0 to get each X.
Order of Operations (PEMDAS)
Make sure to to follow and not skip steps. watch out for potential confusion points. TRY: a^3 -3ab/2b^2-2a , a= 4 and b= -5. also, when in doubt, calculate it.
Multiply fractions
Multiply the tops, then multiply the bottoms, always reduce your answer. Can reduce to multiples to make it easier. Point is to cancel top numbers with bottom. NOTE. same thing for dividing fractions. only need to start by "KEEP, CHANGE, AND FLIP" then ^ approach.
Adding fractions with different denominators
Must rewrite with common denominator. Numerator: add across. NOTE: to find common denominator faster, use LCM strategy for denominators.
Percent Word problems Formula? - John buys x for $299. When paying, there was a 6% sales tax added. Total? - Sally is paying 250/ month. Soon: 20% off a month. New montly payment? - 69.55 with 7% sales tax included. Original price? - 25k car worth. First year decreases by 15%. Second year decreases by 10%. New total?
NEW = ORIGINAL ( 1 +/- R) - 316.94 - 200 - 65 - 19125. If yearly changes, CAN NOT just add up the %s. Must do one at a time.
-x+(-x). Positive or negative?
Negative EX: -7 + (-5) = -12
-x-x. Positive or negative?
Negative. EX: -7-6= -13
(-7)^2 and -7^2. same thing?
No. first is 49 and second is -49.
Two points -> linear equations Writer point slope, slope-int, and standard form from points (1,3) (3,7). - what should you do first?
POINT SLOPE: Y-3 = 2 (x-1) SlOPE INTERCEPT: Y= 2X+1 STANDARD: 2X-1Y = -1 - calculate M. Note: if going from point slope, can just move around to get slope-Int form, thus B. Or plug a point to solve for B.
X- (-x). Positive or negative?
Positive.
Linear Equations Graphing Graph: - Y = (- 3/4)x +5 - 3x -2y = 6 - 4x+ 3y =12 - Y-3 = 2 (x-2) - Y+4 = (-3/2) (x +1)
See answer on notes - For slope intercept form, can just get it from this equation. - For standard form, Solve for Y OR replace 0 for each letter to get the other. - Same^ - For Point- slope form, cross ref from Y - Y1 = M (X -X1) Y1 and X1 will be opposite +/- from already displayed. - ^
Standard Deviation Describe how to solve.
Square root of each numbers listed minus the mean in parentheses and each to the power of two, plus each other. Divided by N-1. Ex: SR (x-90)^2 + (y-90)^2 + (z-90)^2 / 2)
How to solve linear inequalities What is an important rule to remember? These problems are generally easy. Try these harder ones: 1) 5-2 (x+3) > 4+3 (x+2) 2) 5x-3 /4 < 3x-7/3 3) 2/3x +5 > 3/4 x - 1/5
When you divide or multiply by a - number, you flip the sign. 1) better to distribute the immediate number next to the parenthesis. Answer: x < - 11/5 2) better to cancel out both denominators by multiplying at the same time. x < -19/3 3) when dealing w mult denominators, best to find a least common denominator. Can do this by multiplying them all and applying it to the WHOLE equation. Note: does not cancel denominators so have to multiply to numerator and divide by denominator. Answer: 312/5 > x
PEMDAS. what is the "same" step?
adding and subtracting. EX: you did PEMD and now have 32-20+8. you must subtract first. answer: 20
