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x b b2 4ac 2a 1 RADICALS Simplifying 1. Make a big radical & break the number into its prime factors 2. If variables, list them out 3. Look at the index to see what type of groups you're making 4. Pull out the groups & leave the leftovers under the radical Multiplying & Dividing 1. Multiply/divide # by # & radical by radical 2. Simplify all radicals - reduce only the "whole" numbers 3. FOIL if there's an +/- sign Adding & Subtracting 1. Simplify everything 2. Add/subtract the coefficients of the radicals with the same radicand Rationalizing the Denominator (aka Get the Radical Out of the Denominator) 1. Multiply by a fancy one (denominator or conjugate) 2. Simplify radicals in numerator & find perfect square of the denominator then combine 3. Reduce only "whole" numbers at the end Solving Radical Equations YOU CAN DO THIS!!! 1. Isolate the radical 2. Square both sides (may have to FOIL) 3. Solve for the variable 4. Check answers in the ORIGINAL problem – this is MANDATORY! Examples 1. The expression 2. What is the solution set of the equation 9 x 10 x 0 ? 2 6 is equivalent to 3 6 6 3 6 (2) 3 (1) (3) (1) {-1} (2) {9} 2 (4) 2 3. Multiply: (2 3)(6 3) 8 6 4. Simplify: 3 4 324 p r 2 (3) {10} (4) {10, -1} IMAGINARY & COMPLEX NUMBERS Simplifying Negatives Under the Radical 1. Pull out your "i" 2. Simplify the radical Simplifying "i"s 1. Divide the exponent by 4 2. Look at the decimal 3. Remember your "cheer" i -1 -i .25 .5 .75 1 NO Adding/Subtracting Imaginary Radicals 1. Pull out your "i" 2. Simplify & add/subtract the coefficients **CAN ALSO USE iPart** Adding/Subtracting Imaginary #'s 1. Simplify all terms 2. Combine like terms Multiplying Imaginary Radicals 1. Pull out your "i" 2. Multiply #'s and radicals 3. Simplify at the end Multiplying Imaginary #'s 1. Multiply the coefficients 2, Add the exponents 3. Simplify the "i" Dividing Imaginary Radicals 1. Pull out your "i" 2. Divide the #'s & radicals 3. Simplify at the end Dividing Imaginary #'s 1. Divide the coefficients 2. Subtract the exponents 3. Simplify the "i" Complex Numbers - When graphing: (3 + 2i) = (3, 2) Complex Numbers - Multiplying 1. FOIL or use the calculator!! (a + bi mode) Add/Subtract 1. Combine like terms 2. If graphing, make a vector **remember: i2 = -1** Complex Numbers - Dividing 1. Multiply by a "fancy one" - conjugate 2. Simplify the numerator & denominator Multiplicative Inverse 1. 1 over the given number 2. Multiply by a "fancy one" 3. Simplify the numerator & denominator Examples 1. When expressed as a monomial in terms of i, 2 32 5 8 is equivalent to (1) 2 2i (2) 2i 2 2. In a + bi form, the expression 1 is 7 4i equivalent to (3) 2i 2 (4) 18i 2 7 4i 65 65 7 4i (2) 33 33 (1) 3 7 4i 65 65 7 4i (4) 33 33 (3) 3. What is the product of (2 – 5i) and its conjugate in simplest a + bi form? 4. The expression i3 + i(2 – i) is equivalent to (1) -1 + 3i (2) 1 + i QUADRATICS 4 (3) 1 – i (4) 1 + 3i Examples: 1. The product of the roots for the quadratic equation 2x2 – 5x + 9 = 0 is 9 2 (2) 9 (1) 2. What is the nature of the roots of the quadratic whose equation is x2 = -18x + 81? (1) imaginary (2) real, irrational, and unequal (3) real, rational, and unequal (4) real, rational, and equal 5 2 (4) 5 (3) 3. What is the quadratic equation whose roots are (2 – 4i) and (2 + 4i)? 4. Solve for x using the quadratic formula and leave your answer in simplest radical form. x2 = -2x + 4 5. Solve x2 – 6x + 1 = 0 by completing the square. Express the result in simplest radical form. 6. What is the center and radius of the following circle? x2 + y2 + 8x – 6y + 4 = 0 5 EQUATIONS & INEQUALITIES Solving Quadratic Inequalities Algebraically Solving Quadratic Inequalities Graphically Set it equal to 0 and factor Put it on a number line – check “0” to see which way to shade! Absolute Value Equations Absolute Value Equations Isolate the absolute value Drop the absolute value and create 2 equations – one that’s set equal to the positive value, one that’s set equal to the negative value Check all answers in your original equation Linear/Quadratic Systems Examples: 1. What is the solution of the inequality x2 – x – 6 < 0? (3) x 1 x 6 (2) x 2 x 3 (4) x 3 x 2 When solving absolute value inequalities, treat it just like an equation - the only difference is that the solution is not only one number, but a series of numbers The solution will get graphed on a number line Use test points to see which way you can shade – write the solution in notation form too! Linear/Circle Systems A linear equation will have variables with no exponents A quadratic equation will have variables with squared exponents The only way to solve a linear/quadratic system is substitution. (1) x 3 x 2 If the inequality has a < or > symbol, you will need a dotted line to show that the points on those lines are not included in the solution set If the inequality has a < or > symbol, you will need a solid line to show that the points on the line are included in the solution set. You need to use a test point – usually (0, 0) if one is not given – to determine which way you are to shade (inside the parabola or outside the parabola) The linear equation will be the equation without the exponents The equation of the circle will be the equation with x2 and y2 The only way to solve a linear/circle system is by substitution 2. What is the solution set of the equation 2 x x 3 9 ? (1) {12} (2) {2} 6 (3) {2, 12} (4) { } 3. Solve the absolute value inequality, graph the solution set, and write the solution set. 4. Solve the following system of equation algebraically and leave your answer in simplest radical form. 2x 3 5 2x2 + x + 1 = y y=x+7 RATIONAL EXPRESSIONS Undefined To see when a fraction is undefined we set the denominator equal to 0 Remember to factor if you are given a squared term! Simplifying Make sure that you factor first, then reduce!! Multiplying & Dividing Rational Expressions Make sure that you factor first, and then reduce!! When you divide, keep the first fraction, change the division sign to multiplication, & flip the second fraction. Then keep going as if you were multiplying! Adding & Subtracting Rational Expressions When adding & subtracting fractions, you need a common denominator Here’s what we always need to ask ourselves: CAN WE FACTOR THE DENOMINATOR? Factor the Multiply the denominators & take denominators your bits & pieces together Complex Fractions Rational Equations Remember that fractions are really a Either cross multiply or get a common big division problem denominator then ignore the denominator, and solve the numerator! Rewrite the problem as a division problem before factoring and reducing! Remember to check your answer in the original problem! 7 Rational Inequalities Write the inequality as an equation and solve. Determine any values that make the denominator equal 0 (undefined). Make each of the critical values from steps 1 and 2 on a number line. Select a test point in each interval – check to see if the chosen test points satisfy the inequality. Mark the number line to reflect the values and intervals that work. Write your answer in set notation. Try to remain calm…we’ll get through this together! Examples: 1. If the length of a rectangular garden is x2 2x represented by 2 and its width is x 2 x 15 2x 6 represented by , which expression 2x 4 represents the area of the garden? (1) x (2) x + 5 2. For which value of m is the expression 15m2 n undefined? 3 m (1) 1 (3) 3 (2) 0 (4) -3 x2 2 x (3) 2( x 5) x (4) x5 3. What is the value of x in the equation 4. Simplify and leave your answer in simplest x x form. 2? 2 6 (1) 12 (2) 8 x 2 6 x 16 64 x 2 (3) 3 1 (4) 4 8 5. Simplify the following complex fraction. 6. Divide and leave your answer in simplest form. 1 1 x y 1 1 x2 y2 y2 6 y 9 3y 9 y2 9 y 3 RELATIONS & FUNCTIONS Topic Good Things To Know Functions _____ value cannot repeat ____________ line test Relations & Functions One to One Function _____ and _____ cannot repeat must pass _______________ and ______________ line test Onto Function all values of the _____________ are used Domain ____ values Fractions denominators ______ Domain & Range Radical cannot be ___________ > 0 Fraction with Radical in Denominator denominator must be > ____ Range _____ values Graph to see what values are in the range Moving UP or DOWN UP _______________ Transformations DOWN _____________ Moving LEFT or RIGHT LEFT _______________ RIGHT _______________ Reflecting in X-AXIS or Y-AXIS X-AXIS ______________ Y-AXIS ______________ 9 Function Notation & Compositions of Functions Inverse Functions Direct & Inverse Variation f(x), g(x), h(x), etc – another way to write “y = “ Whatever value is inside the parentheses will replace the x in the given function When given points, _________________________________ When given an equation, switch ______ and ______, then solve for ________ To justify a composition f(f-1(x)) = f-1(f(x)) = x DIRECT VARIATION set up a ______________________ INVERSE VARIATION set up _______________________ Examples: 1. The function g(x) is defined as g(x) = 5 – 6x with the domain -4 < x < 2. What is the least element in the range? (1) 29 (2) 5 (3) -7 (4) -4 2. What is the domain of f ( x) x 5 ? (2) (1) , x 5 , x 0 (4) , x 5 (3) , x 5 3. Which of the following relations would not be considered a function? 4. Which equation defines a relation that is not a function? (1) f(x) = {(-4, 2), (1, 0), (9, 7)} (2) g(x) = {(4, -2), (-4, 0), (-9, -7)} (3) h(x) = {(2, -4), (2, 1), (7, 2)} (4) j(x) = {(-2, 4), (0, -1), (-7, -9)} (1) y = 3 – 2x (2) x2+ y2 = 16 (3) y = x2 + 4x + 6 (4) y = -5 5. If f(x) = 3x – 4, and g(x) = x2 – 4x, what is the 6. What is the inverse of the function value of g(f(x))? f(x) = 5 – 2x? 7. The frequency of a radio wave is varied inversely to the wave length. If the wave of 300 meters has a frequency of 1,500 kilocycles per second, what is the length, in meters of a wave with a frequency of 1,000 kilocycles per second? 8. If y = f(x) is shifted five units right and reflected over the x-axis, which of the following equations would represent that transformation? (1) y = -f(x) + 5 (2) y = -f(x + 5) 10 (3) y = -f(x) – 5 (4) y = -f(x – 5) CIRCLES Center-Radius Form Centered at the Origin x2 + y2 = r2 Centered at (h, k) (x – h)2 + (y – k)2 = r2 Standard Form x2 + y2 + ax + by + c = 0 complete the square to get from standard form into center-radius form Examples: 1. Determine the center and radius of the circle whose equation is: x2 + y2 – 2x – 8y + 1= 0 2. What is the equation of the circle below that passes through the point (0, -1)? EXPONENTS Name of Law Explanation of Law Example Multiplication Law Add the exponents 3x5 5 x9 15 x 45 Division Law Subtract the exponents 8 x8 4 x4 4 2x Power Law Multiply the exponents Negative Exponent Law To make the negative exponent positive, move it from the numerator to the denominator (or vice versa) 11 2x 6 4 16 x 24 10 x5 y 2 5x2 2 7 5x y 7 2 x3 y 9 y Power of Zero Law x8 x0 1 8 x Anything to the 0 power equals 1 Fractional Exponent Law 3 7 x 7 x3 The denominator becomes the index! 5 x x 2 2 5 Steps to Solve Equations with Fractional & Negative Exponents 1. Isolate the variable with the exponent 2. To solve for the variable, raise both sides of the equation to the reciprocal power. In order to solve an exponential equation, you must have the same base If the bases are the same, we set the exponents equal to each other and solve for the variable. If the bases are not the same, force them to be the same usually look for bases of 2, 3, 5, or 7 Growth/Decay y = abx Compounding Interest r A P 1 n Continuous Growth/Decay nt A Pe rt Examples: 1 1. Which of the following is equivalent to x ? 81 (1) 3-4x (2) 34 (3) 3-4 (4) 34x 3. What is the value of x in the 1 equation 16 x 2 ? 8 (2) -2 2 4 2 2. The expression 2a 3b 5 is equivalent to 2a b (1) ab3 (3) 2b3 (2) a (4) 2ab13 4. Given the equation y = abx, if the equation models exponential growth, the value of b must be greater than x (1) 1 2a b (1) 1 (2) -1 7 (3) 8 8 (4) 7 12 (3) 0 (4) 2 5. Solve for x: x 27 3 2 6. Andrew received a $3,200 bonus at work. He invested his money in a savings account that was making 4.5% interest that was compounded monthly. Using the equaition nt r A P 1 , where A is the value of the n investment after t years, P is the principal invested, r is the interest rate, and n is the number of times per year it was compounded, determine, to the nearest cent, how much money Andrew would have after 6 years. 4 68 LOGARITHMS Log Rules Exponential Rule Log Rule Example Product (xm)(xn) = xm + n Log mn = Log m + Log n Log 5(4) = Log 5 + Log 4 Quotient xm x mn n x Power (xm)n = xmn Log m = Log m – Log n n Log mn = n Log m Log 5 = Log 5 – Log 2 2 Log x2 = 2 Log x Logs to Exponentials and Exponentials to Logs ba = c Common Logs * Base of 10 * Log x = Log 10 x * Use 10x to solve “Circle the base to finish the race” “Log = Exponent” log b c = a Natural Logs * Base of e * Ln x = Ln e x *Use ex to solve Change of Base Formula log x y Good Logs to Know Log 1 = 0 Log 10 = 1 Log 100 = 2 Ln e = 1 Ln 1 = 0 13 log y log x Examples: 1. The expression 1 log a 3log b is equivalent 3 to (1) log 3 a b 3 (3) log (4) log a 3b 3 3 (2) log a 3b 3. The expression log 3 a b3 x2 y3 is equivalent to z 2. If log 3 = x and log 5 = y, which of the following could represent log 45? (1) 2x + y (2) 2xy (3) x2 + y (4) x2y 4. Solve for x: log (x – 1) + log (2x – 3) = 1 1 log z 2 1 (2) (2 log x + 3 log y) - log z 2 1 (3) (log 2x + log 3y) – log z 2 2 x3 y (4) 1 z 2 (1) (2 log x + 3 log y) + 5. Mouthwash manufacturers are constantly testing various chemicals on bacteria that thrive on human saliva. The death of the bacteria exposed to Antigen 223 can be represented by the function P(t) = 2,000e-0.37t where P(t) represents the number of bacteria from a population of 2,000 surviving after t minutes. a) Determine the number of bacteria surviving 3 minutes after exposure to Antigen 223. b) Using logarithm, determine the number of minutes, to the nearest tenth of a minute, necessary to kill 1500 bacteria. 14 TRIG. FUNCTIONS 3 Basic Trig. Functions Always remember SOH CAH TOA to determine the 3 basic trig. functions sin __________ cos __________ tan __________ Good Things to Know With the Coordinate Axes y x Co-Terminal Angles Add ______ if original angle was negative Subtract ______ if original angle was positive Quadrantal Angles Angles that lie on the quadrants 00, 900, 1800, 2700, 3600 Reciprocal Functions P(x, y) P( , ) x =_____________ csc = _________ = _________ y = _____________ sec = _________ = _________ tan = __________ = __________ *00 300 cot = _________ = _________ 450 600 *900 *1800 *2700 sin cos tan Cofunctions Cofunctions are equivalent if the angles are complementary sin _______ tan _______ sec _______ ARC LENGTH RADIANS DEGREES Substitute _____ in for_____ DEGREES RADIANS Multiply by 15 If there’s no ____, multiply by _____ Examples: 1. A circle has a radius of 4 inches. In inches, what is the length of the arc intercepted by a central angle of 2 radians? (1) 2 (2) 2 (3) 8 (4) 8 3. What is the number of degrees in an angle 11 whose radian measure is ? 12 (1) 1500 (3) 3300 (2) 1650 (4) 5180 2. The expression csc is equivalent to sec sin cos cos (4) sin (1) sin (3) (2) cos 4. The coordinates of a point on the unit circle 3 1 , . If the terminal side of an are 2 2 angle in standard position passes through the given point, what is the measure of ? (1) 2400 (2) 2330 5. What is 2350 expressed in radian measure? (1) 235 (2) 235 (3) 2250 (4) 2100 6. Find the exact value of (sin 2250)(cos 3000). 47 36 36 (4) 47 (3) TRIG. GRAPHS Each value of a trig. function represents something important to graphing: y = a sin bx + d amplitude frequency midline “a” – the amplitude tells us how far above and below the midline the graph will reach – a negative “a” value will reflect the graph over the x-axis “b” – the frequency tells us how many curves we will see between 0 and 2 - the period 2 is based off of the frequency and tells us how it will take before we see one full b trig. curve “d” – the midline tells us the line of horizontal symmetry – this line cuts the graph in half horizontally – this will move the entire trig. graph up (positive midline value) or down (negative midline value) 16 Examples: 1. What is the amplitude of the graph whose equation is y = -2 sin 4x? (1) (2) 2 (3) -2 2. If the period of a cosine curve is , what is the frequency? (1) 2 (3) 2 1 (2) 2 (4) 2 (4) 4 3. Which is an equation of the graph shown below? 3 4. What is the minimum value of the range of y = 3 + 2 sin x? (1) 1 (2) 0 (3) -1 (4) -5 2 -3 1 (1) y 3cos x 2 (2) y = 3 sin 2x (3) y = -3 sin 2x (4) y = 3 cos 2x 3 5. As increases from to , the value of 2 2 sin will 6. What is the frequency of the graph of the 1 equation y 2 cos x 7 ? 2 (1) 2 (3) -2 1 (2) (4) 2 2 (1) increase only (3) increase then decrease (2) decrease only (4) decrease then increase TRIG. IDENTITIES These Identities You NEED To Memorize Reciprocals Quotients Pythagorean These Identities Are On The Reference Sheet SUM AND DIFFERENCE IDENTITIES Identities of the SUM of 2 Angles Identities of the DIFFERENCE of 2 Angles 1. sin (A + B) = sin A cos B + cos A sin B 1. sin (A – B) = sin A cos B – cos A sin B 2. cos (A + B) = cos A cos B – sin A sin B 3. tan A B 2. cos (A – B) = cos A cos B + sin A sin B tan A tan B 1 tan A tan B 3. tan A B 17 tan A tan B 1 tan A tan B DOUBLE ANGLE IDENTITIES Cos 2A 1. cos 2A = cos2A – sin2A Sin 2A 1. sin 2A = 2 sin A cos A 2. cos 2A = 2 cos2A – 1 Tan 2A 2 tan A 1. tan 2 A 1 tan 2 A 3. cos 2A = 1 – 2sin2A sin HALF ANGLE IDENTITIES 1 1 cos A cos A 2 2 1 1 cos A A 2 2 Examples: 12 3 1. If sin x , cos y , and x and y are acute 13 5 angles, the value of cos(x + y) is (1) 21 65 (2) 63 65 (3) 14 65 (4) 7 and x is in quadrant IV, then 25 cos 2x equals 48 25 5. Prove: (2) 527 625 (3) 14 25 (4) (1) sin 2 sin (2) 2 cos (2) cos (3) sec (4) tan 5 and angle A is in quadrant I, 3 what is the value of cos2A? 4. If cos A 6. Cos 700 cos 400 – sin 700 sin 400 is equivalent to (1) cos 300 (2) cos 700 (1) csc is equivalent to cot 134 625 csc2 1 sin 2 cot 2 7. The expression 1 1 cos A A 2 1 cos A 33 65 3. If sin x (1) 2. The expression tan sin 2 is equivalent to sin 2 (3) cos 1100 (4) sin 700 8 and 2700 < A < 3600, what is the 17 value of tan 2A? 8. If cos A (3) 2 cot (4) 2 tan 18 19 Examples: 1. What value of x in the interval 900 < x < 1800 satisfies the equation sin 2 x sin x 0 ? 2. Which of the following is not a solution to the equation 2 cos x – 1 = sec x? (1) 900 (1) 00 (2) 1200 (3) 1350 (4) 1800 3. Solve for the exact value of x in the interval 00 < x < 3600. 4csc x 5 3csc x 4 (2) 1200 (3) 1800 (4) 2400 4. Solve the equation below for all values of x in the interval 00 < x < 3600. Round your answer to the nearest degree. 2sin 2 x 5cos x 4 5. Solve for the exact value of x in the interval 00 < x < 2 . 6. Solve for the exact value of x in the interval 00 < x < 3600. Round to the nearest tenth of a degree. 2 cos 2 x cos x 2 5cos x 3 cos x 20 21 Examples: 1. You must cut a triangle out of a sheet of paper. The only requirements you must follow are that one of the angles must be 60º, the side opposite the 60º angle must be 40 centimeters, and one of the other sides must be 15 centimeters. How many different triangles can you make? (1) 1 (2) 2 2. A garden is in the shape of an equilateral triangle and has sides whose lengths of 10 meters. What is the area of the garden? (1) 25m2 (2) 50m2 (3) 43m2 (4) 87m2 (3) 3 (4) 0 3. In ABC , if AC = 12, BC = 11 and m A = 300, then ABC could be (1) an obtuse triangle only (2) an acute triangle only (3) a right triangle only (4) either an obtuse triangle or an acute triangle 4. While sailing a boat offshore, Donna sees a lighthouse and calculates that the angle of elevation to the top of the lighthouse is 30. When she sails her boat 700 feet closer to the lighthouse, she fins that the angle of elevation is now 50. How tall, to the nearest tenth of a foot, is the lighthouse? 22 SERIES & SEQUENCES Arithmetic Sequences To Find the Nth Term *To Find the Sum of N Terms Geometric Sequences To Find the Nth Term *To Find the Sum of N Terms Examples: 1. The value of the expression 2 n 2 2n 2. Which expression represents the sum of the sequence 3, 5, 7, 9, 11? (1) 12 (1) 2 n 0 (2) 22 (3) 24 (4) 26 5 2n 1 (3) n 1 (2) 5 3n n 1 3. What is the fifteenth term of the sequence 5, -10, 20, -40, 80…? (1) -163,840 (2) 81,920 (3) -81,920 (4) 327,680 5 3n 1 n 1 (4) 5 n 1 n 1 4. Find the first four terms of the recursive sequence defined below. a1= -4 an = 2an-1 – 2n 23 ONE VARIABLE STATISTICS Measures of Central Tendency Mean average - x Median middle number – numbers must be in order Mode number that appears most often Measures of Dispersion Range biggest # - smallest # Interquartile Range Q3 – Q1 Variance (standard deviation)2 Standard Deviation variance **REMEMBER THAT EACH PART OF THE NORMAL CURVE REPRESENTS .5 STANDARD DEVIATIONS FROM THE MEAN** 24 Examples: 1. A new survey is designed to collect data based on the number of miles people drive each month. Which of the following groups would create the least bias in conducting the survey? 2. The Write-O Pen company manufactures pens that have a mean life time of 200 pages with a standard deviation of 12 pages. Approximately what percentage of the pens last between 182 and 212 pages? (1) All students who attend the local high school (2) People at a senior citizens center (3) People entering the mall (4) People riding the subway 3. In a normal distribution, x 2 50 and x 2 10 when x is the mean and is the standard deviation. What is the mean? 4. On a standardized test with normal distribution, the mean is 85 and the standard deviation is 6. If 1400 students took the test, approximately how many students would be expected to score between 79 and 97? PROBABILITY PERMUTATIONS Order matters Key words arrangement/arrange, filling specific roles (president, vp, secretary or 1st, 2nd, 3rd place), ordering/order, license plates, telephone numbers, or making “words” Open up spots to fill, then multiply totalnumber ! Repeated “letters” repeatedletters ! 25 COMBINATIONS Order does not matter Key words committees, chose, chosen, groups, team, gather, or assemble/assembly Make a have/want chart Bernoulli Trials “Exactly” Probability (haveCwant)(swant)(fhave-want) Probability of success Probability of failure (1 – prob. of success) “AT MOST” PROBABILITY consider all the probabilities equal to or less than the given probability (ex.) Mrs. Pace had a class of 10 students. She was to choose AT MOST 7 students to attend a trip. How many students could she have sent? 7, 6, 5, 4, 3, 2, 1, or 0 “AT LEAST” PROBABILITY consider all the probabilities equal to or more than the given probability (ex.) Mrs. Pace had a class of 10 students. She was to choose AT LEAST 7 students to attend a trip. How many students could she have sent? 7, 8, 9, or 10 Binomial Expansion Used like FOIL, but with exponents greater than 2 (x + 4)6 On the reference sheet: Examples: 1. A family with 6 children is selected at random for a study. What is the probability that the family will have at most 2 girls? 2. What is the third term in the expansion of (x – 2)7? 3. In one state, a license plate consists of three letters followed by two digits. If no letter or digit can be repeated, how many different license plates are possible? 4. In a group of 8 students, three are female and five are male. What is the probability that two females and one male will be chosen to work on a subcommittee? 26 TWO VARIABLE STATISTICS Regressions Correlation coefficient (r) how close to the “line” of best fit will the data lie – closest to +1 or -1 is the “best” fit line Linear regressions (LinReg), exponential regressions (ExpReg), logarithmic regressions (LnReg), power regressions (PwrReg), cubic regressions (CubicReg) and quadratic regressions (QuadReg) Linear Logarithmic Exponential y = ax + b y = a + blnx y =abx Power y = axb y= ax3 Cubic + bx2 + cx + d Quadratic y = ax2 + bx + c Example: The accompanying table shows the enrollment of a preschool from 1980 through 2000. a) Write a linear regression equation to model this data. b) How many students did they have in 1998? c) In what year did enrollment reach 50 students? 27 BRING ON THE REGENTS EXAM… GO ON…BRING IT!