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A BUNDLE OF WGU C955 EXAM 2024
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If 200 people are surveyed, how many claim to have had no exercise? {{ Pie chart reflecting the average number of hours exercised per week. No exercise... [Show More] 36%, 1 - 2 hours 28%, 3 - 4 hours 12%, 4 - 5 hours 10%, 5 - 6 hours 8%, 6 - 7 hours 4%, more than 7 hours 2%. }} a 18 b 36 c 72 d Cannot determine - ANSWERS72 Determine the range for the following data set. {1,24,26,28,32,36,38,40,65} a 1 to 65 b 64 c 65 d Cannot determine - ANSWERS64 It is important to start the frequency scale on a bar chart at which value to be certain not to overemphasize a difference in values? a Zero b The lowest measured value c The smallest frequency d As long as the scale is even, it doesn't matter where you start it. - ANSWERSZero If 80 people exercised 4 - 5 hours per week, how many people were surveyed? {{ Pie chart reflecting the average number of hours exercised per week. No exercise 36%, 1 - 2 hours 28%, 3 - 4 hours 12%, 4 - 5 hours 10%, 5 - 6 hours 8%, 6 - 7 hours 4%, more than 7 hours 2%. }} a 80 b 800 c 400 d 50 - ANSWERS800 You are a professional trainer at a local sports academy. You ask your athletes to determine the number of grams of protein they consume for a particular meal. Which of the following would be the best choice to illustrate the shape of the data you collect? a Bar chart b Pie chart c Box plot d None of the above - ANSWERSBox plot What is the most significant difference between histograms and bar charts? a The number of bars used b The use of labels on the axes c The type of data depicted in the graph d The coloring used for each bar - ANSWERSThe type of data depicted in the graph Of the following sets of data, which would you assume should have the greatest range? a Age when a baby gets their first tooth b Age of first-year business students c Age of death d Age of high school graduate - ANSWERSAge of death Determine any outliers in the following data set. {1,24,26,28,32,36,38,40,65} a 1 b 65 c A and B d None - ANSWERSA and B Determine the interquartile range ( IQR ) for the following set of diagnostic test scores. {60,47,65,85,81,77,70,56,47,84,75} a 25 b 57 c 68 d 80 - ANSWERS25 Stem plots display which type of data? a Quantitative b Categorical c Neither Quantitative nor categorical d Quantitative and categorical - ANSWERSQuantitative Determine the median for the following set of diagnostic test scores.{60,47,65,85,81,77,70,56,47,84,75} a 67 b 70 c 47 d 67.9 - ANSWERS70 Determine Q3 for the sorted list of data values. {3,8,8,10,16,20,20,23,27,37,44,45,62,71} a 27 b 37 c 44 d 45 - ANSWERS44 The bitrate of audio files in a sample group of files ranged from 160 kilobytes per second (Kbps) to 256 kilobytes per second (Kbps). What percentage of the audio files will fall within 2 standard deviations of the mean? Assume the data is normally distributed. a 34% b 68% c 95% d 99.7% - ANSWERS95% Which of the following are best used to display categorical data? a Histogram b Dot plot c Pie chart d Stem plot - ANSWERSPie chart When observing a box plot, what percentage of the measured data lies between Q1 and the maximum value in the list? a 75% b 50% c 25% d Cannot determine. - ANSWERS75% Which of the four different sets of numbers would have the greatest standard deviation? a 5,5,5,5,5 b 5,6,7,8,9 c 1,8,16,25,33 d 40,43,45,47 - ANSWERS1,8,16,25,33 Determine the best estimate for the total number of ice creams sold on Monday and Tuesday. {{ Bar Chart reflecting the average number of ice creams sold on each day of the week. Mon. 70, Tue. between 60 and 70, Wed. between 50 and 60, Thur. between 40 and 50, Fri. between 60 and 70, Sat between 30 and 40, Sun. 30. }} a 100 b 112 c 137 d 148 - ANSWERS137 Please use the dot plot below to answer the following question. Dot Plot displaying the following data points: 5, 6, 6, 7, 8, 8, 8, 9, 9, 10. Determine the median for the data. a 7 b 7.5 c 8 d Cannot determine. - ANSWERS8 The return on investment (ROI) in a sample population of investments ranged from 8% to 23% . What percentage of the sample will fall within 1 standard deviation above the mean? Assume the data is normally distributed. a 47.5% b 13.5% c 68% d 34% - ANSWERS34% Arrange the mean, median, and mode in order from least to greatest in a distribution that it is positively skewed. a Median, mode, mean b Mean, median, mode c Mean, mode, median d Mode, median, mean - ANSWERSMode, median, mean If the following data are represented on a stem plot, how many leaves would be shown on the " 6 " stem? {57,63,55,59,52,60,65,56,56,65,55,63} a 5 b 4 c 3 d 2 - ANSWERS5 If 15 people exercised 3 - 4 hours per week, how many people were surveyed? {{ Pie chart reflecting the average number of hours exercised per week. No exercise 36%, 1 - 2 hours 28%, 3 - 4 hours 12%, 4 - 5 hours 10%, 5 - 6 hours 8%, 6 - 7 hours 4%, more than 7 hours 2% .}} a 18 b 180 c 1250 d 125 - ANSWERS125 If 150 people are surveyed, how many claim to have exercised 6 - 7 hours per week? {{ Pie chart reflecting the average number of hours exercised per week. No exercise 36%, 1 - 2 hours 28%, 3 - 4 hours 12%, 4 - 5 hours 10%, 5 - 6 hours 8%, 6 - 7 hours 4%, more than 7 hours 2% .}} a 6 b 60 c 38 d Cannot determine - ANSWERS6 What can sometimes cause a bar graph or histogram to be misleading? a Whether or not the bars are touching b Starting the numerical scale on the vertical axis at a value other than zero c Leaving out a numerical scale on the vertical axis d b and c - ANSWERSb and c Determine any outliers in the following data set. {55,77,64,82,58,75,57,49,106,71,68,76} a 49 b 106 c Both A and B d There are no outliers in the data set. - ANSWERS106 On average, Lightning Communications delivers to their customers, high-speed Internet connections of 70 Mbps, with a standard deviation of 12 Mbps. About what percentage of customers will experience a network speed between 70.0 Mbps and 94.0 Mbps? Assume a normal distribution. a 68% b 34% c 47.5% d 49.85% - ANSWERS47.5% What would be the best type of graph to use to display the age of all employees in a particular division in a company? a Bar chart b Histogram c Scatterplot d Pie chart - ANSWERSHistogram Of the following sets of data, which would you assume should have the smallest range? a Price in dollars ($) of penny stocks currently being traded over-the-counter through the OTC Bulletin Board. b Ages of stockbrokers currently on the trading floor. c The number of trades on the NYSE on any given day. d The ages of interns currently in the college summer internship program. - ANSWERSThe ages of interns currently in the college summer internship program. Assuming a population is normally distributed, what percentage of the population will fall within 3 standard deviations of the mean? a 98.6% b 68% c 95% d 99.7% - ANSWERS99.7% Which of the four different sets of numbers would have the least standard deviation? a 5,5,5,5,5 b 5,6,7,8,9 c 1,8,16,25,33 d 40,43,45,47 - ANSWERS5,5,5,5,5 Determine the range for the following data set. {55,77,64,82,58,75,57,49,86,71,68,76} a 33 b 31 c 27 d 37 - ANSWERS37 Does a box plot include the mean of a set of data? a Yes, a box plot includes both the mean and the median. b No, a box plot does not include the mean. - ANSWERSNo, a box plot does not include the mean. You are designing a study to determine if the amount of an individual's annual 401K contribution is dependent upon the number of hours she or he works per week. You survey a group of 900 men and women aged 20 - 60 and record the number of hours each person works per week versus their total annual 401K contribution. What type of data are you collecting? a Categorical b Qualitative c Quantitative d Both a and b. - ANSWERSQuantitative [Show Less]
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A researcher wants to know if there was a relationship between student age and desire to complete a college degree. To answer this question, the researcher... [Show More] used a local community college as the sampling frame and then used stratified sampling to get a sample of students from 18 to 80 years old. Based on the information given, is there any potential bias in this study? a Yes, because the sampling frame does not match the intended population of the question. b Yes, because the sampling method will not give a representative sample. c Yes, because a voluntary sample should have been used. d No, there will likely be no bias in this study. - ANSWERSYes, because the sampling frame does not match the intended population of the question. A researcher conducts an observational study and finds a correlation between managers' income and the number of college credits earned. The correlation coefficient was r=.85 with a regression equation of y=515x+12000. What can you say about the relationship between these variables? a There is an association between these variables b There is a causation between these variables. c There is no relationship between these variables. d There is not enough information to determine the relationship between the variables. - ANSWERSThere is an association between these variables What technique is used to estimate the profit margin for a production level of 25 thousand units, if a line of best fit is created to estimate profit margin for production levels between 20 to 39 thousand units? a Interpolation b Linearization c Extrapolation d Internalization - ANSWERSInterpolation What is the most appropriate definition of a scatterplot? a A graph that uses dots to demonstrate relationships between two categorical variables. b A graph where lines are shown to represent positive or negative trends. c A graph where the explanatory and response variables are plotted as ordered pairs. d A graph where a positive causation is always represented with dots forming a straight line. - ANSWERSA graph where the explanatory and response variables are plotted as ordered pairs. What does a strong positive correlation between two variables suggest? a The explanatory variable is increasing and the response variable is decreasing b There is an association between the variables c There is a causation between the variables d Cannot determine - ANSWERSThere is an association between the variables {{ Scatterplot of distance from city center vs. rent. The linear equation for this scatterplot is y equals negative one hundred five ten thousandths times x plus ten and three hundred eighty one thousandths. }} Using the scatterplot Distance from City Center vs. Monthly Rent, how far can we expect an apartment to be from the city center if the monthly rent is $ 980 ? Round your answer to the nearest mile. a Around 54 miles b Around 55 miles c Around 56 miles d Around 57 miles - ANSWERSAround 55 miles Which correlation coefficient suggests the weakest correlation? a −0.9 b −0.3 c 0.1 d 1 - ANSWERS0.1 What does it mean for a result or relationship to be statistically significant? a The relationship is not caused by mere chance. b The relationship is caused by chance. c Your hypothesis test has failed. d Your significance level is not high enough. - ANSWERSThe relationship is not caused by mere chance. What is the process used to create the equation for the line of best fit? a Completing the square b Least squares estimation c Fitting the line to the curve d Linear approximation - ANSWERSLeast squares estimation A relationship between two or more variables is known as a(n) ________. a Causation b Association c Cause and effect d Correlation - ANSWERSAssociation Using a line of best fit in slope-intercept form, y=mx+b , what must be true if there is a positive correlation? a m must be >0 . b b must be >0 . c Both m and b must be >0 . d Both m and b must have the same sign. - ANSWERSm must be >0. Consider the following equation, y=−3.2x+2.8 . What is the y -intercept for this equation? a −3.2 b 3.2 c 2.8 d −2.8 - ANSWERS2.8 When linear regression is used to show there is a linear association between two variables, we know the relationship is: a A causation b A correlation c Neither A nor B d Both A and B - ANSWERSA correlation A restaurant owner wants to see if she can use low temperatures to boost soup sales at her restaurant. To study a possible relationship between temperature and soup sales, she collects data throughout the year on the temperature of a given day (ranging between 20 degrees F and 90 degrees F) and the amount of soup sold that day. She performs a linear regression and comes up with a least squares regression line of y=−1.64x+176.6 with r=−0.89 where x is the temperature (in degrees F) and y is the number of daily soup sales. How much soup should she expect to sell on a day that is 50 degrees F? Round to the nearest integer. a 177 orders of soup b 95 orders of soup c 259 orders of soup d 101 orders of soup - ANSWERS95 orders of soup The line of best fit is also known as: a The extrapolation line b The regression line c The interpolation line d None of the above - ANSWERSThe regression line If a trend appears in a large sample of data, the trend may not be replicated if the sample is broken up into smaller subsets. What is this effect known as? a Foster's Theorem b Bayes' Theorem c Simpson's Paradox d Consistency Construct - ANSWERSSimpson's Paradox A variable not included in the study that is related to the measured variables in a study is called a ____________. a Independent variable b Confounding variable c Dependent variable d Lurking variable - ANSWERSLurking variable Using the scatterplot below, what type of correlation is suggested? Scatterplot displaying data points distributed from lower left to upper right. Points are relatively close to one another. a No correlation b Weak negative positive c Moderate positive d Strong negative - ANSWERSModerate positive What must be true about the dots on a scatterplot if there is no correlation? a The dots are far away from the line of best fit. b The dots form no recognizable linear pattern. c The dots are evenly spaced around the graph. d The dots form a non-linear pattern. - ANSWERSThe dots form no recognizable linear pattern. What is (are) a potential problem(s) that can occur when attempting to use regression analysis? a Extrapolation b Lurking variables c Inappropriate sampling d A, B, and C - ANSWERSA, B, and C A researcher conducts an experimental study and finds a correlation between salary and levels of experience. The correlation coefficient was r=.75 with a regression equation of y=515x+17500 . What can you say about the relationship between these variables? a There is an association between these variables [Show Less]
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Discrete data - ANSWERSHas distinct values, can be counted, had unconnected points (think dots) Continuous data - ANSWERSHas values within a range, meas... [Show More] ured not counted, does not have gaps between data points (data is connected lines or curves). Example of discrete data - ANSWERSDays of the week Expressions - ANSWERSA group of symbols such as numbers and operators that has mathematical validity Commutative - ANSWERSThe order in which the numbers appear in the sum can be reversed Identity property - ANSWERSAdding 0 to any number does not change the original number Additive inverse - ANSWERSValues that are equally far from 0 on the number line. Negative - ANSWERSWhen multiplying a positive number by a negative number the result is always Positive - ANSWERSMultiplying a negative number by a negative number results in a positive Factors - ANSWERSIntegers that evenly divide the initial integer Prime number - ANSWERSPositive integer with exactly two positive factors consisting of 1 and itself Composite number - ANSWERSHas at least one positive factor other than one and itself Factorization - ANSWERSProcess of breaking up a composite number into its prime factors fundamental theorem of arithmetic - ANSWERSAny integer greater than one is either Prime or the product of Prime numbers Principal square root - ANSWERSPositive square root of a number Radican - ANSWERSNumber under radical sign √16=4 Open Circle - ANSWERSRepresents less than or greatest than on the number line Perfect square - ANSWERSProduct of any integer with itself yields a perfect square. Whole numbers - ANSWERSpositive numbers with a whole value Integers - ANSWERSNumbers with no fractions or decimal value but can be positive or negative Rational numbers - ANSWERSNumbers that can be expressed as a fraction or decimal values that have that end or repeat forever. Includes all integers since all integers can be expressed as fractions. Real numbers - ANSWERSEverything that can be included in a number line including pi. Fractions - ANSWERSExpress numbers which are part of a whole Numerator - ANSWERSNumber written before the slash or above the fraction bar Proper fraction - ANSWERSNumerator is less than denominator and the value of the fraction is less than one Improper fraction - ANSWERSNumerator is greater than denominator and therefore is greater than one except with negative fractions Mixed numbers - ANSWERSA whole number and proper fraction. A negative sign in front applies to both parts of the mixed number. Multiples - ANSWERSIntegers created by multiplying one number times another number Fractions - ANSWERSExpress numbers which are part of a whole Numerator - ANSWERSNumber written before the slash or above the fraction bar Proper fraction - ANSWERSNumerator is less than denominator and the value of the fraction is less than one Improper fraction - ANSWERSNumerator is greater than denominator and therefore is greater than one except with negative fractions Mixed numbers - ANSWERSA whole number and proper fraction. A negative sign in front applies to both parts of the mixed number. Multiples - ANSWERSIntegers created by multiplying one number times another number Reciprocal - ANSWERSThe number which of multiplied by divisor gives you one (like the fraction flipped over) Terminal decimal - ANSWERSHas digits that end Ratio - ANSWERSComparison of two numbers Rate - ANSWERSA ratio that compares two quantities having different units of measure Proportion - ANSWERSTrue statement in which two ratios are equal to each other. Two days are proportional of they are equivalent. Conditional proportion - ANSWERSOne part of a proportion is a variable or unknown quantity Celsius to Fahrenheit - ANSWERSCelsius x 9/5 + 32 Fahrenheit to Celsius - ANSWERS(Fahrenheit - 32) x 5/9 Constant - ANSWERSNumber with a fixed value. All real numbers are constants Elementary operations - ANSWERSAddition, subtraction, multiplication, division Base - ANSWERSThe number an exponent is written next to Variable - ANSWERSSymbol that represents our holds the place of a numerical value Coefficient - ANSWERSA number by which a variable is being multiplied. Coefficients are written in front of variables. 16x, 16 is coefficient. If there is no number you assume an invisible1. Term - ANSWERSCan be a single constant, a single, or a number of constants and variables multiplied together. Algebraic expression - ANSWERSString of terms connected by division, addition, and subtraction. How to write an algebraic expression - ANSWERSConstants at end. Write terms with the largest exponents first. Always write in descending order of exponent value with constants at the end. Inverse operation - ANSWERSOperations that undo each other. Subtraction is inverse of addition. Division is inverse of multiplication. Like terms - ANSWERSHave the same variable with the same exponent Degree of an expression - ANSWERSRefers to largest exponent in an expression Linear - ANSWERSHas degree of 1 Quadratic - ANSWERSHas degree of 2 Cubic - ANSWERSHas degree of 3 Constant - ANSWERSHas degree of 0 Distributive property - ANSWERSPrinciple used to multiply a single term by multiple terms. If there are parenthesis around multiple terms which are in turn multiplied by a single term, we can use this property. [Show Less]
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Boxplot - ANSWERSan image that has min, Q1, median, Q3, max Histogram - ANSWERSA graphical representation -- bars, measuring the frequency within each i... [Show More] nterval Skewed right - ANSWERSNot a symmetric distribution, the tail is on the right, i.e. extra stuff on the right Measures of center - ANSWERSMedian, the mean (and mode) Measures of spread - ANSWERSRange, IQR & standard deviation Standard Deviation Rule - ANSWERS68% of the data are within 1 standard deviation, 95% are within 2, 99.7 are within 3 standard deviations from the mean. For skewed data, use these for center and spread - ANSWERSIn this situation, we use median (for center) & IQR (for spread) Explanatory variable - ANSWERSIn a study, what we think is the "cause" Response variable - ANSWERSIn a study, what we think is the "effect" Scatter plot - ANSWERSA graphical representation of Q -> Q Two way table - ANSWERSA graphical representation of C -> C Side-by side box - ANSWERSA graphical representation of C -> Q Linear relationship - ANSWERS"shaped like a line" Correlation coefficient, r - ANSWERSBetween -1 and 1; measures how close the points are to the line and if the trend is uphill (positive) or downhill (negative). r = -0.2, for example - ANSWERSThis is an example of a correlation coefficient that represents a weak negative correlation. r = 0.9, for example - ANSWERSThis is an example of a correlation coefficient that represents a strong positive correlation. Linear regression line - ANSWERSA line that fits the data as close as possible, used to make predictions Interpolation - ANSWERSMaking predictions *within* the range of your data. This is usually accurate. Extrapolation - ANSWERSMaking predictions *outside* of the range of your data. This is generally a bad idea. Simpson's Paradox - ANSWERSWhen split up, each data set can have a pattern which goes away when all the data is combined. Only way to prove causation - ANSWERSExperiments, because they account for lurking variables Observational study - ANSWERSA type of study where we measure or survey members of a sample without trying to affect them. Cannot prove causation. Experimental study - ANSWERSA study where you split subjects up randomly and impose a change on one group to study the effect; can prove causation Prospective study - ANSWERSIs a study that's done over time to find results / A study watching for outcomes during the study period Retrospective study - ANSWERSA study that looks backwards to assess outcomes and possible causes after the fact Control group - ANSWERSrandomly assign people or things to groups. One group receives a treatment and the other group does not. This is the group that does not receive treatment Placebo - ANSWERSA substance or procedure that has no effect used for comparison to the real substance or procedure Placebo effect - ANSWERSA beneficial effect produced by the belief of the patient/subject, not by the intervention itself. Experimenter effect - ANSWERSWhen the persons running an experiment affects its results by influencing the subjects inadvertently Open question - ANSWERSA question that gives the responder freedom to answer in many different ways -- harder to analyze with statistics. Closed question - ANSWERSA question with limited choices, e.g. multiple choice or yes/no. Easier to analyze statistically. Unbalanced response - ANSWERSGiving more options that are negative than positive options (or vice versa) which biases the responses towards the more common option Matched pairs - ANSWERSGrouping two similar subjects and giving different treatments/procedures to each in order to compare the differences. For example, having one twin take a medication while the other twin does not. Blind experimental study - ANSWERSWhen information of a study isn't revealed to the participants Double Blind Study - ANSWERSWhen information of study is hidden from the researcher and the participant. Population - ANSWERSThe entire group you are trying to describe or understand. Sampling frame - ANSWERSList of group from which you choose your sample. Sample - ANSWERSThe group that is actually picked to be included in a study Simple random sample - ANSWERSmaking a selection by following a random pattern and selecting without replacement. Unbiased. Systematic sample - ANSWERSSample is selected by listing the sampling frame, then making a selection by following a simple pattern (eg. Every 20th name). Unbiased. Voluntary sample - ANSWERSMembers of the sample may choose not to respond. Similar to Non Response. Convenience sample - ANSWERSParticipants are easy for researcher to access. Tends to increase bias. Cluster sample - ANSWERSSample frame is divided into groups, we select a few groups, then selecting ALL of the members of those groups. Stratified sample - ANSWERSSample frame is divided into groups. Then we choose a random sample (usually the same size) from within EVERY group. Multi-stage sample - ANSWERSMultiple rounds of randomness and grouping. For example: randomly selecting a few groups, then choosing a small random sample just those selected groups. Often a combination of Cluster and Stratified Sampling. The formula for all simple probabilities - ANSWERS(number of possible outcomes for the specific event) / (total number of possible outcomes) For independent events, P(A and B) = ? - ANSWERSP(A)*P(B) For independent events, P(A|B) = ? - ANSWERSP(A) [this is the right side of which probability formula?] P(A|B) = ? - ANSWERSP(A and B) ÷ P(B) P(A or B) = ? - ANSWERSP(A) + P(B) - P(A and B) In general, P(A and B) = ? - ANSWERSP(A)*P(B|A) [Show Less]
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Changing Improper Fractions and Mixed Numbers - ANSWERSImproper fractions can be converted to mixed numbers by following these steps: Write division pro... [Show More] blem with numerator divided by denominator. Divide to determine quotient and remainder. Write mixed number with the quotient as the whole number and the remainder as the numerator over the same denominator. Changing Mixed Numbers Into Improper Fractions - ANSWERSMixed numbers can also be converted to improper fractions by following these steps: Multiply the whole number by the denominator of the fraction. To the product given by step 1, add the number of the numerator. Write the result of step 2 as the numerator of the improper fraction. The denominator of the improper fraction should be the denominator of the original fraction. Simplify the improper fraction by diving the numerator and denominator by all common factors. Discrete Data - ANSWERSHas distinct values, can be counted, has unconnected points (dots) Continuous data - ANSWERSHas values within a range, measured (not counted) does not have gaps between data points. (connected lines or curves) Sign rule for Multiplication and division - ANSWERS1. +# x +# = +# 2. -# x -# = +# A product or division of two numbers of the same sign will result in a positive number 3. -# x +# = -# 4. +# x -# = -# A product or division of two numbers of different signs will result in a negative number Prime Number - ANSWERSA prime number is a number that has exactly two positive factors; 1 and itself. Composite Number - ANSWERSA number that is not prime. It has 2 or more positive factor, including 1 and itself. Prime Factorization - ANSWERSWriting the number as a product of only prime numbers. Greatest Common Factor (GCF) - ANSWERSThe larges number that divides all the given numbers evenly. Multiples of a number - ANSWERSNumbers that can be obtained by multiplying the given number by 1, 2, 3, 4, etc. Least Common Multiple (LCM) - ANSWERSthe smallest positive number that can be divided by the given numbers Centigrade/Fahrenheit Conversions - ANSWERSC = (F - 32) X 5/9 F = (C X 9/5) + 32 Unit Conversions for Household Measures of Volume - ANSWERS1 tablespoon = 3 teaspoons 1 oz = 2 tablespoons 1 cup = 8 oz 1 pint = 2 cups 1 quart = 1 pints 1 gallon = 4 quarts Common Metric Conversions - ANSWERS1 L = 1000 mL 1kg = 1000 g 1 g = 1000 mg 1 mg = 1000 mcg Conversions between Household and Metric Units - ANSWERS1 cc (Cubic Centimeter) = 1 mL 1 oz = 30 mL 1 L = 1.057 qt 1 tsp = 5 mL 1 kg = 2.2 lbs 1 oz = 28.35 g Like Terms - ANSWERSTerms that have the same variable raised to the same power; they can be combined using addition and subtraction Addition/Subtraction Principle - ANSWERSWe can add or subtract the same number to both sides of an equation and the resulting expression remains equal. Multiplication/Division Principle - ANSWERSWe can multiply or divide the same number to both sides of an equation and the resulting expression remains equal. (Divide by 0 is not allowed) Butterfly Method - ANSWERSCross Multiply, if a/b = c/d then a x d = b x c Slope-Intercept Equation - ANSWERSy = mx + b Where "m" is the slope, "b" is the y-intercept, and "x" and "y" follow the coordinate formula (x,y) Slope of a line - ANSWERSThe slope of a line is the ratio of the vertical change between two points on the line to the horizontal change between those two points. rise: (y2 - y1) / run: (x2 - x1) Reducing Fractions Using Prime Factorization - ANSWERSThe steps to reduce a fraction through prime factorization are as follows: List the prime factors of both the numerator and denominator. Cancel the factors that are common to both the numerator and denominator. Multiply across the numerator and denominator. 6/8 6/8 = 2x3/2x2x2x 2x3/2x2x2x = 3/2x2 3/2x2 = 3/4 Reducing Fractions Using Common Factors - ANSWERSThe steps for the common factors method are as follows: Divide numerator and denominator by a common factor. Continue to divide by common factors. Write the reduced factor. -28/42 -28/42 = (-28/7) / (42/7) = -4/6 Reduce -4/6 = (-4/2)/(6/2) = -2/3 Least Common Denominator - ANSWERSThe least common multiple of the denominators of two or more fractions. Let's determine the least common denominator of 13 and −27. Ask "do 3 and 7 have a factor in common?" No. So, this is situation 1. Multiply 3×7=21. 21 is the least common multiple of the numbers 3 and 7, therefore it is the least common denominator for 13 and −27. 21 is the LCD for 13 and −27 Transforming Fractions - ANSWERSDivide the least common denominator by the current denominator. Multiply both the numerator and the denominator by this integer. Let's now transform 1/3 and −2/7 each into their equivalent fractions that share a common denominator of 21 , which we found in the example above. First, convert 1/3 to an equivalent fraction with a denominator of 21 . Divide the LCD (the new denominator) by the current denominator. 21÷3=7 Multiply the numerator and denominators by 7 . (1×7)/(3×7)=721 Adding Fractions with the Same Denominator - ANSWERSAdd or subtract the numerators of all the fractions in the expression Keep the same denominator! (The temptation to add the two denominators is very strong—resist.) If necessary, reduce the answer. Adding Fractions with Different Denominators - ANSWERSFind the least common denominator (LCD). Use the LCD to find the equivalent fractions and rewrite the expression. Add or subtract the numerators of all the fractions in the expression. Keep the denominator the same—do not add them. If necessary, reduce the answer. Adding and Subtracting Mixed Number Fractions - ANSWERSChange the mixed numbers* to improper fractions*. Find the least common denominator (LCD) if the fractions have different denominators and convert to equivalent fractions with the LCD. Add or subtract the numerators of all the fractions in the expression. Keep the denominator the same. Change improper fractions to a mixed number (if needed). If necessary, reduce the fraction to lowest form. Subtract the following mixed numbers: 8 5/6 − 5 1/2 Step 1: Change the mixed number to an improper fraction. 8 5/6 = 53/6 and 5 1/2=11/2 Step 2: Find equivalent fractions with the least common multiple. Convert the fractions to equivalent fractions with the LCM. The least common multiple is 6 , therefore: 53/6 does not need to change Multiply the numerator and denominator of 11/2 by 3 53/6 − 11/2 = 53/6 − 33/6 Step 3: Subtract like fractions. Next, subtract the fractions. 53 / 6−336=206 Step 4: To complete the problem, convert any improper fractions to lowest terms. 20/6 = 3 2/6 Finally, reduce the fraction to its lowest form. 3 2/6 = 3 1/3 Multiplying Fractions - ANSWERSMultiply the numerators to obtain a new numerator. Multiply the denominators to obtain a new denominator. Write the answer in fraction form and reduce it to the lowest terms, if necessary. Change any improper fractions to mixed numbers. *Mixed Number Fractions:* Change any mixed numbers to improper fractions. Multiply the numerators to obtain a new numerator. Multiply the denominators to obtain a new denominator and write the answer in fraction form. Change the improper fraction back to a mixed number. Reduce the mixed number to the lowest terms, if necessary. Dividing Fractions - ANSWERSChange the division sign ( ÷ ) to a multiplication sign ( × ). Write the reciprocal of the second fraction. Multiply the numerators. Multiply the denominators. Write the answer in the form of a fraction. Reduce the fraction to the lowest terms, if necessary. *Mixed Number Fractions:* Change any mixed numbers to improper fractions. Change the division sign ( ÷ ) to a multiplication sign ( × ). Write the reciprocal of the second fraction. Multiply the numerators and denominators as usual. Change the improper fraction to a mixed number. Reduce the fraction to the lowest terms, if necessary. Coefficient - ANSWERSIn algebra, constants* often take the form of coefficients*. A coefficient is a number by which a variable is being multiplied. Coefficients are written in front of variables. So, in 16x , 16 is the coefficient and x is the variable. If a variable is without a number in front of it, the coefficient is 1 . Though it is not written, there is essentially an invisible 1 in front of any variable without a numerical coefficient. Steps for Combining Terms - ANSWERSIdentify Like Terms Move Terms Next to Each other Add or Subtract Distributive Property - ANSWERSDistribute the term outside the parentheses to each of the terms inside the parentheses a(b + c) = ab + ac Distribution of Negative Numbers - ANSWERSWhen in doubt, change all subtraction operations to the addition of negative numbers. Principle of Equality - ANSWERSIf you perform equivalent operations to both sides of an equation, the result will always be an equivalent equation. Steps for Solving an Equation With Complex Expressions - ANSWERSSubstitute any variable's known value for the variable itself Simplify expressions on either side of the equation following order of operations: Distribute Combine Like terms Add and subtract constants Complete any other process that serves to simplify the expression Move terms across the equation, using the Addition and Subtraction Principles of Equality: Move all constants to one side of the equation Get all terms with the variable to be solved on the opposite side of the equation Simplify the expressions on either side of the equation: Combine like terms on one side, if necessary Add and subtract constants on the other side, if necessary Isolate the lone variable on one side of the equation, using the Multiplication and Division Principles of Equality: The variable will be across from its value Check your answer: Plug in your solution to the original equation. Perform the arithmetic on both sides of the equation. If the two sides of the equation are equal, you have successfully solved the equation! Butterfly Method in Algebraic Equations - ANSWERSExample Solve the following algebraic equation: 23/21 x j = 25/13 . Write the algebraic equation in the form ax/b=c/d Remember that a/b(x)=ax/b since x can be converted into x/1 . Now draw "butterfly wings" around the opposite terms. Multiply the numbers in each of the butterfly wings: Getting and equation into Slope-Intercept Form - ANSWERSFirst, make sure the y [Show Less]
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What is 3/4 divided by 2/3? A) 9/8 B) 5/12 C) 5/7 D) 6/7 - ANSWERS9/8 A county park has hiking paths with lengths of 1.05, 3.6, 3.17, and 2.2 miles.... [Show More] What is the total length, in miles, of hiking paths in the park? A) 9.02 miles B) 10.02 miles C) 10.12 miles D) 11.2 miles - ANSWERS10.02 miles If there are 2 tablespoons in 1 fluid ounce, how many tablespoons does the following calculation yield? 4 fl oz - 1.5 tbsp 0.5 tbsp 1 tbsp 2.5 tbsp 6.5 tbsp - ANSWERS6.5 tbsp Solve for X: X - 5/4 = 2/3 A) 3/12 B) 7/12 C) 10/12 D) 23/12 - ANSWERS23/12 Solve for X: X+5/3=2/3 A) -3 B) -1 C) 1 D) 3 - ANSWERS-1 Given the inequality: 2y + 6 > 20 Which graph is the solution? A) {{ y < 3 }} B) {{ y > 6 }} C) {{ y > 7 }} D) {{ y < 7 }} - ANSWERS{{ y > 7 }} Which graph is the solution for y < 8? A) {{ unfilled circle on 8, arrow pointing left }} B) {{ filled circle on 8, arrow point left }} C) {{ unfilled circle on 8, arrow pointing right }} D) {{ filled circle on 8, arrow point right }} - ANSWERS{{ unfilled circle on 8, arrow pointing left }} Which graph is the solution for 4y - 6 > 18? A) {{ y > 4 }} B) {{ y > 6 }} C) {{ y < 4 }} D) {{ y < 6 }} - ANSWERS{{ y > 6 }} What is the correct line graph for y = 3x + 5? A) (0,5) to (2,11) B) (0,-5) to (2,-11) C) (0,3) to (2,5) D) (0,3) to (2,-7) - ANSWERS(0,5) to (2,11) What is the correct line graph for y = -2x + 9? A) (0,9) to (4.5,0) B) (0,9) to (3,0) C) (0,-9) to (5,-19) D) (0,-9) to (5,-24) - ANSWERS(0,9) to (4.5,0) A normally distributed data set has a mean of 25 and a standard deviation of 2. Which percentage of the data falls between 23 and 25? A) 34.0 B) 68.0 C) 95.0 D) 99.7 - ANSWERS34.0 A given data set is normally distributed with a mean of 200 and a standard deviation of 5. Which two values does 95% of the data fall between? A) 180-220 B) 185-225 C) 190-210 D) 195-235 - ANSWERS190-210 In a statistics class, 40 students are asked to write their age on a piece of paper and place the paper in a box. After rotating and shaking the box, 5 pieces of paper are drawn from the box at random. The data results are as follows: 36 22 21 20 19 What is the median for this data set? A) 17 B) 21 C) 24 D) 28 - ANSWERS21 A new video gaming site wants to know what the median age is of its adolescent population so they can focus on activities for these clients. A data analyst recorded the ages of 12 adolescents who used the site over a three-month period. The results are given below: Age ,Frequency 13 ,1 16 ,2 17 ,2 18 ,3 19 ,4 What is the median age of the adolescents? A) 17.0 B) 17.2 C) 18.0 D) 18.6 - ANSWERS18.0 The graph shows a company's profits, in thousands of dollars, for five different regions: {{ Y = Profits in Thousands of Dollars X = A B C D E A = 29 B = 34 C = 15 D = 40 E = 22 }} Based on this graph, what is the closest approximate total profit (in thousands) for all five regions? 100 140 170 200 - ANSWERS140 The bar chart below summarizes the final grade distribution for a statistics course: {{ Y = Count X = A B C D F A = 5 B = 9 C = 11 D = 8 F = 7 }} Which percentage of students earned a B in the statistics course? A) 9% B) 22.5% C) 27.5% D) 40% - ANSWERS22.5% Which statement is true regarding the distribution of the histogram below? {{ Positively skewed histogram }} A) The mean of the distribution is greater than its median. B) The median of the distribution is greater than its mean. C) The mean and the median of the distribution are equal. D) The relationship between the mean and the median cannot be determined from the histogram. - ANSWERSThe mean of the distribution is greater than its median. In one 12-hour shift, a nurse spends four hours at patient bedsides, two hours pulling medications, one hour on breaks, two hours documenting, and three hours doing other activities. An analyst would like to display the data by representing the 12-hour shift as one whole. Which display method should the analyst use to meet this goal? A) Box plot B) Stem plot C) Histogram D) Pie chart - ANSWERSPie chart For which type of website data would a histogram be most appropriate? A) Length of visit in minutes B) Location of visitor by country C) Frequently viewed pages D) Most popular method of arrival - ANSWERSLength of visit in minutes A company has 14 employees. Six employees work day shift, five employees work swing shift, and three employees work night shift. Which type of graph should be used to display how many employees work each shift? A) Stem plot B) Bar graph C) Box plot D) Histogram - ANSWERSBar graph The bar chart below displays the daily number of visits for the five most frequently viewed web pages of a retailer's website: {{ Y=Number of Visits per Day, going from 0 to 1400 in increments of 200 1st Bar=700 2nd Bar=900 3rd Bar=1100 4th Bar=1250 5th Bar=1300 }} Why is this chart an inaccurate representation of the data? A) The horizontal labels are missing. B) A histogram instead of a bar chart should be used for this type of data. C) A pie chart instead of a bar chart should be used for this type of data. D) The vertical axis should start at 600 instead of 0 based on this data. - ANSWERSThe horizontal labels are missing. Two employees, Smith and Jones, had first quarterly sales of $50,000 and $60,000, respectively. The graph below depicts this information: {{ Y=Thousands of Dollars, going from 40 to 100 in increments of 10 X= Smith Jones Smith = 50 Jones = 60 }} What is true about this graph's depiction of the data? A) The graph reflects the results perfectly. B) The graph misrepresents the data by starting the vertical axis at 40, making it seem that Jones had twice Smith's sales. C) The graph misrepresents the data by using different colors for the bars that show Smith's and Jones's sales. D) The graph misrepresents the data by including values on the vertical axis as high as 100 when neither Smith nor Jones had sales that high. - ANSWERSThe graph misrepresents the data by starting the vertical axis at 40, making it seem that Jones had twice Smith's sales. The chart below shows the population of Texas from 1900 through 2000 (in millions of people): {{ Y=Texas Population in millions, going from 0 to 25 in increments of 5 X=1900 1960 1970 1980 1990 2000 }} Why is this graph a misleading representation of this data? A) Rounding to the nearest million distorts the true values. B) The horizontal scale is uneven. C) The vertical scale is uneven. D) The x-axis and y-axis should be reversed. - ANSWERSThe horizontal scale is uneven. A study was conducted to see if blood type influenced height. Which type of classification is this? A) Categorical to categorical B) Categorical to quantitative C) Quantitative to quantitative D) Quantitative to categorical - ANSWERSCategorical to quantitative A study was conducted on the possible relationship between smoking status and whether or not alcohol is consumed. Which type of classification is this? A) Categorical to categorical B) Quantitative to categorical C) Categorical to quantitative D) Quantitative to quantitative - ANSWERSCategorical to categorical A study is conducted on the possible relationship between gender and income of the employees at a marketing company. Which numerical measure is appropriate for this study? [Show Less]
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