Math - Others Questions

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Abe b c d Barb Student Cal N answer 2 1 3400 S 2 Perform the indicated operations to the correct number of significant figures using the rules for significant figure a 37 60 x 1 23 46 2 37 60 0 0130 13000 Questions 3 6 Three students named Abe Barb and Cal make measurements in m of the length of a table Find the means 1 using the data given L3 L 1 4717 1 4753 1 4719 L 1 4711 1 4759 b 0 75 6 7 8 975 1 4723 1 4722 1 4756 1 4727 LA 1 4715 1 4749 1 4705 c 0 0000089 x 6500 00 in scientific notation XLO L On l a 110 4916103 00040 0 0000 11 47540 00043 0 0002 1 4719 0 0004 0005 Only one significant figure is kept in the standard error a and this determines the number of significant figures in the mean The actual length of the table is 1 4715 m 3 Find the percentage differences in length measured by three students error 4 State how one can measure the accuracy of a measurement Apply your idea to the measurements of three students above and state which of the students has the most accurate measurement Why is that your conclusion 5 State the characteristics of data that indicate a systematic error Do any of the three students have data that suggest the possibility of a systematic error If so state which students it is and state how the data indicate your conclusion 6 Which student has the best measurement considering both accuracy and precision State clearly What the characteristics are of the student s data on which your answer is based

Which of the following are possible examples of sampling distributions Select all that apply average male height based on samples of size 30 average SAT score of a sample of high school students all mean trout lengths in a sampled lake mean trout lengths based on samples of size 5 heights of college students at a sampled university

A simple random sample of n measurements from a population is a subset of the population selected in a manner such that which the following is are true Select all that apply Each subset of the population has an equal chance of being included in the sample The simplest method of selection is used to create a representative sample Every sample of size n from the population has an equal chance of being selected Every sample of size n from the population has a proportionally weighted chance of being selected Every member of the population has an equal chance of being included in the sample

What is a population parameter A population parameter is a numerical Give three examples Select all that apply 00 S Q XIX b descriptive meas

Webster s Widgets collects random samples of 100 widgets from their widget factory several times per shift and records the mean weight of the sample in grams The means of 400 samples are summarized in the following frequency table Range 6 87 2 Yes No 7 2 7 6 7 6 8 0 8 0 8 4 8 4 8 8 8 8 9 2 9 2 9 6 Frequency 21 73 103 108 76 15 4 The five number summary of the 400 sample means was found to be min 6 816 Q 7 617 median 8 0075 Q3 8 385 max 9 569 The three smallest values were 6 816 6 825 and 6 833 The three largest values were 9 370 9 514 and 9 569 The mean of the 400 sample means was 7 9877 with a standard deviation of 0 5360 a Sketch a histogram based on the frequency table Does it appear to be roughly symmetric and mound shaped b Compute the interquartile range Determine if there are any outliers in the data Recall that an outlier is a value above Q3 by more than 1 5 times the interquartile range or below Q by more than 1 5 times the interquartile range The rule described above identifies one outlier s c Compute the Pearson index Round your answer to four decimal places Does this indicate that the data is skewed

Assume that x has a normal distribution with the specified mean and standard deviation Find the indicated probability Round your answer to four decimal places USE SALT 28 0 3 8 P x 30 x You may have computed the probability between two values Consider which area of the distribution is appropriate

A relay microchip in a telecommunications satellite has a life expectancy that follows a normal distribution with a mean of 92 months and a standard deviation of 3 1 months When this computer relay microchip malfunctions the entire satellite is useless A large London insurance company is going to insure the satellite for 50 million dollars Assume that the only part of the satellite in question is the microchip All other components will work indefinitely LUSE SALT a For how many months should the satellite be insured to be 98 confident that it will last beyond the insurance date Round your answer to the nearest tenth of a month x months b If the satellite is insured for 84 months what is the probability that it will malfunction before the insurance coverage ends Round your answer to four decimal places c If the satellite is insured for 84 months what is the expected loss to the insurance company in dollars Round your answer to the nearest dollar x d If the insurance company charges 3 million for 84 months of insurance how much profit does the company expect to make in dollars Round your answer to the nearest dollar

If f x x 4x and h 0 find the following and simplify a f x h b f x h f x h

Find the z value such that 39 of the standard normal curve lies between z and z Round your answer to two decimal places USE SALT

f x 2x g x x x 3 Find f g 1 5 11 6

Use the given nth term formula to compute the firs n 4n 3 2 a1 22 33 34 25 an

Consider the following probability P Z 2 14 LUSE SALT Let z be a random variable with a standard normal distribution Find the indicated probability Round your answer to four places P Z 2 14

Compose f g x You must show your work for full crec f x 2x x 1 g x x 1 Find f g x

f x 10 5 10 5 5 10 g x 5 10

The second dose of the COVID 19 vaccine is more likely to produce side effects than the first The time between receiving the shot and the onset of side effects is called the lag time Suppose according to one study the lag times among the subjects that reported side effects from a second dose of the vaccine were normally distributed with a mean of 13 hours with a standard deviation of 4 hours Use the empirical rule to answer the following a What is the probability that a person selected at random from among those that experienced side effects from their second dose of the vaccine had a lag time of less than 9 hours b What is the probability that a person selected at random from among those that experienced side effects from their second dose of the vaccine had a lag time between 13 and 21 hours c Estimate a range of lag times in hours centered about the mean that should include about 95 of all lag times for those experiencing side effects between and hours

with a mean of 7 6 ounces and standard deviation of 0 4 ounce Examine the figure below and answer the following questions Area Under a Normal Curve 0 15 2 35 13 5 H 30 20 0 34 H 68 95 99 7 34 13 5 2 35 0 15 H o 20 H 30 a Estimate the probability that the machine will overflow an 8 ounce cup b Estimate the probability that the machine will not overflow an 8 ounce cup c The machine has just been loaded with 800 cups How many of these cups do you expect will overflow when served

distributed with a mean of 82 minutes and a standard deviation of a 19 minutes Use the figure below to answer the following questions Area Under a Normal Curve 0 15 2 35 13 5 H 30 H 20 H 0 34 f 68 95 99 7 34 H o 13 5 2 35 0 15 H 20 H 30 a Estimate the probability that a randomly selected student will complete their final exam in less than 63 minutes b The final exam is scheduled to allow 2 hours Estimate the probability that a randomly selected student will need more than 2 hours to complete their exam c In a section with 160 students how many students do you expect will need more than 2 hours to complete their exams

ights of female college stu normall istributed with ssuming inches answer the following questions Hint Use the figure below with mean and standard deviation o Area Under a Normal Curve 0 15 2 35 13 5 H 30 H 20 0 34 l 68 95 99 7 34 13 5 H o H 20 30 a What percentage of female college students are taller than 67 inches 2 35 0 15 b What percentage of female college students are shorter than 67 inches c What percentage of female college students are between 64 6 inches and 69 4 inches d What percentage of female college students are between 62 2 and 71 8 inches and standard deviation

Consider the following normal curve 17 Look at the normal curve above and find 19 Look at the normal curve above and find o Look at the normal curve above and find o 21 23

a 6 8 10 12 14 16 18 5 6 7 b 2 3 4 Which has the larger standard deviation figure a figure b What is the mean of the curve in figure a What is the mean of the curve in figure b 8

Find the area of the shaded region in square units y 9 8 7 6 10 5 4 3 2 1 square units 1 f x 8 2x 2 3 4 5

c In light of their ability to buy and sell in world markets at the stated prices on the same graph as their PPC show all of the combinations of the two goods it would be possible for them to consume This is also known as their consumption possibilities curve or CPC Instructions Use the tool provided to draw all combinations of coffee beans and nuts it would be possible for them to consume Plot only the endpoints of this curve 56 52 48 Coffee Beans pounds day ANTENNA BA 44 36 32 28 24 20 16 4 Krisha Tom s PPC PPC 7 38 34 Tools CPC

pose that mean retail price per gallon of regular grade gasoline is 3 49 with a standard deviation of 0 10 and that the retail price per gallon has a bell ed distribution E Please use empirical rule approximations for this problem hat percentage of regular grade gasoline sells for between 3 29 and 3 69 per gallon to 1 decimal What percentage of regular grade gasoline sells for between 3 29 and 3 59 per gallon to 1 decimal What per regular and

3 Jos borrows 1400 to buy a racing bicycle He repays the loan 2 years later in the amount of 1700 What annual rate of simple interest was Jos charged

2 Determine the final balance of each investment a 275 is invested at 6 2 annual simple interest for 10 years b

8 Calculate the mean median mode and range of the set 1 3 7 29 12 15 5 4KC Mean Mode 9 Provide an example of the following Explain your reasoning 2C Depreciating asset Median Range Appreciating asset

1 Determine the simple interest earned on each investmen a 450 is deposited for 4 years and earns 6 5 per year simple interest b 750 year s

tive 597 514 1563 648 1708 1727 1776 793 1810 2005 2015 2025 2053 2173 2204 2244 2355 2514 2543 2890 B Department Store 454 471 476 570 576 595 598 618 633 661 706 714 746 765 782 826 836 854 943 1009 Part a Mean to 2 decimals Part b Standard Deviation to 2 decimals Part c Maximum Minimum Range to 1 decimal Part d First Quartile to 2 decimals Third Quartile to 2 decimals Interquartile Range to 2 decimals Automotive Department Store Formula N A N A N A N A N A N A N A N A N A N A N A N A N A N A N A N A

Find the equation of the parabola having the following properties vertical stretch by factor of 6 opening up horizontal translation 6 units to the right vertical translation 3 units up i ii iii iv

A department of transportation s study on driving speed and miles per gallon for midsize automobiles resulted in the following data Speed Miles per Hour 60 25 50 56 Miles per Gallon 29 25 25 22 31 32 Compute the sample correlation coefficient to 2 decimals and enter negative value as negative number 30 51 40 56 What can you conclude based on your computation of the sample correlation coefficient Select your answer 29 24 20 35 Select the correct interpretation for the sample correlation coefficient i For driving speeds between 24 and 60 miles per hour higher speeds are associated with higher miles per gallon ii For driving speeds between 24 and 60 miles per hour higher speeds are associated with lower miles per gallon iii For driving speeds between 24 and 60 miles per hour lower speeds are associated with lower miles per gallon iv There is no relationship between driving speed and miles per gallon 26 24

The following times were recorded by the quarter mile and mile runners of a university track team times are in minutes Quarter milers Standard deviation to 4 decimals Coefficient of variation to 1 decimal Quarter Mile Times Milers Mile Times 0 92 0 99 4 35 4 59 4 70 4 51 After viewing this sample of running times one of the coaches commented that the quarter milers turned in the more consistent times Use the standard deviation and the coefficient of variation to summarize the variability in the data 4 52 1 06 0 96 1 00 Standard deviation to 4 decimals Coefficient of variation to 1 decimal Does the use of the coefficient of variation indicate that the coach s statement should be qualified i Yes the coefficient shows that as a percentage of the mean the quarter milers times show less variability ii No the coefficient shows that as a percentage of the mean the quarter milers times show more variability

b X Y x During a figure skating routine Jackie and Peter skate apart with an angle of 15 between them Jackie skates for 5 meters and Peter skates for 7 meters a Draw a diagram of this situation and clearly label all measurements How far apart are the skaters to the nearest meter at that point C 2 marks C 1 mark A 2 marks

D Consider a sample with data values of 26 24 21 18 30 35 29 and 24 Compute the range interquartile range variance and standard deviation Round to 2 decimals if necessary Range Interquartile range Variance Standard deviation 0000

4 3 A Find the value of the indicated variable 5 47 Find SB B 4 Find b Find LC 12 Page 6 of 8 rounded to one decimal place A 2 marks rounded to the nearest degree A 2 marks K 2 marks

SHORT ANSWER FULL SOLUTION 39 MARKS show all work and proper form for full marks solutions as demonstrated in class no marks given for guess and check methods 4 x 2 10 on the same grid 4 x 2 10 2 1 a Graph and label the relations y x and y use a scale of 1 unit Draw and label the Axis of Symmetry for y Complete the information requested below y x 2 Axis of Symmetry Vertex Y intercept y 4 x 2 10 Direction of Opening Y intercept Optimal Value Solve for x 2x 3x 5 0 A 4 marks K mark each K 2

Use the following information Sales of organic food have increased rapidly in recent years The demand for organic food seems to be unquenchable says Laura Batcha of the Organic Trade Association Suppose the rate of increase in organic food sales from 2006 to 2016 in a certain country can be modeled by 6 43 1 26x 6 x 16 0 otherwise f x where x represents the number of years since 2000 and f x represents the rate of change in organic food sales in billions of dollars What were the total sales in billions of dollars of organic food in this country from 2007 to 2011 billion

Consider the following A 2016 report from the National Academies of Sciences Engineering and Medicine found that genetically engineered crops such as corn are safe to eat and do not harm the environment Suppose the rate of increase in the number of varieties of a herbicide tolerant genetically engineered crop from 2000 to 2016 can be modeled by the rate function f x 1 58 0 04x 0 0 x 16 otherwise where x represents the number of years since 2000 and f x represents the rate of increase in the number of varieties of the genetically engineered crop per year Use the model to determine the following Calculate the area under f x on the interval 10 x 16 Round your answer to the nearest whole number 13 Interpret the result The area under f x on the interval 10 x 16 describes the total increase in the rate of change in the number of varieties of the genetically engineered crop from 2010 to 2016 The area under f x on the interval 10 x 16 describes the rate of change in the number of varieties of the genetically engineered crop available in 2010 The area under f x on the interval 10 x 16 describes the number of varieties of the genetically engineered crop available in 2010 The area under f x on the interval 10 x 16 describes the total increase in the number of varieties of the genetically

Find the area of the shaded region in square units y 13 12 11 11 60 10 9 8 7 16543 3 2 1 12 3 I square units fix 19 8 1 63 x L 4 5 6 7 8 9 10 11 X

Find the area of the shaded region in square units y 11 10 96 8 7 6 5 4 3 2 1 1 square units fix 10 2x 2 3 4 5 6 e

Consider the following scenario The rate of increase in the number of people who have committed drug crimes in a particular country who used crystal methamphetamine commonly called Ice in this country from 2006 to 2016 can be modeled by the rate function 355 70 1x 0 f x 6 x 16 otherwise where x represents the number of years since 2000 and f x represents the rate of increase in the number of people who have committed drug crimes who used Ice per year Compute the area under f x on the interval 11 x 15 Round your answer to the nearest whole number Interpret the result The area under f x on the interval 11 x 15 describes the total increase in the number of people who have committed drug crimes who used Ice from 2011 to 2015 The area under f x on the interval 11 x 15 describes the total increase in the rate of change in the number of people who have committed drug crimes who used Ice from 2011 to 2015 The area under f x on the interval 11 x 15 describes the number of people who have committed drug crimes who used Ice in 2011 The area under f x on the interval 11 x 15 describes the rate of change in the number of people who have committed 2011

Determine the area of the trapezoid in square units with the given dimensions b 2 4 h 8 2 h 4 8 square units

Determine the area in square units of the trapezoid shown in the figure Consider lengths to be standard unit 0 35 square units 4 1 0 6

Find the area of the shaded region in square units y 8 7 6 5 4 3 2 1 fix 1 3 x 1 square units 2 3 4 5 6 X

Determine the area in square units of the trapezoid shown in the figure Consider lengths to be standard units 17 12 13

Melvin made the three drawings below Li E Which drawings contain EF I II and III o I only o II and III o I and II

4 Graph y 14 2xl and y 4 Then solve using the graphs a 14 2x1 0 b 14 2x1 4 10 19 17 6 9 y axis E JA