Math Questions

Watching TV In 2012 the General Social Survey asked a sample of 1314 people how much time they spent watching TV each day The mean number of hours was 2 85 with a standard deviation of 2 62 A sociologist claims that people watch a mean of 3 hours of TV per day Do the data provide sufficient evidence to conclude that the mean hours of TV watched per day is less than the claim Use the a 0 05 level of significance and the P value method with the TI 84 Plus calculator Part 0 4 Part 1 of 4 a State the appropriate null and alternate hypotheses Ho H This hypothesis test is a Choose one test O O D O O O H O O

1 The table shows the number of vis the Daisy Festival on certain days since May 1 Days Since May 1 Number of Visitors 0 215 3 520 6 725 9 865 12 955 15 1025 18 970 21 874 710 490 24 27 30 207 Which type of function would best model the data A linear B quadratic C exponential D piecewise function

rag the tiles to the correct boxes to complete the pairs 53 75 13s 3 3 ewrite the rational expression 1 71 13 1 3 T S in the form 1 1 and then match qx x and b x to the correct expressions g 1 b I 1 4x 1 H 3 13 712 13 3 0

2 Jada is riding on a Ferris wheel Her height in feet is modeled by the function 2am 10 h m 100 cos ride 110 where m is the number of minutes since she got on the a How many minutes does it take the Ferris wheel to make one full revolution Explain how you know b Sketch two cycles of a graph of h showing all of your thinking work 240 200 160 120 80 40

The number of views on an interesting video after it s uploaded is represented by the following table Which model for V t the number of views t days after its uploaded best fits the data Time days Views 0 10 4 452 8 889 12 1330 16 1770 20 2211 O V t 10 440t O O V t 10 x 11 3 t O V t 10 110t V t 10 x 45 2 t

When Xochitl runs the 400 meter dash her finishing times are normally distributed with a mean of 84 seconds and a standard deviation of 2 5 seconds Using the empirical rule determine the interval of times that represents the middle 68 of her finishing times in the 400 meter race

Consider the following cylinder and cone A 10 10 4 4 Marcel tried to use Cavalieri s principle to show that the two figures have the same volume The base areas are the same Therefore corresponding cross sections have the same area So the volur must be the same What is the first mistake Marcel made

Consider this absolute value function f x 1 8 How can function fbe written as a piecewise function O A O B O C O D f x f x f x f x 8 8 8 8 I 8 8 2 8 I 8 I 8 8 8 8 8 8 8

6 page 193 Find the current balance of the following account Balance from Bank Statement 32 489 50 Checks Outstanding 3589 70 263 15 Deposits Not Yet Recorded 18 702 15 7269 78 Balance

A mother earned 13750 00 from royalties on her cookbook She set aside 20 of this for a down payment on a new home The balance will be used for her son s future education She invests a portion of the money in a bank certificate of deposit CD account that earns 4 and the remainder in a savings bond that earns 7 If the total interest earned after one year is 660 00 how much money was invested at each rate How much money was invested in the CD account Round to the nearest cent

8 A radioactive isotope is decaying at a rate of 18 every hour Currently there are 100 grams of the substance Part B How much will be left one day from now Round your answer to the nearest hundredth

A pendulum is swinging next to a wall The distance from the bob of the swinging pendulum to the wall varies in a periodic way that can be modeled by a trigonometric function The function has period 0 8 seconds amplitude 6 cm and midline H 15 cm At time t 0 5 seconds the bob is at its midline moving towards the wall Find the formula of the trigonometric function that models the distance H from the pendulum s bob to the wall after t seconds Define the function using radians H t

A basic cellular package costs 40 month for 60 minutes of calling with an additional charge of 0 20 minute beyond that time The cost function C z for using z minutes would be If you used 60 minutes or less i e if if a 60 then C z 40 the base charge If you used more than 60 minutes i e z 60 minutes more than the plan came with you would pay an additional 0 20 for each of those z 60 minutes Your total bill would be C z 40 0 20 z 60 If you want to keep your bill at 50 or lower for the month what is the maximum number of calling minutes you can use

3 The graphs shows the amount of a chemical in a water sample at different times after it was first measured Select all statements that are true 2 400 50 2 000 1 600 1 200 800 400 chemical mg M 1 2 3 I time hours A The amount of the chemical the water sample is decreasing exponentially 4 5 B The amount of the chemical in the water sample is not decreasing exponentially C It is not possible to tell for certain whether or not the amount of the chemical is decreasing exponentially D When it was first measured there were 2 000 mg of the chemical in the water sample After 4 hours there were 100 mg of the chemical in the water

Amazon claims that if you are a prime member 85 of your packages will arrive within two business days You have decided that you want to know if this claim is true You take a simple random sample of 25 students at your school and 19 of the students claim that their packages arrived within two business days of ordering

Write the negation of the following statement Pigs can fly or wishes are not wings Choose the correct answer below O A Pigs can not fly and wishes are wings OB If pigs can not fly then wishes are wings OC Pigs can not fly or wishes are wings D Pigs can fly or wishes are wings

Stefan graphs quadrilateral BCDE on a coordinate plane The diagonals of BCDE intersect at point T Which methods could Stefan use to prove that BCDE is a rectangle Select all that apply Show that BT and DT are the same length Then show that CT and ET are the same length Show that BC and ED have the same slope and BE and CD have the same slope Then show that BC and BE have opposite reciprocal slopes Show that BC and ED are the same length BE and CD are the same length and BD and CE are the same length Show that BC and ED are the same length Then show that BC and ED have the same slope

What is the best way to combine these sentences It was a very close finish The crowd was delighted The bay mare won the race A The crowd was delighted because the baymare won the race and it was a very close finish B To the delight of the crowd the bay mare won the race in a very close finish C To the delight of the crowd and also in a very close finish the bay mare won the race

You are standing at the edge of a cliff You look down with an angle of depression of 20 degrees and see a a dog at the bottom that is 130 feet away from where you re standing What is the height of the cliff Round your answer to the nearest tenth and round only once

Question 2 of 10 The graph of F x shown below resembles the graph of G x x but it has been stretched somewhat and shifted Which of the following could be the equation of F x 5 5 49 OA F x 2x2 3 OB F x 0 2x 3 O C F x x 3 OD F x x 3 G X x 5 F X

Which of the following chi square tests is appropriate for analysis of one categorical variable from a single popula O chi square test of homogeneity O chi square test for independence chi square goodness of fit test

Question 4 of 15 To solve this system of equations Ayana isolated y in the first equation and then substituted for y in the second equation What was the result 2y 6x x y 4 A x 3x 4 OB x 6x 4 OC x 3x 4 O D x 6x 4

The points plotted below are on the graph of a polynomial Which of the following x values is the best approximation of a root of the polynomial Check all that apply A x 4 3 B X 6 C x 1 1 D X 1 7 E X 2 4 OF x 1

What is the degree of freedom for the critical t value of a population that has 450 sample differences 224 449 225 451

Question Mary wanted to track the growth of various peppers in her garden so she decided to label them Her garden had RED peppers labeled 1 2 3 4 5 6 GREEN peppers labeled 1 2 3 4 5 and YELLOW peppers labeled 1 2 If a single pepper is picked at random what is the probability that the pepper is YELLOW AND has an ODD number Provide the final answer as a fraction quide your answer below

How would you interpret a statistical significance level of 0 48 This means that the probability for the null hypothesis to be false is 0 48 O This means that the probability for the null hypothesis to be true is 0 48 O This means that the probability for the alternate hypothesis to be true is 1 0 48 This means that the probability for the alternate hypothesis to be false is 1 0 48

Interpret a p value of 0 005 This means that there is 0 005 probability for the null to be false O This means that the probability for observing the test statistic is 0 005 if the null is true O This means that there is 0 005 probability for observing the test statistic if the null is false This means that there is a 0 005 probability of a type Il error

Consider these functions f x 3x3 2 g x Which statements if any are true about these functions 1 The function g x x for all real x II The function g x x for all real x III Functions fand g are inverse functions 3 OA I only OB II only OC I II and III

Which one of these statements is NOT an example of a straw man null hypotheses O Families with cars have the same access to healthcare providers as families without cars O Cats and dogs differ in their interest in human relationships O Students who do their homework regularly get better grades or the same grades as students who do not O There is no difference in the number of doctor visits per year for people who wash their hands more than three times a c compared to those who wash their hands three times or less a day

The offices of president vice president secretary and treasurer for an environmental club will be filled from a pool of 18 candidates Eight of the candidates are members of the debate team a What is the probability that all of the offices are filled by members of the debate team b What is the probability that none of the offices are filled by members of the debate team a P all offices filled by debate team members Round to three decimal places as needed b P no offices filled by debate team members Round to three decimal places as needed

3 Type the correct answer in each box Use numerals instead of words A company manufactures 2 000 units of its flagship product in a day The quality control department takes a random sample of 40 units to test for quality The product is put through a wear and tear test to determine the number of days it can last If the product has a lifespan of less than 26 days it is considered defective The table gives the sample data that a quality control manager collected 39 31 38 40 29 32 33 39 35 32 32 27 30 31 27 30 29 34 36 25 30 32 38 35 40 29 32 31 26 26 32 26 30 40 32 39 37 25 29 34 The point estimate of the population mean is and the point estimate of the proportion of defective units is Next 0

Omar paid 13 29 for a 7 03 kg bag of dog food A few weeks later he paid 13 58 for a 7 26 kg bag at a different store Find the unit price for each bag Then state which bag is the better buy based on the unit price Round your answers to the nearest cent Unit price for the 7 03 kg bag Unit price for the 7 26 kg bag The better buy sper kg sper kg The 7 03 kg bag The 7 26 kg bag Neither They have the same unit price

Find the surface area of the composite figure 4 cm 3 cm 4 cm 13 cm SA 12 cm 2 cm 5 cm 3 cm Enter

Select one answer 10 points In a fictional study suppose that a psychologist is studying the effect of daily meditation on resting heart rate The psychologist believes the patients who not meditate have a higher resting heart rate For a random sample of 45 pairs of identical twins the psychologist randomly assigns one twin to one of two treatments One twin in each pair meditates daily for one week while the other twin does not meditate At the end of the week the psychologist measures the resting heart rate of each twin Assume the mean resting heart rate is 80 heart beats per minute The psychologist conducts a T test for the mean of the differences in resting heart rate of patients who do not meditate minus resting heart rate of patients who do meditate Which of the following is the correct null and alternative hypothesis for the psychologist s study A OH u 80 H 80 B OH 0 H 0 C OH u 0 H 0

Unit 5 Lesson 1 Cumulative Practice 1 Which expression equals 27 A B 2 2 2 2 2 2 2 C 2 7 2 2 2 2 2 2 2 D 2 7 2 Evaluate the expression 3 5 when x is 2 3 The graph shows the yearly balance in dollars in an investment account amount in dollars 5 000 4 000 3 000 2 000 1 000 OT 2 0 4 6 8 10 12 14 number of years a What is the initial balance in the account b is the account growing by the same number of dollars each year Explain how you know c A second investment account starts with 2 000 and grows by 150 each year Sketch the values of this account on the graph d How does the growth of balances in the two account balances compare

Isaiah had 6 inches of snow on his lawn It then began to snow at a rate of 2 inches per hour Assume no snow melted Answer the questions below regarding the relationship between the number of hours since snow began falling and the total amount of snow on Isaiah s lawn

During a 5 day period a florist served a different number of customers at a flower shop each day The mean number of daily customers served during this period was 17 In the following month during another 5 day period the florist served 16 customers per day for four of the days but served 25 customers on the fifth day What is the difference between the mean number of customers the florist served during each of the two five day periods Adapted from Khan Academy 00 O 0 8 O 1 0

Jack bought a car for 17 500 The car loses 750 in value each year Which equation represents the situation Oan 18250n 750 an 750n 18250 an 18250n 750 an 750n 18250

4 Jada rewrites 5 3 as 15x Do you agree with expressions Explain your reasoning 5 Investment account 1 starts with a balance of 200 and doubles every year Investment account 2 starts with 1 000 and increases by 100 each year a How long does it take for each account to double b How long does it take for each account to double again c How does the growth in these two accounts compare Explain your reasor 6 A study of 100 recent high school graduates investigates a link between their childhood reading habits and achievement in high school Participants are asked if they read books every night with another person wher were ages 2 to 5 as well as their grade average for all of their high school class The results are represented in the table A average B average C average D average read books nightly did not read books nightly 16 21 12 3 a What does the 21 in the table represent b What does the 10 in the table represent 10 14 16 8

24 16 8 0 0 A No 1 2 3 Does the graph represent a direct proportion B Yes the constant of proportionality is 16 C Yes the constant of proportionality is 8 D Yes the constant of proportionality is 4

Tal them Jeremy s drone is closer to him than to Leslie and Leslie s drone is closer to her than to Jeremy Jeremy s drone is 30 meters above the ground and he is located 50 meters to the left from the point directly below the drone The angle of elevation from Leslie s location on the ground to her drone is 55 and the distance between her location on the ground and her drone is 70 meters 1 2 3 Create a diagram of all the given information including calculated measurements make sure to add as you complete parts 2 4 Whose drone is higher show your work and make sure to update your drawing with your calculations What is the difference between the heights of the drones show your work and make sure to update your drawing with your calculations 4 The angle of elevation from the lower drone to the higher drone is 25 Use this information to calculate the distance between Jeremy s and Leslie s locations on the ground show your work and make sure to update your drawing with your calculations 5 Jeremy flies his drone vertically so that it is at the same height as Leslie s drone Draw a new diagram of the drones Fill in any information you know 6 Explain why the angle of elevation from Jeremy s location on the ground to his drone is different from the angle of elevation between Leslie s location on the ground and her drone given that both drones

Is x 0 a valid potential solution to the equation log x 2 log x 5 1 You don t need to solve this equation just determine if x 0 is a valid solution It can t be determined from the information given Yes since log 2 and log 5 both exist as valid values for the logarithm No because the logarithm of a negative value is undefined No because log 0 is undefined

Stories in the World s Tallest Buildings The number of stories in each of a sample of the world s 24 tallest buildings follows Construct a grouped frequency distribution and a cumulative frequency distribution with 7 classes 88 70 88 69 85 78 88 55 65 70 77 80 Send data to Excel Part 0 5 Part 1 of 5 75 64 56 72 The class width is What is the class width for a frequency distribution with 7 classes 75 79 55 60 71 60 80 55 X C C E 0 E

The frequency table below summarizes a list of the number of words randomly selected students spelled correctly during a spelling bee Find the mean vide your answer below Value 10 12 13 14 15 16 17 Frequency 7 2 1 316 3 1

the Democratic candidate Let X be the number of people who prefer the candidate when 31 people are surveyed at random pre a What is the distribution of X X Please show the following answers to 4 decimal places b What is the probability that exactly 16 voters who prefer the Democratic candidate in the survey c What is the probability that at most 16 voters who prefer the Democratic candidate in the survey d What is the probability that less than 16 voters who prefer the Democratic candidate in the survey e What is the probability that between 13 and 18 including 13 and 18 voters who prefer the Democratic candidate in the survey

lan wants to figure out if there is a relationship between how much a piece of furniture weighs and how much it costs He samples some items and comes up with the following scatterplot Cost dollars 800 600 400 200 10 20 30 40 50 60 70 80 90 Weight kg Here s lan s description of the scatterplot There is a moderately strong positive linear association between how much a piece of furniture weighs and how much it costs There don t seem to be any obvious outliers What if anything is missing from this description Choose 1 answer Direction of the Points Possible Outliers

points plotted below are on the graph of a polynomial In what range of x values must the polynomial have a root Check all that apply 5 A 2 5 to 1 5 B 2 5 to 3 5 C 3 5 to 4 5 D 1 5 to 2 5 E 5 5 to 6 5 F 1 5 to 0 5

When considering different sampling methods cluster sampling includes the steps list the members of the population use simple random sampling to select a starting point in the population let k number of individuals in the population number of individuals needed in the sample choose every kth individual in the list starting with the one that was randomly selected divide the population into groups use simple random sampling to identify a proportionate number of individuals form each group O Identify individuals of the poulation that are easily accessible obtain data from these individuals use simple random sampling to select a set of groups every individual in the chosen groups is included in the sample

5 50 Traffic flow at 1st Ave and High St is twice the traffic flow at 2nd Ave and Central Compare the graph of the traffic flow at 1st Ave and High St to the graph of the traffic flow at 2nd Ave and Central over time O The period of the graph of the traffic flow at 1st Ave and High St is four times as long as the period of the graph of the traffic flow at 2nd Ave and Central O The period of the graph of the traffic flow at 1st Ave and High St is twice as long as the period of the graph of the traffic flow at 2nd Ave and Central O The period of the graph of the traffic flow at 1st Ave and High St is equally as long as the period of the graph of the traffic flow at 2nd Ave and Central The period of the graph of the traffic flow at 1st Ave and High St is half as long as the period of the graph of the traffic flow at 2nd Ave and Central

The names of 3 boys and 5 girls are written on cards The cards are placed in a bowl Two cards are drawn one at a time without replacement What is the probability that the first card is a girl s name and the second card is a boy s name O A 1 56 OB 5 15 O C 15 56 OD 1 15