Questions

Wendy took a trip from one city to another a distance of 300 mi She traveled part of the way by bus which arrived at the train station just in time for Wendy to complete her journey by train The bus h How long did Wendy spend on the train averaged 30 mi h and the train averaged 75 mi h The entire trip took 51 h

A man is walking away from a lamppost with a light source h 4 m above the ground The man is m 2 m tall How long is the man s shadow when he is d 15 m from the lamppost Hint U similar triangles m

In 8 11 Use Pythagorean s Theorem to find the value of the variable Answers should be in simplest radical form drawings are not to scale 8 3 2 in 7 5 in X 9 10 cm 14 cm X

n 16 19 Find the value of each variable Answers should be in simplest radical form 5 17 45 X 459 14 X 45 24 45

n 6 7 Rationalize the denominator answer in simplest radical form 3 5 7 6 14

A rectangular garden is 25 ft wide If its area is 1125 ft2 what is the length of the garden ft 25 ft x ft

12 List the sides for the triangle in order from shortest to longest drawing is not to scale D 56 The lengths for the sides of a frin 13 List the angles for the triangle in order from smallest to greatest drawing is not to scale 5 9 in 8 2 in 5 2 in B

4 5 2 5 9 5 5 18 8

n 1 5 Completely simplify each radical expression 500 2 6 75 GEOMETRY Unit 7 Te

Determine the following indefinite integral ex 324 e x dx x In 18 et S 324 2x dx 0

4 Barbara is standing near a flagpole and wants to find the height of the flagpole She realizes she can use similar triangles to solve the problem Barbara is 6 feet tall and at the time of the measurement her shadow was 10 feet long At the same time the flagpole casts a shadow 25 feet long Fill in the blanks to find the flagpole s height A T13 14 Agile Assessment h b6 ft ft ft h 6 feet 10 feet

According to the Fundamental Theorem of Algebra how many roots exist for the polynomial function 9x 7 4x 1 3x 4 0 1 root 9 roots 3 roots 4 roots

How many x intercepts appear on the graph of this polynomial function f x x x x x O4x intercepts 1 x intercept 2x intercepts 3x intercepts

Sxsin 2xdx 54 x 2 ex 4 dx

25 Represent Real World Situations The aspect ratio of an image on a screen is the ratio of image width to image height An HDTV screen shows images with an aspect ratio of 16 9 If the area of an HDTV screen is 864 in 2 what are the dimensions of the screen 26 Explain the Error Russell wants to calculate the amount of time it takes for a load of dirt to fall from a crane s clamshell bucket at a height of 16 feet to the bottom of a hole that is 32 feet deep He sets up the following equation and tries to solve it 16 161 32 1 16 16 1 1 1 1 t i Does Russell s answer make sense If not find and correct Russell s error

1 11 n 4n 21 0 A 2 12 C 12 2 B 3 7 D 6 4 12 12 x 8x 9 0 A 7 3 C 4 6 B 4 6 D 9 1

20 1 point Suppose a random sample of 84 men has a mean foot length of 26 9 cm with a standard deviation of 2 1 cm What is an 95 confidence interval for this data 21 52 to 32 28 24 905 to 28 895 22 784 to 31 106 24 8 to 29

14 1 point Which data is qualitative Height Employment status Income Age Previous

9 1 point According to the box and whisker plot shown what is the median value of items sold each month Items Sold Each Month 30 00 30 41 35 40 45 50 55 60 65

Solve See Example 4 Objective 2 Paint costing 19 per gallon is to be mixed with 10 gallons of paint thinner costing 4 per gallon to make a paint that can be sold for 14 per gallon Refer to the table and compute how much be produced X gal Paint Thinner 19 4 x gal n 10 gal 19x 4 10 101

Part 5 of 6 0 83 oints eBook Print References Intro to Graphing Cancer and smoking Looking at the Graph Data tab choose an appropriate dataset to learn about the relationship between smoking and different types of cancer Follow the interactive to choose the most appropriate type of graph and graph the data Based on the data you graphed what type s of cancer appear to have a positive correlation with smoking rates Multiple Choice Breast Lung Melanoma

skipped part Tutorial Exercise Solve See Example 4 Objective 2 A photographer wants to mix 5 liters of a 9 acetic acid solution with a 13 solution to get a 10 solution How many liters of 13 solution must be added Step 1 Let x represent the number of liters of the 13 acetic acid solution There are 5 liters of the 9 solution so there will be x x liters of the 10 solution

a The complex conjugate of 5 8i is 5 8i b 5 8 5 8i X

The 21 foot board in the illustration has been cut into two parts one twice as long as the other How long is each part ft smaller value ft larger value 1 21 ft 2x

Review the incomplete steps in the derivation of the tangent sum identity Step 1 Original expression Step 2 Rewrite using the definition of tangent Step 3 Apply the sine sum identity and cosine sum identity Step 4 Step 5 Simplify using the definition of tangent tan x y sin x y cos x y sin x cos y cos x sin y cos x cos y sin x sin y Which action can be taken to the expression in Step 3 to give an expression for Step 4 divide both the numerator and denominator by sin x sin y divide both the numerator and denominator by sin x cos y O divide both the numerator and denominator by cos x sin y tan x tan y 1 tan x tan y

Calculate the following definite integrals 1 f x sin x dr 3 fi e In x dx 5 f x 1 dx 2 2x cos x dx r 2 4 f sin r cos x dr 6 f sin x x dx

nt 5 int rences Looking at the Graph Data tab choose the appropriate datasets to address the following statements and graph the data Match each statement below to the type of cancer it best describes 1 Common but often survivable Click to select 2 Rare but often lethal Click to select 3 Rare in men more common in women Click to select 4 Incidence rates correlate with smoking rates Click to select 5 About twice as common in men compared to women Click to select

1 Calculate the following indefinite integrals 1 f x sin r e da 2 f 2x cos 3r ln x dr 3 f 4 5 dx 4 f 10 5 dx Cre 1 A

5 Evaluate 1 7 Hint Try to sketch the function to understand L what kind of function we are trying to integrate

OBLEM 1 4p Compute 13 Express solution in algebraic and trigonometric forms 1 j 3 3 16 21 z 1 2j 3p Mark on the complex plane solutions of 4 2j 3 Find decomposition of w z 4z6 4 z5 10 za over C

b aaBBccdd c AaBbCcDd 50 Hint don t do a tetrahybrid cross do monohybrid crosses for each gene then use the multiplication rule 3 Approximately 4000 years ago a small number of people settled in areas of Finland and became separated from the rest of the population These people reproduced but due to the low number of people it caused a loss of genetic diversity in the subsequent offspring which caused many disorders to arise These disorders are collectively known as Finnish heritage diseases This event was so significant that even today one in five Finnish people carry at least one gene related to a Finnish heritage disease A man and a woman both of Finnish heritage are aware of this so they see a genetic counselor They are interested in having a child but fear they may pass on a disease They have their DNA analyzed and it comes back that they are both carriers for the recessive disease known as megaloblastic anemia a type of anemia common in Finnish descent Thankfully if they have an affected child it is treatable a What is the probability that if they have a child it will have megaloblastic anemia b Let s say they decide to have three children total What is the probability that all three AABE Show w

18 In the diagram below PR is a diameter of a circle with centre O Q and S are points on the circumference The tangent to the circle at the point P meets QS produced at T PQS 26 and QPR 42 Calculate a PRS b PRO 6 PTO 2 S Answer a R

A leprechaun places a magic penny under a girl s pillow The next night there are 2 magic pennies under her pillow Each night the number of magic pennies doubles How much money will the girl have after 17 nights How much money will the girl have after 17 nights

The price of a computer component is decreasing at a rate of 10 per year State whether this decrease is linear or exponential If the component costs 110 today what will it cost in three years Is the decline in price linear or exponential linear exponential What will the component cost in three years Round to the nearest cent as needed

A 92 ft tree casts a shadow that is 150 ft long What is the angle of elevation of the sun Round your answer to one decimal place

2 Which sequence of rigid motions will definitely work to take triangle GHJ onto triangle STU 7 A Rotate GHJ using center G until GH is lined up with ST and then reflect over aline halfway between GHJ and STU B Translate GHJ by the directed line segment GS Rotate GHJ using S as the center by angle H ST Reflect G HJ over ST NAME C Translate GHJ by the directed line segment GT Rotate GHJ using Tas the center by angle HTS Reflect G HJ over ST D Translate GHJ by the directed line segment GS Translate G H J by the directed line segment HT Translate G HJ by the directed line segment T 3 Reflect triangle STU across line ST Which of these is a valid reason why the image of U will coincide with J A The image of U and J are on the same side of ST and make the same angle with it at T B The image of U and Jare the same distance along the same ray from T C The image of U and I will not coincide after reflection over ST 2019 by Illustrative Mathematics D Line ST is the perpendicular bisector of the segment connecting U and J because the perpendicular bisector is determined by 2 points that are both equidistant from the endpoints of a segment 4 Here is parallelogram ABCD U DATE M B illustrative Mathematics PERIOD 2

K Listed below are amounts in millions of dollars collected from parking meters by a security company in a certain city A larger data set was used to convict 5 members of the company of grand larceny Find the mean and median for each of the two samples and then compare the two sets of results Do the limited data listed here show evidence of stealing by the security company s employees Security Company Other Companies 1 6 1 3 1 6 13 12 11 1 5 1 1 1 1 1 70 1 5 1 9 1 6 1 7 1 6 2 2 1 9 1 7 1 7 1 8 Find the medians The median for the security company is 1 3 million and the median for the other companies is 1 7 million Type integers or decimals rounded to two decimal places as needed Compare the results Choose the correct answer below OA The mean and the median for the collections performed by other companies are both lower than the mean and the median for the security company OB The median is lower for the collections performed by other companies but the mean is lower for the security company c The mean and the median for the security company are both lower than the mean and the median for the collections performed by other companies OD The mean is lower for the security company but the median is lower for the collections performed by other companies OE The mean and median appear to be roughly the same for all collections Do the limit data listed here show evidence of stealing by the security company s employees OA Since the security company does not appear to have collected lower revenue than the other companies there is no evidence of stealing by the security company s employees OB Since the data is not matched there is no evidence of stealing by the security company s employees OC Since the security company appears to have collected lower revenue than the other companies there is some evidence of stealing by the security company s employees 4

Evaluate the derivative of the following function f t 18 tanh Vi E

Find the derivative of the following function f x x cosh 9x fly

Listed below are amounts in millions of dollars collected from parking meters by a security company in a certain city A larger data set was used to convict 5 members of the company of grand larceny Find the mean and median for each of the two samples and then compare the two sets of results Do the limited data listed here show evidence of stealing by the security company s employees Security Company Other Companies Find the means 1 6 1 3 1 6 1 3 1 2 1 1 1 5 1 1 1 1 1 70 1 5 1 9 1 6 1 7 1 6 2 2 1 9 1 7 1 7 1 8 The mean for the security company is 1 35 million and the mean for the other companies is 1 76 million Type integers or decimals rounded to two decimal places as needed Find the medians The median for the security company is Type integers or decimals rounded to two decimal places as needed million and the median for the other companies is s S million

nstruct a frequency distribution for the data set using the indicated number of Isses In the table include the midpoints relative frequencies and cumulative equencies Which class has the greatest class frequency and which has the least ass frequency 29 Music Blog Reading Times Number of classes 5 Data set Times in minutes spent reading a music blog in a day 7 39 13 25 8 22 0 2 18 2 30 DE 10 11 0 20 20 7 15

Find the derivative of the following function f x x cosh 29x

Find the derivative of the following function f x cosh 5x f x

The price of a computer component is decreasing at a rate of 10 per year State whether this decrease is linear or exponential If the component costs 110 today what will it cost in three years Is the decline in price linear or exponential O linear exponential

structing a Frequency Distribution and a Frequency Hist cercises 31 34 construct a frequency distribution and a frequency hi e data set using the indicated number of classes Describe any patter 33 Reaction Times Number of classes 8 Data set Reaction times in milliseconds of 30 adult females t auditory stimulus 507 389 305 291 336 310 387 454 323 441 388 426 309 416 359 388 307 514 442 373 428 411 382 320 450 337 469 351 422 413

Use the identity cosh x y cosh x cosh y sinh x sinh y to verify the identity cosh 2x cosh x sinh x Let x y Substitute x for y in the equation cosh x y cosh x cosh y sinh x sinh y cosh x y cosh x cosh y sinh x sinh y cosh x cosh x cosh sinh x sinh

A King in ancient times agreed to reward the inventor of chess with one grain of wheat on the first of the 64 squares of a chess board On the second square the Kir would place two grains of wheat on the third square four grains of wheat and on the fourth square eight grains of wheat If the amount of wheat is doubled in this w on each of the remaining squares how many grains of wheat should be placed on square 15 Also find the total number of grains of wheat on the board at this time and their total weight in pounds Assume that each grain of wheat weighs 1 7000 pound How many grains of wheat should be placed on square 15 16384 grains How many total grains of wheat should be on the board after the the grains of wheat have been placed on square 15 32767 grains What is the total weight of all the grains of wheat on the board after the grains of wheat have been placed on square 15 pounds Round to the nearest tenth as needed

Find the arc length parameter along the given curve from the point where t 0 by evaluating the integral s t v T dt Then find the length of the 0 indicated portion of the curve r t 7costi 7sint j 8t k where Osts 2 FIN The arc length parameter along the curve starting at t 0 is s t Type an exact answer using radicals as needed

Graphical Analysis In Exercises 19 and 20 use the frequency histogram to a determine the number of classes b estimate the greatest and least frequencies c determine the class width d describe any patterns with the data 19 Employee Salaries Frequency 300 250 200 150 100 50 S VE 44 5 54 5 64 5 74 5 84 5 94 5 Salary in thousands of dollars

7 x 3x 7 0 9 2x 3x 5 0 11 3x 2x 8 0 8 2x 5x 2 0 10 3x 5x 1 0