Algebra Questions

4 A sailboat is approaching a cliff The height of the cliff is known to be about 2000 m and the boat is about 3464 m from the cliff Determine the angle of elevation from the sailboat to the top of the cliff CLIFF

6 While walking to school you pass a barn with a silo If you are standing at about 40 m from the base of the silo and the silo is 33 5 m tall Using this information and your knowledge of trigonometric ratios calculate the angle of elevation to the top of the silo 33 5 m 40 m

Date Name Ceme This do now must be submitted by the end of class for grade and must be done b starting assignment 20 Do Now 1 Martha has 5 dollars Kelvin has 3 less than twice what Martha has Write an expression to represent how much money Kelvin has 2 What is 30 percent of 60

Julio deposits 1500 in a savings account that pays 2 4 interest per year compounded monthly The amount in the account after n months is given by An 1500 1 0 024 0 024 12 a Find the first six terms of the sequence Round your answers to the nearest cent A A A3 A4 A5 A6 S b Find the amount in the account after 5 years Round your answers to the nearest cent Aso

Module 1 For the function f x 4 3x 1 2 x 5 find the followin y intercept x intercept s leading coefficient degree of the polynomial

e Rudy Meangru Solve for x and check for any extraneous roots log x 6 log x 4

16 x y x y 5 A 51 F X B 380 C 9 D 19 E 22

What statistic did you use O sample proportion O population proportion An article about the relative priorities of protecting the environment and the economy in America summarized a survey of 1 700 adult U S citizens When asked if they expect to feel the effects of climate change in their lifetime 1 037 of the survey participants responded yes The article states that participants were selected to be representative of all adult U S citizens a Estimate the proportion of adult U S citizens who think that they will feel the effects of climate change in their lifetime 0 61 b Use the sample data to estimate the standard error of p Round your answer to three decimal places MY NOTES c Calculate the margin of error associated with the estimate in Part a Hint See Example 9 3 Round your answer to three decimal places PRACTICE ANOTHER I Interpret the margin of error in the context of this problem OIt is unlikely that the estimated proportion of adult U S citizens who think that they will feel the effects of climate change in their lifetime differs from the true population proportion by less than the calculated value It is likely that the estimated proportion of adult U S citizens who think that they will feel the effects of climate change in their lifetime differs from the true population proportion by the calculated value It is impossible that the estimated proportion of adult U S citizens who think that they will feel the effects of climate change in their lifetime differs from the true population proportion by more than the calculated value It is impossible that the estimated proportion of adult U S citizens who think that they will feel the effects of climate change in their lifetime differs from the true population proportion by less than the calculated value O It is unlikely that the estimated proportion of adult U S citizens who think that they will feel the effects of climate change in their lifetime differs from the true population proportion by more than the calculated value

An article included data from a survey of 1 015 hiring managers and human resource professionals The article noted that many employers are using social networks to screen job applicants Of the 1 015 people who participated in the survey 699 indicated that they use social networking sites to research job applicants For the purposes of this exercise assume that the sample can be regarded as a random sample of hiring managers and human resource professionals a Suppose you are interested in learning about the value of p the proportion of all hiring managers and human resource managers who use social networking sites to research job applicants This proportion can be estimated using the sample proportion p What is the value of p for this sample Round your answer to four decimal places p b Based on what you know about the sampling distribution of p is it reasonable to think that this estimate is within 0 02 of the actual value of the population proportion Explain why or why not Round your answer to four decimal places X In addition We know the sampling distribution of p will be centered at the population proportion px and the standard deviation of this distribution can be estimated as 0 02 the sampling distribution is not mound shaped and symmetric X So we cannot say our value of p is likely to be within 0 02 of the actual value because of the following fact The Empirical Rule implies about 95 of our sampling distribution s values will fall within two standard deviations of the center but two standard deviations is greater than 0 02 The Empirical Rule implies about 95 of our sampling distribution s values will be at most one standard deviation away from the center and our standard deviation is less than 0 02 The Empirical Rule implies about 95 of our sampling distribution s values will be at most one standard deviation away from the center but our standard deviation is greater than 0 02 We cannot make use of the Empirical Rule since our sampling distribution isn t mound shaped and symmetric O The Empirical Rule implies about 95 of our sampling distribution s values will fall within two standard deviations of the center and two standard deviations is less than 0 02 X

P The shortest distance between the curves 2y2 x and 3 2 9x 9y 60y 91 0 is

nd a set of parametric equations to represent the graph of the rectangular equation using t x and t 5 x Enter your answers as comma separated lists of equation y x 1 a t x x t ty t b t 5 X t 2 3

that exists B 147 7 c 8 124 b 14 121 Select the correct choice below and if necessary fill in the answer boxes with in the choice A There is only one possible solution for the triangle The measurements for the remaining angles A and C and side a are as follows A 14 4 C 18 a 6 6 Round to the nearest tenth as needed A B There are two possible solutions for the triangle The measurements for the solution with the longer side a are as follows O C 0 A O Round to the nearest tenth as needed Round to the nearest tenth as needed The measurements for the solution with the shorter O O Round to the nearest tenth as needed C Round to the nearest tenth as needed Round to the nearest tenth as needed C There are no possible solutions for the triangle Round to the nearest thousandth as needed a Round to the nearest thousandth as needed side a are as follows a Round to the nearest thousandth as needed

KSJ between 12 00 noon and 1 00 pm are the minute and hour hands of a

1 Find the area of the triangle using the formula A bh and then verify that Heron s formula gives the same result 1 bh Use the formula A 2b The area is 48 Use Heron s formula The area is C 10 16 10

Find the area of the triangle ABC a 105 8 m b 74 7 m c 99 8 m What is the area of the triangle m Round to the nearest square meter as needed Question 12

Question 10 7 3 65 Use an appropriate area formula to find the area of the triangle with the given side lengths a 17 m b 9m c 12 m The area of the triangle is m Round your answer to the nearest tenth

1 3 x y 3 27y4x 4

K Find the measure of 0 in the triangle Do not use a calculator 0 B A B 0 1 C

Diyagram enine izgilerle kesilen iki paralel izgi a ve b yi g stermektedir x in de eri nedir 490 to 380 a b

11 ABC geni gen DBE ye benzer B l m A X in de erini bulmak i in bir denklem kurun ve z n A 4x 3 7x 30 B E

Find the domain of the logarithmmic function y log x Write your answer only as an interval in the space below For infinity write inf Do not 1 4 add any spaces An example of the correctly written answer inf 12 4

Diyagram enine kesilen iki paralel izgiyi g stermektedir 22 3y 10 l s ve 28 7y 30 l s B l m A Bir denklem yaz n ve y nin de erini bulmak i in z n 1 3 re 2 7 5 6 8

Using the graph and table as a reference identify the Domain of the function f x Write your answer in Interval Notation 5 4 3 10 1 2 3 4 f x 1 4 f x 0 11111111111111 0 14285714285714 0 16666666666667 0 2 0 25 0 33333 3333333 Undefined Domain of f x 2 S 32 1 L 44 PL 31 EJ D

2 Solve for x use log where necessary 41 8 a b 22 x 3x

Problem 5 Let W be the subspace of R spanned by the vectors u 1 0 1 0 u2 0 1 1 0 and u3 0 0 1 1 Use the Gram Schmidt process to transform the basis u u2 u3 into an orthonormal basis 4 v 2 0 2 0 v2 V V V 0 v3 3 V3 6 3 6 2 0 2 0 v V6 NE V6 0 V3 13 13 13 V2 3 3 D v 2 0 2 0 v2 V6 V6 6 0 v3 2 0 0 v 6 16 16 0 1 13 13 13 v3 E v V2 B v1 C v 2 0 2 0 v2 V6 V6 N 0 v3 V 3 6 F v 2 0 2 0 v2 V6 v6 6 0 v3 3 6 v3 13 2 0 2 0 v NE VE 0 13 3 V 0 6 6 G v H v 0 2 0 v2 v v 0 v3 6 3 6

Problem 4 Let v 3 1 0 1 v2 0 1 3 1 and b 1 6 1 4 Let W be the subspace or R4 spanned by v and V2 Find projw b Problem 4 Enter your answer symbolically as in these examples Enter the four components separated with commas

Problem 3 Which of the following sets of polynomials form a basis for P2 P1 1 3x 5x P2 5 x ii P 1 x P2 10x x P3 1 11x x iii P 1 P2 1 6x P3 x P4 x Problem 3 A all of them B i only C i and ii only D iii only E none of them F ii and iii G i and iii only H ii only Select

Solve for x and check for any extraneous roots a log x 1 2 b log10 x 3 log 0 x 1 10

8 Use the properties of logarithms to express the following as sum difference or constant multiple In x x 1 x 1

Prof Rudy Meangru 1 Evaluate the following without a calculator a log1000 b log 10 3 2 FI 2023 Due Monday 11 27 c In e

Find the exact values for the six trigonometric functions of the angle 0 in the figure O For the given triangle which of the following ratios represents the trigonometric function sin 0 BC AB O AC BC AB BC BC AB Find the value of sin 0 sin 0 Simplify your answer including any radicals Use integers or fractions for any numbers in the expression For the given triangle which of the following ratios represents the trigonometric function cos 0 BC AC 11 5 AB AC B Find the value of cos 8 cos 0 Simplify your answer including any radicals Use integers or fractions for any num 2

2 Re arrange the following formulas to solve for the indicated variable SHOW YOUR WORK 5 marks a P D 8PY solve for Y

Problem 6 Let S 1 4x 1 3x2 Which of the following polynomials could be added to the set S to form a basis for P2 Problem 6 1 2 4x 3x 11 5 4x12x 111 8 12x 15x s A none of them B all of them C i only D ii and iii only E ii only F iii only G i and ii only H i and iii only Select

Problem 1 Which of the following sets of vectors are independent 1 1 2 1 3 2 0 2 4 1 11 1 2 1 3 2 0 5 6 0 ii 1 2 1 3 2 0 7 10 2 A none of them B ii only C i only D i and iii only E ii and iii only F iii G all of them H i and ii only

Problem 2 Let p 8x 6x 3 Find the coordinate vector of p relative to the following basis for P2 P1 1 P2 1 x P3 1 x x Problem 2 Enter the coordinates separated with commas

Determine the exponential regression of the data below using either a calculator or spreadsheet program 21 6 19 23 13 33 8 47 5 54 2 62 Select the correct answer below Of x 93 264 1 106 Of x 93 264 1 106 O f x 93 264 1 106 O f x 93 264 1 106

Given that f x x 8x and g x x 2 calculate a fog 3 b go f 3

Find the standard form of the equation of the parabola with the given characteristics Vertex 7 6 directrix x 14

7 nin l s nedir A 37 C 143 B 53 D 127 53

3 Diyagram bir enine taraf ndan kesilen iki paralel izgiyi g stermektedir 23 7x 12 l s ise 26 n n l s ka t r A 3x 12 B 7x 12 C 7x 12 D 192 7x 12 34 LO 5 0 6 78

1 At the end of each year Carl and Linda Munson will deposit 2100 into a 401k retirement account Find the amount they will have accumulated in 10 years if funds earn 8 per year 2 Every six months Paul Sewell puts 1400 into an account paying 10

On April 3 the Mears Flag Company borrowed 14 000 to pay for start up costs for its new Showroom The loan ha a simple interest rate of 8 75 and was for 290 days The company was able to make partial payments of 5000 o May 28 and 2500 on October 12 How much will the company owe on the date of maturity Assume 360 days in a year Click the icon to view a table of the number of the day of the year for each date The company will owe on the date of maturity Round to the nearest cent as needed

Determine the due date of the loan using the exact time if the loan is made on the given date for the given number of days April 8 for 270 days Click the icon to view a table of the number of the day of the year for each date due date of the loan is www

from a survey of 1 015 hiring managers and human resource professionals The article noted that many employers are using social networks to screen job applicants Of the 1 015 people who participated in the survey 699 indicated that they use social networking sites to research job applicants For the purposes of this exercise assume that the sample can be regarded as a random sample of hiring managers and human resource professionals a Suppose you are interested in learning about the value of p the proportion of all hiring managers and human resource managers who use social networking sites to research job applicants Thi proportion can be estimated using the sample proportion p What is the value of p for this sample Round your answer to four decimal places p b Based on what you know about the sampling distribution of p is it reasonable to think that this estimate is within 0 02 of the actual value of the population proportion Explain why or why not Round your answer to four decimal places and the standard deviation of this distribution can be estimated as In addition the We know the sampling distribution of p will be centered at the Select sampling distribution is not mound shaped and symmetric X So we cannot O The Empirical Rule implies about 95 of our sampling distribution s values will fall within two standard deviations of the center but two standard deviations is greater than 0 02 say our value of p is likely to be within 0 02 of the actual value because of the following fact O The Empirical Rule implies about 95 of our sampling distribution s values will be at most one standard deviation away from the center and our standard deviation is less than 0 02 O The Empirical Rule implies about 95 of our sampling distribution s values will be at most one standard deviation away from the center but our standard deviation is greater than 0 02 We cannot make use of the Empirical Rule since our sampling distribution isn t mound shaped and symmetric The Empirical Rule implies about 95 of our sampling distribution s values will fall within two standard deviations of the center and two standard deviations is less than 0 02 Submit Answer 3 4 Points DETAILS PREVIOUS ANSWERS MY NOTES 0 200 PECKSTAT3 8 3 503 XP MI MY NOTE An article included data from a survey of 2 183 hiring managers and human resource professionals The article noted that many employers are using social networks to screen job applicants and tha this practice is becomin Of the 2 192 people who participated in the sunoy 1 211 indicated that they use social networking sites such as Facebook MySpace and LinkedIn to

When a website asks you to agree to a privacy policy do you actually read the policy before agreeing Researchers asked people in a representative sample of 4 272 adults in the United States if they read privacy policies and found that 940 said that they always or often read them The paper also says that of the 2 600 people who said they at least look at privacy policies before agreeing to them 32 said that they understood very little or none of the privacy policies they read LUSE SALT a Use the given information to estimate the proportion of people who at look at privacy policies before agreeing to them who understand very little or none of the policies Use a 95 confidence interval You can assume that the sample of 2 600 people is representative of the population of interest Enter your answer using interval notation Round your numerical values to three decimal places MY NOTES Give an interpretation of the interval in context There is a 95 chance that the actual proportion of people who at least look at privacy policies before agreeing to them who understand very little or none of the policies falls within this interval O There is a 99 chance that the true proportion of people who at least look at privacy policies before agreeing to them who understand very little or none of the policies falls directly in the middle of this interval We are 95 confident that the actual proportion of people who at least look at privacy policies before agreeing to them who understand very little or none of the policies is within this interval We are 95 confident that the actual proportion of people who at least look at privacy policies before agreeing to them who understand very little or none of the policies falls directly in the middle of this interval We are 95 confident that the mean number of people who at least look at privacy policies before agreeing to them who understand very little or none of the policies falls within this interval b Would a 90 confidence interval be wider or narrower than the 95 confidence interval from part a A 90 confidence interval would be narrower than the 95 confidence interval from part a because the z critical value is smaller 8

When a website asks you to agree to a privacy policy do you actually read the policy before agreeing Researchers asked people in a representative sample of 4 271 adults in the United States if they read privacy policies and found that 920 said they always or often read them LUSE SALT Use the five step process for estimation problems EMC3 to construct a 99 confidence interval for the proportion of adults in the United States who always or often read privacy policies Enter your answer using interval notation Round your numerical values to three decimal places Interpret the interval There is a 99 chance that the true proportion of adults in the U S who always or often read privacy policies falls directly in the middle of this interval We are 99 confident that the mean number of adults in the U S who always or often read privacy policies falls within this interval We are 99 confident that the true proportion of adults in the U S who always or often read privacy policies falls directly in the middle of this interval We are 99 confident that the true proportion of adults in the U S who always or often read privacy policies falls within this interval O There is a 99 chance that the true proportion of adults in the U S who always or often read privacy policies falls within this interval Submit Answer DETAILS MY NOTES PREVIOUS ANSWERS PECKSTAT3 9 3 051 S MY NOTES

PREVIOUS ANSWERS PECKSTAT3 8 3 503 XP MI An article included data from a survey of 2 183 hiring managers and human resource professionals The article noted that many employers are using social networks to screen job applicants and that this practice is becoming more common Of the 2 183 people who participated in the survey 1 311 indicated that they use social networking sites such as Facebook MySpace and LinkedIn to research job applicants For the purposes of this exercise assume that the sample can be regarded as a random sample of hiring managers and human resource professionals MY NOTES a Suppose you are interested in learning about the value of p the proportion of all hiring managers and human resource professionals who use social networking sites to research job applicants This proportion can be estimated using the sample proportion p What is the value of p for this sample Round your answer to two decimal places b Based on what you know about the sampling distribution of p is it reasonable to think that this estimate is within 0 02 of the actual value of the population proportion Explain why or why not eatona The sampling distribution of f

arry and Sally can both produce fish and fruit Sally can produce 1 kg of fish in 4 hours and 1 kg of fruit in 5 hours Harry can produce 1 kg of fish in 5 hours and 1 kg of fruit in 2 hours Each person wants to have 4 kgs of fish and 6 kgs of fruit per week Each person works for 20 hours a week Who has a comparative advantage in fish Who has a Comparative advantage in fruit O Sally Sally O Harry Sally O Sally Harry O No one Sally O Harry Harry

The birth of a baby is considered to be premature if the baby is born before 37 weeks of pregnancy have been completed According to a study 10 of babies born in the United States in a par year were premature Suppose that a random sample of 57 babies born in the U S in this year will be selected The proportion of the babies who were premature p will be calculated a What are the mean and standard deviation of the sampling distribution of p Round your standard deviation to four decimal places mean standard deviation b Is the sampling distribution of p approximately normal Explain The sampling distribution of p is not approximately normal because n 1 p is at least 10 O The sampling distribution of p is not approximately normal because np is less than 10 The sampling distribution of p is not approximately normal because n 1 p is less than 10 O The sampling distribution of p is approximately normal because np and n 1 p are both less than 10 The sampling distribution of p is approximately normal because n and n 1 p are both at least 10 c What is the smallest value of n for which the sampling distribution of p would be approximately normal n MY N Submit Answer

8 Match each rational function with a description of its end behavior as x gets larger and larger A 9x B C D E F 99x X 99 x x 99x 9 x 99 9x x 1 The value of the expression gets closer and closer to 0 2 The value of the expression gets closer and closer to 1 3 The value of the expression gets closer and closer to 9 4 The value of the expression is 99 5 The value of the expression gets larger and larger in the positive direction 6 The value of the expression gets larger and larger in the negative direction