Algebra Questions

14 Write an solve an equation to find the value s of x that make I m Show all work x 3x 10 eins no 19dzeriw saim SSS

Condense into a single logarithm log4 5 log4 b log4 c log4 d O 5bc log4 d log 5be d Olog be d O log 5 b c

Condense into a single logarithm 9 log x 5logy 11 log z O log xy log z11 log 935 211 log 9x5y log 11

Expand the logarithm log2 m n p5 log m log2 n4 log p5 12 log mn 5 log2 P 3 log2 m 4 log2 n 5 log2 p T 3 log2 m 4 log2 n 5 log2 p

B 1 Verify Solutions Linear Inequality Determine which point or points are solutions of each linear inequality gfiven 2 3x 5y 10 1 x y 3 46 5 3 y 2 5 Ay y 6 x X 2 4 6 5 4 3 2 4 5x 2y 10 4 3 2 1 4 Y AV 6 x 4 X

dentify the graph of g x 2 2 2 2 2 2 2 2 2 2 Choose the description of the transformation from the graph of f x to the graph of g The graph of g is a vertical stretch of the graph off by a factor of The graph of it is a vertical shrink of the graph off by a factor of The graph of jg is a vertical stretch of the graph off by a factor of The graph of g is a vertical shrink of the graph of by a factor of Choose the description of the domain and range The domain is all real numbers The range is the all real numbers The domain is x 20 The range is all real numbers The domain is all real numbers The range is y 0 The domain is all real numbers The range is y 20 and a reflection in the and anfection in the

2 Charlie would like to make at least 200 washing cars this summer He charges 10 per car Write an inequality to represent Charlie s goal amount use w for the number of cars washed Type a response

Estimate the intercepts of the graph of the function 2 y 2x x 1 4 2 4 6 x The x intercept is about and the y intercept is about

77 4x 5y 5 9 1 9 2x 5y 0 5 3 2 11 y2 x 5 6 5 4 3 2 1 y y 4 4 x X 8 10 12 8 6x y 4 10 y y x 2 2 1 3 12 y2 x 1 2 6 5 4 3 2 1 AV Ay Ay 6 x 6 x 6 x

16 The cheerleaders are selling tickets to the spaghetti dinner They need to raise at least 900 The tickets cost 5 each Write an inequality to represent how many tickets they need to sell to meet their goal use t for the number of tickets sold Type a response

5 5 y 8x 4 A B C D 2 y y AV 2 4 4 X X X 6 y y 7x 3 A B C D 6 4 12 6 6 44 V A 21 14 12 Ay Ay Ay 2 2 4 6 x 6 x 6 x

13 Julie is taking a taxi cab to a restaurant in the city The cab charges 3 20 plus 55 per quarter mile Julie only has 15 to spend on the cab Write an inequality to represent the how far away the restaurant can be so that Julie can afford the taxi fare Use m for the number of quarter miles Type a response

14 Sam has saved 250 from working this summer Hel keeps saving at a rate of 20 per week After how many weeks will he have more than 500 Write an inequality to represent this situation use w for the number of weeks Type a response

3 9x 4y 16 A B C D 46 H 12 165 2 6 14 6 4 1 A T 4 x 6 x 42 x 4 4 y2 A B C D 6 8 6 x 3 6 4 2 4 2 12 y 2 4 x 4 6 x

15 Brad is a wrestler trying to make weight He currently weighs 184 pounds If he cuts 2 pounds per week how many weeks will it take him to weigh no more than 165 pounds Write an inequality to represent this situation use w for the number of weeks Type a response

Translate the verbal phrase into an inequality use x as your variable Don t solve The sum of x and 1 is at least 9 Type a response

Graphing Linear Inequalities Sketch the graph of each linear inequality 1 1 4x 3y 6 A B C D 6 4 44 y Ay 2 4 4 2 2 y 2 A B C D 6 6 4 12 1 1 1 y 2 4 X 6 x X

Translate the verbal phrase into an inequality use x as your variable Don t solve The difference of x and 7 is less than 4 Type a response

4 local gym offers two membership options You can pay 50 for the first three months und 4 for each additional month or you can pay 9 per month Explain to a prospective nember what their decision should be

Suppose that you want to estimate the effect of years of education on log wages using those variables and some other explanatory variables You consider estimating by OLS a Explain the conditions needed for obtaining a consistent estimator by OLS bj Give a proof that OLS is consistent for the case of one explanatory variable Explain the role of assumption MLR 4 c Explain what happends to the consistency result if you exclude a relevant explanatory variable

Find all real solutions of 25x 1 3 10z If there are no real solutions or t solution is all real numbers briefly EXPLAIN how you know that is the case

If two bags of popcorn and three drinks cost 14 and four bags of popcorn and one drink costs 18 how much does a drink cost

A regulation size pool table is 9 feet long by 4 5 feet wide Treasure is standing at the lower left wants to hit the white ball so it will bounce off the top cushion and hit the red ball directly in the center From physics she knows that the angle 0 the ball hits the cushion is the same as the angle 02 that it comes off the cushion How far from the top left corner should she aim the white ball The positions of the balls are shown below in feet 1 6 1 1 1 0 0 2 7 2 3 Hint Draw some triangles and try to find a suitable unknown x that you can use to describe the sides of the triangles in terms of the angles Then use 0 0

Annual revenue billions for the Boeing Corporation from 1990 to 2002 is given by R t 1 t 2 2 80 Annual revenue billions that Boeing made just from sales of its 737 airplane in the same period is given by A t 0 22 t 8 30 Note t 0 is January 1 1990 In what year and month was annual revenue excluding sales of 737s at a minimum March Xo November 1996 What was that minimum revenue in billion year 52 x 56 9 nearest 0 1 billion year

7 Write the functions below as compositions of two or more non identical functions f x cos 4x f x 1 2x 4 2x 2x

6 Find the composite function fog for the functions below its domain and its value at x 2 3 x 3 x f x g x 22x

Graph the function g x 2 x 2 x 6 9 8 7 6 5 4 3 2 17 You might need Calculator Y 6 8 7 6 5 4 3 2 1 2 3 x 1 2 3 4 5 6 7 8 9

Graph the equation 3 y x 3 x 7 4 9 8 7 6 5 4 3 2 8 7 6 5 4 30 6 2 14 21 2 23 Y 3 H 11 1 2 3 4 5 6 7 8 9 x

93 Construct a probability plot that will allow you to assess the plausibility of the lognormal distribution as a model for the rainfall data of Exercise 83 in Chapter 1 EXERCISE 83 FROM CHAPTER 1 83 Consider numerical observations x x It is frequently of interest to know whether the x s are at least approxi mately symmetrically distributed about some value If n is at least moderately large the extent of symmetry can be assessed from a stem and leaf display or histogram However if n is not very large such pictures are not par ticularly informative Consider the following alternative Let y denote the smallest x y the second smallest x and so on Then plot the following pairs as points on a two dimensional coordinate system y x X Y 1 X X y y 2 X X There are n 2 points when n is even and n 1 2 when n is odd a What does this plot look like when there is perfect symmetry in the data What does it look like when observations stretch out more above the median than below it a long upper tail b The accompanying data on rainfall acre feet from 26 seeded clouds is taken from the article A Bayesian Analysis of a Multiplicative Treatment Effect in Weather Modification Technometrics 1975 161 166 Construct the plot and comment on the extent of symmetry or nature of departure from symmetry 4 1 7 7 17 5 31 4 32 7 40 6 92 4 115 3 118 3 119 0 129 6 198 6 200 7 242 5 255 0 274 7 274 7 302 8 334 1 430 0 489 1 703 4 978 0 1656 0 1697 8 2745 6

C u 10 Given the vector space V spanning set of V A 8 B 5 span 7 1 2 8 1 1 Find x R such that M 48 6 6 2 4 x is a C 7 D 6

Graph the equation 3 y x 3 x 7 4 1111 9 8 7 6 5 4 3 2 6 88 Y 7 6 5 4 3 2 H 2 3 4 x TTTTT 1 2 3 4 5 6 7 8 9

25 y x 2y 3x 5 y 2z 4 and 1 b y 32 2 and y 32 5 are paralel because the slope of each one is c y 2z 4 and 2X are perpendicular because the product of the spe d y 27 3 and y 2r 3 y 32 3 Section Exercises 44 Exercse 25 y 2x 3 X are perpendicular because the product of the spea y 38 5 Xa perpendicular because the product of the siges y 2 2 23 2 3 2 G

Peter has 440 yards of fencing to enclose a rectangular area Find the dimensions of the rectangle that maximize the enclosed area What is the maximum area CITS A rectangle that maximizes the enclosed area has a length of yards and a width of yards The maximum area is square yards

O 1 000 O 100 Cicer Cremy 10 000 Green Grocery Mart Sales Year 2003 2004 2005 To find out exact sales numbers you need to multiply the numbers in the Sales column by 2006 2007 Sales in thousands of dollars 100 110 140 90 130

A ball is thrown upward and outward from a height of 6 feet The height of the ball f x in feet can be modeled by f x 0 1x 0 8x 6 where x is the ball s horizontal distance in feet from where it was thrown Use this model to solve parts a through c a What is the maximum height of the ball and how far from where it was thrown does this occur The maximum height is feet which occurs feet from the point of release Round to the nearest tenth as needed b How far does the ball travel horizontally before hitting the ground feet Round to the nearest tenth as needed c Graph the function that models the ball s parabolic path Choose the correct graph below OA Height 25 20 15 104 sond 5 O B Height 25 20 15 10 5 0 Q O C Height 25 20 15 10 5 04 BE A Q Q OD Height 25 595 20 15 10 5 04 o 5

Graph the following four quadratic functions x x 3 2 g x x 3 2 h x x 3 2 j x x 3 2 10 O CO 8 L ON 11 3 2 10 9 8 7 6 5 4 3 2 1 MAD 1 2 MAN 1 2 3 4 5

Graph the function 1 h x x 1 x 7 9 8 7 6 5 4 3 2 6 Y 1 8 7 6 5 4 3 2 14 2 3 x 1 2 3 4 5 6 7 8 9

Find the vertex y intercept and x intercept s of the parabola that is defined by the following quadratic function f x x 8x 7 Determine the vertex of the parabola in x y form Determine the y intercept of the parabola in x y form Determine the x intercept s of the parabola in x y form If mulitple x intercepts exist enter the points using a comma separated list If no x intercepts exist enter DNE

Myra sells mugs at the sidewalk fair every week Her revenue from selling a mugs is 8x 0 4x dollars and the cost of producing a mugs is 60 5x dollars a Write an expression for the profit Myra earns from selling mugs P b Find Myr s profit from the sale of 5 20 and 25 mugs P when 5 P when 20 when 25 P

1 5 6 B 2 5 L S 1 3 7 9 8 11 12 13 14 15 16 2 5 d 110 5 Y 217 N 2 5 3 0 2 4

Write the equation of a sine or cosine function to describe the graph 7 m 2 5 NT 0

Using complete sentences and correct mathematical terminology answer the following questions A gardener noticed a rainbow through the arch of the stream of water while he was watering his garden He wondered the height of the rainbow and decided he could use the stream of water to determine it The time t the water is in the air is measured in seconds and the water s height w t is measured in inches above the ground The function that represents t relationship is w t 4 9t2 15t 23 1 Correctly interpret the following calculations within the context of the given scenario above i w 0 4 9 0 15 0 23 23 ii a 4 9 b 15 c 23 h 2a 15 2 4 9 1 53

8 10 of the students in the school play some sort of sport Out of the athletes 30 play more than one sport If there are 600 students in the school how many play exactly one sport

Drag each graph above to match the function below y sinx 1 0 1 Ay 0 T A y cos 2x T G Q y cos x N101N 2x y 2 sinx Ay V I 2x CO ON Ay 2 Ay y sin 2x y 2 cos x U

Click here to watch the video The function graphed is of the form y a sin bx or y a cos bx where b 0 Determine the equation of the graph y Type an expression using x as the variable www G

4 Freshmen and seniors at Southland get out at 3 50 There are 180 freshmen and 100 seniors One day 60 of the freshmen and 80 of the seniors leave the building right away at dismissal How many freshmen and seniors are staying after for an activity in total

9 For a group project the members of the group have to read a 200 page book They split it up by chapter between the four members of the group If Martina reads 30 of the book how many pages do the other members of the group read

7 In a recent survey of some people 333 of them were women 432 of them were men and the remaining were children If 90 of the people surveyed are adults how many children took part in the survey

5 Jim bought strawberries and blueberries He froze 30 of the strawberries he purchased and 50 of the blueberries he purchased If he purchased 9 pound of strawberries and 12 pounds of blueberries how many total pounds of fruit did he freeze

Graph the following function over the interval 2x 2 Give the amplitude y 8cos x Which of the following is the correct graph of the function y 8cos x A 16 46 X B 16 16 K NE What is the amplitude of the function 8cos x function Type an integer or a simplified fraction Q 5 OC 2 16 x 12x Q G OD Save 2x C