Math - Others Questions

5 Three vectors a b and c are mutually perpendicular with b 1 and c 2 If the vectors p 2a 3b 4c and q a 2b 3c are perpendicular calculate the magnitude of the projection of the vector p on the vector a A 4 B 31 C 1 D 6

17 60 The drum has a weight of 80 lb and a radius of gyration ko 0 4 ft If the cable which is wrapped around the drum is subjected to a vertical force P 15 lb determine the time needed to increase the drum s angular velocity from 5 rad s to 25 rad s Neglect the mass of the cable 0 5 ft P

3 Migraine is a neurological disorder that affects about 15 of the world s population according to estimates Among people with this disease 95 regularly suffer from headaches Among people who do not suffer from this disease 90 do not have regular headaches A 5 points What is the probability that a randomly chosen person regularly suffers from Headaches Suffers from migraine B 5 points If a person regularly has headaches what is the probability that he

7 Solve the following equations State exact answers a 5 pts log x log x 2 3 b 5 pts 4x 23x 5

A recent survey concluded that of the teachers in a certain school district had at least 10 years of teaching experience If there are 152 teachers in the district approximately how many have at least 10 years of teaching experience

11 Given f x 4 x 2 x 5 3 x 2 x 6 determine a 3 pts the x intercept s if any give x coordinate s b 3 pts vertical asymptotes in equation form c 3 pts horizontal asymptotes in equation form d 3 pts domain interval notation

13 The fox population in a certain region has a continuous growth rate of 5 percent per year It is estimated that the population in the year 2000 was 30 000 a 4 pts Find a function that models the population t years after 2000 t 0 for 2000 Use P t Poert b 4 pts Use your answer from part a to estimate the fox population in the year 2011 Your answer must be an integer

6 Given y 9 sin 8x 7 6 determine a 4 pts the amplitude b 4 pts the period 4 pts the phase shift and direction

12 5 pts Given f x 2x 12x 22 write the function in standard form that is f x a x h k

7 Solve the following equations State exact answers a 5 pts log x log x 2 3 b 5 pts 4x 23x 5

3 8 5 pts Find the inverse of f x x 5 Don t forget to show your w

10 5 pts Given f x x 3x 9 find f x h f x h for h 0

6 Given y 9 sin 8x 7 6 determine a 4 pts the amplitude b 4 pts the period 4 pts the phase shift and direction

3 7 pts Find c if a 2 52 b 3 79 and C 41 6 Round to two decimal places if needed Assume A is the angle opposite side a B is the angle opposite side b and Cis the angle opposite side c You must draw the triangle to get credit for this problem

5 Consider the following triangle a B b If A 55 and b 19 find the values of a 3 pts B b 3 pts a c 3 pts c

4 Consider 8 293 a 3 pts State an angle coterminal to 0 b 3 pts Sketch 0 c 3 pts What is the reference angle of 293

1 6 pts Find all solutions to 2 cos x 2 0 on the interval 0 x 2 Don t forget to show your work Give exact solutions

2 7 pts Solve the triangle if A 35 C 66 and b 11 Round to two decimal places if needed Assume A is the angle opposite side a B is the angle opposite side b and Cis the angle opposite side c You must draw the triangle to get credit for this problem

1 6 pts Find all solutions to 2 cos x 2 0 on the interval 0 x 2 Don t forget to show your work Give exact solutions

z x e In x 2 0 3

x3 2x 5x 1 x 2 5

control tower Round your answer to the 9 A temporary ramp that is 15 feet long is placed to reach an entrance door that is 4 feet above the ground What is the angle of elevation of the ramp Round your answer to the nearest tenth in a tree stay upright If the

real i rate A S B Dm Quantity of Money Looking at this graph of the money market how might we move from point A to point B O a The Federal Reserve could hold an open market operation and buy bonds b Congress could use fiscal policy and tighten its spending O c The Federal Reserve could hold an open market operation and sell bonds d Government could lift price controls on agricultural goods

g x 22 x 1

1 I zx x n

A B D C D What could this graph be used to illustrate a The welfare benefits when a country exports a good b The welfare benefits when a country imports a good O c How to apply the Big Mac index to the trade model Od The welfare effects of a tariff S Q beef WORLD PRICE

K The graph models the baseball schedule for a week The vertices represent the teams Each game played is represented as an edge between two teams How many games are scheduled for Minnesota during the week List the teams that they are playing How many times are they playing each of these teams List the teams that Minnesota is playing Select all that apply A Miami D Pittsburgh B Green Bay E Cincinnati C Buffalo OF No teams How many times is Minnesota playing each of these teams this week Minnesota is playing Miami time s Cincinnati time s Green Bay time s Pittsburgh time s and Buffalo time s Type whole numbers Miami Green Bay test Minnesota Buffalo Cincinnati Pittsburgh

Find mZD B 1 C 2 mZD D Write your answer as an integer or as a decimal rounded to the nearest tenth

8 A traffic light weighing 15 pounds is suspended by two cables see figure Find the tension in each cable if 0 40 and 0 35 Approximat the answers to one decimal place 0 0

6 Data was collected on the speed and mileage of a car Speed is miles per hour and mileage is miles per gallon speed Y mileage 12 17 18 22 22 26 28 29 35 29 a Is the data Linear Quadratic or Cubic 40 31 b Write the equation of the regression curve 46 33 50 32 56 28 61 26 68 24 76 18 2 points AT 2 points c Use your equation to predict the mileage of a car with a speed of 42 miles per hour 2 points d What is the average rate of change from 55 miles per hour to 60 miles per hour 2 points

m the probability distribution to the right the random variable X represents the number of hits a paseball player obtained in a game over the course of a season Complete parts a through f below a Verify that this is a discrete probability distribution This is a discrete probability distribution because and the of the probabilities is Type whole numbers Use ascending order b Draw a graph of the probability distribution Describe the shape of the distribution Graph the probability distribution Choose the correct graph below O A 0 4 0 3 0 2 0 1 0 0 1 2 3 4 5 Number of Hits Q The distribution Q OB 0 4 0 3 0 2 0 1 0 Describe the shape of the distribution GULLOR 0 1 2 3 4 5 Number of Hits and is Q O C G Do not round 0 4 0 3 0 2 0 1 c Compute and interpret the mean of the random variable X Hx hits Type an integer or a decimal Do not round Which of the following interpretations of the mean is correct 012345 Number of Hits Q O D Q 0 4 0 3 X P x 0 1661 0 3357 0 2878 3 0 1492 4 0 0364 0 0248 between and inclusive 0 0 2 0 1 o 1 2 5 012345 Number of Hits Q B OA The observed number of hits per game will be equal to the mean number of hits per game for most games OB In any number of games one would expect the mean number of hits per game to be the mean of the random variable OC Over the course of many games one would expect the mean number of hits per game to be the mean of the random variable OD The observed number of hits per game will be less than the mean number of hits per game for most games d Compute the standard deviation of the random variable X 0x hits Round to three decimal places as needed e What is the probability that in a randomly selected game the player got 2 hits

A website that reviews recent movies lists 4 five star films the highest rating 15 four star films 16 three star films 9 two star films and 6 one star films Make a frequency table for the data set Include columns for relative frequency and cumulative frequency Complete the table Type integers or decimals rounded to the nearest tenth as needed Cumulative frequency Stars Frequency Relative frequency 5 4 100 3 2 1 Total 10000

The graph of a polynomial function is given What is the smallest degree that the polynomial could have The smallest degree the polynomial could have is Simplify your answer AY th

Complete the following table which shows the performance of two investments over a 5 year period Anjana deposits 5000 in an account that earns simple interest at an annual rate of 4 9 Darin deposits 5000 in an account that earns compound interest at an annual rate of 4 9 and is compounded annually Complete the following table Round to the nearest dollar as needed Year Anjana s Annual Interest 1 2 3 4 5 JUUL Anjana s Balance Darin s Annual Interest Darin s Balance Year 1 2345 Anjana s Annual Interest Anjana s Balance Darin s Annual Interest E

Clint s salary increased from 22 000 to 37 400 over a three year period Helen s salary increased from 27 000 to 45 900 over the same period Whose salary increased more in absolute terms In relative terms Explain Whose salary increased more in absolute terms Select the correct choice below and fill in the answer box es to complete your choice OA Helen s salary increased more because her salary increased by This is more than OB Clint s salary increased more because his salary increased by OC Neither person s salary increased more because both of their salaries increased by Whose salary increased more in relative terms Select the correct choice below and fill in the answer box es to complete your choice A Clint s salary increased more because his salary increased by B Helen s salary increased more because her salary increased by OC Neither person s salary increased more because both of their salaries increased by This is more than the amount that Clint s salary increased the amount that Helen s salary increased This is more than the percent increase of Helen s salary which is This is more than the percent increase of Clint s salary which is

A typical glass of wine contains about 22 grams of alcohol Consider a 92 pound woman with approximately 5 liters 5000 milliliters of blood who drinks two glasses of wine Complete parts a and b below a If all the alcohol were immediately absorbed into her bloodstream what would her blood alcohol content be Round to two decimal places as needed 100 mL Note that a blood alcohol content BAC of 0 08g 100mL is the legal driving limit in the U S A BAC at or above 0 4g 100mL usually leads to coma or death Explain why it is fortunate that in reality the alcohol is not absorbed immediately Choose the correct answer below OA It is fortunate because any amount of alcohol consumption can impair brain function OB It is fortunate that alcohol is not absorbed immediately because this blood alcohol content is above the legal limit for driving and is a dangerous level of intoxication OC It is fortunate that alcohol is not absorbed immediately because although this blood alcohol content is below the legal limit it will impair brain function OD It is fortunate that alcohol is not absorbed immediately because this is a lethal concentration of alcohol and is far beyond the legal limit b Again assume all the alcohol is absorbed immediately but now assume her body eliminates the alcohol through metabolism at a rate of 12 grams per hour What is her blood alcohol content 3 hours after drinking the wine 9 100 mL Is it safe for her to drive at this time Explain Round to two decimal places as needed OA It is safe to drive Her blood alcohol content is lower than it was three hours ago OB It is not safe to drive This is over the legal limit OC It is safe to drive Although is it above the legal limit it is still pretty close

A typical glass of wine contains about 22 grams of alcohol Consider a 92 pound woman with approximately 5 liters 5000 milliliters of blood who drinks two glasses of wine Complete parts a and b below a If all the alcohol were immediately absorbed into her bloodstream what would her blood alcohol content be g 100 mL 1 19 Round to two decimal places as needed Note that a blood alcohol content BAC of 0 08g 100mL is the legal driving limit in the U S A BAC at or above 0 4g 100mL usually leads to coma or death Explain why it is fortunate that in reality the alcohol is not absorbed immediately Choose the correct answer below OA It is fortunate because any amount of alcohol consumption can impair brain function OB It is fortunate that alcohol is not absorbed immediately because this blood alcohol content is above the legal limit for driving and is a dangerous level of intoxication OC It is fortunate that alcohol is not absorbed immediately because although this blood alcohol content is below the legal limit it will impair brain function OD It is fortunate that alcohol is not absorbed immediately because this is a lethal concentration of alcohol and is far beyond the legal limit b Again assume all the alcohol is absorbed immediately but now assume her body eliminates the alcohol through metabolism at a rate of 12 grams per hour What is her blood alcohol content 3 hours after drinking the wine Round to two decimal places as needed g 100 mL Is it safe for her to drive at this time Explain OA It is safe to drive Her blood alcohol content is lower than it was three hours ago OB It is not safe to drive This is over the legal limit OC It is safe to drive Although is it above the legal limit it is still pretty close

The current I in amperes flows through a particular ac alternating current circuit at time 7 seconds is I 220 sin 55 t What is the period of the current

Complete parts a through c below a A warehouse is 62 yards long 28 yards wide and 8 yards high What is the area of the warehouse floor If the warehouse is filled to half its height with tightly packed boxes what is the volum of the boxes b A room has a rectangular floor that measures 26 feet by 15 feet and a flat 6 foot ceiling What is the area of the floor and how much air does the room hold c A grain silo has a circular base with an area of 180 square feet and is 21 feet tall What is the total volume a The area of the warehouse floor is 1736 yd2 Type an integer or a decimal The volume of the boxes in the warehouse is Type an integer or a decimal b The area of the floor is ft2 Type an integer or a decimal The amount of air the room can hold is Type an integer or a decimal c The volume of the grain silo is Type an integer or a decimal ft ft yd

9 A ladder 13 feet long is leaning against the side of a building If the foot of the ladder is pulled away from the building at a constant rate of 8 inches per second how fast is the area of the triangle formed by the ladder the building and the ground changing in feet squared per second at the instant when the top of the ladder is 12 feet above the ground

Determine if the rates are equivale 25 hours to 5 days 8 hour in 2 Explain 2 days

Consider the function y x 3 a State the transformations b Graph the parent function Graph the transformed functio

Graph the equation y 5 4 3 2 1 4 3 2 7 1 1 3 2 3 x 2 2 3

8 intercept 4 liot y intercept 0 12 8 4 8 a Use the graph to identify the x and y intercepts of the graph Note the scale on each axis since they may not be the same 12 16 0

Graph the equation y 5 4 3 2 1 2 1 4 3 1 2 3 4 1 3 5 I 2 1 2 3 A LO

8 4 x intercept 16 y intercept 0 12 8 4 4 8 12 16 Use the graph to identify the x and y intercepts of the graph Note the scale on each axis since they may not be the same 4 0 8

Cramers method TO H02 0 2j VX 306 vy 0 2 0 04 0 015 x A A Val 11 7 28 D vy E B F P B B A B ED BF AP BC 0 2 0 554 33 7 V

Savings Minding the gap refers to the 3 6 months of savings you should have at the ready in case of an emergency The goal is to determine your job security which leads you to the month range you think you will need Example Teachers have high job security so I keep three months salary in savings but my wife is in sales so she keeps six months savings for her job Minding the Gap is that space you keep between you and the danger that forces you into debt I recommend 5 monthly to this category till you reach your monthly goal You use these savings for emergencies but remember it is not an emergency if you are tapping this amount monthly What is the 5 amount How many months total do you think you should have for emergency savings and why How many months will you need to save till you meet your savings goal What should you consider doing with that savings money after you reach your goal

Fill out the black to make the given table below a probability distribution x 0 1 2 3 P x

17 57 The 10 kg wheel has a radius of gyration k 200 mm If the wheel is subjected to a moment M 51 N m where t is in seconds determine its angular velocity when t 3 s starting from rest Also compute the reactions which the fixed pin A exerts on the wheel during the motion M