Basic Math Questions and Answers

3 of 13 When there is moisture on the ground microorganisms are found in the thin layer of water on leaves A monolayer containing these organisms is formed on the top and because of the spreading pressure of this monolayer the floating organisms spread upward when the surface is tilted This is a dispersal method onto newly fallen leaves In the provided figure the horizontal segment represents the ground and the angle t measures the amount by which the surface is tilted Assumed that t is less than 90 The length d is the distance the organisms move and the length u is the change in the elevation d Find a formula giving u in terms of d and t Express numbers in exact form Use symbolic notation and fractions where needed V Assume that the distance the organisms move is 34 centimeters Find the change in elevation if the angle t is 15 and if the angle 1 is 30 Give your answers to the nearest whole number cm

The value expressed in terms of x of one of the trigonometric functions of an acute angle t is given Find the values of the other five trigonometric functions of t in terms of x Use 1 as the hypotenuse cos t 13x 1 Express numbers in exact form Use symbolic notation and fractions where needed sin t cot t csc 1 tan t sec t

Some angles and the length of an altitude of a triangle are given in the figure C A perimeter 30 area 31 45 Find the area and perimeter of the triangle Note that you may wish to find some of the unlabeled sides first Express numbers in exact form Use symbolic notation and fractions where needed B un square uni

of 13 The figure shows points on the unit circle In each case one coordinate is given For the trigonometric point P t H find the missing coordinate and then list the six trigonometric function values of t 1 E y cos 1 F cot 1 B A I G H 3 Express numbers in exact form Use symbolic notation and fractions where needed Crauder et al Preparation for Calculus 1e 2022 Macmillan Learning 33 sin t tan t sec t

Question 7 of 9 This question 3 point s possible The amount after 8 years will be Round to the nearest cent as needed Submit quiz Use the formula for computing future value using compound interest to determine the value of an account at the end of 8 years if a principal amount of 11 000 is deposited in an account at an annual interest rate of 6 and the interest is compounded quarterly 2

If a dealer buys a car from the manufacturer for 6 995 and then sells it for 8 387 his markup is 19 9 8 387 6 995 8 387 In doing this problem Angela calculated Select the correct choice below got an incorrect answer of 16 6 What mistake did she make w OA Angela calculated how much lower the manufacturer s price was compared to the dealer s price OB Angela calculated how much she could save on a new car OC Angela used the gross increase and not the net increase OD Angela used the prices measured in thousands of dollars instead of dollars 2

29 6 is what percent of 160 29 6 is of 160 Type an integer or a decimal

What is 13 25 of 132 is 13 25 of 132 Type an integer or a decimal

In doing this problem Angela calculated make point s possible If a dealer buys a car from the manufacturer for 15 755 and then sells it for 19 158 his markup is 21 6 19 158 15 755 19 158 Select the correct choice below bmit quiz got an incorrect answer of 17 8 What mistake did she OA Angela used the gross increase and not the net increase OB Angela used the prices measured in thousands of dollars instead of dollars OC Angela calculated how much lower the manufacturer s price was compared to the dealer s price OD Angela calculated how much she could save on a new car

point s possible The percent of increase is Round to one decimal place as needed Submit quiz According to a census bureau from 2000 to 2016 the population of a certain region grew from 269 million to 319 million What was the percent of increase

The number 34 is 21 25 of what number The number 34 is 21 25 of Type an integer or a decimal

Use the simple interest formula 1 Prt and elementary algebra to find the missing quantities in the table below 1 1275 1275 P 8500 P 8500 3 r 3 t years point s possible www

Use the formula for computing future value using compound interest to determine the value of an account at the end of 9 years if a principal amount of 2 000 is deposited in an account at an annual interest rate of 5 and the interest is compounded quarterly The amount after 9 years will be Round to the nearest cent as needed E

a 2x 3x y 5 Jadratics using the quadratic formula b 5x 80 y

Vladimir Guerrero Jr hit a massive homerun The height h in meters of the ball is given by h t 1 2 20t 5t2 where t is the time in seconds a At what height did Vladimir hit the ball at b What is the maximum height of the ball c How long is the ball in the air Smu laring of 16 2 127250 To 800 m ribes

1 State the domain range for each of the following relations and if it is a function or not a 2 1 1 0 0 1 1 0 2 1 b 2 1 1 0 0 1 1 0 2 1 c 00 M d c x if f x 11 def 11 g f h I WI 2 Given f x 2x 1 and g x x 1 find a f 2 b g 3 e d x if f x 6

equation h t 5t 100t a What is the height of the flare after 3 seconds b What is the maximum height the flare reached

3 Solve for the roots by factoring a x 9x 18 0 d 0 5a 18a 9 g 0 6x 5x 6 b x 3x 26 8 4a 4a 1 e 6x 54 0 h 6a 25 25a 4 Determine the nature of the roots a 4a 3a 7 0 d 04111 c x x 42 0 f 0 8n 20n i 100 16x 60x b 2x 7x 3 0 d 3b 2b 9

5 pts If f x is a linear function f 3 2 and f 1 3 find an equation for f x

8 10 pts Find the average rate of change of f x x x 6 from x 0 to x 3

3 5 pts Find the polynomial function g x such that all of the following hold a g x has a zero at x 3 with multiplicity 1 b g x has a zero at x 2 with multiplicity 2 g x has a zero at x 1 with multiplicity 2 The graph of g x goes through the point 0 24 Your answer should be a function definition not a graph C

The quantity supplied S and quantity demanded D of I shirts at a concert are given below and D P 1000 25P where P is the price of the T shirts a Please draw the demand curve and supply curve on the same axes 2 b What is the equilibrium price 1 c What is the equilibrium quantity demanded and quantity supplied 1 S P 200 50P

1 5 pts Graph one continuous function f x such that all of the following hold a C f x is increasing on 2 f x is constant on 2 4 f x is decreasing on 4 6 f x is increasing on 6 00

On Saturday 180 vehicles visited Lana s Car Wash Of those vehicles 3 out of every 4 were cars and the rest were trucks How many trucks visiting Lana s Car Wash on Saturday TYPE THE NUMBER ONLY

Do men really spend more money on St Patrick s Day as compared to women A recent survey found that men spend an average of 43 87 while women spend an average of 29 54 Assume that these data were based on a sample of 100 men and 100 women and the population standard deviations of spending for men and women are 32 and 25 respectively Which of the following is the correct value of test statistic Multiple Choice O tdf 3 53 Z 3 53 z 3 53

A fast food franchise is considering building a restaurant at a busy intersection A financial advisor determines that the site is acceptable only if on average more than 300 automobiles pass the location per hour The advisor tests the following hypotheses Ho H 300 HA H 300 The consequences of committing a Type Il error would be that Multiple Choice O the franchiser builds on an acceptable site the franchiser does not build on an acceptable site the franchiser builds on an unacceptable site the franchiser does not build on an unacceptable site

Vermont based Green Mountain Coffee Roasters dominates the market for single serve coffee in the United States with its subsidiary Keurig accounting for approximately 70 of sales Rivals Try to Loosen Keurig s Grip on Single Serve Coffee Market Chicago Tribune February 26 But Keurig s patent on K cups the plastic pods used to brew the coffee is expected to expire this year allowing other companies to better compete Suppose a potential competitor has been conducting blind taste tests on its blend and finds that 47 of consumers strongly prefer its French Roast to that of Green Mountain Coffee Roasters After tweaking its recipe the competitor conducts a test with 144 tasters of which 72 prefer its blend The competitor claims that its new blend is preferred by more than 47 of consumers to Green Mountain Coffee Roasters French Roast Which of the following should be used to develop the null and alternative hypotheses to test this claim Multiple Choice O Ho p 0 47 HA P 0 47 Ho p 0 47 HA P 0 47 Ho 72 HA 72 Ho p 0 50 HA P 0 50

A television network is deciding whether or not to give its newest television show a spot during prime viewing time at night If this is to happen it will have to move one of its most viewed shows to another slot The network conducts a survey asking its viewers which show they would rather watch The network receives 827 responses of which 428 indicate they would like to see the new show in the lineup Which of the following is an appropriate hypotheses to test if the television network should give its newest show a spot during prime time at night Multiple Choice Ho p 0 50 HA P 0 50 Ho p 0 50 HA P 0 50 Ho p 0 50 HA P 0 50 Ho p 0 50 HA P 0 50 H

The Institute of Education Sciences measures the high school dropout rate as the percentage of 16 through 24 year olds who are not enrolled in school and have not earned a high school credential Last year the high school dropout rate was 8 1 A polling company recently took a survey of 1 000 people between the ages of 16 and 24 and found that 6 5 of them are high school dropouts The polling company would like to determine whether the dropout rate has decreased When testing whether the dropout rate has decreased the appropriate hypotheses are Multiple Choice Ho p 0 065 HA p 0 065 Ho p 0 065 HA P 0 065 Ho p 0 081 HA P 0 081 Ho p 0 081 HA P 0 081

1 point Let A 2 4 6 and B 3 4 9 12 For each of the elements shown below determine which of the listed Cartesian products the element belongs to Select all that apply a 4 2 OA BX A B AX A C Ax B D Bx B DE None of the above b 4 4 DA Ax B B AX A C Bx A D Bx B E None of the above c 2 3 A Ax B B Bx B OC Bx A D AX A E None of the above d 2 2 DA Ax B DB Ax A C Bx A D Bx B

Mr Sanchez is making punch for a party using a recipe that calls for 4 cups of seltzer for every 6 cups of lemonade If he wants to make a total of 120 cups of punch how many cups of seltzer will he need O 48 cups of seltzer O 300 cups of seltzer O 200 cups of seltzer O 72 cups of seltzer 2

3 5 pts Identify Circle whether the following situations are binomial or not If they are identify n and p If they are not please explain why not Situation We will draw 10 cards from a standard deck without replacement and count how many face cards we picked We will roll a dice 10 times and count how many times we roll a 1 or a 6 A medication has been shown to be 87 effective in the general population In a trial of 100 patients we will count how many of them the treatment is effective for P Probability of success Probability of getting 106 of favorable outcomes total of outcomes Binomial If so what are n and p If not why not Not Binomial Not Binomial Not Binomial Not The probability of drawing a face card changes It follows a hypergeometric distribution since you are drawing without placement from a finite population The trials from each time rolling a die are independent because the probability of success is the same for each trial This is binomial distribution p 1 3 n 10 N of times dice rolled n 10

1 Draw the graph of a polynomial function that has all of the following characteristics f 2 40 f 3 0 and f 4 0 The y intercept is 0 f x 0 when x 3 and 0 x 4 f x 0 when 3 x 0 and x 4 The range is the set of real numbers

An object moves in simple harmonic motion with period 5 seconds and amplitude 6 cm At time t 0 seconds its displacement d from rest is 0 cm and initially it moves in a negative direction Give the equation modeling the displacement d as a function of time t TT 3 16 co

A person sitting on a Ferris wheel rises and falls as the wheel turns Suppose that the person s height above ground described by the following function h t 21 2 19 7 cos 1 1t In this equation h t is the height above ground in meters and I is the time in minutes Find the following If necessary round to the nearest hundredth Frequency of h revolutions per minute Minimum height above the ground meters Time for one complete revolution minutes X

Scientists are studying the temperature on a distant planet They find that the surface temperature at one location is 20 Celsius They also find that the temperature decreases by 3 Celsius for each kilometer you go up from the surface Let 7 represent the temperature in Celsius and let H be the height above the surface in kilometers Write an equation relating T to H and then graph you equation using the axes below Equation 0 0 X 0 0 8 5 2547 154 10 X 3

Eric is driving on the highway He begins the trip with 12 gallons of gas in his car The car uses up one gallon of gas every 20 miles Let G represent the number of gallons of gas he has left in his tank and let D represent the total distance in miles he has traveled Write an equation relating G to D and then graph your equation using the axes below Equation 14 12 G 10 14 0 0 X S

Write the equation of a sine or cosine function to describe the graph tnt 0 5 J 0 0 X 19 sin

is driving to Chicago Suppose that the distance to his destination in miles is a linear function of his total driving time in minutes Chau has 68 miles to estination after 24 minutes of driving and he has 58 4 miles to his destination after 36 minutes of driving How many miles will he have to his destination 50 minutes of driving Remaining distance in miles Driving time in minutes miles

ppose that the credit remaining on a phone card in dollars is a linear function of the total calling time in minutes When graphed the function gives a lin th a slope of 0 16 See the figure below ere is 34 96 in credit remaining on the card after 31 minutes of calls How much credit was there after 24 minutes of calls Remaining credit in dollars 3496 Calling time

2 4 4b Given A 1 2 1 1 3 0 1 0 5 b Find a matrix B such that AB 1 1 2 0 1 1

Find the necessary sample size Weights of women in one age group are normally distributed with a standard deviation o a 17 lb A researcher wishes to estimate the mean weight of all women in this age group Fin how large a sample must be drawn in order to be 90 percent confident that the sample mean will not differ from the population mean by more than 2 0 lb O 208 O 278 O 194 O 196

The Sugar Sweet Company is going to transport its sugar to market It will cost 4200 to rent trucks and it will cost an additional 150 for each ton of sugar transported Let C represent the total cost in dollars and let S represent the amount of sugar in tons transported Write an equation relating C to S and then graph your equation using the axes below Equation 0 0 4000 500 3000 4500 4000 3500 3000 2500 2000 1500

Module Knowledge Check Write an equation of the form y a sinbx or y a cosbx to describe the graph below 0 51 NLC 9x 2 8 sin cos 0 0 Question

Ben and Carla Covington plan to buy a condominium They will obtain a 223 000 30 year mortgage at 6 5 percent Their annual property taxes are expected to be 1 950 Property insurance is 510 a year and the condo association fee is 235 a month Based on these items determine the total monthly housing payment for the Covingtons Use Exhibit 7 7 Round your intermediate calculations and final answer to 2 decimal places Total monthly housing payment

Bippy Corporation has 400 in debt and 600 worth of equity First calculuate the capital structure weights by filling in cells E20 E22 and E24 E25 Next calculate the Weighted Average Cost of Capital in cells E27 E29 and E31 Tax rate 25 Cost of debt 6 Cost of equity 10

Suppose A and B are angles in standard position with sin A and sin B Find the exact value of cos A B if A is in Q2 and B is in Q3

6 Use bracket s with the expression 5 3x4 6 2 so that it simplifies to 8 Show your work to prove your solution works

5 Simplify the expression 5 2 8 12 4

4 Simplify as much as possible Leave the final answer in exact form