Basic Math Questions and Answers

1 point 256 is equal to b 16 256 64 256

6 1 point Evaluate the expression 1 1 16384 64 a b x 2 x for x 4 and 3 64 d 67 108 864

Section 1 Knowledge and understanding Directions Select the most correct answer for each of the questions below 3 1 1 point Evaluate 2 2 2 b 32 C 32 d 16

2 1 point Simplify 16646 924 3q3 4623 b J 16g4 964c6 C 16a4 934c9 d 9a4b4c6 16

Find the equation of the tangent line to the graph of f x at the given point f x 24x 40 at 1 8 The equation of the tangent line to the graph of f x at the given point is

Find the derivative of the function y 2x 5 5 4x 1 dy 11

The cost of producing x bags of dog food is given by C x 700 400 15x x where 0 x 5000 Find the marginal cost function The marginal cost function is C x Use integers or fractions

Find the derivative of the function y 1 7x

Find the derivative of the function y 8 9x 5 dx

se the quotient rule to find the derivative of the given function 71 21 5t 8 f t

The magnitude and direction of two forces acting on an object are 70 pounds S54 E and 50 pounds N62 E respectively Find the magnitude to the nearest hundredth of a pound and the direction angle to the nearest tenth of a degree of the resultant force

Use the quotient rule to find the derivative of the given function x 6x 1 x 9 y

Find the derivative of the function y 7x 2 2x 5

se the product rule to find the derivative of the given function y 5x 3 3x 4

3 1 Sketch one cycle of the graph of y 3 sin x 90 Include an appropriate scale on each axis

23 Is this the curve y cos x 60 C If it is provide evidence to support it If it isn t explain why it isn t 1 nom 60 240 180 120 60 120 180 X 240 300 360

5 The following table lists average monthly high temperatures C in St Johns NF for one year Feb Mar Apr 62 52 May Jun 79 87 Jul Aug Sep Oct Nov Dec 84 74 60 50 72 93 93 a Determine a sine or cosine equation to model this data Jan 47 b Graph your equation below Average Monthly High Temperatures for Oklahoma City OK Temperature Fahrenheit 100 90 228898899 80 70 60 50 40 30 20 10 10 Month January 1 6 B c Determine an equivalent sine or cosine function that models this data If you used sine in part a use cosine here If you used cosine in part a use sine here 12 14 16 18

8 Determine the period of the function y 60 sin sin 19 x 360 120

2 Write an equation to represent the sinusoidal function in the following graph Sine Function 13 K 60 60 120 ANNA 240 180 120 180 240 300 360

To determine the surface area of a cube multiply the length of one side by itself and then by six since a cube has six equal sides The surface are of a sphere can be calculated using the formula 4tr where r is the radius of the sphere By comparing the surface areas of the cube and sphere we can determine which shape is more efficient in terms of material usage Choosing a shape with a slightly smaller surface area can hel minimize the material required and reduce production costs For example a company manufacturing tree ornaments would perform these calculations to determine the most cost effective shape Similar a company producing food packaging might nee to choose between rectangular boxes or cylindrical containers By analyzing the surface areas of these shapes they can optimize their

Number of people who completed program 13 500 12 000 10 500 9 000 7 500 6 000 4 500 3 000 1 500 y y f x t 0 0 1 2 3 4 5 6789 Years after 2008 A 2008 to 2009 B 2010 to 2011 C 2013 to 2014 D 2016 to 2017 A 8 The graph of the exponential function f shown models the number of people who completed the United Services Military Apprenticeship Program in a given year over a 10 year period According to the model between which two years did the number of people completing the program increase the most

If Leah wants to earn interest of 3 481 55 on his 11 000 00 savings in 4 years at wh nominal interest rate compounded quarterly do you suggest he invests his money

The following transactions were selected from the records of Evergreen Company July 12 Sold merchandise to Wally Butler who paid the 1 000 purchase with cash The goods cost Evergreen Company 600 July 15 Sold merchandise to Claudio s Chair Company at a selling price of 5 000 on terms 3 10 n 30 The goods cost Evergreen Company 3 500 July 16 Sold merchandise to Otto s Ottomans at a selling price of 3 000 on terms 3 10 n 30 The goods cost Evergreen Company 1 900 July 23 Received cash from Claudio s Chair Company for the amount due from July 15 July 31 Received cash from Otto s Ottomans for the amount due from July 16 Required Compute the amount of Net Sales to be reported for the month ended July 31 Answer is complete but not entirely correct

A THE SINE LAW FOR ACUTE TRIANGLES The sine law holds true for any triangle not just right triangles but it is reserved for non right triangles When solving for an unknown side length The sine law is only useful when an In other words you need a full When solving for an unknown angle and other is given

Which reasoning process is shown in the following example We examine the email addresses of 1000 people No two individuals from this group of people have identical email addresses We conclude that for all people no two people have identical email addresses O A reasoning by counterexample B theoretical reasoning C deductive reasoning D inductive reasoning

c AABC given ZA 78 ZB 90 and a 5 9 cm

5 Determine the measure of ZA in each triangle a b A 4 5 cm 8 3 cm B 6 1 cm C 4 7 cm B C 7 4 cm 5 9 cm A c A 8 2 cm 9 4 cm E 15 8 cm

1 Eddie works in the data processing department at the local medical center He is required to keep a weekly time card Use the information in the figure below to calculate the number of hours worked for a each day and b the week Employee Time Card Employee Name Eddie Invin DATE Sun Mon 12 13 Tue 12 14 Wed 12 15 Thur 12 16 IN 8 15 AM 8 30 AM 8 35 AM 8 15 AM OUT 12 00 PM 12 30 PM 12 50 PM 12 10 PM Needham Medical Center Department Data Processing IN OUT 12 30 PM 1 10 PM 1 30 PM 12 45 PM 4 30 PM 5 10 PM 5 00 PM 4 20 PM TOTAL

6 In this question you may take for granted the usual properties of the exponential function and d d r a Let a 0 and consider g x a Show that Here I am identifying log ee VER d d9 x log a a In Hint Write a eloga and use the chain rule b Consider the function h x 1 x 2 Show that h x 1 Hint log 2 0 and 20 for all x R c Show that there exists some x 2 0 such that h x 0 Hint Intermediate Value Theorem d Prove that the root of h in the previous part is the unique root of h on R Hint Part b says that h is strictly increasing see Lemma 4 2 1 of the notes

An online test of English spelling looked at how well people spelled difficult words The bar graph to the right shows how many people per 100 spelled each word correctly a Estimate the number of people per 100 who spelled weird correctly Round to the nearest 5 b In a group consisting of 8717 randomly selected people estimate how many more people can correctly spell weird than inoculate a The approximate number of people per 100 who spelled weird correctly is 85 Type a whole number b In a group consisting of 8717 randomly selected people approximately inoculate Type a whole number Number of People per 100 Spelling Various Words Correctly weird cemetery accommodation harass supersede inoculate 0 20 40 60 80 100 Number of people per 100 more people can correctly spell weird than e

Which of the following materials are used as fibers in fiber reinforced plastics four best answers aluminum oxide boron O cast iron O E glass O epoxy O Kevlar 49 O polyester silicon answers a b d and f

Tutorial Exercise Suppose a computer manufacturer has the total cost function C x 71x 3 300 and the total revenue function R x 371x a What is the equation of the profit function P x for this commodity b What is the profit on 343 items Step 1 c How many items must be sold to avoid losing money a What is the equation of the profit function P x for this commodity Recall that to find the total profit P x we subtract the total cost C x from the total revenue R x Select the equation for the profit function OP x R x C x OP x C x R x P x R x C x OP x C x R x OP x R x x C x

x 5y 25 10 5 x y y 10 5 10 1 y x 5 5 X 10

e g 1 Calculate each side length x a 70 2 5 cm b 12 m X 40

10 The slope Select negative b positive 0 undefined 10 5 5 10 5 10 y 10 5 10 10 X

The circle graph shows the most important problems for the 11 301 952 high school teenagers in a country Without using a calculator estimate the number of high school teenagers for whom drugs is the most important problem Drugs is the most important problem for approximately how many of the high school teenagers OA 2 200 000 OB 1 100 000 OC 6 600 000 D 8 800 000 Most Important Problems for High School Teenagers Doing Well in School 11 Social Pressures and Fitting in Drugs 22 Others 30 Getting along with Parents 2 Getting into College 4 Sexual Issues 3 Crime and Violence in School DOD

Determine the following estimate without using a calculator Then use a calculator to perform the computation necessary to obtain an exact answer How reasona is your estimate when compared to the actual answer A full time employee who works 40 hours per week eams 26 50 per hour Estimate that person s annual income CIS Round 52 weeks to 50 weeks per year and round the hourly wage to the nearest dollar for the estimate The estimate of annual income is Round to the nearest thousand as needed Use 52 weeks per year for the actual income The actual annual income is How reasonable is your estimate when compared to the actual answer Select the correct answer below and fill in the answer box to complete your choice OA The estimate is a little higher than the actual result The difference is OB The estimate is a little lower than the actual result The difference is

The percentage of U S college freshmen claiming no religious affiliation has risen in recent decades The bar graph shows the percentage of first year college students claiming no religious affiliation for four selected years from 1980 through 2012 a Estimate the average yearly increase in the percentage of first year college females claiming no religious affiliation Round the percentage to the nearest tenth b Estimate the percentage of first year college females who will claim no religious affiliation in 2025 Percentage of First year US College Students Claiming No Religious Affiliation Percentage 30 25 Males Females 20 15 10 2 4 69 5 0 1980 16 6 14 5 3 8 10 3 26 2 2000 2012 a The average yearly increase in the percentage of first year college females claiming no religious affiliation is approximately per year Round to the nearest tenth as needed

Identify a pattern in the list of numbers Then use this pattern to find the next number 4 12 36 108 324 A 540 B 972 OC 540 972

Nancy s car cost 14 400 She has enough money to make a down payment of 5 000 Her monthly payments are 210 for 48 months How much greater is the deferred price than the original price O 860 O 10 080 O 680 4 320 K

Chad walks along a road which can be modeled by the equation y 4x where 0 0 represents his starting point When he reaches a certain point A he turns right so that he is traveling perpendicular to the original road until he stops at the point 119 0 What was the point A where Chad turned Provide your answer below

The following Cool Sky reports the following for its first year of operations The company produced 44 000 units and sold 36 000 unit at a price of 140 per unit Direct materials Direct labor Variable overhead Fixed overhead Variable selling and administrative expenses Fixed selling and administrative expenses b Assume the company uses variable costing Prepare its income statement for the year under variable costing Income Statement Variable Costing Sales Less Variable expenses Variable cost of goods sold Variable selling and administrative expenses Contribution margin Less Fixed expenses 60 per unit 22 per unit 8 per unit 528 000 per year 11 per unit 105 000 per year Fixed overhead Fixed selling and administrative expenses

3 4 If a and b are positive integers such that the least common multiple of a b and a b is 1 000 what is the greatest common factor K 1 000 F 10 G 25 H 100 J 200

State if each angle is an inscribed angle If it is name the angle and the intercepted arc 2 1 3 D W 4 M

Find the measure of the arc or angle indicated 5 7 B 80 PE 6 8 W 49 B 70

A rock is thrown upward with a velocity of 21 meters per second from the top of a 22 meter high cliff and it misses the cliff on the way back down When will the rock be 9 meters from ground level Round your answer to two decimal places Gravity Formula

Solve the following quadratic equation by using the quadratic formula If needed submit your answer as a fraction reduced to lowest terms or round your answer to two decimal places Answer 3z 2z 4z 7 Keypad Keyboard Shortcuts

Solve the following polynomial equation Answer 8z 27 0

Solve the quadratic equation by the square root method and write the solutions in radical form Simplify the solutions 8x 20 50 nswer

Let f t be a function on 0 co The Laplace transform of f is the function F defined by the integral F s 0 1 e 1 0 t 3 2 3 t 00 Set up the integral F s F s st t dt Use this definition to determine the Laplace transform