Basic Math Questions and Answers

1 15 a Give the definition of the Laplace transform of a function f t defined for t 0 b Use this definition to calculate L f t for f t e t No credit for any other method

Find the exact value of tan 285

a b 26 a b 86 e itli inde a b ve a b asal say lard a api kact r

Solve the triangle b 4 c 6 and B 20 If a triangle exists find the ar Tri 2 9 07

Solve the triangle a 9 b 7 and c 10 If a triangle exists find the area

4 5 oints 01 15 26 Minstrel Manufacturing uses a job order costing system During the month Minstrel purchased 198 000 of raw materials on credit issued materials to production of 195 000 of which 30 000 were indirect Minstrel incurred a factory payroll of 150 000 of which 40 000 was indirect labor Minstrel uses a predetermined overhead rate of 150 of direct labor cost The total manufacturing costs added during the period is Multiple Choice 540 000 470 000 440 000

4 Use Stokes Law to calculate the terminal velocity of an apple released beneath the surface in a tank of water Assume the water has a temperature of 20 C and that the apple is a sphere The sphere has a diameter such that the volume of the sphere is equal to the volume of an apple with average dimensions of a Golden Delicious apple as shown in Table 2 1 The viscosity of the water is 1 01 x 10 kg m s and the density of the water is 998 kg m

Identify the variables as either Qualitative or Quantitative The population of a town The colors of the houses in a city Flavor names of ice cream at Baskin Robbins

Find the unknown lengths for the similar triangles below 8 Y X 22 5 ft 15 ft a 61 20 ft 25 ft ft If needed round to 2 decimal places I ft If needed round to 2 decimal places a

For the study described below identify the sample A bank manager wants to know the average amount of time customers of his bank have to wait in line As such 300 customers were polled and asked their average wait time at the bank Of these 27 were extremely dissatisfied with the amount of time they had to wait in line in recent months The 27 people who were dissatisfied The customers who were waiting in line All of the bank customers The 300 customers polled

For the study described below identify the population 1500 American women working for companies were polled to determine the percentage that felt that women were under represented in management positions in their company All American women working for large companies All American women The 1500 American women polled O The percentage of American women working for large companies

Find the LCD of the following expressions Write LCD in factored form 3 g 11g 30 LCD and 5g g 5g 6

3 5 m I y lengths for the similar triangles below 10 5 m 13 5 m Q 4 9 m y X m If needed round to 2 decimal place m If needed round to 2 decimal place a

Determine the parent function from which the graph of the function shown below can be otained identify each transformation that can be applied to the parent function in order to obtain the grap function shown below g x 5 6 a Choose the correct parent function 6 5 G 5 Oy Oy 1 Oy logg x Oy loga z OF V b Choose the correct transformation Reflections Select an answer c Choose the correct transformation Stretches Compressions Select an answer d Choose the correct transformation Vertical Shifts Select an answer con below e Choose the correct transformation Horizontal Shifts Select an answer

atch the formula of the exponential function to its graph Graphs of Exponential Functions P 5 435 4 3 54 5 4 3 2 1 4 2 3 4 54 54 4 22 3 2 A 2 3 4 1 54 54 4 3 2 3 2 1 2 2 13 2 3 4 5 Formulas for the Graphs 2 f x 1 b f x 2 c f x 2 d f x

Question 2 4 The point P is on the unit circle If the y coordinate of P is 5 Question Help Video and P is in quadrant III then

Find an angle between 0 and 360 that is coterminal with the given angle 674 is coterminal to 247 is coterminal to 755 is coterminal to 5203 is coterminal to

Question 8 18 Convert to degrees 7 Convert 758 to radians

Question 4 A sector of a circle has a central angle of 150 Find the area of the sector if the radius of the circle is 9 cm

Question 3 Convert the angle 150 to radians Give the exact value and use pi for

Question 2 The half life of Radium 226 is 1590 years If a sample contains 100 mg how many mg will remain after 2000 years mg Give your answer accurate to at least 2 decimal places

Determine whether the two events are disjoint for a single trial Hint Consider disjoint to be equivalent to separate or not overlapping Randomly selecting a car from the vehicle assembly line and getting one that is free of defects Randomly selecting a car from the vehicle assembly line and getting one with a dead battery Choose the correct answer below its 0 of 2 OA The events are disjoint The first event is the complement of the second OB The events are not disjoint The first event is not the complement of the second OC The events are disjoint They cannot occur at the same time OD The events are not disjoint They can occur at the same time

What is wrong with the expression P A P A 0 5 Choose the correct answer below O A Based on the rule of complements the sum of P A and P must always be 1 so that sum cannot be 0 5 B Based on the rule of complements the sum of P A and P A must always be P A O C Based on the rule of complements the sum of P A and P A must always be P A O D Based on the rule of complements the sum of P A and P A must always be 0 so that sum cannot be 0 5

Two dice are tossed Find the probability of getting the sum of the dice equal to 4 Hint Draw a tree diagram of the possibilities of two tosses of a die and then find the sum of the numbers on each branch The probability of getting a sum of 4 is Type a whole number or a simplified fraction

Use the given spinner to draw a tree diagram for spinning the spinner once Then use the diagram to find the number of possible outcomes Choose the correct tree diagram below OA A B OB ABCDE O C A BO D O D A B

Minh a psychology student kept a record of how much time she spent studying for each of her 20 point psychology quizzes and her score on each quiz Hours Spent Studying 0 50 0 75 1 00 1 25 1 50 1 50 1 75 2 00 Quiz Score 10 12 13 14 15 18 18 19 A When Minh studied 1 25 hours her quiz score was 14 OB When Minh studied 1 25 hours her quiz score was less than 14 OC When Minh studied 1 25 hours her quiz score was 1 25 14 c Create a scatter diagram of the paired data Choose the correct scatter diagram below A OB Quiz Score 20 Quiz Score O C 0 0 2 Hours Spent Studying Points 1 45 of 2 20 0 Hours Spent Studying G 17 og and O D Outz Score 204 0 0 2 Hours Spent Studying 20 of Hours Spent Stutying Q Q Save

Graphs of Logarithmic Functions 3 2 54321 5 2 3 4 54 4 3 2 1 5 4 3 2 1 4 2 3 4 54 5 4 3 2 1 5432 1 24 3 5 2 1 2 3 4 5 Formulas for the Graphs a f x log x b f x log x x logi x d f x log x

The table shows the worldwide box office in billions of dollars for the movie industry during the years shown Year 2000 2002 2004 2006 2008 Box office in billions of dollars 22 1 24 5 25 7 26 8 28 5 2002 24 5 Type an ordered pair What is the ordered pair that corresponds to the third row of data given in the table 2004 25 7 Type an ordered pair What is the ordered pair that corresponds to the fourth row of data given in the table 2006 26 8 Type an ordered pair What is the ordered pair that corresponds to the fifth row of data given in the table 2008 28 5 Type an ordered pair b Write the meaning of the ordered pair 2008 28 5 Choose the correct answer below OA In the year 2008 the worldwide box office was less than 28 5 billion OB The worldwide box office was equal to 2008 28 5 billion OC In the year 2008 the worldwide box office was 28 5 billion more than the previous years 503 5 billion

Minh a psychology student kept a record of how much time she spent studying for each of her 20 point psychology quizzes and her score on each quiz Hours Spent Studying 0 50 0 75 1 00 1 25 1 50 1 50 1 75 2 00 Quiz Score 10 12 13 HASBB9 14 15 18 18 19 vvnat is the orderea pair that corresponds to the fifth row of data given in the table 1 5 15 Type an ordered pair What is the ordered pair that corresponds to the sixth row of data given in the table 1 5 18 Type an ordered pair What is the ordered pair that corresponds to the seventh row of data given in the table 1 75 18 Type an ordered pair What is the ordered pair that corresponds to the eighth row of data given in the table 2 19 Type an ordered pair b Write the meaning of the ordered pair 1 25 14 Choose the correct answer below O A When Minh studied 1 25 hours her quiz score was 14 OB When Minh studied 1 25 hours her quiz score was less than 14 OC When Minh studied 1 25 hours her quiz score was 1 25 14

Construct a scatter diagram using the data table to the right This data is from a study comparing the amount of tar and carbon monoxide CO in cigarettes Use tar for the horizontal scale and use carbon monoxide CO for the vertical scale Determine whether there appears to be a relationship between cigarette tar and Co Construct a scatter diagram O A 20 16 12 ACO 0 4 8 121620 8 4 0 Tar OB ACO 20 16 12 8 4 Tar 0 0 4 8 121620 CE O C 20 16 ACO 12 8 4 0 0 4 8 121620 Tar Q Q Tar 16 10 1 12 5 CHRIFT CO 15 12 11 O D ACO 20 96260 16 123 8 45 0 Tar 10 8 16 18 10 Tar 0 4 8 121620 OFFEN CO 10 11 17 18 12 Full data set Tar 2 THS66 9 11 9

0 10 pts 3299 Details dentify the domain of the following functions a f x log 2x 3 Domain b f x ln 7x 7 Domain c f x log5 6x 7

Minh a psychology student kept a record of how much time she spent studying for each of her 20 point psychology quizzes and her score on each quiz Hours Spent Studying 0 50 0 75 1 00 1 25 1 50 1 50 1 75 2 00 Quiz Score 10 12 13 14 15 18 18 19 G a Write this paired data as a set of ordered pairs of the form hours spent studying quiz score What is the ordered pair that corresponds to the first row of data given in the table Type an ordered pair

A student kept a record of how much time he spent studying for each of his 20 point health quizzes and his score on each quiz Complete parts a through d below Hours Spent Studying 0 50 0 75 1 00 1 25 Quiz Score 9 12 14 14 O B 9 12 14 14 15 18 19 20 0 50 0 75 1 00 1 25 1 50 1 75 1 75 2 00 1 50 15 a Write each paired data as an ordered pair of the form hours spent studying quiz score Choose the set of ordered pairs that represents the paired data in the correct form below OA 9 0 50 12 0 75 14 1 00 14 1 25 15 1 50 18 1 75 19 1 75 20 2 00 OC 0 50 9 0 75 12 1 00 14 1 25 14 1 50 15 1 75 18 1 75 19 2 00 20 1 75 1 75 2 00 18 19 20 K

e table shows the worldwide box office in billions of dollars for the movie industry ing the years shown Year 2000 2002 2004 2006 2008 Box office in billions of dollars 22 1 24 5 25 7 26 8 28 5 a Write this paired data as a set of ordered pairs of the form year box office What is the ordered pair that corresponds to the first row of data given in the table Type an ordered pair

At B R K Match each equation with a graph above log x ex 10 In x a red R b green G c blue B d black K

0 10 pts 399 Details If ln x ln x 5 ln 3x then x

10 10 pts 399 Details For what value of x is the following true log x 14 log x log 14 Your answer is X You may enter the exact value or round to 4 decimal

0 10 pts 399 Details Find the largest value of x that satisfies log x log4 x 4 7 X You may enter the exact value or round to 4 decimal

0 10 pts Solve for x log x log x 3 9 8 Details

For the given set of numbers find the mean the median and the mode If necessary round the mean to one decimal place 0 3 0 4 0 6 0 7 0 7 1 0 0 3 0 8 1 2 The mean is Round to one decimal place as needed

In a mathematics class the following test scores were recorded for a student Find the median 74 83 79 62 65 73 The median is Round to one decimal place as needed www

0 10 pts 399 Details Which of the following are equivalent to log 2 Choose all that apply Olog 18 log 9 1 O log 8 10 logo 20 Olog O Logs 1 2 1 O logb 4

0 10 pts 3299 Details Simplify without a Calculator

Write the first five terms of the geometric sequence Find the common ratio r and write the nth term of the sequence as a function of n a 16 ak 1 ak a 3 a3 34 35 r an

What is the value of ZA A 16 4 B 19 1 C 32 8 4 5 cm 8 5 cm A T 9 5 cm

0 10 pts 399 Details Express the following equations in logarithmic form a 3 9 is equivalent to the logarithmic equation b 10 2 0 01 is equivalent to the logarithmic

0 10 pts 2 99 Find the logarithm log 5 11 Details

0 10 pts 399 Details Solve for x log 27 3 m

Function g x 23x 160 p t 230 1 15 f x 26x100 h x 60 0 9 d y 5 2 Question Help Worked Example 1 Type and Behavior Select an answer Select an answer Select an answer Select an answer Select an answer Video Select an answer Select an answer Select an answer Select an answer Select an answer

0 10 pts 399 Details The graph of the function f x 8 can be obtained from the graph of g x 8 by one of the following actions a shifting the graph of g x to the right 8 units b shifting the graph of g x to the left 8 units c shifting the graph of g x upward 8 units d shifting the graph of g x downward 8 units e reflecting the graph of g x in the x axis f reflecting the graph of g x in the y axis Your answer is input a b c d e or f Is the domain of the function f x still Your answer is input Yes or No The range of the function f x is A the value of A is