Math - Others Questions

Suppose that the height in centimeters of a candle is a linear function of the amount of time in hours it has been purning After 15 hours of burning a candle has a height of 22 centimeters After 29 hours of burning its height is 16 centimeters What is the height of the candle after 19 hours Candle height in cm Burning time in hours centimeters X 3

Now we substitute our function of x C x ln 9x 1 250 Step 6 Now we know the fixed costs are 250 Thus we have the following C 0 250 Plugging this into the cost function we can find K 250 C 0 In 0 C x 9 250 K In 19x 1 K 0 X 0 0 1 K 1 Step 7 Finally we can determine the cost function K

Drives Co sells portable hard drives They can sell 800 drives when the price is 65 drive and they can sell 920 drives when the price is 35 drive If x represents the number of drives sold determine the following a What is Drive Co s revenue function R x b What is the price per drive in dollars when revenue is maximized c What is the maximum profit in dollars made from the sale of these drives if Drive Co incurs production costs of 205 per drive and has fixed costs of 695

The radioactive element carbon 14 has a half life of 5750 years A scientist determined that the bones from a mastodon had lost 85 5 of their carbon 14 How old were the bones a the time they were discovered The bones were about years old Round to the nearest integer as needed

13 bed bok int rences 3 Complete the below table to calculate the balance sheet data in trend percents with 2019 as base year Note Round your percentage answers to 2 decimal places Assets Current assets Long term investments Plant assets net Total assets 178 806 148 533 123 060 Liabilities and Equity Current liabilities Common stock Other paid in capital Retained earnings Total liabilities and equity KORBIN COMPANY Balance Sheet Data in Trend Percents December 31 2021 2020 and 2019 2021 2020 2019 100 00 100 00 100 00 100 00 100 00 100 00 100 00 100 00 100 00

Suppose that 10 671 is invested at an interest rate of 6 2 per year compounded continuously a Find the exponential function that describes the amount in the account after time t in years b What is the balance after 1 year 2 years 5 years 10 years c What is the doubling time a The exponential growth function is P t Type exponential notation with positive exponents Do not simplify Use integers or decimals for any numbers in the equati

31 Jake makes a blend of chocolates for the bake sale The dark chocolates are 4 50 per pound and the milk chocolates are 6 00 per pound Jake sells more than 12 pounds total Jake also sells less than 68 50 worth of chocolates Using this information choose the solution set that would be found in the overlapping areas of a graph of Jake s sales O 10 pounds dark 3 pounds milk 11 pounds dark 4 pounds milk 8 pounds dark 3 pounds milk O None of these satisfy both inequalities

ppose that a household s monthly water bill in dollars is a linear function of the amount of water the household uses in hundreds of cubic feet HCF Whe phed the function gives a line with a slope of 1 45 See the figure below he monthly cost for 16 HCF is 46 91 what is the monthly cost for 19 HCF Monthly cost in dollars 46 91 16 Water usage in HCF

2 ABCO 3 A C D EFI G H I 3200 2850 3000 2300 2550 2600 2400 2300 2700 1800 2150 2000 2700 2450 2400 2600 2700 2300 Carolina North ABC Carolina Central DEF Carolina South GHI New Alignment Carolina West ADG Carolina Central BEH Carolina East CFI Part I Critical Thinking of the activity on the previous page 1 In the previous election how many of the 3 seats did each party win Total Votes Total Votes If the new alignment is used and the voting pattern is similar to the previous election how many of the 3 seats will each party win Based upon this difference which party do you believe is proposing the change Attempt to come up with a situation where a type of gerrymandering might occur

Suppose you own a toy company Toy trains sell for 9 20 and toy ponies sell for 5 20 Perhaps you are going to package up the trains and ponies and ship them to a store in your own car You know you can fit no more than 87 toys in your car With these constraints can you take enough toys to the store to sell at least 900 worth O yes O no

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Interest is compounded semianually Find the amount in the account after the given time Principal Rate of Interest Time 1000 3 3 years The amount in the account is Round to the nearest cent

5 Graph the following system on a sheet of paper or graphing utility x 1 and y 3 Determine which of the following points if any satisfy the system More than one answer may be correct check all correct answers 6 6 1 9 5 3 2 9 0 3 4 6 0 0 None of these points satisfy the system

1 Summer says there are 2 hundreds in 3 267 Isaiah says there are 32 hundred in 3 267 The teacher says they are both right How can that be so Explain 1 Fill in the blanks and complete the equations for each array 12 X 4 40 10 3 100 X 5

In a town whose population is 4300 a disease creates an epidemic The number of people N infected t days after the disease has begun is given by the function 4300 N t Complete parts a through c below 0 5t 1 19 6e a How many are initially infected with the disease t 0 Round to the nearest whole number as needed

The points 4 27 and 9 r lie on a line with slope 5 Find the missing coordinate r r 08

Use the compound interest formula to find the account balance A where P is principal r is interest rate n is number of compounding periods per year t is time in years and account balance P T compounded 1 1 59 473 22 Quarterly 82 t The account balance is approximately Simplify your answer Type an integer or decimal rounded to two decimal places as needed

1 Suppose that cos x and cos x x 1 2 7 3 sin x 2 2 Make use of the following facts The period of the sine and cosine is 27 The sine is odd and the cosine is even x 1 cos x for all x Express numbers in exact form Use symbolic notation and fractions where needed Simplify your answer completely R Find the value of sin x 2 3

The first three terms of a sequence are given Round to the nearest thousandth if necessary 13 19 25 Find the 48th term

13 ou are given the graph of a function of the form y A sin B x C with A 0 y 2 R amplitude 8 phase shift 8 4 8 75 27 Identify the amplitude period and phase shift Give the phase shift from the interval 0 2 Give exact answers Use symbolic notation and fractions where needed X period T

MP Reasoning When might you estimate the difference of 603 476 ar 335 291 to the nearest hundred to th nearest hundred thousand

2 REQUIRED You decide to dye your hair various colors for Halloween If you dye 1 3 of it blue 1 4 pink and 1 4 black how much of your original hair color is left 5 6 1 3 1 12 S 20

Postulate 2 6 Plane Line Postulate If two points lie in a plane then the line containing them lies in the plane 2 7 Plane Intersection Postulate If two planes intersect then their intersection is a line Notes 1 If B Extra Practice In Exercises 1 and 2 state the postulate illustrated by the diagram then Example B ER Points D and E lie in plane R so DE lies in plane R The intersection of plane Sand plane T is line l

Evaluate the expression P 7 2 P 7 2

151 121 The solution is

pictogram shows the favourite chocolate of a group of students The number who chose snickers twix have not yet been included Use the clues below to complete the pictogram and the key Wispa OOP Snickers Clues A 26 students said either wispa or bounty B 36 students said snickers C 72 students took part in the survey Twix Bounty D key O 11

A group of people took part in a quiz Table 1 shows the scores of everyone who played From the statements below shade FOUR that are DEFINITELY TRUE A Twelve people took part in the quiz B Nobody scored 23 marks C Everybody scored more than 19 D Twenty four people E The lowest score was 0 F The quiz was out of 25 G At least one person scored more than 24 marks H The most common score was 24 points Table 1 Score Freque 20 21 22 23 24 25 3

1 point Find two vectors and 2 whose sum is 3 2 where V is parallel to 5 2 while U2 is perpendicular to 5 2 U1 V and

Q1 A manager surveys his employees to find out how they travel to work Number of people 25 20 15 10 S Walk Cycle Bus a What is the least popular method of transport b What is the most popular method of transport c Calculate the total number of employees Car

Find a unit vector u in the direction opposite of 3 9 9

A group of parents were asked how far they live from their children s school The results are below Complete the grouped frequency table for this data 0 5 1 7 0 4 1 2 0 3 0 1 0 3 0 9 8 1 5 1 5 3 4 4 5 0 5 10 5 Distance in miles x Frequency f 0 x 1 1 x 2 2 x 5 5 x 10 10 x 20

The table shows how many students take part in after school clubs during the week Complete the pictogram key O 4 Monday Tuesday Wednesday Thursday 8 10 14 9 Monday Tuesday Wednesday Thursday

point 3 possible Determine the number of ways to perform the task described Eight players are to be selected from a 24 player baseball team to visit schools to support a summer reading program In how many ways can this selection be made There are different ways 8 players can be selected from a 24 player baseball team Simplify your answer Type a whole number

1 point What is the unit vector for the vector 17 53 10 76 6 34 000 Answer

1 point Find the length of OR R 2 9 7 OR

1 point Given the matrix a 9 87 A a 4 4 8 2 a find all values of a that make A 0 Give your answer as a comma separated list Values of a 1

assign7 Problem 5 1 point Determine whether the three points P 1 4 6 Q 2 2 3 R 3 2 0 are collinear by computing the distances between pairs of points Distance from P to Q Distance from Q to R Distance from P to R Are the three points collinear y n Note You can earn partial credit

1 point Which of the following vectors is perpendicular to a 1 2 3 and b 1 1 2 A 7 1 3 OB 7 1 3 OC 7 1 3 OD 1 2 6 E 5 5 10 F at least two of the above G none of the above

v 10 9 6 w 2 9 10 Find the cocin

1 point Find a vector orthogonal to both 3 1 0 and to 0 1 2 of the form 00

1 point Find a b if a 3 4 4 and b 0 5 1 a b Is the angle between the vectors acute obtuse or right

assign7 Problem 1 1 point Several unit vectors 7 s t u and e in the xy plane not three dimensional space are shown in the figure Using the geometric definition of the dot product are the following dot products positive negative or zero You may assume that angles that look the same are the same 1 n e 2 7 S 3 e s 44 5 5 t u 6 n t 7 F u 8 e F it 3 Click on graph to enlarge TO Note You can earn 10 partial credit for 2 4 correct answers 60 partial credit for 5 6 correct answers and 80 partial credit for 7 correct answers

Find k such that the following matrix M is singular M 4 4 4 9 k 4 10 2 2 2 4

Question 3 of 6 possible This question 5 point s possible Submit quiz The division of student services at a school is selecting two men and two women to attend a leadership conference in Honolulu Hawaii If 10 men and nine women are qualified for the conference this problem is choosing 4 people from a group of 19 yet the answer is not C 19 4 Explain this How does the fundamental counting principle apply here OC There are unequal numbers of men and women OD The combination should be C 4 19 How does the fundamental counting principle apply here Why is the answer not C 19 4 OA Not all choices of four people were acceptable For example it is not possible to select all four women OB Because the answer should use permutations and is P 19 4 OA Multiply the number of women and their number of conference spaces with the number of men and their number of conference spaces OB We first add the number of ways to select the two women and the number of ways to select the two men 2 2 2

0 898 round to Sf

point s possible A town is forming a committee to investigate ways to improve public safety in the town The committee will consist of three representatives from the six member town council three members of a five person citizens advisory board and three of the 12 police officers on the force How many ways can that committee be formed That committee can be formed in ways Submit quiz CIP 2

Evaluate the expression C 12 7 C 12 7

Use the fundamental counting principle The editor of the Video Gamer is selecting 8 video games from 12 possibilities to review in her online column One will be the featured game and the other 7 will be covered in less detail and in no particular order In how many ways can she make her selection There are ways the editor can make her selection Simplify your answer Type a whole number point s possible www 2

4 17 Billing Date Previous Balance 4 27 Payment 4 29 Charge 5 7 Payment The average daily balance is Multiple Choice 910 34 755 17 1 100 700 300 50