Month: August 2021

math questions

Work the following math problem

Question 1

Duke takes a car in for basic service. The service agent says a few extra repairs are needed, so Duke adds the cost of those repairs mentally, rounding to the nearest 10. What is Duke’s total estimate for the repairs? The costs are as follows:

  • Wheel alignment: $82
  • Transmission fluid flush: $157
  • Cabin air filter: $58

Note: 4 or less rounds down, 5 or more rounds up. For example, 14 becomes 10, while 15 becomes 20.

A. 280   B. 290   C. 300   D. 310

Question 2

Many gas stations give a discount for using cash instead of a credit card. A gas station gives a discount of 10 cents per gallon. William plans to pump 14 gallons. How much will William save by paying cash instead of credit card?   A. 10 cents   B. 24 cents   C. 100 cents   D. 140 cents

Question 3

A new company president is said to have caused the company “to do a 180.” Before the new president, the company was losing money. What is the company most likely doing under the new president?   A.  Losing a lot more money   B. Losing a little more money   C. Losing the same amount of money   D. Making money rather than losing

Question 4

Mo is on a baseball team and hears that a ball thrown at a 45 degree angle from the ground will travel the furthest distance. How should Mo release the ball for the furthest travel?   A. Nearly straight ahead, parallel to the ground   B. About halfway between straight ahead and straight up   C. About 2/3 of the way straight up   D. Nearly straight up, directly above his head

Question 5

One rule of thumb in the fast-food restaurant business is a “4 times markup”: The price of a food item should be four times the price of the ingredients used in making the item. If the cost of ingredients used in making a taco is 1.5 dollars, what should be the price of the taco?   A. 6 dollars   B. 7.5 dollars   C. 5.5 dollars   D. 4 dollars

Question 6

Alex invests $2,000 in a company’s stock. After a year, the value of Alex’s stock has increased to $2,500. What rate of return has Alex received?   A. 50%   B. 80%   C. 25%   D. 11%

Question 7

Travel Ez sells dollars at a rate of ($1.40)/(1 euro) and buys dollars at a rate of ($1.80)/(1 euro). At the beginning of a trip, Sophie exchanged $540 to get 300 euros. At the end of the trip she is left with 40 euros, so she exchanges the 40 euros back to dollars. How many dollars will Sophie get in exchange?   A. $72   B. $22   C. $56   D. $28

Question 8

Ryan remembers numbers using images that look somewhat like each number: 0 is a ball, 1 is a stick, 2 is a hanger, 3 is a comb, 4 is a kite, etc. Ryan remembered a 4-digit phone extension with this story: A person uses a hanger to pop a ball, then flies two kites. What number is Ryan likely remembering?   A. 2,044   B. 2,042   C. 2,004   D. 220

Question 9

Convert 2 3/4 to a decimal number.   A. 0.75   B. 1.50   C. 2.3   D. 2.75

Question 10

Consider a cookie recipe in which 1 1/2 cups of chocolate chips are needed to make 25 cookies. Lara wants to double the number of cookies. How many cups of chocolate chips should she use?   A. 1 1/2   B. 2   C. 2 1/2   D. 3

Question 11

Nik needs to estimate how many books will fit in a bin. Each book is 1 ft tall, 0.5 ft wide, and 0.1 ft thick. The bin is 5 feet wide, 2 feet tall, and 3 feet deep. Based on volume only, about how many books will fit in the bin?   A. 6   B. 66   C. 60   D. 60

Question 12

A person buys 28 bottles of orange juice for a party. The store clerk offers cardboard carrying cases for the bottles, each case holding 6 bottles. How many cases are needed, assuming each case should be filled as much as possible and the person will not be carrying any bottles outside of a case?  A. 1   B. 3   C. 4   D. 5

Question 13

A wall is 500 sq. feet. A gallon of paint covers 160 sq. feet. What is an appropriate conversion factor to help determine how many gallons will be needed to paint the wall?    A. (1 gallon)/(160 sq. feet)

B. (1 gallon)/(500 sq. feet)   C. (160 gallon)/(500 sq. feet)   D. (500 gallon)/(560 sq. feet)

Question 14

Jo is on the phone with a gardener who asks about the square feet of Jo’s backyard. Jo counts 20 steps long and 40 steps wide (with each step being about 3 feet). About how many square feet is the backyard?   A. 120 ft2   B. 360 ft2   C. 800 ft2   D. 7,200 ft2

Question 15

Zoey wants to use her iPad throughout a 6-hour flight. Upon takeoff, she uses the iPad for 2 hours and notices that the battery dropped by 25%, from 100% to 75%. How many total hours can Zoey expect from the iPad on a full battery charge? A.  10 hours   B. 4 hours   C. 8 hours   D. 6 hours

Question 16

The recipe for a fruit smoothie requires 2 cups of fruit per 6 cups of yogurt to maintain a 1/3 ratio. While making the fruit smoothie, Suzy accidentally puts 3 cups of fruit into the pitcher. How many cups of yogurt should be put in the pitcher to maintain the ratio of 1/3?   A. 3 cups   B. 9 cups   C. 1 cup   D. 5 cups

Question 17

Nik, a social worker for a county, helps county residents who are struggling with different issues. Nik logs the following hours meeting with clients (c) or doing other work (o):

  • Mon: 6 c, 4 o
  • Tue: 8 c, 2 o
  • Wed: 9 c, 1 o
  • Thu: 7 c, 3 o
  • Fri: Off

What percent of time did Nik spend with clients on Thursday?   A. 10%   B. 70%   C. 30%   D. 80%

Question 18

A person is holding two drill bits, one is 7/16 and the other is 25/64, and wants to first drill a hole using the smaller bit. To compare, the person expands 7/16 to 64ths. What is the expanded fraction?A. 14/64   B. 21/64   C. 24/64   D. 28/64

Question 19

A house is on an 80,000 sq. ft lot. About how many acres is the lot? There are 43,560 square feet in a acre.   A. 1/2 acre   B. 1 acre   C. 1 1/2 acres   D. 2 acres

Question 20

Sarah is planning a party at a party hall. The meal option is $50 per person and includes the hall for free. The hall-only option is $1,500 but allows an external caterer, which charges $30 per person. Sarah plans to invite 40 people. Which is a better cost comparison?   A. Meal option: $2,700. Hall-only option: $2,000. Hall-only option is cheaper.   B. Meal option: $1,000. Hall-only option: $3,500. Meal option is cheaper.   C. Meal option: $3,000. Hall-only option: $1,200. Hall-only option is cheaper.   D. Meal option: $2,000. Hall-only option: $2,700. Meal option is cheaper.

Question 21

A couple decides that Sophia will drive the first 3/5 of a trip and Lucas the last 2/5. The trip is 100 miles (the whole trip). How far will Sophia drive?   A. 40 miles   B. 60 miles   C. 20 miles   D. 30 miles

Question 22

The price of a sandwich decreases from $8 to $6. What is the percentage decrease in the price of the sandwich?   A. 33%   B.25%   C. 20%   D.14%

Question 23

A box is 24 inches long, 10 inches wide, and 10 inches deep. About how many cubic feet is the box?A. 1.4 ft3   B. 2.8 ft3   C. 240 ft3   D. 2,400 ft3

Question 24

A store in Minnesota advertises that on a holiday, everything is 20% off. A person buys shoes for $40 and socks for $10. In Minnesota there is no tax on shoes or socks. What is the final price?   A. $20  B. $40   C. $50   D. $30

Question 25

A self storage center is a storage room that is 8 feet long, 6 feet wide, and 10 feet high. What is the volume of the room?   A. 24 cubic feet   B. 48 cubic feet   C.140cubic feet   D. 480 cubic feet

Question 26

15 people are expected for a dinner. Three ounces of corn serves one person. A can of corn is nine ounces. How many cans of corn should be bought for the dinner?   A. 18 cans   B.12 cans   C. 3 cans   D. 5 cans

Question 27

6 people will attend a lunch. 2 cans of juice should be provided per person. Determine the total number of cans of juice required.   A.12 cans of juice   B. 6 cans of juice   C. 4 cans of juice   D.3 cans of juice

Question 28

Jules goes on a hike that will last 5 hours total. She brings 12 cups of water. After an hour, she has already drunk 3 cups of water. At that rate, how many cups would Jules need for all 5 hours?   A. 8 cups   B.15 cups   C. 9 cups   D.12 cups

Question 29

Dana is attaching a shelf to a wall and needs the shelf to be perpendicular to the wall. How many degrees should the shelf be relative to the wall?   A. 45   B. 90   C.180   D. 360

Question 30

A circular garden has a diameter of 12 feet. About how much trim is needed to surround the garden by placing trim on the garden’s circumference?   A. 38 feet   B. 48 feet   C. 144 feet   D. 432 feet

Math Discussion

his week focuses on an introduction to geometry. Examine your daily life, and look for examples of the following types of triangles:

  • Right
  • Acute
  • Obtuse
  • Scalene
  • Isosceles
  • Equilateral

For example, yield signs are examples of acute triangles, and also examples of equilateral triangles.

Respond to the following in a minimum of 175 words:

  • Share your daily examples.
  • How might this exercise and information be used to assist someone as they try to relate the importance of geometry to their daily life?
  • Provide an example of a problem you solve based on your chosen triangle example.

Technology In The Mathematics Classroom

As education advances in the 21stst century, educators must be prepared to use technology to engage students in learning, enhance instruction, and support students with exceptionalities.

Create a 7-10 slide digital presentation for a staff development session for elementary school teachers  on the use of technology in the mathematics classroom.

Your presentation should include:

  • Three technologies that can be used in the mathematics classroom to enhance instruction . Technology incorporated could include apps, computer programs, videos, websites, etc. Your choices should represent varied technologies. For each technology, include the following:
    • A detailed description of the technology including the features of the technology, how it works, and the elementary grade levels where it is developmentally appropriate
    • Benefits of using the technology in a mathematics classroom and how it fosters students’ engagement, communication, and confidence in using technology.
    • A mathematics classroom example of the use of the technology. Explain how teachers and students would interact with the technology for a specific math lesson
  • One assistive technology to support the communication and learning of students with communication disabilities.
  • A title slide, presenter’s notes, and a reference slide

The digital presentation should include graphics that are relevant to the content, visually appealing, and use space appropriately.

The Scenario: Park Furnishings Manufactures School And University Classroom Furniture

Park Furnishings manufactures school and university classroom furniture. The company has two production plants, located at Easton and Weston. The Easton plant produce tables and chairs and the Weston plant produces desks and computer workstations. Park has a working day of 7.5 hours and employs twenty workers at each plant. You may assume that there is a total of 24 working days every month.

All Park products are manufactured using finished pressed wood and polished aluminium fittings. Including scrap, each table and desk uses 20 m2 of pressed wood whereas each chair and workstation needs 12.5 m2 and 30 m2 respectively. A total of 240000 m2 of pressed wood is available each month and is divided equally between the two plants. The aluminium fittings that reinforce the legs of all the production items are purchased from an outside supplier. Each plant can purchase up to 9500 boxes of fittings per month and one box is required for every item of furniture produced. Production times are 72 minutes per table, 18 minutes per chair, 90 minutes per desk and 2 hours per workstation.

The unit profit for chairs and tables are £39 and £72 respectively, whereas each desk and workstation generates profits of £105 and £142 respectively.

Park is considering combining operations of both plants into a single factory. This consolidation will have the advantage of combining all available production resources as well as reducing administration costs by £1420 per month; however they have estimated that the cost of renovating and equipping the factory will be £1100000. Due to the current financial position Park Furnishings is only prepared to go ahead with the combined operation if it saves money in the first year of operation.

 

Let

· x1 represent the number of tables made per month;

· x2 represent the number of chairs made per month;

· x3 represent the number of desks made per month;

· x4 represent the number of workstations made per month;

where x1,x2,x3,x4 ≥0

 

(a) Easton

Enter the constraints for the Easton plant and the expression to be optimised.

Maximise:  x1 +  x2

subject to

x1 +  x2≤      [Wood]

x1 +  x2≤      [Metal fittings]

x1 +  x2≤     [Labour]

Sketch the constraints and hence find the values of

· (i) a,b,c, the intersections of the Wood, Metal Fittings and Labour constraint respectively with the x1-axis;

· (ii) d,e,f,the intersections of the Wood, Metal Fittings and Labour constraint respectively with the x2-axis;

Enter the values, to the nearest integer in the appropriate boxes below:

Enter a:
Enter b:
Enter c:
Enter d:
Enter e:
Enter f:

Now draw a sample profit line on your graph. Choose a value of the profit (P>0) and using this value, find the values of

(i) g, the intersection of your sample profit line with the x1x1-axis;

(ii) h, the intersection of your sample profit line with the x2x2-axis;

Enter the values, to the nearest integer in the appropriate boxes below:

Enter P:
Enter g:
Enter h:

Determine the optimal solution for x1 and x2 to the nearest integer and the profit that this solution will generate and enter your solution below.

The optimal solution is x1=  ,     x2=

Profit: £

Select the two constraints which intersect to give the optimal solution.

The optimal solution is the intersection of   Select Wood Metal Fittings Labour x1 ≥ 0 x2 ≥ 0  with   Select Wood Metal Fittings Labour x1 ≥ 0 x2 ≥ 0

 

(b) Weston

Enter the constraints for the Weston plant and the expression to be optimised.

Maximise:  x3 +  x4

subject to

x3 +  x4≤      [Wood]

x3 +  x4≤      [Metal fittings]

x3 +  x4≤      [Labour]

Sketch the constraints and hence find the values of

· (i) a,b,c, the intersections of the Wood, Metal Fittings and Labour constraint respectively with the x3-axis;

· (ii) d,e,f, the intersections of the Wood, Metal Fittings and Labour constraint respectively with the x4-axis;

Enter the values, to the nearest integer in the appropriate boxes below:

Enter a:
Enter b:
Enter c:
Enter d:
Enter e:
Enter f:

Now draw a sample profit line on your graph. Choose a value of the profit (P>0) and using this value, find the values of

· (i) g, the intersection of your sample profit line with the x3x3-axis;

· (ii) h, the intersection of your sample profit line with the x4x4-axis;

Enter the values, to the nearest integer in the appropriate boxes below:

Enter P:
Enter g:
Enter h:

Determine the optimal solution for x3 and x4 to the nearest integer and the profit that this solution will generate and enter your solution below.

The optimal solution is x3=  ,     x4=

Profit: £

Select the two constraints which intersect to give the optimal solution.

The optimal solution is the intersection of   Select Wood Metal Fittings Labour x3 ≥ 0 x4 ≥ 0  with   Select Wood Metal Fittings Labour x3 ≥ 0 x4 ≥ 0

 

(c) Combined

Enter the constraints for combining the plants and the expression to be optimised.

Maximise:  x1 +  x2 +  x3 +  x4

subject to

x1 +  x2+  x3 +  x4≤   [Wood]

x1 +  x2+  x3 +  x4≤  [Metal fittings]

x1 +  x2+  x3 +  x4≤  [Labour]

Determine the optimal solution for x1,x2,x3,and x4 and the profit that this solution will generate and enter your solution below. ( Enter the optimal solution correct to 3dp and the profit to the nearest pound.)

The optimal solution is x1=  ,     x2=  ,     x3=  ,     x4=

Profit: £

Is it economically sensible to combine the two plants?   Select Yes No I do not know

The scenario

Park Furnishings manufactures school and university classroom furniture. The company has two production plants, located at Easton and Weston. The Easton plant produce tables and chairs and the Weston plant produces desks and computer workstations. Park has a working day of 7.5 hours and employs twenty workers at each plant. You may assume that there is a total of 24 working days every month.

All Park products are manufactured using finished pressed wood and polished aluminium fittings. Including scrap, each table and desk uses 20 m2 of pressed wood whereas each chair and workstation needs 12.5 m2 and 30 m2 respectively. A total of 240000 m2 of pressed wood is available each month and is divided equally between the two plants. The aluminium fittings that reinforce the legs of all the production items are purchased from an outside supplier. Each plant can purchase up to 9500 boxes of fittings per month and one box is required for every item of furniture produced. Production times are 72 minutes per table, 18 minutes per chair, 90 minutes per desk and 2 hours per workstation.

The unit profit for chairs and tables are £39 and £72 respectively, whereas each desk and workstation generates profits of £105 and £142 respectively.

Park is considering combining operations of both plants into a single factory. This consolidation will have the advantage of combining all available production resources as well as reducing administration costs by £1420 per month; however they have estimated that the cost of renovating and equipping the factory will be £1100000. Due to the current financial position Park Furnishings is only prepared to go ahead with the combined operation if it saves money in the first year of operation.

 

Let

· x1 represent the number of tables made per month;

· x2 represent the number of chairs made per month;

· x3 represent the number of desks made per month;

· x4 represent the number of workstations made per month;

where x1,x2,x3,x4 ≥0

 

 

(a) Easton

Enter the constraints for the Easton plant and the expression to be optimised.

 

Maximise:  x1 +  x2

 

subject to

x1 +  x2≤      [Wood]

x1 +  x2≤      [Metal fittings]

x1 +  x2≤     [Labour]

Sketch the constraints and hence find the values of

· (i) a,b,c, the intersections of the Wood, Metal Fittings and Labour constraint respectively with the x1-axis;

 

· (ii) d,e,f,the intersections of the Wood, Metal Fittings and Labour constraint respectively with the x2-axis;

 

Enter the values, to the nearest integer in the appropriate boxes below:

Enter a:  Enter b:  Enter c:  Enter d:  Enter e:  Enter f:

 

Now draw a sample profit line on your graph. Choose a value of the profit (P>0) and using this value, find the values of

(i) g, the intersection of your sample profit line with the x1x1-axis;

(ii) h, the intersection of your sample profit line with the x2x2-axis;

 

 

Enter the values, to the nearest integer in the appropriate boxes below:

 

Enter P:  Enter g:  Enter h:

Determine the optimal solution for x1 and x2 to the nearest integer and the profit that this solution will generate and enter your solution below.

The optimal solution is x1=  ,     x2=

Profit: £

Select the two constraints which intersect to give the optimal solution.

The optimal solution is the intersection of        with

 

(b) Weston

Enter the constraints for the Weston plant and the expression to be optimised.

Maximise:  x3 +  x4

subject to

x3 +  x4≤      [Wood]

x3 +  x4≤      [Metal fittings]

x3 +  x4≤      [Labour]

 

Sketch the constraints and hence find the values of

· (i) a,b,c, the intersections of the Wood, Metal Fittings and Labour constraint respectively with the x3-axis;

 

· (ii) d,e,f, the intersections of the Wood, Metal Fittings and Labour constraint respectively with the x4-axis;

 

 

 

 

Enter the values, to the nearest integer in the appropriate boxes below:

Enter a:  Enter b:  Enter c:  Enter d:  Enter e:  Enter f:

Now draw a sample profit line on your graph. Choose a value of the profit (P>0) and using this value, find the values of

· (i) g, the intersection of your sample profit line with the x3x3-axis;

· (ii) h, the intersection of your sample profit line with the x4x4-axis;

Enter the values, to the nearest integer in the appropriate boxes below:

Enter P:  Enter g:  Enter h:

Determine the optimal solution for x3 and x4 to the nearest integer and the profit that this solution will generate and enter your solution below.

The optimal solution is x3=  ,     x4=

 

Profit: £

 

Select the two constraints which intersect to give the optimal solution.

The optimal solution is the intersection of        with

 

(c) Combined

Enter the constraints for combining the plants and the expression to be optimised.

Maximise:  x1 +  x2 +  x3 +  x4

 

 

 

 

 

 

subject to

x1 +  x2+  x3 +  x4≤   [Wood]

x1 +  x2+  x3 +  x4≤  [Metal fittings]

x1 +  x2+  x3 +  x4≤  [Labour]

 

Determine the optimal solution for x1,x2,x3,and x4 and the profit that this solution will generate and enter your solution below. ( Enter the optimal solution correct to 3dp and the profit to the nearest pound.)

The optimal solution is x1=  ,     x2=  ,     x3=  ,     x4=

 

Profit: £

Is it economically sensible to combine the two plants?

Applied Mathmatics

Consider the frictionless rod, i.e. β=0. The equation of motion becomes

m (d^2 r)/(dt^2 )-mω^2 r=-mg sin⁡(ωt)

with g=9.81 m/s^2 and a constant angular speed ω.

The rod is initially horizontal, and the initial conditions for the bead are r(0)=r_0 and r^′ (0)=v_0.

A)Analytically solve this initial value problem for r(t) B)Consider the initial position to be zero, i.e. r_0=0. Find the initial velocity, v_0, that results in a solution, r(t), which displays simple harmonic motion, i.e. a solution that does not tend toward infinity. C)Explain why any initial velocity besides the one you found in part B) causes the bead to fly off the rod. D)Given r(t) displays simple harmonic motion, i.e. part B), find the minimum required length of the rod, L, as a function of the angular speed, ω. E)Suppose ω=2, graph the solutions, r(t), for the initial conditions given here: r_0=0 and initial velocities of v_0=2.40, 2.45, 2.50, and the initial velocity you found in part B). Use 0≤t≤5

Project 2: A bead sliding along a rod

Simple Harmonic Motion

A bead is constrained to slide along a rod of length . The rod is rotating in a vertical plane with a constant angular speed, , about a pivot in the middle of the rod. The pivot allows the bead to freely slide along the rod, i.e. the pivot does not impede the movement of the bead.

Let denote the distance of the bead away from the pivot where can be positive or negative.

 

 

 

 

 

 

Free Sliding Bead

Applying Newton’s second law provides a balance of forces due to gravity, friction, centripetal acceleration, and linear acceleration. The equation resulting from these forces is

where is the mass of the bead, is the coefficient of viscous damping, is the constant speed of angular rotation, is the acceleration due to gravity, and is the distance between the pivot and the bead.

The rod is initially horizontal, and the initial conditions for the bead are and .

Equation of Motion

Consider the frictionless rod, i.e. . The equation of motion becomes

with and a constant angular speed .

The rod is initially horizontal, and the initial conditions for the bead are and .

Analytically solve this initial value problem for

Consider the initial position to be zero, i.e. . Find the initial velocity, , that results in a solution, , which displays simple harmonic motion, i.e. a solution that does not tend toward infinity.

Explain why any initial velocity besides the one you found in part B) causes the bead to fly off the rod.

Given displays simple harmonic motion, i.e. part B), find the minimum required length of the rod, , as a function of the angular speed, .

Suppose , graph the solutions, , for the initial conditions given here: and initial velocities of , and the initial velocity you found in part B). Use

Problem 1

Consider the frictionless rod, i.e. . The equation of motion becomes

with and a constant angular speed .

The rod is initially horizontal, and the initial conditions for the bead are and .

You will need to write an Improved Euler Method system solver to find and

Numerically solve for when , , and . Solve in the time interval . Use step sizes and compare your results. Also, compare your best numerical answers with your analytic answers from Problem 1 part E).

Numerically solve for when , , and is selected to give simple harmonic motion, i.e. Problem 1 part B. Use small step sizes, e.g. etc. Solve for the longest time interval that provides reasonable values for . Compare your results to the analytic solution that gives simple harmonic motion. What does this demonstrate about numerical solutions?

Problem 2

Applied Mathematics

This project looks at the thickness of nonplanar graphs.  Thickness is a difficult topic due to the lack of theoretical results.  However, an investigation into the thickness of nonplanar graphs offers excellent insight into planar graphs.  Below are the specific requirements for Project 2.

Use Theorem 4.11 on page 90 to help with the requirements.
– Select and discuss a graph, G, with thickness 2
— Show the graph and provide all of the descriptive information
— Show the planar graphs that can be superimposed to form G
– Select and discuss a graph, H, with thickness 3
— Show the graph and provide all of the descriptive information
— Show the planar graphs that can be superimposed to form H
– Select and discuss a maximal planar graph with 8 vertices
— Show the graph and provide all of the descriptive information
— Discuss how the addition of a single edge creates a graph of thickness 2
— Show the planar graphs that can be superimposed to form the graph with its additional edge
– Discuss some generalizations about graphs of thickness 2
— Let us know what you learned during this project
— Provide additional graphs as required

A few notes about format: use MS PowerPoint for your presentation; develop a presentation that is 10-20 slides in length; incorporate audio files into your presentation in order to explain your work; use Equation Editor for all mathematical symbols, e.g. x ∈ X or Cl(A) ⋂ Cl(X-A); and select fonts, backgrounds, etc. to make your presentation look professional.

Mathematics Term 1 Block 6 Assignment Questions

Mathematics Term 1 Block 6 Assignment Questions

Note: Please provide the formulae in your calculations

1. The following are the heights in centimetres of 24 people.

(a) Complete the following frequency distribution table.

Height Mid-

height ( x )

 

Tally

Frequency ( f )

.f x x x− 2

( )x x− 2

.( )f x x−

145 –149 147 II 2 294 -18.75 351.5625 703.125

150 –154 152 IIII 4 608 -13.75 189.0625 756.25

155 –159 157 III 3 471 -8.75 76.5625 229.6875

160 –164 162 I 1 162 -3.75 14.0625 14.0625

165 –169 167 IIII 4 668 1.25 1.5625 6.25

170 –174

175 –179

180 –184

Totals

Use the above information to: (b) Construct a histogram showing these results.

156 162 174 183 177 169 153 150

151 172 158 171 169 174 180 183

184 154 182 148 168 149 167 159

(c) Calculate the mean (for grouped data) and the modal class.

(d) Calculate the variance and the standard deviation for grouped data to 4 significant figures. Check your answers with a calculator.

2. Find the mean, median, range, quartiles and the inter-quartile range for each of the following sets of data. (There is no need to group the data.)

(a) 25, 22, 24, 21, 20, 18, 16, 19, 24, 19, 18, 17, 20, 21, 22. (b) 29, 28, 27, 30, 31, 32, 34, 31, 30, 28, 26, 35, 26, 31, 33, 30, 31, 25.

3. Complete the following table and use the information to find the mean,

median and standard deviation (to 3 significant figures) for the distribution.

x f .f x x x− 2( )x x− 2.( )f x x−

3 1 3 -4 16 16

4 2 8 -3 9 18

5 3 15 -2 4 12

6 5 30 -1 1 5

7 7 49 0 0 0

8 6

9 3

10 3

Totals:

Math Assignment

  1. During the year, Coronado Boat Yard has incurred manufacturing costs of $420,000 in building three large sailboats. At year-end, each boat is about 70 percent complete. How much of these manufacturing costs should be recognized as expenses in Coronado Boat Yard’s income statement for the current year?
  2. A company that assembles trucks produces 60 trucks during the current year and incurs $4.5 million of material, labor, and overhead costs. Fifty-three trucks were sold during the year and each is allocated the same amount of costs. How much of the $4.5 million assembly costs should appear on the company’s income statement for the current year?  (Enter your answers in dollars and not in millions of dollars.)
  3. During the current year, the cost of direct materials purchased by a manufacturing firm was $340,000, and the direct materials inventory increased by $65,000. What was the cost of direct materials used during the year?
  4. Road Warrior Corporation began operations early in the current year, building luxury motor homes. During the year, the company started and completed 50 motor homes at a cost of $60,000 per unit. Of these, 48 were sold for $105,000 each and two remain in finished goods inventory. In addition, the company had six partially completed units in its factory at year-end. Total costs for the year (summarized alphabetically) were as follows.

Direct materials used

$

728,000

Direct labor

908,000

Income tax expense

100,000

General and administrative expenses

500,000

Manufacturing overhead

1,510,000

Selling expense

Required:

a. Compute the total manufacturing costs charged to work in process for the current year.

b. Compute the cost of finished goods manufactured for the current year.

c. Compute the cost of goods sold for the current year.

d. Compute the gross profit on sales for the current year.

e. Compute the ending inventories of (1) work in process and (2) finished goods for the current year.

a.

Total manufacturing costs

b.

Cost of finished goods manufactured

c.

Cost of goods sold

d.

Gross profit on sales

e-1

Ending inventory of work in process

e-2

Ending inventory of finished goods

MA 1025 MOD 1 DB

Part 1

  1. Find and post an article (mathematical, statistical, etc.) that discusses a range of data.
  2. Describe the article and the range of data discussed in the article.
  3. Utilize interval notation to represent the data in your pos

Week 3 Discussion

This week focuses on applications of geometry. Respond to the following in a minimum of 175 words:

  • How would you explain to a classmate the difference between perimeter and area of two-dimensional shapes?
  • How about the difference between surface area and volume of three-dimensional shapes?
  • What examples or activities would you use to help a classmate understand the differences?