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    Algebra

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    Family of ideals in a ring

    Show that the intersection of any family of ideals in a ring is an ideal. Show that the ideal generated by a subset S of a ring R is the intersection of all ideals J of R such that S <= J <=R.

    How many birds are needed to decorate the table?

    Caitlin is decorating a rectangular table . She wants to decorate the table with paper cutouts birds. She plans to tape a bird every 6 inches around the table and at every corner . The table is 2 feet wide and 5 feet long; How many birds are needed to decorate the table?

    Finance/Accounting Problem1. Compute the present value of a $100 cash flow for the following combinations of discount rates and times: 2. Compute the future value of a $100 cash flow for the following combinations of discount rates and times:

    1. Present Values. Compute the present value of a $100 cash flow for the following combinations of discount rates and times: 1. r = 8 percent. t = 10 years. 2. r = 8 percent. t = 20 years. 3. r = 4percent. t = 10 years. 4. r = 4 percent. t = 20 years. 2. Future Values. Compute the future value of a $100 cash flow fo

    Algebra - Weight of the Pyramid

    A new pyramid has been found in South America. The pyramid has a rectangular base that measures 62 yd by 180 yd, and has a height of 100 yd. The pyramid is not hollow like the Egyptian pyramids and is composed of layer after layer of cut stone. The stone weighs 432 lb per cubic yard. How many pounds does the pyramid weigh?

    Volume of a Hemisphere Word Problem

    A dentist places a gold filling in the shape of a cylinder with a hemispherical top in a patient's tooth. The radius of the filling is 3 mm. The height of the cylindrical portion is 4 mm. If dental gold costs $16.00 per cubic millimeter, how much did the gold for the filling cost? Round to the nearest cent. Use pi &#8776; 3.14.

    Arithmetic and Geometric Sequences and Series

    Use the arithmetic sequence of numbers 2, 4, 6, 8, 10... to find the following: a) What is d, the difference between any two consecutive terms? b) Using the formula for the nth term of an arithmetic sequence, what is 101st term? c) Using the formula for the sum of an arithmetic sequence, what is the sum of the first 20 t

    Variables, Term and Powers

    --Is there a difference between -7^2 and (-7)^2 --Consider a number without any variables, say, 10. Is 10 a term?

    What was the unknown number?

    When 8 more than a certain unknown number was divided by that number, the result was 3. What was the unknown number?

    Ratio of Imports to Exports

    If United States imports increased 20 percent and exports decreased 10 percent during a certain year, the ratio of imports to exports at the end of the year was how many times the ratio at the beginning of the year?

    Break-even, Charges and Investments

    1. A theatre spends $5000. building a set for a new play. Each performance of the play costs the theatre $700. The theatre sells $1200. worth of tickets for each performance. How many performances must the theatre put on to break even? 2. An amusement park charges admission plus a fee for each ride. Admission plus two

    Functions

    Determine whether each relation is a function: x^2 = 1 + y^2 y = (square root of x + 5) Determine the domain and range of each relation y = 2x - 3 Graph each function and state the domain and range y = 0.3x y = l x-2 l

    Basic Ratio Equations for Job Direct or Indirect

    1) Is the ratio between number of workers and time required to complete a job direct or indirect? 2) The formula for profit (P) is cost (C) minus overheard (O). Write an equation for profit and then translate it to solve for cost 3) Solve for t d=rt My solution was t=d/t. Is that correct 4) Solve for S (C-S)/n=R

    Writing Equations from Sample Word Problems

    1. A quantity of 13% acid solution is being diluted with 3% acid solution. The final solution must be 8% acid and contain 90 ml. How much of each solution must be combined to accomplish this? 2. A rectangular fence is to be constructed with 500ft of fencing. The length of the fence is to be 3.5 times the width of the fence

    How long, in seconds, does she have to get out of the way ( a story is 12 feet).

    The height (h) (in feet) of an object that is dropped from the height of (s) feet is given the formula h=s-16t^2, where (t) is the time the object has been falling. A 5 foot tall woman on a sidewalk looks overhead and sees a window washer drop a bottle from the fifth story. How long, in seconds, does she have to get out of the w

    Arithmetic and Geometric Sequences and Series

    1) Use the arithmetic sequence of numbers 2, 4, 6, 8, 10... to find the following: a) What is d, the difference between any two consecutive terms? b) Using the formula for the nth term of an arithmetic sequence, what is 101st term? Answer: c) Using the formula for the sum of an arithmetic sequence, what is the sum of the fi

    Completing the Square

    4. Solve by completing the square: Radicands must be enclosed within [ ]. x2 + 4x + 2 = 0

    Earthquakes and the Richter Scale

    The intensity level of an earthquake is based on the Richter scale. Using logarithms, the Richter scale measures an earthquake relative to (as a ratio of) the weakest possible tremor. -What is the formula for measuring earthquakes? -Why is a 7.0 earthquake ten times stronger than a 6.0 earthquake? Pick an earthquake in

    Discriminants

    If I am using the quadratic formula to solve a quadratic equation ax2 + bx + c = 0, the discriminant is b2 - 4ac. This discriminant can be positive, zero, or negative. (When the discriminant is negative, then we have the square root of a negative number. This is called an imaginary number, sqrt(-1) = i. ) Explain what the val

    Sums of Geometric Sequences : Checkerboard Problem

    A traveling salesman (selling shoes) stops at a farm in the Midwest. Before he could knock on the door, he noticed an old truck on fire. He rushed over and pulled a young lady out of the flaming truck. Farmer Brown came out and gratefully thanked the traveling salesman for saving his daughter's life. Mr. Brown insisted on givin

    Arithmetic Sequence

    Use the arithmetic sequence of numbers 1, 3, 5, 7, 9,...to find the following: 1. What is d, the difference between any 2 terms 2. Using the formula for the nth term of an arithmetic sequence, what is 101st term? 3. Using the formula for the sum of an arithmetic sequence, what is the sum of the first 20 terms? 4. U

    Solving Equations

    1. Square root 0f x-1=3 2. The square root of x3 = 8 3. The square root of x2 = x an identity (true for all values of x)? 4. V = s3. Find the length of a side of a cube if the Volume is 729 cm3.