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Triangles/334212: if one angle of a right triangle is 70 degrees,then how many degrees are there in the smallest angle? 1 solutions Answer 239471 by solver91311(16868)   on 2010-08-23 17:09:05 (Show Source): You can put this solution on YOUR website! If it is a right triangle, one of the angles has to measure . One other angle is given as . The sum of the measures of the three angles of any triangle is . John My calculator said it, I believe it, that settles it

Linear-equations/334213: A student has earned scores of 87, 81, and 88 on the first 3 of 4 tests. If the student wants an average (arithmetic mean) of exactly 87, what score must she earn on the fourth test? 1 solutions Answer 239470 by solver91311(16868)   on 2010-08-23 17:05:55 (Show Source): You can put this solution on YOUR website! Think about how we take an average. We add up all of the numbers and divide by the number of numbers. The final average for our student will be the sum of all 4 test scores divided by 4. Let's say we want to achieve an overall average of for data elements given data elements. We know that So we can say that But , the answer to the question, can be found by: Which is to say: So add up the scores for the tests already taken and subtract that sum from the product of the total number of tests multiplied by the desired overall average. Done. John My calculator said it, I believe it, that settles it

Subset/334211: Suppose B is a proper subset of C If n(C) =8, what is the minimum number of elements of B? 1 solutions Answer 239469 by solver91311(16868)   on 2010-08-23 17:03:38 (Show Source): You can put this solution on YOUR website! The minimum number of elements in B is zero, because the null set is a proper subset of any set other than the null set. John My calculator said it, I believe it, that settles it

Miscellaneous_Word_Problems/334210: A carpenter is building a rectangular room with a fixed perimeterof 112 ft. What dementions would yeild the maximum area? What is the maximum area? The lenght that would yeild the maximum are is __?__ft 1 solutions Answer 239467 by solver91311(16868)   on 2010-08-23 16:51:44 (Show Source): You can put this solution on YOUR website! Let's solve this one in general, that is for any given perimeter. Let w represent the width of the field. Let l represent the length of the field. The perimeter of a rectangle is: So The area of a rectangle is the length times the width so a function for the area in terms of the width is: Algebra Solution: The area function is a parabola, opening downward, with vertex at: Since the parabola opens downward, the vertex represents a maximum value of the area function. The value of the width that gives this maximum value is one-fourth of the available fencing. Therefore, the shape must be a square, and the area is the width squared. Calculus Solution: The area function is continuous and twice differentiable across its domain, therefore there will be a local extrema wherever the first derivative is equal to zero and that extreme point will be a maximum if the second derivative is negative. Therefore the maximum area is obtained when And the shape is therefore a square. And that maximum area is: John My calculator said it, I believe it, that settles it

Problems-with-consecutive-odd-even-integers/334191: How many integers are there between 6 x 10^98 and 5 x 10^100 (not counting 6 x 10^98 and 5 x 10^100 )? a 4.94 x 10^100 -1 b 4.94 x 10^99 -1 c 4.94 x 10^98 -1 d 494 e 493 1 solutions Answer 239466 by solver91311(16868)   on 2010-08-23 16:46:06 (Show Source): You can put this solution on YOUR website! First change so that it is expressed in the same power of 10 that the other number is in. So, reduce the exponent by 2, and move the decimal point two places right. Now that the decimal points line up, you can just subtract the numbers: But just subtracting two integers gives you the number of integers between them including one of the endpoints. Since you want to eliminate both endpoints, you need to subtract 1 more unit. Furthermore, you need to put the decimal point back where it belongs. Hence: John My calculator said it, I believe it, that settles it

Miscellaneous_Word_Problems/334189: Eighty people are trapped in a ski lodge. They have enough food to last eight days. It takes five days to reach help (and five days for help to get back to the lodge). What is the fewest number of people to send for help (with sufficient food) so that those staying behind will be rescued before food runs out? 1 solutions Answer 239463 by solver91311(16868)   on 2010-08-23 16:13:49 (Show Source): You can put this solution on YOUR website! The trick to this one is to realize that the group of people who trek out to look for help will only need 5 days food (presumably there will be unlimited food for them once they get reach help in 5 days) while the group of people who remain at the lodge will need 10 days food, the 5 days it takes the other group to get out and the 5 days it takes the rescuers to return to the lodge. If you consider one food unit to be sufficient food to feed one person for 1 day, then there must be 80 times 8 = 640 food units available. Let represent the number of people who leave to get help. Then must be the number of people who remain at the lodge. So Just solve for John My calculator said it, I believe it, that settles it

Quadratic_Equations/334180: I need help solving an equation please. I need to solve the equation The square root of x over the square root of x -3 plus 5 over the square root of x. 1 solutions Answer 239461 by solver91311(16868)   on 2010-08-23 16:00:05 (Show Source): You can put this solution on YOUR website! What you described was: But you said you needed help solving an equation. What you described is not an equation. An equation is something that looks like {something} = {something else}. Notice the equals sign? That's where the word equation comes from. Since you don't have an equation or an inequality, you can't "solve" anything. Your expression can be simplified, but that's not what you asked. John My calculator said it, I believe it, that settles it

test/334181: Is nvr too late to be the best in math & algebra Is it ?? 1 solutions Answer 239460 by solver91311(16868)   on 2010-08-23 15:53:23 (Show Source): You can put this solution on YOUR website! While you are at it, strive for improvement in your ability to communicate in the English language. John My calculator said it, I believe it, that settles it

Travel_Word_Problems/334054: A poodle is shot of a cannon at a circus The height of the dog after t seconds is given by h=-16t^2+32t+8 A)Find the height of the dog after 1 second? B)How long until the dog hits the ground? C)Find the max height that the poodle will attain? 1 solutions Answer 239459 by solver91311(16868)   on 2010-08-23 15:48:06 (Show Source): You can put this solution on YOUR website! where and a) calculate b) set and solve the quadratic for c) calculate the -coordinate of the vertex of your parabola using: Then calculate the value of the function at that time value, i.e. (Note: same answer as part a) Public Service Notice: No animals, in particular poodles, were harmed during the calculation of the solution to this problem. John My calculator said it, I believe it, that settles it

Money_Word_Problems/334171: Solve using the five-step problem-solving process. Show all steps necessary to arrive at your solution. A semicircular window of radius 14 inches is to be laminated with a sunblock coating that costs $0.70 per square inch to apply. What is the total cost of coating the window, to the nearest cent? (Use п = 3.14. Hint: Area of Circle: A = пr2) 1 solutions Answer 239458 by solver91311(16868)   on 2010-08-23 15:27:33 (Show Source): You can put this solution on YOUR website! Calculate the area of the whole circle using the formula you have and then divide by 2 because you are dealing with a semicircle. Then multiply by $0.70 and round off to the nearest one-hundredth. John My calculator said it, I believe it, that settles it

Trigonometry-basics/334167: If a right triangle has a hypotenuse with length 15cm. If one of the acute angles of the triangle is 25degrees, find the length of the two shorter sides of the triangle correct to the nearest tenth of a centimeter. 1 solutions Answer 239457 by solver91311(16868)   on 2010-08-23 15:23:39 (Show Source): You can put this solution on YOUR website! Let represent one leg of the triangle. Let represent the other leg. Then: I'll leave you alone to spend some quality time with your calculator. John My calculator said it, I believe it, that settles it

Mixture_Word_Problems/334164: 12) A person earns an annual salary of $75,000. The person will receive a 5% raise the next year. Approximate the person’s salary after the 5% raise. Answer: $78,750 Please confirm this is right. Thanks 1 solutions Answer 239451 by solver91311(16868)   on 2010-08-23 15:08:33 (Show Source): You can put this solution on YOUR website! Exactly. John My calculator said it, I believe it, that settles it

Conjunction/334136: Construct a truth table for ~(~q^p) 1 solutions Answer 239449 by solver91311(16868)   on 2010-08-23 15:05:46 (Show Source): You can put this solution on YOUR website! John My calculator said it, I believe it, that settles it

Trigonometry-basics/334138: if t is in quadrant II and csc t=2, find the value of cot t. 1 solutions Answer 239447 by solver91311(16868)   on 2010-08-23 14:52:46 (Show Source): You can put this solution on YOUR website! in Quadrant II which is to say: In Quadrant II, and Hence and Furthermore: So But for Quadrant II so we need Next: Hence: John My calculator said it, I believe it, that settles it

Inequalities/334149: 0.6x + 1 < 1.0x - 2 1 solutions Answer 239440 by solver91311(16868)   on 2010-08-23 14:31:57 (Show Source): You can put this solution on YOUR website! What a handsome little inequality. Exactly what did you want to do with this? What is it that you don't understand about it? How can we help you with it? Did you mistake this site for the Psychic Hot Line and presume that we can just guess what it is you want or need? John My calculator said it, I believe it, that settles it

Inequalities/334150: 2/3 (2x-1)>10 1 solutions Answer 239439 by solver91311(16868)   on 2010-08-23 14:31:44 (Show Source): You can put this solution on YOUR website! What a handsome little inequality. Exactly what did you want to do with this? What is it that you don't understand about it? How can we help you with it? Did you mistake this site for the Psychic Hot Line and presume that we can just guess what it is you want or need? John My calculator said it, I believe it, that settles it

Equations/334141: 42 Solve the equation: 2y/3 = 4 43 Solve the equation: -3c/7 = -6 44 Solve the equation: 4x/9 = 6 45 Solve the equation: -8v/17 = 16 46 Solve the equation: 3w/4 = -1/2 47 Solve the equation: -13p/20 = -1/5 49 Solve the equation: t/2 + 5/12 = 5/6 50 Solve the equation: -7/10 = 3a/4 - 13/20 51 Solve the equation: 3.4n + 6.2 = -7.4 52 Solve the equation: 11.6b - 5 = 9.5 54 Solve the inequality: 2k/5 - 4/15 ≥ -2/3 55 Solve the inequality: 7d/11 + 2 < 2/3 Thanks in advance! :) 1 solutions Answer 239438 by solver91311(16868)   on 2010-08-23 14:29:20 (Show Source): You can put this solution on YOUR website! You are a bit premature with your thanks. Read the Instructions Particularly the one that says "One question per post." John My calculator said it, I believe it, that settles it

real-numbers/334147: Which of the following statements is false? a.There is a greatest negative integer. b.Between any two rational numbers, there is another rational number. c.Between any two irrational numbers, there is another irrational number. d.There is a least non-negative rational number. e.There is a greatest negative rational number 1 solutions Answer 239437 by solver91311(16868)   on 2010-08-23 14:27:53 (Show Source): You can put this solution on YOUR website! Statements d and e are false. John My calculator said it, I believe it, that settles it

Linear_Equations_And_Systems_Word_Problems/334073: Hi there, I had tried to solve this word problems...can't figure it out!! Everytime, I come up with different answers. Any help would be greatly appreciated. Thanks. " At the end of the year, a business has made a profit of $154,000. They must calculate the amount of tax due to the federal government and to the state. The federal tax rate is 30%, and the state tax rate is 10%. State taxes (ST) are deductible before federal taxes (FT) are calculated, and federal tax are deductible before states taxes are calculated. In other words, state taxes are subtracted from the profits before the 30% federal tax is calculated, and federal taxes are subtracted from the profits before the 10% state tax is calculated. 10% or 30 % of 154,000 does not require a system of equations to solve. Create and solve a system of equations to figure out how much state and federal taxes are owed by this company. 1. Identify the variables first. Do not confuse the tax rate with the amount of tax. 2. Set up a system of two equations. This is the only way that this problem can be solved. 3. Solve the system. Remember to report the answer in dollars." 4. Using the addition (elimination) method to solve systems of equations. Replace the ? with your student number. 1 solutions Answer 239430 by solver91311(16868)   on 2010-08-23 13:32:04 (Show Source): You can put this solution on YOUR website! Let represent the amount of tax paid to the state. Let represent the amount of tax paid to the federal government. According to the problem, we start with $154K, subtract the amount paid to the feds and then take 10%, like this: Likewise, the other equation is set up like this: This system of equations is set up perfectly to use the substitution method, so take the expression that is equal to in the first equation, and put it in place of in the second equation: A little arithmetic and a very little algebra gets us to: rounded to the nearest dollar. Make the opposite substitution: You can finish up yourself, I think. John My calculator said it, I believe it, that settles it

Trigonometry-basics/334129: Find the exact solutions of x^2-(y-6)=36 and y=-x^2 1 solutions Answer 239423 by solver91311(16868)   on 2010-08-23 13:02:34 (Show Source): You can put this solution on YOUR website! Rearrange your first equation so that it, like the other one, becomes expressed as a function of Now set the two things that are equal to equal to each other. Then by substitution into the second equation: Hence, the solution set is: John My calculator said it, I believe it, that settles it

Quadratic_Equations/334116: Given the function f(x)=5x^2-10x-4, what is the domain of f? 1 solutions Answer 239417 by solver91311(16868)   on 2010-08-23 12:49:57 (Show Source): You can put this solution on YOUR website! Your function is a polynomial, that is it is an expression of finite length constructed from variables and constants, using only the operations of addition, subtraction, multiplication, and non-negative, whole-number exponents. Therefore the domain is the set of real numbers. Said another way, there are no real number values that can be substituted for for which is undefined. John My calculator said it, I believe it, that settles it

test/334107: HI, pls help me solve myproblem. i am planning to install a fire pump. w/ 100psi pressure. i would want to completely empty a given tank for 30mins. with max height it can be. pls help me... thank you... 1 solutions Answer 239411 by solver91311(16868)   on 2010-08-23 12:41:32 (Show Source): You can put this solution on YOUR website! You have not provided sufficient information. The pressure rating of your pump bears no relationship whatsoever to the pump's volume rate capacity. Is it a 60 gpm pump? 100 gpm? 120? What? You say nothing about the shape or size of your tank -- nothing to give anyone a clue as to the actual volume of the tank as a function of the tank's height. So, all I can tell you is that you need to determine the volume capacity of your pump in volume units per minute, and multiply that times 30 minutes. That will be the amount you can pump in 30 minutes. Then you need to create a function that describes the volume of your tank as a function of its height. Set that function equal to the volume you calculated in the step above and then solve for the height that gives you that function value. John My calculator said it, I believe it, that settles it

Triangles/334126: The hypotenuse of a right triangle is 8 inches longer than the shorter leg. The longer leg is 4 inches longer than the shorter leg. Find the length of the shorter leg. 1 solutions Answer 239406 by solver91311(16868)   on 2010-08-23 12:32:00 (Show Source): You can put this solution on YOUR website! Let represent the measure of the short leg. Then must represent the measure of the long leg, and must represent the measure of the hypotenuse. Use Pythagoras: Expand the two squared binomials, collect like terms, and solve the resulting quadratic for , the measure of the short leg. John My calculator said it, I believe it, that settles it

Quadratic_Equations/334101: use the five step problem process translate reword carry-out check state a square support unit in a t.v. set is made with a side measuring 5 centimeters. A new model being designed for the upcoming year will have a large square with a side measuring 5.3 centimeters. By how much will the area of the square be increase? 1 solutions Answer 239402 by solver91311(16868)   on 2010-08-23 12:00:10 (Show Source): You can put this solution on YOUR website! Multiply 5.3 times 5.3. Then multiply 5 times 5. Subtract the second result from the first. John My calculator said it, I believe it, that settles it

test/334081: how to put square and cube 1 solutions Answer 239400 by solver91311(16868)   on 2010-08-23 11:58:34 (Show Source): You can put this solution on YOUR website! What do you mean? John My calculator said it, I believe it, that settles it

test/334082: how to use square and cubes 1 solutions Answer 239399 by solver91311(16868)   on 2010-08-23 11:58:19 (Show Source): You can put this solution on YOUR website! What do you mean? John My calculator said it, I believe it, that settles it

Polynomials-and-rational-expressions/334089: 1. In this problem, we analyze the profit found for sales of decorative tiles. A demand equation (sometimes called a demand curve) shows how much money people would pay for a product depending on how much of that product is available on the open market. Often, the demand equation is found empirically (through experiment, or market research). a. Suppose a market research company finds that at a price of p = $20, they would sell x = 42 tiles each month. If they lower the price to p = $10, then more people would purchase the tile, and they can expect to sell x = 52 tiles in a month’s time. Find the equation of the line for the demand equation. Write your answer in the form p = mx + b. Hint: Write an equation using two points in the form (x,p). 20=42x + b and 10= 52x +b A company’s revenue is the amount of money that comes in from sales, before business costs are subtracted. For a single product, you can find the revenue by multiplying the quantity of the product sold, x, by the demand equation, p. b. Substitute the result you found from part a. into the equation R = xp to find the revenue equation. Provide your answer in simplified form. The costs of doing business for a company can be found by adding fixed costs, such as rent, insurance, and wages, and variable costs, which are the costs to purchase the product you are selling. The portion of the company’s fixed costs allotted to this product is $300, and the supplier’s cost for a set of tile is $6 each. Let x represent the number of tile sets. c. If b represents a fixed cost, what value would represent b? $300 d. Find the cost equation for the tile. Write your answer in the form C = mx + b. C=6x + 300 The profit made from the sale of tiles is found by subtracting the costs from the revenue. e. Find the Profit Equation by substituting your equations for R and C in the equation . Simplify the equation. f. What is the profit made from selling 20 tile sets per month? g. What is the profit made from selling 25 tile sets each month? h. What is the profit made from selling no tile sets each month? Interpret your answer. i. Use trial and error to find the quantity of tile sets per month that yields the highest profit. j. How much profit would you earn from the number you found in part i? k. What price would you sell the tile sets at to realize this profit? Hint: Use the demand equation from part a. 2. The break even values for a profit model are the values for which you earn $0 in profit. Use the equation you created in question one to solve P = 0, and find your break even values. 3. In 2002, Home Depot’s sales amounted to $58,200,000,000. In 2006, its sales were $90,800,000,000. a. Write Home Depot’s 2002 sales and 2006 sales in scientific notation. You can find the percent of growth in Home Depot’s sales from 2002 to 2006 by following these steps: • Find the increase in sales from 2002 to 2006. • Find what percent that increase is of the 2002 sales. b. What was the percent growth in Home Depot’s sales from 2002 to 2006? Do all your work by using scientific notation. The Home Depot, Inc. (2007, March 29). 2006 Annual Report. Retrieved from http://www6.homedepot.com/annualreport/index.html 4. A customer wants to make a teepee in his backyard for his children. He plans to use lengths of PVC plumbing pipe for the supports on the teepee, and he wants the teepee to be 12 feet across and 8 feet tall (see figure). How long should the pieces of PVC plumbing pipe be? 1 solutions Answer 239398 by solver91311(16868)   on 2010-08-23 11:57:00 (Show Source): You can put this solution on YOUR website! Re-read the rules for posting questions on this site, particularly the part that says: One problem per submission. Do not dump your whole homework in one question Read the Instructions John My calculator said it, I believe it, that settles it

Matrices-and-determiminant/334119: use the echelon method to solve the system of two equations in two unknowns. x-3y=-4 -7x-2y=28 please show work 1 solutions Answer 239396 by solver91311(16868)   on 2010-08-23 11:52:43 (Show Source): You can put this solution on YOUR website! Hence, the solution set is John My calculator said it, I believe it, that settles it

Volume/334112: How much water would a container hold in gallons if the tank is 6 foot by 2 foot by 2 foot? Thank you. 1 solutions Answer 239393 by solver91311(16868)   on 2010-08-23 11:14:07 (Show Source): You can put this solution on YOUR website! The number of cubic feet in a rectangular solid container is given by the length times the width times the height. Each cubic foot is approximately 7.5 gallons. John My calculator said it, I believe it, that settles it

Functions/333938: The question that I am working on is this: Determine the domain of the average cost, in dollars, that you anticipate the average American family might be willing to pay for one gallon of white milk. Provide a reasonable range, keeping in mind that some families do not drink milk, no matter the cost (that's a hint on the low end of this domain). Required format for writing domain and range is: ____less than or equal to x less than or equal to _____. I need to know if I did this correctly. I put down 0 less than or equal to x less than or equal to 1.68. Did I comprehend this correctly. This first question has to be correct in order to answer all of the following questions. Thank you. 1 solutions Answer 239283 by solver91311(16868)   on 2010-08-22 19:49:08 (Show Source): You can put this solution on YOUR website! I have no idea where you are buying your milk, but the average price of a gallon of whole milk in the US in the second quarter calendar 2010 was $3.06. Click here You have the bottom end of the interval specified correctly -- unless you can find an instance where someone is willing to pay someone else to consume their milk, in which case you could assign a negative value to the low end of the interval. John My calculator said it, I believe it, that settles it

Finance/333922: Solve directly when Fvt =PV0* (1+r)^t The t and the 0 is supposed to be small like X 2 1 solutions Answer 239266 by solver91311(16868)   on 2010-08-22 18:51:35 (Show Source): You can put this solution on YOUR website! Ok, but what do you mean by "Solve directly"? You have provided no parameters for the problem at all. John My calculator said it, I believe it, that settles it