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Proportions/603458: 4837.86 is 6% of x. What is x? 1 solutions Answer 380703 by solver91311(16877)   on 2012-04-25 15:52:07 (Show Source): You can put this solution on YOUR website! Multiply both sides by John My calculator said it, I believe it, that settles it

Finance/603019: Hi, I have a statistics exam on friday and I just have no idea on what to do. Looking at the passed papers this is one of the questions that i just cant figure out. Please help me out. a) A manufacturer of outdoor clothing produces jackets and trousers. Each jacket requires 1 hour to make, whereas each pair of trousers takes 40 minutes. The materials for each jacket cost £32 and those for a pair of trousers cost £40. The manufacturer can devote only 34 hours per week to the production of jackets and trousers and the manufacturer’s total weekly cost for materials must not exceed £1200. The manufacturer sells the jackets at a profit of £12 each and the trousers at a profit of £14 per pair. Market research indicates that the manufacturer can sell all the jackets that are produced. a) Determine how many jackets and trousers the manufacturer should produce each week in order to maximize profit? (70 marks) b)Due to changes in demand, the manufacturer has decided to decrease the number of production hours from 34 hours to 27 hours per week. What effect will this have on the level of profit? Hence estimate the value of the marginal cost of one less hour in production time. (You may use either an algebraic or graphical approach providing a clear rationale is given to prove that your solution is in fact the optimum.) 1 solutions Answer 380531 by solver91311(16877)   on 2012-04-24 16:07:37 (Show Source): You can put this solution on YOUR website! Let represent the number of jackets and represent the number of trousers manufactured. Since we are assuming that you will sell all that you make, the total profit is given by: and this is the function that we want to maximize subject to the following constraints: Labor constraint: Materials constraint: Non-negative constraints (you can't make a negative number of either jackets or trousers) Integer constraint (you can't sell fractional parts of jackets or trousers) Graph each of the constraint inequalities. Note the feasibility polygon that is defined by the region where ALL of the constraint inequalities overlap. A theorem of Linear Programming guarantees that if a unique optimum solution exists, it will be one of the vertices of the feasibility polygon. Make a list of the ordered pairs that describe all of the vertices of the feasibility polygon. If any of the coordinates of any of the vertices are NOT integers, pick the nearest point to the actual vertex that both has integer coordinates and is inside the feasibility area. Once you have your table of points with integer coefficients, test each point by substituting the coordinate values in place of and in the objective function (the profit function in this case) and calculate the result. Since this is a maximize problem, select the point that provides the largest solution as your optimum point. For part b, change the labor constraint inequality to: then redraw your graph and re-test all of the feasibility vertices. Compare the solution in part a to part b. John My calculator said it, I believe it, that settles it

Angles/603010: Determine the smaller angle between the hands of a clock at 12:20. Show or explain how you got your answer. 1 solutions Answer 380525 by solver91311(16877)   on 2012-04-24 15:44:02 (Show Source): You can put this solution on YOUR website! The angular difference between the 12 where the minute hand was at exactly 12 and the 4 which is where the minute hand is at exactly 12:20 is exactly one-third of a circle. But while the minute hand was moving through this one-third of the whole circle, the hour hand was moving one-third of the way from the 12 (where it was at 12 o'clock exactly) to the 1 (where it will be when the minute hand gets all the way back around to the 12). The angular difference between the 12 and the 1 is one-twelfth of a circle. So the minute hand has moved a full one-third of the circle but the hour hand has moved one-third of one-twelfth of the circle. Then recall that there are 360 degrees in a circle. You Win! You get to do your own arithmetic. John My calculator said it, I believe it, that settles it

Equations/603001: I need help to solve 1-2x+4x=8 show how to do it 1 solutions Answer 380523 by solver91311(16877)   on 2012-04-24 15:33:02 (Show Source): You can put this solution on YOUR website! Collect like terms in the LHS. Add -1 to both sides Multiply by the reciprocal of the coefficient on the variable. John My calculator said it, I believe it, that settles it

Exponential-and-logarithmic-functions/603002: Which expressions are equivalent to the one below? Check all that apply. log[5]5 * log[2] 4 A. 2 * log[5]5 B. 3*5 C. 2 D. 2*7 1 solutions Answer 380521 by solver91311(16877)   on 2012-04-24 15:29:21 (Show Source): You can put this solution on YOUR website! So hence and hence John My calculator said it, I believe it, that settles it

Equations/603007: please show how to solve 10x+15=45 1 solutions Answer 380520 by solver91311(16877)   on 2012-04-24 15:24:43 (Show Source): You can put this solution on YOUR website! Add -15 to both sides. Then multiply by . John My calculator said it, I believe it, that settles it

Equations/603003: What is the first step in solving this equation? 9p + 12 = 57 A. adding 12 to each side B. subtracting 12 from each side C. multiplying each side by 9 D. dividing each side by 9 Please help! 1 solutions Answer 380519 by solver91311(16877)   on 2012-04-24 15:23:41 (Show Source): You can put this solution on YOUR website! The best way to answer this question so that the process will be clear in your mind is to actually perform each of the 4 operations listed and see which one of them actually gets you closer to a solution. Three of the operations listed will just create a bigger mess, and one of them makes things simpler. John My calculator said it, I believe it, that settles it

Trigonometry-basics/602906: Hi, I need help with my homework. We are learning about the sum and difference of identities. Here is the problem: What is the value of sin(A-b) if tan A = 9/40 and A is in the first quadrant, while cos B = -4/5 and B is in the third quadrant? I really don't get this homework. What is up with A and B? Do we need to plot the graph as well? It's confusing me. I'm sorry if I'm asking stupid questions, I missed our class today, you see. I hope someone can explain this to me properly so I'll catch up with the lesson. Thank you! 1 solutions Answer 380496 by solver91311(16877)   on 2012-04-24 13:39:18 (Show Source): You can put this solution on YOUR website! A is an angle and they tell you it is in the first quadrant and that the tangent is B is another angle. You are given that this angle is in the third quadrant and that the cosine is They want to subtract the measure of angle B from the measure of angle A and then take the sine of the difference. For such an operation you need the difference formula for sine: Remember that tangent is sine over cosine, so: So Square both sides: Use the Pythagorean Identity and substitute: Collect like terms: Take the positive (remember, QI) square root: And Again, the positive square root: Similarly you can get from to . QIII, both sine and cosine are negative. Now you have the four values you need to plug into: You can do your own arithmetic. Then, for futher study, here are the other three formulas you will need: Sum and Difference Formulas John My calculator said it, I believe it, that settles it

Triangles/602912: In PQR, mP = 60, mQ = 30, and mR = 90. Which of the following statements about PQR are true? 1 solutions Answer 380489 by solver91311(16877)   on 2012-04-24 12:25:40 (Show Source): You can put this solution on YOUR website! What "following statements"? John My calculator said it, I believe it, that settles it

Geometry_proofs/602872: Assume that abcd is a rhombus. Prove that ac is prependicular to bd (let e be the point of intersection$ 1 solutions Answer 380488 by solver91311(16877)   on 2012-04-24 12:24:30 (Show Source): You can put this solution on YOUR website! Draw the diagonals forming 4 triangles. Since it is a rhombus, it is also a parallelogram. The diagonals of a parallelogram bisect each other. AB congruent AD, defn of rhombus AE congruent AE, reflexive equality BE congruent DE, diagonals of parallelogram bisect each other Triangle ABE congruent triangle ADE by SSS Angle BED is a straight angle, hence measures 180 degrees. Angle AEB congruent Angle AED by CPCT measure of BED equals measure AEB + measure AED measure of BED equals 2 times measure AEB measure AEB is 90 QED. John My calculator said it, I believe it, that settles it

Exponential-and-logarithmic-functions/602881: What is x^2+10x-12000 factored? 1 solutions Answer 380485 by solver91311(16877)   on 2012-04-24 12:08:02 (Show Source): You can put this solution on YOUR website! The given trinomial cannot be factored over the rational numbers. Depending on your instructions you can either declare the trinomial to be prime, or factor it over the irrationals. If your instructor expects you to factor it over the irrationals, set the trinomial equal to zero and solve using the quadratic formula. You will obtain two roots, and . The factors of the trinomial are then and . John My calculator said it, I believe it, that settles it

Probability-and-statistics/602653: Below are the home states of 19 college professors. New Jersey Ohio Michigan Georgia Nebraska Wisconsin Ohio South Carolina Pennsylvania Michigan Georgia New Jersey Wisconsin Georgia Ohio Florida Georgia New Jersey South Carolina i. Make a frequency table using these 9 states: Florida Georgia Michigan Nebraska New Jersey Ohio Pennsylvania South Carolina Wisconsin My work: States Tally Frequency Florida | 1 Georgia |||| 4 Michigan || 2 Nebraska | 1 New Jersey ||| 3 Ohio ||| 3 Pennsylvania | 1 South Carolina || 2 Wisconsin || 2 ii. What is (are) the mode(s)? There are 3 (1s) and 3 (2s) iii. Does it make sense to talk about the average for this data? Why or why not? Really not sure how to come up with this answer iv. Using your frequency table draw a pie chart to display the distribution of home states by filling in the following table: Home State Frequency Percentage of total Measure of Central Angle (in degrees) Florida Georgia Michigan Nebraska New Jersey Ohio Pennsylvania South Carolina Wisconsin My Work: Home State Frequency Percentage of total Measure of Central Angle (in degrees) Florida 1 1/19*100=5.26% .0526*360=18.94 degrees Georgia 4 4/19*100=21.05% .2105*360=75.78 degrees Michigan 2 2/19*100=10.53% .1053*360=37.91 degrees Nebraska 1 1/19*100=5.26% .0526*360=18.94 degrees New Jersey 3 3/19*100=15.79% .1579*360=56.84 degrees Ohio 3 3/19*100=15.79% .1579*360=56.84 degrees Pennsylvania 1 1/19*100=5.26% .0526*360=18.94 degrees South Carolina 2 2/19*100=10.53% .1053*360=37.91 degrees Wisconsin 2 2/19*100=10.53% .1053*360=37.91 degrees Anyone know if this is correct? And can someone tell me how to figure out part iii.? 1 solutions Answer 380363 by solver91311(16877)   on 2012-04-23 20:24:38 (Show Source): You can put this solution on YOUR website! The mean (or average) doesn't tell you anything meaningful about this data. The mode is a much more meaningful measure of central tendancy in this case, and the mode of this data (4 in Georgia) is going to stick right out when you create your pie chart because Georgia's piece of the pie will be larger than the others. In contrast to the mean for this data, the mode points to a specific data point where as there is no place that has an "average" number of college professors. John My calculator said it, I believe it, that settles it

Geometry_Word_Problems/602652: 1. The border around a square painting is 4cm wide. Each side of the painting is 40cm long. Find the area of the border. 2. A rectangular flower-bed measures 10m by 6m. It has a path 2m wide around it. Find the are of the path. 3. A rectangular piece of glass measures 60cm by 46cm. When it is placed on a table, it leaves a margin 4cm wide all round it. What is the area of the table-top NOT covered by the glass? 4. A rectangular carpet is placed on the floor of a room which measures 8m by 7m. It leaves a margin 1m wide around it. Find the area of the carpet. 1 solutions Answer 380362 by solver91311(16877)   on 2012-04-23 20:15:56 (Show Source): You can put this solution on YOUR website! The area of the whole thing is 48 times 48 cm. The area of just the picture is 40 times 40. Subtract the area of the picture from the area of the whole thing. John My calculator said it, I believe it, that settles it

Volume/602638: A cube has volume of 4,906 cm3. What is the lenght of each edge of the cube? 1 solutions Answer 380361 by solver91311(16877)   on 2012-04-23 20:14:03 (Show Source): You can put this solution on YOUR website! The cube root of 4906. But I'll bet you really meant to type 4096, in which case the edge of the cube is the cube root of 4096 which is 16. Centimeters, of course. John My calculator said it, I believe it, that settles it

Rational-functions/602642: What are some ways that adding radical expressions is similar to adding polynomial expressions? How are the two processes different? 1 solutions Answer 380359 by solver91311(16877)   on 2012-04-23 20:09:12 (Show Source): You can put this solution on YOUR website! In order to add radicals, they have to be the same, just like the variables in a polynomial. You can add 1 fernblatz plus 2 fernblatzes to get 3 fernblatzes, but you can't add 1 fernblatz and 1 horbesnort because they are two different things. You can add Just like you can add but you can't add Just like you can't add John My calculator said it, I believe it, that settles it

Linear_Equations_And_Systems_Word_Problems/602640: A person invested $17,000 for one year,part at 10%, part at 12%, part at 15%. The total annual income from these investments was $2,110. The amount of money invested at 12% was $1,000 less than the amount invested at 10% and 15% combined. Find the amount invested at each rate. 1 solutions Answer 380358 by solver91311(16877)   on 2012-04-23 20:03:20 (Show Source): You can put this solution on YOUR website! Solve the 3X3 system. Recommend the substitution method to eliminate y first. Then solve for z in terms of x and solve the rest by substitution as well. John My calculator said it, I believe it, that settles it

Money_Word_Problems/602639: a couple inherit $40000 and deposi it in a fixed term deposit that pays 4.5% p.a. compounded quarterly. They withdraw the money as soon as they have over $45000. how long did they keep the money in that account? 1 solutions Answer 380356 by solver91311(16877)   on 2012-04-23 19:54:12 (Show Source): You can put this solution on YOUR website! Solve for John My calculator said it, I believe it, that settles it

Numbers_Word_Problems/602595: one number is 36 more than another number. Find the smallest possible value for their product. one number is x the next would be x + 36 product would be x^2 + 36x .... How do I find the smallest product? 1 solutions Answer 380355 by solver91311(16877)   on 2012-04-23 19:51:57 (Show Source): You can put this solution on YOUR website! Graph is a parabola opening upward. Vertex is at So fill in the numbers: And do the arithmetic to find , then plug that value into to find the value of the function at the vertex which is the minimum value of the function and hence the smallest product. John My calculator said it, I believe it, that settles it

Volume/602623: what is the volume of a cylinder if the area of the base is 50 square inches and the height is 12 inches 1 solutions Answer 380349 by solver91311(16877)   on 2012-04-23 19:30:36 (Show Source): You can put this solution on YOUR website! The volume of a cylinder in cubic units is the area of the base in square units times the height in units. John My calculator said it, I believe it, that settles it

Money_Word_Problems/602612: suppose you invest $1500 in an acount paying 4.75% annual interest. what is the account balance after 25 years with the interest compounded annualy, semiannually, quarterly and monthly 1 solutions Answer 380348 by solver91311(16877)   on 2012-04-23 19:29:20 (Show Source): You can put this solution on YOUR website! Don't forget that is expressed as a decimal Plug in your numbers. For annual compounding, , for semiannual, , for quarterly, , and for monthly, . John My calculator said it, I believe it, that settles it

Sequences-and-series/602616: One sequence is 7,11,15,19,23... Second sequence is 1,10,19,28,37 - the number 19 is in both sequences. If both sequences continue, what is the next number that is in both sequences? 1 solutions Answer 380347 by solver91311(16877)   on 2012-04-23 19:23:26 (Show Source): You can put this solution on YOUR website! In the first one the common difference is 4. In the second one the common difference is 9 John My calculator said it, I believe it, that settles it

Angles/602499: if m angle 2 = 74 degrees then what does m angle 6 = 1 solutions Answer 380346 by solver91311(16877)   on 2012-04-23 19:15:20 (Show Source): You can put this solution on YOUR website! Did you actually read the part of the instructions for posting that says "We don't have your book or your homework assignment or anything except what you tell us"? How do you expect anyone to answer you with no other information but what you provided? Use your head for something besides a hat rack. John My calculator said it, I believe it, that settles it

Radicals/602529: I would be very happy if you would help me solve this equation: 18 over 6 divided by sqrt(2) 1 solutions Answer 380307 by solver91311(16877)   on 2012-04-23 17:30:19 (Show Source): You can put this solution on YOUR website! I would be very happy to try to help you solve whatever equations you have, but what you have expressed is NOT an equation. Equations have two expressions, one on either side of an equals sign. You have one expression and no equals sign. Expressions, in and of themselves, do not have a "solution". John My calculator said it, I believe it, that settles it

percentage/602520: Hello 350 is what percent of 1250? Thank you 1 solutions Answer 380303 by solver91311(16877)   on 2012-04-23 17:21:52 (Show Source): You can put this solution on YOUR website! Divide 350 by 1250. Multiply the answer by 100. John My calculator said it, I believe it, that settles it

Linear-equations/602525: write the equation of the line in slope-intercept form m=-5/4,y-intercept(0,-3/4 1 solutions Answer 380302 by solver91311(16877)   on 2012-04-23 17:19:53 (Show Source): You can put this solution on YOUR website! The slope intercept form is: where is the slope and is the -coordinate of the -intercept. John My calculator said it, I believe it, that settles it

Graphs/602522: Solve the conjunction -6 _< 3 +x<4. Thank you. 1 solutions Answer 380300 by solver91311(16877)   on 2012-04-23 17:17:18 (Show Source): You can put this solution on YOUR website! Just add -3 to each part of the compound inequality. John My calculator said it, I believe it, that settles it

Trigonometry-basics/602425: Verify that the equation is an identity: sin^4 - cos^4 = 2sin^2 - 1 Also please show the steps if you can. It will be a lot of help since I'm not at all good with Math. Thank you! :) 1 solutions Answer 380225 by solver91311(16877)   on 2012-04-23 13:58:19 (Show Source): You can put this solution on YOUR website! Factor the difference of two squares in the LHS: Note that the right-hand factor in the LHS is just the Pythagorean Identity: Then, using the Pythagorean identity again in the form , substitute: Combine terms in the LHS: John My calculator said it, I believe it, that settles it

Mixture_Word_Problems/602423: If 5 quarts are needed to paint, how many gallons and quarts should I buy? 1 solutions Answer 380222 by solver91311(16877)   on 2012-04-23 13:47:04 (Show Source): You can put this solution on YOUR website! There are 4 quarts in a gallon. John My calculator said it, I believe it, that settles it

Exponential-and-logarithmic-functions/602419: logx + log(x-3)=1 can you help me find the answer to this question so that i can have a better understanding of what logarithms are? 1 solutions Answer 380221 by solver91311(16877)   on 2012-04-23 13:44:50 (Show Source): You can put this solution on YOUR website! Logarithms are exponents. Remember the sum of the logs is the log of the product: If the base is not specified, the base is assumed to be 10, hence using the definition of logarithms from above: Anything raised to the 1 power is just that thing, hence: Put the quadratic into standard form and solve. Hint: it factors. John My calculator said it, I believe it, that settles it

Geometry_Word_Problems/602413: The diameter of a construction pipe is 3ft . If the pipe is 17ft long, what is its volume? (Use the value 3.14 for 2 , and round your answer to the nearest cubic foot. Be sure to include the correct unit in your answer.) 1 solutions Answer 380220 by solver91311(16877)   on 2012-04-23 13:38:32 (Show Source): You can put this solution on YOUR website! A pipe is a cylinder. The volume of a cylinder is given by Remember that the diameter is twice the radius. John My calculator said it, I believe it, that settles it

Polynomials-and-rational-expressions/602416: How do i solve (3x-6)(2x+3)=0 1 solutions Answer 380219 by solver91311(16877)   on 2012-04-23 13:35:09 (Show Source): You can put this solution on YOUR website! Use the Zero Product Rule, to wit: or John My calculator said it, I believe it, that settles it