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# Recent problems solved by 'solver91311'

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 Polygons/428607: a regular decagon with a perimeter of 70ft. find the area.round to the nearest tenth1 solutions Answer 297878 by solver91311(16868)   on 2011-03-29 12:16:56 (Show Source): You can put this solution on YOUR website! The area of a regular -gon with side length is given by: For your problem, n = 10 and s = 70 divided by 10. Do your own arithmetic. John My calculator said it, I believe it, that settles it
 Graphs/428605: In an electric kettle with good insulation, o.85kg of water is warmed by an electric reisitor of 25 ohms which is connected to avoltage of 230V. in what time will the temperature of water rise by 20 degress celcius? specific heat capaicty of water is 4190j/kg *c1 solutions Answer 297870 by solver91311(16868)   on 2011-03-29 11:31:21 (Show Source): You can put this solution on YOUR website! This is a math site. Unless you provide the formula, take your question to a site that does physics. Try the physics board on Cramster. John My calculator said it, I believe it, that settles it
 Length-and-distance/428606: A tree is standing next to a 40-foot high building. The tree has an 18-foot shadow, while the building has a 16-foot shadow. How tall is the tree, rounded to the nearest foot? 1 solutions Answer 297868 by solver91311(16868)   on 2011-03-29 11:28:15 (Show Source): You can put this solution on YOUR website! is to 40 as 18 is to 16: Cross-multiply and then solve the resulting linear equation for , rounding as required. John My calculator said it, I believe it, that settles it
 Surface-area/428289: An acre is 45,360 square feet. If the area has 4 sides, what is the formula for obtaining the length of the sides? i.e. x squared equals 45,360... so the formula for obtaining the value of x is ?????1 solutions Answer 297731 by solver91311(16868)   on 2011-03-28 18:16:54 (Show Source): You can put this solution on YOUR website! Just knowing that the area has 4 sides doesn't help you much. Even if you had specified that the area was a rectangle, (which you didn't, meaning the area could be bounded by any sort of general quadrilateral), you still don't know enough to determine the dimensions of the sides. For example, you could have a square that is just a little less than 213 feet on a side (), or you could have a rectangle that is 1 inch by 544,320 feet. You just have no idea without knowing some other fact about the relationship between the length and the width. John My calculator said it, I believe it, that settles it
 Exponential-and-logarithmic-functions/428183: Graph each function on the same coordinate plane. List any similarities and differences between graphs. y=3^x y=3^-x1 solutions Answer 297681 by solver91311(16868)   on 2011-03-28 14:57:11 (Show Source): You can put this solution on YOUR website! The green one is John My calculator said it, I believe it, that settles it
 Quadratic_Equations/428168: Find the maximum value of the function: y=-x^2+8x-41 solutions Answer 297676 by solver91311(16868)   on 2011-03-28 14:35:04 (Show Source): You can put this solution on YOUR website! Since the lead coefficient is negative, the parabola opens downward. Therefore, the vertex is a maximum. First find the x-coordinate of the vertex. Take the opposite of the coefficient on the first degree term and divide it by 2 times the lead coefficient. The maximum value of the function is the value of the function at the vertex. Take the x-coordinate you just found and evaluate the function at that x-value. John My calculator said it, I believe it, that settles it
 Polynomials-and-rational-expressions/428149: Suppose that a polynomial function of degree 5 with rational coefficients has 2-3i, -5 and the square root of 7 as zeros. Find the other zeros. I am having a terrible time with this problem. I understand the degree of 5 means there are five zeros. I believe the answer is 2+3i and - square root of 7. Help me step by step this please. 1 solutions Answer 297673 by solver91311(16868)   on 2011-03-28 14:30:13 (Show Source): You can put this solution on YOUR website! Your answer is exactly correct. For a polynomial equation with real coefficients, complex roots always occur in conjugate pairs. The irrational conjugate roots theorem says: Let be any polynomial with rational coefficients. If is a root of , where is irrational and and are rational, then another root is . So, if you have a complex root then you are guaranteed to have another complex root . Likewise, if you have an irrational root where and , then you are guaranteed to have another irrational root Therefore is a root guarantees that is a root and guarantees John My calculator said it, I believe it, that settles it
 Triangles/428152: If a proof says: "Given: Triangle CDF is an isosceles triangle whose shortest side is line segment FD." Is that the same as perpendicular?1 solutions Answer 297665 by solver91311(16868)   on 2011-03-28 14:09:53 (Show Source): You can put this solution on YOUR website! No. An isosceles triangle has two sides of equal measure. Hence, the third side is either longer than each of the two equal sides or shorter than each of the two equal sides. In order for FD to be the shortest side, the triangle must represent the latter condition and FD is the one unequal side. You can also deduce that segments CD and CF are congruent. John My calculator said it, I believe it, that settles it
 Polynomials-and-rational-expressions/428153: The sum of a number and 6 times its reciprocal is 5. Find the number(s). Thanks 1 solutions Answer 297663 by solver91311(16868)   on 2011-03-28 14:05:11 (Show Source): You can put this solution on YOUR website! I already did this one today. But here it is again in case you missed it. Let represent the number. Then is the reciprocal of the number, and is 6 times the reciprocal. The sum is 5, so: Multiply by Put the quadratic into standard form: Solve the quadratic for . Hint: it factors. John My calculator said it, I believe it, that settles it
 Probability-and-statistics/428144: if p(A)=0.85 find the compliment of A,P OF A COMPLIMENT 1 solutions Answer 297662 by solver91311(16868)   on 2011-03-28 14:03:06 (Show Source): You can put this solution on YOUR website! COMPLIMENT: An expression of esteem, respect, affection, or admiration. It would depend a great deal upon the exact nature of outcome A to determine what someone might say to express esteem, respect, affection, or admiration for outcome A. It is nearly certain that no matter how unpopular outcome A might be that there will be more than one compliment for that outcome. Hence, to find "the" compliment is likely impossible, depending on the size of the population that actually has an opinion of any kind regarding outcome A. COMPLEMENT: (of a probalistic outcome) The complement of an event is the set of all outcomes in the sample space that are not included in the outcomes of that event. The probability of an event plus the probability of the complement of that event is always 1. Hence: John My calculator said it, I believe it, that settles it
 Rational-functions/428103: What is the domain of Q(x)= x+8/x^2+36x1 solutions Answer 297659 by solver91311(16868)   on 2011-03-28 13:44:58 (Show Source): You can put this solution on YOUR website! That depends a great deal on how much of your function that follows the "/" is in the denominator of the rational part of the function, to wit: has a different domain than and both have a different domain than: Repost your question using parentheses to eliminate ambiguities, that is either: Q(x) = x + (8/x^2) + 36x Q(x) = x + 8/(x^2 + 36x) Q(x) = x + 8/x^(2 + 36x) John My calculator said it, I believe it, that settles it
 Problems-with-consecutive-odd-even-integers/428126: How do I graph even integers between -9 and -1?1 solutions Answer 297654 by solver91311(16868)   on 2011-03-28 13:25:11 (Show Source): You can put this solution on YOUR website! Find all of the integers that are divisible by 2 between those two limits. John My calculator said it, I believe it, that settles it
 Equations/428131: 3x+4y=15 -4x-3y=-20 I need to solve this through the addition method. Is there an easy way to do this?1 solutions Answer 297647 by solver91311(16868)   on 2011-03-28 13:03:11 (Show Source): You can put this solution on YOUR website! I cannot answer the question you asked. The problem is that "easy" is a relative term. What is easy for some is difficult for others, furthermore there are a number of specific ways to attack this problem for which the ease of accomplishment varies slightly. Below find what I consider to be the easiest method -- just how easy that is for you is something I am unable to guess. In order to solve a system by the addition method, you must find a multiplier for one of the equations or a pair of multipliers, one for each of the equations such that the resulting coefficient on one of the variables in one of the equations is the additive inverse of the coefficient of that same variable in the other equation. In your case, if you multiply the first equation by 3 and the second equation by 4, the coefficients on y end up being 12 and -12. Then when you add the two equations term by term, the coefficient on y in the result is zero, effectively eliminating the y variable and leaving you with a single equation in a single variable, in this case x. By the way, because the goal of the method is to eliminate one of the variables, the Elimination Method is a more descriptive name than the Addition Method. John My calculator said it, I believe it, that settles it
 Exponents-negative-and-fractional/428134: Evaluate the following 4(-12y)0 power 4/3z 0power 1 solutions Answer 297644 by solver91311(16868)   on 2011-03-28 12:51:32 (Show Source): You can put this solution on YOUR website! Anything to the zero power is 1 John My calculator said it, I believe it, that settles it
 Polynomials-and-rational-expressions/428105: The sum of a number and 6 times its reciprocal is 5. Find the number(s). thanks.1 solutions Answer 297633 by solver91311(16868)   on 2011-03-28 11:41:48 (Show Source): You can put this solution on YOUR website! Let represent the number. Then is the reciprocal of the number, and is 6 times the reciprocal. The sum is 5, so: Multiply by Put the quadratic into standard form: Solve the quadratic for . Hint: it factors. John My calculator said it, I believe it, that settles it
 Percentage-and-ratio-word-problems/428113: Please help me solve this proportion. 1 solutions Answer 297630 by solver91311(16868)   on 2011-03-28 11:33:28 (Show Source): You can put this solution on YOUR website! means So just cross-multiply and solve the resulting linear equation for John My calculator said it, I believe it, that settles it
 Angles/428112: The measures of two supplementary angles are in the ratio 5:7. What is the measure of the largest angle?1 solutions Answer 297629 by solver91311(16868)   on 2011-03-28 11:30:52 (Show Source): You can put this solution on YOUR website! Supplementary angles' measures sum to 180 degrees. If the ratio of two supplementary angles is 5 to 7, then the smaller one is 5/12 (because 5 + 7 = 12) of 180 and the larger is 7/12 of 180. Calculate 7/12 of 180. John My calculator said it, I believe it, that settles it
 Polynomials-and-rational-expressions/428107: solve 2/xy + 5/x1 solutions Answer 297628 by solver91311(16868)   on 2011-03-28 11:18:34 (Show Source): You can put this solution on YOUR website! You can't "solve" this because there is no relational operator (equals or inequality sign). You can combine the two rational expressions given the condition that and . If that is what you want, resubmit and ask the correct question. John My calculator said it, I believe it, that settles it
 logarithm/428108: can u help me with this ln(ln(x))=11 solutions Answer 297626 by solver91311(16868)   on 2011-03-28 11:14:35 (Show Source): You can put this solution on YOUR website! Use To write: Then use again to write: John My calculator said it, I believe it, that settles it
 Rational-functions/426851: Find the center and radius of the circle x^2+y^2-18x+4y+4=01 solutions Answer 296845 by solver91311(16868)   on 2011-03-24 20:16:04 (Show Source): You can put this solution on YOUR website! is the equation of a circle with center at and radius Move the constant to the RHS Divide the coefficient on the first degree term by 2 and square the result. Add that result to both sides, completing the square in . Do the same thing with the coefficient on the first degree term. Collect terms in the RHS and factor the two perfect square trinomials in the LHS. Finally, rewrite your equation thus: Now you can determine the center and radius by inspection. Compare to the pattern given at the beginning. John My calculator said it, I believe it, that settles it
 Rational-functions/426817: A rectangular pool has dimensions of 40 ft and 60 ft. If the pool has a patio area around it that equals the area of the pool, how wide is the distance from the pool edge to the patio edge? I am supposed to solve this using the quadratic equation.1 solutions Answer 296842 by solver91311(16868)   on 2011-03-24 20:02:58 (Show Source): You can put this solution on YOUR website! Let represent the width of the patio. Then the overall dimensions of the pool including the patio are by . If the area of the patio and the area of the pool are the same, then the area of both of them together must be two times the area of the pool, namely 2 times 2400 or 4800 square feet. Solve the quadratic for . It factors. Discard the negative root. John My calculator said it, I believe it, that settles it
 Linear-systems/426296: which kind of function best models the data in each table? choose an equation to model the data. x/y -1/2.2 0/0 1/2.2 2/8.8 3/19.8 possible answers: linear y=2.2x quadratic y=2.2x^2 exponential y=2.2^x1 solutions Answer 296572 by solver91311(16868)   on 2011-03-23 19:58:02 (Show Source): You can put this solution on YOUR website! This function is symmetric about the y-axis. -1 gets you to the same function value as 1. No exponential equation is symmetric to the y-axis, and only a purely horizontal line would be symmetric to the y-axis. The model must be a quadratic. Check: Square -1 to get 1 times 2.2 is 2.2 Square 0 to get 0 times 2.2 is 0 Square 1 to get 1 times 2.2 is 2.2 Square 2 to get 4 times 2.2 is 8.8 and so on. John My calculator said it, I believe it, that settles it
 Probability-and-statistics/426302: A committee of four people is to be selected from six Democrats and four Republicans. What is the probability that all are Democrats?1 solutions Answer 296570 by solver91311(16868)   on 2011-03-23 19:49:57 (Show Source): You can put this solution on YOUR website! If you consider chosing a Democrat for any one of the positions as a success (nothing to do with politics, it is simply a way of looking at the problem), then you want the probability of 4 successes in 4 trials where the probability of success on any given trial is 0.6. I say 0.6 because there are 10 people to choose from and 6 are considered a success. Alternatively, if your conservative politics simply won't allow you to consider selecting a Democrat as a success, you could calculate the probability of 4 failures (failure to pick a Republican) in 4 trials where the probability of success is 0.4. You will find that it reduces to the exact same calculation. The probability of successes in trials where is the probability of success on any given trial is given by: Where is the number of combinations of things taken at a time and is calculated by So, for this problem you could either compute: or And remembering that and , So either way, it reduces to You can do your own arithmetic. John My calculator said it, I believe it, that settles it
 Travel_Word_Problems/426299: Find the speed of a car that travels 325 miles in 5 hours. 1 solutions Answer 296569 by solver91311(16868)   on 2011-03-23 19:35:22 (Show Source): You can put this solution on YOUR website! Divide the distance by the time. John My calculator said it, I believe it, that settles it
 Circles/426295: how do i find the area of a circle 1 solutions Answer 296568 by solver91311(16868)   on 2011-03-23 19:32:11 (Show Source): You can put this solution on YOUR website! Square the radius and multiply by Leave the answer in terms of for an exact answer, or use an appropriate approximation for to get a numerical approximation of the area. John My calculator said it, I believe it, that settles it
 Word_Problems_With_Coins/426284: There is a jar with nickels and quarters in it. There are 95 coins in the jar and the coins total $12.95. How many of each coin is there? 1 solutions Answer 296566 by solver91311(16868) on 2011-03-23 19:29:34 (Show Source): You can put this solution on YOUR website! Let represent the number of nickels. Let represent the number of quarters. Then cents is the value of the nickels, and cents is the value of the quarters, and the total value of the coins,$12.95, can also be specified as 1295 cents. Solve the system for John My calculator said it, I believe it, that settles it
 Exponential-and-logarithmic-functions/426274: Find the Inverse x 1.) f(x)=2 x 2.) g(x)=[1/3] (x) 3.) y=e1 solutions Answer 296563 by solver91311(16868)   on 2011-03-23 19:17:03 (Show Source): You can put this solution on YOUR website! Sorry, you only get one problem per post. I'll do #3. Solve for x in terms of y: Take the natural log of both sides: Use But so Swap positions of x and y John My calculator said it, I believe it, that settles it
 Probability-and-statistics/426266: In how many ways can 10 instructors be assigned to seven sections of a course in mathematics? is the answer 1209600 ways?1 solutions Answer 296560 by solver91311(16868)   on 2011-03-23 18:51:12 (Show Source): You can put this solution on YOUR website! No. You want the number of ways to select 7 things from 10 things. is the number of combinations of things taken at a time and is calculated by So begin with the formula and plug in your numbers: First, realize that So the arithmetic simplifies to: John My calculator said it, I believe it, that settles it
 Equations/426264: Hello, I'm stuck on this question of my homework: Two vertical poles 8m and 3m high stand 12 m apart. Determine the distance between the tops of the poles. We are supposed to use the formula: a²+b²=c² and maybe some other formulas. We are learning about right angle triangles. I hope this makes sense, Thanks. 1 solutions Answer 296557 by solver91311(16868)   on 2011-03-23 18:41:51 (Show Source): You can put this solution on YOUR website! The 8 meter pole is 5 meters taller than the 3 meter pole, so you have a right triangle that has a long leg measuring 12 meters (the horizontal distance between the poles) and a short leg measuring 5 meters (the difference in the heights), and a hypotenuse that represents the straight line distance between the tops of the two poles, the measure of which is the answer to this problem. You can do one of two things at this point. You can do the arithmetic: or you can simply recognize that 5 and 12 are the two smaller numbers of the Pythagorean Triple 5-12-13, and get the answer directly. John My calculator said it, I believe it, that settles it
 Probability-and-statistics/426225: I did ask this question awhile ago. Draw a spinner that fits all four clues below: 1. The probability of spinning a 2 is equal to the probability of spinning a 1. 2. The probability of spinning ALL the NUMBERS is NOT EQUAL. 3. The probability of spinning a number other than a 1 is 75%. 4. There are three numbers on the spinner. My question is: Why is the probability of spinning ALL the Numbers Not equal? What do you mean by that? Can you please explain it further. Thak you so much.1 solutions Answer 296554 by solver91311(16868)   on 2011-03-23 18:36:06 (Show Source): You can put this solution on YOUR website! In the first place, you don't need clue 2 to solve the problem, although clue 2 does fit in the end. If the probability of NOT spinning a 1 is 75%, then the probability of spinning a 1 must be 1 - 0.75 = 0.25 = 25% Then since the probability of spinning a 2 is equal to the probability of spinning a 1, then the probability of spinning a 2 must also be 25%. That leaves 50% for the third number whatever number that might be. So even though the probability of spinning a 1 is the same as the probability of spinning a 2, each of these has a different probability than spinning the third number. John My calculator said it, I believe it, that settles it