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Numbers_Word_Problems/447576: find the sum of the first 500 counting numbers 1 solutions Answer 308100 by solver91311(17059)   on 2011-05-10 13:43:18 (Show Source): You can put this solution on YOUR website! 500 + 1 = 501 499 + 2 = 501 498 + 3 = 501 . . . 251 + 250 = 501 And there are 500/2 = 250 such pairs. In general, the sum of consecutive positive integers is given by: So for your problem: Super Double Plus Extra Credit: What is the sum of the even integers between 200 and 300 inclusive? John My calculator said it, I believe it, that settles it

Expressions-with-variables/447577: Solve for a specified variable The formula P=B/1+s is used to determine what amount of principal P should be invested for 1 year at a simple interest rate in order to have B dollars after a year. I wasn't sure whether I should put this here, or in money word problems. Sorry if I'm in the wrong place, but I'd be very relieved to have some help with this problem. 1 solutions Answer 308096 by solver91311(17059)   on 2011-05-10 13:24:50 (Show Source): You can put this solution on YOUR website! So for which variable, or , did you want to solve ? John My calculator said it, I believe it, that settles it

Quadratic-relations-and-conic-sections/447535: which conic section is formed by the followin equation 4y^2=-4x^2+36 a. parabula b. circle c. ellipse d. hyperbola 1 solutions Answer 308095 by solver91311(17059)   on 2011-05-10 13:20:35 (Show Source): You can put this solution on YOUR website! Put your equation in to standard form: Has both an x squared and a y squared term: NOT a parabola The x squared and y squared terms have the same sign: NOT a hyperbola The coefficients on the x squared and y squared terms are equal: NOT an ellipse Sorry, but I have no idea what a "parabula [sic]" is. John My calculator said it, I believe it, that settles it

Rational-functions/447233: What is the equation of a line that is parallel to the line and passes through the point (-2, 8)? 1 solutions Answer 307921 by solver91311(17059)   on 2011-05-09 19:39:20 (Show Source): You can put this solution on YOUR website! There is a problem with the way you asked your question. You cannot find "the" equation of a line. The set of equations which graph to a given line is infinite, hence the best anyone can do is to derive an equation that is represented by a graph that is parallel to a line whose graph is a given equation and which passes through a given point. In your case, the given equation is in slope-intercept form, namely , so that the slope of the line represented by the given equation can be determined simply by inspection of the coefficient on the term. Parallel lines have identical slopes, hence an equation of a line parallel to the line represented by your original equation will have an identical coefficent on the term. Use the point-slope form of an equation of a line: where are the coordinates of the given point and is the determined slope. John My calculator said it, I believe it, that settles it

Graphs/447236: -6x+3y=12 1 solutions Answer 307918 by solver91311(17059)   on 2011-05-09 19:30:03 (Show Source): You can put this solution on YOUR website! What part of the instruction: "Please try to ask your question clearly and fully so that it MAKES SENSE. We are not mind readers. We do not have your textbook in front of us. All we know is what you wrote," do you not understand? John My calculator said it, I believe it, that settles it

Travel_Word_Problems/447163: Matt and Anna Killian are frequent fliers on fast-n-go airlines. They often fly between two cities that are a distance of 1680 miles apart. on one particular trip, they flew into the wind and the trip took 4 hours. The return trip with the wind behind them, only took about 3.5 hours. find the speed of the wind and the speed of the plane in still air 1 solutions Answer 307916 by solver91311(17059)   on 2011-05-09 19:27:23 (Show Source): You can put this solution on YOUR website! Remember Distance = Rate times Time Let represent the speed of the plane in still air. Let represent the speed of the wind. The rate of the plane against the wind is and the rate of the plane with the wind is . Using : and Divide the first equation by 4 and the second by 3.5: Add the two equations: and then substitute 450 back into either of the orginal equations to compute John My calculator said it, I believe it, that settles it

Linear-equations/447165: Which is a point that lies on the graph of the equation: 2x-y=8? A (3,-2) B (-2, 6) C (-3,-2) D (-2,-6) 1 solutions Answer 307882 by solver91311(17059)   on 2011-05-09 18:07:11 (Show Source): You can put this solution on YOUR website! The first value in an ordered pair is the x-value. The second value is the y-value. Substitute the first value in each of the ordered pairs in place of x and substitute the second value in each of the ordered pairs in place of y. Do the arithmetic each time. If the result is a true statement, then the point is on the graph, otherwise it is not on the graph. John My calculator said it, I believe it, that settles it

Sequences-and-series/447147: For any integers n, let ® n be defined as the sum of the distinct prime factors of n. For instance, ® 36=5, because 2 and 3 are the only prime factors of 36 and 2+3=5. What is the smallest value of w for which ® w=12 ? 1 solutions Answer 307880 by solver91311(17059)   on 2011-05-09 18:03:53 (Show Source): You can put this solution on YOUR website! Hint: 5 + 7 = 12 John My calculator said it, I believe it, that settles it

Exponents/447153: how do i change 2y(-5) into positive exponents only? btw. -5 is the exponent. 1 solutions Answer 307875 by solver91311(17059)   on 2011-05-09 17:52:24 (Show Source): You can put this solution on YOUR website! Negative exponents in a numerator become positive exponents in a denominator. John My calculator said it, I believe it, that settles it

Travel_Word_Problems/447157: On a digital clock, a time like 6:06 is called a "double" time because the number representing the hours is the same as the number representing the minute. Other such "doubles" are 8:08 and 9:09. What is the smallest time period between two such doubles? 1 solutions Answer 307872 by solver91311(17059)   on 2011-05-09 17:51:06 (Show Source): You can put this solution on YOUR website! To get from one double to the next you always add 1 hour and 1 minute (61 minutes) because it is always 1 more hour and 1 more minute, except for one particular situation. Think about it. John My calculator said it, I believe it, that settles it

Inequalities/447158: 5x-7 lesser or equal to 2x+5 1 solutions Answer 307871 by solver91311(17059)   on 2011-05-09 17:48:12 (Show Source): You can put this solution on YOUR website! Add -2x to both sides. Add 7 to both sides. John My calculator said it, I believe it, that settles it

logarithm/445194: I am supposed to find how many words found after the time limit (t) here is the equation: L(t)=225(1-e^-0.0061t). I am supposed to find how, after 30min. and 60min., many words the student has learned. 1 solutions Answer 306741 by solver91311(17059)   on 2011-05-04 19:45:44 (Show Source): You can put this solution on YOUR website! That depends. You didn't say what time units represents in your function. If is in minutes, then just substitute 30 and 60 and do the arithmetic (using the calculator, of course). If represents hours, then substitute 0.5 and 1.0 for . John My calculator said it, I believe it, that settles it

Triangles/445198: The Earth is approximately a sphere. Its diameter is about 12 730 Km. Whater covers approximately 66% of the Earth's surface. How many Square kilometers of land covers the earth? AND HOW? 1 solutions Answer 306739 by solver91311(17059)   on 2011-05-04 19:40:00 (Show Source): You can put this solution on YOUR website! Divide the given diameter by 2 to obtain the radius and then use the radius in the formula given in the answer to problem 445192. Take 34% of your answer to get the land area. John My calculator said it, I believe it, that settles it

Surface-area/445192: what is the surface area of a sphere with a radius of 2 feet?? AND HOW? 1 solutions Answer 306737 by solver91311(17059)   on 2011-05-04 19:36:17 (Show Source): You can put this solution on YOUR website! The surface area of a sphere is 4 times the area of a circle with identical radius. Unless you are given a precision specification for your answer, leave the answer in terms of John My calculator said it, I believe it, that settles it

Surface-area/445182: A landscaper is preparing a circular flowerbed. The bed has a 12 - foot diameter. He will need 13 plants per square yard. How many plants should he buy? AND HOW?? Thanks 1 solutions Answer 306736 by solver91311(17059)   on 2011-05-04 19:31:25 (Show Source): You can put this solution on YOUR website! Divide the given diameter by 2 to obtain the radius in feet. Divide the radius in feet by 3 to obtain the radius in yards. Square the radius and multiply the result by an approximation of suitable for your required level of precision. This calculation will provide you with the area of the circle in square yards. Multiply the calculated area by 13 and round to the nearest whole number. (unless you think the hero of this story knows of a nursery that will sell him fractional parts of a plant) Notes on approximation of for this problem. Either , , or any representation of to greater precision will result in the same number of plants after rounding to the nearest whole number of plants. John My calculator said it, I believe it, that settles it

Equations/445177: what are the steps you can use to solve t/7 +4>6 1 solutions Answer 306734 by solver91311(17059)   on 2011-05-04 19:19:03 (Show Source): You can put this solution on YOUR website! Presuming you mean: then Add -4 to both sides. Multiply both sides by 7 John My calculator said it, I believe it, that settles it

Triangles/445127: a flower bed is in the shape of a triangle with one side twice the length of the shortest side, and the third side is 25 feet more than the length of the shortest side. find the dimensions if the perimeter is 165 feet 1 solutions Answer 306718 by solver91311(17059)   on 2011-05-04 18:14:38 (Show Source): You can put this solution on YOUR website! Solve for , then calculate and . John My calculator said it, I believe it, that settles it

Permutations/445117: Could you please explain, 'How many combinations of three letters each can be made out of the following:' ROYBGIV ROYBGIV ROYBGIV Kind regards, Rod Horton. 1 solutions Answer 306716 by solver91311(17059)   on 2011-05-04 18:11:40 (Show Source): You can put this solution on YOUR website! That depends on how you are using the word "Combination." In the strict mathematical sense it means how many different ways to choose groups where the order of elements in an individual group doesn't matter. Furthermore, elements are typically not repeated. So, if ROY is a different combination than YRO or ORY, or if RRB is a valid choice, then you are using combination in a non-standard way. In such case, there are 7 ways to chose the first of the three times 7 ways to chose the second of the three times 7 ways to pick the third element, for a total of 343 different arrangements. If order matters but you can't duplicate, then there are 7 ways to pick the first element, 6 ways to pick the second element, and 5 ways to pick the 3rd element for a total of 210 different arrangements. However, the number of combinations (where order doesn't matter) of n things taken k at a time is given by: So for 7 things taken 3 at a time: Notice that this result is the previous result divided by 6, which, by the way is the number of ways that three different things can be arranged, for example ROY, RYO, YOR, YRO, OYR, ORY. John My calculator said it, I believe it, that settles it

Volume/445101: how do you find the volumes of cylinders, spheres, and cones? 1 solutions Answer 306705 by solver91311(17059)   on 2011-05-04 17:43:26 (Show Source): You can put this solution on YOUR website! The volume of a cylinder is the area of the circular base times the height: The volume of a cone is one-third of the volume of a cylinder with the same height and base radius: Don't believe it? Try it. Get your hands on one of those clear plastic cylinders that Geometry teachers use -- one with an open base on one end. Also get a cone that is the same height and base radius. Fill the inverted cone with sand (or sugar or whatever) exactly to the top, then pour it into the cylinder. Repeat and repeat. The cylinder will be exactly full with no sand left over. The volume of a sphere is times the volume of a cube with side measure equal to the sphere's radius. John My calculator said it, I believe it, that settles it

absolute-value/445095: |r-9|=-3 no solution or solution????? 1 solutions Answer 306695 by solver91311(17059)   on 2011-05-04 17:21:34 (Show Source): You can put this solution on YOUR website! What value can you put inside of a pair of absolute value bars such that the value of the absolute value function is less than zero? Use the definition of absolute value as a guide to answering. What is the significance of five question marks? Does the number of question marks give an indication of the degree of your lack of understanding? If so, how does four question marks differ from five? Is it a linear or exponential relationship? John My calculator said it, I believe it, that settles it

Graphs/445079: how would you graph the quadratic function y=xsquared-4x+2 1 solutions Answer 306692 by solver91311(17059)   on 2011-05-04 17:16:04 (Show Source): You can put this solution on YOUR website! The same way I would graph any quadratic function. Given the quadratic function: I would first calculate the -coordinate of the vertex: Then I would calculate the -coordinate of the vertex: Then I would plot the vertex point: Then I would plot the -intercept: Then I would use the properties of symmetry to plot the point symmetric to the -intercept: Then I would calculate the discriminant, . If then I would know that there are no -intercepts. In this case I would select an integer value close to and calculate the function value at that independent variable value. I would repeat this step with different independent variable values as often as I felt necessary to give an indication of the shape of the curve. If then I would know that I have already plotted the -intercept, namely the vertex. I would proceed to plot another couple points as in the situation described above. If , then I would know that there are two distinct real roots and therefore two -intercepts. I would set the function equal to zero and solve the resulting quadratic equation by the most convenient means. Once I had determined the two values for the roots, and , I would plot the two points: and . Generally speaking, that is sufficient to give an idea of the shape of the curve, so all that is left is to draw a smooth curve through all of your plotted points. If you are unsure of the curve's shape by this point, then by all means select some different values for the independent variable and calculate the function value to give yourself additional data points to use. John My calculator said it, I believe it, that settles it

Quadratic_Equations/444975: During a chemistry experiement, the cork in a 0.5 foot tall beaker with an effervescent solution pops off with an initial velocity of 20 feet per second. How many seconds does it take for the cork to hit the table? 1 solutions Answer 306630 by solver91311(17059)   on 2011-05-04 14:04:51 (Show Source): You can put this solution on YOUR website! Substitute known values: Solve for the positive root. Hint: Does not factor. Use the quadratic formula. The way the problem is worded I would submit my answer in simplified radical form. Hint #2: , and don't forget the negative sign on the lead coefficient. John My calculator said it, I believe it, that settles it

Geometry_Word_Problems/444974: A rectangular Persian carpet has a perimeter of 232 inches. The length of the carpet is 22 inches more than the width. What are the dimensions of the carpet? 1 solutions Answer 306628 by solver91311(17059)   on 2011-05-04 13:53:00 (Show Source): You can put this solution on YOUR website! Solve for , then calculate John My calculator said it, I believe it, that settles it

Travel_Word_Problems/444972: From a point on a river, two boats are driven in opposite directions, one at 10 miles per hour and the other at 6 miles per hour. in how many hours will they be 64 miles apart? 1 solutions Answer 306627 by solver91311(17059)   on 2011-05-04 13:49:54 (Show Source): You can put this solution on YOUR website! You would think at first blush that the speed of the river current would make a difference in this problem. But if you consider that the current will have exactly the same effect on both boats, the actual speed of the current is immaterial. If one boat is going 10 mph and the other 6 mph in the opposite direction, then the boats are moving apart at 10 + 6 = 16 mph. How long does it take to go 64 miles at 16 mph? John My calculator said it, I believe it, that settles it

Evaluation_Word_Problems/444965: Solve the problem using the five steps to solving algebra questions. Show all of your work step by step please. Five steps: 1. Familiarize yourself with the problem. 2. Translate to mathematical language. (This often means writing an equation.) 3. Carry out some mathematical manipulation. (This often means solving an equation.) 4. Check your possible answer in the original problem. 5. State the answer clearly, using a complete English sentence. The parking lot at a grocery store has 70 cars in it. 60% of the cars are red. How many cars are red? 1 solutions Answer 306622 by solver91311(17059)   on 2011-05-04 13:23:31 (Show Source): You can put this solution on YOUR website! 1. Familiarize: "Hello, problem. My name is John." Wait for response. Not hearing a response, continue with step 2 while making a mental note to complain to your teacher/instructor/professor about this problem's lack of social graces. 2. "the cars" and 70 are the same thing, "of" means multiply, and 60% means 0.60, so: the number of cars in the grocery store parking lot that are red. 3. I only do the algebra part. The arithmetic part is yours to do. 4. Divide your answer by 70. You should get 0.6. Divide your answer by 0.6. You should get 70. If not, repeat step 3. 5. of the 70 cars in the grocery store parking lot are red. John My calculator said it, I believe it, that settles it

Mixture_Word_Problems/444955: how much water should be added to 26 mL of 17% alcohol solution to reduce the concentration to 13%? 1 solutions Answer 306617 by solver91311(17059)   on 2011-05-04 13:00:35 (Show Source): You can put this solution on YOUR website! Solve for . John My calculator said it, I believe it, that settles it

Exponents-negative-and-fractional/444951: For what values of x is the function y = 3 to the "x" power(x is an exponent) between 0 and 1? 1 solutions Answer 306615 by solver91311(17059)   on 2011-05-04 12:56:14 (Show Source): You can put this solution on YOUR website! For Or Depending on what you mean by "between". John My calculator said it, I believe it, that settles it

Quadratic_Equations/444661: the question is write and solve an equation to find the length and with of the rectangle whose width os 3 less than the length. the area is 4cm 1 solutions Answer 306458 by solver91311(17059)   on 2011-05-03 20:47:45 (Show Source): You can put this solution on YOUR website! Let represent the width of the rectangle (note spelling of width, not "with"). Then must represent the length. Since the area is the length times the width, represents the area. You state that the area is 4 cm but that is clearly wrong. Area is measured in square units, not linear units, hence the area must be 4 square centimeters. And in standard form: Just solve for , discard the negative root (since you are trying to determine a postive measure of length), and then calculate John My calculator said it, I believe it, that settles it

Expressions-with-variables/444657: Evaluate the following expressions when x=3, y=-2, and z=-1 2-3x/6+2y(x-1/4)-4z 1 solutions Answer 306454 by solver91311(17059)   on 2011-05-03 20:38:25 (Show Source): You can put this solution on YOUR website! Just replace all of the variables with the indicated values, then do the arithmetic. John My calculator said it, I believe it, that settles it

Equations/444628: May you please help me on this word promblem? : a chess tournament starts with 64 people commpeting. The ecponential function, y=64(1/2)^x describes how many people are remaining in the tournament after x rounds. how many rounds will it take to reach a champion? 1 solutions Answer 306453 by solver91311(17059)   on 2011-05-03 20:36:49 (Show Source): You can put this solution on YOUR website! To reach a champion, , so: John My calculator said it, I believe it, that settles it

Quadratic_Equations/444589: How do you find a quadratic equation if you are only given the solution? Is it possible to have different quadratic equations with the same solution? 1 solutions Answer 306433 by solver91311(17059)   on 2011-05-03 19:24:43 (Show Source): You can put this solution on YOUR website! Let's assume that and are the roots of some quadratic equation Then with a little algebra we can see that and . Reversing the Zero Product Rule, we can write: Apply FOIL Then let , , and and substitute: The only fly in the ointment is that you can take any real number, say and apply it as a factor: You still have the same roots to the equation, but when you multiply it out you get: Which means that there are an infinite number of quadratic equations with a given pair of roots (or given root with a muliplicity of 2) but they only differ by a factor common to all three terms in the trinomial representation of the quadratic. John My calculator said it, I believe it, that settles it