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 logarithm/198851: Express as a single logarithm 1/2 Log a X + 3 Log a Y - 2 Log a X 1 solutions Answer 149336 by jim_thompson5910(28595)   on 2009-06-03 17:14:24 (Show Source): You can put this solution on YOUR website! Start with the given expression. Rewrite the logs using the identity Convert to radical notation. Combine the first two logs using the identity Combine the logs using the identity So
 Probability-and-statistics/198806: from a group of 6 men and 4 women, a committee of 3 is to be selected at random. find P(at least 2 women)1 solutions Answer 149335 by jim_thompson5910(28595)   on 2009-06-03 17:10:34 (Show Source): You can put this solution on YOUR website!Simply find the probability of 2 women or 3 women. In other words, P(at least 2 women) = P(2 women) + P(3 women)
 Geometric_formulas/198800: This question is from textbook geometry can you please help me answer the following ((( What is the locus of points in a plane that are equidistant from points A and B in the plane? )))1 solutions Answer 149334 by jim_thompson5910(28595)   on 2009-06-03 17:08:15 (Show Source): You can put this solution on YOUR website!The locus of points in a plane that are equidistant from points A and B in the plane is a line that is the perpendicular bisector to line that connects the two points.
 Linear-equations/198850: solving x-y=6 for y results in y=-x+6 1 solutions Answer 149331 by jim_thompson5910(28595)   on 2009-06-03 16:51:00 (Show Source): You can put this solution on YOUR website! Start with the given equation. Subtract from both sides. Rearrange the terms. Divide both sides by to isolate y. Break up the fraction. Reduce.
 Mixture_Word_Problems/198832: How much soil containing 45% sand do you need to add 1ft of soil containing 15% sand in order to make a soil containing 35% sand?1 solutions Answer 149330 by jim_thompson5910(28595)   on 2009-06-03 16:46:00 (Show Source): You can put this solution on YOUR website!This question has been answered here. Edit: From the previous solution, the given equation is Start with the given equation. Distribute Multiply both sides by 100 to clear out the decimals. Distribute and multiply. Subtract from both sides. Subtract from both sides. Combine like terms on the left side. Combine like terms on the right side. Divide both sides by to isolate . Reduce. ---------------------------------------------------------------------- Answer: So the solution is which means that you need 2 cubic feet of soil containing 45% sand.
 Probability-and-statistics/198845: At Ajax Spring Water, a half-liter bottle of soft drink is supposed to contain a mean of 520 ml. The filling process follows a normal distribution with a known process standard deviation of 4 ml. (a) Which sampling distribution would you use if random samples of 10 bottles are to be weighed? Why? (b) Set up hypotheses and a two-tailed decision rule for the correct mean using the 5 percent level of significance. (c) If a sample of 16 bottles shows a mean fill of 515 ml, does this contradict the hypothesis that the true mean is 520 ml?1 solutions Answer 149329 by jim_thompson5910(28595)   on 2009-06-03 16:42:19 (Show Source): You can put this solution on YOUR website!This question has already been answered here.
 Numbers_Word_Problems/198849: An express train and a local train both leave Gray's Lake at 12:00 noon and head for Chicago 60 miles away. The express travels twice as fast as the local and arrives 2 hours ahead of it.Find the speed of each train. 60m/2h= t + 12n I cannot get the right answer.1 solutions Answer 149328 by jim_thompson5910(28595)   on 2009-06-03 16:40:14 (Show Source): You can put this solution on YOUR website!Let time of express train and time of local train Also, let speed of express train and speed of local train Since the "express train travels twice as fast as the local train", this means that Also, because "the express train arrives 2 hours ahead of the local train", this tells us Now let's set up the formula for the local train: Start with the distance rate time formula Plug in , and Divide both sides by . So after isolating the second speed, we get Now let's set up the formula for the express train: Start with the distance rate time formula Plug in , and Plug in and Plug in Multiply Multiply both sides by . Distribute Subtract from both sides. Combine like terms. Divide both sides by -60 to isolate . Divide So it takes 4 hours for the local train Go back to the local train formula Plug in Divide both sides by 4. Divide. So the speed of the local train is 15 mph Now simply double the speed of the local train to get So the speed of the local train is 15 mph and the speed of the express train is 30 mph. Note: nowhere in the solution above is a mention of 12:00 noon. This information is unnecessary and it is put in there to throw you off.
 Polynomials-and-rational-expressions/198848: please help me solve this 8y^4+12y^2-176 divided by 2y-41 solutions Answer 149327 by jim_thompson5910(28595)   on 2009-06-03 16:28:06 (Show Source): You can put this solution on YOUR website! Start with the given expression. Factor the numerator Factor the denominator Factor 4 to get 2*2 Cancel out the common terms. Simplify Expand and multiply So where
 Surface-area/198847: This question is from textbook Directions state: Find the perimeters and areas of the squares and rectangles in questions 7-10. The figure shown in the text has a picture of a square which is dissected in the middle to form two right triangles. The triangle has two 45 degree and one 90 degree angles. All that is given is six square root of two (6 square root 2) for the hypotenuse of the adjacent right triangles. My apoogies but I do not have a square root symbol key on my computer keyboard. As you can tell I need to solve for the perimeter and area, but I do not even know how to without data given for either side one or side two.1 solutions Answer 149325 by jim_thompson5910(28595)   on 2009-06-03 16:11:37 (Show Source): You can put this solution on YOUR website!If we just focus on one triangle, we get To find the unknown length, we need to use the Pythagorean Theorem. Remember, the Pythagorean Theorem is where "a" and "b" are the legs of a triangle and "c" is the hypotenuse. Since the legs are and (ie the legs are equal) this means that and Also, since the hypotenuse is , this means that . Start with the Pythagorean theorem. Plug in , , Square to get . Combine like terms. Divide both sides by 2. Reduce Take the square root of both sides. Note: only the positive square root is considered (since a negative length doesn't make sense). Evaluate the square root of 36 to get 6 So the side length of the square is 6 units. Now simply plug this side length into the following formulas (note: "s" is the length of the side of the square): Perimeter: . So the perimeter is 24 units. Area: . So the area is 36 square units.
Linear-equations/198846: state the x and y-intercept of y=4x-7
1 solutions

Answer 149319 by jim_thompson5910(28595)   on 2009-06-03 15:40:06 (Show Source):
You can put this solution on YOUR website!

#### x-intercept

To find the x-intercept, plug in and solve for x

Plug in .

Subtract 4x from both sides.

Divide both sides by to isolate .

Reduce.

So the x-intercept is .

------------------------------------------

#### y-intercept

To find the y-intercept, plug in and solve for y

Plug in .

Multiply and 0 to get 0.

Simplify.

So the y-intercept is .

Linear-equations/198844: what is the x-intercept of the line 4x+y=4
1 solutions

Answer 149318 by jim_thompson5910(28595)   on 2009-06-03 15:36:19 (Show Source):
You can put this solution on YOUR website!

#### x-intercept

To find the x-intercept, plug in and solve for x

Plug in .

Simplify.

Divide both sides by to isolate .

Reduce.

So the x-intercept is .

Linear-equations/198841: find both intercepts of the line 3x+4y=-12
1 solutions

Answer 149316 by jim_thompson5910(28595)   on 2009-06-03 15:26:25 (Show Source):
You can put this solution on YOUR website!

#### x-intercept

To find the x-intercept, plug in and solve for x

Plug in .

Multiply and 0 to get 0.

Simplify.

Divide both sides by to isolate .

Reduce.

So the x-intercept is .

------------------------------------------

#### y-intercept

To find the y-intercept, plug in and solve for y

Plug in .

Multiply and 0 to get 0.

Simplify.

Divide both sides by to isolate .

Reduce.

So the y-intercept is .

Notice that if we graph the equation , we can see that the graph has the x-intercept and the y-intercept

Graph of

 Linear-equations/198840: fine the slope of the line that contains (4,5) and (4,4)1 solutions Answer 149315 by jim_thompson5910(28595)   on 2009-06-03 15:20:33 (Show Source): You can put this solution on YOUR website!Note: is the first point and is the second point . Start with the slope formula. Plug in , , , and Subtract from to get Subtract from to get Remember, you cannot divide by zero. So this means that the slope is undefined.
 Linear-equations/198839: Rewrite the equation in slope-intercept form. 8x-3y-5=01 solutions Answer 149313 by jim_thompson5910(28595)   on 2009-06-03 15:15:55 (Show Source): You can put this solution on YOUR website! Start with the given equation. Add 5 to both sides. Subtract from both sides. Rearrange the terms. Divide both sides by to isolate y. Break up the fraction. Reduce. So the equation is now in slope intercept form where the slope is and the y-intercept is note: the y-intercept is the point
 Linear-equations/198838: Find the slope and y-intercept of the line 6x-3y=721 solutions Answer 149312 by jim_thompson5910(28595)   on 2009-06-03 15:08:58 (Show Source): You can put this solution on YOUR website! Start with the given equation. Subtract from both sides. Rearrange the terms. Divide both sides by to isolate y. Break up the fraction. Reduce. So the equation is now in slope intercept form where the slope is and the y-intercept is note: the y-intercept is the point
 Equations/198836: A firm prints advertising leaflets. They have a set-up fee of £100 and charge 5p per leaflet. Explain in words how to find the total cost of printing N leaflets. Hence explain why the total cost £(C) is given by the formula C = 100 + 0.05N. I am sorry to ask for help but I have never been very good with algebra and I am still awaiting a battery for my TI84. 1 solutions Answer 149308 by jim_thompson5910(28595)   on 2009-06-03 14:45:39 (Show Source): You can put this solution on YOUR website!No matter how many leaflets you buy, you will pay at least £100. So that's why the constant cost of 100 is in there. Any leaflets you buy, you'll be paying 0.05 (or 5%) of a pound per leaflet. So this is why 0.05N is added. Here are some examples: If you buy 100 leaflets, then N=100 and... C = 100 + 0.05(100) = 100 + 5 = 105 So the total cost is £105 Or if you buy 300 leaflets, then N=300 and... C = 100 + 0.05(300) = 100 + 15 = 115 So the total cost is £115
 logarithm/198808: Hello! A function f(x) is given. f(x) = log5(log10(x)) (a) Find the domain of the function f (b) Find the inverse function of f. f -1(x) = thanks for your help! 1 solutions Answer 149307 by jim_thompson5910(28595)   on 2009-06-03 14:33:20 (Show Source): You can put this solution on YOUR website!a) Since you cannot take the log of 0 or a negative value, this means that and (for the outer and inner logs) If we solve , we get . So combining the inequalities and (ie perform a set union), we get . So the domain of is ------------------ b) Start with the given function. Replace f(x) with "y" Switch each x and y Rewrite the equation using the property: ====> Rewrite the equation again using the property: ====> So the inverse function is
 Probability-and-statistics/198810: Write two data sets with a range equal to 35 but with different standard deviations. You do not need to calculate the standard deviations. 1 solutions Answer 149305 by jim_thompson5910(28595)   on 2009-06-03 14:23:04 (Show Source): You can put this solution on YOUR website!Data Set #1: 1, 5, 33, 36 Range = 36 - 1 = 35 Standard Deviation is relatively large (since the data values are spread out) Data Set #2: 1, 2, 4, 7, 9, 12, 13, 14, 16, 19, 20, 21, 25, 27, 29, 30, 31, 34, 35, 36 Range = 36 - 1 = 35 Now the standard deviation is slightly smaller (since the data values are closer together)
 Probability-and-statistics/198815: A set of data with a mean of 58 and a standard deviation of 6.3 is normally distributed. Find the value that is 2 standard deviations below the mean. Round your answer to the nearest tenth. 1 solutions Answer 149303 by jim_thompson5910(28595)   on 2009-06-03 14:16:33 (Show Source): You can put this solution on YOUR website!Simply subtract 2 times the standard deviation from the mean to get: 58-2*6.3=58-12.6=45.4 So the value that is 2 standard deviations below the mean is 45.4
 Geometric_formulas/198799: This question is from textbook geometry can you please help me answer the following ((( What is the locus of points in space that are equidistant from two parellel planes? )))1 solutions Answer 149302 by jim_thompson5910(28595)   on 2009-06-03 14:14:25 (Show Source): You can put this solution on YOUR website!If you either draw a picture or hold up two sheets of paper (for the two planes), you'll see that the locus of points form a third plane that is right in the middle of the two parallel planes.
 Quadratic_Equations/198828: Write three quadratic equations, with a, b, and c (coefficients of x2, x, and the constant) as: Integers Rational numbers Irrational numbers I don't understand how to set these up... can someone give me some examples and explanations so i can form my own equations?1 solutions Answer 149301 by jim_thompson5910(28595)   on 2009-06-03 14:11:06 (Show Source): You can put this solution on YOUR website!1. Integers: any whole number Let a=2, b=6, c=-12 (which are all whole numbers) 2. Rational Number: any number that is a ratio (or fraction) of two integers. So and are rational numbers Let ,, (which are all fractions of whole numbers) 3. Irrational number: any number that cannot be represented by a fraction of two integers. For example and are irrational numbers , , , ,
 Functions/198829: What kind of function is, Y= -2x squared + 1?1 solutions Answer 149300 by jim_thompson5910(28595)   on 2009-06-03 14:09:30 (Show Source): You can put this solution on YOUR website!The function is a quadratic polynomial function.
 Quadratic_Equations/198830: Joe has a collection of nickels and dimes that is worth $6.05. If the number of dimes was doubled and number of nickels was decreaseed by 10, the value of the coins would be$9.85. how many dimes does he have? f(x) = ax^2 + bx + c = 0 using this formula I cannot figure the answer out. please help.1 solutions Answer 149299 by jim_thompson5910(28595)   on 2009-06-03 14:08:48 (Show Source): You can put this solution on YOUR website!This question has been answered here. Did you have any questions about it?
 Probability-and-statistics/198809: Use the following set of values for exercises 8–13. 0.3 0.6 0.9 1.3 0.4 0.6 1.2 1.4 1.1 0.2 0.2 please Find the mean, median, and mode(s) of the data set. Round answers to the nearest hundredth, if necessary. 1. Find the range. 2. Find the interquartile range. 3. Find the standard deviation. Round to the nearest hundredth. 4. Find the 25th and 75th percentiles. thanks for helping me out!1 solutions Answer 149297 by jim_thompson5910(28595)   on 2009-06-03 14:05:51 (Show Source): You can put this solution on YOUR website!First sort the numbers into ascending order (from least to greatest): 0.2,0.2,0.3,0.4,0.6,0.6,0.9,1.1,1.2,1.3,1.4 Range: To find the range, subtract the smallest number (in this case 0.2) from the largest number (in this case 1.4) like this: So the range is 1.2 Interquartile Range: First, find the median for the first half of the data set (ignore the median): Median of 0.2, 0.2, 0.3, 0.4, 0.6 is 0.3 (since this is the middle most value) Now find the median of the last half of the data set (ignore the median): Median of 0.9, 1.1, 1.2, 1.3, 1.4 is 1.2 (since this is the middle most value) So the 1st and 3rd quartiles are 0.3 and 1.2 respectively. This means that the interquartile range is 1.2 - 0.3 = 0.9 Note: the interquartile range is the difference between the 1st and 3rd quartiles Note: I'm assuming that you want the sample standard deviation. Standard Deviation: Step 1) Find the mean: So the mean is roughly 0.75 (rounded to the nearest hundredth). ---------------------------------------------------------- Step 2) Find the differences between the mean and every value: Now subtract EVERY value from the mean (0.75) to get: 0.2-0.75 = -0.55, 0.2-0.75 = -0.55, 0.3-0.75 = -0.45, 0.4-0.75 = -0.35, 0.6-0.75 = -0.15, 0.6-0.75 = -0.15, 0.9-0.75 = 0.15, 1.1-0.75 = 0.35, 1.2-0.75 = 0.45, 1.3-0.75 = 0.55, 1.4-0.75 = 0.65, So you should have a new column of values: -0.55, -0.55, -0.45, -0.35, -0.15, -0.15, 0.15, 0.35, 0.45, 0.55, 0.65, ---------------------------------------------------------- Step 3) Squaring the differences: Now square EVERY value in the last column to get: (-0.55)^2 = 0.3, (-0.55)^2 = 0.3, (-0.45)^2 = 0.2, (-0.35)^2 = 0.12, (-0.15)^2 = 0.02, (-0.15)^2 = 0.02, (0.15)^2 = 0.02, (0.35)^2 = 0.12, (0.45)^2 = 0.2, (0.55)^2 = 0.3, (0.65)^2 = 0.42, So you should have a new column of values: 0.3, 0.3, 0.2, 0.12, 0.02, 0.02, 0.02, 0.12, 0.2, 0.3, 0.42, ---------------------------------------------------------- Step 4) Adding up the squares: Now add up the values of the last column: 0.3 + 0.3 + 0.2 + 0.12 + 0.02 + 0.02 + 0.02 + 0.12 + 0.2 + 0.3 + 0.42 = 2.02 ---------------------------------------------------------- Step 5) Divide the sum by n-1: Divide that sum by one less than the number of values in the list (in this case, it is n-1=11-1=10). ---------------------------------------------------------- Step 6) Take the square root of the quotient: Take the square root of to get Now round to the nearest hundredth to get . So the standard deviation is roughly . If you don't like that method, then here's another way: First sort the numbers into ascending order (from least to greatest): 0.2,0.2,0.3,0.4,0.6,0.6,0.9,1.1,1.2,1.3,1.4 Standard Deviation: where is the average, is the ith number, and is the number of numbers So we can replace N with 11 Subtract to get 10 Replace with 0.75 Expand the summation (replace each with the respective number) Subtract the terms in the parenthesis Square each term Add up all of the terms Multiply Take the square root Round to the nearest hundredth So the standard deviation is roughly 25th and 75th percentiles: The 25th and 75th percentiles are simply the first and third quartiles. We found these earlier to be 0.3 and 1.2. So the 25th and 75th percentiles are 0.3 and 1.2