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 absolute-value/198054: solve |2x-7|=12, show all work1 solutions Answer 148532 by jim_thompson5910(28598)   on 2009-05-27 20:49:48 (Show Source): You can put this solution on YOUR website! Start with the given equation Break up the absolute value (remember, if you have , then or ) or Set the expression equal to the original value 12 and it's opposite -12 Now lets focus on the first equation Add 7 to both sides Combine like terms on the right side Reduce Now lets focus on the second equation Add 7 to both sides Combine like terms on the right side Divide both sides by 2 to isolate x Reduce So the solutions to are: and
 Inequalities/198058: 3(7 + 2x) ≤ 30 + 7(x - 1) can someone help me resolve this inequality for my algebra class Thank you Debra 1 solutions Answer 148530 by jim_thompson5910(28598)   on 2009-05-27 20:47:48 (Show Source): You can put this solution on YOUR website! Start with the given inequality. Distribute. Combine like terms on the right side. 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 . note: Remember, the inequality sign flips when we divide both sides by a negative number. Reduce. ---------------------------------------------------------------------- Answer: So the answer is
 Graphs/198037: Graph y1 solutions Answer 148508 by jim_thompson5910(28598)   on 2009-05-27 19:03:49 (Show Source): You can put this solution on YOUR website!Simply graph the line and shade the entire region below the graph since the inequality sign is "<" (less than).
 Inequalities/198036: Solve and graph the inequality x-3>(or equal to) 71 solutions Answer 148506 by jim_thompson5910(28598)   on 2009-05-27 19:00:54 (Show Source): You can put this solution on YOUR website! Start with the given inequality. Add to both sides. Combine like terms on the right side. ---------------------------------------------------------------------- Answer: So the answer is So the answer in interval notation is [) Also, the answer in set-builder notation is Here's the graph of the solution set
 Probability-and-statistics/198022: A coin is tossed and a 6-sided die is rolled. What is the probability that the coin shows head and the dies shows a 4?1 solutions Answer 148500 by jim_thompson5910(28598)   on 2009-05-27 18:17:06 (Show Source): You can put this solution on YOUR website!P(heads AND rolling a 4) = P(heads) * P(rolling a 4) P(heads AND rolling a 4) = (1/2) * (1/6) P(heads AND rolling a 4) = (1*1)/(2*6) P(heads AND rolling a 4) = 1/12
 Average/198020: The average of a,b,c, and d is (1)a+b+c+d over4 (2)a+b+c+d/4 (3)4a+4b+4c+4d/4 (4)4(a+b+C+d)1 solutions Answer 148498 by jim_thompson5910(28598)   on 2009-05-27 18:13:09 (Show Source): You can put this solution on YOUR website!Recall, the average of a set of numbers is the sum of those numbers divided by the number of values being added. So the average of a,b,c, and d is
 Graphs/198021: Which ordered pair is a solution of the following system of equations? x+y=5 x-y=-1 1.(2,-3) 2.(2,3) 3.(3,-2) 4.(3,2) 1 solutions Answer 148497 by jim_thompson5910(28598)   on 2009-05-27 18:10:10 (Show Source): You can put this solution on YOUR website! Start with the given system of equations: Add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this: Group like terms. Combine like terms. Simplify. Divide both sides by to isolate . Reduce. ------------------------------------------------------------------ Now go back to the first equation. Plug in . Multiply. Subtract from both sides. Combine like terms on the right side. So the solutions are and . Which form the ordered pair . So the answer is the second choice. This means that the system is consistent and independent. Notice when we graph the equations, we see that they intersect at . So this visually verifies our answer. Graph of (red) and (green)
 Distributive-associative-commutative-properties/198018: The fraction x²+2x-8/x-2 is equivalent to (1)3x+4 (2)(x-4)(x+2)/(x-2) (3)x-4 (4)x+4 1 solutions Answer 148495 by jim_thompson5910(28598)   on 2009-05-27 17:58:09 (Show Source): You can put this solution on YOUR website! Start with the given expression. Factor to get . Highlight the common terms. Cancel out the common terms. Simplify. So simplifies to . In other words, where
 Expressions-with-variables/198012: I have gotten thru 4 of the 8 questions on my worksheet and am stuck with this one. the direction say to "solve each system by elimination" 12x - 7y = -10 -4x + 3y = 10 I can't seem to get either side to cancel out.1 solutions Answer 148492 by jim_thompson5910(28598)   on 2009-05-27 17:48:33 (Show Source): You can put this solution on YOUR website! Start with the given system of equations: Multiply the both sides of the second equation by 3. Distribute and multiply. So we have the new system of equations: Now add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this: Group like terms. Combine like terms. Simplify. Divide both sides by to isolate . Reduce. ------------------------------------------------------------------ Now go back to the first equation. Plug in . Multiply. Add to both sides. Combine like terms on the right side. Divide both sides by to isolate . Reduce. So the solutions are and . Which form the ordered pair . This means that the system is consistent and independent. Notice when we graph the equations, we see that they intersect at . So this visually verifies our answer. Graph of (red) and (green)
 Exponents/198011: The sum of two binomials is 3x²-5x.If one of the binomials is 2x²-x, what is the other?1 solutions Answer 148491 by jim_thompson5910(28598)   on 2009-05-27 17:44:45 (Show Source): You can put this solution on YOUR website!If "A" and "B" are two binomials which add to a third binomial "C", then this means that . If we know what "A" and "C" are, then we can subtract "A" from both sides to solve for "B" like so: So in this case, , , and "B" is our unknown binomial Start with the given equation. Plug in and Distribute Combine like terms. So the unknown binomial is
 Expressions-with-variables/197930: (((x^2-y^2)/(x^3-y^3))*((x^2+xy+y^2)/(x^2+2xy+y^2)))1 solutions Answer 148489 by jim_thompson5910(28598)   on 2009-05-27 17:38:58 (Show Source): You can put this solution on YOUR website! Start with the given expression. Factor to get . Factor to get . Factor to get . Combine the fractions. Highlight the common terms. Cancel out the common terms. Simplify. So simplifies to . In other words,
 Equations/198003: Solve for x in terms of a, b, and c: ax/c=b.1 solutions Answer 148487 by jim_thompson5910(28598)   on 2009-05-27 17:14:20 (Show Source): You can put this solution on YOUR website! Start with the given equation. Multiply both sides by "c". Divide both sides by "a". So the solution is
 Polynomials-and-rational-expressions/198002: please help me solve this problem: (x+y)^41 solutions Answer 148486 by jim_thompson5910(28598)   on 2009-05-27 16:55:20 (Show Source): You can put this solution on YOUR website! Start with the given expression To expand this, we're going to use binomial expansion. So let's look at Pascal's triangle: 1    1   1    1   2   1    1   3   3   1    1   4   6   4   1    Looking at the row that starts with 1,4, etc, we can see that this row has the numbers: 1, 4, 6, 4, and 1 These numbers will be the coefficients of our expansion. So to expand , simply follow this procedure: Write the first coefficient. Multiply that coefficient with the first binomial term and then the second binomial term . Repeat this until all of the coefficients have been written. Once that has been done, add up the terms like this: Notice how the coefficients are in front of each term. However, we're not done yet. Looking at the first term , raise to the 4th power and raise to the 0th power. Looking at the second term raise to the 3rd power and raise to the 1st power. Continue this until you reach the final term. Notice how the exponents of are stepping down and the exponents of are stepping up. So the fully expanded expression should now look like this: Distribute the exponents Multiply Multiply the terms with their coefficients So expands and simplifies to . In other words,
 Equations/198001: x+3=-5 1 solutions Answer 148484 by jim_thompson5910(28598)   on 2009-05-27 16:52:41 (Show Source): You can put this solution on YOUR website! Start with the given equation. Subtract from both sides. Combine like terms on the right side. ---------------------------------------------------------------------- Answer: So the solution is
 Travel_Word_Problems/198000: This question is from textbook a train travels 70mi/hr. how far does it travel in 45 min?1 solutions Answer 148479 by jim_thompson5910(28598)   on 2009-05-27 16:37:23 (Show Source): You can put this solution on YOUR website!Note: 45 minutes = 0.75 hours Start with the distance-rate-time formula. Plug in and Multiply So the train travels 52.5 miles.
 Linear-systems/197997: A first number plus twice a second number is 5. Twice the first number plus the second totals 4. Find the numbers.1 solutions Answer 148476 by jim_thompson5910(28598)   on 2009-05-27 16:25:09 (Show Source): You can put this solution on YOUR website!"A first number plus twice a second number is 5. Twice the first number plus the second totals 4" translates to the system: Start with the given system of equations: Multiply the both sides of the first equation by -2. Distribute and multiply. So we have the new system of equations: Now add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this: Group like terms. Combine like terms. Simplify. Divide both sides by to isolate . Reduce. ------------------------------------------------------------------ Now go back to the first equation. Plug in . Multiply. Add to both sides. Combine like terms on the right side. Divide both sides by to isolate . Reduce. So the solutions are and . which means that the first number is 1 and the second number is 2
 Equations/197946: Value of c=2x-y subject to the constraints: x>=1 x<=4 y<=8 x-3y<=-2 The last constraint really confuses me. Thanks for your time. Mike1 solutions Answer 148473 by jim_thompson5910(28598)   on 2009-05-27 16:06:13 (Show Source): You can put this solution on YOUR website!Simply graph every inequality on the xy plane. These graphs will form a closed polygon. It turns out that the values that will optimize "c" will be the x and y values that are at the vertices. So simply plug in the x and y values at the vertices to see which value yields the largest/smallest value of "c". Let me know if this makes sense.
 Polynomials-and-rational-expressions/197993: Hello, could you please help me find the product of this problem:1 solutions Answer 148471 by jim_thompson5910(28598)   on 2009-05-27 16:00:45 (Show Source): You can put this solution on YOUR website! Start with the given expression. Expand. Remember something like . Now let's FOIL the expression. Remember, when you FOIL an expression, you follow this procedure: Multiply the First terms:. Multiply the Outer terms:. Multiply the Inner terms:. Multiply the Last terms:. --------------------------------------------------- So we have the terms: , , , Now add every term listed above to make a single expression. Now combine like terms. So FOILs to . In other words, .
 Exponential-and-logarithmic-functions/197953: The concentration C of a drug in the bloodstream at time t (in hours) can be approximated by C=100(1-e^-0.5t). What will the concentration be after 8 hours? I am lost..... Please help. Thanks.1 solutions Answer 148470 by jim_thompson5910(28598)   on 2009-05-27 15:58:40 (Show Source): You can put this solution on YOUR website! Start with the given equation. Plug in Multiply -0.5 and 8 to get -4 Evaluate (by use of a calculator) to approximately get Subtract Multiply So the concentration is approximately 98.168. I'm assuming that we're talking about a percentage. If so, then there's about 98.168% of the drug left over after 8 hours.
 Probability-and-statistics/197960: Use the following set of values for questions.. 0.3 0.6 0.9 1.3 0.4 0.6 1.2 1.4 1.1 0.2 0.2 8. Find the mean, median, and mode(s) of the data set. Round answers to the nearest hundredth, if necessary. 10. Find the range. 11. Find the interquartile range. 12. Find the standard deviation. Round to the nearest hundredth. 13. Find the 25th and 75th percentiles. thank you so much for the help:)1 solutions Answer 148458 by jim_thompson5910(28598)   on 2009-05-27 15:07:48 (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 Mean: To find the mean, add up all of the numbers and divide the sum by the number of numbers (which in this case is 11). So the mean is roughly 0.745454545454545 which rounds to 0.75 (to the nearest hundredth) ------------------------------------------------------- Median: To find the median, count off about 5 spaces(it's close to half of the size of the list) until you hit the middle number. Now count count off about 5 spaces from the end of the list until you hit the middle. 0.2, 0.2, 0.3, 0.4, 0.6, , 0.9, 1.1, 1.2, 1.3, 1.4 Median=0.6 So the median is 0.6 ---------------------------------------------- Mode: To find the mode, simply look for any repeating numbers. If there is one number that occurs more frequently than any other number, then that number is the mode. In this case, the numbers 0.6 and 0.2 repeat themselves 2 times. So the mode is 0.6 and 0.2 Note: you can have more than one mode 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