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Graphs/511246: Write an equation of the line through the given point with the given slope. Write the equation in slope-intercept form.
(3,3); m=-3
1 solutions
Answer 342071 by solver91311(16868)   on 2011-10-07 17:30:27 (Show Source):
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Linear-systems/511243: Using the elimination method, how do I solve this problem: x/2+y/3=-3; x/2+2y=-8. I have tried to use the regular elimination method by adding down the columns, but fractions confuse me so I keep getting the answer wrong. Please help.
1 solutions
Answer 342069 by solver91311(16868) on 2011-10-07 17:24:29 (Show Source):
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Age_Word_Problems/511218: "The ratio of my age to my mother's age today is 3:5.
In five years time the ratio will be 7:11.
Let x be the sum of our ages today.
Set up a linear equation and use it to find our ages in five years.
Start the equation like this:
3x/8+5 =..."
I have started the linear equation but do not know how to continue it. This is all I have so far:
3x/8+5 = 7/18(x+10)
Thank You
1 solutions
Answer 342058 by solver91311(16868) on 2011-10-07 16:03:22 (Show Source):
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Angles/511171: two angles are supplementary if one angle has a measure twice the other angle what are the measure of the angle
1 solutions
Answer 342031 by solver91311(16868) on 2011-10-07 13:39:59 (Show Source):
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Rate-of-work-word-problems/511128: Tina can wash the windows of an office building in 3/4 the time it takes her apprentice. One day they worked together for 2hrs. 16mins. and then Tina continued alone. It took her 4hrs. 32 mins. more to complete the job. How long would it take her apprentice to wash all the windows alone?
3/4(x) + x = 544
3x + 4x = 2176
7x = 2176
x = 310.86
310.86/60 = 5hr 11mins but this can't be right
1 solutions
Answer 342030 by solver91311(16868) on 2011-10-07 13:35:30 (Show Source):
You can put this solution on YOUR website!
Let  represent the number of minutes it would take the apprentice working alone to complete the part of the task that Tina and the apprentice worked on together. Then  is the number of minutes Tina would have taken on that part of the task if working alone. Then the apprentice could do  of that part of the job in one minute, and Tina could do  of that part of the job in one minute. Since 2 hours and 16 minutes is 2 times 60 plus 16 equals 136 minutes, working together they performed  of the job in one minute.
You can check the arithmetic for yourself, but it comes out to  minutes.
That is the amount of time, working alone, it would take the apprentice to do the part where they worked together.
The amount of time Tina would take for that same part of the job would simply be 3/4 of that time, or  minutes.
Tina, then, working by herself would have taken 238 minutes to do the first part and then 272 minutes (4 hrs, 32 minutes) to do the second part for a total of 510 minutes.
But if Tina takes  of the time the apprentice takes, then the apprentice takes  of the time that Tina takes. So the apprentice would take:
 minutes or 11 hours, 20 minutes.
John
My calculator said it, I believe it, that settles it
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Graphs/511158: Determine whether each of the given pairs of lines are parallel or perpendicular, or neither
4x- 3y =6 and 3x + 4y =8
1 solutions
Answer 342025 by solver91311(16868) on 2011-10-07 12:56:19 (Show Source):
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Probability-and-statistics/511144: A quiz cosists of 10 multiple-choice questions, each with 6 possible answers. For someone who makes random guesses for all of the answers, find the probability of passing if the minimum passing grade is 50 %.
1 solutions
Answer 342021 by solver91311(16868) on 2011-10-07 12:33:23 (Show Source):
You can put this solution on YOUR website!
This one is easy if you would be satisfied with a wild approximation. A snowball in hell would have a better chance. Here's why.
Here we are faced with getting at least 5 out of 10 correct. That means we need to find the probability of getting exactly 5, then exactly 6, then 7...and so on up to 10, and then add these probabilities.
The probability of  successes in  trials where  is the probability of success on any given trial is given by:
\ =\ \left(n\cr k\right\)\left(p\right)^k\left(1\,-\,p\right)^{n\,-\,k})
Where ) is the number of combinations of things taken at a time and is calculated by !})
Since we need the sum of several of these calculations:
\ =\ \sum_{k\,=\,5}^{10}\left(10\cr\,k\right\)\left(\frac{1}{6}\right)^k\left(\frac{5}{6}\right)^{10\,-\,k})
You can save yourself the calculation of one of the terms by realizing that the probability of something happening is equal to 1 minus the probability of it not happening and then performing the sum:
\ =\ 1\ -\ P_{10}\left(\leq4,\frac{1}{6}\right)\ =\ \sum_{k\,=\,0}^{4}\left(10\cr\,k\right\)\left(\frac{1}{6}\right)^k\left(\frac{5}{6}\right)^{10\,-\,k})
That is only 5 terms instead of 6.
You can also save yourself a good deal of work if you realize that taking 1/6 to the 8th, 9th, and 10th power is going to result in some mighty big denominators and therefore some mighty small terms. In fact, the value of these three terms will be lost in any reasonable round-off of the numeric approximation of the answer. Hence:
\ \approx\ \sum_{k\,=\,5}^{7}\left(10\cr\,k\right\)\left(\frac{1}{6}\right)^k\left(\frac{5}{6}\right)^{10\,-\,k})
Is close enough (only off by 2 in the 5th decimal place), and you only have to calculate 3 terms.
And finally, if all of this nasty arithmetic leaves you cold, and no one will ever think ill of you for feeling that way, open a spreadsheet, Excel on the PC or Numbers on the Mac, then pick a cell and enter the following formula:
})
and get your answer directly upon hitting the Enter key.
John
My calculator said it, I believe it, that settles it
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Travel_Word_Problems/510213: A migrating elephant herd started moving at a rate of 6 miles per hour. One elephant stood still and was left behind. Then this stray sensed danger and began running at a rate of 10 miles per hour to reach the heard. The stray caught up in 5 minutes. How long (in hours) did the stray run to catch up? How far did it run?
1 solutions
Answer 341748 by solver91311(16868) on 2011-10-05 19:18:30 (Show Source):
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Linear-equations/510199: i am having trouble with the following problem:
the table lists data regarding average salaries of several professional athletes in 1991 and 2001
1990 - 262,000
2001 - 1,420,000
Use the data to find a linear function that fits the data.
Use the function to predict the average salary in 2005 and 2010.
I have read the text numerous times and I do not understand how to arrive at the answer. Please help! Thank you
1 solutions
Answer 341747 by solver91311(16868) on 2011-10-05 19:09:35 (Show Source):
You can put this solution on YOUR website!
Let the first year of your data (whether it is 1990 or 1991 you don't make clear) be represented by 0 as a value for your independent variable (x generally, but whatever you are using to represent your horizontal axis) then each subsequent year adds one. So if 1990 is your first year 0 as an x value represnts 1990, 1 represents 1991, and so on. Then the dependent variable, i.e., the value of the function at each of the two data points you are given is the actual salary value. Since both salaries given end in 3 zeros, just drop the three zeros and label your graph values as $1000s.
Now each of your two data points has two values, an x value representing the year and a y value representing the value of the function (i.e. the salary) for that year. You can now create two ordered pairs, ) and ) , using the data from the table.
Knowing the coordinates of two points on a straight line, you can write an equation that represents all of the points on that line by using the two point form of an equation of a line:
(x\ -\ x_1) )
where and are the coordinates of the given points.
So plug in your coordinates, do the arithmetic, and simplify. Then determine the appropriate x-value for the two years you want to predict and plug that value in for x in the equation you just derived and do the indicated arithmetic to predict the salary value for that year.
John
My calculator said it, I believe it, that settles it
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