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Find the area of the floor and the area of the rug and subtract them.  These will not be "nice" answers.  They will instead be expressions.   Area of the floor: if the length is x and the width is 6 feet greater, then the width can be thought of as x + 6.   A...

Use the ideal gas law, PV = nRT, where P = pressure in atm, n = number of moles, T = temperature in Kelvins, and R = 0.08206 (which is a constant when we use atmosphere or atm)   Kelvins is Celsius + 273     2.29(V) = 29.5(0.08206)305.7   Solve...

Note: I assume the -3x should be -3x2.     To find the x coordinate of the vertex, use x = -b/(2a).  In your case, a = -3, b = -4, c = -9.     So x = -(-4)/(2(-3)) which equals 4/(-6) which reduces to -2/3.   The you plug in -2/3 into the x variable...

x = -b/(2a)

Say you survey a bunch of people and get their numerical opinions on 1 thing.  You then do some statistics and you find the mean and standard deviation.   The empirical rule says that 99.7% of your results will within 3 standard deviations above or 3 standard deviations below your...

Binomial distribution uses a p and q to denote the probability of something happening and the probability that something doesn't happen.  If he is correct 90% o the time then then probability that he is correct is 0.9 and the probability that he is incorrect is 0.1 or 10% of the time. ...

I don't think you mean factor.  I think you mean expand.   I think that this is the simple way: making it (x -1)(x-1)(x-1) and then multiply the first two parentheses to get (x2 -1x -1x +1)(x -1).  You don't have to but simplify the first set of parentheses to get (x2-2x...

This is a weird set-up, usually the x is after the 5/6.  This is a proportion (2 fractions that are equal).  With proportions you can always use cross multiplication and divide.  Multiply the numerators with the opposite denominators and set them equal to each other. Therefore: (-2)(6)...

In each parentheses you have a number that means "x" and a number that means "y".  The first number is the number that means "x".  So the 0 in (a), the -1 in (b), the -2 in (c), the -5 in (d).  since the inequality given is x < or equal to -2, which...

Assuming that it is American roulette, The number 19 appears once out of 38 other numbers.  that means you have a 1/38 probability of winning.    that 1/38 chance will pay you \$35 and the 37 other ties will pay you \$-1.  So let's say you play only 38 times.  Probability...

The notation is saying you can get a 4% discount on you order if you pay within 10days.  Or you can get a 2% discount if you pay within 20 days.  If you don't pay with either, then the full amount is due in 30 days.    Since the invoice is dated July 27th and you pay...

Direct variation means that when one variable gets larger/smaller, the other variable gets proportionally larger/smaller.    So all direct variation problem can use the form y = kx, where k is a number that is consistent for the entire problem.    Such as y =...

parallel lines have equal slopes. Find the slope of each and compare.   to find the slope between 2 points:  use slope formula (y1- y2)  / (x1 - x2) = (2 - 8) / (-6 - 4) = -6 / -10 = 3/5   to find the slope of a line that is already an equation, change the equation...

a. consecutive rolls mean multiplication of each individual probability.  there is 1 one on a die, and 6 total outcomes which means a 1/6 probability each time(no need to subtract 1, you can't take the #1 off of a die.)   next multiply 1/6 times 1/6 times 1/6 times....a total of...

Probability is the # of possible outcomes desired /  # of possible total outcomes.  In problems like this when you have consecutive draws, you find the probability of each individual draw and then multiply your results.   a. there are 4 reds to possible draw from the urn,...

You can really just plug start plugging in numbers for either x or y and solve for the other variable, like -3(10) +4y = 8.  ---> -30 +4y = 8  ---> 4y = 38 ---> y = 9.5.  Therefore (10, 9.5) is a point you can graph.    I wouldn't start with...

1. I am a little unsure what you mean by money is worth 7.25%  Do you mean interest rate?  And does the problem tell you to use a specific method i.e.(average rate of return, net present value?)    2. Average rate of return: For each proposal: add up the returns and divide...

Is the 5 somewhere in a number, i.e. 2,564?  In this case the value of 5 is actually 500 since it is in the hundreds place.