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# Recent problems solved by 'richwmiller'

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 Miscellaneous_Word_Problems/252729: I'm having trouble setting up this problem. At a certain high school the respective weights for the following subjects are: Mathematics 3, English 3, History 2, Science 2, and Art 1. What is a student's average whose marks were the following: Geometry 89, American Literature 92, American History 94, Biology 81, and Sculpture 85? Thanks in advance, Daniel1 solutions Answer 184796 by richwmiller(9135)   on 2009-12-30 17:41:17 (Show Source): You can put this solution on YOUR website!Usually for an average you just add up the amounts (in this case grades-89,92,94,81,and 85) and then divide by the number of items.(in this case 5) I don't know what this weights business refers to. I checked at various schools and the weights are decimals or percents. http://mathforum.org/library/drmath/view/57605.html perhaps they are multipliers here and a weight of 2 means it counts twice? 3*89+3*92+2*94+2*81+85=978 for a total of 11 978/11=88.9
 percentage/252715: what is the total cost in dollars of a \$45 shirt with 5% sales tax?1 solutions Answer 184771 by richwmiller(9135)   on 2009-12-30 14:22:45 (Show Source): You can put this solution on YOUR website!Let x=the cost of the shirt 1.05x will the the cost plus 5% tax x=45 y=cost +tax y=1.05*45
 Average/252719: a 32 oz bottle of water costs \$2.88. what is the cost per ounce?1 solutions Answer 184768 by richwmiller(9135)   on 2009-12-30 14:19:22 (Show Source): You can put this solution on YOUR website!divide 288 by 32 to get the cost per ounce.
 Graphs/252720: Y=x2-X-61 solutions Answer 184767 by richwmiller(9135)   on 2009-12-30 14:17:59 (Show Source): You can put this solution on YOUR website!Thank you for showing us your Christmas equation. I think it was a nice present. Did you perhaps have a question about it? Or is this show and tell?
 Quadratic_Equations/252708: convert y=3x^2+18x+30 to vertex form by completing the square convert y= -2x^2+28x-7 to vertex form by completing the square trying to figure this out.1 solutions Answer 184766 by richwmiller(9135)   on 2009-12-30 14:15:23 (Show Source): You can put this solution on YOUR website!Since the rules of this site say not to submit similar problems, I removed the second one. We are not here to do your homework for you but to teach you. Let's take y=3x^2+18x+1 First you need to complete the square and then convert it to vertex form. so how do you complete the square? and what is the vertex form? You need to show that you have tried something.
 Linear-equations/252711: how to write a algrebric equation in words 1 solutions Answer 184765 by richwmiller(9135)   on 2009-12-30 14:08:43 (Show Source): You can put this solution on YOUR website!In English we might have asked, "How do you write an algebraic equation in words?" Have you heard of word problems? That problems present the problem in words instead of equations. So if say I am twice as old as my son, I mean that f=2s f is twice s. where f= father and s=son Of course that is a simple example.
Coordinate-system/252710: can you help me gragh this parabola.y= 3x^2 - 6x + 1
1 solutions

Answer 184763 by richwmiller(9135)   on 2009-12-30 14:01:31 (Show Source):
You can put this solution on YOUR website!
 Solved by pluggable solver: SOLVE quadratic equation with variable Quadratic equation (in our case ) has the following solutons: For these solutions to exist, the discriminant should not be a negative number. First, we need to compute the discriminant : . Discriminant d=24 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 1.81649658092773, 0.183503419072274. Here's your graph:

can you help me graph this parabola?
y= 3x^2 - 6x + 1
vertex is one, minus two
opens up
pick some whole numbers for x and calculate y
choose some x above and below 1 so that you gets both sides of the parabola.

 Miscellaneous_Word_Problems/252713: 1) A rectangular field is 300 yards by 500 yards. Aroadway of width x yards is to be built inside the field. This problem concerns the region inside the roadway. a) Write the length and width of the region as a function of x. What kind of functions are these? b) Write the area of this region as a function of x. What kind of function is this? c) Predict the area of the region if x= 5, 10, and 15 d) What is the widest the roadway can be and still leave 100,000 square yards in the region I am unable to get past a. I don't even know how to draw a picture of the problem because it doesn't specify if the roadway is horizontal, vertical, or diagnol...please help..thank you!!! 1 solutions Answer 184761 by richwmiller(9135)   on 2009-12-30 13:53:28 (Show Source): You can put this solution on YOUR website!I agree with you. It is poorly written.
 Quadratic_Equations/252643: In 1920, the record for a certain race was 46.6 sec. In 1940 it was 46.2 sec. Let R(t)= the record in the race and t= the number of years since 1920. Find the linear function that fits the data R(t)= What is the predicted record for 2003? 2006? In what year will the record be 44.62 sec? 1 solutions Answer 184738 by richwmiller(9135)   on 2009-12-30 11:36:34 (Show Source): You can put this solution on YOUR website!set t=year and R(t)=race time use r(t) as the y and t as the x find the find the slope difference in y's over difference in x's m is slope m=(y1-y2)/(x1-x2) then plug one point data as y and x y=m(x)+b and solve for b then substitute r(t) for y and t for x and then substitute 2003 and later 2006 for t and find r(t) for the final question, find t when r(t)=44.62
 Polynomials-and-rational-expressions/252699: A caterer charges a fixed cost for preparing dinner plus an additional cost for each person served. You know the cost for 100 students will be \$750 and the cost for 150 students will be \$1050. Find the caterer's fixed cost and the cost per student served.1 solutions Answer 184735 by richwmiller(9135)   on 2009-12-30 11:24:49 (Show Source): You can put this solution on YOUR website!100 at 750 150 at 1050 so the last 50 cost 300 300/50=6 dollars each 100*6=600 750-600=150 so the caterer charges 150 plus 6 dollars per person check 150+150*6=50+1000 x+100y=750 x+150y=1050 subtract second from first 50y=300 y=6 x+6*100=750 x=150
 Travel_Word_Problems/252690: May rides her bike the same distance that leah walks. may rides her bike 10 km/h faster than leah walks. if it takes may 1 h and leah 3 h to travel that distance, how fast does each travel?1 solutions Answer 184726 by richwmiller(9135)   on 2009-12-30 10:44:43 (Show Source): You can put this solution on YOUR website!rt=d let x be leah's speed may's speed is 10+x (10+x)*1=3x 10+x=3x 10=2x x=5 x+10=15 so may goes 15 kmh and leah 5
 Rate-of-work-word-problems/252693: If 15 men can do a piece of work in 90 days, in how many days can 30 men do the same work?1 solutions Answer 184724 by richwmiller(9135)   on 2009-12-30 10:40:47 (Show Source): You can put this solution on YOUR website!We are assuming that the other 15 added will work at the same pace/rate as the first 15 which is not always a wise assumption. in one day 15 men do 1/90 of the job so 30 men should be able to do 2/90 in the same day or 1/45 of the job in one day so in 45 days 30 men should be able to finish the job
 Probability-and-statistics/252695: There are 60 red marbles and 40 blue marbles in a bag. How many blue marbles must be added so that the probability of drawing blue is 75% ?1 solutions Answer 184721 by richwmiller(9135)   on 2009-12-30 10:26:07 (Show Source): You can put this solution on YOUR website!for a probability of 75%, 75% of the marbles must be blue. 3/4 must be blue if there were 60 blue marbles the probability would be 50% if there were 120 blue marbles it would 66.7% or 2/3 if 1/4 were red and 3/4 were blue then it would 75% 1/4x=60 x=240 240-40 is 200 so 200 more blue marbles are needed
 Miscellaneous_Word_Problems/252697: In a school of 80 students, 24 are enrolled in algebra, 49 in music, and 11 students are in both algebra and music. How many students are NOT in either algebra or music? A) 7 B) 15 C) 18 D) 35 E) 62 1 solutions Answer 184719 by richwmiller(9135)   on 2009-12-30 10:18:54 (Show Source): You can put this solution on YOUR website!There are 80 students. 13+38+11=62 enrolled 80-62=18 so that those in both are not counted twice i removed those eleven from both algebra and music and then added them once 18 are not in either algebra or music
 Percentage-and-ratio-word-problems/252680: Sam, a store employee, bought a shirt for \$9 using the employee discount of 40% off retail. The store marks up all merchandise 50% on cost. How much did the store pay for the shirt?1 solutions Answer 184709 by richwmiller(9135)   on 2009-12-30 09:32:15 (Show Source): You can put this solution on YOUR website!What do we know? We know the employee cost\$9 and discounts 40% and markup rates 50%. so if we can find the markedup price we can find the store cost. So Sam paid \$9 with a 40% discount 1.00-.40=.60 .60x=9 3x/5=9 3x=45 x=15 check .40*15=2/5*15=2*3=6 15-6=9 ok markedup or retail price was 15 dollars so 1.5y=15 3/2x=15 3y=30 y=10 store cost check 50%*10=5 10+5=15 .40*15=6 15-6=9 ok How odd that the employee buys below the store's cost!!
 Miscellaneous_Word_Problems/252666: If a and b are different positive integers, and 5a + 2b = 34 is an integer, what is the sum of all possible values of a? A) 6 B) 10 C) 12 D) 14 E) 161 solutions Answer 184696 by richwmiller(9135)   on 2009-12-30 07:26:51 (Show Source): You can put this solution on YOUR website!5a+2b=34 Answers could be a=6 and b=2 2b must be even but b can be even or odd. so if 2b must be even then 5a must be even so a must be even since 5 is odd and 34 is even. If you subtract an even number from an even number, you get an even number. a must be less than 7 since 5*7=35 and both a and b must be positive. But the answers are sums of a not a itself 10 is possible because 5*4+2*7=34 6+4=10 5*2+2*12=34 so we could have 6,4 and 2 for a total of 12 since 6, 4 and 2 are possible values for a 14 can't be since it would need 2 twice. 16 has a similar problem with 4 since we already have a sum of 12 a sum of 16 would need 4 again. so the highest sum possible for a would be 12 using 2,4 and 6. We could also have a =0 and b would equal 17 but the sum of the a's would not change.
 Miscellaneous_Word_Problems/252668: There is a mile marker every mile on the trail. Between mile 32 and 237, how many mile markers? A) 203 B) 204 C) 205 D) 206 E) 2071 solutions Answer 184694 by richwmiller(9135)   on 2009-12-30 07:09:32 (Show Source): You can put this solution on YOUR website!This is a trick question in several ways. When you subtract 32 from 237 you get 205. but what exactly is the 205? Does 205 include 32 and/or 237? It includes only one of them. Do we want to include 32 and 237? If we take the question literally "between" does not include 32 nor 237. So the answer should be 204 if we take the question literally. We would only want from 33 to 236 which has 204 markers inclusive. If we want to include both 32 and 237 then the answer is 206.
 Expressions-with-variables/252675: 4x+4y=32 x+4y=81 solutions Answer 184693 by richwmiller(9135)   on 2009-12-30 06:59:25 (Show Source): You can put this solution on YOUR website!subtract the second from the first 3x=24 x=8 x+4y=8 8+4y=8 subtract 8 from both sides 4y=0 y=0 check 4x+4y=32 4*8+4*0=32 32=32 check
 Divisibility_and_Prime_Numbers/252667: Not including the number one (1) which is always a common but not prime factor, 54 and 81 have how many common factors? A) 1 B) 2 C) 3 D) 4 E) 5 1 solutions Answer 184692 by richwmiller(9135)   on 2009-12-30 06:55:11 (Show Source): You can put this solution on YOUR website!81 has 3*3*3*3 54 has 3*3*3*2 so they have the prime number 3 in common but they also have 3,9,27 in common so they have three common factors not including one
 Square-cubic-other-roots/252641: Sarah needs to make a cake and some cookies. The cake requires 3/8 cup of sugar and the cookies require 3/5 cup of sugar. Sarah has 15/16 cups of sugar. Does she have enough sugar, or how much more does she need?1 solutions Answer 184675 by richwmiller(9135)   on 2009-12-29 22:01:25 (Show Source): You can put this solution on YOUR website!We have several fractions with various denominators. We need to add 3/8 and 3/5 to see if the sum is less than or equal to 15/16 5*8=40 but 16 is not a factor of 40 5, 8 and 16 are all factors of 80 So we multiply 3/8 by 10/10 and get 30/80 3/5 by 16/16 and get 48/80 15/16 by 5/5 and get 75/80 So now we add 48/80 and 30/80 and get 78/80 and see that it is more than 75/80 So technically there is not enough sugar but recipes are not usually that strict. She needs 3/80 cups of sugar
 Complex_Numbers/252585: what is the answer to the complex number x=2-3i1 solutions Answer 184567 by richwmiller(9135)   on 2009-12-29 14:23:42 (Show Source): You can put this solution on YOUR website!Depends on what it is you want. Your question is similar to what is the answer to 2/3? x=2-3i is in standard format and is simplified as much as possible. We could plot it on the complex plane. Is that your question?
 Trigonometry-basics/252523: how do I go about solving sec(arcsin8/17)?1 solutions Answer 184494 by richwmiller(9135)   on 2009-12-29 04:25:23 (Show Source): You can put this solution on YOUR website!start inside the parentheses first let x= arcsin(8/17) remember if y=arcsin(x) then x=sin(y) after you solve for x then solve for sec(x)
 Probability-and-statistics/252525: 1+3+5+7+9+11+13+15+17+19=100 now pick any 5 digits which make the sum of 50 ?1 solutions Answer 184493 by richwmiller(9135)   on 2009-12-29 04:00:47 (Show Source): You can put this solution on YOUR website!this was answered yesterday since all are odd and 5 odds equal an odd it can't be done
 Linear_Algebra/252519: Can someone please point me in the right direction with this experiment. Probabilities and Binomial Experiments. U.S. Population by Region. The U.S. population by region (in millions) for selected years is given in the table. Find the probability that a U.S. resident selected at random satisfies the following: a.) lived in the West in 1997. b.) lived in the Midwest in 1995. c.) lived in the Northwest or Midwest in 1997. d.) lived in the South or West in 1997. e.) What are the odds that a randomly selected U.S. resident in 2000 was not from the South? REGION 1995 1997 2000 Northwest 51.4 51.6 53.6 Midwest 61.8 62.5 64.4 South 91.8 94.2 100.2 West 57.7 59.4 63.2 (Answers) a. .222 b. .235 c. .426 d. .574 e. 302 to 167 1 solutions Answer 184491 by richwmiller(9135)   on 2009-12-29 01:43:14 (Show Source): You can put this solution on YOUR website!the first thing to do is finish the table with totals for us population for each year in question REGION 1995 1997 2000 Northwest 51.4 51.6 53.6 Midwest 61.8 62.5 64.4 South 91.8 94.2 100.2 West 57.7 59.4 63.2 sum(1995)=51.4+61.8+91.8+57.7 sum(1997)=51.6+62.5+94.2+59.4=267.7 sum(2000)=53.6+64.4+100.2+63.2 a) lived in west in 1997 59.4/267.7=.2219=.222 so the part over the whole= probability
 Linear_Algebra/252520: Concept Check. If the probability of an event is .857, what is the probability that the event will not occur? (Answer) .143 1 solutions Answer 184489 by richwmiller(9135)   on 2009-12-29 01:16:49 (Show Source): You can put this solution on YOUR website!certainty =100%=1.00 1.00=.857 (yes) + n(no) 1.00-.857=.143= n
 Coordinate-system/252502: Solve the following system of equations algebraically: 2y = 8 − x y − 2x = −1 1 solutions Answer 184487 by richwmiller(9135)   on 2009-12-29 00:55:29 (Show Source): You can put this solution on YOUR website!put the two equations in the same order 2y=8-x y=2x-1 y=-1+2x (A) 2y=8-x (B) multiply (A) by 2 2y=-2+4x (C) 2y=8-x (B) 2y=2+4x (c) subtract C from B 0=6-3x subtract 6 from both sides 6=3x divide both sides by -3 2=x substitute 2 for x in any equation 2y=8-x 2y=8-(2) 2y=8-2 2y=6 y=3 x=2 check y=2x-1 3=2(2)-1 3=3 ok
 Numbers_Word_Problems/252512: when N is divided by 5, the remainder is 3. what is the remainder when 7N is divided by 5?1 solutions Answer 184485 by richwmiller(9135)   on 2009-12-29 00:41:00 (Show Source):
 Coordinate-system/252499: What is the solution for the following system of equations? x = -y x + 2y = 6 1 solutions Answer 184484 by richwmiller(9135)   on 2009-12-29 00:39:46 (Show Source): You can put this solution on YOUR website!substitute -y for x in the second equation -y+2y=6 y=6 x=-y substitute 6 for y x=-6
 Travel_Word_Problems/252514: What average acceleration does it take to stop a car traveling at 60 kph in 8 seconds1 solutions Answer 184483 by richwmiller(9135)   on 2009-12-29 00:37:14 (Show Source): You can put this solution on YOUR website!v=vinit+acceleration *time 0=60+acc*8 -60=acc*8 acc=-60/8 acc=-30/4 acc=-15/2 acc=-7.5 kps which of course is deceleration