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Tutors Answer Your Questions about Miscellaneous Word Problems (FREE)
Question 241175: Reconciling remainders. Find a positive integer smaller
than 500 that has a remainder of 3 when divided by 5, a
remainder of 6 when divided by 9, and a remainder of 8
when divided by 11.
Answer by ankor@dixie-net.com(6693)   (Show Source):
You can put this solution on YOUR website!Reconciling remainders.
Find a positive integer smaller than 500 that has a remainder of 3 when divided by 5,
a remainder of 6 when divided by 9, and a remainder of 8 when divided by 11.
:
we know
x = multiple of 5 + 3, last digit is either 3 or 8
x = multiple of 9 + 6
x = multiple of 11 + 8,
:
Find a multiple of 11 + 8, last digit is 3 or 8
then test to see if it is a multiple of 9 with a remainder 6
:
working downward from 500, I came up with 393
(I used the table on the TI83, with the equation y = 11x + 8, look for last digit of 3 or 8)
:
393/5 = 78 r3
393/9 = 43 r6
393/11= 35 r8
:
There is probably a neater way of doing this but I can't come up with it
Question 241238: How many centimeters equal one kilometer?
Answer by unlockmath(117)  (Show Source):
You can put this solution on YOUR website!Hello,
There are 100 centimeters in meter. There are 1000 meters in 1 kilometer. Do you know from this data how to solve the problem? Try it and see. Good luck.
RJ Toftness
www.math=unlock.com
Question 241178: I have literally spent an entire day on this question. I think that it must be an inequality and some division must take place, but I am unable to find the solution. Here is the question:
A car rental company has two rental rates. Rate 1 is $63 per day plus .18 per mile. Rate 2 is $126 per day and .09 per mile. If you plan to rent a car for one week, how many miles would you need to drive to pay less by taking rate 2?
Any help is greatly appreciated.
Found 2 solutions by kensson, scott8148:
Answer by kensson(7)  (Show Source):
You can put this solution on YOUR website!For rate 1, you pay 
For rate 2, you pay 
For R2 < R1, you have 
Subtract  from each side to leave 
Divide by 0.09 to give 
m is then at least 4900 miles! 700 miles a day is a lot of driving.
Answer by scott8148(3382)  (Show Source):
You can put this solution on YOUR website!7 days in a week
set the two costs equal to find the "break even" milage
7(63) + .18m = 7(126) + .09m
subtracting [.09m + 7(63)] ___ .09m = 7(63)
dividing by .09 ___ m = 7(700) = 4900 miles
you need to drive MORE THAN this to save money with rate 2
Question 241163: 4 more than 3
how would i right that
4+3?
Answer by edjones(3295)  (Show Source):
Question 241084: A closed box is to be a rectangular solid with a square base and a volume of 12 cubic feet. Find the most economical dimensions if the top of the box is twice as expensive as the sides and the bottom?
Answer by ankor@dixie-net.com(6693) (Show Source):
You can put this solution on YOUR website!A closed box is to be a rectangular solid with a square base and a volume of 12 cubic feet.
Find the most economical dimensions if the top of the box is twice as expensive as the sides and the bottom?
:
Let dimension of the square bottom = x, area of the bottom and top = x^2
volume
let h = the height of the box
x^2 * h = 12
h = 
:
Surface area,
Since the top cost twice as much as the bottom, we can treat them like 3x^2 instead of 2x^2,
:
S.A. = 3x^2 + 4(x*h)
Replace h with
SA = 3x^2 + 4x*
Cancel an x
SA = 3x^2 + 
:
Plot this equation
:
Minimum surface area is minimum expense, occurs when x = 2 inches
:
Find h:
h =
h = 
h = 3 inches
:
2 by 2 by 3 is the dimensions of the box
:
You can see that if the top and bottom cost the same we would have
2x^2 + and the graph would be:
about x = 2.25 inches
:
:
HOpe this made sense to you
Question 241051: At 7:29 a.m. the temperature was -4 degrees F; at 7:32 a.m. the temperature was 45 degrees F. What was the average rate of change in temperature (per minute)?
A) 16.3 B) 49 C) -16.3 D) 24.5
Answer by checkley77(7049)  (Show Source):
Question 240918: Give an example of the sum of two binomials that is a trinomial.
Answer by edjones(3295) (Show Source):
Question 240920: Give an example of the sum of two binomials that has four terms.
Can the sum of two binomials have more than four terms?
Answer by stanbon(26269) (Show Source):
You can put this solution on YOUR website!Give an example of the sum of two binomials that has four terms.
(x^4+x^2)+(x^3+5) = x^4+x^3+x^2+5
----------------------------------------------
Can the sum of two binomials have more than four terms?
No
===========
Cheers,
Stan H.
Question 240830: a cathedral tower 200 feet high is 250 feet from a chruch tower 150 feet high. On top of each tower is a pigeon. The two pigeons fly off at the same time and at the same speed directly to some grain on the level straight road between the towers. The pigeons reach the grain at the same time.
How far is the grain from the foot of the cathedral tower?
Answer by solver91311(5072)  (Show Source):
Question 240745: i have a problem with an i in it and i wanted to know what these types of problems are called. here is an example:
1.) -7i+12i
(its not the ones where you would get 5i because im not talking about that way)
i hope me giving you a heads up helps
Answer by edjones(3295) (Show Source):
Question 240608: Radioactive element R decays exponentially at a rate of 4% per year. If we begin with 5 grams of R, how long (to the nearest tenth of a year) will it take for only 3 grams to remain?
I started with the A=Aoe^rt where A=3 Ao=5 r=0.04 and t is what I needed to find. I then to ln3=ln5+0.04tlne. Then I got the 0.04t=(ln3-ln5)/lne....
Answer by scott8148(3382) (Show Source):
Question 240450: the sum of a number and 24 is equal to 4 times the number. what is the number
Answer by checkley77(7049) (Show Source):
Question 240232: Veronica High School has 85 seniors, each of whom plays on at least one of the school’s three varsity sports teams: football, baseball, and lacrosse. It so happens that 74 are on the football team; 26 are on the baseball team; 17 are on both the football and lacrosse teams; 18 are on both the baseball and football teams; and 13 are on both the baseball and lacrosse teams. Compute the number of seniors playing all three sports, given that twice this number are members of the lacrosse team.
Answer by Theo(675)  (Show Source):
You can put this solution on YOUR website!This is what I came up with.
ST = total number of seniors
FT = total number of seniors playing football
BT = total number of seniors playing baseball
LT = total number of seniors playing lacrosse
F = number of seniors playing football only.
B = number of seniors playing baseball only.
L = number of seniors playing lacrosse only.
FL = number of seniors playing football and lacrosse only.
FB = number of seniors playing football and baseball only.
BL = number of seniors playing baseball and lacrosse only.
FBL = number of seniors playing football and baseball and lacrosse.
We know that all seniors play on at least one sport.
The total number of seniors can be accounted for by the equation:
ST = F + B + L + FB + FL + BL + FBL
What we know so far:
ST = 85
FT = 74
BT = 26
LT = ???
F = ???
B = ???
L = ???
FB = 18
FL = 17
BL = 13
FBL = 0
We know that FT = 74
Since FT = F + FB + FL + FBL, we get 73 = F + 18 + 17 + 0 = F + 35.
This makes F = 39 which means that 39 seniors that play football only.
We assign 39 people to F.
Our tally is now:
ST = 85
FT = 74
BT = 26
LT = ???
F = 39 (removed ???)
B = ???
L = ???
FB = 18
FL = 17
BL = 13
FBL = 0
We know that BT = 26
We also know that BT = B + FB + BL + FBL
Since FB = 18 and BL = 13, and BT = 26 and FBL = 0, then the equation becomes:
26 = B + 18 + 13 + 0 which becomes:
26 = B + 31
We have 5 more people than total people on the team.
Since the team is composed of FB and BL only, and we are assuming that the numbers shown are correct, then we must have people who play Baseball AND Football.
These would be classified as FBL because they play on all 3 sports.
This means we have 5 people who being counted twice.
We subtract 5 people from FB and 5 people from BL and we add 5 people to FBL to get:
BT = B + FB + BL + FLB becomes:
26 = B + 13 + 8 + 5 because our category of FBL just became 5 from 0.
Baseball equation now becomes:
26 = B + 13 + 8 + 5 = B + 26
This becomes 26 = B + 26 which makes B = 0 which now accounts for all of the members of the baseball team.
The tally for Baseball is now:
B = 0
FB = 13 (down from 18)
BL = 8 (down from 13)
FBL = 5
BT = 0 + 13 + 8 + 5 = 26 (checks out ok because BT was given as 26).
Our overall tally now becomes:
ST = 85
FT = 74
BT = 26
LT = ???
F = 39 (removed ???)
B = 0 (removed ???)
L = ???
FB = 13 (down from 18)
FL = 17
BL = 8 (down from 13)
FBL = 5 (up from 0)
The equation for FT has to change because we dropped 5 FB and added 5 FBL.
The tally for Football is now:
F = 39
FB = 13 (down from 18)
FL = 17
FBL = 5
FT = 39 + 13 + 17 + 5 = 74 (checks out ok)
This does change the overall tally any further. It just corrects the account for Football.
We check the tally for total seniors again to see if anything is missing.
F = 39
B = 0
L = ???
FB = 13 (down from 18)
FL = 17
BL = 8 (down from 13)
FBL = 5
ST = 39 + 0 + L 13 17 + 8 + 5 = L + 82
We are missing 3 seniors.
The only category that is not completed is the number of seniors who only play lacrosse, and since all seniors must be playing at least one sport, these 3 seniors must be playing lacrosse.
We assign them to lacrosse by making L = 3.
Out tally for seniors now becomes:
F = 39
B = 0
L = 3
FB = 13 (down from 18)
FL = 17
BL = 8 (down from 13)
FBL = 5
ST = 39 + 0 + 3 + 13 + 17 + 8 + 5 = 85 (checks out ok)
The tally for the lacrosse team now becomes:
L = 3
FL = 17
BL = 8 (down from 13)
FLB = 5
LT = 3 + 17 + 8 + 5 = 33
LT is now equal to 33.
Our overall tally now becomes:
ST = 85
FT = 74
BT = 26
LT = 33 (removed ???)
F = 39 (removed ???)
B = 0 (removed ???)
L = 3 (removed ???)
FB = 13 (down from 18)
FL = 17
BL = 8 (down from 13)
FBL = 5 (up from 0)
Our tally for seniors now becomes:
F = 39
B = 0
L = 3 (up from 0)
FB = 13 (down from 18)
FL = 17
BL = 8 (down from 13)
FBL = 5 (up from 0)
ST = 39 + 3 + 13 + 17 = 8 = 5 = 85 (checks out ok).
All the seniors are accounted for.
The number of seniors who play on all three sports is 5.
The only part that is questionable is the statement "Compute the number of seniors playing all three sports, given that twice this number are members of the lacrosse team."
What that means exactly is a mystery to me. I have computed the number of seniors who play all three sports. The number has to be 5 in order to make all other numbers check out. At least twice this number are members of the lacrosse team so I would have to say that the statement is satisfied.
The total accounting for all the seniors is now:
ST = 85 (given)
FT = 74 (given)
BT = 26 (given)
LT = 33 (calculated)
F = 39 (calculated
FB = 13 (calculated down 5 from 18 given)
FL = 17 (given)
FBL = 5 (calculated)
BL = 8 (calculated down 5 from 13 given)
B = 0 (calculated)
L = 33 (calculated)
Tally for Football is now:
F = 39
FB = 13
FL = 17
FBL = 5
FT = 39 + 13 + 17 + 5 = 74 (checks out ok)
Tally for Baseball is now:
B = 0
FB = 13
BL = 8
FBL = 5
BT = 0 + 13 + 8 + 5 = 26 (checks out ok)
Tally for Lacross is now:
LT = L + FL + BL + FBL
L = 3
FL = 17
BL = 8
FBL = 5
LT = 3 + 17 + 8 + 5 = 33 (checks out ok)
Tally for Seniors is now.
F = 39
B = 0
L = 3
FB = 13
FL = 17
BL = 8
FBL = 5
ST = 39 + 0 + 3 + 13 + 17 + 8 + 5 = 85 (checks out ok)
Question 240250: The four children in the Dempsey family have a combined age of 25 years. Jennifer’s oldest brother is six times as old as she is. Her next-to-oldest brother is 5 years older than she is, and the youngest of her brothers is twice Jennifer’s age. How old is each of the Dempsey children?
Answer by ankor@dixie-net.com(6693) (Show Source):
You can put this solution on YOUR website! The four children in the Dempsey family have a combined age of 25 years.
Jennifer’s oldest brother is six times as old as she is.
Her next-to-oldest brother is 5 years older than she is, and the youngest of her brothers is twice Jennifer’s age.
How old is each of the Dempsey children?
:
Let the 4 children's ages be, j, a, b, c
:
Write an equation for each statement:
:
" The four children in the Dempsey family have a combined age of 25 years."
j + a + b + c = 25
:
" Jennifer’s oldest brother is six times as old as she is."
a = 6j
:
" Her next-to-oldest brother is 5 years older than she is,"
b = j + 5
:
" and the youngest of her brothers is twice Jennifer’s age."
c = 2j
:
How old is each of the Dempsey children?
:
Note that each are in terms of j, so we just substitute
j + a + b + c = 25
j + 6j + (j+5) + 2j = 25
combine like terms
j + 6j + j + 2j + 5 = 25
10j = 25 - 5
10j = 20
j = 
j = 2
:
Now you use the equations we have, to find the ages a, b, c.
Check by adding them up and seeing if they equal 25
Question 240249: A bag contains five red marbles, three green marbles, and four blue marbles. How many green marbles must be added to the bag so that the probability of drawing a green marble is 3/4?
Answer by Theo(675) (Show Source):
You can put this solution on YOUR website!T = 5+3+4 = 12
This means the total number of marbles is equal to 5 red plus 3 green plus 4 blue which equals a total of 12.
G = 3
This means the number of green marbles you are starting out with is 3.
P(G) is now 3/12 = 1/4
P(G) means the probability that you will draw a green marble is equal to .25 right now.
We want:
P(G) = 3/4
We need to add X number of green marbles.
P(G) = 3/4 = (X+3) / (12 + X)
This means that we need to add x number of green marbles to the total. This will change both the numerator of the equation (number of green marbles) and the denominator of the equation (number of total marbles).
We need to solve for X.
(X + 3) / (X + 12) = 3/4
Multiply both sides by (X+12) to get:
(X+3 = 3/4 * (X + 12)
Simplify to get:
X + 3 = (3/4)*X + (3/4)*12
Simplify further to get:
X + 3 = (3/4)*X + 9
Subtract 3 from both sides of this equation to get:
X = (3/4)*X + 9 - 3
Subtract (3/4)*X from both sides of this equation to get:
X - (3/4)*X = 9 - 3
Combine like terms to get:
(1/4)*X = 6
Multiply both sides of the equation by 4 to get:
X = 6 * 4 = 24
Number of green marbles should be 24.
Add 24 green marbles to 3 and you get 27.
Add 24 to 12 and you get 36
27/36 = .75 = 3/4
the probability of getting a green marble now is .75 because 75% of the marbles out of the total number of marbles are green.
Question 240234: Find the number of revolutions made by a circular wheel of area 1.54 m2 in
rolling a distance of 176 m.
Answer by vleith(1977) (Show Source):
You can put this solution on YOUR website!Use the area to rid the radius of the wheel
So the radius is 0.7m
Now use the equation for circumference
 meters
How many circumferecnes are in 176m?
Allowing for rounding, I would say 40 revolutions.
Question 240136: Film with a width of 35 millimeters is projected onto a screen where the width is 5 meters. What is the scale factor of this enlargement?
Answer by Alan3354(6079)  (Show Source):
You can put this solution on YOUR website!Film with a width of 35 millimeters is projected onto a screen where the width is 5 meters. What is the scale factor of this enlargement?
5 meters = 5000 mms
5000/35 =~ 143 times linearly
---------------------
The enlargement of the area is apx the square of that, = 20449 times the area.
Question 239892: Two joggers are running around an oval track in opposite directions. One jogger runs around the track in 56 seconds. The joggers meet every 24 seconds. How many seconds does it take for the second jogger to run around the track?
Answer by ankor@dixie-net.com(6693) (Show Source):
You can put this solution on YOUR website! Two joggers are running around an oval track in opposite directions.
One jogger runs around the track in 56 seconds.
The joggers meet every 24 seconds.
How many seconds does it take for the second jogger to run around the track?
:
Let t = time for the 2nd jogger to run around the track
:
The 1st time they meet the 1st jogger has covered  or  of the track.
Therefore
The 2nd jogger has covered  of the track in 24 seconds
then
t = 24
t = 24 * 
t = 6(7)
t = 42 seconds time of the 2nd jogger
Question 240105: A wire is used to anchor a 20 foot high pole. One end of the wire is attached to the top of the pole. The other end is fastened to a stake five feet away from the bottom of the pole. Find the length of the wirse, to the nearest tenth of a foot.
Can someone help me? - not sure how to start the problem....thank you.
Answer by solver91311(5072) (Show Source):
Question 239952: Suppose you tie a rope around the earth at the equator (circumference approx. 25,000 miles). Let's say you pull the rope as tight as it will go and then add back 6 feet of slack before tying the knot. If the extra rope is distributed evenly around the globe will there be enough space between the rope and the surface of the earth for a worm to crawl under? Assume the earth is a perfect sphere and the rope does not stretch.
Answer by ankor@dixie-net.com(6693) (Show Source):
You can put this solution on YOUR website!Suppose you tie a rope around the earth at the equator (circumference approx. 25,000 miles).
Let's say you pull the rope as tight as it will go and then add back 6 feet of slack before tying the knot.
If the extra rope is distributed evenly around the globe will there be enough
space between the rope and the surface of the earth for a worm to crawl under?
Assume the earth is a perfect sphere and the rope does not stretch.
:
Whatever you add to the circumference, divide that by pi, that's what's added to the diameter.
 = 1.909859 ft added to the diameter
we want to know what's added to the radius
Divide it by 2 and you have .955 ft (about 11.46 inches) plenty room for a worm
Question 239895: Find the sum of 40 percent of 1/4 and 50 percent of 1/5.
Answer by RAY100(1637) (Show Source):
Question 239811: I need help with this problem.
In order for a chemical reaction to take place, the Fahrenheit temperature of the reagents must be at least 184.49ºF. Find the Celsius temperatures at which the reaction may occur. Use C =
Answer by College Student(210)  (Show Source):
You can put this solution on YOUR website!These are the equations:
°F to °C Deduct 32, then multiply by 5, then divide by 9
°C to °F Multiply by 9, then divide by 5, then add 32
.
Use your calculator find the solution.
Question 239747: Two houses on the same side of the street have house numbers that are consecutive even integers. The sum of the integers is 58. What are the two house numbers?
Answer by Theo(675) (Show Source):
Question 239543: a house has 2 rooms of equal area. 1 room is square and the other is a rectangle 4 ft narrower and 5 ft longer than the square one. find the area of each room.
Answer by checkley77(7049) (Show Source):
You can put this solution on YOUR website!x^2=(x+5)(x-4)
x^2=x^2+x-20
x=20 ft. is the size of the square room.
Proof:
20^2=(20+5)(20-4)
400=25*16 (25 by 16 is the size of the rectangle room).
400=400
Question 239606: I have 5 pictures, picture "A" must remain in the center. How many possible combinations/arrangements can be made with the four other pictures (b, c, d, e)?
Answer by solver91311(5072) (Show Source):
You can put this solution on YOUR website!
I presume that you are making a single row of pictures with A in the center.
So the pictures must end up in the following arrangement:
X X A X X
There are 4 ways to choose the first picture. For each of those ways, there are three ways to pick the second picture. So there are 4 times 3 = 12 ways to pick the first two pictures. The third picture is fixed, so that doesn't change anything, and there are still 12 ways to choose the first three pictures. For each of those ways there are 2 ways to pick the 4th picture, so 12 X 2 = 24 ways to pick the first 4. Then there is 1 way to pick the last one. so 24 X 1 = 24. Total of 24 ways.
John
Question 239339: The length of the minute hand of a clock is 5 cm. Find the area swept by the
minute hand during the time period 6 : 05 a m and 6 : 40 a m.
Answer by vleith(1977) (Show Source):
You can put this solution on YOUR website!Each 5 minute segment is  of a circle. In this problem the minute sweeps from 6:05 to 6:40. That is 7 five minute segments. Which means the area swept is 7/12 of the area on the clock face.
You are told 
But we only swept 7/12 of the full area. So the area we want is
 cm^2
Question 239277: Can someone please help me with this? I need to have it done before tomorrow. Thanks in advance.
Stephanie, the Team Manager of a soccer team, purchases many soccer balls from a retailer and sells them to all the players at her soccer club at a price of x dollars each. She can sell 600 – 15x balls per week. Find a polynomial that represents the weekly revenue for the balls. Find the revenue for a week in which the price is $12 per ball. Use the parabolic graph to illustrate the law of diminishing return, if it occurs in this case. In order for Stephanie to receive the maximum weekly revenue, how would you, as Business Manager, recommend for the price per ball?
Answer by stanbon(26269) (Show Source):
You can put this solution on YOUR website!Stephanie, the Team Manager of a soccer team, purchases many soccer balls from a retailer and sells them to all the players at her soccer club at a price of x dollars each. She can sell 600 – 15x balls per week. Find a polynomial that represents the weekly revenue for the balls.
Revenue = (price)(quantity)
R(x) = x(600-15x)
----------------------------------
Find the revenue for a week in which the price is $12 per ball.
R(12) = 12(600-15*12) = 7200 - 180 = $7020
----------------------------------
Use the parabolic graph to illustrate the law of diminishing return, if it occurs in this case.
------------------------
In order for Stephanie to receive the maximum weekly revenue, how would you, as Business Manager, recommend for the price per ball?
---
Around $20
===============================
Cheers,
Stan H.
Question 239161: Gabriella is a waitress at the Hampton Grille. In one night she earned at least $75 while working a six-hour shift. If Gebriella earned $31.50 in tips, find all possibilities for the amount she earned in wages per hour. Represent your answer both algebraically and graphically.
Answer by stanbon(26269) (Show Source):
You can put this solution on YOUR website!Gabriella is a waitress at the Hampton Grille. In one night she earned at least $75 while working a six-hour shift. If Gebriella earned $31.50 in tips, find all possibilities for the amount she earned in wages per hour. Represent your answer both algebraically and graphically.
---------------------------------------------
Earnings = wages + tips
E(x) = x + 31.50 >= 75
---
Solve for "x":
wages = x >= 43.50
=========================
I'll leave the graph to you.
Cheers,
Stan H.
Question 239153: The low temperatures for the previous two days were 62 and 58. What would the temperature for the third day need to be such that the average daily temperature is at least 64.
Answer by checkley77(7049) (Show Source):
Question 239043: ok i really need help on this problem. i am in honors algebra 2 and i dont know what to do. Please help me solve the word problem: A rectangle is 3 times as long as it is wide. If the length and the width are both decreased by 4 cm, the resulting rectangle has area 28cm squared. Find the dimensions of the original rectangle.
Answer by Theo(675) (Show Source):
You can put this solution on YOUR website!A rectangle is 3 times as long as it is wide. If the length and the width are both decreased by 4 cm, the resulting rectangle has area 28cm squared. Find the dimensions of the original rectangle.
L = 3W
(L-4) * (W-4) = 28
Replace L with 3W to get:
(3W-4) * (W-4) = 28
remove parentheses by multiplying out the factors to get:
3W^2 - 16W + 16 = 28
subtract 28 from both sides to get:
3W^2 - 16W - 12 = 0
this factors out to:
(3W+2) * (W-6) = 0
This makes 3W = -2 or W = 6
W can't be negative so W = 6 is the only valid answer.
if W = 6, then L = 3W makes L = 18
You have L = 18 and W = 6
substitute in the original equation to get:
(L-4) * (W-4) = 28 becomes:
(18-4) * (6-4) = 28 which becomes:
14 * 2 = 28 which becomes:
28 = 28 which is true so the values for L and W must be good.
Your answers are:
L = 18 and W = 6
Question 238935: The second hand of a clock is four inches long. To the nearest inch, how far does the tip of the second hand travel in 45 seconds?
Answer by nerdybill(2446)  (Show Source):
You can put this solution on YOUR website!The second hand of a clock is four inches long. To the nearest inch, how far does the tip of the second hand travel in 45 seconds?
.
If the tip went the entire circle of 60 seconds it would have traveled:
Circumference = (pi)(2r)
where
pi is 3.14
r is radius
.
Circumference = (3.14)(2)(4)
Circumference = (3.14)(8)
Circumference = 25.12
.
If we only traveled for 45 seconds:
45/60 * 25.12
= 3/4 * 25.12
= .75 * 25.12
= 18.84
To the nearest inch:
19 inches
Question 238907: A student averages 84 on five tests if the student recieved 84,82,81,and 79 on the first four exams what grade did the student recieve on the fifth exam?
Answer by unlockmath(117) (Show Source):
You can put this solution on YOUR website!Hello,
To find the average of numbers, we need to add all the numbers and divide by 5.
Since one of the numbers is unknown we'll represent by x so the equation will be:
(84+82+81+79+x)/5 = 84 Combine like terms gives us:
(326+x)/5 = 84 Multiply both sides by 5
326 + x = 420 Subtract both sides by 326 gives us:
x = 94 There you go, he needs a 94 on the test to have an average of 84.
RJ Toftness
www.math-unlock.com
Question 238777: Can you translate this into an algebraic expression?
The product of 38% and some number
Answer by checkley77(7049) (Show Source):
Question 238715: Your last science test was worth 180 points. The test contained 42 questions, which were worth either 3 points, or 5 points each. How many 5-point questions were on the test?
Answer by checkley77(7049) (Show Source):
You can put this solution on YOUR website!3x+5(42-x)=180
3x+210-5x=180
-2x=180-210
-2x=-30
x=-30/-2
x=15 5 point questions were on the test.
42-15=27 3 points questions were on the test.
Proof:
3*15+5*27=180
45+135=180
180=180
Question 238729: Twenty-seven congruent cubes are glued together to form a larger cube. All six faces of the larger cube are painted pink. What is the product of the number of small cubes that have a single pink face and the number of small cubes that have three pink faces?
Answer by JimboP1977(76)  (Show Source):
You can put this solution on YOUR website!The way I would attack this problem is to actually draw the cube which comprises of 3 layers of 9 small cubes all together.
Then looking at the cube you can count the small cubes that have a one face painted and those that have three.
Looking at the larger cube you can see that the the middle smaller cube of each face of the larger cube has one face coloured. So that is 6 small cubes with 1 face.
The small cubes with three faces coloured are the corner ones of the larger face. So that is 8 cubes.
So the answer is 6*8 = 48.
There may be a more mathematical way of doing this that other tutors can elabourate on...
Does this help?
Question 238668: A custom blend of bird seed is to be mixed from seed mixtures costing $0.75 per pound and $1.25 per pound. How many pounds of each seed mixture are used to make 200 pounds of custom-blend bird seed costing $0.95 per pound?
Answer by checkley77(7049) (Show Source):
You can put this solution on YOUR website!1.25x+.75(200-x)=.95*200
1.25x+150-.75x=190
.50x=190-150
.50x=40
x=40/.50
x=80 pounds of $1.25 seed is used.
200-80=120 pounds of $.75 seed is used.
Proof:
1.25*80+.75*120=.95*200
100+90=190
190=190
Question 238679: Use inductive reasoning to predict the next complete line in the pattern.
55 - 6 = 49
565 - 67 = 498
5665 - 678 = 4987
Please help me. I have no idea where to even being
Found 2 solutions by solver91311, stanbon:
Answer by solver91311(5072) (Show Source):
You can put this solution on YOUR website!
First number, first calculation, zero 6s.
First number, second calculation, one 6
First number, third calculation, two 6s.
First number, fourth calculation, hmmm, what do you think?
Second number, first calculation, 6
Second number, second calculation, 67
Second number, third calculation, 678
So what do you think for this one?
Last pattern
49
498
4987
4987? What do you think replaces the (?)?
John
Answer by stanbon(26269) (Show Source):
You can put this solution on YOUR website!predict the next complete line in the pattern.
55 - 6 = 49
565 - 67 = 498
5665 - 678 = 4987
============================
56663 - 6789 = 49876
=============================
Cheers,
Stan H.
Question 238412: separate 24 into two parts in which one number is 8 times the number
Answer by checkley77(7049) (Show Source):
Question 238453: two adults and three children with a canoc on moosc island want to go to canary island . the canoc can hold either one adult and one child or three children .how many trips does the canoc have to make from one island to the other to ferry everyone across ?
a) 2 b) 3 c) 4 d) 5 e) 6
Answer by checkley77(7049) (Show Source):
You can put this solution on YOUR website!FIRST TRIP=3CHILDREN (DROP OFF 2 CHILDREN)
RETURN TRIP=1 CHILD
THIRD TRIP 1 ADULT & 1 CHILD (DROP OFF 1 ADULT)
RETURN=1 CHILD
FIFTH TRIP 1 ADULT + 1 CHILD (DROP OFF 1 ADULT & 1 CHILD)
ANSWER D) 5 TRIPS.
Question 238494: A toy company spends $1500 each day for factory expenses plus $8 fer teddy bear. How many bears must the company sell in one day to equal its daily cost?
Answer by Fombitz(2113)  (Show Source):
Question 238457: at ruthie store , donuts regularly cost 65 cents each. but on sundays, they are on sale for $6 per dozen .how much money would you save if you bought 4 dozen donuts on sale rather than at the regular price?
a) $2 b) $5.35 c) $7.20 d) $7.80 e) $24.00
Answer by checkley77(7049) (Show Source):
Question 238493: One health club charges a $44 sign up fee and $30 per month. Another health club charges a $99 sign up fee and $25 per month. For what number of months is the cost the same?
Answer by checkley77(7049) (Show Source):
Question 238435: Using Bayes Theorem: A certain disease occurs in % of the population. A test for the disease is fairly accurate: it misclassifies people with the disease as healthy % of the time and reports that a healthy person is diseased just % of the time. Suppose that a person tests positive for the disease. Compute the probability that the person does not have the disease. Round your answer to two decimal places.
I do not understand how to use this theory - so much to consider and plug into the formula. I might be overthinking it. HELP
Answer by Theo(675) (Show Source):
You can put this solution on YOUR website!this is the best tutorial on the web I could find that should help you to understand this material.
bayes theorem by vassar
a and b are two mutually exclusive events.
p(a) = probability of a occurring.
p(na) = probability of a not occurring.
p(b) = probability of b occurring.
p(nb) = probability of b not occurring.
p(b|a) = probability of b given a occurs.
p(nb|a) = probability of b not occurring given that a occurs.
p(b|na) = probability of b given a does not occur.
p(nb|na) = probability of b not occurring given that a does not occur.
they go on to give a formula for p(b) and p(nb)
p(b) = [p(b|a) * p(a)] + [p(b|na) * p(na)]
this means that the probability of b occurring is equal to:
the probability of b occurring given that a occurs times the probability of a occurring, plus the probability of b occurring given that a does not occur times the probability of a not occurring.
p(nb) = p(nb|a) * p(a) + p(nb|na) * p(na)
this means that the probability of b not occurring is equal to:
the probability of b not occurring given that a occurs times the probability of a occurring, plus the probability of b not occurring given that a does not occur times the probability of a not occurring.
they then go on to the finale by giving you the formulas for p(a|b) and p(na|b) and p(na|nb) and p(a|nb)
Those formulas are:
p(a|b) = p(b|a) * p(a) / p(b)
p(na|b) = p(b|na) * p(na) / p(b)
p(na|nb) = p(nb|na) * p(na) / p(nb)
p(a|nb) = p(nb|a) * p(a) / p(nb)
The particular formula you are interested in would be:
If you define being well as a as having the disease and b as testing positive for the disease, then the formula that you would be interested in would be:
a = having the disease.
na = not having the disease.
b = test positive for the disease.
nb = test negative for the disease.
you want to know the probability that the person that tests positive for the disease does not have the disease.
this means you want to know p(na|b)
na means you don't have the disease.
b means you test positive for the disease.
From above, the formula is:
p(na|b) = p(b|na) * p(na) / p(b)
since p(b) = [p(b|a) * p(a)] + [p(b|na) * p(na)]
then your formula becomes:
p(na|b) = p(b|na) * p(na) / ([p(b|a) * p(a)] + [p(b|na) * p(na)])
To put this into number, let's assume the following:
p(a) = .2
p(na) = .8
This means that the probability of having the disease is .2 and the probability of not having the disease is .2.
p(b|a) = .95
p(nb|a) = .05
this means that the probability of being tested positive if you have the disease is .95 and the probability of being tested negative if you have the disease is .05.
p(nb|na) = .7
p(b|na) = .3
this means that the probability of being tested negative if you don't have the disease is .7 and the probability of being tested positive if you don't have the disease is .3.
this means the test is pretty good at detecting the disease if it's present but not so good at detecting the absence of the disease if it's not present.
your factors are:
p(a) = .2
p(na) = .8
p(b|a) = .95
p(nb|a) = .05
p(b|na) = .3
p(nb|na) = .7
the formula you are going to work with is:
p(na|b) = (p(b|na) * p(na) / ([p(b|a) * p(a)] + [p(b|na) * p(na)])
this formula becomes:
p(na|b) = (.3 * .8) / (.95 * .2) + (.3 * .8)
this becomes:
p(na|b) = .24 / (.19 + .24)
this becomes:
p(na|b) = .24 / .43
this becomes:
p(na|b) = .558139535
given these numbers, there's a 55% chance that the person who tested positive is actually healthy.
with a higher degree of accuracy, these number should go down dramatically.
let's improve the accuracy and see where that takes us.
the numbers we were using were:
p(a) = .2
p(na) = .8
p(b|a) = .95
p(nb|a) = .05
p(b|na) = .3
p(nb|na) = .7
we'll improve the accuracy of detecting the disease when it's present and also improve the accuracy of detecting the disease when it's not present.
our new numbers will be:
p(a) = .2
p(na) = .8
p(b|a) = .99
p(nb|a) = .01
p(b|na) = .02
p(nb|na) = .98
our formula is still:
p(na|b) = (p(b|na) * p(na) / ([p(b|a) * p(a)] + [p(b|na) * p(na)])
this formula becomes:
p(na|b) = (.02 * .8 / [(.99 * .2) + (.02 * .8)]
this becomes:
p(na|b) = .016 / .214
this becomes:
.074766355
The probability that he doesn't have the disease given that he is tested positive for the disease becomes 7.5%.
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