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mananth answered: 12270 problems
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Circles/318452: A circle has a radius of 8 inches. Find the area of a sector of the circle if the sector has an arc that measures 45°.
1 solutions
Answer 227920 by mananth(12270)   on 2010-06-28 23:27:39 (Show Source):
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Miscellaneous_Word_Problems/318241: you are given 8 identical coins and a balance scale. seven of the coins weight the same, but the eighth is lighter. you many use the balcne three times to determine which coin is lighter. show how you do this.
1 solutions
Answer 227783 by mananth(12270) on 2010-06-28 10:54:40 (Show Source):
You can put this solution on YOUR website!FIRST weigh
put 4 on each side.
the lighter one -will go up.
second weighment
put 2 on each pan.
the lighter one -pan will go up.
third weighment
put one on each
the lighter one will go up.
..
That's it.
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Pythagorean-theorem/318210: a guy wire is necessary to support
the telephone pole. If the height of the pole is 36 feet and
the guy wire is to be placed 15 feet from the base of the pole
how long a wire is needed?
1 solutions
Answer 227777 by mananth(12270) on 2010-06-28 09:48:09 (Show Source):
You can put this solution on YOUR website!pole height =46
horizontal distance from pole on ground to where it is pegged = 15 ft.
they form the legs of a right triangle =
let length of wire be l
..
l^2=36^2+15^2
l^2=1521
l=39 feet
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Equations/318161: Soup Kitchen
A soup kitchen is preparing a meal for a large number of people. The basic recipe for the sauce
requires 15 ounces (oz) of crushed tomatoes to serve 8 people. The chefs expect to serve 100
people, and crushed tomatoes are sold in 24 oz cans. How many cans should the chefs purchase?
1 solutions
Answer 227755 by mananth(12270) on 2010-06-28 01:45:24 (Show Source):
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Miscellaneous_Word_Problems/317885: If the perimeter of a rectangular courtyard is 36 yd, and the length is 3 yd longer than twice the width, then what are the length and width?
1 solutions
Answer 227627 by mananth(12270) on 2010-06-27 08:57:56 (Show Source):
You can put this solution on YOUR website!If the perimeter of a rectangular courtyard is 36 yd, and the length is 3 yd longer than twice the width, then what are the length and width?
..
widthe be x
length = 2x+3
..
Perimeter = 2L+2W
2x+2(2x+3)=36
2x+4x+6=36
6x+6=36
6x=30
x=5
width = 5
length = 2*5 +3=13
..
CHECK
2*13+2*5=36
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Miscellaneous_Word_Problems/317886: Gwen mixes 5 pounds of dried cranberries that sell for $4 per pound with some dried apples that sell for $3 per pound. If she wants the mix to be worth $3.25 per pound, then how many pounds of apples should she use?
1 solutions
Answer 227626 by mananth(12270) on 2010-06-27 08:54:36 (Show Source):
You can put this solution on YOUR website!Gwen mixes 5 pounds of dried cranberries that sell for $4 per pound with some dried apples that sell for $3 per pound. If she wants the mix to be worth $3.25 per pound, then how many pounds of apples should she use?
..
apples be x lbs.
cost = $3
..
cranberries 5 lbs
cost $4
..
Mix x+5 lbs
cost $ 3.25
..
3x+4*5=3.25(x+5)
3x+20=3.25x+16.25
0.25x=20-16.25
0.25x=3.75
x= 3.75/0.25
x=15 lbs of apples
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Percentage-and-ratio-word-problems/317890: John earns 3600 dollars per month. He spends 8 1/3% of his income towards house rent and 33 1/3% towards food. Find the amount he spends on rent.
1 solutions
Answer 227624 by mananth(12270) on 2010-06-27 08:46:23 (Show Source):
You can put this solution on YOUR website!John earns 3600 dollars per month. He spends 8 1/3% of his income towards house rent and 33 1/3% towards food. Find the amount he spends on rent.
..
8 1/3 on house = 25/3 %
25/3 % on on 3600 how much ?
25/3 * 3600/100
25*36 /3
12*25
=300
he spends $ 300 on House rent
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Systems-of-equations/317833: A cyclist travels 54 miles in 6 hours going against the wind and 52 miles in 4 hours with the wind. What is the rate of the cyclist in still air and what is the rate of the wind?
1 solutions
Answer 227615 by mananth(12270) on 2010-06-27 04:19:50 (Show Source):
You can put this solution on YOUR website!let speed of cycle be x in still air
speed of wind =y
..
6(x-y)=54
4(x+y)52
..
6x-6y=54
x-y=9
4x+4y=52
x+y=13
..
add the two equations
x-y+x+y=22
2x=22
x=11 mph. speed of cycle
x-y=9
11-y=9
y=2
speed of wind = 2 mph
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Systems-of-equations/317840: A motorboat takes 4 hours to travel 192 miles going upstream. The return trip takes 2 hours going downstream. What is the rate of the boat in still water and what is the rate of the current?
1 solutions
Answer 227614 by mananth(12270) on 2010-06-27 04:14:40 (Show Source):
You can put this solution on YOUR website!let speed of boat be x mph
speed of current be y mph
..
speed * time = distance
4(x-y)=192
x-y=48
..
2(x+y)=192
x+y=96
add both the equations
x-y+x+y=96+48
2x=144
x=72 mph. speed of boat
..
x-y=48
72-y=48
y=72-48
24 mph speed of current
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Travel_Word_Problems/317855: A student walks and jogs to college each day. she averages 5km/h walking and 9km/h jogging. The distancefrom home to college is 8km and she makes the trip in 1 hour. How far does the student jog?
I can't seem to get it set up right to get the correct calculation. I used 5km(X) +9 km(y) = 8km.
1 solutions
Answer 227613 by mananth(12270) on 2010-06-27 04:04:49 (Show Source):
You can put this solution on YOUR website!let her walk x km.
she will jog 8-x km
..
walking speed = 5km/hr
jogging speed = 9km/hr
..
distance to college 8km.
walking time + jogging time = total time
x/5+ 8-x /9 =1
9x+40-5x /45=1
4x+40=45
4x=5
x= 5/4 km
she walks 5/4 km
1.25 km
so she jogs 8-5/4
32-5 /4
27/4
6.75 km
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Angles/317851: The measure of an angle is 8 degrees less than three times the measure of the angle's suplement. Find the measure of the angle.
1 solutions
Answer 227611 by mananth(12270) on 2010-06-27 00:26:22 (Show Source):
You can put this solution on YOUR website!let the angle be x
the other angle is 3x-8
..
x+3x-8=180
4x-8=180
4x=188
x=47 deg
the other angle is 3*47-8
=141-8
=133 deg
CHECK
133+47=180
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Systems-of-equations/317849: Solve using the Addition/Elimination Method
6x + 8y = 18
-3 -4y = -9
The answer I got was 0=0 always true. I'm needing a second opinion.
Thank you! It's greatly appreciated.
1 solutions
Answer 227610 by mananth(12270) on 2010-06-27 00:21:33 (Show Source):
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Probability-and-statistics/317842: Ray Bond sells handcrafted yard decorations at county fairs. The variable cost to make these is
$20 each, and he sells them for $50. The cost to rent a booth at the fair is $150. How many of these
must Ray sell to break even?
1 solutions
Answer 227608 by mananth(12270) on 2010-06-27 00:09:36 (Show Source):
You can put this solution on YOUR website!Let the break even quantity be x
$20 s cost for each .
Total cost = 20x
Booth rent = 150
sales will be 50x
20x+150=50x
30x=150
x=5 Numbers
CHECK
5*20+150=250
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Expressions-with-variables/317843: The sum of the angles of every triangle in a plane is 180 degrees. The measure of the largest angle of the triangle is 10 degrees more than one angle and 20 degrees more than the other. What is the measure of the largest angle?
1 solutions
Answer 227600 by mananth(12270) on 2010-06-26 23:45:53 (Show Source):
You can put this solution on YOUR website!the largest angle be x deg
one angle = x-10
second angle = x-20
..
x+x-10+x-20=180
3x-30=180
3x=180+30
3x=210
x=70 deg
the other angle will be 70-10=60deg
third angle = 70-20=50deg
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Miscellaneous_Word_Problems/317724: When Dave walks to school, he averages 90 steps per minute, each of his steps are 75 cm long. It takes him 16 minutes to get to school. His brother, Jack, going to school by the same route,averages 100 steps per minute, but his steps are only 60 cm long. How long does it take Jack to get to school?
1 solutions
Answer 227559 by mananth(12270) on 2010-06-26 19:07:55 (Show Source):
You can put this solution on YOUR website!dave takes 90 steps /minute , length of each step = 75 cm, walks for 16 minutes
Total distance walked = 16*75*90=108 000 cm
..
jack takes 100 steps of 60 cm each = 6000 cm /minute
distance = 108 000 cm
rate = 6000 steps/minute
..
distance / rate = time
108 000 / 6000
=18 minutes
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Travel_Word_Problems/317793: a motorboat can maintain a constant speed of 16 mile per hour relative to the water. the boat makes a trip upstream to a certain point in 20 minutes; the return trip takes 15 minutes. what is the speed of the current?
1 solutions
Answer 227556 by mananth(12270) on 2010-06-26 19:00:09 (Show Source):
You can put this solution on YOUR website!a motorboat can maintain a constant speed of 16 mile per hour relative to the water. the boat makes a trip upstream to a certain point in 20 minutes; the return trip takes 15 minutes. what is the speed of the current?
..
upstream in 20 minutes = 1/3 hours
Down stream in 15 minutes = 1/4 hours
..
let speed of current = x mph
upstream speed will be 16-x
down stream speed will be 16+x
..
distance is same to & fro
distance= rate * time
..
1/3 * (16-x) = 1/4*(16+x)
4*(16-x)=3*(16+x)
64-4x=48+3x
7x=16
x=2.28 mph
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Equations/317736: Simplify: x^2+3x-4 division sign X^2+5x-6
X^2+6x+8 x^2+7x+6 the problem should be the first row on top with the division sign in the middle
1 solutions
Answer 227555 by mananth(12270) on 2010-06-26 18:47:41 (Show Source):
You can put this solution on YOUR website!X^2+6x+8 / x^2+7x+6
x^2+4x+2x+8 / x^2+6x+x+6
x(x+4)+2(x+4) / x(x+6)+1(x+6)
(x+6)(x+2) / (x+1)(x+6)
=(x+2) / (x+1)
..
x^2+3x-4 / X^2+5x-6
x^2+4x-x-4 / x^2+6x-x-6
x(x+4)-1(x+4) / x(x+6)-1(x+6)
(x-1)(x+4) / (x-1)(x+6)
(x-4) / (x+6)
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