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same as =
which is
= 8

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on your calc divide 12 by 11 and see what you get

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how do you find the missing number to get a certain average with 5 numbers.
:
Let x = the missing grade
An example the 5 grades: 84, 88, 79, 92, x
The certain average is 85
:
The equation
= 85
which is:
= 85
multiply both sides by 5,
343 + x = 5*85
343 + x = 425
subtract 343 from both sides
x = 425 - 343
x = 82 would be the missing grade to obtain an 85 average

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: A boardwalk is parallel to and 210 ft inland from a straight shoreline.
A sandy beach lies between the boardwalk and the shoreline.
A man is standing on the boardwalk, exactly 750 ft across the sand from his beach umbrella, which is right at the shoreline.
The man walks 4ft/s on the boardwalk and 2 ft/s on the sand.
How far should he walk on the boardwalk before veering off onto the sand if he wishes to reach his umbrella in exactly 4 min 45 s?
:
Change 4 min 45 sec to 285 sec
:
Find the distance from the man to a point (p) on the boardwalk directly opposite the umbrella.
:
p =
p = 720 ft
;
Let x = the dist the man will walk on the boardwalk, before onto the sand
The distance walked on the sand will be the hypotenuse of a triangle with the legs of 210' and (720-x) or
:
Write the time equation
b.w. time + sand walk time = 285 sec
+ = 285
:
Get rid of the denominators, mult by 4, results
x + = 1140
:
After a lot math obtained a quadratic equation of:
3s^2 - 3480x + 950400 = 0
Two solutions
x = 720
x = 440 ft. the reasonable solution is the distance he walked on the boardwalk

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Davin and Iris decided to run at a heart-shaped track with a perimeter of 1600 meters.
They start at the same point and run in opposite directions.
If the ratio of Davin's speed to Iris's speed is 3:2 and they meet again after 8 minutes, how fast is Davin in meters per minute?
:
let D = Devin's speed in met/min
let I = Iris's speed
:
When they meet they will have run a total of 1600 meters
Write a distance equation, dist = time * speed
:
D's dist + I's dist = 1600
8D + 8I = 1600
simplify, divide by 8
D + I = 200
I = (200-D); we can use this form for substitution
:
It says,"the ratio of Davin's speed to Iris's speed is 3:2 "
=
substitute (200-D) for I
=
Cross multiply
2D = 3(200-D)
2D = 600 - 3D
2D + 3D = 600
D =
D = 120 met/min is Devin's speed
:
:
Check solution by finding the dist each runs (I's speed: 200-120 = 80 met/min)
8(120) = 960
8(80) = 640
--------------
totals: 1600 m, confirms our solution

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The perimeter of a semicircle is doubled when the radius is increased by one.
Find the radius of the semicircle.
:
the perimeter of a semicircle =
:
=
Divide both side by pi
2r = r+1
2r - r = 1
r = 1 is the radius of the semicircle

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Find RS if R = -210 and S = 33...
:
RS means R*S, therefore
-210 * 33 = -6930

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Just use some basic algebra operations
:
9 + 2.7t = -4.8t -6?
2.7t + 4.8t = -6 - 9
7.5t = - 15
t =
t = -2
Check solution in original equation, replace t with -2
:
(5y+8) = 4y - 5
Get rid of that fraction, multiply both sides by 2
5y + 8 = 2(4y - 5)
5y + 8 = 8y - 10
5y - 8y = -10 - 8
-3y = -18
y has to be positive, multiply both sides by -1
3y = 18
y =
y = 6
Check this solution the same way

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Adding the same number to both the numerator and the denominator of a fraction does not change the fraction's value?
:
Let's see if that's possible
:
Let the fraction be
let x = the number added to num and den
:
=
Cross multiply
4(x+3) = 3(x+4)
4x + 12 = 3x + 12
4x - 3x = 12 - 12
x = 0, is the only number for this to be true

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it took 20 min to go up stream. 15 to come back. the speed off the current is 5 mph.
What is the speed of the boat?
:
We are dealing with mph therefore:
Change 20 min to hr
Change 15 min to hr
:
let s = speed of boat in still water
then
(s-5) = effective speed up stream
and
(s+5) = effective speed down stream
:
Write a dist equation; dist = speed * time
:
up dist = down dist
(s-5) = (s+5)
multiply by 12 to get rid of those fractions, results
4(s-5) = 3(s+5)
4s - 20 = 3s + 15
4s - 3s = 15 + 20
s = 35 mph speed of boat in still water

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twenty-six less than the product of nine and the difference of a number and one is four times the number.
what is that number?
:
Write what it says:
-26 + 9(x-1) = 4x
normally written
9(x-1) - 26 = 4x
9x - 9 - 26 = 4x
9x - 35 = 4x
9x - 4x = 35
5x = 35
x =
x = 7
:
:
Check it in the original equation
-26 + 9(7-1) = 4(7)
-26 + 54 = 28

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Of the final grades received by the students in a certain math course,
1/5 are A ’s, 1/4 are B ’s, 1/2 are C ’s and the remaining 10 grades are D ’s.
What is the number of students in the course?
:
Let x = total number of students
:
x = x + a + x + 10
Multiply by 20 to clear the denominator
20x = 20*x + 20*a + 20*x + 20(10)
Cancel the denominators and we have
20x = 4x + 5x + 10x + 200
20x = 19x + 200
20x - 19x = 200
x = 200 students
;
You can check the solution, replace x with 200 in the original equation

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a man drives regularly from his office to his home when he drives 36 kph he arrives home 3 minutes late than usual.
When he drives 45 kph he arrives 3 minutes earlier than usual.
Find his usual driving time, and the distance from his office to his home?
:
Let t = his usual driving time
:
Change 3 min to hrs. = .05 hrs
:
Write a dist equation, Dist = speed * time
:
45(t-.05) = 36(t+.05)
45t - 2.25 = 36t + 1.8
45t - 36t = 1.8 + 2.25
9t = 4.05
t =
t = .45 hrs which is; .45(60) = 27 minutes, his normal driving time
;
Find the distance when he is 3 min early (24 min)
45* = 18 km
:
Check the distance when he is 3 min late (30 min)
36* = 18 km
:
Summarize, 27 min normal drive time, 18 km is the distance

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One Grandfather has 3 grandchildren
a, b, & c
:
the difference between two children was 3 years.
b - c = 3
b = (c+3)
:
Her eldest grandchild was 3 times the youngest one
a = 3c
:
and the elder one 2 years more than the sum of the other two.
a = b + c + 2
replace b with (c+3); replace a with 3c
3c = (c+3)+ c + 2
3c = 2c + 5
3c - 2c = 5
c = 5 yrs is the youngest
then
a = 3(5)
a = 15 yrs is the eldest
:
:
Confirm this by finding the age of b
b = 5 + 3
b = 8
Check solutions in the statement:
" the elder one 2 years more than the sum of the other two."
15 = 5 + 8 + 2

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Hey, this isn't so hard, just follow closely what we are doing here
:
In 2004 Major League Baseball, Barry Bonds, playing for the San Francisco Giants of the National League, collected 44 hits in 117 at-bats in his first 49 games.
1. The ratio of number of hits to number of at-bats, rounded to the nearest thousandth, is a player’s batting average. What was Bond’s batting average in his first 49 games?
Answer Box (Type your work and answer below)
Set the ratio hits to at-bats and convert to a decimal.
:
= .376 is his batting average for the first 49 games
:
:
2. Based on the ratio of number of hits to number of games, how many hits would he get in a 162-game season?
Answer Box (Type your work and answer below)
Set a proportion and solve for the unknown.
:
Let h = no. of hits
=
cross multiply
49h = 162*44
49h = 7128
h =
h ~ 145 hits in 162 games
:
:
3. Based on the ration of number of hits to number of at-bats and assuming he bats 400 times in 2004, how many hits would he get?
Answer Box (Type your work and answer below)
Set a proportion and solve for the unknown.
:
Let h = no. of hits
=
Cross multiply
117h = 400 * 44
117h = 17600
h =
h ~ 150 hits in 400 at-bats
:
:
By checking work records, a plumber finds that Raul can plumb a house in 48 hr. Mira can do the same job in 36 hr.
4. Write a rational equation that represents the real-life scenario described above.
Answer Box (Type your work and answer below)
See section 6.8 of this week’s course reading.
:
Let t = time required when they work together
let the completed job = 1
+ = 1
:
5. How long would it take Raul and Mira if they would have worked together to complete the same job?
Answer Box (Type your work and answer below)
Use the equation you set in problem 4 and solve it.
+ = 1
Multiply by 144 to clear the denominators
144* + 144* = 144
cancel out the denominators and you have
3t + 4t = 144
7t = 144
t =
t ~ 20.6 hrs working together

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can 6", 4", and 10" be a triangle
:
No, think about it, the sum of two sides has to be greater than one side, right?
Is there any way you could draw this triangle, obviously not.

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Let d, a, t, b, represent the no. trees planted by ea man,
write an equation for each statement
:
Dan, andy, Tim and Bret planted a total of 34 trees.
d + a + t + b = 34
:
Dan planted three times as many as Bret.
d = 3b
:
Tim planted as many as Dan and Bret combined.
t = d + b
replace d with 3b
t = 3b + b
t = 4b
:
Andy planted half as many as Bret.
a = b
or
a = .5b

How many trees did each plant?
d + a + t + b = 34
replace: d with 3b, a with .5b , t with 4b
3b + .5b + 4b + b = 34
8.5b = 34
b =
b = 4 trees by Brett
:
You should be able to find the no. of trees, the other 3 men planted
Check that your solutions add up to 34.

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A sample of 138 firecrackers contained 7 "duds".
How many duds would you expect in a sample of 2346 firecrackers?
:
We can use a ratio equation
let d = no. of duds in 2346 f.c.
:
=
cross multiply
138d = 2346 * 7
d =
d = 119 duds in a sample of 2346 f.c.

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i have five digits.
a, b, c, d, e
:
my tens digit is 2 less than my hundreds digit.
d = c - 2
:
my thousands digit is 3 more than my hundreds digit.
b = c + 3
:
my ten thousands digit is equal to my hundreds digit.
a = c
;
my tens digit is 3.
d = 3
:
the sum of my digits is 25.
a + b + c + d + e = 25
Replace the above with the given equations
c + (c+3) + c + 3 + e = 25
3c + 6 + e = 25
3c + e = 25 - 6
3c + e = 19
from the 2nd equation, d = c-2, and we are given that d=3, therefore
c - 2 = 3
c = 5
3(5) + e = 19
e = 19 - 15
e = 4
:
Using the above information we find that:
a = 5
b = 8
c = 5
d = 3
e = 4
-------
tot 25
what number am i.. : 58534

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The speed of a moving walkway is about 4.5 feet per second.
Walking on the moving walkway, it takes Karen a total of 20 seconds to travel 45
feet with the movement of the walkway and then back again against the movement of the walkway.
What is Karen's normal walking speed?
:
Let x = K's normal walking speed in ft/sec
then
(x+4.5) = K's speed going the same as the walkway
and
(x-4.5) = K's speed going against the walkway
:
Write a time equation: time = dist/speed
:
with time + against time = 20 sec
+ = 20
:
Multiply by (x+4.5)(x-4.5)
(x+4.5)(x-4.5)* + (x+4.5)(x-4.5)* = 20(x+4.5)(x-4.5)
:
Cancel the denominators FOIL the right side and you have:
45(x-4.5) + 45(x+4.5) = 20(x^2 - 4.5x + 4.5x - 20.25)
:
45x - 202.5 + 45x + 202.5 = 20(x^2 - 20.25)
:
90x = 20x^2 - 405
A quadratic equation
20x^2 - 90x - 405 = 0
Simplify, divide by 5
4x^2 - 18x - 81 = 0
Use the quadratic formula to find x

a=4; b=-18; c=-81

:

:

we only care about the positive solution here

x =
x = 7.28 ft/sec is K's normal walking speed
:
:
You can confirm this by finding the time for each direction:
45/(7.28+4.5) = 3.82 sec
45/(7.28-4.5) = 16.18 sec
---------------------------
round trip time:20.00 sec
:
Did you understand the steps we took here?

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what is the square root of x to the 8th power? Please show me the work so that I may learn how to solve these problems.
:

Factor it to reveal a perfect square

The square root of x^4 * x^4, would have to be:
x^4, right?

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How much distance (in feet) does a vehicle travel per second at 85 miles per hour?
:
= 124.67 ft/sec

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Four times the supplement of angle A exceeds 8 times the complement of angle A by 28.
Find the measure of angle A.
:
We know:
(180-A) = the supplement of Angle A
and
(90-A) = the complement of Angle A
:
We can write the equation like this:
4(180-A) - 8(90-A) = 28
720 - 4A - 720 + 8A = 28
therefore
4A = 28
A = 28/4
A = 7 degrees
:
:
See if that works:
180-7 = 173 is the supplement
90 - 7 = 83 is the complement
"Four times the supplement of angle A exceeds 8 times the complement of angle A by 28."
4(173) - 8(83) =
692 - 664 = 28!!
"

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In a coordinate system, how can we get an equation? for example, a slope intersects X at (3,0) & Y at (0,2). whats the equation of line?
:
Using the slope intercept form: y = mx + b
"a slope intersects X at (3,0)"
m(3) + b = 0
3m + b = 0
:
Y at (0,2).
0m + b = 2
b = 2
:
Rewrite the 1st equation, replacing b with 2
3m + 2 = 0
3m = -2
m =
so our equation is: y = x + 2, in the slope/intercept form
:
But they want it in standard form, so rearrange it to
x + y = 2
without fractions, so multiply the eq by 3, results:
2x + 3y = 6, (which is (B )
:
:
You can confirm this by substituting the given x and y coordinates
3,0
2(3) + 3(0)= 6
6 = 6
and
0,2
2(0) + 3(2) = 6
6 = 6

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Just write an equation for exactly what it says
:
"The variable y is equal to 3 more than 5 times the variable x?"
y = 3 + 5x
usually written
y = 5x + 3
:
"If 7 is added to 3/5 of the variable x, the result is equal to the variable y."
7 + x = y
usually written
y = x + 7

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Man jogs 10 km/hr. to stadium.
He drives back at 60 km/hr. and saves one hour.
How far was the stadium.
:
First find the times, write a distance equation, dist = speed * time
Let t = his jogging time
then
(t-1) = his driving time
:
jog dist = drive dist
10t = 60(t-1)
10t = 60t - 60
60 = 60t - 10t
60 = 50t
t =
t = 1.2 hrs to jog it, then obviously, .2 hrs to drive it
:
Find the dist:
10 * 1.2 = 12 km to the stadium
Check the dist
.2(60) = 12 km also

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Steve gives Jim a 500m head start.
Also, steve agrees to start 15 min after jim.
If Steve travels at 17 km/hr, and Jin at 14km/hr, how long will it take Steve after he starts to overtake Jim?
:
We are dealing with km/hr, therefore:
Change 15 min to .25 hrs
Change 500 m to .5 km
:
Let t = travel time for Steve to catch up with Jim
then
(t+.25) = travel time of Jim, when he is caught
:
Write a distance equation; dist = speed * time
:
S's dist = J's dist + .5 km
17t = 14(t+.25) + .5
17t = 14t + 3.5 + .5
17t - 14t = .5 + 3.5
3t = 4
t =
t = 1 hr or 1 hr 20 min for Steve to catch Jim

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How much water evaporated from 90 mg of a 2% salt solution to produce a 3% salt solution?
:
Let x = amt of water required to evaporate
:
Write an amt of salt equation, amt remains the same only the per cent changes
:
.02(90) = .03(90-x)
1.8 = 2.7 - .03x
.03x = 2.7 - 1.8
.03x = .9
x =
x = 30 mg of water has to evaporate

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A swimming pool was 25 yards long by 45 feet wide.
It needed 3 inches of water added so that the pool was filled.
How many cubic feet of water must be added to the pool to fill it up?
:
Change 25 yds to 75 ft
Change 3 inches to .25 ft
:
75 * 45 * .25 = 843.75 cu/ft of water required

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a chemistry lab have 75ml of pure acid which must be diluted to a solution that is 10% acid.
How many milliliters of water should they add?
:
let x = amt of ml of water required
A simple equation based on the amt of acid
75 = .10(x+75)
75 = .1x + 7.5
75 - 7.5 = .1x
67.5 = .1x
x =
x = 675 ml of water required

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When matt was 11 years old, geom was 15.
:
how many years must pass for matt to be seven years older than one-half as old as Geom?
let y = no. of yrs for this to true
11 + y = .5(15+y) + 7
Get rid of the decimal mult both sides by 2
2(11 + y) = 15 + y + 14
22 + 2y = y + 29
2y - y = 29 - 22
y = 7 yrs for this to be true
:
:
check this
11 + 7 = .5(15+7) + 7
18 = .5(22) + 7
18 = 11 + 7