Questions on Word Problems: Mixtures answered by real tutors!

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The rate of motorcycle is 40 mph greater than the rate of a bicycle. The motorcycle travels 150 miles in the same amount of time as the bicycle travels 30 miles. Find the rate of the motocycle.

m=rate of motorcycle
b=rate of bike
m=b+40

150/b+40=30/b-----------------------because miles over mph gives you the time, which is equal in this case.

Cross multiply
150b=30b+1200

Subtract 30b from both sides
120b=1200

Divide both sides by 120
b=10

m=b+40
m=10+40
m=50

Answer:
Bike=10mph
Motorcycle=50mph
----------------------------------------------------------------------------
two people working together can do a job in 3 hrs. How long will it take the slower person to do the same job if one of them is 3 times as fast as the other?

together=1/3 (of the job in an hour)
one person=x
other person=3x

x+3x=1/3

Combine like terms
4x=1/3

Divide both sides by 4
x=1/12

1/12 of the job in one hour, so the whole job in 12 hours.

Answer: The slower person can do the job alone in 12 hours.
* The faster person can do the job alone in 4 hours.

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---------> working eqn
but is 120ml more than --->
Substituting,




For
Simply add to check via working eqn:


Thank you,
Jojo

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Let x=amount of 9% solution needed
Now we know that the amount of pure cleaning solution in the 9% mixture (0.09x) plus the amount of pure cleaning solution in the 13% mixture (0.13*10) has to equal the amount of pure cleaning solution in the final mixture (0.11(10+x)). So our equation to solve is:
0.09x+0.13*10=0.11(10+x) get rid of parens and simplify
0.09x+1.3=1.1+0.11x subtract 1.1 and also 0.09x from each side
0.09x-0.09x+1.3-1.1=1.1-1.1+0.11x-0.09x collect like terms
0.2=0.02x divide each side by 0.02
x=10 pints----------------------------------amount of 9% solution needed
CK
0.09*10+0.13*10=0.11*20
0.9+1.3=2.2
2.2=2.2

Hope this helps---ptaylor

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Some times, with mixture problems such as this one, it might be a little easier if you think in terms of just the antifreeze rather than the mixture.
You are told that Samantha needs 20 quarts of 50% antifreeze. First, change the percentage to its decimal equavalent (50% = 50/100 = 0.5).
Now 50% of 20 quarts of antifreeze mixture is really 0.5 (20) = 10 quarts of pure antifreeze.
The amount of 40% antifreeze mixture to be added is (20-x) quarts, that is this is the amount, added to the x quarts of pure antifreeze to get the 20 quarts.
Now let x = the amount of pure (100% = 1) antifreeze to be added to (20-x) quarts of 40% antifreeze mixture.
The amount of 40% antifreeze mixture is 0.4(20-x) quarts of antifreeze.
Now you can write an equation to solve for x, the number of quarts of pure antifreeze that Samantha needs.
Perform the indicated multiplication.
Combine the x's
Subtract 8 from both sides.
Finally, didvide both sides by 0.6 to get x by itself.
or x = 3 1/3
So Samantha needs to mix 3 1/3 quarts of pure antifreeze with 20-x = 20-3 1/3 = 16 2/3 quarts of 40% antifreeze mixture to obtain 20 quarts of 50% antifreeze mixture..

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Let x be the length of the shorter one, the the length of the longer one is x + 11.
As their total length is 75, we can set up an equation:
x + (x + 11) = 75
Solving for x,we have
2x + 11 = 75
2x = 64
x = 32
So their lengths are 32 and 43 ft respectively.

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Let the length of the 1st part be x.
x, x+2 and 2(x+2) are the length of the 3 parts.
x+x+2+2(x+2)=10
2x+2+2x+4=10
4x+6=10
4x=4
x=1 m
So the lengths are 1, 3, 6 m
.
Ed

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We respect everybody here but there's no harm in trying this one:
Remember the following:
= liters of acid = unknown????
= liters of solution = unknown???
= final stage of acid when mixed w/ solution
Now, we all know when we add the volume of & we get 32 Liters. To show:

-----------------> eqn 1
Now, "percent of concentration" makes the difference on how many "Liters" of acid we need to put. Putting this into eqn,
------------> working eqn
In summary of the working eqn, 30% of Liters of acid + 10% of Liters of solution equals 15% of 32 Liters of the NEW acid solution.
.
In eqn 1 we get, and substitute in our working eqn:




---------------> amount of Acid Solution that must be added.
FOR THE AMOUNT of SOLUTION, go back eqn 1,
,
--------------> amount of SOLUTION that must be added.
Besides,


Thank you,
Jojo

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You haven't given enough info to solve. How much 10% solution do you start with?

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A 4% salt solution is mixed with a 16% salt solution. How many milliliters of each solution are needed to obtain 600 millilters of a 10% solution?
.
Let x = amount of 4% salt solution
then
600-x = amount of 16% salt solution
.
.04(x) + .16(600-x) = .10(600)
.04x + 96 - .16x = 60
96 - .12x = 60
96 - 60 = .12x
36 = .12x
300 milliliters of 4% salt solution = x
.
600-x = 600-300 = 300 milliliters of 16% salt solution

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7) .6x+40*.2=.3(40+x)
.6x+8=12+.3x
.6x-.3x=12-8
.3x=4
x=4/.3
x=13.33 quarts of 60% alcohol is needed.
proof:
.6*13.33+8=.3(40+13.33)
8+8=.3*53.33
16=16
---------------------------------------------------
6) 40*.2=8 pounds of salt.
For a 50% solution you need 2*8=16 pounds of water.
40-16=24 pounds of water must be evaporated.

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Snakes have no feet so the 56 feet must belong to the colection of iguanas, and, since each iguana has 4 feet, there are 56/4 = 14 iguanas.
Each iguana has two eyes, so the 14 iguanas have 28 of the 50 eyes, leaving 22 eyes for the snakes, and each snake has two eyes, so there must be 22/2 = 11 snakes.

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If Steve can mix 20 drinks in 5 minutes, Sue can mix 20 drinks in 10 minutes, Jack can mix 20 drinks in 15 minutes, how much tie will it take if all 3 of them work together to mix 20 drinks?
:
Here's an easy way to do this:
:
Let t = time required when they all work together
Let the completed job = 1 (the mixing of 20 drinks)
:
+ + = 1
Multiply equation by 30 to get rid of the denominator:
:
6t + 3t + 2t = 30
:
11t = 30
t =
t = 2.727 hrs. Change the decimal hrs to minutes: .727 * 60 = 43.6 min
or
t = 2 min 44 sec

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first you need to arrange these integers in assending values:
3 4 4 4 4 4 4 5 5 5 6 6 6 7 8
the mean (average )=sum/number of integers:
mean=75/15=5 answer.
medium=the middle integer:
medium=5 answer.
mode=the most frequent integer.
mode=4 (freqency=6) answer.

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Mean : or average, sum the values and divide by total number of values.
Mean = .
.
.
.
Median : Order the set from smallest to largest, find the middle value.
(3,4,4,4,4,4,4,5,5,5,6,6,6,7,8)
Since there are 15 values, the 8th value is the median.
Median = 5.
.
.
.
Mode: We can look at the data with a horizontal bar graph with each X representing one occurence.
The value with the most occurences is the mode.
.
.
.
3:X
4:XXXXXX
5:XXX
6:XXX
7:X
8:X
.
.
.
The mode is 4.

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You are being asked to make several 'groups' and then put the entries into those groups. Once you have done that, you are being asked to make two plots with the resulting data.
Generally 5 to 7 groups makes for a nice chart.
Look at the data and see that the smallest entry is 14 and the largest is 27.
So there are 13 years in the range of data. Lets make 5 groups. Each group will be 3 years wide. Start the first group as 13-15. The next is 16-18. etc .
Now sift your data into those groups.
13-15 | 4 (14 15 15 15 )
16-18 | 13
19-21 | 3
22-24 | 1
25-27 | 4
Now plot a bar chart and polygon

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If beaker A contains a 15% solution of sulfuric acid and beaker B contains a 20% solution of sulfuric acid, how much from each beaker should be used to make 6 liters of a 18% solution of sulfuric acid?
----------------------
EQUATIONS:
Quantity Equation: a + b = 6 L
Active Ingrediant: 0.15a + 0.20b = 0.18(6) = 1.08
----------------
Rearrange for elimination:
15a + 15b = 90
15a + 20b = 108
------------------
Subtract 1st from 2nd to get:
5b = 18
b = 3.6 L (amt. of 15% solution in the mix)
Since a+b=6, a = 6-3.6 = 2.4 L (amt. of 20% solution in the mix)
======================================
Cheers,
Stan H.

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In words:
(liters of acid in beaker A) + (liters of acid in beaker B) / (total liters of solution in A and B) = % solution of acid
Let A = liters of solution needed from beaker A
Let B = liters of solution needed from beaker B

Note that we are told liters

Multiply both sides by

And since




liters
Given is


2.4 liters of solution are needed from beaker A
and 3.6 liters of solution are needed from beaker B
check answer:






OK

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Let's call the amount from beaker A, A.
Let's call the amount from beaker B, B.
The total final volume is 6 liters.
1.
The final concentration is 18%.
2.
Let's multiply equation 2 by 100 to get rid of decimals.
2.
2.
2.
We can use eq. 2 to solve for B in terms of A.
2.


Now substitute this into eq. 1 and solve for A.
1.



Now back substitute to find B,



2.4 liters of solution A and 3.6 liters of solution B.

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A mixture containing 6% salt is to be mixed with 2 ounces of a mixture which is 15% salt, in order to obtain a solution which is 12% salt. How much of the first solution must be used?
:
How do you solve a problem "Interactively"?
:
Anyway.
:
Let x = amt of 1st solution required
:
.06x + .15(2) = .12(x+2)
:
.06x + .3 = .12x + .24
:
.3 - .24 = .12x - .06x
:
.06 = .06x
:
x = 1 oz of the 1st solution required
:
:
Check solution:
.06(1) + .15(2) = .12(1+2)
.06 + .30 = .36

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Let's call the unkown amount, x.

Let's multiply both sides by 100 to get rid of decimals.




1 ounce of the 6% solution is needed.

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I used EXCEL to calculate 5 random numbers.
They are (95,31,42,71,47) or (31,42,47,71,95) ordered from smallest to largest.
Mean :
Median : 3rd number ranked smallest to largest :
Mode : Each number only occurs only once. No additional information gained from the mode.
Midrange : (1/2)(Min+Max)=

Shown on the graph are the mean(green line), the median(red line), and the midrange(blue line) along with the 5 data points.
Looks like the median estimates too low, the midrange estimates too high, which leaves the mean as the best measure in this case.
This happened because there were two data points close to each other (42,47).

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a mixture of food a and b is to be made so that it contains at least 45 oz of nutrient N2. the cost per pound of a is $4 and each pound of A contains 1 oz of N1 and 2 oz of N2. Food b cost $8 per pound and each pound contains 1.5 oz of N1 and 0.5 of N2. if the weight of the mixture must not exceed 40lb, how many pound of each should be used so that the total cost is a minimum?
;
Just get 23 lbs of Food a, that gives you 46 oz of N2, less than 40 lb, at 4$ a lb
;
There is no constraint on N1, so I quess we ignore that.

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a. Counting principle - 2 frames x 2 colors x 3 seats = 12 choices
b. Difficult to make a tree diagram with the software limitations, I can list all the possibilities and you can make it. This would answer c) also.
(Male,Red,Soft)
(Male,Red, Medium)
(Male,Red, Hard)
(Male,Blue,Soft)
(Male,Blue, Medium)
(Male, Blue, Hard)
(Female,Red,Soft)
(Female, Red, Medium)
(Female, Red, Hard)
(Female, Blue,Soft)
(Female, Blue, Medium)
(Female, Blue, Hard)

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A 100 KILOGRAM MIXTURE OF 0.69 KG. OF PINTO BEANS AND 0.89 KG. KIDNEY BEANS IS VALUED AT 81.00. HOW MANY KILOGRAMS OF EACH DOES IT CONTAIN?.
----------------
Quantity equation : p + k = 100
Value equation: 0.69p + 0.89k = 81
-------------------
solve by any method to get:
p = 40 and k = 60
======================
Cheers,
Stan H.

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How would you put this in expected value and fair price of ticket?
1000 tickets for prizes are sold for $2 each. Seven prizes will be awarded – one for $400, one for $200, and five for $50. Steven purchases one of the tickets. (Give solutions as decimals accurate to the nearest hundredth.)
a) Find the expected value

Note that we include -$2 as a "negative prize" in the likelihood that 
Steven doesn't win at all and loses his $2.  

Prizes  | Probability |  Expectation
 $398   |     .001    |      $0.398
 $198   |     .001    |      $0.198
 $ 48   |     .001    |      $0.048
 $ 48   |     .001    |      $0.048
 $ 48   |     .001    |      $0.048
 $ 48   |     .001    |      $0.048
 $ 48   |     .001    |      $0.048
 $ -2   |     .993    |     -$1.986
-------------------------------------
Total expectation =         -$1.15 
 
The expected value is -$1.15 or a LOSS of $1.15

That is, if this raffle were held every week, and Steven
played it every time, he would average losing $1.15 per
game.

---------------------------------------------------------

b) Find the fair price of the ticket

The easiest way to do this problem is just to pretend that
they give him his ticket price back in the problem above.  
So we then just add $2 to the -$1.15 and get $2 - $1.15 = $0.85.  

But to work it out: 

Let the fair price be $x

We put -x where we put -2 above and
-.993x for the expectation, and 0 for
the Total expectation:

Prizes    | Probability |  Expectation
 $400-x   |     .001    |      $0.40-.001x
 $200-x   |     .001    |      $0.20-.001x
 $ 50-x   |     .001    |      $0.05-.001x
 $ 50-x   |     .001    |      $0.05-.001x
 $ 50-x   |     .001    |      $0.05-.001x
 $ 50-x   |     .001    |      $0.05-.001x
 $ 50-x   |     .001    |      $0.05-.001x
 $ -x     |     .993    |     -$0.993x
-------------------------------------
Total expectation =             $0.000 

Add the right column and make an equation:



                         0.85 - x = 0
                             0.85 = x   


That is, if this raffle were held every week, and the price were
85 cents, and Steven played it every time, he would average 
breaking even.  That fair ticket price is 85 cents. 

Edwin

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I'm really having diffuculties trying to understand
this question.

11. (3 pts) The results of a survey for an airline 
are shown below:

Traveler   |   Male |  Female | Total
-------------------------------------
Business   |    57  |   92    |  149
Vacation   |    72  |   74    |  146
-------------------------------------
Total      |   129  |  166    |  295
Use the chart to find the probability that the traveler was 
a)	male 

Well, let's see how many of the Total 295 were males.
I'll color the Male column red:

Traveler   |   Male |  Female | Total
-------------------------------------
Business   |    57  |   92    |  149
Vacation   |    72  |   74    |  146
-------------------------------------
Total      |   129  |  166    |  295

You see that there are 129 Males out of 295 Travelers.
So you put 129 ove 295 and get the fraction 
and that's the answer.


b)	on vacation given the traveler was male

Since we are given that the traveler was male, then we 
can eliminate everything but just what is given, the
Male column. So all that remains in the chart is this:

Traveler   |   Male |  Female | Total
-------------------------------------
Business   |    57  |         |     
Vacation   |    72  |         |  
-------------------------------------
Total      |   129  |         |  

So there are 72 males on on vacation out of 129 given males.
So we put 72 over 129 and get  and reduce
that reduces to 

-------------------------

c)	female given the traveler was on business 
       (Give solutions as  fractions in lowest terms.)


Since we are given that the traveler was on business, we
can eliminate everything but just what is given, the
Business row. So all that remains in the chart is this:

Traveler   |   Male |  Female | Total
-------------------------------------
Business   |    57  |   92    |  149
Vacation   |        |         |  
-------------------------------------
Total      |        |         |  

So there are 92 females on business out of 149 given travelers on
business. So we put 92 over 129 and get  which
doesn't reduce.

Edwin

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In words:
(final liters of glucose)/(final toal liters of broth) = final percent glucose
I'm told that the final percent glucose is 50.1%
How much glucose is in the 16.1 liters of 57% broth?
liters
I'm not told how much 40.2% broth I have, so I'll call the
liters of this broth
There is glucose in this broth

mulltiply both sides by


liters
The amount of 50.1% broth is
liters answer
Check my math, but I think the method is good

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A solution of 75% pesticide is to be mixed with a solution of 51% pesticide to form 48 liters of a 64% solution. How much of the 75% solution is needed?

x=liters of 75%
48-x=liters of 51%
coefficient=percent

75(x)+51(48-x)=64(48)

Distribute
75x+2448-51x=3072

Combine like terms
24x+2448=3072

Subtract 2448 from both sides
24x=624

Divide both sides by 24
x=26

x=liters of 75%
48-x=liters of 51%

Answer:
liters of 75%=26
liters of 51%=22

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a plant manager needs a solution of 77% herbicide to be mixed with a solution of 67% herbicide to form 30 liters of 74% solution. How many liters of the 77% solution must he use?

x=liters of 77%
30-x=liters of 67%
coefficient=percent

77x+67(30-x)=74(30)------------------------solution of 77% herbicide mixed with a solution of 67% herbicide = 30 liters of 74% solution.


Distribute
77x+2010-67x=2220

Combine like terms
10x+2010=2220

Subtract 2010 from both sides
10x=210

Divide by 10
x=21

x=liters of 77%
30-x=liters of 67%

Answer:
liters of 77%=21
liters of 67%=9

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How much pure water must be mixed with 3 pints of 70% developer to produce a
mixture that is 13% developer?
.
He started with:
3 pints of 70% developer
That means the amount of developer in the solution is:
.70 * 3 = 2.1 pints
.
Let x = amount of water added
then
2.1/(x+3) = .13(x+3)
2.1 = .13(x+3)^2
16.154 = (x+3)^2
16.154 = x^2 + 6x + 9
0 = x^2 + 6x - 7.154
.
Since you can't factor, you must apply the quadratic equation.
Doing so, produces two solutions one positive and one negative. We can throw out the negative solution cause it doesn't make sense. Therefore, the positive answer must be our solution:
x = 1.02 pints
.
Below is the solution of the quadratic equation:

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=64.616 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 1.01920390127199, -7.01920390127199. Here's your graph:

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there were 3/4 as many women as there were men in a train yesterday. at the next station, 12 women and 6 men got in. as a result, there were 6/7 as many women as men on the train. how many men and women were in the train at first?
.
Let M = # of men
(3/4)M = # of women
.
(6/7)(M+6) = (3/4)M + 12
To get rid of all the denominators, multiply both sides by 28:
24(M+6) = 21M + 336
24M + 144 = 21M + 336
24M-21M = 336-144
3M = 192
M = 64 (Number of men in the train at first)
.
(3/4)64 = 3(16) = 48 (Number of women in the train at first)

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an airplane made a 2040-kilometer trip in the direction of the wind in 5 hours last tuesday. if the trip against the direction of the wind took an hour longer, find the rate of the plane in still air and the velocity of the wind.
--------------
Let "p" and "w" represent the plane speed and the wind speed.
--------------
With-wind DATA:
distance = 2040 km ; time = 5 hrs ; rate = 2040/5 = 408 kph
--------------
Against-wind DATA:
distance = 2040 km ; time = 6 hrs ; rate = 2040/6 = 340 kph
--------------
EQUATIONS:
p + w = 408
p - w = 340
-------------
Add to get:
2p = 748
p = 374 kph (speed of the plane in still air)
------------
Substitute into p+w = 408 to solve for w:
374 + w = 408
w = 34 kph (speed of the wind)
==================================
Cheers,
Stan H.

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a grocer mixes 12kg of one grade of beans with 10kg of another grade to obtain a blend worth 540 pesos. he then makes a second blend worth 610 pesos by mixing 8kg of the first grade with 15kg of the second grade. find the price per kilogram of each grade?
---------------------------------------
Let "a" be the price of 1st bean and "b" be the price of 2nd bean.
--------------------------------------
Value Equation: 12a + 10b = 540
Value Equation: 8a + 15b = 610
-------------------
Solve the system by substitution, elimination, or matrix to get:
a = 20 p
b = 30 p
==============
Cheers,
Stan H.

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If the class is 400
And, he is ranked 44th
From the top he would be:
400 - 44 = 356
.
Percentage-wise:
356/400 * 100 = 89%

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One card is selected at random from a standard 52-card deck of playing cards. Find the probability that the card selected is a red king.
-----------
There are two red kings in the deck.
P(red king) = 2/52 = 1/26
===========================
Cheers,
Stan H.

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Paul's Plumbing charges $35 for any service call plus an additional $40 an hour for labor. A service call from Robert's Rapid Repair Plumbing costs $45 plus and additional $40 and hour for labor. When is the total price for a service the same for both companies? when is it better to use Paul's Plumbing? explain your answer in terms of slopes and y-intercepts.
:
Since they charge the same for labor ($40), Paul's is always $10 cheaper
:
In terms of graphs, they have the same slope (40x) so the lines are parallel and never intersect. the y intercepts will be different, 35 & 45

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A license plate is to consist of two letters followed by three digits.
How many different license plates are possible if the first letter must be a vowel, and repetition of letters is not permitted, but repetition of digits is permitted?
-------------
Ans: 5*25*10*10*10 = 125000
============================
Cheers,
Stan H.

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13. (4 pts) At an annual flower show, 6 different entries are to be arranged in a row.

a) How many different arrangements of the entries are possible?
Ans: 6! = 720
------------------------
b) If the owners of the 1st, 2nd, and 3rd place entries will be awarded prizes of $100, $50, and $25 respectively, how many ways can the prizes be awarded?
And: 6C3 = 6!/[6-3)!3!] = 7*6*5/1*2*3 = 35 ways
===========================
Cheers,
Stan H.

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13/20=.65 or 65% chance that the next call will be answered.

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In your jar, you have a total of:
5+16+8 =29
.
Of the 29:
8+5 = 13 are NOT green
.
Therefore, the probability of NOT picking a green marble is:
13/29

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9. (6 pts) A couple plan to have exactly three children. (Need line segments? Use these)
(You may also hand draw your work and scan it in and save it in your .doc file,
as a .jpg or .pdf. Your choice.)
(a) Construct a tree diagram and list the sample space.
I'll let you draw the tree.
In the 1st column put "b" and "g" for boy or girl
In the 2nd column put "b" and "g" to the right of each of the column 1 entries
In the 3rd column put "b" and "g" to the right of each of the column 2 entries

(b) Find the probability that the family has at least two girls.
at least two girls: bgg, gbg, ggb, ggg
P(at least two g's)= 4/8 = 1/2
==================
Cheers,
Stan H.

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find the z values for the upper and bounds of the range and then find the portion of the distribution represented

lower __ z=(550.67-636.55)/89.46 __ z=-.96 (approx)

upper __ z=(836.94-636.55)/89.46 __ z=2.24 (approx)

this range represents about 82% of the distribution

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how much water must be evaporated from a 10 kg solution which has 4% salt to make a solution of 10% salt?
:
Let x = amt of water evaporated
:
Write an equation based on the amt of salt.
(the amt of salt does not change, only the per cent of salt changes)
:
.04(10) = .10(10-x)
.4 = 1 - .1x
.4 - 1 = -.1x
-.6 = -.1x
x =
x = 6 liters of water evaporated
;
:
Check solution
.04(10) = .1(10-6)
.4 = .4

You can put this solution on YOUR website!
x=$30 drum
y=$20 drum

30x+20y=160
x+y=7

Solve for x
x=7-y

Plug that in
30(7-y)+20y=160

Distribute
210-30y+20y=160

Combine like terms
210-10y=160

Subtract 210
-10y=-50

Divide by -10
y=5

x+y=7
x+5=7
x=2

2 $30 drums
5 $20 drums
--------------------------------------------------------------------------
30x+20y=160
x+y=7

These are two lines that you must graph. First, get them into y=mx+b form by isolating y in each.

20y=160-30x
y=8-30/20x
y=-3/2x+8

y=7-x
y=-x+7

Now graph them:
y=-3/2x+8

Solved by pluggable solver: DESCRIBE a linear EQUATION: slope, intercepts, etc

Equation describes a sloping line. For any equation ax+by+c = 0, slope is . X intercept is found by setting y to 0: ax+by=c becomes ax=c. that means that x = c/a. 160/30 = 5.33333333333333. Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is 160/20 = 8. Slope is -30/20 = -1.5. Equation in slope-intercept form: y=-1.5*x+8.

y=-x+7

Solved by pluggable solver: DESCRIBE a linear EQUATION: slope, intercepts, etc

Equation describes a sloping line. For any equation ax+by+c = 0, slope is . X intercept is found by setting y to 0: ax+by=c becomes ax=c. that means that x = c/a. 7/1 = 7. Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is 7/1 = 7. Slope is -1/1 = -1. Equation in slope-intercept form: y=-1*x+7.

Notice that the one point that both lines contain is at (2,5)...(which may be difficult to see on these graphs). Once you graph them on your own, you will see this better. That is how you verify your solution by graphing.

You can put this solution on YOUR website!
company purchased 8 work shirts and 17 work pants at $273. Next month purchased additional 16 shirts & 13 pants for $357.
how much was each shirt & pant?
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8s + 17p = 273
16s+ 13p = 357
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Solve by any method you know to get;
s = $15
p = $9
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Cheers,
Stan H.