Questions on Algebra: Average answered by real tutors!

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The answer is 13,373.
The mountain starts 5,914 feet BELOW sea level. This would mean it's a negative number.
The mountain RISES 19,287 feet. This would mean it's a positive number.
So add -5,914+19,287 and get 13,373

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A mountian with a base 5,914 feet below sea level rises 19,287 feet. What is the elevation above sea level of its peak? What is the elevation of mountain's Peak?
--------------
Draw the picture.
Height of the mountain above sea level = 19,287-5914 = 13,373 ft.
Same answer for both questions.
---------------------------------
Cheers,
Stan H.

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Warning! Josmiceli's solution is incorrect.
He thought the smaller missing
number had to be at least 1 larger
than the median, but it can be equal
to the median. Here's the correct
solution by Edwin:

Let the two missing number be x and y, where x is the
smaller of the two missing numbers and y is larger of the
two missing numbers.



Now we arrange the 11 given numbers from smallest to largest:

156, 175, 199, 225, 300, 320, 325, 326, 421, 504, 520

Since there are 13 numbers, an odd number of numbers, the
7th one must be the median because: Of the other 12 numbers, 
half of them, 6, are below 325 and the other 6 are above 325. 

Since 325 is already the 7th one from the bottom in the 
list, the smaller one, x, must be either equal to 325
or larger. but the difference will be the greatest
when the smaller, x, is exactly 325. So, substituting
325 for x is



So the smaller missing number is 325, and
the larger missing number is 364.

Edwin

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I'll call the 2 missing items and
By the definition of mean:





The definition of median is that there are as many items less than
as there are greater than the item
That means there are 6 items greater than 325 and 6 items less than 325
I count 6 items smaller than 325, so both and
must be greater than 325
It is known that these two items have the greatest possible difference.
What if I make one item 326. That qualifies it as above 325


The items are 326 and 363

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This question is not complete. Write the entire question again.
Thanks

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first you solve for 6-3/4 You need to find the common denominator for both numbers in this case it is four. the number 6 becomes 24/4 you haven't changed the number it is still the same quantity but you can now perform the subtraction part with the fraction.64/4-3/4=21/4 divided by 3=7/4
8 divided by 1 is still eight but we need to find a common denominator to solve the problem in this case it is 3. 24/3-1/3=23/3

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I assume that the fractions are mixed numbers as stated.
6-3/4 ÷ 3 =
I would change 6_3/4 to an improper fraction as step one.
So, 6_3/4 = 27/4
We now have:
27/4 divided by 3
You can write any number over 1 because any number divided by 1 = itself.
In other words, 3 can be written as 3/1.
27/4 divided by 3/1
We reverse 3/1 to 1/3 and change the problem from division to multiplication.
We do this because multiplication and division are inverses of each other.
We now have 27/4 X 1/3 = 9/4
Do the same with the other question.
Understand?

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rate =distance/time
:
40/5=8mph
:
40/10=4mph
:
the first rate is twice what the second rate is or it exceeds it bymph

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40 miles in 5 hours. then 60 miles in 10 hours. then 40 miles in 20 hours.what was his averge speed for all three legs of the trip?
-------------------------
The total distance is 40 + 60 + 40 = 140 miles
The total time is 5 + 10 + 20 = 35 hours
140 miles/35 hours = 4 miles/hour, or 4 mph

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you look for factors of 45 that will add up to 18.
45 = 9*5 the sum of which is 9 + 5 = 14 (no good)
45 = 3*15 the sum of which is 3 + 15 = 18 (good)
your factors are:
(z+15) * (z+3)
you multiply these together to get:
z^2 + 18z + 45
---

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Start with the given polynomial


Rearrange the terms in descending order.

Solved by pluggable solver: Factoring using the AC method (Factor by Grouping)

In order to factor , first multiply the leading coefficient 1 and the last term 45 to get 45. Now we need to ask ourselves: What two numbers multiply to 45 and add to 18? Lets find out by listing all of the possible factors of 45 Factors: 1,3,5,9,15,45, -1,-3,-5,-9,-15,-45, List the negative factors as well. This will allow us to find all possible combinations These factors pair up to multiply to 45. 1*45=45 3*15=45 5*9=45 (-1)*(-45)=45 (-3)*(-15)=45 (-5)*(-9)=45 note: remember two negative numbers multiplied together make a positive number Now which of these pairs add to 18? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 18 |||||| First Number | Second Number | Sum 1 | 45 | 1+45=46 3 | 15 | 3+15=18 5 | 9 | 5+9=14 -1 | -45 | -1+(-45)=-46 -3 | -15 | -3+(-15)=-18 -5 | -9 | -5+(-9)=-14 We can see from the table that 3 and 15 add to 18. So the two numbers that multiply to 45 and add to 18 are: 3 and 15 So the original quadratic breaks down to this (just replace with the two numbers that multiply to 45 and add to 18, which are: 3 and 15) Replace with Group the first two terms together and the last two terms together like this: Factor a 1z out of the first group and factor a 15 out of the second group. Now since we have a common term we can combine the two terms. Combine like terms. Answer: So the quadratic factors to Notice how foils back to our original problem . This verifies our answer. ---------------------------------------------------------------------------------------------------

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1). Factor Out the GCF in this expression:
〖15x〗^2 y^2-〖9xy〗^2+〖6x〗^2 y
2). Use grouping to factor each Polynomial completely:
x^3+ax+3a+〖3a〗^2
3). Factor this polinomial. If it is prime, please tell me.
18z + 45 + z^2
the same with the next one:
4). 〖3x〗^3 y^2-〖3x〗^2 y^2+〖3xy〗^2
--------------------------------------
your posting is very confusing.
Cheers,
Stan H.

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Since the car traveled the first lap (one mile) at 30 miles per hour, it took 2 minutes (T= D/S = 1 mile/30 mph = 1/30 hour = 2 minutes)to finish the first lap. Since the goal is is to cover the track twice (2 miles) at an average speed of 60 miles per hour, the car will take T = D/S
2 miles/60 mph = 1/30 hour = 2 minutes for both laps.
I'm getting the same nonsensical answer as you did. Are you sure that you transcribed the problem correctly?

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A car went around a one mile track at a speed of 30 miles per hour. At what speed must the car travel on its second time around the track if the driver wants to average 60 miles per hour for the two mile trip?
---------------------
Time required to go one mile at 30mph:
t = d/r = 1mi/30 mph = (1/30)of an hour = 2 minutes
------------------------
Time required to go two miles at 60 mph:
t = d/r = 2mi/60 mph = (2/60) of an hour = 2 minutes
--------------------
So, for the car to average 60mph it would have to cover the 2 miles in 2 minutes.
But the car has already taken 2 minutes to go 1 mile at 30 mph.
----
So there is no speed that the car can travel on the 2nd mile to average
60 mph for the 2-mile journey.
========================================
Cheers,
Stan H.

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If Steven can mix 20 drinks in 5 minutes, then in 1 minute he can mix 4 drinks.
If Sue can mix 20 drinks in 10 minutes, then in 1 minute she can mix 2 drinks.
If Jack can mix 20 drinks in 15 minutes, then in 1 minute he can mix 20/15 =4/3 drinks.

Let x = time it will take all 3 mixing drinks together to mix 20 drinks.
Then in 1 minute, all will be able to mix 20/x drinks.

Now, number of drinks of Steven in 1 minute + no drinks by Sue in 1 minute + no drinks by Jack in 1 minute = Number of drinks by all in 1 minute.




Multiply both sides of the equation by the LCD which is 3x:



minutes (approximately)


R^2

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Sally can paint 1/4 of the job per hour
John can paint 1/6 of the job per hour
:
together the can paint (1/4+1/6)of the job per hour
:
LCM is 24
:
6/24+4/24=10/24=5/12( of the job per hour(together))
:
5/12(t)=1(job)
:
cross multiply
:
5t=12
:
hours to complete job together

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First thing to do is clear the denominators. We will need to come back to this step later to verify our 'answer' is a valid one. So cross multiply and clear them.
Now expand
simplify
collect like terms


Will that value if k make either of the original denominators = 0? No it won't so, 1/10 is a valid possibility.
Check the original equation using x=(1/10) and verify it satisfies the equation. Does it?


which is true. so the answer is 1/10

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clear the denominator on the right side. Multiply both sides by x
clear the denominator on the left side y multiplying both sides by (x+2)
expand using distribution
isolate like terms (subtrsct 3x from both sides)
isolate x by dividing both sides by 2

Follow?

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Solve for x:
Multiply both sides by x.
Next, multiply both sides by (x+2).
Simplify the right side.
Subtract 3x from both sides.
Finally, divide both sides by 2.

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lets call the probability they(SF) doesnt play in super bowl x... the probability they will play lets call y which equals 9x.
:
9x+x=1
:
10x=1
:
=10% probability of SF not playing in SB
:
=90% probability of SF playing in next SB

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D=RT
(5+5)=r(.5+.75)
10=1.25r
10/1.25=r
r=8 mph. was their average speed.

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It Took Rakeli and Marisa 30 minutes to skate 5 miles to the ice cream shop. On the trip back home, the route was uphill and it took 75 minutes. Find the average speed for the round trip. Round you answer to the nearest tenth.
---------------------
The skated 10 miles in 105 minutes, or 1.75 hours.
v = 10miles/1.75 hours = 40/7 mph
v = 5.7 mph
They're not very good skaters.

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let msrp =m
:
m-.08m=107272
:
.92m=107272
:
msrp is dollars

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5/9( of all of them)(x)=10
:

:

:
total amount of muffins

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well I cant see the shaded area but I think I know what they are after .
:
Area of the total is Area of the interior portion is we have = =sq in
:
dollars

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Trevor needs a 93 on his second quiz to average 90. What score did Trevor receive on his first quiz??
-------------
Let "x" be score on 1st quiz:
EQUATION:
(x+93)/2 = 90
x+93 = 180
x = 87
===========
Cheers,
Stan H.

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Day 1; 6; 16; 22; 30
balance($) 550; 285; 210; 210; 175
Days 1 to 6:
(550-285)/5=-$53 per day. THE GREATEST DAILY DECREASE.
Days 6 to 16:
(285-210)/10=-75/10=-$7.50 per day.
Days 16 to 22:
(210-210)/6=0/6=$0 per day.
Days 22 to 30:
(210-175)/8=-35/8=-$3.38 per day.

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Day 1; 6; 16; 22; 30
balance($) 550; 285; 210; 210; 175
Days 1 to 6:
(550-285)/5=-$53 per day. THE GREATEST DAILY DECREASE.
Days 6 to 16:
(285-210)/10=-75/10=-$7.50 per day.
Days 16 to 22:
(210-210)/6=0/6=$0 per day.
Days 22 to 30:
(210-175)/8=-35/8=-$3.38 per day.

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Day 1; 6; 16; 22; 30
balance($) 550; 285; 210; 210; 175
Days 1 to 6:
(550-285)/5=-$53 per day. THE GREATEST DAILY DECREASE.
Days 6 to 16:
(285-210)/10=-75/10=-$7.50 per day.
Days 16 to 22:
(210-210)/6=0/6=$0 per day.
Days 22 to 30:
(210-175)/8=-35/8=-$3.38 per day.

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Day 1; 6; 16; 22; 30
balance($) 550; 285; 210; 210; 175
Days 1 to 6:
(550-285)/5=-$53 per day. THE GREATEST DAILY DECREASE.
Days 6 to 16:
(285-210)/10=-75/10=-$7.50 per day.
Days 16 to 22:
(210-210)/6=0/6=$0 per day.
Days 22 to 30:
(210-175)/8=-35/8=-$3.38 per day.

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(9*108)=972
(972+X)/10>110
972+X=1,100
X=1,1000-972
X=128 IS THE MINIMUM SCORE NEEDED FOR THE 10th GAME.

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Perimeter P=2L+2W:::W=L+3.....take W's value and P's value and plug them into the Perimeter eq.
:
96=2L+2(L+3)...distribute
:
96=4L+6...subt 6 form both sides
:
4L=90
:
length of the pool
:
width of the pool

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The perimeter of a swimming pool is 96 meters. The width is 3 meters more that the length of the pool. Find the length and width of the pool.
.
Let x = length of the pool
then
x+3 = width of the pool
.
Remember, the perimeter of any rectangle is:
W + W + L + L
2W + 2L
2(W + L)
.
So, rewriting the above with our variable we have:
96 = 2(x + x+3)
96 = 2(2x+3)
96 = 4x+6
90 = 4x
22.5 meters = x (length of pool)
.
width:
x+3 = 22.5+3 = 25.5 meters (width of pool)

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302/18=x/7
18x=7*302
18x=2114
x=2114/18
x=$117.44 would be her salary for 7 hours

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1.(2a-7)(a+9)=0
The solution to this quadratic equation is a=7/2 or a=-9
You need to set each factor to equal 0.

2.64x^2-9=0
Add 9 to both sides

Divide both sides by 64
x^2=9/64
Take the sq rt of the numerator and denominator
x=3/8
3.x(x+3)=18
Use the distributive property
x^2+3x=18
Subtract 18 from both sides

x^2+3x-18=0

This equation can be easily factored into
(x+6)(x-3)=0
The solutions for this quadratic equation are x=-6 and x=3
1.2ab+2ay+bx+xy
2a(b+y)+x(b+y)
since both terms contain b+y
you can then redistribute the terms (a+x)(b+y)
To double check use the FOIL method and see that you have the same equation you started with.

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1.(2a-7)(a+9)=0
2A^2-7A+18A-63=0
2A^2+11A-63=0
---------------
2.64x^2-9=0
(8X+3)(8X-3)=0
---------------
3.x(x+3)=18
X^2+9X-18=0
--------------
factor:
1.2ab+2ay+bx+xy
2A(B+Y)+X(B+Y)
(2A+X)(B+Y)

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let x = first number.
x+1
x+2
x+3
x+4
= the other 4 numbers.
the average = sum of the total divided by 5.
sum of the total is 5x + 10
(5x+10)/ 5 = (x+2)
average is (x+2)
-----
x+2 = average = 12
subtract 2 from both sides of equation.
x = 10
-----
first number in series is x = 10
last number in series is x + 4 = 14.
-----
sum of 10 + 14 = 24.
-----
to prove answer is correct, substitute 10 for x
x = 10
x+1 = 11
x+2 = 12
x+3 = 13
x+4 = 14
----
sum of 10+11+12+13+14 = 60
average = 60 / 5 = 12
smallest number is x = 10
largest number is x + 4 = 14
-----
answer looks good.
x = 10
x + 4 = 14
sum = 24
-----

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Average age of A & B is 24 years, therefore their sum = 48 yrs
:
average of B, C & D is 22 years, therefore their sum = 66 yrs
Assume B = 23 yrs old,
:
The sum of the ages A, B, C & D is:
:
Ensure that A + B add up to 48
Ensure that B + C + D add up to 66
:
25 + 23 + 22 + 21 = 91
:
Assume that B = 25 yrs old then
23 + 25 + 20 + 21 = 89
;
I don't think there is a unique solution

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---> EQN 1
---> EQN 2
Combine similar terms in EQN 1 then add to EQN 2:


= ----->
=
For x:
via EQN 1: ---> --->
See graph:
--- see both lines interesect at points(5,-2)
*Remember: green line --->
Red line ---->
Thank you,
Jojo

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Let x = amount of skim milk added
.
.092 + .02x = .064(1+x)
.092 + .02x = .064+.064x
0.028 + .02x = .064x
0.028 = .044x
0.6364 liters = x (amount of skim milk to add)

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Let the fourth number be x.
Then the average of the four number can be expressed as:

As the average is 638.4, we have

Solving the equation for x, we obtain

(multiply both sides by 4)

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216+159.8+301.25+x=638.4*4
677.05+x=2553.6
x=2553.6-677.05
x=1876.55
.
Ed

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a. 100x14=1400 A where A is greater than 100.
b. 4x24=96 B where B is less than 100.

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Given where T is the lenght of the person;s tibia
A person with a tibia of 32.4cm would be

cm
You're on your own for part two. It is rally hard to take measurement like that over the internet :)