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MathLover1 answered: 6799 problems
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test/723986: Please simplify the expression if possible: x^2 - 3x - 10 / x^2 + 5x + 6
1 solutions

Answer 443522 by MathLover1(6801) About Me  on 2013-03-09 18:38:58 (Show Source):
You can put this solution on YOUR website!

%28x%5E2+-+3x+-+10%29+%2F+%28x%5E2+%2B+5x+%2B+6%29.......substitute -+3x with 2x-5x, and 5x with 2x%2B3x

%28x%5E2+%2B2x-5x+-+10%29+%2F+%28x%5E2+%2B+2x%2B3x+%2B+6%29...group

%28%28x%5E2+%2B2x%29-%285x+%2B10%29%29+%2F+%28%28x%5E2+%2B+2x%29%2B%283x+%2B+6%29%29

%28x%28x+%2B2%29-5%28x+%2B2%29%29+%2F+%28x%28x+%2B+2%29%2B3%28x+%2B+2%29%29

%28%28x-5%29%28x+%2B2%29%29+%2F+%28%28x%2B3%29%28x+%2B+2%29%29

%28%28x-5%29cross%28%28x+%2B2%29%29%29+%2F+%28%28x%2B3%29cross%28%28x+%2B+2%29%29%29

%28x-5%29+%2F+%28x%2B3%29



test/723989: Please simplify the expression if possible: x^2 + 10x + 24 / x^2 - 16
1 solutions

Answer 443516 by MathLover1(6801) About Me  on 2013-03-09 18:18:56 (Show Source):
You can put this solution on YOUR website!

%28x%5E2+%2B+10x+%2B+24%29+%2F+%28x%5E2+-+16%29
%28x%5E2+%2B+10x+%2B+24%29+%2F+%28x%5E2+-+4%5E2%29

factor completely %28x%5E2+%2B+10x+%2B+24%29 and %28x%5E2+-+4%5E2%29

x%5E2+%2B+10x+%2B+24.......substitute 10x with 4x+%2B6x

x%5E2+%2B+4x+%2B6x+%2B+24...group

%28x%5E2+%2B+4x%29+%2B%286x+%2B+24%29

x%28x+%2B+4%29+%2B6%28x+%2B+4%29

%28x+%2B6%29%28x+%2B+4%29
and
%28x%5E2+-+4%5E2%29...use the rule a%5E2-b%5E2=%28a-b%29%28a%2Bb%29
%28x+-+4%29%28x+%2B+4%29

now plug it in your expression

%28%28x+%2B6%29%28x+%2B+4%29%29+%2F+%28%28x+-+4%29%28x+%2B+4%29%29...simplify

%28%28x+%2B6%29cross%28%28x+%2B+4%29%29%29+%2F+%28%28x+-+4%29cross%28%28x+%2B+4%29%29%29

%28x+%2B6%29+%2F+%28x+-+4%29




Linear-equations/723995: 6(x-1)/7=2(x+4)/8
1 solutions

Answer 443512 by MathLover1(6801) About Me  on 2013-03-09 18:09:06 (Show Source):
You can put this solution on YOUR website!

6%28x-1%29%2F7=2%28x%2B4%29%2F8
6%28x-1%29%2F7=cross%282%29%28x%2B4%29%2Fcross%288%294
6%28x-1%29%2F7=%28x%2B4%29%2F4....cross multiply
6%28x-1%29%2A4=%28x%2B4%29%2A7
24%28x-1%29=7%28x%2B4%29
24x-24=7x%2B28
24x-7x=24%2B28
17x=52
highlight%28x=52%2F17%29


test/724001: I need help on my test
1 solutions

Answer 443510 by MathLover1(6801) About Me  on 2013-03-09 18:01:13 (Show Source):
You can put this solution on YOUR website!
post your questions here


test/723990: Please simplify the expression if possible: x^3 - x^2 - 12x / x^3 - 9x
1 solutions

Answer 443505 by MathLover1(6801) About Me  on 2013-03-09 16:40:28 (Show Source):
You can put this solution on YOUR website!

+%28x%5E3+-+x%5E2+-+12x%29+%2F+%28x%5E3+-+9x%29
+x%28x%5E2+-+x+-+12%29+%2F+x%28x%5E2+-+9%29
+cross%28x%29%28x%5E2+-+x+-+12%29+%2Fcross%28+x%29%28x%5E2+-+9%29

now factor +%28x%5E2+-+x+-+12%29...replace -x with 3x-4x
%28x%5E2%2B3x-4x-12%29...group
%28%28x%5E2%2B3x%29-%284x%2B12%29%29
%28x%28x%2B3%29-4%28x%2B3%29%29
%28x-4%29%28x%2B3%29
and
write %28x%5E2+-+9%29 as %28x+-+3%29%28x%2B3%29

plug both in your expression

+%28%28x-4%29%28x%2B3%29%29+%2F+%28%28x+-+3%29%28x%2B3%29%29

+%28%28x-4%29cross%28%28x%2B3%29%29%29+%2F+%28%28x+-+3%29cross%28%28x%2B3%29%29%29

+%28x-4%29+%2F+%28x+-+3%29



Sequences-and-series/723968: Find the nth term of each arithmetic sequence described
a1=6,d=3,n=12
Please help i need work for this problem i do not understand, then i will be able to solve others. Thank You
1 solutions

Answer 443504 by MathLover1(6801) About Me  on 2013-03-09 16:21:25 (Show Source):
You can put this solution on YOUR website!

a%5Bn%5D+=+a%5B1%5D%2B%28n-1%29d
a%5B12%5D+=+6%2B%2812-1%293
a%5B12%5D+=+6%2B11%2A3
a%5B12%5D+=39

check:
if n=1
6+=+6%2B%281-1%293
6+=+6%2B%280%293
6+=+6....first term is correct, a%5B1%5D+=6
if n=2
a%5B2%5D+=+6%2B%282-1%293
a%5B2%5D+=+6%2B3
a%5B2%5D=9....... a%5B2%5D+=9
if n=3
a%5B3%5D+=+6%2B%283-1%293
a%5B3%5D+=+6%2B6
a%5B3%5D=12....... a%5B3%5D+=12
if n=4
a%5B4%5D+=+6%2B%284-1%293
a%5B4%5D+=+6%2B9
a%5B4%5D=15....... a%5B4%5D+=15
:
:
:
if n=12
a%5B12%5D+=+6%2B%2812-1%293
a%5B12%5D+=+6%2B33
a%5B12%5D=39....... a%5B12%5D+=39






test/723973: Please simplify the expression of possible. 2x^2 + x/4x
1 solutions

Answer 443501 by MathLover1(6801) About Me  on 2013-03-09 15:59:56 (Show Source):
You can put this solution on YOUR website!

I guess you have this:
%282x%5E2+%2B+x%29%2F4x...if so, than you have
x%282x+%2B+1%29%2F4x
cross%28x%29%282x+%2B+1%29%2F4cross%28x%29
%282x+%2B+1%29%2F4


Square-cubic-other-roots/723936: How do you simplify a problem with a number in front of the square root and variables by the radical? For example: 2 to the square root of 147 x^6 y^7? Thanks so much:)
1 solutions

Answer 443499 by MathLover1(6801) About Me  on 2013-03-09 15:55:42 (Show Source):
You can put this solution on YOUR website!

if you have this:

2sqrt%28147+x%5E6+y%5E7%29 it will be

2sqrt%283%2A49%28x%5E3%29%5E2%28y%5E3%29%5E2y%29

2%2A7x%5E3y%5E3%2Asqrt%283y%29

14x%5E3y%5E3%2Asqrt%283y%29


Polynomials-and-rational-expressions/723911: S=4lw+2wh for h

1 solutions

Answer 443495 by MathLover1(6801) About Me  on 2013-03-09 15:43:14 (Show Source):
You can put this solution on YOUR website!

S=4lw%2B2wh....solve for h
S-4lw=2wh
%28S-4lw%29%2F2w=h


Graphs/723956: Find the slope of the line.
-4x-7y=5
1 solutions

Answer 443484 by MathLover1(6801) About Me  on 2013-03-09 15:09:33 (Show Source):
You can put this solution on YOUR website!

-4x-7y=5..first write it in slope-intercept form y=mx%2Bb; means, you need to solve it for y
-4x-5=7y
-%284%2F7%29x-5%2F7=y
or
y=-%284%2F7%29x-5%2F7
so, the slope of the line is -%284%2F7%29


Polynomials-and-rational-expressions/723921: what is equivalent to (3+y)^4
1 solutions

Answer 443483 by MathLover1(6801) About Me  on 2013-03-09 15:06:04 (Show Source):


�t�e�s�t/723947: The sum of two numbers is 10. The sum of their squares is 68 . Find the numbers.
Can you please help me? Thanks so much in advance:)
1 solutions

Answer 443482 by MathLover1(6801) About Me  on 2013-03-09 15:00:05 (Show Source):
You can put this solution on YOUR website!

let numbers be x and y
given:
The sum of two numbers is 10.
x%2By=10....eq.1
The sum of their squares is 68.
x%5E2%2By%5E2=68....eq.2
solve the system:
x%2By=10....eq.1
x%5E2%2By%5E2=68....eq.2
__________________________
start with eq.1
x%2By=10....eq.1 ...solve for y
y=10-x..... substitute it in eq.2

x%5E2%2B%2810-x%29%5E2=68....eq.2 ...solve for x
x%5E2%2B10%5E2-20x%2Bx%5E2=68
2x%5E2%2B100-20x=68
2x%5E2-20x%2B100-68=0
2x%5E2-20x%2B32=0.......simplify, divide all by 2
x%5E2-10x%2B16=0.......use quadratic formula
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%28-%28-10%29+%2B-+sqrt%28+%28-10%29%5E2-4%2A1%2A16+%29%29%2F%282%2A1%29+
x+=+%2810+%2B-+sqrt%28+100-64+%29%29%2F2+
x+=+%2810+%2B-+sqrt%28+36+%29%29%2F2+

x+=+%2810+%2B-+6%29%2F2+
solutions:
x+=+%2810+%2B+6%29%2F2+
x+=+16%2F2+
x+=+8+
or
x+=+%2810+-6%29%2F2+
x+=+4%2F2+
x+=+2

now find y
y=10-x
y=10-8
y=2
or
y=10-x
y=10-2
y=8
solution pairs are: x+=+8+ and y=2
or x+=+2+ and y=8



real-numbers/723942: True or False
1. The set of numbers less than zero but greater than 1 is the empty set.
2. The set of even integers less than zero is a finite set.
3. If the replacement set of x is {1, 2, 3, 4, 5}, then the solution set for the statement is 3x=27 is {9}.

Thanks so much for your help!
1 solutions

Answer 443478 by MathLover1(6801) About Me  on 2013-03-09 14:23:57 (Show Source):
You can put this solution on YOUR website!
1. numbers less than zero:
{.-1,-2,-4,-6,-8,.....-infinity.}
but greater than {.1: 2,3,4,5,.....infinity.}
as you can see, there are no common elements; so,
True, is the empty set


2. False, it is infinite
{ -2,-4,-6,-8,.....-infinity}

3. If the replacement set of x is {1, 2, 3, 4, 5}, then the solution set for the statement is 3x=27 is {9}.
False, there is no 9 in the replacement set of x



Inequalities/723929: In a typical group of 1000 workers from each of the boatbuilding, iron foundry, and amusement park/arcade industries, there were 30 more injuries in iron foundries (I) than in amusement parks/arcades (A). There were 12 more injuries in amusement parks/arcades than in boatbuildings (B). Among these workers, there were 387 nonfatal occupational injuries. How many injuries took place in each industry?
I'm guessing (keyword being guessing) that:
Data:1000 workers, I had 30 more than A and A had 12 more than B and the total is 387.
Variable: A= amusement parks/arcades, B= boatbuildings, I= iron foundry
Plan: B+(B+A)+(B+I)= 387
Equation: B+(B+12)+(B+30)=387
3B+42 = 387
-42 -42
3B = 345
3B/3 345/3
B = 115
Solution: A= 127, B= 115, and I= 145
Am I right?
1 solutions

Answer 443474 by MathLover1(6801) About Me  on 2013-03-09 14:00:30 (Show Source):
You can put this solution on YOUR website!

there were 387 nonfatal occupational injuries
let the boat-building injuries be B,amusement park/arcade injuries be A, and iron foundry injuries be I
given:
B%2BA%2BI=387
A=B%2B12
I=A%2B30...substitute A ...=> I=B%2B12%2B30...=> I=B%2B42
B%2BA%2BI=387...plug in all values
B%2B%28B%2B12%29%2B%28B%2B42%29=387...solve for B
3B%2B12%2B42=387
3B%2B54=387
3B=387-54
3B=333
B=333%2F3
highlight%28B=111%29
now find A and I
A=B%2B12
A=111%2B12
highlight%28A=123%29

I=B%2B42
I=111%2B42
highlight%28I=153%29
check their sum:
B%2BA%2BI=387
111%2B123%2B153=387
387=387
check your solution: A= 127, B= 115, and I= 145
Am I right?
your equation: B%2B%28B%2B12%29%2B%28B%2B30%29=387 ...you put I=%28B%2B30%29, but it is given that I had 30 more than A, or I=A%2B30
so, you need to put

B%2BA%2B%28A%2B30%29=387
since also given that A had 12 more than B, we know that A=B%2B12 and we go back to I and substitute A
I=A%2B30...=>...I=B%2B12%2B30=B%2B42
now, plug it in equation
B%2B%28B%2B12%29%2B%28B%2B42%29=387



Equations/723935: answers to these please and how you worked them out
1. 6a=48
2.4y-15=21
3.5p+9=39

1 solutions

Answer 443466 by MathLover1(6801) About Me  on 2013-03-09 13:19:42 (Show Source):
You can put this solution on YOUR website!

1. 6a=48......solve for a
a=48%2F6
highlight%28a=8%29
2.4y-15=21......solve for y
4y=21%2B15
4y=36
y=36%2F4
highlight%28y=9%29
3.5p%2B9=39......solve for p
5p=39-9
5p=30
p=30%2F5
highlight%28p=6%29




decimal-numbers/723867: estimate the answer by rounding 453+158+204+555+361
1 solutions

Answer 443452 by MathLover1(6801) About Me  on 2013-03-09 10:36:37 (Show Source):
You can put this solution on YOUR website!
it's not clear to what you need to round it: to the nearest tents or to the nearest hundreds
453%2B158%2B204%2B555%2B361
453 you can round it to 450 (to the nearest tents) or 500 ( to the nearest hundreds)
158 you can round it to 150 (to the nearest tents) or 200 ( to the nearest hundreds)
204 you can round it to 200 (to the nearest tents) or 200 ( to the nearest hundreds)
555 you can round it to 560 (to the nearest tents) or 600 ( to the nearest hundreds)
361 you can round it to 360 (to the nearest tents) or 400 ( to the nearest hundreds)
if you need to round it to to the nearest tents, than you will have
450%2B160%2B200%2B560%2B360=1730
but, if you need to round it to to the nearest hundreds
, than you will have
500%2B200%2B200%2B600%2B400=1900


Inverses/723882: Use the communative law of multiplication to write an equivalent expression for s+5t
1 solutions

Answer 443450 by MathLover1(6801) About Me  on 2013-03-09 10:25:47 (Show Source):
You can put this solution on YOUR website!

Multiplication of numbers is commutative when a%2Ab=b%2Aa; a product isn’t changed at rearrangement of its factors
s%2B5t=s%2Bt%2A5


test/723761: The AT&T plan cost $25 more per month than the Verizon plan, but charges less for every text message sent.
You test the AT&T plan for two month. You sent 100 texts and it cost $35.00 for the first month. You sent 50 texts and it cost you $32.50 for the second month.
You test the Verizon plan for two month. You sent 100 texts and it cost $40.00 for the first month. You sent 50 texts and it cost you $22.50 for the second month.
How much money does each plan charge per month? How much money does each plan charge per text message? At how many text messages do the two plan cost the same amount?
please help
1 solutions

Answer 443368 by MathLover1(6801) About Me  on 2013-03-08 22:00:50 (Show Source):
You can put this solution on YOUR website!
..post your question here and we will help you...


test/723762: Help me
1 solutions

Answer 443367 by MathLover1(6801) About Me  on 2013-03-08 22:00:11 (Show Source):
You can put this solution on YOUR website!
what is your question?...post it here and we will help you...


Equations/723757: (2x-5)(9x-15)=0
1 solutions

Answer 443366 by MathLover1(6801) About Me  on 2013-03-08 21:58:53 (Show Source):
You can put this solution on YOUR website!
%282x-5%29%289x-15%29=0...here you have completely factored quadratic equation (graph is a parabola); so, you will have two roots

if 2x-5=0....=>...2x=5....=>...x=5%2F2...=>...x=2.5
and
if 9x-15=0....=>...cross%289%293x=cross%2815%295....=>...3x=5...=>...x=5%2F3...=>...x=1.7

+graph%28+600%2C+600%2C+-5%2C+5%2C+-5%2C+10%2C%282x-5%29%289x-15%29%29+


Functions/723664: Please help me solve this equation (((f(x)= √4x+16)))
Consider the function
a) Find the domain and range.
b) Find f(3).
Please show work. I do not understand this at all and wish to know how to figure this stuff out on my own.
1 solutions

Answer 443307 by MathLover1(6801) About Me  on 2013-03-08 19:44:43 (Show Source):
You can put this solution on YOUR website!
if you have this:
f%28x%29=sqrt%284x%29%2B16


b) Find f%283%29
f%283%29=sqrt%284%2A3%29%2B16
f%283%29=sqrt%2812%29%2B16
f%283%29=3.46%2B16
f%283%29=19.46




but, if you have this:
f%28x%29=sqrt%284x%2B16%29



b) Find f%283%29
f%283%29=sqrt%284%2A3%2B16%29
f%283%29=sqrt%2812%2B16%29
f%283%29=sqrt%2828%29
f%283%29=5.29



Miscellaneous_Word_Problems/723718: How to translate the following problem into a equation?
Taryn drove 158 mile of a 275 mile trip. Ben drove the remainder of the trip. How far did Ben drive?
1 solutions

Answer 443295 by MathLover1(6801) About Me  on 2013-03-08 18:31:44 (Show Source):
You can put this solution on YOUR website!

if Ben drove x mile, than
x=275-158
x=117 the remainder of the trip that Ben drive


Equations/723701: 0+50 multiply by 1 - 60 - 60 multiply by 0 + 10 = what is the answer
1 solutions

Answer 443292 by MathLover1(6801) About Me  on 2013-03-08 18:21:33 (Show Source):
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if you mean this:
%280%2B50%29%281-60%29-%2860%280+%2B+10+%29%29
%2850%29%28-59%29+-+%2860%2A10+%29
-2950+-+600+
-3550+


Reduction-of-unit-multipliers/723688: you travel 875 yards 75 seconds ,how many miles per hour is that?
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Answer 443261 by MathLover1(6801) About Me  on 2013-03-08 15:15:04 (Show Source):
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875yd%2F75s=+2625+ft%2F75s...first convert yards to feet
2625+ft%2F75s=35%28ft%2Fs%29...convert ft to miles, 1ft=0.0001894mil and seconds in hour 1s=0.0002778h
35%28ft%2Fs%29=35%2A+0.0001894%2F0.0002778%28mil%2Fh%29
35%28ft%2Fs%29=0.006629%2F0.0002778%28mil%2Fh%29
35%28ft%2Fs%29=23.863636363636367+%28mil%2Fh%29

so, 875yd%2F75s=23.863636363636367+%28mil%2Fh%29


Quadratic-relations-and-conic-sections/723666: What are the focus and directrix of the parabola with the equation y = 1/12x2?
focus: (3, 0) ; directrix: y = –3
focus: (–3, 0) ; directrix: y = 3
focus: (0, 3) ; directrix: y = –3
focus: (0, –3) ; directrix: y = 3
1 solutions

Answer 443257 by MathLover1(6801) About Me  on 2013-03-08 14:55:43 (Show Source):
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The standard equation for a parabola with its axis vertical is:
%28x+-h%29%5E2+=+4a%28y-k%29 ...(1)
The vertex is (h,+k).
The focus is (h,+k+%2B+a).
The directrix is y+=+k+-a.
you have
y+=+%281%2F12%29x%5E2+...solve for x%5E2
y+%2F%281%2F12%29=+x%5E2+
12y+=+x%5E2 ....write it in form given above
12%28y-0%29+=+%28x-0%29%5E2+
as you can see
h=0
k=0
4a=12...=>...a=3
than,
the vertex is (h,+k)=(0,0)
the focus is (h, k+%2B+a)= (0, 0+%2B+3)=(0,+3)
the directrix is y+=+k+-a...=>..y+=+0-3...=>..y+=-3
so, your answer is:
focus: (0,+3) ; directrix: y+=-3



Functions/723680: How do you rewrite an equation in function notation?
The example I was given is
x-7y=35
f(x)=?
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Answer 443255 by MathLover1(6801) About Me  on 2013-03-08 14:32:28 (Show Source):
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x-7y=35
f%28x%29=?......as you know f%28x%29=y; so, all you need to do is to solve given equation for y
x-7y=35
x-35=7y
x%2F7-35%2F7=y
y=%281%2F7%29x-5
so, f%28x%29=%281%2F7%29x-5


Triangles/723486: triangle ABC has an exterior angle at C. if the measure of the exterior angle is represented by 4x-10, angle B is represented by x, and angle A is 2x+20 what is the measure of the exterior angle
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Answer 443195 by MathLover1(6801) About Me  on 2013-03-07 22:43:41 (Show Source):
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an exterior angle is equal to sum of two remote interior angles; so, you will have

C=A%2BB
4x-10=%282x%2B20%29%2Bx......solve for x
4x-10=3x%2B20
4x-3x=10%2B20
x=30.......the measure of the angle B
C=4x-10
C=4%2A30-10
C=120-10
C=110.......the measure of the exterior angle
A=2x%2B20
A=2%2A30%2B20
A=60%2B20
A=80.......the measure of the angle A


Quadratic-relations-and-conic-sections/723467: I need the step by step process to classify this conic section using the discriminant I was sick the day of the lesson and really have no clue on how to begin I would greatly appreciate it if you could include the equation that this problem is based on also.-
+6x%5E2-2y%5E2%2B24x%2B2y-1=0+
1 solutions

Answer 443193 by MathLover1(6801) About Me  on 2013-03-07 22:30:20 (Show Source):
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The discriminant of the equation Ax%5E2+%2B+Bxy+%2B+Cy%5E2+%2B+Dx+%2B+Ey+%2B+F+=+0 is the quantity B%5E2+-+4AC.
Assuming A, B and C are not+all +0 and that degenerate cases are excluded.
Then,
if B%5E2+-+4AC+%3C+0, the graph is an ellipse or a circle
if B%5E2+-+4AC+=+0, the graph is a parabola
if B%5E2+-+4AC+%3E+0, the graph is a hyperbola
you have
6x%5E2-2y%5E2%2B24x%2B2y-1=0.....where A=6, B=0,C=-2,D=24,E=2, and F=-1
B%5E2+-+4AC=0%5E2+-+4%2A6%2A%28-2%29=-24%2A%28-2%29=48
so, B%5E2+-+4AC+%3E+0, the graph is a hyperbola
+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+6x%5E2-2y%5E2%2B24x%2B2y-1%3E=0%29+


test/723401: Median,mode & range for:
24,23,22,17,18,23,19
1 solutions

Answer 443191 by MathLover1(6801) About Me  on 2013-03-07 22:13:50 (Show Source):
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The mean is the usual average, so:
+%2824%2B23%2B22%2B17%2B18%2B23%2B19%29%2F7+=+20.86
The median is the middle value, so I'll have to rewrite the list in order:
17,18,19,22,23,23,24.....the middle value is 22
The "range" is just the difference between the largest and smallest values.
24-17=7


Sequences-and-series/723418: Please help me solve: Write the rule for the arithmetic series a5=12 d=5
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Answer 443176 by MathLover1(6801) About Me  on 2013-03-07 21:14:40 (Show Source):
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a rule for creating nth term formula: a%5Bn%5D=d%28n-1%29%2Ba%5B1%5D
given:
d=5
if we have a%5B5%5D=12, means n=5
12=5%285-1%29%2Ba%5B1%5D....find first term
12=25-5%2Ba%5B1%5D
12=20%2Ba%5B1%5D
12-20=a%5B1%5D
-8=a%5B1%5D.....first term
so, the nth term formula is:
a%5Bn%5D=5%28n-1%29-8
so, the arithmetic series:-8,-3,2,7,12....


Geometric_formulas/723308: what is the geometric mean of 2a and 4a
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Answer 443138 by MathLover1(6801) About Me  on 2013-03-07 18:21:56 (Show Source):
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What is the geometric mean of: 2a and 4a?

take the product 2a+%2A4a=8a%5E2
because there are only two numbers, the nth root is the square root, and the sqrt%288a%5E2%29=2a%2Asqrt%282%29