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Posts by Reiny

Total # Posts: 38,657

Math
4 inches ---> 6 ft 1 inch -----> 6/4 ft or 1.5 ft

maths
"4th term is 7" ---> a+3d = 7 "7th term is 13" ---> a+6d = 13 subtract them: 3d = 6 d = 2 sub back into my first equation to find a, then use the Sum of Terms formula to find sum(20)

math
The previous one is (2n-2) the next one after 2n is (2n+2

Math
8 bananas at 50 g each is 400 g what is 400/1000 times $6.50 ?

Math
x- 4/5 = 12/15 x = 4/5 + 12/15 x = 12/15 + 12/15 = 24/15 = 8/5

Math
(x-3)^2 + sin(x-3) + 7

sequence help plz
clearly an arithmetic series with a = 5 and d = 6 sum(2n) = (2n/2)(10 + (2n-1)(6)) = n(10 + 12n - 6) = 4n + 12n^2

math
so your chord is also 3 cm from the centre. construct the right-angles triangle look at the angle it makes at the centre, cosØ = 3/6 = 1/2 Ø = 60° the chord subtends an angle of 120°

MATH @Damon @ms. Sue
notice for Option 1: 1100 1210 1331 1210 / 1100 = 1331 / 1210 = 1.1 so we have a geometric progression, making the function exponentinal term(n) = 1100 (1.1)^(n-1) , where n is the number of years in Option 2: 1100 1200 1300 we have 1200 - 1100 = 1300 - 1200 = 100 we have a ...

maths
16 2/3% = 50/300 = 1/6 check: on my calculator 1/6 = .166666... or 16 2/3%

Math
500 (2^(t/12)) = 800 , where t is in hours 2^(t/12) = 1.6 take logs of both sides, and use the rules of logs t/12 log2 = log 1.6 t/12 = log 1.6/log 2 t = 12(log 1.6/log 2) = appr 8.1 hours

Algebra
John1 meant to say 3(-3x) = -9x , not -6x then 2x - 9x = 6 -7x = 6 x = -6/7 ---> not found in any of the answers, so I suspect a typo somewhere y = -3(-6/7) = 18/7 (-6/6 , 18/7) is the correct solution This answer works in both equations

Algebra
rate last year = 1300/1250 = 1.04 if rate is the same, next year: 1300(1.04) = 1352

Math
what is 8 ÷ (2/3) ?

Math
In the second term, I counted 6 of "(" and 7 of ")", so mismatched brackets. I will assume you meant: cos(x)/(1-tan(x)) + (sin (x))* cos(x))/ (sin (x)- cos(x)) then: = cosx/( 1 - sinx/cosx) + sinx cosx/(sinx - cosx) = cosx/( (cosx - sinx)/cosx) - sinxcosx/(...

Math
I usually change everything to sines and cosines (tan(x) +cot(x))/ (tan(x)*cot(x)) = (sinx/cosx + cosx/sinx) / (sinx/cosx * cosx/sinx) = (sin^2 x + cos^2 x)/(sinxcosx) / 1 = 1/(sinxcosx) ----> I know 2sinxcosx = sin 2x so sinxcosx = (1/2)sin2x = 2/sin 2x or 2 csc 2x or from...

Math
(1+tan(x))* (1+cot(-x)) = (1 + sinx/cosx)(1 + cosx/sinx) = [ (cosx + sinx)/cosx][ (sinx + cosx)/sinx] = (sin^2 x + cos^2 x + 2sinxcosx) / (sinxcosx) = (1 + 2sinxcosx)/(sinxcos) = 1/(sinxcosx) + 2 or = secs cscx + 2

math
solve these equations: 1. 20-x = 10 2. 10x - 12 = 18 at the end you say "what is the number 7" ?????

Math
greater --- x lesser --- x-1 x+x-1 = 15 solve and sub into my definitions

Geometry
clearly the ellipse has a vertical major axis centre is (2,1) , b = 3 For this ellipse: e = c/b 1/3 = c/3 c = 1 a^2 + c^2 = b^2 a^1 + 1 = 9 a^2 = 8 (x-2)^2/8 + (y-1)^2/9 = 1

Geometry
"Angle D is nine less than twice the measure of Angle C" D = 2C - 9 and we know C+D = 180 , so .....

Coordinates
Show that two of the three line segments have slopes that are negative reciprocals of each other.

Math
c(x) = 8 + 1.5x

Maths
a = 120000 m/s^2 v = 120000t + c when t=0, v = 0 , so c = 0 s = 60000t^2 + k , where s is the distance, k a constant when t=0, the plane hasn't gone anywhere so 0 = 0 + k, k = 0 s = 60000(t^2) when t = 4, s = 60000(4) = ...

Maths
draw a perpendicular from the centre to the chord. draw the radius to the end of the chord. You have a right-angled triangle with one leg of 6 and a hypotenuse of 10. Use Pythagoras

Math
That is some wind!!! I think you have a typo and meant that the plane's speed is 650 mph. however, taking it as is: let the plane's speed be x mph from city x to city y: distance = 8(x-650) from city y to city x: distance = 5(x+650) 8(x-650) = 5(x+650) solve for x , ...

Mathematics
draw the science circle totally within the math circle enter 56 in the science circle, put 17 in the science only circle 82-73 or 9 take neither science nor math.

Maths
x(1.8)(r) = x 1.8r = 1 r = 1/1.8 = .555.. so the discount rate should be .444... or appr 44.4% e.g. suppose the item cost $100 after markup, selling price = 180 to end up with $100, we have to discount it $80 80/180 = .44444 notice 1 - .4444... = .555...

Geometry
This makes no sense to me. If the octagon is equiangular (all angles are equal) , how can the side be of different lengths ?

math
Join the centres and you will have an equilateral triangle with sides 1 m Also the band will form 3 arcs , each of 120°. So the band covers the entire distance around the circle, that is, its circumference. Notice that if you complete the rectangle, we know the long side ...

math
let the time be t minutes distance covered by Ali = 48t distance covered by Tina = 62t 48t + 62t = 1320 solve for t

statistics
cutting through the chase .... prob(your stated event) = C(10,7)(1/5)^7 (4/5)^3 = 120(1/78125)(64/125) = appr .0008

Maths
from the second: 4x + 10y = 50 4x = 50-10y into the first: 50-10y - 3y = 11 -13y = -39 y = 3 then 4x = 50 - 30 x = 5

Math
sheets left after 1st week = 4/5 of 500 = 400 after 2 more weeks 3/5 of those are left = 240 or, long way: papers used in 1st week = (1/5)(500) = 100 left: 400 he uses 2/5 of those: (2/5)(400) = 160 leaving him 400 - 160 or 240 at the end of 3rd week

Algebra
|4-6|^3 - |5-9| / |3(6-5)| + |35-7)| = 8 - 4/3 + 28 = 104/3

math
The order of these items does not matter so I will use combinations Size -- C(3,1) = 3 meats --C(7,1) = 7 veggies --C(5,2) = 10 cheese -- C(4,1) = 4 number of pizzas = 3x7x10x4 = 840

Math
number of erasers ---- x number of pencils ----- x+10 22x + 14(x+10) = 446 solve for x

maths
1. Show that two of the three line segments have slopes that are negative reciprocals of each other. 2. let the fourth point be (x,y) Make a sketch to see which lines would be parallel. You will have 2 equations in 2 unknowns

math
Let the 3 numbers in GP be a , ar, and ar^2 after first change: a , ar+2, ar^2 are now in AP that is, ar+2 - a = ar^2 - (ar+2) ar^2 - 2ar + a -4 = 0 ** after 2nd change: a, ar+2 , ar^2 + 9 , are now in GP again, (ar+2)/a = (ar^2 + 9)/(ar+2) (ar+2)^2 = a(ar^2 + 9) a^2 r^2 + 4ar...

Geometry and shape
Thanks Steve, e.g. a regular hexagon or octogon , etc

Geometry and shape
Only the rhombus, equilateral means equal, a parallelogram does not necessarily have 4 equal sides

Math
No idea what you are saying.

math
First of all your third angle is 68° , not 132° You are not asked to state the lengths of the sides, simply list them in order of size. The property to use is: In any triangle , the longest side is opposite the largest angle, the smallest side is opposite the smallest ...

math
Sketch is the big thing!! On mine , I extended AC to M so that angle BMC = 60° Also you can see that angle MCB = 60° (external angle) So triangle CBM is equilater, and since CM = 12 CB = MB = 12 Also, since ABC is isosceles and CA = CB CA = 12 now by the sine law: AB/...

maths
Use you sum(n) terms formula (11/2)(2a + 10d) = 891 but d = 15 (11/2)(2a + 150) = 891 11(2a + 150) = 1782 2a + 150 = 162 continue once you have a, just use your formula term(28) = a + 27d = .... etc

pre-algerabra
But you didn't double. but, yes, if the drawing is to scale, then you must multiply each dimension by the same scale factor for yours: 10/12.5 = 4/x 10x = 50 x = 5 so a room 10 ft by 12.5 ft ----> 4 units by 5 units in your drawing.

calculus
you should know that using the metric system, a = -4.9 m/s^2 distance = -4.9t^2 + 48t + c, where c is the initial height velocity = -9.8t + 48 given: v = -50 -50 = -9.8t + 48 9.8t = 98 t = 10 When t=0 , distance = 0+0+c = c when t = 10, distance = -4.9(100) + 48(10) + c = c - ...

Math
let the other angles be 7x and 10x so : 7x + 10x + 95 = 180 solve for x, and sub into my definitions

Math
Just did this for you in your earlier post http://www.jiskha.com/display.cgi?id=1485495789

Mathematics
original amount in A ---- x original amount in C ---- x-20 after the pouring: A has x-15-10 B doesn't matter C has x-20 + 10 = x - 10 difference between C and A = x-10 - (x-20) = x-10 -x + 20 = 10

Math (Advanced probability)
expected wins: .15(1) = .15 .05(5) = .25 .01(50) = .50 1/10000(500) = .05 total expected wins on one ticket = .95 That is, if they charged 95 cents for a ticket , everybody would break even in the long run. So to make a 40% profit, they should charge .95(1.4) or $ 1.33

Math
Looks like a binomial distribution question. I read your question to say that exactly 5 are to respond. prob(response) = .15 prob(no response) = .85 prob(5 of 15 respond) = C(15,5) (.15)^5 (.85)^10 = appr .0449

Math
You are missing the fact that they could be ordered according to increasing or according to decreasing age. Each would be ordered by age. so prob = 2/120 = 1/60 = appr .0167

Math
What is 5! ?

Math
your post is incomplete. You did not state the rate of exchange, without it any of the answers are possible

Math
The y-intercepts are of great help. It also helps to have an idea what the general shape of different polynomials are. e.g. A fourth degree generally has the shape of a W , etc Also a reasonable number of ordered pairs can be calculate and plotted to show the shape of the ...

Math
plan 1: cost = 14 + .06n , where n is the number of minutes plan 2: cost = 22 solve: 14 + .06n= 22

Pre Cal 12
Square to be cut out : x cm by x cm then the height of the box is x, and the base is 12-2x by 8-2x, where 0 < x < 4 volume = x(12-2x)(8-2x) = 36 x(6-x)(4-x) = 9 x(24 - 10x + x^2) = 9 x^3 - 10x^2 + 24x - 9 = 0 I tried x = ±1, ±3 and x = 3 was a solution. by ...

Algreba
easiest way: since your new line is perpendicular to x+2y = -7 this new line must look like 2x - y = c but (2,3) lies on it, so 2(2) -3 = c = 1 new line: 2x - y = 1

Algebra
Their normals are <3,-2,0> and <1,2,4> The only way that the two planes could not intersect is if they are parallel or plane equation is a multiple of the other. Since their normals are not parallel, neither are the planes

mathematics
for the AS" first term --- a third term -- a+2d ninth term -- a+8d but those terms form a GP (a+2d)/a = (a+8d)/(a+2d) (a+2d)^2 = a(a+8d) a^2 + 4ad + 4d^2 = a^2 + 8ad 4d^2 - 4ad = 0 d^2 - ad = 9 d(d-a) = 0 d = 0 ---> not too interesting or a = d but term 7 of the AS = ...

math
Since these are special positions, the order counts, so what is 15x14x13 ?

HELLO CAN ANYONE HELP ????!!!!!!!
I think you have a typo and you wanted to compare y = 2^x with y = log2 x They are inverses of each other. Proof: start with y = 2^x the inverse is formed by interchanging the x and y's ----> x = 2^y which in log form would be : y = y = log2 x

I'm stuck on math plz help!!
see your other post above when you posted as "R"

Statistics
The first friend will have the birthday on some given day, doesn't matter when. The prob that the second friend will have a different birthday = 364/365 the prob that the third friend will have a birthday from the other two = 363/365 prob that all three have different ...

Pre-Cal
SW is a direction. Make a sketch on the N-S-E-W grid SW is in the third quadrant, dividing it into two parts of 45° each. Draw such a line OP, marking its length as 400 mph, and O at the origin. Draw a line PR horizontally to the right and mark it 50. So now you have a ...

algebra
What about it?

Math
It says the other two angles are equal, so your triangle must be isosceles. Let each of those equal angles be x x + x + 110 = 180 solve for x

math
only the 2 or 3 can be used at the front without the odd restriction: number of such number = 2x2x1 = 4 we can actually list them: 345, 354, 435, 453 notice that 1 of them is even so there are only 3 of them or suppose it starts with the 4: only the two odds are left, so ...

Maths
Steve did this http://www.jiskha.com/display.cgi?id=1394768509 See other variations of the same question in the Related Questions below

Math
the ratio of sides of your triangle are 1:?3:2 or x : ?3x : 2x given x = 16 other sides are 16?3 and 32 perimeter = .... just add them up

Math Pre-Calc 12
let the base be x by x cm let the height be y given: 4x + y = 120 y = 120 - 4x V = x^2 y = x^2(120-4x) = 120x^2 - 4x^3 dV/dx = 240x - 12x^2 = 0 for a max of V 12x^2 - 240x = 0 12x(x- 20) = 0 x = 0 ----> yields a minimum volume or x = 20 so the box is 20 cm by 20 cm by 40 cm...

Algebra
direction vector of P1P2 = <2 , -2, 0> so the equation of the plane which had <2, -2, 0> as its normal is 2x - 2y + 0z = c but A(1,3,-2) lies on it, so 2(1) - 2(3) + 0 = c c = -4 plane equation: 2x - 2y = -4 or x - y = -2 equation of line through P1P2: x = 2 + 2t y...

Math/Algerbra
87 mg needs 4 mL 1 mg needs 4/87 mL 173 mg needs (4/87)(173) mL or appr 7.954 mL or just use a ratio: 87/4 = 173/x 87x = 4(173) x = 4(173)/87 ----> same as above

Ap algebra
you can't use the quadratic formula on 2+3X^2-X^3=0 , since it is not a quadratic, it is a cubic Do you have a typo? Assuming it is correct, lets see if it factors: let f(x) = 2 + 3x^2 - x^3 f(1) = 2 + 3 - 1 ? 0 f(-1) = 2 + 3 - (-1) ?0 f(2) = 2 + 12 - 8 ? 0 f(-2) = 2 + 12...

Math
Are you using the US gallon or the Imperial gallon? (one of the many problems in not using metric!) I will assume US, so 1 US gallon = 3.97 litres and 1 mile = 1.61 km I will do the 2nd question, you do the first one. 1 gallons ---> 107 miles 3.97 l -----> 107 miles 1 l...

Math
number of gallons for each ginger --- 3x cranberry -- 2x orange -- x cost: 2(3x) + 4(2x) + 5x ? 38 19x ? 38 x ? 2 take it from there, remember I said ? .

maths
of the 30 fruits, how many are "either grape or banana" ? How many are "not bananas" ?

Math
let the width of the lawn be x yds field --- 25 yds by 100 yds area = 2500 yds^2 field including the lawn around it: (25+2x) by (100+2x) yds area = (25+2x)(100+2x) yds^2 area of lawn = (25+2x)(100+2x) - 2500 you said: (25+2x)(100+2x) - 2500 = 2(2500) 2500 + 250x + 4x^2 - 2500...

mat
You are given the time it took for the first car to go 599.5 miles in 5.5 hours. Using rate = distance/time the rate of the first car is 599.5/5.5 = 109 mph So the slower car went at 102 mph And the slower car would take 599.5/102 hrs or 5.87745 hrs or 5 hrs and 53 minutes 5:...

Math 11
speed of ferry ---- x km/h speed of car ----- x+60 km/h time for ferry = 175/x time by car = 175/(x+60) What are you told about these times? Form your equation from that fact.

Math 11
length of squares to be cut out ---- x base ----- 15-2x by 20-2x (15-2x)(20-2x) = 104 solve for x and you have the size of the cut-out The rest is easy

Math 11 Foundations
each of the two equal sides ---- x the single side ------- y given: 2x + y = 60 y = 60-2x area = xy = x(60-2x) x(60-2x) = 400 expand, and solve the quadratic

Math
3+1/4*cos(theta)=13/4 1/4*cos(theta)=13/4 - 3 = 1/4 cos(theta)= 1 we know cos 0 = 1 so Ø = 0

Find the equation of the perpendicular line
steps: - find the midpoint for the given points - find the slope of the line passing through those points - the slope of the line you want is the negative reciprocal of that slope - find the equation using the method you learned.

Standard Form
steps: - find the slope of the line passing through the given points - find the equation using the method you learned.

Specify a Period on the graph
for y = cos(kx), the period is 2?/k apply this to your question

Trig
the way you typed it: 2+1/3tan(theta)=2 1/3tanØ = 0 tanØ = 0 then Ø = 0, 180°, 360°, ... since the period of tanØ = 180°, you can obtain a new answer by simply adding or subtracting multiples of 180° to any answer. did you mean 2 + 1...

math geometry
What method have you learned. There are multiple ways to answer the question, e.g. Heron's formula etc

Geometric Progression.
ar^4 - ar^3 = 13.5 ar^3(r - 1) = 13.5 ** ar^3 - ar^2 = 9 ar^2(r-1) = 9 *** divide ** by *** r = 13.5/9 = 1.5 sub into *** a(1.5)^2 (1.5-1) = 9 a(1.125) = 9 a = 9/1.125 = 8 first term is 8, common ratio = 1.5 or 3/2 check: the terms are: 8, 12, 18, 27, 40.5, ... term5 - term4...

Geometry
Not clear if we want only the lateral surface area or the area including the base. Including the base does not make a not of sense in a storage container for grain, but ... LSA = ?rl, where l is the slant height l^2 = 24^2 + 8^2 l = ?640 LSA = ?(8)?640 = appr 635.81 ---> ...

Math
We have a GS with a = 3600 and r = 1.01 , n = 12 sum(12) = a(r^12 - 1)/(r-1) = 3600(1.01^12 - 1)/.01 = 45,657.01

Geometry
What sphere ?

maths
I am sure you meant: 16x^2- 4x^(x-1) -12 = 0 Wow, what a nasty equation. We have no standard way to handle that one. 16x^2 -12 = 4x^(x-1) by inspection, x = 1 is an obvious solution Let's see what Wolfram can do with it .... http://www.wolframalpha.com/input/?i=solve+16x%...

Math
divide (x^3+7x^2+11x+2) by (x+2) using either long division or synthetic division. or factor (x^3+7x^2+11x+2) , it does

Math
number for George --- x Deb has ----- .4x Tom has 5(.4x) or 2x x + .4x + 2x = 204 solve for x

math
not complete, see your previous post of this

Math
Poor presentation. Each new line should have an equal sign in front. You lost the square root operation in the second line. Secondly, where did the 2 go? Ahhh, it came back in the third line. Hope you see my point. 2?72 + ?32 = 2?36 ?2 + ?16 ?2 = 12?2 + 4?2 = 16?2

Math
number of 2-pointers ---- x number of 3-pointers ---- 74-x 2x + 3(74-x) = 160 solve for x

Math
(-x^2-94x+600)/(x+100) = -(x^2 + 94x - 600)/(x+100) = -(x+100)(x - 6)/(x+100) yup, the divisor is a factor of the dividend. You claim that you know how to do long division. Then your result should have yielded the same conclusion. Mine did.

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