Posts by Reiny

Total # Posts: 39,065

Math
number of advanced tickets ---- x number of at door tickets ----- 480-x 4x + 5(480-x) = 2100 solve for x

math
Is the "discount" confusing you ? I believe most textbooks would handle it like this: Let the annual discount rate be i 1-i = (1 - .005)^12 = .995^12 = .94162 i = .058377 or a discount of 5.8377% Had it been just plain old interest ..... let the nominal rate be i (1+...

Algebra
f(x)={x^2, if x ? -4 {x^3, if -4 < x ? 1 {?x, if x > 1 so if x = -4, it belongs to the first function f(-4) = (-4)^2 = 16 if x = 4, we have the last function f(4) = ?4 = 2

Mathematics
"where t is the time in hours from....." is incomplete Did you mean from noon ? Let's assume it is after noon, else make the necessary adjustments at 9:45 pm , t = 9.75 set your calculator to radians d = 3.163 metres The min of 3cos 30t is -3 and its max is +3 So...

Math
cost of gift ---- x cost for each of the nine originals = x/9 cost per student with 13 paying = x/13 x/9 - x/13 = 33.32/9 times 117 13x - 9x = 3898.44 4x = 3898.44 x = 974.61 check: original share = 974.61/9 = 108.29 new share = 974.61/13 = 74.97 saving per share = 33.32 , as ...

Math
number of skiers --- x number of boarders ---- 2x , notice x : 2x = 1 : 2 2x - x = 1250 etc

math
Han's starting number ------ x , counts backwards by 100 Sally's starting number ----- 300 counts forward by 10 after 6 counts, Sally is 360 after 6 counts, Han's is at x - 600 x - 600 = 360 x = 960

Algebra
let the number of 50 notes be 3x let the number of 20 notes be 5x , notice they are in 3:5 ratio number of 10 notes = 25 - 3x - 5x or 25 - 8x value of notes equation: 50(3x) + 20(5x) + 10(25-8x) = 590 150x + 100x + 250 - 80x = 590 170x = 340 x = 2 sub back into my definitions

Algebra
let the amount of aluminum added be x kg .55(160) + x = .7(160+x) 88 + .55x + x = 112 + .7x .85x = 24 x = appr 28.24 kg

Math
a+2d = -1 a+6d = 11 subtract them: 4d = 12 d = 3 from a+2d = -1 , a = -7 term(n) = a+(n-1)d = -7 + 3(n-1) = -7 + 3n - 3 = 3n - 10 "the numbers of which must be added to get a sum of 430" I will assume you mean, "how many terms are needed to have sum of 430"...

Algebra
follow the same steps I showed you in your previous question.

Algebra
speed of jet in still air ---- x mph speed of wind ---- y mph 4(x+y) = 1008 ---> x+y = 252 4(x-y) = 832 ----> x-y = 208 add them: 2x = 460 x = 230 from x+y = 252 , y = 22

College Algebra
let the time taken to catch up be t hours distance covered by the sister be 65t distance covered by Sarah is 60(t+2) but the went the same distance, so ... 65t = 60(t+2) solve for t

Algebra
let the smallest angle be x then the next smallest angle is 3x+26 You know in a right-angled triangle the two smaller angles must add up to 90° , so x + 3x+26 = 90 solve for x ....

Math medication problems
One confusion that could arise is to use cc vs ml http://thecompounder.com/2015/04/13/cc-vs-ml-whats-the-difference/ the ordered rate was 600 cc/8 hours = 75 cc/hour The pharmacist erroneously calculated this to be 200 ml/hr or 200 cc/hr

Algrebra
your slope for BD should have been 9/1 or 9 To be a rhombus, the slopes of the diagonals should have been negative reciprocals of each other the negative reciprocal of -1/5 would be +5 which it isn't. so ABCD is not a rhombus Another way to check: The sides are not equal ...

math
Just translate into Math "three consecutive numbers" ---> x, x+1, x+2 "the sum of the second and the third numbers " --- x+1 + x+2 "exceeds the first by 14" ---> x+1 + x+2 - x = 14 now just solve for x, and sub back into my definitions

math
Since we are going to need minutes anyway .... rates are: wash/20, wash/15, and wash/15 combined rates = 11wash/60 time to finish the wash with all three washing = wash/(11wash/60) = 60/11 minutes = appr 5.45 minutes make use of my answer in your concluding statement.

math
3x5+10x3/ 20-(5+6) = 15 + 30/20 - 11 = 15 + 3/2 - 11 = 5 1/2 or 11/2 or 5.5 what you did is 3x5+10x3/ (20-(5+6))

pre algebra
from : an-3a +8=b an = 3a + b - 8 n = (3a + b - 8)/a

math
Damon, mea culpa. "old-timers" setting in.

math
oops, forgot to turn off my "bold" text. Many students (and teachers) make this more difficult than it has to be. Step1 : plot the given point, join it to the origin. Using this as the hypotenuse, draw an altitude to the x-axis and complete the right angled triangle...

math
Many students (and teachers) make this more difficult than it has to be. Step1 : plot the given point, join it to the origin. Using this as the hypotenuse, draw an altitude to the x-axis>/b> and complete the right angled triangle. Step 2: Unless you are already in the ...

algebra 1
92 feet per minute is a rate, it means that each minute you travel 92 ft, they just the equivalent in miles per hour, or mi/hour 92 ft / 1 minute = (92/5280) ft / (1/60) hour ---- 1 ft = 1/5280 miles, so 92 ft = 92/5280 miles ---- 1 minute = 1/60 hour = (92/5280)(60) mph = ...

calc
I just answered that for you in your previous post .

calc
I would do it the same way, except ?3/3 is not associated with one of the standard angles. did you mean ?3/2 again ? so if sin 3x = ?3/2 3x = 60° or 3x = 120° x = 20° or x = 40° period = 360/3 = 120° so add 120° to any angle until you go over 360° ...

calc
among the repertoire of "trig things I should know" has to be the trig ratios of standard angles like 0, 30, 45, 60, and 90° one is that sin 60° = +?3/2 as well as sin 120° = ?3/2 , by the CAST rule so if sin 2x = ?3/2, then 2x = 60° or 2x = 120° ...

Algebra
Besides being an integer -22 also belongs to the set of rational numbers it is NOT an irrational number like you listed

oops - Algebra 1
that last equation should have been 13x - 4y = -3

Algebra 1
I would first of all eliminate those decimals -4.5x-2y=-12.5 times 2 ------> -9x - 4y = -25 or 9x + 4y = 25 3.25x-y=-0.75 times 4 -------> 13x - 4y = 3 now just add them and things will work out

Math
How about Trump's wall ?

Math
'a' is odd, 5 choices 'b' is divisible by 3, 3 choices 'c' is even , 4 choices 'd' is prime, 4 choices. So what is 5x3x4x4 ?

math
solve for x, the score on her third test. (x + 95 + 87)/3 ? 90

Math
5/4 teaspoons per 3/8 cup 1 teaspoon per (3/8)÷(5/4) or (3/8)(5/4) or 15/32 cup or 1 teaspoon per 1/2 cup, after all , how "accurate" is the measure of a "teaspoon"

Algebra : Please Help?
for both, make a table of values. I would use -3 to +3 for the first one, and you should get a parabola that opens downwards for the second, y = -2/?x , clearly we can only use x > 0 pick x's that are perfect squares, such as 1, 4, 9, 16, ... It should look like this ...

Algebra
number of feet of first ---- x number of feet of the foot-advantaged ---- x+8 solve for x x + x+8 = 36

Algebra
Let the time taken be t hours distance covered by first car = 60t distance covered by 2nd car = 70t 60t + 70t = 180 solve for t, the time until they meet.

Algebra : Please Help?
see later post of your same question

Algebra
number of $100 bills ---- x number of $50 bills ----- x+36 number of $20 bills ----- 8x equations based on the value of the bills: 100x + 50(x+36) + 20(8x) = 9240 solve the equation and sub back into my definitions

Math
Since it is a square, all four sides are equal let each side be x so perimeter = 4x area = x^2 now it says: perimeter = 1/8 of the area 4x = (1/8)x^2 multiply each side by 8 32x = x^2 , divide by x 32 = x , and there you have it ! Dad's current age ---- D Dad's age 5 ...

Calculus
instantaneous compounding implies: amount = deposit x e^(rt) , where r is the rate expressed as a decimal so amount = 12000(e^(.06)(5)) = 12000 e^.3 = ... you have a function key on your calculator which does e^x , it is usually the 2nd function key of ln x

Math
Good for you to notice that, I must have lost my card-sense. Actually we are both wrong. The number cars run from 2 - 10, and in 4 suits that makes 36. of which 20 are even and 16 are odds (count them on your fingers) so make the necessary adjustments in c)

Math
Since you are returning the card after the first event, you are dealing with independent probabilities That is, the outcome of the second event does not depend on the outcome of the first. a) there are 12 picture cards so prob(event) = (12/52)(12/52) = .... b) There are 39 non...

Maths
I was trying to establish at what level of math you are working. That is why I asked about DeMoivre's theorem. As a short answer: ?(12 - 22?2) = ?(22?2 - 12) i = appr 19.11 i

Maths
looks like you want ?(12 - 22?2) looks like you are trying to take the square root of a negative. Have you heard of DeMoivre's theorem?

math
after first eating, 7/8 of cake is left so he ate 2/5 of that, leaving (3/5)(7/8) or 21/40 of the cake. he gave 1/4 of that to the cat, leaving him with (3/4)(21/4) or ...... of the cake

Math
"Present age of bob is equal to abbay age 8year" ---> Abby is 8 years older than Bob let Bob's present age be x Abby's present age is x+8 "four year hence Bob age respectively ratio to Abby's age is 4:5" ----> (x+4)/(x+12) = 4/5 cross-...

Math
first contract: i = .144/12 = .012 n = 24(12) =288 PV = 290000 paym = ? paym( 1 - 1.012^-288)/.012 = 290000 = ...... -----> X After making the 68th payment, balance of loan = 29000(1.012)^68 - X( 1.012^6868 = - 1)/.012 = ...... Y This becomes the PV of a new contract, with ...

Math
first procedure: amount alcohol removed = 300 ml amount of alcohol left = 700 ml or .7(1000) topped up with 300 ml of water alcohol left in the 1000 ml = 700 ml percentage of alcohol in the mixture = 70% = .7 2nd procedure: amount of alcohol removed = .7(300) ml amount of ...

Algebra
I will set up the U-Haul equation for you cost = .25m + 35, where m is the number of miles you set up the Budget equation. then equate .25m + 35 = (your Budget expression) and solve for m

Mathematics
actually multiplication and division are performed in the order they come, from left to right so we have 16 ÷ 4 * 2 = 4 * 2 = 8 http://www.wolframalpha.com/input/?i=16+%C3%B7+4+*+2 https://www.google.ca/search?source=hp&q=16%2F4*2&oq=16%2F4*2&gs_l=psy-ab.3..0i7i30k1l4....

Math
a+2d = 4a ---> 2d = 3a ----> a = 2d/3 sub that into a+5d = 17 2d/3 + 5d = 17 17d/3 = 17 d = 3 then a = (2/3)(3) = 2 You don't specify how many terms you want in the series, but you should know the formula Now that we know a and d, it is easy

Math
50 (2x-5)^2 -162 (3y-2)^2 = 2 [25(2x-5)^2 - 81(3y-2)^2 ] now I see a difference of squares = 2[ (5(2x-5) + 9(3y-2) )( (5(2x-5) - 9(3y-2) )] = 2[ (10x-25 + 27y - 18)(10x - 25 - 27y + 18) ] = 2(10x + 27y - 43)(10x - 27y - 7) check my arithmetic

Algebra.
You really should be able to do this .... brother's age ---- x Sara is two years older , so her age is x+2 "sum of their ages is 29" sum --- + their ages ---- I defined them for you is ---- = Now form the equation, and solve it. Let me know how it worked out for you

Probability (Please check answer and assist)
As I said, I am not familiar with your notation. counting Y as a vowel, Prob(vowel) = 1/5 Prob(consonant) = 4/5

Probability (Please check answer and assist)
I have seen this question for several days now. More than likely, the reason you are not getting a reply is due to your notation. Secondly, I am baffled by your choices. - for a vowel , use a value of 1 - for a consonant, use a value of 2 - "other retrieved letters"...

Math
Three cases: only ann wins : (1/3)(7/8)(19/20) = 13/480 only may wins: (2/3)(1/8)(19/20) = 38/480 only vea wins : (2/3)(7/8)(1/20) = 14/480 prob(as stated) = 13/480 + 38/480 + 14/480 = ....

math
routine chain rule .... s = (2 - t)^2 ds/dt = 2(2-t)^1 (-1) I will let you clean it up

math
I read that as : (4*10^3)(3*10^4) = 12*10^7 = 1.2 * 10^8

Math
Hard to tell, since you have no units on 3/5 x 6 x 10. Furthermore, since you have 3 multipliers, it suggests 3 dimensions and we would be talking cubic units, not square units. Nevertheless, 3/5 x 6 x 10 = 36

Geometry
offsets ? the diagonal would be the hypotenuse of a triangle with sides 19 and 11 d^2 = 11^2 + 19^2 solve for d , (it will be irrational)

Math
side of larger square = ?400 = 20 inches area of smaller square = 100 so the side of the smaller square is 10

geometric progression
I suspect a typo in the 2nd term. Did you mean ... 1+1/2+1/4+1/8.... I will suspect as much then a = 1 , r = 1/2 sum of n terms = 1(1 - (1/2)^n )/(1 - 1/2) = 2(1 - (1/2)^n ) = 2 - (1/2)^(n-1) or 2 - 2^(1-n) testing my answer: sum of first 4 terms, n = 4 = 1 + 1/2 + 1/4 + 1/8...

Math
There are 3 ft in 1 yard, thus 9 square feet in 1 square yard. so how many square yards in 57600 square feet ??

Math
|x| = 17

Math
Just treat it as if it were an equation, but keep the ? sign let me know what you get .

Unitary method
5 mice can eat 5 kg of rice in 10 days, so 1 mouse can eat 5 kg of rice in 50 days then 10 mice can eat 5 kg of rice in 5 days.

math
stop at x ? ?8 Whatever were you doing after that ??

Math
calculate his cost price how many eggs will he sell? How many dozen is that? multiply the number of dozen sold by 15, that is his revenue profit/loss = revenue - cost price , if negative, you have a loss percent profit/loss = profit or loss/cost price * 100

Math
(a - b)^2 = a^2 - 2ab + b^2 vs 25x^2 - 40xy + 16y^2 what do you think?

Statistics
One interesting way would be to show it in Pascal's triangle: 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 1 6 15 20 15 6 1 1 7 21 35 35 21 7 1 1 8 28 56 70 56 28 8 1 .... notice that in any row, entries equidistant from either the left or the right are equal. in my last ...

Algebra
solving x^4 - 13x^3 + 31x^2 + 126 = 0 is not easy. Wolfram is a powerful website that gives us the following: http://www.wolframalpha.com/input/?i=solve+x%5E4+-+13x%5E3+%2B+31x%5E2+%2B+126%3D0 Notice we have 2 reals, and 2 complex roots. Since we are given exact real roots of ...

algebra
x^4 - 13x^3 + 31x^2 + 126 what about it ?

Commercial low
You've got to be kidding ! Your really expect somebody to give you a 2000 word reply, with a given font, and double spacing ????? (notice the correct way of double spacing)

math
The areas of similar shapes are proportional to the square of their corresponding sides area of banner : area of sign = 54^2 : 17^2 = 2916 : 289 = appr 10.1 : 1 OR, the long way .... area of banner = 54x36 = 1944 inches^2 for the sign, we need the width 17/54 = w/36 w = 36(17/...

math
a) P = (.98)^t , you had that b) 1/2 = .98^t .5 = .98^t take logs of both sides and use log rules ... log .5 = t(log .98) t = log .5/log .98 = appr 34.4 years c) P = 6(.98)^38 = aprr 2.78 g makes sense, since the half-life of 34.4 years would have reduced it to 3 g , and we ...

Math
number of legs of one (the smiler) ---- x number of legs of the other ---- y smiling one said: x+2 = y-2 -----> x - y = -4 ** other said: y+2 = 3(x-2) y+2 = 3x - 6 3x - y = 8 *** subtract: *** - ** 2x = 12 x = 6 , then y = 10 state your conclusion

new math
Why are you repeating this question ? It was answered in detail yesterday .... https://www.jiskha.com/display.cgi?id=1505338640 Did you not read the replies ?

Algebra
"Enter only the numerical part of the answer, that is, if your answer is d miles, enter only value of d without the units (miles)." that tells me that you are only looking for the answer to what is clearly an on-line test or assignment. This site does not work like ...

math
You have 3 choices for the first digit and 3 choices for the middle digit, but only 2 choices for the last digit number of possible numbers = (3)(3)(2) = 18

math
cost of biscuit ---- x p cost of crisp ------ x+4 p 2(x+4) + 5x = 176 solve for x

algebra
See my previous reply to your earlier post of this

trigonometry
Sketch the situation. On my sketch, I labeled the top of the monument as A and its bottom as B, with B on ground level I placed the man at a point 9 m above ground at some distance away from the monument and labeled that P I drew a horizontal from P to meet AB at Q I now have ...

algebra
(3x + 10) : x^2 = 1 (3x+10)/x^2 = 1 x^2 = 3x+10 x^2 - 3x - 10 = 0 (x - 5)(x + 2) = 0 x=5 or x = -2

Math
cost price = 220 rupees So he sold 114 eggs at 2.5 rupees income = 114(2.5) = .... profit = income - cost price = ....

College Math
y ? 4x draw a solid straight line y = 4x, then shade in the region below the line 4x + 5y ? 20 5y ? -4x + 20 y ? (-4/5)x + 4 draw a solid straight line y = (-4/5)x + 4 , then shade in the region below the line

Math
I read that as: (1/7)(2/4)÷(2/9) + 5/6 - 3/5 = (1/7)(1/2)(9/2) + 25/30 - 18/30 = 9/28 + 7/30 = 135/420 + 98/420 = 233/420

Math
now: number of cats --- n number fleas per cat --- 2n total number of fleas = 2n^2 after removal episode: number of cats = n-2 fleas removed from those cats = 2(2n) = 4n fleas removed from remaining cats = 3(n-2) = 3n - 6 fleas remaining = 2n^2 - 4n - (3n-6) = 2n^2 - 7n + 6 2n...

correction: math
equation should have been x+7 + x+3 = 82 etc

math
Now: Monica's age ---- x Nancy's age ---- x-4 seven years from now: Monica ---- x+7 Nancy ----- x-4 + 7 = x + 3 so x-4 + x+3 = 82 continue

geometry
describe the diagram

Math
see my previous reply to your same question. Btw, you posted the same question just a few minutes apart. Patience is a virtue.

Math
You have 3 unknowns but only two equations, so you can't "solve" for a unique solution.

geometry
You have shown it for a specific case, but that does not prove it in general. Why don't we just do it It appears that x^2 + 1 is the largest side, then is (x^2 - 1)^2 + (2x)^2 = (x^2 + 1)^2 ???? Left side = x^4 - 2x^2 + 1 + 4x^2 = x^4 + 2x^2 + 1 Right side = x^4 + 2x^2 + 1...

Geometry
I will assume that N is on BC. So you have two right-angled triangles, BNA and CNA. In BNA, BN^2 = 20^2 - 12^2 , so BN = 16 in CNA, CN^2 = 15^2 - 12^2 CN = 9 so BC = 25 , and 25^2 = 20^2 + 15^2 so by Pythagoras, we have right angle at A

math
number of 3/4 cup servings = 11/2 ÷ 2=3/4 = 22/3 cups so each person would get 22/30 cups or appr .73 of a cup

new math
I sure hope that they still teach the following simple divisibility checks: - to be divisible by 2, the number must be even - to be divisible by 3, add up the digits of the number, if the sum is divisible by 3, so is the number - to be divisible by 4 , the last two digits must...

Please explain
let x = .151515... there are 2 digits that repeat, so multiply each side by 100 (if 3 digits were to repeat, I would multiply by 1000 etc) 100x = 15.1515... subtract the two equations 100x - x = 15.1515... - .1515... 99x = 15 x = 15/99 = 5/33 check with a calculator If you had...

Math
burnhours of the lightbulb = 3(22.8) = 68.4 time for a bulb that burns 7 hours/day = 68.4/7 =9.77 or 9.8 years or the time is inversely proportional to the rate T = k/R 22.8 = k/3 k = 3(22.8) = 68.4 T = 67.4/R = 67.4/7 = appr 9.8 Notice the calculations are the same

Math
Do not use your own "reply" to ask a new question. number of handshakes = C(5,2) = 10

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