# Posts by Reiny

Total # Posts: 38,776

Maths
Let's compare the value of \$1 at the end of 10 years at both types of interest: compound: Value = 1(1.06)^10 simple: let the rate be r interest = 1(10)(r) = 10r value = 1 + 10r so 1 + 10r = 1.06^10 10r = 1.790847... - 1 r = .0790847... rate = 7.91% to 2 decimals

Math
the general term of an AS is a + (n-1)d, where a is the first term, d is the common difference, and n is the number of terms so : a = 0 a+9d = 15 0+9d = 15 d = 15/9 = 5/3 For 10 to be one of the terms a + (n-1)d = 10 0 + (n-1)(5/3) = 10 times 3: 5(n-1) = 30 5n-5 = 30 5n = 35 n...

Algebra
(x-1/2)-(x-2/2)+(x-3/2)-...-(x-100/2) = x - 1/2 - x + 2/2 + x - 3/2 - .... - x + 100/2 = x-x+x-x+x-....-x -1/2 + 2/2 - 3/2 - ... + 100/2 looking at the last term, we see there are 100 terms, so the x's drop out = -1/2 + 2/2 - 3/2 - ... + 100/2 = (-1/2)(1 - 2 + 3 - .... + ...

You are correct at 36/7 another way to look at it: there are 12 half-hours in 6 hours. Have Katie look at a clock. So the length is 12*(6/7) = 36/7 inches

Math
In your trig repertoire , you should know the 3 basic trig values of angles 0°, 30°, 45°, 60°, 90° by knowing the ratio of sides of the 30-60-90 and the 45-45-90 degree triangles. This is very very important in any further study of trig. I will do the only...

Math
FG----> 25+6.5n, where n is the number of games GB ---> 57 + 2.5n 25 + 6.5n = 57 + 2.5n 6.5n - 2.5n = 57 - 25 carry on

Math
hint: sure looks like the coach is collecting \$22 from each player. So on Friday, he collects from 2 players, or \$ .....? So from p players, he collects \$ .... ?

Math Help
The order does not matter, so this is a "combination" problem Number of possible 4 cards from the reds = C(26,4) or 26!/(22!4!) number of possible 4 cards from all = C(52,4) or 52!/(48!4!) prob(your event = C(26,4)/C(52,4) = 14950/270725 = 46/833 = appr .055

Math (Probability)
Prob(a one) = 1/6 prob(a one) twice = (1/6)(1/6) = (1/6)^2 .. prob(a one) ten times = (1/6)^10 = 1/60466176 = appr .000000016 These are independent events, that is, the die has no memory of what happened before, so each roll is a new event e.g. suppose we flip a coin 3 times. ...

Math - Calc/Algebra/Trig
your derivative is ok -4cos^2(x)sin(x)+sin(x) = 0 sinx( -4cos^2 x + 1 ) = 0 sinx = 0 ----> x = 0, ±?, ±2?, ... or 4cos^2 x = 1 cos^2 x = 1/4 cosx = ± 1/2 so x is in any of the 4 quadrants x = ±?/3, ±2?/3 , 4?/3, ±5?/3

math
"The sum of the 9th term is 117" makes no sense. Do you mean : the sum of the first 9 terms is 117 or The 9th term is 117 ?

You should have an idea what y = 1/x looks like, y = 1/(x+6) simply shifts the y = 1/x six units to the left. the 5 instead of the 1 means that the y value is 5 times as great, so it rises faster or there is a vertical stretch by a factor of 5 e.g. the point (1,1) on y = 1/x ...

Math
From your diagram, you should see than tan30° = 20/x, where x is the distance you need. However, a tower 20 cm high ???? You probably meant 20 metres.

Math
7. correct 8. area = 29 side = ?29 which is between 5 and 6 since 5^2 = 25 and 6^2= 36 , and your 29 falls between those two

Algebra
consecutive odd numbers are 2 apart let the first be x then the 2nd is x+2 and the third is x+4 "the sum of 4 times the largest is -191" makes no sense, "sum" is the result of addition , not multiplication If you meant that the result of 4 times the largest...

math
3/4x+5/6x=5x-125/3 the LCD is 12, so multiply each term by 12 9x + 10x = 60x - 500 easy from here.... 2(3x-7)+4(3x+2)=6(5x+9)+3 6x - 14 + 12x + 8 = 30x + 54 + 3 I am sure you an handle it from here

Math
For 1. , just replace the x with a+b 2. f(g(x)) = f(2x+5) = -2(2x+5)

Math
sum = -1/12 - 4/9 = -19/36 difference = -1/12 - (-4/9) = 13/36 (-19/36) ÷ (13/36 = -19/13

40 hrs a week at \$17.00 for 52 weeks = \$35,360 Where does the \$28,285.28 come from? No idea what the rest of the stuff is supposed to mean.

So much missing information! "WAGE---\$ 17.00-an hour---------ANUALLY---28,285.28" --- how many hours a week, how many working weeks in a year? "APARTMENT VALUE 17.34hrs/pay period towards an apartment value of \$934/month----ANUALLY---\$11,208----TOTAL-------\$39,...

algebra
6123/x = x + (1/2)x/x times x 6123 = x^2 + (1/2)x times 2 2x^2 + x - 12246 = 0 (x - 78)(2x + 157) = 0 x = 78 or x = -157 check: 6123/78 = 78 + remainder of 39 , which is 1/2 of 78 6123/-157 ? -157 + (????) the divisor is 78

Your first step should have been to simplify the expression: (x^2+x-6)/(x^2-9) = (x+3)(x-2)/( (x+3)(x-3) ) = (x-2)/(x-3), x ? 3 take over

IB Calculus
since a(t) = 2t - 16 when a(t) = 0 t = 8 v(8) = 64 - 16(8) + 4 = ......

Math
Find the volume of the large box Find the volume of the inner box Subtract the two results.

nope, look up distributive property in your text or notes and look up examples

Calculus
V = (4/3)?r^3 dV/dt = 4? r^2 dr/dt plug in the given stuff 50 = 4?(100)^2 dr/dt dr/dt = 50/(4?(100)^2 ) = .... cm/min

math
The first three are rational numbers. For the last one, no idea what the ## in 250## stands for

Math
original: Andy ---- a Jack ----- j after first give-away: Andy ---- a/2 Jack ----- j + a/2 after 2nd give-away: Jack --- (2/3)(j + a/2) Andy ---- a/2 + (1/3)(j+a/2) (2/3)(j + a/2) = 20 2(j + a/2) = 60 2j + a = 60 *** a/2 + (1/3)(j+a/2) = 20 times 6 3a + 2(j + a/2) = 120 3a + ...

math
The interest in the first year would simply be .1(14,000) = \$1,400 The fact of 5 equal payments for 5 years has nothing to do with this. Now for the 2nd year's interest, we need to do further calculations

statistics and probability
I agree with it, but I find I would like to meet that .8144 of a person.

Math
Hasn't the minute hand completed 1/4 of a rotation? Just look at the face of a clock

Math
let f(x) = x^3 + kx - 4 if x-2 is a factor, then f(2) = 0 f(2) = 8 + 2k - 4 = 0 2k = -4 k = -2

combined rate is 15 litres per minute. amount in 6 min = 6(15) = 90 litres. volume in tank = 2400h cm^3, where h is the height = 2.4h litres, since 1000 c^3 = 1 litre so 2.4h = 90 h = 90/2.4 cm = 37.5 cm <--- the depth of water after both taps ran for 6 minutes b) Does the ...

algebra
let the time form 11:00 to the time of overtaking be t hrs distance gone by the truck = 54t distance gone by the van = 64(t-1) but they went the same distance, so ... 54t = 64(t-1) solve for t, and add it to 11:00

math
3s + 4j = 360 s + 3j = 220 -----> s = 220 - 3j sub that into the first and solve for j then find s

algebra
Plane's speed --- x mph wind speed ----- y mph 2(x-y) = 180 x-y = 90 1(x+y) = 180 x+y = 180 add them: 2x = 270 x = 135 back in x+y= 180 135+y=180 y = 45 state a proper conclusion.

Algebra
"and" usually suggests addition, e.g. what is 5 and 6 ? let the number be n "the sum of 4 times a number and 30" --> 4n+30 now twice that ---> 2(4n+30) = 8n + 60

Cal 1
S(-3) = 6(-27) + 8(9) + 5 = -85 S(-1) = 6(-1) + 8 + 5 = 7 avg velocity = (7 + 85)/(-1 + 3) = 46

Math-Geometry
Good job, you have 1. shown that opposite sides are parallel 2. adjacent sides form a right angle.

Math-Geometry
I would first of all plot the points. That would give you an idea which sides would form the rectangle. Since in a rectangle: 1. opposite sides are parallel, you can show this by finding the slopes 2. slopes of adjacent sides are negative reciprocals of each other. Use your ...

Math
or number of bags needed --- n amount of peanuts he bought 2n lbs number of bags he needs to buy = 2n/(5/6) = 12n/5 <---- must be a whole number the smallest number of n to make it so, is n = 5 number of bags needed = 5

Math
all 3 digit number divisible by 6: 102 108 114 120 126 132 138 144...978 984 990 996 How many of those are there ? (996-102)/6 + 1 = 150 or: An AG with a=102, d = 6, term(n) = 996 term(n) = a+(n-1)d 996 = 102 + 6(n-1) 6n-6 = 894 6n = 900 n = 150 Of those which ARE divisible by...

math
so shaded part = 6/20 = 3/10 or 30%

math
prob(yellow) = 1/6= x/36, so x = 6 , 6 yellows prob(orange) = 3/4 = y/36, so y = 27, 27 orange remaining 3 must be orange or 1/6 + 3/4 = 11/12 leaving 1/12 for the purple (1/12)(36) = 3 purple

Maths
midpoint of (-5,12) and (-1,-12) = ( (-5-1)/2 , (12-12)/2 )) = (-3, 0) I will use vectors to find the points of trisection i.e. in the ratio of 1:2 one point = (1/3)(7,10) + (2/3)(-8,-5) = (7/3, 10/3) + (-16/3 , -10/3) = (-9/3 , 0) = (-3,0) which is the midpoint of above other...

Math
In your sketch that you made, you will notice that the diagonals right-bisect each other, creating 4 congruent right-angled triangles. Each of them has angles 30:60:90 degrees the ratio of sides for such a triangle is 1:?3:2 where 2 is the hypotenuse Our hypotenuse is 8 so the...

math
I am sure you meant: f(x) = e^x b) f(6) = e^6 f(4) = e^4 avg rate of change from x=4 to x=6 = (e^6 - e^4)/(6-4) = ... , use your calculator

Algebra
invested at 2% --- x invested at 3% --- 7000-x .02x + .03(7000-x) = 184 carry on

Trigonometry
When you say "a 10 inch wheel" I will assume you have a radius of 10 arc length = rØ, where Ø is in radians 225° = 5?/4 radians 450 = r(5?/4) r = 360/? inches = appr 114.59 inches (big wheel) A point on the smaller wheel has to move 450 inches as ...

Algebra
4^4 x 8^8 x 16^16 are all powers of 2 = (2^2)^4 x (2^3)^8 x (2^4)^16 = 2^8 x 2^24 x 2^64 = 2^96 so what do you think?

Algebra
looks pretty standard to me. Perhaps you mean: |y|-2=0 |y| = 2 y = 2 or y = -2

college algebra
from your data, if h is the height above the water h = -4.9t^2 + 28t + 38 set h = 7 4.9t^2 - 28t - 31 = 0 use the quadratic formula to solve for t, use the positive result

college math
At a time of t hours after the action started, - distance remaining for the northbound car before reaching intersection is 3 - 20t - distance remaining for the westbound car before reaching the intersection is 4 - 30t let d be the distance between them d^2= (3-20t)^2 + (4-30t...

y = -x^2 + 2x + 5 the x of the vertex is -b/(2a) = -2/(-2) = 1 plug in x = -1, y = -1+2+5 = 6 vertex is (1,6) -4x^2+7x+5=0 4x^2 - 7x - 5 = 0 x = (7 ± ?129)/8 = appr (7±11)/8 = appr 18/8 or -4/8 or appr 2.5 or -1/2 your choice is good 5x^2 - 20 = 15x x^2 - 3x - 4...

Math; Calculus
from the given data: h = -16t^2 + 55t + 6 this is a parabola, we need its vertex. the t of the vertex is -b/(2a) = -55/-32 = 55/32 seconds plug that into equation to find max height it is in the air for h > 0 let's see when h = 0 0 = -16t^2 + 55t + 6 16t^2 - 55t - 6 = 0...

Algebra
speed of current --- y speed of swimming ---- x x+y = 5 x-y = 2 solve, I suggest adding them, etc

Algebra
amount of cashews --- x lbs amount of raisins ---- 4.5 - x lbs 2.5x + 1.25(4.5-x) = 2(4.5)

math
let the second be x ft long then the first is x+4.25 the third is x+2.24 x + x+4.25 + x+2.24 = 10 carry on

math
cost price = 525 18 eggs = 1.5 dozen selling price = 23.5(26) = ... profit or loss = selling price - 525 = .... percent profit = ....

math
collins meant: (a+b+c)/2 = s

number base help plz
Steve is simply using the definition of a number with a different base. Just like 57810 = 5(10^2) + 7(10^1) + 8(10^0) 1234 = 1(4^2) + 2(4) + 3 = 16 + 8 + 3 = 24 + 3 ---> Steve noticed the multiples of 8 = 3(8) + 3 = 338

Math
Say what ?

algebra
your function is a straight line - from your equation we can tell that the slope is -2 and the line passes through (-8,7) All you need is another point and you can draw it. Why not pick something nice like x = 0 So we get: y-7 = -2(8) y = -16+7 = -9 take over

Calculus
A rough sketch of the two functions y = x , and y = 1+sinx will show that y = x clearly crosses y = 1 + sinx only once. So your statement is not correct. evidence: http://www.wolframalpha.com/input/?i=solve+x%3D1%2Bsin(x)

Algebra
x/3 + 5 = 3x/2 times 6. 2x + 30 = 9x 7x = 30 x = 30/7 check: (1/3)(30/7) + 5 = 45/7 3/2(30/7) = 45/7 my answer is correct

math
They do not intersect at (3,4) (3,4) does not satisfy g(x) = 2^x - 1 RS = 2^3 - 1 = 7 LS = 4, no good (3,4) work in f(x) = -5/3x + 9 RS = -5/3(3) + 9 = 4 So it does work in the other equation. did you mean g(x) = 2^(x-1) ?? RS = 2^2 = 4 = RS you must have meant that! so ...

math
Did you make a sketch?? The difference in their connection points is 4 m. and you have a triangle with base 10, height 4 and missing hypotenuse x^2 = 4^2 + 10^2 carry on

Math
Maria "guessed" correctly, I got the same answer. So none of the answers supplied are correct. Either typo or misprint.

Matj
I will assume the difference to be between pairs of coupons possible cases: 5,1 6,1 6,2 7,1 7,2 7,3 8,1 8,2 8,3 8,4 9,1 9,2 9,3 9,4 9,5 10,1 10,2 10,3 10,4 10,5 10,6 total 21 number of pairs = C(10,2) = 45 prob(of your event) = 21/45 = 7/15

math
Hint: The diagonals of a rhombus right-bisect each other. Another hint: Make a sketch. What type of triangles do you see? Do you know the legs of those triangles?

Math
What is the LCM of 2, 6, and 9 ?

algebra
time spent cyling --- x hrs times spent running --- (2.5 - x) hrs 10x + 6(2.5-x) = 21 carry on

math
Scott is absolutely right, if you had taken the 10 seconds to complete his calculations.

n
Let's use a sine curve, we could use a cosine as well amplitude is 10, so h = 10sin kt the period is 6 minutes, so 2?/k = 6 ----> k = ?/3 sofar: h = 10sin (?/3 t) this has a min of -10, but our min is to be +1, so we have to raise everything up by 11 so far: h = 10sin...

Math
Number of Yen remaining = 110682 - 87438.78 = 23243.22 \$1100US = 110682 Yen 1 Yen = 1100/110682 = \$.009938382 so 23243.22 Yen = .009938382(23243.22) = \$231 or 1100/110682 = x/23243.22 x = 231

math
correct, only a = 0 if x = 0 then in x/y=2 0/y = 2, which cannot be, so x ? 0 if y = 0, we would be dividing by zero to get 2, which is rather silly, so y ? 0 if a = 0, x/y =2 has nothing to do with it, but x*y*0 = 0, which is true

math
size of original piece of material: x cm by x cm after cut-out base is (x-8) by (x-8) height = x V = x(x-8)^2 = 576 x^3 - 16x^2 + 64x - 576 = 0 Nasty equation to solve. Have you learned any methods to solve a cubic? Newton's Method is probably the best way, but you have to...

Algebra
x=3, so Alysia is 3 and Adam is 33 3+33 = 36

Algebra
Ms. Sue meant to say: x + 30+x = 36

Algebra 1
Yes, except since this is money in dollars you would round it to the nearest cent. \$500,637.91

Algebra 1
What is 20000(1.05)^66 ?

Math
rate of first ---- x rate of 2nd ---- y 1500(3)x - 1500(3)y = 13.50 x-y = .003 the difference is .3%

polynomial
I don't understand how looking at the graph of y=2x³+x²+x+8 , which does not have a "nice" rational solution, will help you in solving y = 2x^3 + x^2 - x + 5. The latter also has an irrational solution. http://www.wolframalpha.com/input/?i=y%3D2x%C2%B3%...

Maths
you are solving, 6750(1.05)^t = 8000 1.05^t = 1.185185.. take log of both sides, and use log rules t = log 1.185185.../log 1.05 = 3.482239 so that is 3 years and .482239 years multiply the decimal part by 12 to get 3 years, 5.7868.. months so 3 years, 5 months and .7868 months...

maths
graphing utility?? why? 6sinx + 3cosx = 0 divide by cosx 6sinx/cosx + 3 = 0 6tanx = -3 tanx = -1/2 we know that the tangent is negative in II or IV and we know tan (.4636) = +.5 x = ?-.4636 = appr 2.678 or x = 2? - .4636 = appr 5.820 If you insist: http://www.wolframalpha.com/...

Math
12.5 litres takes the car 168.75 km then 1 L takes the car 168.75/12.5 km then 15 L will take the car .....

Math
Why do you think this question might deal with the concept of a Lowest Common Multiple ?

Math
How many square cm are there in 1 square metre? - then how many in 1/2 square metre ?

Math
simplify and re-arrange ... y-5 = (2/7)(x-11)

Math
of course it isn't right x = 3 would be a vertical line. A quick sketch will show you that your 2 points do not lie along a vertical line slope = m = (-8-8)/(5-3) = -16/2 = -8 equation: y-8 = -8(x-3) re-arrange to whatever form you learned.

Slopes
slope = m = (7-4)/(-5-0) = ... once you find m, replace it in the equation y-4 = m(x+6) arrange into the form that you are familiar with.

Algebra II

Math
p5^y + 5^-y = 5 p5^y + 1/5^y = 5 now replace px + 1/x = 5 times x px^2 + 1 = 5x px^2 - 5x + 1 = 0 which is what we want

calculus
V= (4/3)? r^3 dV/dt = 4? r^2 dr/dt when V = 64 64 = (4/3)? r^3 48/? = r^3 r = (48/?)^(1/3) = appr 2.4814 ---> I stored the 10 decimal answer in dV/dt = 4? r^2 dr/dt 20 = 4?(2.4814..)^2 dr/dt dr/dt = appr .2585 inches/min

Math
You must know the binomial expansion and the general term of the expansion!! 5th term = C(9,4) (4^4)(-x/5)^5 = 126 (256)(-x^5)/3125 = -32256/3125 x^5 oops, just did in descending powers, so C(9,5) 4^5 (-x/5)^4 = 126(1024)(x^4/625) = 129024/625 x^4 , in ascending order

Maths
distance at original speed = (1/4)(60 km = 15 km time at reduced speed = 15/36 hours = 5/12 hr = 25 minutes

Geometry
clearly the largest circle will have a diameter of 4 ft, or a radius of 2 ft area = ?(2^2) = 4? ft^2 = ...... In this time of calculators, using 3.14 for ? and then rounding off that rounded constant is rather silly. Most calculators have a special key for ?, use it.

Maths
correct your spelling and incomprehensible gibberish

Math
Yes, could have been easily checked by taking 20% of it.

Math
regular price ---- x it said the 20% discount came to \$15 well, .2x = 15 x = 15/.2 = ......

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