Thursday

July 31, 2014

July 31, 2014

Total # Posts: 26,926

**Math**

a) the only even prime is the number 2 so prob = 1/6 b) primes less than 5 are : 2 and 3 so prob = 2/6 = 1/3 c) if not a 6, then it must be: 1, 2, 3, 4, or 5 how many of those are prime? d) which of 1 or 2 is prime ? e) how many even's < 4 are prime? etc.

**Algebra**

(√5a^-2)/(√10a^-1) = (√5 a)/(√10 a^2) = 1/(√2 a)

**Math**

volume of whole apple = (4/3)π(6^3) = 288π cm^3 volume of inner part of apple with radius 5 cm = (4/3)π(5^3) = 500π/3 cm^3 part of apple within 1 cm of outside = 288π - 500π/3 = 364π/3 prob(being in outer part of apple) = (364π/3) / (288...

**Math**

expected income = .2(0) + .3(-1000) .25(-10000) + .25(20000) = 2200

**Math**

Let the line joining (1,-4) and (6,-4) be the base of your triangle. This is a horizontal line, and it should be easy to see that its length is 5 let the height be h (1/2)(5)h = 20 5h = 40 h = 4 so any point on the x-axis (or 4 units above your base) would be such a third poin...

**math**

So they must enter in the order G B B B G number of ways = 2 * 3*2*1 * 1 = 12

**Math**

could be 1. YY --->(5/29)(4/28) = 20/812 2. GG ---> (7/29)(6/28) = 42/812 ... 5. BB ---> 4/29)(3/28) = 12/812) Add them up (20 + 42 + .. + 12)812 = ....

**Math**

so prob that 5 of the 10 smoke = C(10,5)(.4^5)(.6^5) = appr .2 40% of college students smoke ??? Are those stats from the 50's ?

**Math**

number of slices per pizza = 360/40 =9 so for 2 pizzas we have 18 pieces and at 1 slice per person, we would have 18 people. (cutting a pizza into 9 pieces ??? Good luck Are you going to lay a protractor on the pizza and measure 40° ?)

**Math - Answer Check**

What is (2/3) of (2 1/10) ? = (2/3)(21/10) = 7/5 units of distance or 1.4 units or 1 2/5 units

**Math**

First one is easy. The cow can cover 3/4 of a circle with radius 40 (the missing quarter is the barn) area = (3/4)(π(40^2) = 1200π yds^2 2nd one: let's tie the cow up at the top left corner. with a rope of 75 yds, the cow can cover (3/4)(π(75^2) or 4218.75&#...

**math**

Since cost usually varies with the area and the area is proportional to the square of the corresponding sides, the area would be 4 times as large, thus the cost would be 4($1.5) or $6.00 ( ratio of sides = 2:1 so ratio of areas = 2^2 : 1^2 = 4 : 1 ratio of costs = 4 : 1 )

**Math**

√(3f^3) = √3 * √(f^2) * √f = √3*f*√f = f√3√f = f√(3f)

**Math**

Taking it just the way you typed it ... = √3/( (√f)^-3) = √( 3/f^-3) = √(3f^3) = f√(3f)

**math**

? ? ? What does that mean?

**math**

I would make time (t) my horizontal axis marking it up to 5 hours. Make your vertical axis the calorie axis , marking it as 100 , 200, ... up to 1000 calories. plot the ordered pairs (1,300) , (2, 600) , (3, 900) and (4,1200) you should get a straight line Notice (0,0) should ...

**Calculus**

mmmhh v = ∫(5t/4)(t^2 + 1)^2 dt = (5t/4)(((1/3)(1/(2t)) (t^2 + 1)^3 + c = (5/24)(t^2 + 1)^3 + c differentiate to get ((5/4)(t)(t^2 + 1)^2

**Calculus**

right now: price of rent = 900 number of units rented = 50 Let the number of $25 increases be n (e.g. If n= 2 , new rent is 900+2(25) = 950 if n = 5 , the new rent 900 + 5(25) = 1025 so the new rent = 900 + 25n number rented = 50-n maintenance cost = 75(50-n) Profit = P = (900...

**Calculus**

Make a sketch ... Place the first vehicle A at the origin P, showing the position of the first vehicle draw a short line east of P and label it A2 Place the second vehicle B at a distance of 5 above P showing the initial position of the second vehicle draw line downwards from ...

**math**

Steve did this for you http://www.jiskha.com/display.cgi?id=1398006054 All that was required of you want a bit of "counting" .

**Math Help**

You have been helped repeatedly by several tutors for these same type of questions. I think it is time that you try them yourself and show where your difficulties lie with these. e.g In every one, wasn't the first step to find the LCD ? We then multiplied each term by that...

**trig**

16cos(x)-3sec(x)=0 16cos(x) = 3sec(x) 16cosx = 3/cosx cos^2 x = 3/16 cosx = ± √3/4 x = 1.123 or x = π - 1.123 = 2.0186 or x = P + 1.123 = 4.266 or x = 2π - 1.123 = 5.160

**algebra**

you LCD is 12 so .... 6x/12 + 4y/12 - 3z/12 = (6x + 4y - 3z)/12

**math**

given function: y = x+1 Two step process inverse function: (interchange x and y variables) 1. x = y+1 2. solve new equation for y y = x-1 so f^-1 (x) = x-1 Use the above two step method for finding any inverse if it exists.

**Math Help? Check my answers.**

#1 Aren't the terms decreasing by 8 ? So after 6 , you would have -2, -10, -18 #2 aren't the terms increasing by 3 each time ??? So how can you possibly get 14 as the next number after 12 ??? #3 I am puzzled by your choices you started with -1, 9, 19, 29, adding 10 eac...

**math**

Draw a "side view" of the cut sphere. draw a line from centre of the circular cut to the centre of the sphere. You will have a right-angled triangle with base 10 (half the diameter of the circle) and a hypotenuse of 15. let the third side be h h^2 + 10^2 = 15^2 h = &...

**Math**

Your given example illustrates a case where there is a definite number of ways for things to happen, thus it is a theoretical probability situation, you had that one. But you said: You draw five cards from a standard deck of 52 cards. P(heart) = 4/5 (fraction) Did you mean the...

**ALGEBRA**

For any centre (a,b) and radius r, the equation of the circle is (x-a)^2 + (y-b)^2 = r^2 look at your second equation, (x+6)^2 + (y-4)^2 = 16 or 4^2 doesn't it fit that pattern perfectly ? for a centre of (-6,4) and radius of 4 Now you can sketch it. Do the same for the fi...

**math**

think of money $.700 = 70 cents $.007 = .7 cents which would you rather have ? or .700 contains 7 tenths .007 contains zero tenths, none, nada, nichts, nil. ...

**math**

No, the area of similar shapes is proportional to the square of the corresponding sides So 2:1 ----> 2^2 : 1^2 = 4 : 1 The area would be 4 times as large, or quadrupled. Proof: area of original = 5*3 = 15 new sides are 10 and 6 new area = 10*6 = 60 and 60 = 4 times 15

**triangle measurements**

Are you sure that there was no angle given, or perhaps the area was given? With only 2 pieces of information, we can't go further.

**triangle measurements**

Trying very hard to visualize a triangle that has a "top length" and a "lower length". You appear to give the length of 2 sides, which is not enough information to find anything else.

**angle measurements HELP ME PLZ QUICKLY!!!**

Yes, it is right-angled triangle. I thought you had answered A) and used "a" as your answer. Since you don't use any capitals in your sentence, and use "no" instead of "know" etc, it was easy to mis-interpret your answer. Your statement : I th...

**angle measurements HELP ME PLZ QUICKLY!!!**

yes, you are wrong I don't know how much more of a hint I could have given you. 1. I ruled out your choice with a reason for doing so 2. I gave you a very blatant hint !

**angle measurements HELP ME PLZ QUICKLY!!!**

An acute angle is an angle less than 90° your triangle has a 90° angle, often called a "right angle" Do you wish to rethink your choice? Aghast at : I no what this triangle would look like thought u should no!

**Math**

monthly rate = .0575/12 = .004791666.. n = 12(12) = 180 P ( 1 - 1.00479166..^-180)/.00479166.. = 250000 I get P = $ 2076.03

**math**

using the formula x = (-2 ± √(4 - 4(3)(2) )/6 = (-2 ± √ -20)/6 = (-2 ± 2√5 i )/6 = (-1 ± √5 i )/3

**bearings**

for intersection , use substitution in the 2nd equation 2x + 3y - 21 = 0 2x + 3(4x-7) = 21 2x + 12x - 21 = 21 14x = 42 x = 3 y = 4(3) -7 = 5 so we have the line going through (3,5) and (-2,8) slope of line = (8-5)/(-2-3) = -3/5 using (3,5) y-5 = (-3/5)(x-3) times 5 5y - 25 = -...

**Pre-Cal**

what about it? here is a picture of it http://www.wolframalpha.com/input/?i=y%3D%281%2F2%29cos%284%28t-6%29%29%2B6

**math**

Wow, 17% interest from a savings account ? anyway .... P( 1 - 1.17^-20)/.17 = 250000 .. P = $57, 309.99 this might seem unreasonably high, but remember the interest rate is unreasonable, As a matter of fact his fund will earn .17(250,000) or $42,500 in interest the first year,...

**Math**

This time you want future amount i = .065/52 = .00125 P( 1.00125^312 - 1)/.00125 = 15000 ... P = 39.34 weekly payment is $39.34

**Math**

see same question in first of "Related Questions" below

**Math**

Car payments are usually calculated using compound interest. monthly rate = .07/12 = .005833333.. let the payment be P P( 1 - 1.0058333^-60)/.0058333 = 14000 P = 14000/50.50199.. = $277.22

**Math**

P(1.02)^20 = 5500 P = 5500/1.02^20 = 3701.34

**math**

if he knows the side to be x f(x) = x^2

**Math**

d(t) = 250 - 100t when t = 0 , d(0) = 250 ---> (0 , 250) when d(t) = 0 250 - 100t = 0 -100t = -250 t = 2.5 ----------------> (2.5 , 0) the d(t) intercept is 250 (just like the y-intercept of y = mx + b) the t intercept is 2.5 meaning: at the beginning the plane was 250 m...

**Algebra 2**

looks like y = (1/3)x , so you might call 1/3 as the constant of variation.

**Calculus**

After t hours, ship A has traveled 20 t km ship B has traveled 25t I sketched a right-angled triangle with legs 120-25t and 20t let D be the distance between them , making D the hypotenuse D^2 = ((120- 25t)^2 + (20t)^2 at 8:30 , t = .5 D^2 = 11656.25 D = 107.964.. 2D dD/dt = 2...

**Algebra1**

given: a = 3 term(33) = a+32d = -253 32d = -256 d = -8 sum(33) = (33/2)(first + last) = (33/2)(3 -253) = -4125

**maths**

still can't read what you are typing.

**calculus**

x ' (t) = 9t^2 - 81t + 162 so objects are "speeding up" when x ' (t) > 0 and slowing down when x ' (t) < 0 Consider the zeros of the expression 9t^2 - 81t + 162 = 0 t^2 - 9t + 18 = 0 (t-3)(t-6) = 0 t = 3 or t = 6 so the t of the vertex would be half...

**maths**

check your typing, I can't make out what you are saying.

**Math**

Did you want Maximum profit ? find the vertex of your parabola the x of the vertex is -b/(2a) = -1.4/(2(-.02)) = 35 days p(35) = 1.4(35) - .02(35)^2 - 20 = 4.5 whatever units

**math (SIMPLE INTEREST)**

repeat steps I showed you in your previous post (5 and 1/4 years = 5.25 years , or use 21/4 years )

**math (SIMPLE INTEREST)**

I = PRT = 20000(.11)(4.5) = 9900 so amount = 20000+9900 = .... (4 years, and 6 months = 4.6 years)

**algebra**

let's take the first 3 points and find the equation of the plane containing them direction vector #1: (-3,2,2) direction vector #2: (1,2,1) normal to these , take the cross-product = (-2, 5, -8) or (2, -5, 8) in the opposite direction equation of plane is 2x - 5y + 8z = c ...

**math**

Their normals are (1,4,-1) and (5,-3,-7) respectively clearly they are not parallel, or one of the normals would be a multiple of the other nor are they coincident let's look at their dot product: (1,4,-1) . (5,-3,-7) = 5 - 12 + 7 = 0 So they are perpendicular or orthogonal.

**Physics waves- check answer please**

in air , v = 331.4m/s + 0.606m/s/degree celsius times T = 331.4 + .606(30) = 349.58 m/s time to travel 1.2 km = 1200/349058 = 3.4327 seconds in water: time = 1200/1498 = .801 seconds time difference = 3.4327 - .801 or 2.63 seconds for yours, ok, so far, but you have not yet co...

**math**

Something is sightly off mathematically 7/10 + 1/5 + 1/6 > 1 some must have arrived by more than one method. (insufficient data or bogus question)

**math**

more by car than foot = 7/10 - 1/6 = "How many fewer came by foot? " = 1 - 7/10 - 1/5 = assuming they came by one of those 3 ways.

**probability**

at most 5 dots --> 2 , 3, 4, 5 dots 11, 12, 21, 22, 23, 32 ---> 6 ways showing odd number of dots: 3, 5, 7 , 9 , 11 {12, 21, 23, 32, 43, 34 , 54, 45 , 65 , 56} so we want {at most 5 dots} AND {showing odd sum} = {12, 21, 23, 32} or 4 ways prob(stated event) = 4/36 = 1/9

**math**

solve: 5000(1.07)^n = 10000 1.07^n = 2 log both sides log 1.07^n = log 2 n log1.07 = log2 n = log2/log1.07 = appr 10.24 It will take appr 10 years

**Math (Number Theory)**

... = (1+n)+(1+n)+(1+n)+... for a total of n/2 such binomials = (n/2)(n+1 or n(n+1)/2 or (1/2)(n)(n+1) or (n^2 + n)/2

**Math**

That's better. multiply each term by 12 , the LCD 6x - 4 = 3x 3x = 4 x = 4/3 you are correct.

**math**

Proof of my answer: now ----- 3250 end of 1st year: 3250(1.06) = 3445 end of 2nd year: 3445(1.06) = 3651.70 end of 3rd year: 3641.70(1.06) = 3870.80 >> as I had before suppose they did 3250(1.06)3.5 = 3985.23 which is one of the choices, BUT contradicts the concept of &q...

**math**

Trick question? Since the compounding is annually, the amount at 3.5 years is the same as it was after 3 years amount = 3250(1.06)^3 = 3870.80

**Math**

you have a geometric series, where a = 6 , r = -4 I suspect you have a typo. S(1) to me means the sum of 1 term that would simply be 6

**calc**

y^3 = 16x^2 when x = 4 y^3 = 16(256) y = 16 3y^2 dy/dt = 32x dx/dt sub in our values 3(256) (-1) = 32(4) dx/dt dx/dt = -768/128 = -6

**Math**

You have no right side of an equation. There was no equation to solve. Retype your question please

**Math**

Write fractions this way: x/2 - 1/3 - x/4 LCD = 12 6x/12 - 4/12 - 3x/12 = (3x - 4)/12 Your answer makes no sense. (It doesn't even have an x term)

**Math**

2 = 1( 1.0275)^n log 2 = n log 1.0275 n = log2/log1.0275 = ....

**Math question**

Did you notice that each term is half of the previous one? Which type of sequence matches that property?

**Inverse Trig**

for both cases, since for any -π/2 < y < 0 the sine will be negative, we only have to concern ourself with angles in the first quadrant. so if y = arcsin (√3/2) then y = π/3 ( I know sin 60° = sin π/3 = √3/2 ) and for the second one y = ...

**Inverse Trig**

look at the sine curve, it is zero, or crosses the horizontal axis at 0 , ±π , ±2π .. or in general kπ , where k is an integer.

**Inverse Trig**

since sin(?) and arcsin(? are inverses of each other, arcsin( sin (6π) ) = 6π , but that is beyond your stated boundary. so arcsin(sin 6π) = arcsin 0 = 0 , π , 2π

**Math**

Each hour is equal to 30° or π/6 radians So to go from 3:00 to 5:00 would take 2π/6 or π/3 the arclength = rØ = 6(π/3) or 2π inches = appr 6.28 inches or circumference = 2π(6) = 12π the time from 3:00 to 5:00 represents 1/6 of a ro...

**Math**

add them: 17x = 16 x = 16/17 back in 1 9(16/17) + 2y = 8 2y = 8 - 144/17 y = -4/17 they intersect at the point (16/17 , -4/17)

**algebra**

centre would be the midpoint of the the two given points, which would be C(-3,3) so the equation is (x+3)^2 + (y-3)^2 = r^2 plug in one of the points given to find r^2

**GRAPHING HELP**

x = − 1/3^2+4 is a vertical line , (I don't see a y value) must be a typo

**alg.**

for y = ax^2 + bx + c the x of the vertex is given by -b/(2a) once you have that x, sub it back into the original equation to find the corresponding y of the vertex.

**math**

look below at the first of "Related Questions", Steve gave an answer to the same question.

**trigonometry**

3 sinØ = 1.5 , 0 ≤ Ø ≤ 4 sinØ = 1.5/3 = .5 the sine is positive in I or II Ø = π/6 or Ø = π - π/6 which is 5π/6 the period of sinØ is 2π, so adding another 2π to π/6 yields 13π/6 , wh...

**math**

If you are first of all looking for the integral of v=25sin50πt it should be -1/(2π) cos(50πt) + c the rest is physics, about which I know very little . from there the mean is usually found by ... 1/(10-0) ( -1/(2π) cos (500π - (-1/2π cos(0) ) = 1...

**math**

If it is right-angled, then x^2 + x^2 = (x^2)^2 x^4 - 2x^2 = 0 x^2(x^2 - 2) = 0 x = 0 , which is no good or x^2 = 2 x = √2 then the area = (1/2)(x)(x) = 1/2 (√2)^2 = (1/2)(2) = 1 square unit

**math**

7% per month ???? in the middle ages , they would burn folks on the stake for rates like that. It was called usury. anyway .... interest on balance = .07(1734.50) = $121.42 actual repayment from loan = 165-121.42 = $43.59 Balance next month = 1734.50 - 43.59 = $ 1690.92

**math**

prob(red, then blue) = (4/10(5/9) = 20/90 = 2/9 you do the rest

**math**

actually it is much bigger than that 1st place --- 10 different runners 2nd place ---9 3rd place ---8 ... last place --- 1 runner number of ways = 10*9*8*7*...*2*1 = 3,628,800 What your 10*9*8 is is the ways 1st, 2nd and third place could happen

**Math**

you have an arithmetic series: 4 + 6 + 8 + ... Easy to see that after 3 days, you will have already spent 18 hours, so you need one extra day of only 2 more hours to have a total of 20 hrs.

**math**

and g(x) is .... ??

**math**

current number of rooms = 30 current price per room = 12 let the number of additional increases of $1 be n numbers of rooms rented = 30 - 2n number of rooms not rented = 30 - (30-2n) = 2n price per room = 12 + n Profit = (12+n)(30-2n) - 4(30-n) - 1(2n) = 360 + 6n -2n^2 - 120 +...

**Trig Maths**

or from Steve's 5√3 sinθ = 21 cosθ sinØ/cosØ = 21/5√3 tanØ = 21/5√3 , and the tangent is + in I and III Ø = 1.18 in I or Ø = π + 1.18 = 4.32 in III

**Math**

number of 50's ---- x number of 10's ---- 2x number of 5's ----- 2(2x) = 4x Now, consider the value of those notes to form your equation. 50x + 10(2x) + 5(4x) = 1080 50x + 20x + 20x = 1080 90x = 1080 x = 12 we defined 10's as 2x so she has 2(12) or 24 $10 bills...

**math**

x + x(.08)(3) = 15000 1.24x = 15000 x = 12096.77

**math**

8. amount invested at 12% -- x amount invested at 8% --- 3000-x .12x + .08(3000-x) = 3200 times 100 12x + 8(3000-x) = 320000 4x = 29600 x = ??? (more than she invested!!!!) I think you have a typo, should the interest be RM 320 ?? That way it works out nicely, change the 3200 ...

**Math**

|3x+1|-|2-x|<3 Formal Way: Case 1 |3x+1| < 3 + |2-x| 3x+1 < 3 + |2-x| AND -3x-1 < 3 + |2-x| |2-x| > 3x-2 AND |2-x| > -3x-4 which leads to a) 2-x > 3x-2 OR -2+x > 3x-2 -4x > -4 OR -2x > 0 x < 1 OR x < 0 ----> x < 1 b) 2-x > -3x - 4 O...

**maths**

3x = 6y looks trivial, just divide by 6 y = (3/6)x + 0 y = (1/2)x + 0 for equations that contain all 3 terms, there is a two-step process 1. move all terms except the y term to the right side of the equal sign ----> 2y = 6x - 2 2. divide each term by the coefficient of the ...

**math**

a = 3 , d = 6 term(n) = a + (n-1)d 123 = 3 + (n-1)(6) 120 = 6n - 6 126 = 6n n = 126/6 = 21 there are 21 terms

**naths**

midpoint is (4,5) y - 5 = 2(x-4) arrange it any way you have to

**Math**

log2+ 3log1 = log 2 + 3(0) = log2 you SHOULD know that log 1 = 0

**maths**

from the 2nd: y = 5-x plug into the 1st: 2(5-x) - 5x = 3 I am sure you can finish that

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