Answers by visitors named: Nonetheless

Let half the journey, time wise, be x hours. Thus the full journey time is 2x hours. Avg speed = total distance/total time 80 = total distance/2x Thus total distance=160x km For the first part of the journey, his distance travelled was speed x time, or 50...

8 years ago

If the mean = 6.6, then the probability density function is: f(x) = (1/6.6)e^(-x/6.6) P(x>10) = 1- int_{0}^{10} ((1/6.6)e^(-x/6.6))dx = e^(-10/6.6) ~ 0.2198 P(4<x<8) = P(x>4) - P(x>8) = e^(-4/6.6) - e^(-8/6.6) ~ 0.2479

8 years ago

The smaller barrel holds 336 L, but it is only 5/6 full. 1/6 of 336 is 336/6 = 56 L So 5/6 of 336 is 5 times this amount: 5 x 56 = 280 L of apple cider in the smaller barrel. The 280 L is now poured into the larger barrel. This 280 L fills 4/9 of the barr...

8 years ago

Elevation in this case is a measure of how high a location is relative to sea level. It's a good idea to draw a vertical line to model this problem, and then put a tick mark on the middle of the line to represent an elevation of 0 ( sea level). Now put a...

8 years ago

Let x be the estimated number of the 3000 people who are attending their first concert. 35/200 = x/3000 To isolate x, multiply both sides by 3000: 3000(35/200) = 3000(x/3000) 525 = x

8 years ago

Change in angular velocity is 3000 rpm - 1200 rpm = 1800 rpm. This happens over a period of 10 seconds, or 1/6 of a minute. Angular acceleration = change in angular velocity/change in time = 1800/(1/6) = 10800 rpm^2 Number of rotations made during this ti...

8 years ago

The upper quartile is the median of just the upper half of the data. Just like the median, its value depends on whether you have an even or odd number of pieces of data. First place your data in ascending order: 5, 8, 10, 20, 25, 30, 35, 40, 45 You have 9...

8 years ago

efficiency = work output/work input = 241 J / 272 J = ? (Mult. Answer by 100 to convert to %)

8 years ago

Force diagram: Fn pointing up Fg pointing down Fa pointing right/upwards at 32 deg. to horizontal Fk pointing left Vertical forces equation (up is positive): Sled is not moving up or down so: Fn + Fg + Fa = 0 Fn + (-9.81)(22) + 50 sin 32 = 0 Use the above...

8 years ago

First find Fn on the 2 kg mass. Net force along an axis perpendicular to the ramp surface is 0, so: Fn + Fgcos40 = 0 Fn + (-9.81)(2)cos40 = 0 Solve for Fn Now work out net force of system: Fa + Fgsin40 + Fk = 9.81(1) + (-9.81)(2)sin40 + (0.3)(Fn) Plug in...

8 years ago

Google the specific heat of silver: 0.2386476 J/gC Convert kg to g: 14.3 kg = 14300 g Google the melting point of silver: 961.8 C Thus the required temperature change is 961.8 - 44 = 921.8 C 0.2386476 J/gC x 14300 g x 921.8 C = _______ J of heat

8 years ago

1) From a Table of Water Vapour Pressure (in kPa), find for water at 25 C, pressure = 3.17 kPa. 105.3 kPa - 3.17 kPa = 101.83 kPa 2) gas law constant, R = 0.0821 L-atm/mol-K Convert other units to match those used in R: 101.83 kPa/101.325 kPa/atm = 1.005...

8 years ago

What is the velocity of the water? Also, is the swimmer at 45 deg such that they are swimming against the current or with the current?

8 years ago

This resource may be helpful: Search: Gas Law Problems- Combined Gas Law Chemteam comes up first - worksheet with solutions to some similar problems

8 years ago

The temperature must be in deg C if using water's specific heat capacity of 4.18 kJ/(kg*C). Heat absorbed by water = 3kg * 4.18 kJ/(kg*C) * (212 C - 15 C) = 2470.38 kJ Heat created by 2.5 kW kettle in 9.5 minutes = 2.5 kJ/s * (9.5 min * 60 s/min) = 1425 k...

8 years ago

Search "z=f(x, y) is defined implicitly by an equation of form F(x, y, z)=0" The second result, "Implicit Differentiation..." (a pdf) will be helpful.

8 years ago

Set h to 0: 0 = -16t2 + 144t Factor to find the t-intercepts. These are the times when the height is 0 ( i.e. when rocket is on ground).

8 years ago

F= qvB = (3 x 10^-12 C)(300 m/s)(8.0 x 10^-5 T) = ?

8 years ago

Let the harbour be point H. Is your 47 deg <HAB or <HBA? It makes a difference.

8 years ago

This is a binomial distribution. A tree diagram or 2^n will give you the sample space of 32. Then: 1. P(X>1) = 1 - P(X=0) - P(X=1) = 1 - 1/32 - 5/32 = ? 2. Mean = np = (5)(0.5) = ? 3. SD = sqrt(np(1-p) = ?

8 years ago

After 3 tosses, you can have HHH, HHT, HTH, THH, HTT, THT, TTH, or TTT (8 outcomes). Now list your products. E.g. For HHH: (#H)(#T) = (3)(0) =0 Work out the rest of the products, and put how many are > 1 over 8. This is a binomial distribution, so: Var(X)...

8 years ago

Let x be the number of puppies in the litter. Cost per puppy = 120/x Revenue per puppy = 120/(x - 4) Profit per puppy = 5 Profit = Revenue - Cost Plug in the above expressions and solve.

8 years ago

Light pole height/light pole shadow length = Laura's height / Laura's shadow length x / 15 = 5 / 6 x = ?

8 years ago

Your question is of this type: Integral of du / (a^2 + u^2) = (1/a) tan-1(u/a) +c

8 years ago

Your equation needs brackets aroun vf - vi. vf = 285.1km/h vi = 155.0 km/h t = 11.5 s Plug them into your equation and solve for a.

8 years ago

Prior to subbing speeds into your equation, make sure you first convert km/h to m/s.

8 years ago

Substitute 1.2 for x and solve for y: 8(1.2) - 5y = 14 9.6 - 5y = 14 -5y = 4.4 y = -0.88

8 years ago

First convert 40 km/hr to m/hr: 40 km/hr x 1000 m/km = 40 000 m/hr Now convert 40 000 m/hr to m/s: 40 000 m/hr / 3600 s/hr ~ 11.11 m/s acceleration = change in velocity / change in time = (11.11 m/s - 0 m/s) / 10 s = ?

8 years ago

A) LS = cos^4(x) -sin^4(x) = (cos^2(x) - sin^2(x)) (cos^2(x) + sin^2(x)) = (cos (2x)) (1) = cos (2x) = RS B) There must be a typo in your second problem. If you plug an actual angle into it, LS is not equal to RS.

8 years ago

Heat lost = Heat gained Let x be the final temperature of the mixture. (100)(60 - x)(4.184)=(200)(x - 30)(4.184) Solve for x

8 years ago

Based on the sampling of 25, we can estimate that the chance of drawing an orange ball is 7/25. Let's say we did a sampling of 50. This tells us that, since 50 is 2 x 25, we could estimate that the chance of drawing an orange ball is then 14/50. Some stud...

8 years ago

This forum doesn't display diagrams. However, since your question specified A = 5 and B = 8, I assume your first two answers are correct. However, more description is required to determine if your other answers are correct.

8 years ago

For a chi squared calculator, search: socscistatistics tests chi square 1st result

8 years ago

Null hyp: They are not independent. Alt hyp: They are independent.

8 years ago

For y=4x, draw a straight line passing through (0,0) and (1,4). For y=(1/4)x, draw a straight line passing through (0,0) and(4,1). y=8/x is a reciprocal function. For just the first quadrant, sketch a smooth curve passing through (1,8), (2, 4), (4,2), and...

8 years ago

Rearrange: (x^2 + 6xy + 9y^2) - (25m^2 -40mn + 16n^2) Factor as perfect squares: = (x +3y)^2 - (5m - 4n)^2 Factor again as difference of squares: = (x + 3y + 5m - 4n)(x + 3y - 5m + 4n)

8 years ago

Let x be the base length. Let y be the altitude length. x + y = 55 --> y = 55 - x ....eq1 x^2 + y^2 = 60^2....eq2 Sub eq1 into eq2: x^2 + (55 -x)^2 = 60^2 Solve for x, and then use eq1 to solve for y.

8 years ago

Is D meant to represent the midpoint of side MN (i.e. where the median from O touches it)? If so, angle ODN is obtuse, so can't be 40 degrees. Perhaps a typo?

8 years ago

Constant velocity means net force is 0. Fa + Fk = 0 Fa + (120 kg)(-9.81 m/s^2)(0.2) = 0 Fa = 235.44 N

8 years ago

With replacement: (13/52)(13/52)(13/52)(13/52) =(1/4)^4 = ? Without replacement: (13/52)(12/52)(11/52)(10/52) = ?

8 years ago

4 terms between means 5 "jumps" from 15 to 87. 87 - 15 = 72 d = 72/5 = 14.4 15, 29.4, 43.8, 58.2, 72.6, 87

8 years ago

Angular acceleration of flywheel: alpha = (120 rad/s - 0 rad/s)/14 s alpha ~ 8.571 rad/s^2 Moment of inertia of flywheel: I = mk^2 I = (50kg)(0.3 m)^2 I = 4.5 kg*m^2 Torque applied by motor: Ta - Tf = I*alpha Ta - 0.07 N*m = (4.5 kg*m^2)(8.571 rad/s^2) Ta...

8 years ago

Thanks for catching the denominator errors. (Drawing can mean either with or without replacement; depends on the textbook, country, etc. so always good to clarify)

8 years ago

Yes, that works. Just be sure to use lowercase "y" in your equation to match the variable in your sentence.

8 years ago

You could use volume = pi*r^2h

8 years ago

P = 15/20 = 3/4 Since 3/4 of the experimental group bought roses, we can estimate that 3/4 of the larger group would do so too. 3/4 * 120 = ______ people

8 years ago

Since the child is blonde, and blonde hair is recessive, the child has two blonde hair genes, bb. In order for this to happen, the child would need to have inherited a "b" from each parent. The parents can't be bb because that would mean they too were blo...

8 years ago

What have you tried? A quick search of force between two charges gives you Coulomb's Law: F=(k*Q1*Q2)/d^2 Make sure your charges are in Coulombs and d is in metres.

8 years ago

As a start: Because she is making regular deposits to save money, at the same frequency as compound interest is being accrued, this is a standard future value annuity. Use the future value annuity formula, taking care about which variable the question is...

8 years ago

Right

8 years ago

Do a search on: "A race car is initially travelling at 75 mph at point A as it enters the S-curve shown." First result, Kinematics of Particles - Curvilinear Motion Has this question, with a video and further explanations as to how to go about solving it.

8 years ago

PV=nRT Since your volume and pressure are provided in L and atm, respectively, you can use the version of the gas law constant that has these units: R= 0.082057 L*atm/(K*mol) Now convert temperature from deg C to deg K: T=273 K + 30 C = _____K Substitute...

8 years ago

PV=nRT V,R, and T remain the same before and after the leak. Let the combined moles of He and Xe be n1 before the leak, and n2 after the leak. Before the leak: n1=874V/RT Because n1 is equally split between He and Xe, the mole fraction of n1 that is He is...

8 years ago

Correction: under "Before the leak:" , 437V should be 437V/RT

8 years ago

A speed of 166.35 mph means he travels 166.35 miles in one hour. If he can travel this many miles in one hour, how far can he travel in 5 hours?

8 years ago

8 years ago

You are right about the negative answer. Assuming the stone is thrown straight up, d=(10 m/s)(10 s) + (1/2)(-10 m/s^2)(10 s)^2 d= -400 m It coud be possible if the stone were thrown straight up, over a deep pit. It would mean that the stone was located 40...

8 years ago

A better description is needed, since this forum doesn't display images.

8 years ago

Populations normally grow exponentially, so transforming your data with logarithms should work. What base did you use? You might also try the natural logarithm.

8 years ago

Yes.

8 years ago

It looks good most of the way; just a small error near the end: First work out -2.1 + 13.13, and then divide the result by 0.24. Same correction needed for your second solution.

8 years ago

On the first line, the 2 should get distributed only across the first set of brackets: (2x+4)(x+2)-4=28 Work it down again similar to what you did, then get all your terms to one side of the equation. Solve by factoring (if possible) or by using the quadr...

8 years ago

Looks like you used 500 as your principle, P, but 500 is your interest, I. Use I=Prt and solve for P.

8 years ago

"7 more than twice Jenny's age" means 2 times Jenny's age plus 7

8 years ago

Time required to stop: theta = (1/2)(w0 + w)*t 163(2π) rad = (1/2)(30(2π) rad/s +0 rad/s)*t t ~ 10.87 s Angular acceleration of wheel: = (0 rad/s - 30*2π rad/s) / 10.87 s ~ -17.3 rad/s^2 Required slowing torque: T = I * alpha = (0.015 kg*m^2)(-17.3 rad/s^...

8 years ago

Let d be the distance she drives to school, in km. Let t be the difference between the time school starts and the time the teacher leaves for school, in hours. 5 minutes = 1/12 hours 4 minutes = 1/15 hours d=s*t d=24 * (t+1/12).....eq1 d=(1.25)(24) * (t-1...

8 years ago

Let x be the time running, in minutes. Then 2x, 4x, 8x, and 16x are the times on the bike, truck, car, and helicopter, respectively, in minutes. Total time = 2 hours and 4 minutes = 124 minutes x + 2x + 4x + 8x + 16x = 124 x = 4 minutes 4 minutes = 240 se...

8 years ago

That's correct. Then, 2x^2+8x-24=0 2(x^2+4x-12)=0 2(x+6)(x-2)=0 x = -6, x = 2

8 years ago

The coefficient of determination is always positive.

8 years ago

The independent variable is the one that you are able to change - the mass of the car. The dependent variable is distance, because we are seeing what happens to it as a result of changing the car's mass. Controls: 1. Starting position 2. Path 3. Some opti...

8 years ago

List all the possible outcomes: 1, 2, 3, 4, 5, 6 There are 6 of them. List all the even numbers: 2, 4, 6 There are 3 of them. So the chance of rolling an even number is 3/6, or 1/2. Use similar logic for a number less than 5. ( it wasn't clear from your q...

8 years ago

The 4 possible outcomes are HH, HT, TH, TT. So theoretically, HH should occur 1in 4 times. 1/4 = x/20 x = 5 So why is it actually 2 in 20 when theoretically it should be 5 in 20? One reason is that theoretical probabilities gain more accuracy with larger...

8 years ago

Let x be the number of years after which A and B have the same amount of money. 500 + 50x = 500(1.05)^x Work out x with a table of values or a graphing calculator to get x=0 (doesn't count) or x ~ 27 years.

8 years ago

"E in terms of M" is like "y in terms of x", so let M be the independent variable and let E be the dependent variable. Thus we have two points on this linear graph: (25, 40) and (125, 280) Use m=(E2 - E1)/(M2 - M1) to get the slope. Sub slope and one of t...

8 years ago

6c1 * 8c2 = 6 x 8 x 7/2 = 168

8 years ago

The shape does matter as the question asks for the rate in cubic ft/ min. If this were a cylinder, we could express this rate of change of volume in terms of t as: Pi*r^2 * dd/dt cubic ft/min. However, an inverted cone shape does not make sense for this q...

8 years ago

The difference between -5 mC and -6.6 mC is 1.6 mC. Half of this amount, 0.8 mC, is how much charge the -6.6 mC body must give to the other body so that they are equally charged. 0.8 mC x 6.24150975⋅10^15e/mC = _______ electrons

8 years ago

(22/50)(100) = ____ %

8 years ago

Great question! Student can solve by using y in terms of x and then verify their answer by using x in terms of y. Also like Reiny's elegant solution.

8 years ago

Yes, good work!

8 years ago

(2/3)(2x + 19) - 11 = 95 x = _____

8 years ago

The file is just photo.gif (the rest is the path). The type of link is an image link.

8 years ago

Let x be the magnitude of the first force (and the larger force). Let y be the magnitude of the second force. Greatest resultant happens when they act in the same direction: x + y = 29 Least resultant happens when they act in opposite directions: x - y =...

8 years ago

Angular acceleration: = change in speed/ change in time = [(5500 - 9000)*(2pi/60) rad/s] / 7.5 s = -48.869 rad/s^2 T = angular acceleration*moment of inertia = ______ N*m

8 years ago

AD is 30. (Add AK and KD, both given) Since AB = CD, this is an isosceles trapezoid. Thus we have symmetry: Given that BK is perp. To AD with AK = 10 We can draw CL perp to AD; and by symmetry, LD will also be 10. This leaves KL as 10 ( given that KD is 2...

8 years ago

You pulled black 7 times out of 20. Let x be estimated number of black cubes in the bag of 200 cubes. 7/20 = x/200 x = ____ Use a similar process for estimating The number of red cubes in the bag.

8 years ago

(3/5)(2/4) = ?

8 years ago

Resistance is proportional to length, so it will also increase by 20%.

8 years ago

Take the smallest 5 digit number, 10000, subtract 23, and divide the result by 36 - this gives 277.14, so the smallest integer multiplier we can use on 36 to get a five digit number is 278. Now use a graphing calculator (or Excel spreadsheet) to generate...

8 years ago

a) P3 initially accelerating in the + x direction means the net force on P3, in the y direction, is 0: [(kq1q3)/(r13^2)]sin45 + [(kq2q3)/(r23^2)]sin53.36 = 0 Divide out common factors k and q3, and sub in known quantities to solve for q2: [(70.5 * 10^-6)/...

8 years ago

dd/dt has units of ft/min. The question asks for flow rate in ft^3/min....

8 years ago