# Posts by MathMate

Total # Posts: 11,748

**Trig laws**

Given Area of triangle ABC=7.52 m² ∠B=40° c=6 m Need to find a. We can use the trigonometric formula for area, namely Area=(1/2)ac(sin(B)) which can be solved to give a=(2*Area)/(c*sin(B)) =(2*7.52)/(6*sin(40°))

**Probability**

The sample space consists of 24=16 outcomes. A. more tails than heads: 1. exactly three tails: TTTH TTHT THTT HTTT 2. exactly four tails: TTTT So calculate the probability. You can try in a similar way to solve the second part.

**Probability**

Use the relation: P(A∪B)=P(A)+P(B)+P(A∩B) and solve P(A) Note: ∩ = & c a p ;

**Probability**

Choosing r unordered sets from n is given by nCr = n!/((n-r)!r!)

**Compute**

Missing information. You'll need three pieces of information to find the fourth in the following relation: P(A∪B)=P(A)+P(B)-P(A∩B)

**Probability**

7P5, where nPr=ordered set of r items chosen from n. =n!/(n-r)!

**Trig laws help**

Use cosine law: a²=b²+c²-2bc(cos(A))

**Probability**

If P(B)=p, then P(B')=1-p

**Physics**

Friction or not, the work done is W = F.D (scalar product) If force is applied in the same direction as the displacement, then work done is simply the product of the magnitude of the force and the distance travelled, namely W= 21N*3.3m = 69.3 J

**physics**

Not really. For an object which accelerates from rest, the variation of speed with time is given by: final velocity=initial velocity + acceleration * time = 0 + 10 m/s² * 2 s =20 m/s (note how the units cancel to give m/s)

**Physics**

Total distance = 120 km For an average of 60km/h, total time available = 120/60=2 hours Distance left = 120-30=90 km Time left = 2-1 = 1 hour What is the speed need for the remaining distance?

**Algebra/Steve**

Mary Ann, Hope your surgery goes well and have a speedy recovery.

**math**

largest 9 digit number without repeating: - must have 9 digits 999999999 - must use different digits - zero excluded (to have the largest number) - must be in reverse order starting from 9 987654321 - must be even, so invert last two digits Say 987654321 987 654 312 So what is...

**physics**

The fundamental frequency of a wave along a taut string is f=√(T/m)/(2L) T=tension in N m=mass of string in kg/m Since the fundamental mode of vibration consists of only half a wave, the wave velocity is f*2L, or λ=√(T/m). Here N=139 N, m=0.0036 kg/m v=&...

**math**

fraction of tank filled by A per minute = 1/3 fraction of tank filled by B per minute = 1/6 Fraction of tank filled in first two minutes = 1/3+1/6 = 1/2 Can you take it from here?

**Physics :)**

You're welcome! :)

**Physics**

Yes, but only in the first part. m was inadvertently omitted in the second part, my apologies. k=2mgh/x²

**Physics**

Initial velocity=√(2gh) h=height reached. Spring constant=k compression = x = 0.125m Potential energy=(1/2)mv²=mgh =(1/2)kx² solve for k in (1/2)kx² = mgh k=2gh/x²

**physics**

Assuming no air resistance, and PE at bottom of tower to be zero, then At the maximum height, mgh=(224mg+m(80²)/2 h=224+80²/(2g) [assume g=32.2 '/s² =224'+99.38' =323.38' At bottom of tower, mv²/2 = m(80²)/2+mg(224) solve for v to get v...

**venn diagram**

If 10 failed in both, that means 130-10=120 passed at least one subject. Since 85 passed math, 60 passed science, there are 145 passes from 120 students. We conclude that 145-120=25 passed both. Hence (b) 120-25=95 passed (or failed) exactly one subject. For (a), 60 passed ...

**Maths**

Q1. HCF and LCM could be found using 1. factoring 2. Euclidean algorithm Q2. Let H(p,q) denote the HCF of positive integers p,q, and L(p,q) denote the LCM of p,q, then H(p,q)*L(p,q)=pq

**Physics**

26 m/s is about 10% from stalling for a Cessna 150. With a tailwind, the airspeed does not change, but it will be added to the ground speed ("actual velocity"). With a headwind, the airspeed does not change either, but it will be subtracted from the ground speed. ...

**physics**

Explained with the help of diagrams here: http://web.physics.ucsb.edu/~lecturedemonstrations/Composer/Pages/64.42.html

**Math - correction**

*1,499,999

**Math**

149,999 is the greatest integer that may be rounded to the nearest million.

**Physics**

It will gather speed because of acceleration due to gravity. The acceleration is g=9.8 m/s²

**Physics-half way fin.**

I get 62.5 using g=9.8

**mathematics**

The same as X or Z.

**Physics**

Kinetic energy is proportional to mass and also varies with the square of the velocity. So the new kinetic energy =(5*105 joules)*(114/50)²

**ap physics**

Magnitude:use Pythagoras theorem (note 90° between the teammate and the green). Angle (from point of view of teammate) = atan(120/60)+75° West of south since the golfer is at 75° west of south from the point of view of the teammate.

**Physics**

Assuming both sides of the canyon are at the same elevation, then use the range equation: range = vi²sin(2θ)/g 6.5=vi²sin(2*9.45°)/9.8 vi=sqrt(6.5*9.8/sin(18.9°) =14.0 m/s

**Physics-check plz**

All correct!

**physics**

vi=-30m/s a=-g=-9.8 m/s² vf=vi+at =-49.6 m/s Height =average velocity*time =(-30-49.6)/2 * 2 sec =-79.6 m The negative sign means that the rock is lower than the initial position.

**physics**

Ignore air resistance => no energy loss PE at 40.0 m = mgh = 40*9.8m J =392 J PE=KE=(1/2)mv² vi=sqrt(2gh)=sqrt(2*9.8*40) = 28 m/s Time = 2 * time it takes to reach highest point = 2*(28/9.8) = 5.71 s

**physics**

vf=vi+aΔt =0-9.8*3 =-29.4 m/s Distance =average velocity*time =-14.7*3 =-44.1 m

**Survey of Mathamtics**

Calculate the effective interest, i.e. actual performance over a year: Local bank = (1+0.065/12)^12 =1.066971852002543 Credit union = (1+0.0675/2)^2 = 1.0686390625 So the credit union pays a little more.

**engineering economics analysis**

You cannot, directly. You can always try to put a link, or copy and paste.

**college physics**

The signal has to make a return trip, so the total distance is 2*1.5=3m Number of round trips per second = 344/3 = 114.7

**math**

Starting from 102, the minimum number of chicken sandwiches has to be divisible by 8 and 3, i.e. 24, that leaves 78 tunas, etc. So possible combinations may be Chicken/Tuna 24 / 78 48 / 54 72 / 30 96 / 6

**physics**

1. Use substitution x=u-&pi/2; dx=du ∫csc(u-π/2)cot(u-π/2)du =∫csc(x)cot(x)dx =∫cos(x)dx/sin²(x) =∫d(sin(x))sin²(x) =-1/sin(x)+C

**question incomplete**

Please complete the question.

**Physics**

To find the velocity in the last two seconds, we need to first find the time it takes to arrive at the end of the street of 250 length, and assuming uniform acceleration. The distance travelled is given by Δx = vi(t)+(1/2)at² where vi=initial velocity (m/s) a=...

**math please help**

I assume you forgot the parentheses in the numerator, Lim (sin(x)-(x^3/6))/x^5 as x->0 It would be easy to change sin(x) to a polynomial, the limits of which are easy to find. If you expand sin(x) by Taylor's series, you'd get sin(x)=x-x³/6+x^5/120... So the ...

**Math**

Each coin can land heads or tails with equal probability of 1/2. Dropping a coin four times has 2^4=16 possible outcomes. (a) three heads By enumeration: There are four possible outcomes, so the probability is 4/16. THHH,HTHH,HHTH,HHHT. The number of combinations for 3H can be...

**Math**

Calculate the product of the net gain (i.e. gain minus the bet of $3) and the probability of each outcome. Add all the products to get the expectation of the game. Note that the probabilities of all the outcomes must add up to exactly 1.0

**ALGERBRA**

Number of possible combinations of 5 (distinct) numbers out of 30 = 30C5 Probability of winning if n different tickets are bought = n/(30C5) where 30C5 =30!/((30-5)!5!)

**math**

There three ways of choosing 1 girl out of three (3C1) and (5C2) ways of choosing 2 boys out of 5. Total number of ways = (3C1)(5C2) = (3)(10) = 30

**Math**

Assuming all three coins are fair, you could use a probability tree or a table to list all possible outcomes (Ω) and calculate the probabilities accordingly. H=head T=tail All 8 possible outcomes HHH HHT HTH HTT HHH THT TTH TTT You can use the table to answer the above ...

**finite math - answered before**

This (or a similar one) question has been answered before. If you have a follow-up to the answer, please respond to the previous question, or make reference to it. If it is a similar question, then please show your efforts by first studying the previous answer, and attempting ...

**finite math**

This question has been answered before. Do you check your previous posts?

**finite math**

B=bachelor's degree H=high income P(H)=0.105 P(H|B) =P(H∩B)/P(B) =0.215 => P(H∩B)=P(H|B)*P(B) =0.215*0.105 >0 So H and B are not independent.

**finite math**

Is it (a) P(F/E), (b) P(F\E), or (c) P(F|E)? If it is (c), conditional probability, then P(F|E)=0.1/0.4=0.25 (a similar question was answered before)

**finite math**

How many are "succesful picks", and how many in total?

**finite math**

Please refer to your previous batch of questions. An almost identical question was answered completely and explained.

**Physics**

equate PE=spring potential energy (1/2)kx²

**finite math**

Judging from other questions, I am sure you are capable of answering this question.

**probability - question incomplete**

There are three statements and no question.

**finite math**

Do you mean P(F|E), the conditional probability that F happens given that E has happened? P(F|E)=P(E∩F)/P(E)=0.1/0.5=0.2

**finite math**

If at least one has not written, then there are only 5 to consider. p=0.29 q=(1-0.29)=0.71 P(at least one out of 5) =1-P(none out of 5) =1-q^5 =1-0.18 =0.82

**finite math**

is part (a) a given condition or you're expected to calculate the said event?

**finite math**

Assume random selections and outcomes. P(1 snake)=0.94461=p P(2 snakes)=p² P(3 snakes)=p³ ...

**probability**

#of orange balls=2 #of red balls = 5 Total number of balls = 25 P(orange ∪ Red) =P(orange)+P(red)-P(orange∩red) =2/25+5/25-0 =7/25

**probability**

P(E∪F)=P(E)+P(F)-P(E∩F) If E and F are mutually exclusive (ME), then P(E∩F)=0, and consequently P(E∪F)=P(E)+P(F)=0.41+0.47=0.88

**finite math**

Do you use "outcome" to mean elementary events? The elementary events of F are 3,6,7.

**math**

Set up: M=J+2000 J=B-400. L=S+1500 S=443 S=B-60 From the chain of equations, it would be possible to substitute backwards from the known values. Given: S=443 and S=B-60, so B=S+60=? L=S+1500=? J=B-400=? M=J+2000=?

**physics**

Angles of incidence and refraction are angles measured from the normal. If n represents the refractive index between air and the medium, the equation that governs the relationship between them is n=sin(θi)/sin(θr) which gives the value of θr as θr=sin-1...

**statistics**

μ=42 σ=1.5 so Z(38)=(38-μ)/σ Look up a normal distribution table for the probability of exceedingZ(38), which is the same as the probability of not exceeding -Z(38). Post your answer for checking if you wish.

**Stats**

Have you started looking at the question? What are your thoughts?

**Physics**

The force required to produce the acceleration is given by Newton's second law F=ma. If m is mass in kg, a is acceleration in m/s² then force F is in newtons. To this force must be addded the frictional force 740 N to overcome friction. Note: the force unit newton is ...

**Math: Trig**

arcsec(-2) is the same angle as arccos(-1/2) The angle 2pi/3 is correct, so is 4pi/3. Depending on the domain required, you may have to put in both values (for 0-2pi). If that is not the problem, then you have to read carefully the instructions how to answer the question, how ...

**Geometry**

If you just want the area, use Hero's formula: Let p = (a+b+c)/2 = half-perimeter Area = √(p(p-a)(p-b)(p-c)) If it's really the altitude you need, then find each angle using the cosine law: cos(A)=(b²+c²-a²)/(2bc) where a,b,c are lengths of sides ...

**Geometry**

* = 2√(3)b

**Geometry**

Hint: Call the lengths of medians 3b, 3b and 3a. The length of the base = 2√((2b)²-a²) The length of one of the congruent sides = 2√((2b)²-b²) = 2&radc;(3)b

**physics**

F=ma => a=F/m F=-(13.4+14.7) N m=71 kg evaluate acceleration (should be negative)

**Math**

Since it is open ended, only "lateral area" is significant. AL = p*h p=perimeter of base h=height of prism

**physics**

Use the same equation as before: F=(m-ρv)g N where v=volume of the iron object, and v=m/8000 m³ Be sure to convert all values into SI units.

**Algebra II**

Is πn a sequence or is it a function? At the beginning of the question define what πn is to represent?

**Algebra II**

To me, Πn=product of integers from 1 to n, which is equivalent to n!. It evidently is not because the expression would way exceed 1. So please explain what Πn is supposed to represent.

**physics**

Archimedes principle states that the buoyant force equals the weight of fluid displaced. Fresh water has a density of ρ=1000 kg/m³ Sea water from deep in the ocean has a mass density of ρ=1050 kg/m³. Average sea water has a mass density of ρ=1030 kg/m&...

**math**

* Y'∪Z'= YΔZ= {30,40,70,80,90,100}

**math**

When you deal with complements, the first question to ask is do we know the universal set E? Here we assume E=Z (integers) X'∩Y = Y\X = {10,20,40,60,90,100} Y'&cup'Z'= YΔZ= {30,40,70,80,90,100} (X\Z)'={10,20,30}' depending what E equals (Y\Z...

**algebra**

hint: x=1/3

**algebra**

At 8%, she gets RM1200. At 7%, she gets RM1050. Let x be the fraction he invested at 8%, the 1-x is what he invested at 7%. we have x*1200+(1-x)1050=1100 Solve for x.

**Math**

Would you like to calculate lateral surface areas or volumes of solids? Please post an example of what you'd like to calculate.

**math**

If you know the rule between exterior angle θ and the number of sides, n: θ=360/n then 360/(n-1)-360/(n+2)=6 Solve for n, then calculate θ for each polygon. (answer is between 10 and 15, reject negative root)

**physics**

The equation for range is R(θ)=v²sin(2θ)/g Examine the values of sin(2θ) to arrive at the correct ratio .

**Chemistry**

One mole of HCl is required to prepare 1 L of 1N solution. Calculate number of moles (n) required to prepare 200/1000 L of 0.5N solution. Find molecular mass M of HCl in g mass of pure HCl required = nM g Volume of given acid required = nM ÷ (1.18*0.37) g÷(g/mL)

**physics**

What is the question? Need to find the period, T? use T=2π√(L/g) for small oscillations.

**Physics**

The minimum initial velocity will create at least the kinetic energy (1/2)mv² to equal the potential energy gained, mgh, where h is the height difference between the horizontal rod and the cg of the person from the ground. Make assumptions to the value of this difference...

**Physics**

Magnitude: F=ma Direction: see figure.

**physics - insufficient information**

Sorry, wish we could help, but without the figure or a text version of it, we do not know what the given data are.

**physics**

This is a problem of levers which can be solved by taking moments. Three forces are involved, L the left hand, R the right hand, and W the weight of the pole equal to 50N. It is not clear but will be assumed that the cg of the pole is 2.00m to the left of the left hand, as ...

**Physics :)**

You're welcome!

**Physics**

Time (hours) = Distance (km) ÷ Speed (km/h) Divide by 24 to convert into days.

**Physics**

T (period) = time/rev = 20 sec/ 30 rev = 2/3 sec/rev ω(angular speed) =30 rev/20 seconds =30/20 rev / sec =30/20*2π radians / s Velocity =rω =0.008m*ω m/s

**math check**

5P5=5!/(5-5)!=?

**Physics**

Upstream=300 metres/(2-1)=300 s Downstream=300/(2+1)=100 s

**Math**

If you follow the rules of PEDMAS, what you wrote means: a + (b/10) = a - (0.1b^2/a) -b Please confirm if you really mean if(a+b)/10 = (a-0.1b²)/(a-b) Also, post what your answer is, and explain.

**PHYSICS**

For a projectile with initial velocity=vi projection angle = θ with horizontal The time of flight =2visin(θ) If time is doubled with θ unchanged, vi is doubled. From range = vi²sin(2θ)/g you can figure out the increase of the range when time (and ...

**PHYSICS**

There is no rule. It depends on the path. Average velocity = (final position-initial position)/Δt Average velocity = ∫c dx /Δt (line integral)