The question says Find P(A) if P(A)=0.7, so P(A)=0.7 Do you mean P(A')=1-P(A)=1-0.7=0.3?
All correct except the first. A point from the inside of a simple figure will cross an odd number of times to connect to any point outside.
Yes, it makes life a little easier. I love integers! :)
Let the series be a, ax, ax² "The third term is 3.2 times the sum of the other two" means ax²/(a+ax)=3.2 cross multiply: ax²=3.2(a+ax) cancel common factor a (≠0) & multiply by 10 10x²-32x-32=0 =>x=4 or x= -4/5 Reject solution where |x|<1...
Algebra 1 - use parentheses
According the the BEDMAS rules, the expression you posted simplifies to 25-1-3x-10 =14-3x which is probably not what is intended. All fractions have implicit parentheses on the numerator and denominator. You have probably omitted to insert them when you transcribe the expressi...
Precalculus...repost.. The tutor didn't quite answ
The tutor was saying plug -7.5 in for x in +16x^2+200x +600=0, which means that -7.5 is indeed a root of -16x^2-200x -600=0. The fallacy lies in the statement: " plugged -7.5 in for x in -16x^2-200x-600 the result does not equal to +600" The result should equal to z...
"Assume the +x-direction is up along the slope and the +y-direction is perpendicular to the slope and out of the ground." Since the perpendicular component of the velocity "digs" into the ground, so by definition of the y-axis, it is negative.
Good catch, didn't see the details!
Let v=ground velocity of plane = 500 m/s Since slope is rise/run, so the angle of the "ground" relative to the horizontal θ=tan<-1>(3/100) Component of velocity vector perpendicular to the ground = v*sin(θ) = ?
See earlier post: http://www.jiskha.com/display.cgi?id=1400921781
I guess my typo made more confusion than anything else! :( a1/2 ÷ a² is the mathematical equivalent of a1/2 / a² so no worries. I wrote the ÷ specifically to avoid confusion since two "/" signs were in the expression.
a1/2 ÷ a² is the mathematical equivalent of a1/2 / a² so no worries. I wrote the ÷ specifically to avoid confusion since two "/" signs were in the expression.
If you mean a1/2 ÷ a² then by the law of exponents, 1/a² becomes a-2 and the expression equals a1/2+(-2) =?
Voltage (volts) = current (amp) * resistance (Ω) or I=V/R (amps) V=220 volts Case 1: each resistance alone, R=24Ω Case 2: in series, R=2*24=48Ω Case 3: in parallel, R=1/(1/24+1/24)=12Ω You can then calculate current I in each case using formula above.
Horizontal range = v²sin2θ/g => solve for v(initial). Kinetic energy after launch = (1/2)mv² Elastic potential energy before launch =(1/2)kx² Equate potential energies before and after launch to find k, the elastic constant of the mechanism.
Math - SHM
Given T seconds =k √L (cm) where k is an arbitrary constant to be determined. Also given 0.63=k√9 Therefore we can determine the constant k. k=0.63/√9=0.21 The relation now reads: T(L)=0.21√L where T is period in seconds and L is length of pendulum in c...
Assuming the distance is x miles. Then with tail wind, ground speed=240+40=280 mph against wind, ground speed = 240-40=200 Total time x/280 + x/240 = 6 Solve for x to get the maximum one-way distance.
y-component of any force equals ysin(θ) where θ is the (counterclockwise) angle with the +x-axis. So the y-component of the resultant =ΣFsin(θ) =8sin(30)+8sin(120) =?
Consider the graph with V = [A, B, C, X, Y, Z] and
V is a set of vertices. E is a set of edges (lines joining the vertices) (a) Two distinct vertices are adjacent when there is an edge joining the two. So to list vertices adjacent to Y , we need to go through all the edges and select those that include Y as a vertex. The other...
MATH HELP PLEASE!!
Quoting: "Homework Posting Tips Please show your work. Tutors will not do your homework for you. Please show your work for any question that you are posting. ..."
See answer to previous post. This one would be an excellent example for practice.
12 gal. ÷ (7/8-1/8) =16 gal. Does not look like a huge tank!
"Est-ce que" is a standard phrase to introduce a question without inversion of subject and verb. Similar to "Is it that..."
Tu: personal pronoun, second person singular. Fais - second person singular for "do".
Domain means a set containing all possible values of the first value of the selected ordered pairs. Can you identify which ordered pairs she chose?
1 rod = 5 1/2 yards = 3*(5 1/2) feet = 33/2 feet So one foot =1/(33/2) rod = 2/33 rod
P(a)=12.21=14.7*e-0.21a Solve for a: e-0.21a=12.21/14.7 Take log on both sides, log(e(x))=x -0.21a=log(12.21/14.7) a=log(12.21/14.7)/(-0.21) =?
20C4 where nCr=n!/((n-r)!r!)
Do you have a figure to go with it?
Maths A level
Cross sectional area =π(40²) =1600π change in height per unit time =dh/dt =(rate change in volume/cross sectional area) =-32πh^(0.5)/1600π =-0.02h^(0.5) The sign is negative because h decreases with time.
W=wind speed A=air speed Equation are set up using Speed*Time = distance, or Distance/Speed = Time 2800/(A-W)=4 2/3 ...(1) 2800/(A+W)=4 ...(2) Solve system of equations for A and W.
P(being female | the person earns over $75,000) =P(F∩O)/P(O) =(585/1200)/(1070/1200) =585/1070 P(F)=650/1200 =>P(F∩O)/P(O) ≠ P(F), i.e. P(F∩O) ≠ P(F)*P(O) therefore they are not independent.
G=6.67384 × 10-11 m3 kg-1 s-2 M=4.56*10^24 kg r=7.09*10^6 m Using Newton's law of gravitation, g=Force/1 kg mass =GM/r² m/s²
An equation is not a function, but a function can be part of an equation. For example, f(x)=0 is an equation, while f(x) is a function. A function is like a black box that churns out values when given an input value or input values.
velocity, acceleration (both are vectors)
Difference in interest rate =3.75%-3.5% =0.25% Difference in $ = $50 Use direct proportion 0.25% : 50$ 100% : ?
focus(6,0), directrix x=-3 means If the distances are equal, then the squares of the distances from directrix and focus are also equal, so (x-(-3))²=(x-6)^2+(y-0)^2 (x+3)²-(x-6)²=y² Factor by difference of two squares 18(x-1.5)=y² (x-1.5)=y²/(4*4....
All of these can produce a congruent figure, depending on the parameters. Rotations and translations ALWAYS produce a congruent figure. Reflection produces a congruent figure if the object has at least one line of symmetry. Images of dilations are mostly not congruent with the...
B) divides AB in the ratio 1:5, but not 5:1. look for a choice which is 5/6 from point B instead.
What do you think?
Do not forget implicit parentheses of fractions, meaning that the expression should have been written (4x²-4x)/8x which equals 4x(x-1)/8x =(x-1)/2
Probability of getting the right answer for 1 question = 1 choice out of 5, or p=1/5. Assuming independence among the 10 questions, probability of getting all 10 right = p10 Probability of passing (getting 6 or more right out of 10) using binomial probabilities =10C6*p^6q^4 + ...
When pressure is constant: P1/T1 = P2/T2 Temperature should be in °K.
chemistry - which equation?
Balance which equation?
This is a different problem from the one you posted earlier. x+y = (x-y)+25 Solve for y=12.5 and x can be any number. Thus x/y can be any number (infinite number of solutions)
Assume 2x/((x-2)(x+2)) = A/(x-2)+B(x+2) Right hand side =(A(x+2)+B(x-2))/((x-2)(x+2)) =((A+B)x+(A-B))/((x-2)(x+2)) Compare denominators on both sides and equate coefficients of powers of x to get A+B=2 A-B=0 from which A=B=1 So the decomposition into partial fractions is 1/(x+...
-890 kJ / 1 mole ? kJ / 6.25 moles
Difference in solubility = 6.8-0.33 g =6.47 g/100 ml. 10 g / ? ml. (of solution)
Use the component method to break down each vector into x,y components. 8km North = <0,8> 5km at 60° = <5cos60°,5sin60°> Assuming angle is in Cartesian plane (counterclockwise from east) and not bearing (clockwise from north). Add the two vectors and ca...
physics - erratum
The minimum is when they are lined up and opposite to each other, and the maximum is when they are lined up and in the same direction.
The resultant of two vectors A and B can have a magnitude ranging between ||A||±||B||. The minimum is when they are lined up and opposite to each other, and the minimum is when they are lined up and in the same direction. Now you can make your choice of answers.
The cube has 6 faces, so 6 outcomes. When two different dice are thrown, there are a total of 6*6=36 outcomes. You can make a table of the 36 outcomes and find out how many of them are the same (6 out of 36). Alternatively, you can think of the red cube is thrown first with an...
Draw the line x=13 (which is a vertical line). Now can you decide which side of the line is the inequality satisfied, to the right, or to the left of the line?
Use proportions: 248.24 : 50% x : 100% x=(100/50)*248.24=?
Can you first check out where pharynx is located?
Tax rates and rules are different for different countries, and states/provinces. In most countries, tax rates depend on income level, so adds another parameter. To answer the after-tax part, you need to specify the tax rates.
Earnings=20000*7.5% 30% marginal tax bracket means he pays 30% of his investment earnings in taxes. Tax=earnings * 0.30
nPr=n!/(n-r)! 4Pr=4!/(4-r)!=24/(4-r)! unless you know the value of r, this is the furthest we can go.
Between 0° and 90° - I 90°-180° - II 180°-270° - III 270°-360° - IV
You can add a table between the other two, and the third table can sit only two more.
Energy/work in joules.
Work done (energy required) = mgh m=50 kg g=9.8 m/s² h=difference in elevation in metres.
Given 4 resistances, and we need to sort out which one is which. Assume that the resistances are non-zero. We know that two resistances in parallel is always smaller than any of the two. Similarly, two resistances in series is always greater than any of the two. So the two sin...
sec(θ) = 1/cos(θ) so the given formula gives: distance = 120/cos(θ). You can use your calculator to find the distance and make your choice accordingly.
The equation is written in the form x=a(y-h)^2+k where a=2, h=1, k=3 so the vertex is at (k,h)=(3,1) The axis of symmetry is at y=h, or y=1.
Circle centred at origin: x²+y²=r² where r=radius. Here radius = √((√5)²+0²)=√5
Geometry - need more information
In a 30-60-90 triangle, the shortest side is half the longest side, because sin(30°)=1/2. We do not know what a,b and c stand for, namely which one is hypotenuse.
To solve this problem, you would draw a diagram of the rod. Then indicate the pivot and the first load. Find the distance d1 between the first load P1 and the pivot: this is the lever arm for the first load. To balance, then load P2 multiplied by d2 must equal P1*d1. Since d1=...
almost... vapour density is relative to H2. So M~2*vapour density=78.
The best way to improve is to practise. Discuss with his teacher for options.
As Damon said, check the units. If you divide, the units do not give joules.
m=200 g c=0.897 J/g°C ΔT=10°C Calculate heat required, ΔQ using ΔQ=mcΔT
Would you like to show your work?
3H2+N2--> 2NH3+2709J Molecular mass of H2=2*1.008=2.016 According to the equation: 3*2.016 g H2 => 2709 J x g H2 => 5000 J Use proportion.
I hope it's not a trick question. Between the two dates, there are indeed 27 Tuesdays, so there are 27*8=216 person-days needed. Since 10 does not divide 216, they may not equally divide unless the days are split into shifts.
"as shown below..."
Please proofread your question. Does your question use proper grammar, capitalization and spelling, and contain all necessary information?
You would plot time (months) along the x-axis, and the weight along the y-axis. Positive slope means the y-values increase with increase in x-values, and negative slope means the y-values decrease as x increases. Since losing weight means weight decreases with time, you have a...
All limit problems are different. If only the limit is known without knowing the question, we don't know the answer. Please post the complete question in order and answer can be formulated.
There is a good chance you have missed out parentheses in the numerator and the denominator. All fractions have implicit (i.e. understood) parentheses in the numerator and denominator. I believe your question means (x²+6x+9)/(5x+15) even though the question does not actua...
Assuming you want the difference in days between dates. It's a messy counting problem. First note that the dates are written in MM/DD/YYYY format. Difference in Months: October-May=31+30+31+31+30=153 days Difference in days 28-17=11 days Difference in years 2002-1987=15 ye...
Please proofread your question. Does your question use proper grammar, capitalization and spelling?
I guess Steve's interpretation of the question is correct. There was no indication of power! Please go with Steve's solution.
If you are looking at solving 3sin(θ)=sin-1(θ) then you would be solving f(x)=3sin(x)-asin(x)=0 in which case the trivial solution x=0 can be obtained by inspection. If you're looking for 3sin(θ)=1/sin(θ) then there are 4 solutions between 0 and 2&p...
The best way to solve these problems is to follow the instructions, draw the figure with the coordinates of each point, and then apply the transformation (rotation). I will give you a kickstart by giving the coordinates of the figure (not a rectangle). A(0,0) B(2,0) C(4,0) D(4...
a=12 c=30/2=15 b=√(15^2-12^2)=9 For a hyperbola with horizontal axis, x²/a²-y²/b²=1 x²/12²-y²/9²=1
Did you read the post previous to yours? It should help you get the right answer.
First, find the rule for a rotation of 180°, which is R(O,180): (x,y)->(-x,-y) so (3,-5) -> (-(3),-(-5)) can you take it from here?
The 25% means that she pays up front $6000 so she only needs to finance $18000. Over a period of 36 months, n=36=periods of one month i, monthly interest = 0.1/12 P, principal = 18000 R=rate=1+i=1+1/120 Monthly payment, A =PRn(R-1)/(Rn-1) =18000*(1+1/120)36*(1/120)/((1+1/120)3...
Figure out the rule of the sequence in terms of n, the number of terms We have common difference =6 T(0)=-12 T(1)=-6 T(2)=0 T(3)=6 Let's try T(n)=-12+6n so T(1)=-12+6=-6 T(2)=-12+6*2=0 T(3)=-12+6*3=6,... It works. So T(50)=-12+50*6=288
It's the same as calculating the distance between two points. ||A||= sqrt((-13-2)²+(9-1)²) =17
P(Bull's eye)=(6/16)²=0.1406 approx.
Math - need more data
To calculate the probability, we need to know the size of the dartboard and the radius of the bull's eye. A six-inch radius bull's eye has to be bigger than the eye of any living animal on earth!
90 km/hour = 90/3.6=25 m/s deceleration rate, a = 5 m/s² time= 25/5 = 5 seconds Must be a new braking system :)
Apply F=ma (Newton's second law) where F=force (in N) m=mass in kg a=acceleration in m/s² so F=ma=10kg * 5 m/s²=50 N If the spring balance is graduated in kilograms (mass), which is the usual case, then it will show ma/g=5 kg (approximately).
Total force on 4 legs =5 N + 9*9.8 N = 93.2 N Area of contact of each leg = 2.5*10-3 m² Pressure on each leg = 93.2/(4*2.5*10-3 = 9320 N/m² = 9320 Pa (pascals)