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Skolem Sequences

Please see the attached file for the fully formatted problem. A Skolem sequence of order n is a sequence (s1, s2,...,s2n) of 2n integers satisfying the conditions: i) for every k in {1,2,3...,n} there exist exactly two elements si and sj with si = sj = k and ii) if si = sj = k with i<j then j - i = k. Find all Skolem seq

Isolating variables

Given the formula below, make (i) h and (ii) a the subject of the formula A = 1/2*h*(a+b) Given the formula below, change the subject of the formula to P A = [P(1+r)^n-1]/r

Subject of equation

Rearrange the following expression such that b is on the left hand side of the equality: d = 1.3[(ab)^0.625)/(a+b)^0.25]

Word Problem

The level (Loudness) of sound is measured in decibels which is related to the intensity if sound (I) which is measured in watts per cm^2. One can convert from one measure to the other using the following formula d=10 log (I/10^-16) Due to the installation of acoustical tiles in an auditorium, the noise level was reduced from

Hydrolics problem. Trying to figure out how far a raft will sink in water

Given: raft consists of 4 sealed barrels laying on their sides with demensions of 21 in. diameter, 3 ft. in length, and weighing 30 lbs. each. The barrels are attached by a wooden deck weighing 179 lbs. find: how far does the raft sink below the waters surface with a specific weight of the water being 62.38 lb./cubic foot.

Simultaneous Equations

State whether the following system of equations is solvable or unsolvable. If it is solvable, find the solution. 3(y-1) = 2(x-3) 3> y-2x = -3

Word problem (airports)

1998 airports are each connected in both directions to exactly three other airports. Any airport can be reached from any other airport by a sequence of flights. It is decided to close down 200 of the airports, no two of which are connected by a single flight. Show that this can be done in such a way that any remaining airport ca

Word Problem

What o'clock is it when the time from noon is 9/11 of the time to midnight?

Math word problem

You went on a diet and lost 15% of your body weight. you currently weigh 167 lbs. what was your pre-diet weight (to the nearest tenth of a pound)?

Business word problems

A company sells three products, TV's, VCR's and Stereos. If the ratio of TV's, VCR's and stereo's sales is 3:4:2 and total sales are $9,360, what is the amount of sales in dollars for each of the TV, VCR, stereo? A keg holds 64 litres of beer. Suppose that 16 litres are replaced with water. Then an additional 16 litres

Variable meaning

I want help understanding the following statement. I need to be able to use this formula but I don't quite get it. What does the little n stand for? So suppose my universe is 15 usability problems and each subject gets 20% of them (the L) how do you use the little N in this equation to get the result? Here is the paragraph t

Sequence Proof

Please see the attached file for the full problem description. Given Sn and S&#8712; (0,&#8734;). If Sn &#8594;S, prove &#8707;&#945;>0, &#8707;&#925;&#8712;N s.t. &#8704;n &#8805; &#925;, an>&#945;.

Subset and Subgroup Problem

If G is a group and gEG, define C(g)={zEG|zg=gz} show that C(g) is a subgroup of G (the centralizer of g in G). Note: E means element of

Roots of a rational function

Q: Consider the polynomial function f(x)=4x^4-13x^2+9 a. What is the maximum number of real roots you would expect and why? b. Find the real roots of the polynomial function. Using factoring by substitution, or substitution and the quadratic formula to find the real roots

Solve for x

How would you go about solving for x, when x to the tenth power = 2.533836? Thanks! x^10= 2.533836

Solving Equations Question

Find the general solution, if possible. Otherwise find a relation that defines the solutions implicitly: xy' - y = 2y (ln y - ln x)

Grid problem

Five children live in the town of Gridley which is represented by a grid of streets. On the x axis are the streets A, B and so on until Q. On the Y axis, the streets go from descending order from 15th Avenue down to 1st Avenue (in other words as you go up the Y axis, the avenues go down). So at the origin would be the interse

Rearranging formulas

A battery is put on charge.The relationship between the charging current, i amperes,and the time, t hours passed,is given by the formula i=3e^(-0.36) show that the formula for i can be arranged to give the time t as t=1/0.63log e (3/i) could you please show me working out steps!

Word problem

Aaron's age is 3 times that of Jodi. In 4 years he will be twice Jodis age. Use guess, test and revise to setup an equation representing these facts. Where x is Jodi's age.


Joane bought 3 1/2 Lbs of strawberries on Monday. Her family ate 1 2/3 Lbs on Tuesday. How many pounds were left on Wednesday?

Distance Question

You are traveling 55 mph over a bridge that is 4260 ft. long. How long does it take to cross the bridge? Help me!

Relations between Non-Parallel Planes

Let P1 and P2 be two dimensional planes that are not parallel. If these planes are contained in R3 then they must intersect in a line. Prove that if they are contained in R4 instead then they can intersect either along a line, or at a single point. (HINT)- A two dimensional plane in R4 is determined by two equations in four unkn

Solving for n as a Factorial

Does there exist a natural number n such that [n!/(n-4)!] = 11,880 ? if so find n, if not explain why not (Hint: factor 11,880 into its prime factors)