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[L - F] / D + 1 = N, where L=Last term, F=First term, D=Common difference, N=Number of terms

[-17 - 88] / -3 + 1 =N

[- 105] / - 3 + 1 = N

[-105/-3] + 1 = N

    35       + 1 =N

N = 36 - So -17 is the 36th term - 1 =35 terms before -17 appears.

Nice, Omi   !!!!

The total  number of integers   =  250 - 25 + 1   = 226

And the perfect cubes  in this group are    27, 64, 125, 216   = 4

So...the number of integers that are not perfect cubes  =  [ 226 - 4 ] =  222

On each toss  we have 8 possibilities

So...the number of possible sequences possible  = 8^6  = 262144 

Hi Fiora,

I did look at your question but it was bejond me. :(

Do not post multiple questions here Kay, it is an abuse of the site.

We are not here for you to cheat from.

PLUS

Guest helped you and you did not even have the decency to say thanks! 

That is an interesting question and good answers from both guest and Rom.

Thanks :)

It was checkmarked because it got an answer.

If someone wants to comment on or ask about the answer or the question, they can still do so.

That is what you did and I am even answering you. 

I think this is the best interpretation for this question. 

But yes it is, at best, a poorly written question and it has been answered.

It looks like it has been through an interpreter and the interpreter has not worked adequately.

Convert from moles into grams:
5 mol of P4O6 (tetraphosphorus(III) hexoxide)

Split the chemical formula P4O6 into a tally of its elements:
atom | tally
O |       6
P |       4

Using the atomic masses of the elements O (15.999 u) and P (30.973761998 u), calculate the total mass of each element in 1 molecule of P4O6:
atom | tally | atomic mass | mass in molecule
O |        6 |     15.999 u |              95.994 u
P |         4 |     30.973761998 u | 123.89504799 u

Calculate the molecular mass of P4O6 by adding the mass of each type of atom:
95.994 u + 123.89504799 u = 219.89 u

Since 1 u corresponds to 1 g/mol, the molar mass of P4O6 equals 219.89 g/mol. The number of grams equals the molar mass of P4O6 multiplied by the molar amount:

(5 mol) * 95.994 =479.97 grams of Oxygen + (5 mol)* (123.895 g/mol) =619.475 grams of Phosphorus =1,099.45 grams in 5 moles of P4O6

\(9\sqrt{56x^7y^{12}}= \\ 9\sqrt{4 x^6 y^{12}\cdot 14 x} = \\ 9(2x^3y^6)\sqrt{14x} = \\ 18x^3y^6\sqrt{14x}\)

Let triangle ABC be a right triangle such that B is a right angle. A circle with diameter of BC meets side AC at D. If the area of ABC is 150 and AC = 25, then what is BD?

The problem is symmetric in x vs. 1/x so we can find the number of integers between 0 and 1000 that are either a power of two or 3 and just double the answer.

Note that any non-zero power of 2 is even and any non-zero power of 3 is odd so these two sets are disjoint.

There are 10 powers of 2, 0-9, and 6 non-zero powers of 3 that are less than 100.

We use non-zero power for 3 since we only want to count 1 = 2⁰ = 3⁰ once

That gets us 16 from 0 to 1000.  Doubling this we get 32 but we don't want to count \(1 = \dfrac{1}{1}\)

twice so we subtract 1 from this getting 31 as you found.

\(2^9=512\)

\(3^6=729\)

Those are the largest positive powers of 2 and 3 under 1000.

\(2^{-9}=0.001953.....\)

\(3^{-6}=0.0013717.....\)

These are the smallest negative powers greater than  \(\frac{1}{1000}\)

Therefore, we have \(9-(-9)+1=19\) different powers of 2 between \(\frac{1}{1000}\) and 1000.

We also have \(6-(-6)+1=13\) different powers of 3 between \(\frac{1}{1000}\) and 1000.

This gives us \(19+13=32\) total integers...

32 is the answer I got but someone is going to have to check over my work :b

\(\text{apparently }\sum \limits_{k=1}^n ~k! \cdot k = (n+1)! - 1 \\ 0!=1 \\ \text{so the expression shown }=(n+1)!-1+1 = (n+1)! \\ \text{so the largest prime }<(n+1) \text{ is what we're after}\\ \text{and this is }47.\)

The fifth solution is z=0

A and B are two points on a circle with center O, and C lies outside the circle, on ray AB. Given AB = 24, BC = 28, and OA = 15, find OC.

x^2 +3x - 28  factors as  ( x +7) ( x - 4)

x^2  - 7x  - 12  factors as  ( x - 3) ( x - 4)

So....the (x - 4)  factors will "cancel" in the numerator /denomnator  and we  are left with

[ x + 7 ]

_______

 [ x - 3 ]

\(\text{let }U \text{ be the set of whole numbers }1-100 \\ \text{and let }V \text{ be }U \text{ with the multiples of 3 and 4 removed}\\ |V| = |U| - |\text{multiples of 3 < 100}| - |\text{multiples of }4 \leq 100| + |\text{multiples of both 3 and 4} \leq 100|\)

\(|U| = 100 \\ |\text{multiples of 3}<100| = 33 \\ |\text{multiples of 4}\leq 100| = 25 \\ |\text{multiples of 3 and 4}\leq 100| = |\text{multiples of 12}\leq 100| = 8 \\ |V| = 100 - 33 - 25 + 8 = 50\)

I got 8.33/9 as well having the same work, but it is wrong? Do you see anything wrong with your work?

I got 8.33/9 as well having the same work, but it is wrong? Do you see anything wrong with your work?

\(z = r e^{i \theta},~0 \leq r, ~0 \leq \theta < 2\pi \\ z^4 = r^4 e^{i 4 \theta} = |z| = r = re^{i 2k\pi}, k \in \mathbb{Z} \\ r = 1,~ 4\theta = 2k \pi \\ \theta = 0,~\dfrac{\pi}{2},~\pi,~\dfrac{3\pi}{2} \text{ the solutions repeat after this} \\ z = 1, i, -1, -i\)

The radius of the Earth  = 8000/2  = 4000 miles

We  can  figure the distance  to the horizon  using a right triangle

The distance from  the center of the Earth to any object above the Earth's surface  = the hypotenuse = 4000  + h      where h is the height of the object [in  miles ] above the Earth's surface

And the radius of the Earth  is equal to one leg of the right triangle

And the distance from the object to the horizon, D,  is the other leg

So...we have this general formula to determine D

D  = √ [ (4000 + h)^2  - 4000^2]

So....

(a)  D  = √ [ (4000 + 1)^2  - 4000^2 ]  ≈ 89.4 miles

(b)  D  =   √ [ (4000 + 6)^2  - 4000^2 ]  ≈  219.2  miles

(c)  D  = √ [ (4000 + 100)^2  - 4000^2 ]  = 900 miles

A mortgage is in the amount of $800,000. The origination fee is 0.4%, the intangible tax is 0.2%, and there are 3.5 discount points. 
Which of the following is the total cost of the origination fee, the intangible tax, and the discount points? (3 points)

A. $28,000

B. $32,800

C. $29,600

\($5.00 - $0.05 = $4.95\)

- Daisy