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As guest found, here is the table with deposits at the END of the months:

If the payments are not specifically stated to be made at the beginning of the period, then it is automatically assumed that they are made at the end of the period.

This is the formula used to calculate that:

FV=P{[1 + R]^N - 1/ R}

FV =150 x {[1 + 0.08/12]^15 - 1} / (0.08/12)

FV =150 x {[ 1.0066667]^15 -1} / (0.0066667)

FV =150 x {       0.10480422 / 0.0066667}

FV =150 x              15.7205541......

FV =$2,358.09 - Balance of the savings plan.

 Equate the marginal revenues to marginal costs and solve for x.

 5000 -20x =300 + 1/4x^2, solve for x

x = ~103 items sold.

Revenues =5000x - 10x^2

                 =5000*103 - 10* 103^2

                 =515,000 - 106,090

                 =$408,910 - total revenues for 1 month.

Total costs =300x + 1/12x^2

                  =30,900 + 884.08

                  =$31,784.08 - total costs for 1 month.

Total revenues - Total costs =$408,910 - $31,784.08 =$377,125.92 - The firm's maximum monthly profit.

From an online calculator (using equation #2 at bottom) deposits at BEGINNING of month:  ($2373.82)

Yes, you have to:

First, 8 miles- 8 miles=60 minutes, 2 miles=15 minutes

Next, 10 miles- 10 miles=60 minutes, 5 miles=30 minutes

Thus, \(5+2=\boxed{7}\) miles.

yes

you need to convert minutes to hours, you can use a ratio

then 8*(15/60) + 10*(30/60) = 7 miles

Evaluate the decision

a) about 40

b) about 30

c) at age 20 the chessmasters skills begin to increase, with the most increase around age 30 until it peeks around age 40. The the skill takes a decline after age 40 and never recovers.

d) you could probably just google these graphs, not sure how to post graphs here anyway

4x+6y <= 200

x >= 6

y <= 8

6x + 10y >= 100

why i write, universal motivations

these suggest the first one as the answer. as the first one talks about motives.

A-T= Total of 20 letters

Vowels from A-T= A,E,I,O

So, we have 4 vowels and 20 total letters.

Thus, \(\frac{4}{20}=\boxed{\frac{1}{5}}\)

\(\frac{6x}{3x}=\frac{6}{3}=\boxed{2}\)

Each of the 4 people has a choice of 3 other hats, not including his/her hat.

Therefore, there are: 4 x 3 = 12 ways that this can happen.

Prime numbers: 2, 3, 5, 19

[19 - 5] / [2*2 + 3]  =

    14 /  7

= 2

Since 10! =3,628,800 = 2^8 * 3^4 * 5^2 * 7.

But 2^8 =(2^2)^4 =4^4

As an alternative,  we can use the Law of Cosines to solve this

The interior angle of a hexagon = 120°....so....

AD^2  = 10^2 + 10^2  - 2 (10 *10) cos (120°)

AD^2  = 200  - 200 (- 1 / 2)

AD^2  =  200 + 100

AD = √ [300]  ≈  17.32  units

I already drew a diagram, but don't know how to upload it from my computer.

First you connect the point A to the two points that construct the line segment labeled 10. 

AD is congruent to the line segment perpendicular to the side labelled 10. 

You have constructed a 30 - 60 - 90 triangle. The hypotenuse is 20.

The leg is the square root of 20^2 - 10^2.

Can someone tell me how to upload an image, then this solution would be much clearer. 

Thanks

For a polygon, the SUM of the internal angles is  (n-2) * 180    (n=6 for hexagon)

(6-2)*180 = 720     Thus EACH angle is :   720/6 = 120 degrees

So the large angle of the triangle is 120 degrees    the other two are equal to each other

  there are 180 degrees in any triangle:   

   (180-120) / 2 = 30 degrees for each of the smaller angles.

Now use the law of sines

10/sin30 = x/(sin120)

10/(.5)  * (sqrt3 )/ 2 = x

10 sqrt 3

10/sin30  *  sin 120  =  17.32

The problem can be rewritten as 6/3, or 2. So, the answer to the problem is 2.

Arc length  =  radius *  ( theta  in rads)

12 pi  =  18 *  theta       divide both sides  by  18

12 pi  / 18  =  theta

2 pi / 3  =  theta  =  120°