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These are always a little difficult for me to think of the correct function!!!

a. Call x the number  of additional people hired ........  so we have

Sales =  (30 + x) (50000 - 1000x)  =   -1000x^2 + 20000x + 1500000

b. To find the number of additional hires that will maximize revenue......we can use

x =  -20000 / [ -2 * 1000]  =  -20000 / -2000  =  10 additional people hired will maximize the revenue

The max sales  will be   (30 + 10) (50000 - 1000 (10) )  =  40 * 40000  = $ 1,600,000

The 121st element will be the first number in the 16th row = 1 ...  [ I am letting the "1"  at the top of the triangle be the first row ]

The sum of the entries in any row will be  2^(r - 1)   where r is the row number

So....the sum of the first 121 elements will be 

16

Σ  2^(r - 1)  +  1   =   [ 65535 + 1 ]   =  65536

1

If so, then I'll rewrite it as x-0.125x=8560 just for clarity (it is easier to read like that).

\(x-0.125x=8560\)

First, I would factor an x out of the left side.

\(x(1-0.125)=8560\)

Subtract 0.125 from 1

\(x(0.875)=8560\)

Divide both sides by 0.875.

8560/0.875 = 9782.85714

\(x=9,782.85714\)

So your @ number is 9,782.85714. (If you round up at all, it won't work.)

12.5% is the same as 0.125, so is what you are asking equivalent to @-0.125@=8560? 

Area of the "side"  =

pi * (  sum of the top and bottom radii) * sqrt [ ( diffrence of radii)^2 + height^2 ] =  

pi * ( 10 +  4 ) * sqrt [ (10 - 4)^2 + 8^2 ]  = 

pi * (14) * sqrt [ 100]  = 

pi * 14 * 10  = 

140 pi  cm^2

Area of top/bottom  =  pi  [ 10^2 + 4^2]  =   116 pi cm^2

So....the total surface area is    [ 140 + 116] pi cm^2  =   256 pi cm^2

Always happy to help out a Bama fan....LOL!!!!!

The sum of rows 0 through n is = -1 + 2^(n + 1)=-1 + 2^(15+1) =65,535  ??  Just guessing !!

2ax+2y=b 

5x+ y=  -3   ⇒  10x + 2y  = -6

So.....we will have infinite solutions when

2a  = 10    ⇒ a = 5

And

b = -6

So  { a, b}  = { 5, -6 }

Ahh....glad you caught that CPhill !!! 

Hectictar's answer is correct if the tank is a cylinder....however....a cone is a little different because of the variable cross-sections

We  can use similar triangles here......call the radius of the tank  r and the height h

So.....if the water is filled to 3/4 of the inverted cone's height.....we have

r / h  =  x / [3/4] h     where x =  the radius of the cone formed at the 3/4 water level

So.....x =  3/4 r

So.....the volume of the water  when the tank is full is   pi * r^2 * h / 3

And the volume of water at the 3/4  level  is   [pi *  [ (3/4) r ] ^2 * [ (3/4)] h ] / 3 =

[ 27/64] pi* r^2 * h / 3

So....the percent of the cone filled with water  is   27/64  ≈ .4219  ≈ 42.2%

I got 2 to the 15 power but why?

http://web2.0calc.com/questions/in-how-many-ways-can-you-spell-the-word-cool-in-the-grid-below-you-can-start-on-any-letter-then-on-each-step-you-can-step-one-letter-in-an

Let the place that they touch be x meters from the 300 m wall

Then the distance from the 500 m wall will be 1200 - x

Then....the total distance, D, can be expressed as

D = sqrt [ x^2 + 300^2 ] + sqrt [ (1200 - x)^2 + 500^2 ]

This can be solved with Calculus, but it's a little messy

A graph seems better : 

https://www.desmos.com/calculator/jwjzdpvz1b

The graph shows that the minimum distance is achieved when x = 450m

And the minimum distance  ≈  1442 m

By the way......we can show that this is true if

arctan [ 300 / 450]   =  arctan [ 500 / 750 ]  ......and this is true  !!!!

0.999999999999.... is equal to 1

4 was incorrect... Do you have any other answers?

I counted 64 ways, that was wrong too.

An integer is a whole number; a number that is not a fraction.

Adding is group two things together and subtracting is taking something away from something else.

2 + 4 = 6

9 + 10 = 21, I mean 19

21 - 10 = 11

x - x = 0

Hope this helps! Good luck on the test!

Thanks!!!

∠GCE  =  ∠CBJ      because they are corresponding angles.

And

∠CBJ  and  ∠DBF  are vertical angles, so  ∠CBJ  =  ∠DBF

∠DBF  =  37º

So...     ∠GCE  =  ∠CBJ  =  ∠DBF  =  37º

----------

∠ABP  and  ∠CBD  are vertical angles, so  ∠ABP  =  ∠CBD

From the information given, ∠CBD  =  ∠CDB

∠CDB  and  ∠EDQ  are vertical angles, so  ∠CDB  =  ∠EDQ

So....     ∠ABP  =  ∠CBD  =  ∠CDB  =  ∠EDQ

∠ABP  =  ∠EDQ

5x - 7  =  2x + 11

3x  =  18

x  =  6

So we know...      ∠ABP  =  5x - 7  =  5(6) - 7  =  23°

∠ABD  and  ∠ABP  form a straight line, so  ∠ABD + ∠ABP  =  180°

∠ABD + 23°  =  180°

∠ABD  =  180° - 23°  =  157°

Only need help with 1 now

\(2-(-7)\)

Anything minus a negative is the same as adding them together, as two negatives cancel out.

\(2-(-7)=2+7=9\)

75% as a decimal is 0.75.

Let's call the height of the cone  " h " and the area of its base  " a ".

volume of cone  =  (1/3)(a)(h)

The water will also be in the shape of a cone, with a height that is 3/4 that of the container.

volume of water  =  (1/3)(a)(3/4 * h)

volume of water  =  (3/4) * (1/3)(a)(h)

volume of water  =  (3/4) * volume of cone

volume of water  =  75% of the volume of cone

75% of the cone's volume is filled with water.

I count  4  

When a quadratic equation is in the form  f(x)  =  a(x - h)² + k ,  the vertex is  (h, k)

For this problem, they tell us the vertex is  (-1, 5) , so we know that

f(x)  =  a(x - -1)² + 5

f(x)  =  a(x + 1)² + 5

We know it goes through the point  (2, -13) , which means  f(2) = -13

f(2)  =  a(2 + 1)² + 5       And  f(2) = -13

-13  =  a(2 + 1)² + 5

-13  =  9a + 5

-18  =  9a

-2  =  a

Now we've found  a  , so we know that