All Answers 358237 Answers

We can find the common ratio, thusly

18* r^2   = 8    rearrange as

r^2  = 8/18

r^2  = 4/9      take the positive root of both sides

r = 2/3

So.........the length of the second arc  = 18 (2/3)   = 12 ft

Solve for x:
-x/4 = 1/10

Multiply both sides of -x/4 = 1/10 by -4:
(-4 (-x))/4 = (-4)/10

(-4)/4 = (4 (-1))/4 = -1:
--1 x = (-4)/10

(-1)^2 = 1:
x = (-4)/10

Express -4/10 in its lowest form by cancelling out gcd(-4, 10) = 2 from the numerator and denominator. -4/10  =  (2 (-2))/(2×5)  =  -2/5:
Answer: |  x = (-2)/5

D)

Beacuse in a Geometric series you MULTIPLY by the same number over and over again while a arithmetic sequence you add or subtract by the same number over and over again. in this case it is doing nither which makes the awnser D..

It is not geometric......for it to be geometric, the ratio between successive terms must be equal

So .......

Ratio of second term to the first term  = -4 / 2      = -2

But

Ratio of the third term to the second term  = -16/-4 =  4

5^-6  = 1/5⁶   = 1/5³ * 1/5³  = 1/125 * 1/125  = 1/15625   or   0.000064  as mathismeh said

384pi  = pi * r^2 * 24    divide both sides by 24 pi

384 / 24  = r^2  simplify

16  = r^2      take the positive square root of both sides

4cm   = r = radius

- C (10,3)  * (2x)⁷ (3y)³   =

- 120 * 128x7 * 27y3  =

-414720 x⁷ y³

8.01 x 10²³

.000064

in that order? 156

using order of operations? 33

33.

33.

a) The graph of a normal curve with a mean of 64" and a standard deviation of 3.5" is a bell-shaped curve with its    

     maximum value at x = 64.

Important points:  

     mean - 3 deviations:     64 - 3(3.5)  =  64 - 10.5   =  53.5     

     mean - 2 deviations:      64 - 2(3.5)  =  64 - 7       =  57

     mean - 1 deviation:        64 - 3.5                           =  60.5

     mean:                                                                    =  64

     mean + 1 deviation:       64 + 3.5                           =  67.5  

     mean + 2 deviations:     64 + 2(3.5)  =  64 + 7       =  71           

     mean + 3 deviations:     64 + 3(3.5)  =  64 + 10.5  =  74.5  

b)  If there are 3000 plants, approximately how many will be taller than 71"?

     71"  is 2 standard deviations above the mean. The region between two standard deviations below the mean and two        standard deviations holds approximately 95% of the plants.

     Therefore there will be approximately 5% of the plants divided equally between being taller than two standard              

     deviations above the mean and being shorter than two standard deviations below the mean. Thus, there will be  

     approximately  2.5% of the plants taller than 71":  0.025 x 3000  =  75 plants.

there are, of course, fractions.

in this case, you enter x/y         ex. 1/2  =  .5

be careful when plugging them into the calculator though, because the calculator goes by the Order of Operations. 

so if you are trying to do 4 times 9/3, and entered it as 9/3*4, you wouldn't get the right answer.

parenthesis are friends!!!

(9/3)*4 is correct

2.334476386 / 354.00001 x 36442 = (unneccessary 2nd =) 240.3191696480791874.

but im sure you all ready knew that

0.5(5-7x0)=8-(4x+6)

2.5-3.5x=8-4x-6

-2.5        -2.5

------------------

-3.5x=5.5-4x-6

-3.5x=-0.5-4x

+0.5    =0.5

--------------

-3.5x+0.5=-4x

-3.5x        -3.5x 

-------------------

0.5=-0.5x

---    ------

-0.5  -0.5

-1=x

20% of $900 = $180

45% of $900 = $405

180 + 405 = 585

so subtract from the original total (900) and...

 = $315

i went the long way to show steps, the shorter way would be to take 35% of $900. 

I'm not sure what is meant by "scalar" projection, but, calling  V₁ = (3,5)   and V₂  = ( 7, -2), the projection of   V₁ onto V₂ is given by :

proj _V2  V₁  =    [V₁ * V₂] * [ V₂ ]

                        ------------

                         ll  V₂  ll ²

V1 * V2   = [3 *7 + 5 (-2)] =  [21 - 10  ]  =   11

ll V2 ll ²  =  7² + (-2)²  = 49 + 4   = 53

So

proj _V2  V₁  =    [11] * [ V₂ ]       =   < 77/53 , -22/53  >

                        -------

                         [53]

2) V₁ + V₂   =  < 3 + 7 , 5 +  - 2 >   =  < 10, 3  >

3) V₁ - V₂  = < 3 - 7, 5 - (-2) >   =  < -4, 7  >

4) V₂ - V₁  =  < 7 - 3, -2 - 5>   = < 4,  -7  >

Hey thanks for the info CPhill!

[4/5](15x-25)-1= [3/7] (21-7x)        distribute the 4/5 and 3/7 over the terms in parentheses

12x - 20  - 1   =  9 - 3x       combine like terms

12x - 21  = 9 - 3x               add 3x, 21 to both sides

15x  = 30      divide both sides by 15

x  = 2

Let x be the greatest  number of DVDs that she can order.......then.....

x *(cost of each DVD) +  shipping cost   ≤ 100   ....so we have

x * 15.99 + 9.99 ≤ 100      subtract 9.99 from each side

x * 15.99  ≤ 90.01           divide both sides by 15.99

x  ≤  90.01 / 15.99  =   about 5.6 DVDs   ....but  she can't quite afford 6, so she must settle for 5

Here's the graph :     https://www.desmos.com/calculator/hreijk0scn