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You plant 20 marigold seeds and 12 of them grow into flowers that bloom. If you plant 10 more ?merigolds, predict how many would bloom?

12 / 20 =60% of the marigolds bloomed.

60% =0.6 x 10 =6 more marigolds expected to bloom.

12 + 6 = 18 expected number of marigolds out of 30 planted.

about 46 and 2/3 minutes

i^8 = 1

Use the ratio 20/12. 

\(20 \over 12 \)\(=\)

\(30 \over x\)

Cross multiply, and you'll get \(12x = 20*30\)

\(12x = 600\) 

\(x= 600/12 = 20\) 

Thus, 20 seeds would bloom.

There are a few different ways to get the inverse sin .

You can press the  " 2nd "  button in the top left, then press  " acos "

...or...

You can type in " acos(  ) ," " arccos(  ) ," or " cos^-1(  ) " into the bar.

In fraction form, your expression looks like this:

\(\frac{\frac{1}{2}}{7}\)

To do this, we will have to utilize a rule with fractions. It states that \(\frac{\frac{a}{b}}{c}=\frac{a}{bc}\). Applying this fraction rule alone is enough to solve this problem.
 

\(\frac{\frac{1}{2}}{7}=\frac{1}{2*7}=\frac{1}{14}=0.0\overline{714285}\)

it's 1/14

a trick for dividing with fractions: 

1/2 divided by 7=

1/2 times the inverse of 7

1 times 1 is 1

2 times 7 is 14

this gives u the answer of 1/14

nvm it's (4, 17)

5 red marbles are made of glass.....there are 15 total marbles

So...the probability of selecting a red one made of glass   =  5 / 15  =  1 / 3

2. The volume  =  side^3  = (3 ft)^3 = 27 ft^3

Water has a weight of about 62.416 lbs/ ft^3

So.....the weight of the water  =   27 * 62.416  ≈ 1685 lbs

No way the table supports that  !!!!

The density of water doesn't change no matter how much is in the aquarium....

1) The  new volume, V,   is given by

(8 - 2x) (10 - 2x) x =

(80 - 36x  + 4x^2) x  =

4x^3 - 36x^2 + 80x   

We can find the  maximum of this curve  using  Calculus

12x^2 - 72x + 80  = 0   divide through by 4

3x^2 - 18x + 20  = 0

Using the quadratic formula and solving for x  we have that  there are two possible solutions

 x = 3 - √(7/3) ≈  1.4725  = 1.5    or    x  =   3 +√(7/3) ≈  4.5275  = 4.5

Looking  at the graph of the volume function here, it's clear  that the first answer produces the maximum  volume  : https://www.desmos.com/calculator/fdqkzsy7cq

If   16^n = 1/64  , find the value of n .

\(16^n=\frac1{64} \\~\\ (2^4)^n=\frac1{(2^6)} \\~\\ (2^4)^n=2^{-6} \\~\\ 2^{4\cdot n} = 2^{-6} \\~\\ 4\cdot n=-6 \\~\\ n=\frac{-6}4 \\~\\ n=-1.5\)

x^3  = 20x + 7y   

y^3  = 7x + 20y

Subtract the two equations

x^3  - y^3  = 13x - 13y

(x-y) (x^2 + xy + y^2)  = 13 (x - y)    divide both sides by ( x - y)

x^2 +  xy + y ^2   =  13  →  x^2 + y^2  =  13 - xy   (1)

Add the two equations

x^3 + y^3  =  27x + 27y

(x + y) ( x^2  - xy + y^2)  = 27 (x + y)   divide both sides by (x + y)

x^2 - xy + y^2  =  27  →  x^2 + y^2  =  27 + xy    (2)

Then.....setting (1)  and (2)   equal, we have that

13 - xy  =  27 + xy

2xy  = -14

xy  =  -7

[ Note....other solutions  are possible...for instance  the trivial solution of (x, y) = (0, 0)  produces xy = 0 ]

Thank you, CPhill.

It's two

a^3  +  1/a^3    if    a + 1/a  = 6

Note:  if  a + 1/a   = 6   then

(a + 1/a)^2  = 36

a^2 + 2 + 1/a^2  = 36

a^2 + 1/a^2  =  34

Factor  a^3  +  1/a^3   as

(a +  1/a) ( a^2 - 1 + 1/a^2 )  =

( a + 1/a) ( [a^2 + 1/a^2] - 1)  =

(6) ( [34] - 1)  =

(6) (33)  =

198

First, you must convert 16% to something that is a bit more manageable. I'll convert it to a fraction. Remember that \(a\%=\frac{a}{100}\).

Therefore, \(16\%=\frac{16}{100}\). However, \(\frac{16}{100}\) can be put in simplest terms by dividing the numerator and denominator by their GCF, 4. Let's do that:

\(\frac{16}{100}\div\frac{4}{4}=\frac{4}{25}\)

"Of" in this problem is actually referring to multiplication. 16% of 50 is the same as saying 16% multiplied by 50. 

\(\frac{4}{25}*\frac{50}{1}=\frac{200}{25}=8\)

Therefore, \(16\%\hspace{1mm}\text{of}\hspace{1mm}50=8\)

Let  sides  a,b  be the legs  and c the hypotenuse

Three possibilities

1st  way  =   product of the legs / 2

2nd way =    (1/2) (a)(c)sin B    

Where B is the included angle between sides a and c

Also.....     (1/2) (b) (c) sin A    would work, too

3rd  way.....something known as "Heron's" Formula

The area, A, is given by

√ [  s (s - a) (s - b) ( s - c) ]  

Where  s  = the semi-perimeter =   [ a + b + c ] / 2

16/100 * 50  = 16/2 = 8

Ignore that text at the top :)

If you have 5 pears and you eat 3 you need to do the equation 5-3 which is 2 but if you have half a pear then you need to do the equation 2-0.5 (0.5 is a half) you do this becuase you have 2 left but ate a half and when you have done the equation 2-0.5 you end up with 1.5

Hope i could have been of help 

-Randon guy

1)  We have a right triangle....  Since we know the side opposite the angle and the hypotenuse, we can use the inverse sine  (arcsin) to find the agle that the ladder makes

So  we have...

arcsin (11.8 / 12)  ≈  79.5 °      [unsafe ]

2) The perimeter  =  4(15)  = 60 ft

The combined length of both diagonals  =   2 * √2  * side length  =   2 * √2 * 15  =

30 √2   ≈  42.4 ft

So.....the total  required  =   [ 60 + 42.4] / 20   =  5.12 rolls  =  6 rolls

3)   The triangle height  =  5√3  cm

So....the area  =

(1/2) base * height   =  (1/2) (5) (5√3)  =  (25/2)√3  ≈  21.7  cm

1)   x^2 + y^2 - 4x + 2y - 11 = 0     add  11  to both sides  and  rearrange 

x^2 -  4x  + y^2  +  2y    =  11

Complete the square on x......take (1/2)  of 4  = 2, square it  = 4  and add to both sides

x^2 - 4x + 4  + y^2 + 2y  =  11 + 4

Complete the square on y.....take (1/2) of 2 = 1, square it =  1  and add to both sides

(x^2 - 4x + 4)  +  ( y^2 + 2y + 1)  =  11 + 4 + 1

Factor the perfect square trinomials in each set of parentheses and simplify the right side

(x - 2)^2  +  (y + 1)^2   =  16

The center  is   ( 2, -1)   and the radius  =   4

2) The center  is   (-1,1)   and the radius  is 3

So...the equation is   

(x + 1)^2  +  ( y - 1)^2  =  9

3)  We have the form

4p(y - k)  =  (x - h)^2    where (h, k)  is the vertex  and p is the distance between the vertex and the focus

The  vertex  can be found  as

( -2,   [ y coordinate of the focus + y value of the directrix]/ 2 )  =

(  - 2, [ 4 +2] / 2 )    =   ( -2, 6/2)  =   ( -2, 3)

So....the distance between the focus (-2, 4) and the vertex (-2, 3)   =  1  = p

So......the equation  becomes

4(1) ( y -3)  = ( x + 2)^2

4(y - 3)  =  ( x + 2)^2

Here's a graph  : https://www.desmos.com/calculator/tyvpqyor1i

Here is a YouTube video explaining the procedure for   (1)

https://www.youtube.com/watch?v=09aYOtI7v2g

And here's another one for  (2)

https://www.youtube.com/watch?v=YEX2mhvbYuo

3) We have to know the measure of θ   before we can provide a definite answer

But....the  area is given by

(1/2)* radius^2 * θ        if  θ  is in radians

or

pi * radius^2  *   (θ / 360)     if  θ  is in degrees