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If you put TWO numbers evenly spaced  between 1/8 and 1/4   you will trisect the number line

   from 1/8 to 1/4   is   1/8     you need to add   1/3  of 1/8  to find the first point

                                  1/3 x 1/8 = 1/24

        1/8 + 1/24 =  3/24 + 1/24 = 4/24 = 1/6      (first point)

THEN you need to add 2/3 of 1/8 to    1/8 to find the second point

2/3 * 1/8 = 2/24                   2/24 + 1/8 = 2/24 + 3/24 = 5/24    (second point)

You have 16 numbers...... list them in increasing order

add them all      then divide the sum by 16 to find the MEAN  (= average)

the MEDIAN is the number in the MIDDLE of the list

   there really is no MIDDLE number....so take the TWO middle numbers, add them then divide by 2  to find the MEDIAN

The MODE is the number that occurs the most often in the list of numbers......  give it a try !

But how though, I dont understand

1. 14/2=7
 

2. 2+32=34

There's an answer here:  https://web2.0calc.com/questions/please-help-me-hard-geo-question 

Actually, this problem was asked twice before this one, but Alan's looked so good I didn't even check the other one. 

is big chungus from Saturn  

The genesis of Big Chungus is revealed when saying his name backwards. 

When the two-digit integer MM, with equal digits, is multiplied by the one-digit integer M, the result is the three-digit integer NPM. What is the greatest possible value of NPM? 

MM x M = NPM   You need to know a digit(s) that, when multiplied by itself, gives a product that ends with itself. 

I know of these:  1, 5, and 6    I'm not counting zero. 

Of those, 6 is the largest, so I submit, for your approval, 66 x 6 = 396

_.

Just to let you know, f(x) = (-27/18x^2 + 1/2x + 4). f(2) = -1, f(-1) = 2, and f(-4) = -22 .

8 X 3 X 4

i get it now, thank you so much electricpavlov!! :D

Let's saolve the system of equations

Multiply first equation by -2

-12x-8y=-14    and add to second equation

kx+8y =7

(-12+k)x = -7

x = -7 / (-12+k)          Thus when k = 12  this would not be a real number     (denominator would be ' 0 ' ) 

10 gallons to start with

adding 'x' gallons of water      final volume = 10 + x

.9 (10) = amount of vineger

.1(10) = amount of water

amount of vineger before and after water addition is constant

.9(10) = .6(10+x)  

9 = 6 + .6x

3 = .6x

x = 5 gallons of water to be added

1000 m / 150 min    x   1.5 min =   .........   m  

1 km = 1000 m

2.5 hr = 150 min

90 sec = 1.5 min

Area of circle = pi r²

                         pi (3²) = 9 pi  units²

Possible rectangles and areas of each:

1 x 3  = 3

2 x 2  = 4   

  ( 3+4))/ 2   =3.5 units²

(I assumed a 3 x 1 rectangle was the same as a 1 x 3 rectangle)

x^2 + x - 6 > 0

(x-2)(x+3) >0     now you can see where BOTH factorsare negative it will be > 0    or if they are both negative it will be >0

x-2 is negative for x < 2       and positive for    x >2

x+3 is negative for x <3       and positive for    x > -3

            x< -3                                  x>2

-3>x>2

Here is graph :

https://www.desmos.com/calculator/sbybddoj1z

There are 3 groups of skaters as follows:

4 x 11 x 10 =440 ways. But 1st,  2nd and 3rd prizes can be awarded in 3! =6 ways.

Therefore, there are: 440 x 6 =2,640 ways.

f,g, and h are all polynomial functions, so they all adhere to the following general form shown below.

\(f(x)=a_nx^n+a_{n-1}x^{n-1}+a_{n-2}x^{n-2}+...+a_2x^2+a_1x^1+a_0\\ g(x)=b_nx^n+b_{n-1}x^{n-1}+b_{n-2}x^{n-2}+...+b_2x^2+b_1x^1+b_0\\ h(x)=c_nx^n+c_{n-1}x^{n-1}+c_{n-2}x^{n-2}+...+c_2x^2+c_1x^1+c_0 \)

The constant term of \(f(x)\), represented as \(a_0\) in the general form, is \(-4\). In the function \(h(x)\), the constant term is 3. One way to guarantee that a polynomial function will output its constant term is to substitute in \(x=0\) for that polynomial. 

\(h(0)=f(0)*g(0)\\ c_0=a_0*b_0\\ 3=-4b_0\\ b_0=\frac{-3}{4}\\ \therefore g(0)=b_0=\frac{-3}{4}\)

Multiply the two numbers to get your answer:

 2^4 * 3 * 5^3          x          2^8 * 3^4 * 5^2       =    ..........   pieces of mail

2⁴⁺⁸  3¹⁺⁴  5³⁺²       You can finish  ......

There are TWO sides of dimensions  2.4  x  8

also since ya need 2.32 rolls     you will need   2.32 rolls x 20 m/roll = 46.4 meters      'linear meters' of fabric (I think this is what they are asking)

For real roots the disciminat has to be positive

b²-4ac>0        3^2-4(1)(k) > 0

9-4k>0

4k > 9

k > 9/4       so from the list   0- 9 is ten numbers of which 3-9 will result in real roots      7/10

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Ok I'm not 100% sure about this but here goes:

Since there are 5 blue pencils and 11 total pencils, the probability of picking a blue pencil is 5/11.

Now, without replacement, there is 1 yellow pencil and 10 total pencils. The probability of picking a yellow pencil is 1/10.

The expression is (5/11)(1/10).