geno3141

Since it fills at the rate of 16 L/min, the slope of the function is 16.

Since there is initially 350 LIf , the y-intercept of the function is 350.

Therefore, the function is:  V(t)  =  16t + 350.

If the pond has a capacity of 1694 L:   1694  =  16t + 350

                                                             1344  =  16t

                                                                   t  =   ...

To find the total number of bricks, you can use this formula:  Sum  =  n(t₁ + t_n) / 2

where  n = number of numbers = 17

           t₁ = first number = 118

           t_n = last number =  ??

To find t_n, you can use the formula:  t_n = t₁ + (n - 1)·d

where d = common difference = -5

--->   t_n  =  118 + (17 - 1)·(-5)  =  38

--->   Sum  =  17(118 + 38)/2  =  1326 bricks.

If the function is this:  f(t)  =  (-3/2)t + 8

the rate of change is the slope.

The slope of this function is -3/2.

Bob has the fewest cards; call the amount that Bob has:  x

Allen has four times as many cards as Bob; Allen has 4x

Jane has twice as many cards as Allen; Jane has 8x

Together, they have 468 cards:  x + 4x + 8x  =  468

                                                                13x  =  468

                                                                    x  =  36

Bob:     x  =  36

Allen:  4x  =  ...

Jane:  8x  =  ...

Can you include a picture or give a fuller description?

Urn 1 has 6 red balls and 2 black balls (total = 8 balls)

--  the probability of drawing a red ball from this urn is 6/8.

Urn 2 has 2 red balls and 2 black balls (total = 4 balls)

--  the probability of drawing a red ball from this urn is 2/4.

Urn 3 has 5 red balls and 2 black balls (total = 7 balls)

--  the probability of drawing a red ball from this urn is 5/7.

Since an urn is selected at random, the probability of drawing each urn is 1/3.

To find the final probability of selecting a red ball: for each urn -- multiply the probability of drawing an urn

times the probability of drawing a red ball from that urn, and add these three answers together.

Total proability:  (1/3)(6/8) + (1/3)(2/4) + (1/3)(5/7)  =  0.655

Since ABC is a right triangle, use the Pythagorean Theorem:

            (r + 12)²  =  r² + 36² 

   r² + 24r + 144  =  r² + 1296

                     24r  =  1152

                         r  =  48

The rate of change of a linear function is its slope; therefore, the rate of change of

f(x)  =  -5x + 9  is  -5.

If  f(x)  =  x⁴ - 3x² + 2  and  g(x)  =  2x⁴ - 6x² + 2x - 1.

If you create the function  c·g(x)  and let  c = -½  then  c·g(x)  =  -½( 2x⁴ - 6x² + 2x - 1 )

                                                                                                  =  - x⁴ + 3x² - x + ½

f(x) + c·g(x)  now is  (x⁴ - 3x² + 2) + (- x⁴ + 3x² - x + ½)  =  2 - x + ½  =  -x + 2½

and has degree 1.

If  g(x)  =  4 - x²,

then  g( g(x) )  =  4 - (4 - x²)²  =  4 - (16 - 8x² + x⁴)  =  4 - 16 + 8x² - x⁴  =  -12 + 8x² - x⁴

I don't know what the "5x - 2" refers to ...