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A  particular right pyramid has a square base, and each edge of the pyramid is four inches long. What is the volume of the pyramid in cubic inches? Express your answer as a decimal to the nearest hundredth.

Let the side of the cube =S

SA of a cube =6 x S^2

V of a cube =S^3

S^3/6 = 6S^2

S^3 =36S^2 divide both sides by S^2

S = 36 - the side of the cube

V of cube =36^3 =46,656 cubic units.

Area of a square =S^2 - square units.

Sqrt(46,656) = 216 - units - side length of the square.

1- 0.25

2-0.35

So, 0.35+0.25=.6, or 60%

I agree with Melody!

Assuming no-one had both pasta and chicken

1/3 + 5/12 → 4/12 + 5/12 → 9/12 → 3/4  i.e. 3/4 of the guests ate the pasta and chicken 

Assuming the remaining 1/4 ate the beef, then  (1/4)N = 24   (where N is total number of guests).

 N = 24*4  or N = 96  i.e. there are 96 guests in total.

See https://web2.0calc.com/questions/help_24903 now.

Here's #1 for you:

Collect the terms on right hand side over a common denominator:

\(\frac{A}{x-2}+\frac{B}{x+1}\rightarrow\frac{A(x+1)+B(x-2)}{(x-2)(x+1)}\rightarrow\frac{(A+B)x+A-2B}{x^2-x-2}\)

Compare this with \(\frac{x+7}{x^2-x-2}\)

To make them the same compare the numerators.  It is clear we must have:

A + B = 1   and

A - 2B = 7

Subtract the second from the first to get: 3B = -6  so B = -3

Put this back into the first to get A - 3 = 1  so  A = 4

Hence (A, B) = (4, -3)

For #2  

Set x = each term in turn and solve for x.  if the result lies in the range given for each term then that result is valid.  If not it isn't.

For #3

Can't see the whole expression!

For #4

First plug sqrt(2) into h to get, say m = h(sqrt(2))

Then plug m into h to get h(m) which is h(h(sqrt(2))) 

.

Simply add up all the numbers in the f column to get a total, then divide each number in the f column by that total to get the individual p values.

25%+35% = 60%

Problem 1)

f(x)  =   x³ + 3x² + 4x - 7

g(x)  =  -7x⁴ + 5x³ + x² - 7

We only need to look at the  x³  terms.

x³  +  5x³  =  6x³     so the coefficient of  x³  in  f(x) + g(x)  is  6 .

Problem 2)

f(x)  =  x⁴ - 3x² + 2

g(x)  =  2x⁴ - 6x² + 2x - 1

a)

The largest possible degree of  f(x) + a * g(x)  is just  4 .

b)

If  b  =  -1/2 , then the  x⁴  terms cancel and the  x²  terms cancel in  f(x) + b * g(x)  so the degree would be  1 .

1.

Function A:

Function B:

f(x)  =  |x| − 4

The x-intercepts of a function are the x values when that make the function equal 0.

In function A, the x-intercepts are  -2  and  1  .

In Function B, the x-intercepts are  4  and  -4 .

So each function has two x-intercepts.

2.

Function A:

f(x)  =  -x² + 4

Function B:

When  x = -3 ,  f(x)  =  f(-3)  =  -(-3)² + 4  =  -9 + 4  =  -5

When  x = -3 ,  g(x)  =  g(-3)  =  1

-5   <  1         so...

f(-3)  <  g(-3)

x-intercepts occur where y= 0

Function A   has TWO  at x=-2 and x=1

Function B has TWO where x = 4 and -4 

A when x = -3     -  (-3)^2 +4 = -5

B when x = -3                       =1       (given)      Whatever choice matches this...you didnt list one that does.

Here is solution:

Thanks so much, CPhill! Very good, yay! 

We have  5 odd integers....

P (both odd)   =  5/9  * 4/8    =    5/9 * 1/2   =   5/18

The guest has assumed replacement......my answer  assumes without replacement

12 face cards out of 52 cards

12/52    =   3/13

Wow  !!!....  that's  nice guest   !!!!

Note that   A  is 2   units to the left  of  B

So.....D  is 2 units to  the left of C  =  ( 4 - 2, 0 )  =  (2, 0)

So.....the sum of its coordinates   =  2

a)  Lower limit   = 1st term =   1     

Upper limit  =  18th term  =  18

b)  We need to find the 18th  term.....this  is  3 + 7(18 - 1)  =

3 + 7 * 17   = 

  122

The sum  is  given by :

[ 1st term + 18th term ]  *  number of terms / 2  =

[ 3 + 122 ]  *  18  / 2  =

[ 125 ]  * 9  =

1125  beads  !!!

a)  A decline of 10%  per year  means that the common ratio between terms  is ⇒  r  = .9

So.....geometric

b) aⁿ  =  1250 (.9)^n-1     where n  is the value at the beginning  of the nth year

c)  6th year   =   1250 (.9) ^{6 - 1}   =  1250 (.9)⁵  = $738.11 

A travels at 81 mph

B travels at    324/ 4   =  81 mph

So...

The distance Train A traveled in 1 h is equal to the distance Train B traveled in 1 h.

18.

Since  each successive term  is greater than the previous term.....this series will diverge and will not have a definite sum.......another way to see this is that the common ratio  is 3......for a series to converge, r  must have an absolute value < 1

19.

a)     a₁  = 9,    a_n  = a_n-1 + 2

b)   a_n  =  9  + 2 (n - 1)

c)  a₁₂  =  9 + 2(12 - 1)   =   9 + 2*11  =  9 + 22   =   31 seats

We see it once in a year, twice in a week but never in a day. What is it?