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Looks like your choice is good, NSS

See  here  :   https://www.wolframalpha.com/input/?i=.0000541x%5E3++-.00789x%5E2%2B.452x+%2B+1.888++for+x++%3D+8,+23,+60,81

Let's see how helperid found this

P  =  2  [ W + L ]       so we have

162   =  2 [ (2x - 3)  + (3x + 4 )]       simplify within the brackets

162  = 2  [ 5x + 1]     divide both sides by 2

81  =  5x  +   1        subtract  1 from both sides

80  = 5x         divide both sides by 5

16  = x

Just as helperid found....!!!!!

Perimeter = 2[ L + W], where L=Length, W=Width.

Perimeter =2[(3x + 4) + (2x - 3)] =162

162 =2[3x + 2x + 4 - 3] 

162 =2[5x + 1] 

162 =10x + 2  subtract 2 from both sides

160 =10x         divide both sides by 10

x = 160/10

x =16

A hotel is in the shape of a  cylinder, with a circular foundation. The circumference of the foundation is 5 times the radius, increased by 72.96 ft. Find the radius of the circular foundation. Use 3.14 as an approximation for

piπ.

Circumference of the foundation is    5r + 72.96       (1)

And circumference is  given by    2 * 3.14 * r       (2)

Setting (1)  = (2)   we have that

5r  + 72.96   =  2 * 3.14 * r        simplify the right side

5r + 72.96  = 6.28 r          subtract 5r from  both sides

72.96  = 1.28r        divide both sides by  1.28

57  = r        [  i.e.....the radius is 57 ft  ]

x = 16 (assuming the 2 expressions given are the length and width)

P ( M  ∩ O  )   =  75  / [ 350 + 300 + 200 + 175 + 75 + 100  ]  = 75 / 1200  = 1/16  = .0625

P (M) * P (O)  = [350 + 200 + 75] / 1200  *    [75 + 100] / 1200  = 

625 / 1200  *  175 / 1200  =

25/48  * 7/48    =

175  / 2304  ≈  .076

Not Independent

r = 6, d = 12, a = \(9\pi\)

189 (rounding down)

it was the first choice

Here's my best guess for the second one....assuming that x  is the number of years after 1900, the correct function is third one......see the outputs here for this function  [rounded to the nearest integer ]

https://www.wolframalpha.com/input/?i=.139x+%2B+6.57++for+x++%3D+37,+68,95

The first is a little difficult, but we might be able to eliminate some answers

The point ( 1 , -1)  is on the graph

Note that if we substitute 1 into the polynomial, we can add the coefficients and constant of each polynomial and should come up with -1

So...look at the first answer...we add  2 - 3 - 2  + 1  =  -2   so this is not the answer

Look at the third answer....we add  1 - 2 + 3 + 2 - 1  =  -3  so this is not the answer

Now...look at the second  answer...if we put 4 into the function, we get

(4)^4 -2(4)^3 - 3(4)^2 +2(4) + 1  =   256 - 128 - 48 + 8 + 1  =  89

But we should get   329

So......the fourth answer is correct

How much heavier is the package of biscuit mix?

Was it \(\frac{x}{4}-\frac{5y}{2} + \frac{3}{x}\), or \(\frac{x}{4}(\frac{-5y}{2})\frac{3}{x}\). In the latter case, the answer would be \(\frac{-15y}{8}\).

~1.04

Linear (Constant rate of change that is via addition)

4

25 (but line has a negative slope)

The degree of the polynomial  is found by the product of the first terms in each set of parentheses....thus......we have

x^4 * x^3 * x   =   x^8   ⇒    degree 8

Actually, helperid, your answer is probably more correct......we usually number the first row as "row 0 "

So...the first row where we will have an interior integer is row 2

So....the answer of 2ⁿ - 2   for n ≥ 2 is actually better given the traditional numbering scheme

thanks

(a)  They raised the flag at a steady rate the whole time.

(b)  They raised it quickly at first then as it got higher they slowed down.

(c) They raised it then lowered it a little then raised it then lowered it a little over and over. Maybe the flag falls down a tiny bit after each time they raise it.

(d) They raised it slowly at first, then faster.

(e) They raised it slowly, then really fast, then slow again.

(f) They raised the entire thing in 0 seconds, in one instant. Also that means the flag was at all of the different heights at the same time.

The most realistic one might be  c , or it could be  e  ...?

Oh let me double check

Sorry

The probability that you flip a coin and it landing on tails given that you  rolled a "3" on the dice is just  1/2.....these events are independent......the outcome of one does not affect the other

You're right CPhill! I made a dumb mistake. Thanks for checking my answer! 

x/4- 5y/2 +3/x

Manuel.....there is nothing to "solve"....we must have an "=" sign somewhere to "solve" something

1/x-1 + 2/x =  x/x-1      subtract  the first fraction from both sides

2/x  =  x/ [ x - 1 ] - 1/ [ x - 1 ]

2/x  =  [ x - 1 ]  / [ x - 1 ]      cross-multiply

2 [x - 1]  = x [ x - 1 ]

2x - 2  =  x^2  - x    rearrange as

x^2 - 3x + 2   = 0      factor  as

(x - 2) ( x - 1)  = 0      set each factor to 0 and solve for x  and we find that

x  = 2     or     x  = 1

The second solution makes an original denominator 0 we must reject that solution

So...the only solution is that  x =  2   ....you are correct  !!!

The sum of the interior integers in the nth row of Pascal's Triangle in your scheme is :

2^{n -1}  -  2       [ where n is an integer > 2 ]

So....the sum of the interior intergers in the 7th row is   2^(7-1) - 2  = 2⁶ - 2  = 62

I noticed a pattern a long time ago...

The direct numbers can be found by 11^r, and the sum can be found using 2^r. This means that the sum of the interior numbers on row 7 = 2⁷ - 2, or 126. As a matter of fact, the function is: \(\sum\triangle(r) = maximum([0, 2^{r}-2])\), where maximum (array) = the maximum value in the array.