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r=12

I think that's incorrect

∑[(n*1/2^n), n, 1, ∞] =converges to 2.

∑[1/((2 n + 1) (2 n + 3)),n, 0, 201] =202/405 =~converges to 1/2.

5q+5x2

:3 this is the answer

Let the number of coach tickets =C

Then  the number of 1st class tickets =11 -  C

$170C + $1,120(11 - C) = $5,670

$170C + $12,320 - $1,120C =$5,670

-$950C = -$6,650

C = - $6,650 / -$950

C = 7 - Coach tickets that Sarah bought.

11 - 7 = 4 - First class tickets she bought.

i)  Q1 is approximately one-fourth of the way to the highest number; therefore, about three-fourths of the states have a tax greater than 35 cents.

ii)  Similarly Q3 is approximately three-fourths of the way to the highest number; therefore, about one-fourth of the states have a tax greater than $1.07.

If both pairs of opposite sides are congruent and if both pairs of opposite angles are congruent, the figure could be a rectangle or a square or a parallelogram; it could not be a trapezoid.

#26:

| -5|  =  5

| 5 |  =  5

| -3 |  =  3

| 8 |  =  8

Therefore,  -5  and  5  have the same absolute value.

#27:

a)  For the first 10 days, the stock had a total increase of  10 x $0.30  =  $3.00.

b)  For the next 10 days, the stock had a total decrease of  10 x $0.45  =  $4.50.

c)  For the last 10 days, the stock had a total increase of  10 x $0.25  =  $2.50.

d)  The total increase was  $3.00 - $4.50 + $2.50  =  $1.00.

e)  What the stock will do in the future is unknown ...

C.   Its has only one pair of congruent sides

Oreo

14 + 2g  = 20         subtract 14 from both sides

2g  = 6               divide both sides by 2

g  = 3    =    [games that Blue Jays lost ]

Trapezoid

Let us find the edge length

Draw a segment from the apex of the tetrahedron perpendicular to the base.....this is the height....call the point where this segment intersects the base, A

Draw  a segment  from one of the bottom vertexes (call this point  B)  to  A

Find the midpoint  of one of the sides connecting to B....label this point  C

And BC  = (1/2) the side length  = (1/2)s

So.....we have the right triangle ABC lying on the base

And we have this relationship

cos 30°  =  ( BC) / (BA)

cos (30°) = (1/2)s / (BA)

BA  =  (1/2)s / [√ 3 / 2]  =  s / √ 3 

So......we have another right triangle...one leg is the height, one leg is BA and the hypotenuse is the side length......and we have......

√ [ 20^2 + BA^2]  = s

√ [ 20^2  + (s/√3)^2  ]  = s  

√ [(1200 + s^2) / 3 ]  = s

[1200 + s^2] / 3  = s^2

1200 + s^2  = 3s^2

1200  = 2s^2

600  = s^2

√ 600  = s

10√ 6   = s  ≈  24.49  inches

About 17.4131

We can solve this with a graph [ linear programming ]

Let x  = number of  $75 tires to be sold and y  = the number of $ 85 tires to be sold

Here are the constraints to be graphed :

x + y ≤ 300 

3y ≤ 2x

And the objective function to be maximized is this

75x +  85y

A look at the graph here : https://www.desmos.com/calculator/5dtkxwrxak  will show that the max occurs at the corner points of the intersection of the two inequalities

There is only one corner point at  ( x , y)  = (180, 120)

Putting this into the objective function produces

75(180) + 85 (120)  = $ 23700

log √[5x] + log √[20x]

Note that we can use the properties   

log a  + log b  = log [ a * b ]           and  log a^b  = b*log a

So we can write

log √[5x] + log √[20x]   = 

log (5x)^1/2 + log (20x)^1/2  =  

(1/2)  [ log (5x)  + log (20x) ]  =

(1/2) [  log (5x  * 20x) ]  =

(1/2) log ( 100 x²)  =

log (100x²)^1/2  =

log  √ [ 100x² ]

log (10x)      which can also be simplified as  

log 10 + log x  =

1 + log x

29.     Cost per yard x total yards purchased  = Total cost

So.....    3.87  x 5.50   ≈  $ 21.29

28.     {28, 61, 63, 65, 66, 67, 68, 69, 82, 86, 87}

The outlier appears to be 28

Mean with outlier  =   742 / 11  ≈  67.45

Without outlier  = 714 / 10  = 71.4

Let the number of coach tickets =C

Then  the number of 1st class tickets =11 -  C

$170C + $1,120{11 - C) = $5,670

$170C + $12,320 - $1,120C =$5,670

-$950C = -$6,650

C = - $6,650 / -$950

C = 7 - Coach tickets that Sarah bought.

11 - 7 = 4 - First class tickets she bought.

According to Merriam Webster, the meaning of math is

1) the science of numbers and their operations, interrelations, combinations, generalizations, and abstractions and of space configurations and their structure, measurement, transformations, and generalizations 

8)

If John starts with $$305$ and then spends 3 dollars a day, John is now losing money from the amount he started with. Since d indicates the amount of days that John is losing money, we can derive the following expression to describe the situation:
 

$305-3d$

This is the only expression which describes the situation accurately because John begins with 305 and is now subtracting 3 dollars per day. Therefore, the answer is 4th bullet point.

9)

In this problem, we need to realize that each variable has a different meaning and to which equation does this specific scenario correlate to. We know the following information:

$\text{Sweaters}\hspace{1mm}(s)=28$

With this information alone, we can eliminate the second and 4th answers because the coefficient in front of the s is 14--not 28. Let's keep going. 

$\text{T-shirts}\hspace{1mm}(t)=14$

Since the coefficient of t is 14, we know that the first answer is the only answer that meets both conditions that

1) s has a coefficient of 28

2) t has a coefficient of 14

Therefore, the answer is A.

You can use grouping to isolate the variable in the equation $mx+nx=p$

The original expression is $3^{-8}*3^5$. In order to do this, we can use the fact that the base of both exponents are the same and then simplify.

$x=\frac{p}{m+n}$

Thank so much!!!! That's so awesome