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help fo polygon 

These are combinations problems.

Assuming independence, a person who makes 70% of his shots:

Probability of making exactly 3 of 5 shots:  ₅C₃·(0.70)³·(0.30)²  =  10·(0.70)³·(0.30)²  =  0.3087

Probability of making exactly 4 of 5 shots:  ₅C₄·(0.70)⁴·(0.30)¹  =  5·(0.70)⁴·(0.30)¹  =  0.36015

Probability of making all 5 shots:  (0.70)⁵  =  0.16807

Probability of making at least 3 shots:  0.3087 + 0.36015 + 0.16807  =  0.83692

1.   The area of a rhombus - in terms of its diagonals - is :

[d1* d2] / 2      where d1 and d2 are the diagonal lengths

So.......the original area has been quintupled.......the effect on each diagonal is to increase the original length by √5......to see why this is so......let the original area =

[d1 * d2]/ 2

Now....increase each diagonal lenght by √5   and we have

Area =   [√5d1 * √5d2] / 2    =  5 [d1*d2] / 2    =  5 times the original area

2.  If the area is halved.......the circumference is 1/√2  as much as before

To see this.......note that if the original circumference was 14pi  ft....the radius = 7 ft

And the original area = pi*r^2  =  pi*49   = 49pi ft^2

So.....1/2 of this =  49pi/2  ft^2.....and we can solve for the new radius thusly :

49pi/2 = pi *r^2      divide by pi on both sides

r^2  = 49/[2]

r = 7/ [√2]  ft

So....the new circumference  = 2 * pi * [7/√2]   =  14pi/√2  = 14pi * (1/√2) ft

3.25 KILOgrams = 3250 GRAMS    add 45 grams  to get  3295 GRAMS    or 3.295 KILOgrams

sqrt(180)=13.4164078649987382

At the current exchange rate, £5 is $7.25 USD. Note that this is subject to change later.

TIMESTAMP: Tuesday, May 31st, 2016

Exactly how do you MAKE a 3-sided die?      Is it round on the ends?

Because it is multiplying a fraction by a fraction, which in turn makes a smaller fraction.

.00000025*.00000025 = 0.0000000000000625, which is smaller than .00000025.

-7pi/2 = -10.9955742875642763

Since -11 (that is the number simplified) is less than 0, we can assume that it is NOT between 0 and 2pi

A ratio of 3:2 indicates that there are 5 equal parts that comprise the total of 60

The apples  are   3/5 of this =  3/5 * 60   = 36

And the oranges  are 2/5 of this   = 2/5 * 60  = 24

Here's another option :

30  = 5 (x + 1)    divide both sides by 5

6  = x + 1     subtract 1 from both sides

5 = x

To start things off if a power is in a fraction form it means that it wants you to take the root of the denominator. A rewrite is best suited to solve these kinds of problems.

Let's take your example, 36^(1/4)...

Here's the rewrite...

\(\sqrt[4]{36}\)

I don't feel like doing the exact answer but here's an estimate

2.4494897427831781

A denotation for Planck's Constant perhaps?   Can you give some context?

7x8

12 

Reorder the terms: 30 = 5(1 + x)

                               30 = (1 * 5 + x * 5)

                               30 = (5 + 5x)

Solving: 30 = 5 + 5x

Solving for variable 'x'.:

Move all terms containing x to the left, all other terms to the right.

Add '-5x' to each side of the equation. 30 + -5x = 5 + 5x + -5x

Combine like terms: 5x + -5x = 0

                                   30 + -5x = 5 + 0

                                   30 + -5x = 5

Add '-30' to each side of the equation. 30 + -30 + -5x = 5 + -30

Combine like terms: 30 + -30 = 0

                                   0 + -5x = 5 + -30

                                  -5x = 5 + -30

Combine like terms: 5 + -30 = -25

-5x = -25 

Divide each side by 5: x = 5

Answer: x = 5

0.5 

lava?

This looks to be a square pyramid.....

We need to find the slant height of the sides......this is given by : sqrt [ 7.6^2 +3^2)   =   8.17068

So.....the total surface area =   area of the base  +  area of the four congruent triangles comprising the sides =

6^2   + 4*(1/2)(6)(8.17068)  =  about 134.048 units^2

Let the total cost function  = C(x).....so we have  :

C(x)  = 12 + 1.75x       where x is the number of toppings desired

c = 12 + 1.75x

-4 + 3(h + 1)  =  3(h + 1) + h

Notice that you have the "3(h + 1)" term on both sides. Subtract it from both sides:

        -4 + 3(h + 1)  =  3(h + 1) + h

             - 3(h + 1)  =  -3(h + 1)

--->   -4                 =                   h

So your answer is:  h = -4

Answer: 134.05

A pyramid is a three-dimensional figure made up of a base and triangular faces that meet at the vertex, V, which is also called the apex of the pyramid.

The number of triangular faces depends on the number of sides of the base.  For example, a pyramid with a rectangular base has four triangular faces, whereas a pyramid with a hexagonal face is made up of six triangular faces, and so on.

The lower face ABCD is called the base and the perpendicular distance from the vertex, V, to the base at O is called the height of the pyramid.  The total surface area of a pyramid is the sum of the areas of its faces including its base.

Note that: A square pyramid has four equal triangular faces and a square base and A pyramid does not have uniform (or congruent) cross-sections.

Hope that this will help you 

f(x)=-16t^2+80t-54

The max value for t is given by   -b/2a  =  -80 / [2(-16)]  = -80/-32  = 2.5 seconds

And the max height can be found by subbing 2.5 back into the function.....

So we have  :

-16(2.5)^2 + 80(2.5) - 54   =  46 ft

As an alternative.....the max height can also be found thusly:

c - b^2 / [4a]     =  -54 - [80]^2 / [ 4(-16)]  =  -54 + [6400/64]  = -54 + 100  = 46 ft