Answer:
1) 1 element
2) 13 elements
3) 22 elements
4) 40 elements
Step-by-step explanation:
1) Only one element will have no tails: the event that all the coins are heads.
2) 13 elements will have exactly one tile. Basically you have one element in each position that you can put a tail in.
3) There are 
elements that have exactly 2 tails. From those elements we have to remove the only element that starts and ends with a tail and in the middle it has heads only and the elements that starts and ends with a head and in the 11 remaining coins there are exactly 2 tails. For the last case, there are 
possibilities, thus, the total amount of elements with one tile in the border and another one in the middle is 78-55-1 = 22
4) We can have:
- A pair at the start/end and another tail in the middle (this includes a triple at the start/end)
- One tail at the start/end and a pair in the middle (with heads next to the tail at the start/end)
For the first possibility there are 2 * 11 = 22 possibilities (first decide if the pair starts or ends and then select the remaining tail)
For the second possibility, we have 2*9 = 18 possibilities (first, select if there is a tail at the end or at the start, then put a head next to it and on the other extreme, for the remaining 10 coins, there are 9 possibilities to select 2 cosecutive ones to be tails).
This gives us a total of 18+22 = 40 possibilities.
1 and 16, 2 and 8, 4 and 4.
Formula: SA = 2πr² + 2πrh
h =40 in
Diameter d =12 in.
Radius = r = d/2 = 12/2 = 6 in
SA = 2π6² + 2π*6*40 = 72π + 480π = 552π (in²)
SA = 552π = 552*3.14 = 1733.28 (in²)
Answer: 1733.28.
The <em>vertex</em> form of the <em>quadratic</em> equation, written in <em>standard</em> form, f(x) = 2 · x² - 20 · x + 8 is f(x) + 75 = 2 · (x - 5)².
<h3>What is the vertex form of a quadratic equation?</h3>
In this problem we have a <em>quadratic</em> equation in <em>standard</em> form, whose form is defined by f(x) = a · x² + b · x + c, where a, b, c are <em>real</em> coefficients, and we need to transform it into <em>vertex</em> form, defined as:
f(x) - k = C · (x - h)² (1)
Where:
- (h, k) - Vertex coordinates
- C - Vertex constant
This latter form can be found by algebraic handling. If we know that f(x) = 2 · x² - 20 · x + 8, then its vertex form is:
f(x) = 2 · x² - 20 · x + 8
f(x) = 2 · (x² - 10 · x + 4)
f(x) + 2 · 25 = 2 · (x² - 10 · x + 25)
f(x) + 75 = 2 · (x - 5)²
The <em>vertex</em> form of the <em>quadratic</em> equation, written in <em>standard</em> form, f(x) = 2 · x² - 20 · x + 8 is f(x) + 75 = 2 · (x - 5)².
To learn more on quadratic equations: brainly.com/question/1863222
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