Answer:
B. {16, 19, 20}
Step-by-step explanation:
The <em>triangle inequality</em> requires for any sides a, b, c you must have ...
a + b > c
b + c > a
c + a > b
The net result of those requirements are ...
- the sum of the two shortest sides must be greater than the longest side
- the length of the third side lies between the difference and sum of the other two sides
__
If we look at the offered side length choices, we see ...
A: 8+11 = 19 . . . not > 19; not a triangle
B: 16+19 = 35 > 20; could be a triangle
C: 3+4 = 7 . . . not > 8; not a triangle
D: 5+5 = 10 . . . not > 11; not a triangle
The side lengths {16, 19, 20} could represent the sides of a triangle.
_____
<em>Additional comment</em>
The version of triangle inequality shown above ensures that a triangle will have non-zero area.
The alternative version of the triangle inequality uses ≥ instead of >. Triangles where a+b=c will look like a line segment--they will have zero area. Many authors disallow this case. (If it were allowed, then {8, 11, 19} would also be a "triangle.")
Answer:
There will be 9897.47€ in the account.
La cantidad será de 9897.47€.
Step-by-step explanation:
Future value with annuity:
The future value formula, for an annuity, is:
An annuity means that a number of payments happen during the period(an year, for example.
P is the value of the deposit, r is the interest rate, as a decimal, and n is the number of deposits.
In this question:
1000 € each year, so 
Interest rate of 6%, so 
One application per year for 8 years, so 
Total amount:
There will be 9897.47€ in the account.
La cantidad será de 9897.47€.
Answer:
The probability you will get a head at least once is 50%.
Step-by-step explanation:
Since the question is asking about the probability you will get, we can assume we’re answering based on theoretical probability. This type of probability is based on logic.
A coin always has two sides, one with head and the other with tails. So we can easily represent this as half and half. 1/2 as a fraction. 0.5 as a decimal. 50% as a percent. This means that P(H) will be equal to any one of these as they are all the same. The same can be said for the probability that a head does not appear, in other words, a tail appears. The reason being that the probability is split evenly between the two. This will again mean that P(T) will equal to any one of those.
So, A = 50% and B = 50%. The probability you will get a head at least once is 50%.
Let's call he width of the notebook w and the length l
w*l=80
2(w+l)=36
w+l=18
w=18-l
(18-l)*l=80
-l^2+18*l-80=0
l=8 or 10
Therefore, the notebook is 8 by 10 inches
