Answer:
a=3, b=3, c=5
Step-by-step explanation:
4
÷1
=a
=
÷
=
×
=
=3
=3
The required probability for three numbers rolled on the dice are the sides of a triangle is 31/36.
<h3>What is probability?</h3>
The area of mathematics known as probability studies potential outcomes of events as well as their relative probabilities and distributions. It is based on the likelihood that something will occur. The justification for probability serves as the main foundation for theoretical probability.
Here,
When three dice are rolled, there are 63=216 possible outcomes, or triplets (x, y, z).
Once more, in a triangle, any two sides added together are larger than the third side, or (x+y)>z.
As a result, 186 outcomes or triplets are possible and satisfy this property.
Hence, the required probability is 186/216=31/36.
The required probability is 31/36 for three dice rolls to produce triangle sides.
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Answer:
PEMDAS
Step-by-step explanation:
USE PEMDAS
Answer:
Hence the function which has the smallest minimum is: h(x)
Step-by-step explanation:
We are given function f(x) as:
- f(x) = −4 sin(x − 0.5) + 11
We know that the minimum value attained by the sine function is -1 and the maximum value attained by sine function is 1.
so the function f(x) receives the minimum value when sine function attains the maximum value since the term of sine function is subtracted.
Hence, the minimum value of f(x) is: 11-4=7 ( when sine function is equal to 1)
- Also we are given a table of values for function h(x) as:
x y
−2 14
−1 9
0 6
1 5
2 6
3 9
4 14
Hence, the minimum value attained by h(x) is 5. ( when x=1)
- Also we are given function g(x) ; a quadratic function passing through (2,7),(3,6) and (4,7)
so, the equation will be:
Hence on putting these coordinates we will get:
a=1,b=3 and c=7.
Hence the function g(x) is given as:

So,the minimum value attained by g(x) could be seen from the graph is at the point (3,6).
Hence, the minimum value attained by g(x) is 6.
Hence the function which has the smallest minimum is h(x)