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salantis [7]
2 years ago
10

A die with 12 sides is rolled. What is the probability of rolling a number less than 11?

Mathematics
1 answer:
jeyben [28]2 years ago
5 0

Answer:

83 1/3%

Step-by-step explanation:

List the possible answers.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12

There is 12 possible results. Now count how many of those results are less than 11. The answer is 10. 10/12 results are less than 10. 10 divided by 12 is 83 and 1/3.

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Step-by-step explanation:

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Write two different ratios equal to 6:30
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Keisha has $2.00 she wants to buy four notepads. Does she have enough money and explain your reasoning
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Determine whether the equation x^3 - 3x + 8 = 0 has any real root in the interval [0, 1]. Justify your answer.
nikdorinn [45]

Answer:

The equation does not have a real root in the interval \rm [0,1]

Step-by-step explanation:

We can make use of the intermediate value theorem.

The theorem states that if f is a continuous function whose domain is the interval [a, b], then it takes on any value between f(a) and f(b) at some point within the interval. There are two corollaries:

  1. If a continuous function has values of opposite sign inside an interval, then it has a root in that interval. This is also known as Bolzano's theorem.
  2. The image of a continuous function over an interval is itself an interval.

Of course, in our case, we will make use of the first one.

First, we need to proof that our function is continues in \rm [0,1], which it is since every polynomial is a continuous function on the entire line of real numbers. Then, we can apply the first corollary to the interval \rm [0,1], which means to evaluate the equation in 0 and 1:

f(x)=x^3-3x+8\\f(0)=8\\f(1)=6

Since both values have the same sign, positive in this case, we can say that by virtue of the first corollary of the intermediate value theorem the equation does not have a real root in the interval \rm [0,1]. I attached a plot of the equation in the interval \rm [-2,2] where you can clearly observe how the graph does not cross the x-axis in the interval.  

6 0
2 years ago
Answer this question step by step​
KiRa [710]

I hope this help you

3 0
2 years ago
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