Answer:
x = -5/3
Step-by-step explanation:
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2 answers:
Answer:
The experimental probability of rolling a prime number is 75%, which is 25% more than the theoretical probability.
Step-by-step explanation:
Given : A special 8-sided die is marked with the numbers 1 to 8. It is rolled 20 times with these outcomes :
3 4 5 2 7 1 3 7 2 6 2 1 7 3 6 1 8 3 5 6
To find : The experimental probability of rolling an odd number is ____%, which is ____% more than the theoretical probability?
Solution :
1) Theoretical probability
Sample - 1,2,3,4,5,6,7,8
Rolling a prime number from sample is 2,3,5,7=4
Total sample = 8
The theoretical probability of rolling a prime number is
In percentage, 0.5=50%
2) The experimental probability
Outcomes - 3 4 5 2 7 1 3 7 2 6 2 1 7 3 6 1 8 3 5 6
The outcomes that are prime are:
{ 3 2 5 7 1 3 7 2 2 1 7 3 1 3 5}
Number of favorable outcomes= 15
Total number of outcomes = 20
Now, The experimental probability of rolling a prime number is
In percentage, 0.75=75%
As 75%-50%=25%
Therefore, The experimental probability of rolling a prime number is 75%, which is 25% more than the theoretical probability.
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Answer:
Below, you can see the graph of the function:
f(x) = x + cos(k*x)
for different values of k, as follows:
red: k = 1
green: k = 2
orange: k = 0.
Now let's find the values of k such that our function does not have local maxima nor local minima.
First, remember that for a given function f(x), the local maxima or minima points are related to the zeros of the first derivate of f(x).
This means that if:
f'(x0) = 0.
Then x0 is a maxima, minima or an inflection point.
Then if a function is such that the f'(x) ≠ 0 , ∀x, then this function will not have local maxima nor minima.
Now we have:
f(x) = x + cos(k*x)
then:
f'(x) = 1 - k*sin(k*x)
This function will be zero when:
1 = k*sin(k*x)
1/k = sin(k*x)
now, remember that -1 ≤ sin(θ) ≤ 1
then if 1/k is smaller than -1, or larger than 1, we will not have zeros.
And this will happen if -1 < k < 1.
