Please help. Will give brainliet
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Given the table showing the distance Randy drove on one day of her vacation as follows:
![\begin{tabular} {|c|c|c|c|c|c|} Time (h)&1&2&3&4&5\\[1ex] Distance (mi)&55&110&165&220&275 \end{tabular}](https://tex.z-dn.net/?f=%5Cbegin%7Btabular%7D%0A%7B%7Cc%7Cc%7Cc%7Cc%7Cc%7Cc%7C%7D%0ATime%20%28h%29%261%262%263%264%265%5C%5C%5B1ex%5D%0ADistance%20%28mi%29%2655%26110%26165%26220%26275%0A%5Cend%7Btabular%7D)
The rate at which she travels is given by
If Randy has driven for one more hour at the same rate, the number of hours she must have droven is 6 hrs and the total distance is given by
distance = 55 x 6 = 330 miles.
The rate at which she travels is given by
If Randy has driven for one more hour at the same rate, the number of hours she must have droven is 6 hrs and the total distance is given by
distance = 55 x 6 = 330 miles.
Answer:
0.0082 = 0.82% probability that he will pass
Step-by-step explanation:
For each question, there are only two possible outcomes. Either the students guesses the correct answer, or he guesses the wrong answer. The probability of guessing the correct answer for a question is independent of other questions. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
In which is the number of different combinations of x objects from a set of n elements, given by the following formula.
And p is the probability of X happening.
In this problem we have that:
.
If the student makes knowledgeable guesses, what is the probability that he will pass?
He needs to guess at least 9 answers correctly. So
0.0082 = 0.82% probability that he will pass
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.
