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zvonat [6]
2 years ago
6

Marlene rides her bike at a rate of 16 miles per hour. The time in hours that she rides is represented by the variable t, and th

e distance she rides is represented by the variable d. Which statements are true of the scenario? Check all that apply. The independent variable, the input, is the variable d, representing distance. The distance traveled depends on the amount of time Marlene rides her bike. The initial value of the scenario is 16 miles per hour. The equation t = d + 16 represents the scenario. The function f(t) = 16t represents the scenario.
Mathematics
1 answer:
jekas [21]2 years ago
6 0
<h2>Answer:</h2>

The statement that is true about the scenario is:

  • The distance traveled depends on the amount of time Marlene rides her bike.
  • The function f(t) = 16t represents the scenario.
<h2>Step-by-step explanation:</h2>

The time that she rides is represented by 't'

and the distance she traveled is represented by 'd'

Now, it is given that:

Marlene rides her bike at a rate of 16 miles per hour.

This means that the distance she rides in ''t" hours is given by:

        d=16t

Since, speed is the ratio of distance over time and it is given that the speed is:   16 miles per hour.

i.e.

\dfrac{d}{t}=16\\\\i.e.\\\\d=16t

Hence, the distance depends upon time.

i.e. the independent variable is time and the dependent i.e. the output is distance traveled.

Also, the initial value is zero.

i.e. at t=0 we have: d=0

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Step-by-step explanation:

The center for Simulation A and Simulation B will be roughly equal.

Overall Sample size of Simulation A = 1500 * 100 = 150000

Overall Sample size of Simulation B = 2000 * 50 = 100000

Since the sample size for Simulation A is greater, the variability of Simulation will be less.

Therefore, The answer is  C) The centers will roughly be equal, and the variability of simulation A will be less than the variability of simulation B.

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Market-share-analysis company Net Applications monitors and reports on Internet browser usage. According to Net Applications, in
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Answer:

a) There is a 2.43% probability that exactly 8 of the 20 Internet browser users use Chrome as their Internet browser.

b) There is an 80.50% probability that at least 3 of the 20 Internet browsers users use Chrome as their Internet browser.

c) The expected number of Chrome users is 4.074.

d) The variance for the number of Chrome users is 3.2441.

The standard deviation for the number of Chrome users is 1.8011.

Step-by-step explanation:

For each Internet browser user, there are only two possible outcomes. Either they use Chrome, or they do not. This means that we can solve this problem using concepts of the binomial probability distribution.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinatios of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

In this problem we have that:

Google Chrome has a 20.37% share of the browser market. This means that p = 0.2037

20 Internet users are sampled, so n = 20.

a.Compute the probability that exactly 8 of the 20 Internet browser users use Chrome as their Internet browser.

This is P(X = 8).

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 8) = C_{20,8}.(0.2037)^{8}.(0.7963)^{12} = 0.0243

There is a 2.43% probability that exactly 8 of the 20 Internet browser users use Chrome as their Internet browser.

b.Compute the probability that at least 3 of the 20 Internet browsers users use Chrome as their Internet browser.

Either there are less than 3 Chrome users, or there are three or more. The sum of the probabilities of these events is decimal 1. So:

P(X < 3) + P(X \geq 3) = 1

P(X \geq 3) = 1 - P(X < 3)

In which

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

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P(X = 1) = C_{20,1}.(0.2037)^{1}.(0.7963)^{19} = 0.0538

P(X = 2) = C_{20,2}.(0.2037)^{2}.(0.7963)^{18} = 0.1307

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0105 + 0.0538 + 0.1307 = 0.1950

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E(X) = np

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E(X) = 20*0.2037 = 4.074

The expected number of Chrome users is 4.074.

d.For the sample of 20 Internet browser users, compute the variance and standard deviation for the number of Chrome users.

We have that, for a binomial experiment, the variance is

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So

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The variance for the number of Chrome users is 3.2441.

The standard deviation is the square root of the variance. So

\sqrt{Var(X)} = \sqrt{3.2441} = 1.8011

The standard deviation for the number of Chrome users is 1.8011.

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