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love history [14]
4 years ago
15

Two scientists are running experiments testing the effects of a vaccine on different control groups. The results are shown in th

e graph using the functions f(x) and g(x): Which statement best describes the graph of f(x) and g(x)?
A- The graph of g(x) will eventually exceed the graph of f(x)
B- The graph of f(x) will eventually exceed the graph of g(x)
C- The graphs will both have their y-intercept equal to 5
D- The graphs will both have their y-intercept equal to 2
PLEASE HELP ME!!!!

Mathematics
2 answers:
kupik [55]4 years ago
7 0

Answer:

The correct option is B.

Step-by-step explanation:

The graph of f(x) is g(x) is given.

Graph of both functions intersect each other at a point. Before the point of intersection g(x)>f(x) and after the point of intersection g(x)<f(x).

The graph of f(x) will eventually exceed the graph of g(x). Therefore the correct option is B.

Function g(x)<f(x) for the large value of x, So option A is incorrect.

From the given graph it is clear that the y-intercept of f(x) is 0.2 and y-intercept of g(x) is 2.

So, option C and D are incorrect.

Alexxandr [17]4 years ago
4 0

Answer: I believe <em>the answer is B</em>.

Although, if the answer to this question isn't B, it should defiantly be C.

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(b) The probability that the height is between 66 and 71 inches is 0.4679.

(c) The probability that the height is more than 71 inches is 0.2578.

Step-by-step explanation:

The data given in the question is:

Mean (μ) = 68.4

Standard Deviation (σ) = 4

Let X denote the height of men. We will use the normal distribution z-score formula to calculate the z-score and then look up the probability in the normal probability distribution table. The z-score formula is:

z = (X - μ)/σ

(a) For P(X<66), first calculate the z value.

z = (66-68.4)/4

z = -0.6 (Look up this value in the standard normal distribution table)

P(z<-0.6) = 0.2743

The probability that his height is less than 66 inches is 0.2743.

(b) P(66<X<71)  = P(X<71) - P(X<66)

We need to find P(X<71) so, calculating the z-value:

z = (71-68.4)/4

z = 0.65

P(z<0.65) = 0.7422

P(66<X<71)  = 0.7422 - 0.2743

P(66<X<71)  = 0.4679

The probability that the height is between 66 and 71 inches is 0.4679.

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P(X>71) = 0.2578

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Previous concepts  

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".  

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Let X the random variable of interest, on this case we now that:  

X \sim Binom(n=7, p=0.51)  

The probability mass function for the Binomial distribution is given as:  

P(X)=(nCx)(p)^x (1-p)^{n-x}  

Where (nCx) means combinatory and it's given by this formula:  

nCx=\frac{n!}{(n-x)! x!}  

For this case we want to find this probability:

P(X \geq 3)

And we can use the complement rule for this case:

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

If we find the individual probabilities we gotL

P(X=0)=(7C0)(0.51)^0 (1-0.51)^{7-0}=0.0068  

P(X=1)=(7C1)(0.51)^1 (1-0.51)^{7-1}=0.0494  

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And replacing we got:

P(X \geq 3) = 1- [0.0068 +0.0494 +0.1543]= 0.7895

 

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