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3 years ago

If ,f(x)=x^3-x what is the average rate of change of f(x) over the interval [1, 5]?

Mathematics

2 answers:

Andrej [43]3 years ago

8 0

Answer:

Its b.30

Step-by-step explanation:

Brums [2.3K]3 years ago

6 0

Answer:

Option b is correct

30 is the average rate of change of f(x) over the interval [1, 5]

Step-by-step explanation:

Average rate of change (A(x)) of f(x) over interval [a, b] is given by:

$A(x) = \frac{f(b)-f(a)}{b-a}$ ....[1]

As per the statement:

Given the function:

$f(x) = x^3-x$

We have to find the average rate of change of f(x) over the interval [1, 5].

At x = 1

then;

$f(1) = 1^3-1 =1-1 = 0$

At x= 5

then;

$f(1) = 5^3-5 =125-5 =120$

Substitute these given values in [1] we have;

$A(x) = \frac{f(5)-f(1)}{5-1}$

⇒ $A(x) = \frac{120-0}{4}$

⇒ $A(x) = \frac{120}{4}=30$

Therefore, the average rate of change of f(x) over the interval [1, 5] is, 30

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Answer:

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3 years ago

A survey was conducted two years ago asking college students their top motivations for using a credit card. To determine whether

salantis [7]

Answer:

See explanation

Step-by-step explanation:

Solution:-

- A survey was conducted among the College students for their motivations of using credit cards two years ago. A randomly selected group of sample size n = 425 college students were selected.

- The results of the survey test taken 2 years ago and recent study are as follows:

Old Survey ( % ) New survey ( Frequency )

Reward 27 112

Low rate 23 96

Cash back 21 109

Discount 9 48

Others 20 60

- We are to test the claim for any changes in the expected distribution.

We will state the hypothesis accordingly:

Null hypothesis: The expected distribution obtained 2 years ago for the motivation behind the use of credit cards are as follows: Rewards = 27% , Low rate = 23%, Cash back = 21%, Discount = 9%, Others = 20%

Alternate Hypothesis: Any changes observed in the expected distribution of proportion of reasons for the use of credit cards by college students.

( We are to test this claim - Ha )

We apply the chi-square test for independence.

- A chi-square test for independence compares two variables in a contingency table to see if they are related. In a more general sense, it tests to see whether distributions of categorical variables differ from each other.

- We will compute the chi-square test statistics ( X^2 ) according to the following formula:

$X^2 = Sum [ \frac{(O_i - E_i)^2}{Ei} ]$

Where,

O_i : The observed value for ith data point

E_i : The expected value for ith data point.

- We have 5 data points.

So, Oi :Rewards = 27% , Low rate = 23%, Cash back = 21%, Discount = 9%, Others = 20% from a group of n = 425.

Ei : Rewards = 112 , Low rate = 96, Cash back = 109, Discount = 48, Others = 60.

Therefore,

$X^2 = [ \frac{(112 - 425*0.27)^2}{425*0.27} + \frac{(96 - 425*0.23)^2}{425*0.23} + \frac{(109 - 425*0.21)^2}{425*0.21} + \frac{(48 - 425*0.09)^2}{425*0.09} + \frac{(60 - 425*0.20)^2}{425*0.20}]\\\\X^2 = [ 0.06590 + 0.03132 + 4.37044 + 2.48529 + 7.35294]\\\\X^2 = 14.30589$

- Then we determine the chi-square critical value ( X^2- critical ). The two parameters for evaluating the X^2- critical are:

Significance Level ( α ) = 0.10

Degree of freedom ( v ) = Data points - 1 = 5 - 1 = 4

Therefore,

X^2-critical = X^2_α,v = X^2_0.1,4

X^2-critical = 7.779

- We see that X^2 test value = 14.30589 is greater than the X^2-critical value = 7.779. The test statistics value lies in the rejection region. Hence, the Null hypothesis is rejected.

Conclusion:-

This provides us enough evidence to conclude that there as been a change in the claimed/expected distribution of the motivations of college students to use credit cards.

6 0

4 years ago

39 is what percent of 52?

Schach [20]

Answer:

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Step-by-step explanation:

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3 years ago

First, the population is subdivided by metropolitan area. Then a crime researcher uses a random number generator to select twent

ss7ja [257]

Answer:

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Step-by-step explanation:

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These smaller sub-groups are called as strata.

These sub-groups are formed on the basis of similar characteristics and attributes shared by the population.

It is also known as proportional random sampling.

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4 years ago

Does the table show a direct proportional relationship? If so, what is the constant of proportionality?

lesantik [10]

Answer:

C. Yes, 3.5.

Step-by-step explanation:

If there is a relationship of direct proportionality for every ordered pair of the table, then the constant of proportionality must the same for every ordered pair. The constant of proportionality ( $k$ ) is described by the following expression:

$k = \frac{y}{x}$ (1)

Where:

$x$ - Input.

$y$ - Output.

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