0.25 + 1 + 4 + 16 + 64 Enter the values used in finding a partial sum.
2 answers:
Answer: The required values are
Step-by-step explanation: We are given a partial sum as follows :
0.25 + 1 + 4 + 16 + 64.
We are to find the values of
From the given partial series, we note that
the series is a geometric one with first term 0.25 and common ratio calculated as follows :
Also, since there are 5 terms in the given sum, so the value of n is 5.
Thus, the required values are
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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:
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,
- 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.
So first we need to know the order of operations
P - Parenthesis
E - Exponents
M - Multiplication
D - Division
A - Addition
S - Subtraction
Then the special cases:
(I have attached a picture below)
Lets get into action!
(5a - 2)(5a + 2) - 3( 1 - a ) - 3a
25a² - 4 - 3 + 3a - 3a
25a² - 7
25a² - 7 is the answer
P - Parenthesis
E - Exponents
M - Multiplication
D - Division
A - Addition
S - Subtraction
Then the special cases:
(I have attached a picture below)
Lets get into action!
(5a - 2)(5a + 2) - 3( 1 - a ) - 3a
25a² - 4 - 3 + 3a - 3a
25a² - 7
25a² - 7 is the answer