If f(x) is an odd function, which statement about the graph f(x) must be true?
1 answer:
Answer:
The correct answer is A) It has rotational symmetry about the origin.
Step-by-step explanation:
In principle, the graph of an odd function is symmetric with respect to the origin. This simply means that the point (0 ,0) acts as a mirror line to the function so that one half of the function looks exactly like the other half when reflected over the origin.
A function f(x) is said to be odd if and only if;
f(-x) = -f(x)
The ultimate example of an odd function is the sine function. Consider the function below;
f(x) = sin(x)
Then;
f(-x) = sin(-x) = -sin(x) = -f(x)
Working with actual values;
sin(-30) = -sin(30) = -0.5
A graph of the function f(x) = sin(x) is shown in the attachment below;
If the graph is rotated about the origin, we would still end up with the same graph.
In summary, an odd function is symmetric with respect to the origin and has rotational symmetry about the origin.
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I hope the picture is legible.
Answer:
For 90 minutes of TV there will be 24 mins of commercials
Step-by-step explanation:
You start with 30 and keep adding 30 mins each time until you get to 90. (So..30..60..90) each time you add 30mins you add 8 more minutes to the commercials)
30 mins tv----8mins commercials
60 mins tv----16mins commercials
90 mins tv----24mins commercials
Hope this helps, good luck!
Answer:
Step-by-step explanation:
Hello!
The objective is to test if the purchase frequencies of new-car buyers follow the distribution of the shares of the U.S. automobile market for 1990.
You have one variable of interest:
X: Brand a new-car buyer prefers, categorized: GM, Japanese, Ford, Chrysler and Other
n= 1000
Observed frequencies
GM 193
Japanese 384
Ford 170
Chrysler 90
Other 163
a) The test to use to analyze if the observed purchase frequencies follow the market distribution you have to conduct a Goodness to Fit Chi-Square test.
The conditions for this test are:
- Independent observations
In this case, we will assume that each buyer surveyed is independent of the others.
- For 3+ categories: each expected frequency (Ei) must be at least 1 and at most 20% of the Ei are allowed to be less than 5.
In our case we have a total of 5 categories, 20% of 5 is 1, only one expected frequency is allowed to have a value less than 5.
I'll check this by calculating all expected frequencies using the formula: Ei= n*Pi (Pi= theoretical proportion that corresponds to the i-category)
E(GM)= n*P(GM)= 1000*0.36= 360
E(Jap)= n*P(Jap)= 1000*0.26= 260
E(Ford)= n*P(Ford)= 1000*0.21= 210
E(Chrys)= n*P(Chrys)= 1000*0.09= 90
E(Other)= n*P(Other)= 1000*0.08= 80
Note: If all calculations are done correctly then ∑Ei=n.
This is a quick way to check if the calculations are done correctly.
As you can see all conditions for the test are met.
b) The hypotheses for this test are:
H₀: P(GM)= 0.36; P(Jap)= 0.26; P(Ford)= 0.21; P(Chrys)= 0.09; P(Other)= 0.08
H₁: At least one of the expected frequencies is different from the observed ones.
α: 0.05
k= number of categories of the variable.
This test is one-tailed right this mean you'll reject the null hypothesis to high values of X²
Decision rule using the critical value approach:
If ≥ 9.488, reject the null hypothesis
If < 9.488, don't reject the null hypothesis
The value of the statistic under the null hypothesis is greater than the critical value, so the decision is to reject the null hypothesis.
Using a 5% level of significance, there is significant evidence to conclude that the current market greatly differs from the preference distribution of 1990.