Answer:
Step-by-step explanation:
<u>Rational Numbers</u>
A rational number is any number that can be expressed as a fraction
for a and b any integer and b different from 0.
As a consequence, any number that cannot be expressed as a fraction or rational number is defined as an Irrational number.
Let's analyze each one of the given options
The first part of the number is indeed a rational number, but the second part is a square root whose result cannot be expressed as a rational, thus the number is not rational
The second part is an exact square root (resulting 4) but the first part is a known irrational number called pi. It's not possible to express pi as a fraction, thus the number is irrational
The square root of 121 is 11. It makes the whole number a sum of a rational number plus an integer, thus the given number is rational
As with the first number, the square root is not exact. The sum of a rational number plus an irrational number gives an irrational number.
Correct option:
Answer:
0.4
Step-by-step explanation:
The numbers -3.5 and -3.1 have a difference in value of 0.4
An easy way to look at this is to remove the decimal points. 35 - 31 is equal to 4, so that would make the difference 0.4.
Because both numbers are negative, the x must be a positive.
Therefor, 0.4 - 3.5 = -3.1
Answer:
Step-by-step explanation:
Solutions, zeros, and roots of a polynomial are all the same exact thing and can be used interchangeably. When you factor a polynomial, you solve for x which are the solutions of the polynomial. Since, when you factor a polynomial, you do so by setting the polynomial equal to 0, by definition of x-intercept, you are finding the zeros (don't forget that x-intercepts exist where y is equal to 0). There's the correlation between zeros and solutions.
Since factoring and distributing "undo" each other (or are opposites), if you factor to find the zeros, you can distribute them back out to get back to the polynomial you started with. Each zero or solution is the x value when y = 0. For example, if a solution to a polynomial is x = 3, since that is a zero of the polynomial, we can set that statement equal to 0: x - 3 = 0. What we have then is a binomial factor of the polynomial in the form (x - 3). These binomial factors found from the solutions/zeros of the polynomial FOIL out to give you back the polynomial equation.
Answer:
ii) a Bonferonni-corrected alpha level of 0.0167 to control the type I error rate for the overall inference to 5% .
Step-by-step explanation:
Previous concepts
Analysis of variance (ANOVA) "is used to analyze the differences among group means in a sample".
The sum of squares "is the sum of the square of variation, where variation is defined as the spread between each individual value and the grand mean"
The hypothesis for this case are:
Null hypothesis: 
Alternative hypothesis: Not all the means are equal 
Since we reject the null hypothesis we want to see which method it's the best to determine which group(s) is (are) different is pairwise two-sample t-tests each assessed using.
And on this case the best option is:
ii) a Bonferonni-corrected alpha level of 0.0167 to control the type I error rate for the overall inference to 5% .
The reason is because the Bonferroni correction "compensates for that increase by testing each individual hypothesis at a significance level of 
who represent the desired overall alpha level and m is the number of hypotheses". For our case m=3 hypotheses with a desired 
, then the Bonferroni correction would test each individual hypothesis at 
One advatange of this method is that "This method not require any assumptions about dependence among the p-values or about how many of the null hypotheses are true" . And is more powerful than the individual paired t tests.
