The given set is not a vector space over R.
To prove that the set {p(x) E R3[x] : p'(1) = p(0)} with regular operations is not a vector space over R, we need to show that at least one of the eight axioms of a vector space is violated. Let p(x) = 2x + 1 and q(x) = -x + 4 be two polynomials in the set.
Closure under addition: p(x) + q(x) = 2x + 1 - x + 4 = x + 5. However, (x+5)'(1) = 1 ≠ (x+5)(0) = 5, so x + 5 is not in the set. Therefore, the set is not closed under addition.
Since one of the axioms is violated, the set {p(x) E R3[x] : p'(1) = p(0)} with regular operations is not a vector space over R.
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studying the number of visitors to a website during a 24 hour period would most likely involve which of the following type of variable? a. continuous b. qualitative c. discrete d. quantitative
The variable represents the number of visitors to the website, which is a countable value. Studying the number of visitors to a website during a 24-hour period would most likely involve a quantitative type of variable.
This is because the number of visitors can be measured and expressed as numerical values. Quantitative variables can be further classified as either continuous or discrete. In this case, the number of visitors is discrete because it can only take on whole numbers. It cannot be fractional or continuous. It is important to determine the type of variable in research studies as it affects the type of statistical analysis that can be used to analyze the data. By knowing that the number of visitors is a quantitative variable, researchers can choose appropriate statistical tests to analyze the data accurately.
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