33rd USAMO 2003
... Show that for each n we can find an n-digit number with all its digits odd which is divisible by 5n. Solution Induction on n. For n = 1 we have 5. So suppose N works for n. Consider the five n+1 digit numbers 10n + N, 3·10n + N, 5·10n + N, 7·10n, 9·10n. We may take out the common factor 5n to get th ...
... Show that for each n we can find an n-digit number with all its digits odd which is divisible by 5n. Solution Induction on n. For n = 1 we have 5. So suppose N works for n. Consider the five n+1 digit numbers 10n + N, 3·10n + N, 5·10n + N, 7·10n, 9·10n. We may take out the common factor 5n to get th ...
Transcendence of Various Infinite Series Applications of Baker’s Theorem and
... In chapter 4 we generalize the series studied in chapter 2 to include multivariable series of similar form. We give a full analysis and calculate closed forms. These results are completely new and have not appeared anywhere in the literature. We have: Corollary 4.10 Let f be an algebraic valued func ...
... In chapter 4 we generalize the series studied in chapter 2 to include multivariable series of similar form. We give a full analysis and calculate closed forms. These results are completely new and have not appeared anywhere in the literature. We have: Corollary 4.10 Let f be an algebraic valued func ...
Caffeine in bloodstream (mg)
... original graph does not pass the horizontal line test. That is, for each output value (SA), there are two input values (r). Graphing the relation in part (e) shows a sideways parabola. It does not pass the vertical line test. That is, for each input (SA), there are two outputs (r). ...
... original graph does not pass the horizontal line test. That is, for each output value (SA), there are two input values (r). Graphing the relation in part (e) shows a sideways parabola. It does not pass the vertical line test. That is, for each input (SA), there are two outputs (r). ...
One-Way Analysis of Variance
... Planned Comparisons PASS performs power and sample size calculations for user-specified contrasts. The usual F test tests the hypothesis that all means are equal versus the alternative that at least one mean is different from the rest. Often, a more specific alternative is desired. For example, you ...
... Planned Comparisons PASS performs power and sample size calculations for user-specified contrasts. The usual F test tests the hypothesis that all means are equal versus the alternative that at least one mean is different from the rest. Often, a more specific alternative is desired. For example, you ...
least common multiple - Kyrene School District
... Try This: Example 1 Dog cookies come in packages of 6, and bones in bags of 9. If there are 18 dogs, what is the least number of packages and bags needed so that each dog has a treat box with one bone and one cookie and there are no bones or cookies left over? Draw cookies in groups of 6. Draw bones ...
... Try This: Example 1 Dog cookies come in packages of 6, and bones in bags of 9. If there are 18 dogs, what is the least number of packages and bags needed so that each dog has a treat box with one bone and one cookie and there are no bones or cookies left over? Draw cookies in groups of 6. Draw bones ...
Elementary mathematics
Elementary mathematics consists of mathematics topics frequently taught at the primary or secondary school levels. The most basic topics in elementary mathematics are arithmetic and geometry. Beginning in the last decades of the 20th century, there has been an increased emphasis on problem solving. Elementary mathematics is used in everyday life in such activities as making change, cooking, buying and selling stock, and gambling. It is also an essential first step on the path to understanding science.In secondary school, the main topics in elementary mathematics are algebra and trigonometry. Calculus, even though it is often taught to advanced secondary school students, is usually considered college level mathematics.