answer:-2 Explanation: The expected value is calculated as follows: Expected value = (Probability of winning * Value of winning) + (Probability of losing * Value of losing) Expected value = (0.2 * 100) + (0.8 * -10) Expected value = 20 - 8 Expected value = -2

answer:To integrate the given expression, we can use the substitution method. Let {eq}u = 4x^{5} - 3 {/eq} Then {eq}du = 20x^{4}dx {/eq} Substituting into the integral, we get: {eq}int dfrac{x^{4}dx}{(4x^{5}-3)^{6}} = int dfrac{1}{20u^{6}}du {/eq} Now we can use the power rule of integration: {eq}int u^{n}du = dfrac{u^{n+1}}{n+1} + C {/eq} Applying this rule, we get: {eq}int dfrac{1}{20u^{6}}du = dfrac{1}{20} cdot dfrac{u^{-5}}{-5} + C {/eq} {eq}= -dfrac{1}{100u^{5}} + C {/eq} Substituting back for u, we get the final answer: {eq}int dfrac{x^{4}dx}{(4x^{5}-3)^{6}} = -dfrac{1}{100(4x^{5}-3)^{5}} + C {/eq} where C is an arbitrary constant.

answer:A scientific law is a concise and observable phenomenon in the natural world that consistently holds true whenever it is experimentally tested. It primarily focuses on stating what will be observed but does not delve into the underlying reasons for the observation. For instance, Ohm's Law describes how electric current is directly proportional to voltage and inversely proportional to resistance, but it does not explain why this relationship exists. In contrast, a theory is a comprehensive, well-substantiated explanation for a set of related phenomena. It not only describes observations but also offers a mechanism or cause behind them. The theory of evolution by natural selection, proposed by Charles Darwin, explains how species change over time and adapt to their environments, providing a robust framework for understanding biodiversity. The work of Gregor Mendel serves as a good example. Mendel's laws of inheritance describe the patterns of trait inheritance in pea plants, which are considered laws because they consistently predict offspring characteristics. However, the mechanism behind this inheritance, later explained by the discovery of genes and DNA, is a theory known as the genetic theory.

answer:The formula for the nth partial sum of an arithmetic sequence is given by S_n = frac{n}{2}(2a_1 + (n - 1)d). Applying the given values: S_9 = frac{9}{2}(2 cdot frac{95}{37} + (9 - 1) cdot frac{11}{5}) Now, we'll calculate the sum: S_9 = frac{9}{2} left(frac{190}{37} + frac{8 cdot 11}{5}right) S_9 = frac{9}{2} left(frac{190}{37} + frac{88}{5}right) To find a common denominator, let's multiply frac{88}{5} by frac{37}{37}: S_9 = frac{9}{2} left(frac{190}{37} + frac{308}{37}right) S_9 = frac{9}{2} cdot frac{498}{37} Now, multiply: S_9 = frac{9 cdot 498}{2 cdot 37} S_9 = frac{4482}{74} Simplifying the fraction: S_9 = frac{2241}{37} S_9 = frac{18927}{185} The 9th partial sum, S_9, is frac{18927}{185}.