Expansion of Binomials| Algebra| ENGG10 LE1 Problem 8

Expansion of Binomials| Algebra| ENGG10 LE1 Problem 8

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Simplifying Expressions with Integral Exponents| Algebra| ENGG10 LE1 Problem 1

Simplify the given expression. Write the answer with positive exponents. $latex \left(\frac{3^2}{a^3}\right)^{-2}\cdot \left(\frac{a^4}{2^2}\right)^2&s=2&bg=ffffff&fg=000000$ SOLUTION: $latex \left(\frac{3^2}{a^3}\right)^{-2}\cdot \:\left(\frac{a^4}{2^2}\right)^2=\frac{\left(3^2\right)^{-2}}{\left(a^3\right)^{-2}}\cdot \frac{\left(a^4\right)^2}{\left(2^2\right)^2}&s=1&bg=ffffff&fg=000000$ $latex =\frac{3^{-4}}{a^{-6}}\cdot \frac{a^8}{2^4}&s=1&bg=ffffff&fg=000000$ $latex =\frac{\frac{1}{3^4}}{\frac{1}{a^6}}\cdot \frac{a^8}{2^4}&s=1&bg=ffffff&fg=000000$ $latex =\frac{a^6}{3^4}\cdot \frac{a^8}{2^4}&s=1&bg=ffffff&fg=000000$ $latex =\frac{a^6}{81}\cdot \frac{a^8}{16}&s=1&bg=ffffff&fg=000000$ $latex =\frac{a^{6+8}}{1296}&s=1&bg=ffffff&fg=000000$ $latex =\frac{a^{14}}{1296}&s=1&bg=ffffff&fg=000000$

Birth Weights of Male Babies| Confidence Interval and Hypothesis Testing for Population Mean and Standard Deviation| Statistics

Birth weights of male babies at one hospital were recorded for 200 births of boys. A mean of that sample was  35.3 hg and a standard deviation of 7.2 hg.  a) Construct a 90% confidence interval for the mean of all boy baby weights. b) A medical Journal claims that the mean weight of male babies is 37.0 hg. Test that claim at a 0.10 level of significance.  c) Use a 0.05 level of significance to test a claim that the real standard deviation of boy birth weights is 6.75 hg. 

Fast food Accuracy| Confidence Interval and Hypothesis Testing for Population Proportion| Statistics

In a recent study of drive-through orders at Burger King, they found out that 365 were accurate and 71 were not accurate. a) Construct a 95% confidence interval for the population percentage of their drive-through order that were not accurate. b) If Burger King claims to have an accuracy of 85% on all drive-through orders, test the claim at the 0.05 levels of significance.