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question:In early 2010, 33% of subprime mortgages in a certain country were in distress, meaning that their holders were either being foreclosed on or were at least 90 days delinquent on their payments. The federal government is hopeful that this percentage has declined due to mortgage aid programs that were initiated during the year. To test this hypothesis, a random sample of 400 subprime mortgages was selected later in 2010. From this sample, it was found that 123 mortgages were in distress. Using α = 0.10, answer parts a and b below. a. Determine the null and alternative hypotheses. b. Determine the critical value(s) of the test statistic.

answer:** **a. Hypotheses:** {eq}H_0: pi = 0.33{/eq} {eq}H_1: pi < 0.33{/eq} Where: {eq}H_0{/eq} is the null hypothesis, which states that the population proportion of subprime mortgages in distress is equal to 0.33. {eq}H_1{/eq} is the alternative hypothesis, which states that the population proportion of subprime mortgages in distress is less than 0.33. **b. Critical Value:** {eq}z_{alpha} = -1.28{/eq} The critical value is found using a standard normal distribution table or calculator. For a significance level of α = 0.10, the critical value is -1.28. This means that if the test statistic is less than -1.28, we will reject the null hypothesis.

question:A steel cable with a density of 7860 kg/m³ has a tension of 1.04*10⁴ N. If a transverse wave travels along the cable at a speed of 22.515 m/s, what is the cross-sectional area of the cable?

answer:Using the formula for the speed of a transverse wave on a string, v = √(T/μ), where T is the tension and μ is the linear mass density, we can solve for the linear mass density: μ = T/v² μ = (1.04*10⁴ N) / (22.515 m/s)² μ = 20.5146 kg/m Since linear mass density is equal to the cross-sectional area multiplied by the density of the material, we can solve for the cross-sectional area: A = μ/ρ A = (20.5146 kg/m) / (7860 kg/m³) A = 2.61*10⁻³ m²

question:What is Linkage Disequilibrium (LD) in population genetics, and how does it affect the genetic structure of a population?

answer:Linkage Disequilibrium (LD) refers to the non-random association of alleles at different genetic loci within a population. This occurs when the frequency of allele combinations is either higher or lower than expected if the loci were independent and associated randomly. Explanation: Loci are considered to be in disequilibrium when their alleles show a pattern of association that deviates from the randomness that would be observed under independence. This deviation implies that haplotypes, or specific combinations of alleles, do not occur at their expected frequencies. LD serves as a sensitive measure of the population genetic forces shaping a genome. The pattern of LD across a genome provides valuable insights into the processes that have influenced its structure, including both natural and artificial selection. Moreover, LD contains information about a population's historical events and can constraint the potential response to these selective pressures. In genetic studies, particularly those focused on identifying or localizing genes linked to disease susceptibility, LD is a crucial concept. The extent of LD between two alleles is influenced by factors such as the time since mutation events, genetic distance, and the population's historical demographics.

question:Describe how to determine if a shape has reflection symmetry.

answer:To determine if a shape has reflection symmetry, draw an imaginary line (axis) through the shape. If the part of the shape on one side of the axis is identical to the part on the other side, the shape has reflection symmetry.

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