/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 24 Where does all the water go? Acc... [FREE SOLUTION] | 91Ó°ÊÓ

91Ó°ÊÓ

Where does all the water go? According to the Environmental Protection Agency (EPA), in a typical wetland environment, \(38 \%\) of the water is outflow; \(47 \%\) is seepage; \(7 \%\) evaporates; and \(8 \%\) remains as water volume in the ecosystem (Reference: U.S. Environmental Protection Agency Case Studies Report 832 -R-93-005). Chloride compounds as residuals from residential areas are a problem for wetlands. Suppose that in a particular wetland environment the following concentrations \((\mathrm{mg} / 1)\) of chloride compounds were found: outflow, \(64.1 ;\) seepage, \(75.8\); remaining due to evaporation, \(23.9 ;\) in the water volume, \(68.2\). (a) Compute the weighted average of chlorine compound concentration \((\mathrm{mg} / \mathrm{l})\) for this ecological system. (b) Suppose the EPA has established an average chlorine compound concentration target of no more than \(58 \mathrm{mg} / 1 .\) Comment on whether this wetlands system meets the target standard for chlorine compound concentration.

Short Answer

Expert verified
The wetland system does not meet the EPA's target since the weighted average concentration is 67.113 mg/L, which is higher than the target of 58 mg/L.

Step by step solution

01

Understand the Problem

We need to calculate the weighted average of chloride compound concentrations in a wetland system. Different parts of the wetland contribute different percentages to the overall water handling. Each section (outflow, seepage, evaporation, water volume) has a corresponding percentage and chloride concentration that will be used to compute the weighted average.
02

Identify the Weights and Values

Identify the given data: - Outflow: 38% weight, 64.1 mg/L concentration. - Seepage: 47% weight, 75.8 mg/L concentration. - Evaporation: 7% weight, 23.9 mg/L concentration. - Water Volume: 8% weight, 68.2 mg/L concentration.
03

Calculate Each Component's Contribution

Convert percentages to decimals and calculate each component's contribution to the weighted average. - Outflow contribution: 0.38 * 64.1 = 24.358 - Seepage contribution: 0.47 * 75.8 = 35.626 - Evaporation contribution: 0.07 * 23.9 = 1.673 - Water volume contribution: 0.08 * 68.2 = 5.456
04

Sum the Contributions

Add all the contributions from each component:\[ 24.358 + 35.626 + 1.673 + 5.456 = 67.113 \]
05

Check Against EPA's Target

The EPA target for chloride concentration is 58 mg/L. The computed weighted average is 67.113 mg/L. Compare the two values to determine if the system meets the target.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91Ó°ÊÓ!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Chloride Concentration
Understanding chloride concentration plays a crucial role in evaluating the health of a wetland ecosystem. Chloride is a type of ion typically found in saline and brackish environments. In this context, chloride concentration refers to the number of chloride ions in the water, measured in milligrams per liter (mg/L).
This is significant because excessive amounts of chloride can be harmful to aquatic life and the overall ecosystem's functioning. Chloride concentrations in the water largely depend on external sources like road salts and residential runoff.
In our exercise, the chloride concentration is provided for four different segments of the wetland: outflow, seepage, evaporation, and the remaining water volume. Each of these segments has varying chloride levels, which are used to calculate the average concentration across the entire wetland system. Calculating this average is essential to understand the current chloride levels against environmental guidelines, ensuring that the ecosystem remains within acceptable safety and health boundaries.
Wetland Ecosystem
Wetlands are a critical component of natural landscapes, serving as buffers against floods, filters for pollutants, and habitats for diverse wildlife. These ecosystems are complex interactions between water, soil, and living organisms, which makes maintaining their balance essential for their health.
Wetlands manage water through different processes—outflow, seepage, evaporation, and retention in the soil and plants. Each function has a distinct role in how the wetland operates.
  • Outflow: This is the movement of water out of the wetland, downstream to rivers or streams.
  • Seepage: Water slowly filters through the ground. It helps to recharge underground aquifers.
  • Evaporation: Some water evaporates into the atmosphere, contributing to the water cycle.
  • Water Volume: This is the remaining water stored within the wetland ecosystem.
Managing these processes effectively is essential for the health of the ecosystem. When measuring variables like chloride, understanding how these parts interact is key to assessing environmental impacts.
Environmental Statistics
Environmental statistics involve gathering quantitative data to make informed decisions about ecological health and management. It includes analyzing concentrations of pollutants, such as chloride, to ensure ecosystems are within safe limits. The process of calculating a weighted average from various contributing factors showcases one such statistical method.
In our exercise, we applied the concept of a weighted average to calculate chloride concentration. Each wetland section contributes to overall water handling differently, influencing the average concentration differently.
Steps involve: - Converting reported percentages into decimal form as weights. - Multiplying these weights by the chloride concentration of each section. - Summing these results to acquire the overall weighted average. Using this statistical analysis, one can compare the computed average with predetermined environmental standards, like the EPA targets mentioned in the exercise. This helps determine if the system meets environmental safety targets, crucial for preserving and protecting the wetland.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

When computing the standard deviation, does it matter whether the data are sample data or data comprising the entire population? Explain.

Each of the following data sets has a mean of \(\bar{x}=10 .\) \(\begin{array}{llllll}\text { (i) } 8 & 9 & 10 & 11 & 12\end{array}\) \(\begin{array}{llllll}\text { (ii) } 7 & 9 & 10 & 11 & 13\end{array}\) \(\begin{array}{llllll}\text { (iii) } 7 & 8 & 10 & 12 & 13\end{array}\) (a) Without doing any computations, order the data sets according to increasing value of standard deviations. (b) Why do you expect the difference in standard deviations between data sets (i) and (ii) to be greater than the difference in standard deviations between data sets (ii) and (iii)? Hint: Consider how much the data in the respective sets differ from the mean.

Pax World Balanced is a highly respected, socially responsible mutual fund of stocks and bonds (see Viewpoint). Vanguard Balanced Index is another highly regarded fund that represents the entire U.S. stock and bond market (an index fund). The mean and standard deviation of annualized percent returns are shown below. The annualized mean and standard deviation are based on the years 1993 through 2002 (Source: Morningstar). Pax World Balanced: \(\bar{x}=9.58 \% ; s=14.05 \%\) Vanguard Balanced Index: \(\bar{x}=9.02 \% ; s=12.50 \%\) (a) Compute the coefficient of variation for each fund. If \(\bar{x}\) represents return and \(s\) represents risk, then explain why the coefficient of variation can be taken to represent risk per unit of return. From this point of view, which fund appears to be better? Explain. (b) Compute a \(75 \%\) Chebyshev interval around the mean for each fund. Use the intervals to compare the two funds. As usual, past performance does not guarantee future performance.

How large is a wolf pack? The following information is from a random sample of winter wolf packs in regions of Alaska, Minnesota, Michigan, Wisconsin, Canada, and Finland (Source: The Wolf, by L. D. Mech, University of Minnesota Press). Winter pack size: \(\begin{array}{rrrrrrrrr}13 & 10 & 7 & 5 & 7 & 7 & 2 & 4 & 3 \\ 2 & 3 & 15 & 4 & 4 & 2 & 8 & 7 & 8\end{array}\) Compute the mean, median, and mode for the size of winter wolf packs.

Kevlar epoxy is a material used on the NASA space shuttles. Strands of this epoxy were tested at the \(90 \%\) breaking strength. The following data represent time to failure (in hours) for a random sample of 50 epoxy strands (Reference: R. E. Barlow, University of California, Berkeley). Let \(x\) be a random variable representing time to failure (in hours) at \(90 \%\) breaking strength. Note: These data are also available for download at the Online Study Center. \(\begin{array}{llllllllll}0.54 & 1.80 & 1.52 & 2.05 & 1.03 & 1.18 & 0.80 & 1.33 & 1.29 & 1.11 \\ 3.34 & 1.54 & 0.08 & 0.12 & 0.60 & 0.72 & 0.92 & 1.05 & 1.43 & 3.03 \\ 1.81 & 2.17 & 0.63 & 0.56 & 0.03 & 0.09 & 0.18 & 0.34 & 1.51 & 1.45 \\ 1.52 & 0.19 & 1.55 & 0.02 & 0.07 & 0.65 & 0.40 & 0.24 & 1.51 & 1.45 \\ 1.60 & 1.80 & 4.69 & 0.08 & 7.89 & 1.58 & 1.64 & 0.03 & 0.23 & 0.72\end{array}\) (a) Find the range. (b) Use a calculator to verify that \(\Sigma x=62.11\) and \(\Sigma x^{2} \approx 164.23\). (c) Use the results of part (b) to compute the sample mean, variance, and standard deviation for the time to failure. (d) Use the results of part (c) to compute the coefficient of variation. What does this number say about time to failure? Why does a small \(C V\) indicate more consistent data, whereas a larger \(\mathrm{CV}\) indicates less consistent data? Explain.

See all solutions

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.