Chapter 10.3, Problem 50E

A tank contains 200 gal of fresh water. A solution containing 4 lb/gal of soluble lawn fertilizer runs into the tank at the rate of 1 gal/min, and the mixture is pumped out of the tank at the rate of 5 gal/min. Find the maximum amount of fertilizer in the tank and the time required to reach the maximum. Find the time required to reach the maximum amount of fertilizer in the tank. t= min (Type an integer or decimal rounded to the nearest tenth as needed.)

Suppose the random variable X is normally distributed with mean 80 and standard deviation 16. Find following probabilities. Find ‘b’ such that P(X ≥ b) = 0.975. Find the probability using a normal distribution table AND using ti-83 calculator. SHOW ALL STEPS PLEASE.

Thumbi Irrigation Scheme in Mzimba district is under threat of flooding. In order to mitigate against the problem, authorities have decided to construct a flood protection bund (Dyke). Figure 1 is a cross section of a 300m long proposed dyke; together with its foundation (key). Survey data for the proposed site of the dyke are presented in Table 1. Table 2 provides swelling and shrinkage factors for the fill material that has been proposed. The dyke dimensions that are given are for a compacted fill. (1) Assume you are in the design office, use both the Simpson Rule and Trapezoidal Rule to compute the total volume of earthworks required. (Assume both the dyke and the key will use the same material). (2) If you are a Contractor, how many days will it take to finish hauling the computed earthworks using 3 tippers of 12m³ each? Make appropriate assumptions. DIKE CROSS SECTION OGL KEY (FOUNDATION) 2m 1m 2m 8m Figure 1: Cross section of Dyke and its foundation 1.5m from highest OGL 0.5m…

Suppose the random variable X is normally distributed with mean 80 and standard deviation 16. Find following probabilities. Equation:  P(85 ≤ X ≤ 102).  Find the probability using a normal distribution table AND using ti-83 calculator. SHOW ALL STEPS PLEASE.

Data set is Bachelor Degree's Conferred by Race and Ethnicity.

The parametric equations of the function are given as x = 3cos 0 - sin³0 and y = 3sin 0 - cos³0. dy d2y Calculate and dx dx².

4. Vons, a large supermarket in Grover Beach, California, is con- sidering extending its store hours from 7:00 am to midnight, seven days a week, to 6:00 am to midnight. Discuss the sam- pling bias in the following sampling strategies:

3. Natalie Min is an undergraduate in the Haas School of Busi- ness at Berkeley. She wishes to pursue an MBA from Berkeley and wants to know the profile of other students who are likely to apply to the Berkeley MBA program. In particular, she wants to know the GPA of students with whom she might be compet- ing. She randomly surveys 40 students from her accounting class for the analysis. Discuss in detail whether or not Natalie's analysis is based on a representative sample.

See data attached. SoftBus Company sells PC equipment and customized software to small companies to help them manage their day-to-day business activities. Although SoftBus spends time with all customers to understand their needs, the customers are eventually on their own to use the equipment and software intelligently. To understand its customers better, SoftBus recently sent questionnaires to a large number of prospective customers. Key personnel—those who would be using the software—were asked to fill out the questionnaire. SoftBus received 82 usable responses, as shown in the file. You can assume that these employees represent a random sample of all of SoftBus's prospective customers. SoftBus believes it can afford to spend much less time with customers who own PCs and score at least 4 on PC Knowledge. Let's call these the "PC-savvy" customers. On the other hand, SoftBus believes it will have to spend a lot of time with customers who do not own a PC and score 2 or less on PC…