 Recent questions in Upper Level Math
Upper Level Math
ANSWERED ### The table shows the number of students in a school's beginning and advanced orchestra classes. The student pay a fee for instruction books: $5 for brass,$5 for woodwinds, and $8 for strings. Find the amount each class will spend on books. $$\begin{array}{|c|c|}\hline&Advanced&Beginning\\ Brass&12&28\\ Strings&22&25\\ Woodwinds&18&30\\ \hline \end{array}$$ Upper Level Math ANSWERED asked 2021-10-05 ### The following definition is discussed in advanced mathematics courses. $$f(x)=\begin{cases} 0 & \text{if xx is a rational number}\ 1 & \text{if xx is an irrational number} \end{cases}$$ Evaluate $$f(−34)$$, $$-\sqrt2$$, and $$\displaystyle{f{{\left(\pi\right)}}}$$. Upper Level Math ANSWERED asked 2021-10-04 ### Assume that all the distributions are normal, average is always taken to be the arithmetic mean xˉ or μ. A college Physical Education Department offered an Advanced First Air course last semester. The scores on the comprehensive final exam were normally distributed, and the the z scores for some of the students are shown below: Robert, 1.11 Juan, 1.66 Susan, –1.9 Joel, 0.00 Jan, –0.65 Linda, 1.46 (c) Which of these students scored below the mean? Upper Level Math ANSWERED asked 2021-10-01 ### The college physical education department offered an advanced first aid course last semester. The scores on the comprehensive final exam were normally distributed, and the z scores for some of the students are shown below: Robert, 1.10 Juan, 1.70 Susan, -2.00 Joel, 0.00 Jan, -0.80 Linda, 1.60 If the mean score was μ=150μ=150 with standard deviation σ=20,σ=20, what was the final exam score for each student? Upper Level Math ANSWERED asked 2021-09-30 ### One reason for the increase in the life span over the years has been the advances in medical technology. The average life span for American women from Email-trough 2007 is given by $$\displaystyle{W}{\left({t}\right)}={49.9}+{17.1}{\ln{{t}}}{\left({1}\leq{t}\right)}$$ where W(t) is measured in years and t is measured in 20-year intervals, with t=1 corresponding to the beginning of 1907. a. Show that W is increasing on (1, 6). b. What can you say about the concavity of the graph of W on the interval (1, 6)? Upper Level Math ANSWERED asked 2021-09-30 ### The following advanced exercise use a generalized ratio test to determine convergence of some series that arise in particular applications, including the ratio and root test, are not powerful enough to determine their convergence. The test states that if$ $$\lim_{n \rightarrow \infty} \frac{a_{2 n}}{a_{n}}<1 / 2$$ then $$\displaystyle\sum{a}_{{{n}}}$$ converges, while if $$\lim_{n \rightarrow \infty} \frac{a_{2 n+1}}{a_{n}}>1 / 2$$ then $$\displaystyle\sum{a}_{{{n}}}$$  diverges. Let $$\displaystyle{a}_{{{n}}}={\frac{{{n}^{{{\ln{{n}}}}}}}{{{\left({\ln{{n}}}\right)}^{{{n}}}}}}$$. Show that $$\frac{a_{2n}}{a_{n}} \rightarrow 0$$ as $$\displaystyle{n}\rightarrow\infty$$

Upper Level Math
ANSWERED ### Advances in medical science and healthier lifestyles have resulted in longer life expectancies. The life expectancy of a female whose current age is x years old is $$f(x)=0.0069502x2−1.6357x+93.76 (60≤x≤75)$$ years. What is the life expectancy of a female whose current age is 65? Whose current age is 75?

Upper Level Math
ANSWERED ### Driven by technological advances and financial pressures, the number of surgeries performed in physicians' offices nationwide has been increasing over the years. The function $$\displaystyle{f{{\left({t}\right)}}}=-{0.00447}{t}^{{{3}}}+{0.09864}{t}^{{{2}}}+{0.05192}{t}+{0.8}{\left({0}\leq{t}\leq{15}\right)}$$ gives the number of surgeries (in millions) performed in physicians' offices in year t, with t=0 corresponding to the beginning of 1986. a. Plot the graph of f in the viewing window [0,15] $$\times$$ [0,10]. b. Prove that f is increasing on the interval [0, 15].

Upper Level Math
ANSWERED ### Overproduction of uric acid in the body can be an indication of cell breakdown. This may be an advance indication of illness such as gout, leukemia, or lymphoma. Over a period of months, an adult male patient has taken eight blood tests for uric acid. The mean concentration was $$\bar{x}=5.35 \mathrm{mg}$$ . $$\mathrm{dl.}$$ The distribution of uric acid in healthy adult males can be assumed to be normal, with $$\sigma=1.85 \mathrm{mg}$$. $$\mathrm{dl}$$ .Find a 95% confidence interval for the population mean concentration of uric acid in this patient's blood. What is the margin of error?

Upper Level Math
ANSWERED ### Overproduction of uric acid in the body can be an indication of cell breakdown. This may be an advance indication of illness such as gout, leukemia, or lymphoma. Over a period of months, an adult male patient has taken eight blood tests for uric acid. The mean concentration was x¯=5.35mg/dl. The distribution of uric acid in healthy adult males can be assumed to be normal with σ=1.85mg/dlσ=1.85mg/dl. What conditions are necessary for your calculations?

Upper Level Math
ANSWERED ### The U.S. Census Bureau compiles census data on educational attainment of Americans. From the document Current Population Reports, we obtained the 2000 distribution of educational attainment for U.S. adults 25 years old and older. Here is that distribution. [Table] A random sample of 500 U.S. adults (25 years old and older) taken this year gave the following frequency distribution. [Table] Decide, at the 5% significance level, whether this year’s distribution of educational attainment differs from the 2000 distribution.

Upper Level Math
ANSWERED ### Painful bone metastases are common in advanced prostate cancer. Physicians often order treatment with strontium-89 (89Sr), a radionuclide with a strong affinity for bone tissue. A patient is given a sample containing 4 mCi of $$\displaystyle{89}^{{{S}{r}}}$$. If 20% of the $$\displaystyle{89}^{{{S}{r}}}$$ remains in the body after 90 days, write a function of the form $$\displaystyle{Q}{\left({t}\right)}={Q}{0}{e}^{{−{k}{t}}}$$ to model the amount Q(t) of radioactivity in the body t days after the initial dose. b. what is the biological half-life of $$89^{Sr}$$ under this treatment? Round to the nearest tenth of a day.

Upper Level Math
ANSWERED ### Young’s modulus is a quantitative measure of stiffness of an elastic material. Suppose that for aluminum alloy sheets of a particular type, its mean value and standard deviation are 70 GPa and 1.6 GPa, respectively (values given in the article “Influence of Material Properties Variability on Springback and Thinning in Sheet Stamping Processes: A Stochastic Analysis” (Intl. J. of Advanced Manuf. Tech., 2010: 117–134)). If X¯ is the sample mean Young’s modulus for a random sample of n = 16 sheets, where is the sampling distribution of X¯ centered, and what is the standard deviation of the X¯ distribution?

Upper Level Math
ANSWERED ### B. G. Cosmos, a scientist, believes that the probability is $$\displaystyle{\frac{{{2}}}{{{5}}}}$$ that aliens from an advanced civilization on Planet X are trying to communicate with us by sending high-frequency signals to Earth. By using sophisticated equipment, Cosmos hopes to pick up these signals. The manufacturer of the equipment, Trekee, Inc., claims that if aliens are indeed sending signals, the probability that the equipment will detect them is $$\displaystyle{\frac{{{3}}}{{{5}}}}$$. However, if aliens are not sending signals, the probability that the equipment will seem to detect such signals is $$\frac{1}{10}$$. If the equipment detects signals, what is the probability that aliens are actually sending them?

Upper Level Math
ANSWERED ### Advances in medical science and healthier lifestyles have resulted in longer life expectancies. The life expectancy of a male whose current age is x years old is f(x)=0.0069502x^2−1.6357x+93.76 (60≤x≤75) years. What is the life expectancy of a male whose current age is 65? A male whose current age is 75?

Upper Level Math
ANSWERED ### As of October, 2016 the world`s largest pumpkin weighed 1190 kilograms. In order to grow a record-setting pumpkin, the fruits mass must increase by an average of $$1.27ft^3/day$$. If we assume that the dinsity of raw pumpkin is approximately $$0.50g/cm^3$$ we can convert this to an increase in volume of $$1.27ft^3/day$$. Question: If the volume of a spherical pumpkinn is increasing at $$\frac{1}{27}ft^3/day$$, then how fast is the surface area of the pumpkin changing when the diameter of the pumpkin is b ft? Give your answer with two decimal places, and ensure that you include unots. Note: Equations for the volume and surface area of a sphere are on D2L in several places.

Upper Level Math
ANSWERED ### Although tea is the world’s most widely consumed beverage after water, little is known about its nutritional value. Folacin is the only B vitamin present in any significant amount in tea, and recent advances in assay methods have made accurate determination of folacin content feasible. Consider the accompanying data on folacin content for randomly selected specimens of the four leading brands of green tea. $$\begin{array} \\ \text{Brand}& \text{Observations}\\ \hline 1&7.9&6.2&6.6&8.6&8.9&10.1&9.6\\ 2&5.7&7.5&9.8&6.1&8.4\\ 3&6.8&7.5&5.0&7.4&5.3&6.1\\ 4&6.4&7.1&7.9&4.5&5.0&4.0 \\ \hline \end{array}$$ (Data is based on “Folacin Content of Tea,” J. Amer. Dietetic Assoc., 1983: 627–632.) Does this data suggest that true average folacin content is the same for all brands? a. Carry out a test using α=.05α=.05 via the P-value method. b. Assess the plausibility of any assumptions required for your analysis in part (a). c. Perform a multiple comparisons analysis to identify significant differences among brands.

Upper Level Math
ANSWERED ### Classify each of the studies as either descriptive or inferential. Explain your answers. In an article titled “Teaching and Assessing Information Literacy in a Geography Program” (Journal of Geography, Vol. 104, No. 1, pp. 17-23), Dr. M. Kimsey and S. Lynn Cameron reported results from an on-line assessment instrument given to senior geography students at one institution of higher learning. The results for level of performance of 22 senior geography majors in 2003 and 29 senior geography majors in 2004 are presented in the following table. Level of performance Met the standard: 36−48 items correct Passed at the advanced level: 41−48 items correct Failed: 0−35 items correct Percent in 2003 82%50%18% Percent in 2004 93%59%7% Level of performance Met the standard: 36−48 items correct Passed at the advanced level: 41−48 items correct Failed: 0−35 items correct Percent in 2003 82% 50% 18% Percent in 2004 93% 59% 7%

Upper Level Math
ANSWERED ### Maurice and Lester are twins who have just graduated from college. They have both been offered jobs where their take-home pay would be $2500 per month. Their parents have given Maurice and Lester two options for a graduation gift. Option 1: If they choose to pursue a graduate degree, their parents will give each of them a gift of$35,000. However, they must pay for their tuition and living expenses out of the gift. Option 2: If they choose to go directly into the workforce, their parents will give each of them a gift of $5000. Maurice decides to go to graduate school for 2 years. He locks in a tuition rate by paying$11,500 for the 2 years in advance, and he figures that his monthly expenses will be $1000. Lester decides to go straight into the workforce. Lester finds that after paying his rent, utilities, and other living expenses, he will be able to save$200 per month. Their parents deposit the appropriate amount of money in a money market account for each twin. The money market accounts are currently paying a nominal interest rate of 3 percent, compounded monthly. Lester works during the time that Maurice attends graduate school. Each month, Lester saves $200 and deposits this amount into the$5000 money market account that his parents set up for him when he graduated. If Lester's initial balance is u0=5000,un is the current month's balance, and un−1 is last month's balance, write an expression for un in terms of un−1.
ANSWERED 