Consider the given function and the table. Now, with the help of the values given in the table, plot a graph as, 
Here, it can be seen that by plotting the data, the obtained graph represents a parabola. Therefore, the function which represents the data table is \(\displaystyle{g{{\left({x}\right)}}}={c}{x}^{{{2}}}\). The point \(\displaystyle{\left(-{4},\ -{32}\right)}\) is on the graph. So, substitute the point, \(\displaystyle{\left(-{4},\ -{32}\right)}\), in \(\displaystyle{g{{\left({x}\right)}}}={c}{x}^{{{2}}}\).
\(\displaystyle-{32}={c}{\left(-{4}\right)}^{{{2}}}\)
\(\displaystyle-{32}={c}{\left({16}\right)}\)
\(\displaystyle{\frac{{-{32}}}{{{16}}}}={c}\) Solving further, \(\displaystyle{c}=\ -{2}\) So, \(\displaystyle{g{{\left({x}\right)}}}=\ -{2}{x}^{{{2}}}\) Hence, the function that can be used to model the data is \(\displaystyle{g{{\left({x}\right)}}}={c}{x}^{{{2}}}\) and the value of constant is \(\displaystyle{c}=\ -{2}\).
Question
Determine which of the following functionsf(x)=cx, g(x)=cx^{2}, h(x)=csqrt{|x|}, text{and} r(x)= frac{c}{x}
Answers (1)
Relevant Questions
Which possible statements about the chi-squared distribution are true?
a) The statistic \(X^{2}\), that is used to estimate the variance \(S^{2}\) of a random sample, has a Chi-squared distribution.
b) The sum of the squares of k independent standard normal random variables has a Chi-squared distribution with k degrees of freedom.
c) The Chi-squared distribution is used in hypothesis testing and estimation.
d) The Chi-squared distribution is a particular case of the Gamma distribution.
e)All of the above.
The following quadratic function in general form, \(\displaystyle{S}{\left({t}\right)}={5.8}{t}^{2}—{81.2}{t}+{1200}\) models the number of luxury home sales, S(t), in a major Canadian urban area, according to statistical data gathered over a 12 year period. Luxury home sales are defined in this market as sales of properties worth over $3 Million (inflation adjusted). In this case, \(\displaystyle{\left\lbrace{t}\right\rbrace}={\left\lbrace{0}\right\rbrace}\ \text{represents}\ {2000}{\quad\text{and}\quad}{\left\lbrace{t}\right\rbrace}={\left\lbrace{11}\right\rbrace}\)represents 2011. Use a calculator to find the year when the smallest number of luxury home sales occurred. Without sketching the function, interpret the meaning of this function, on the given practical domain, in one well-expressed sentence.
The table shows the temperatures T (in degrees Fahrenheit) at which water boils at selected pressures p (in pounds per square inch). A model that approximates the datais: \(\displaystyle{T}={87.97}\ +\ {34.96}\ \text{In}\ {p}\ +\ {7.91}\ \sqrt{{{p}}}\) a) Use a graphing untility to plot the data and graph the model in the same veiwing window. How well does the model fit the data? b) Use the graph to estimate the pressure at which the boiling point of water is \(300^{\circ}\) F. c) Calculate T when the pressure is 74 pounds per square inch. Verify your answer graphically.
The following table represents the Frequency Distribution and Cumulative Distributions for this data set: 12, 13, 17, 18, 18, 24, 26, 27, 27, 30, 30, 35, 37, 41, 42, 43, 44, 46, 53, 58
\(\begin{array}{|c|c|} \hline \text{Class}&\text{Frequency}&\text{Relative Frequency}&\text{Cumulative Frequency}\\ \hline \text{10 but les than 20}&5\\ \hline \text{20 but les than 30}&4\\ \hline \text{30 but les than 40}&4\\ \hline \text{40 but les than 50}&5\\ \hline \text{50 but les than 60}&2\\ \hline \text{TOTAL}\\ \hline \end{array}\)
What is the Relative Frequency for the class: 20 but less than 30? State you answer as a value with exactly two digits after the decimal. for example 0.30 or 0.35
An experiment designed to study the relationship between hypertension and cigarette smoking yielded the following data.
\(\begin{array}{|c|c|} \hline Tension\ level & Non-smoker & Moderate\ smoker & Heavy\ smoker \\ \hline Hypertension & 20 & 38 & 28 \\ \hline No\ hypertension & 50 & 27 & 18 \\ \hline \end{array}\)
Test the hypothesis that whether or not an individual has hypertension is independent of how much that person smokes.
The following table shows the average yearly tuition and required fees, in thousand of dollars, charged by a certain private university in the school year beginning in the given year.
\(\begin{array}{|c|c|}\hline \text{Year} & \text{Average tuition} \\ \hline 2005 & $17.6 \\ \hline 2007 & $18.1 \\ \hline 2009 & $19.5 \\ \hline 2011 & $20.7 \\ \hline 2013 & $21.8 \\ \hline \end{array}\)
What prediction does the formula modeling this data give for average yearly tuition and required fees for the university for the academic year beginning in 2019?
Identifying Probability Distributions. In Exercises 7–14, determine whether a probability distribution is given. If a probability distribution is given, find its mean and standard deviation. If a probability distribution is not given, identify the requirements that are not satisfied. Cell Phone Use In a survey, cell phone users were asked which ear they use to hear their cell phone, and the table is based on their responses (based on data from “Hemispheric Dominance and Cell Phone Use,” by Seidman et al., JAMA Otolaryngology—Head & Neck Surgery , Vol. 139, No.
5). \(\begin{array}{|c|c|}& P(x)\\ Left & 0.636 \\ Right & 0.304 \\ No\ preference & 0.060\end{array}\)
A random sample of \(\displaystyle{n}_{{1}}={16}\) communities in western Kansas gave the following information for people under 25 years of age.
\(\displaystyle{X}_{{1}}:\) Rate of hay fever per 1000 population for people under 25
\(\begin{array}{|c|c|} \hline 97 & 91 & 121 & 129 & 94 & 123 & 112 &93\\ \hline 125 & 95 & 125 & 117 & 97 & 122 & 127 & 88 \\ \hline \end{array}\)
A random sample of \(\displaystyle{n}_{{2}}={14}\) regions in western Kansas gave the following information for people over 50 years old.
\(\displaystyle{X}_{{2}}:\) Rate of hay fever per 1000 population for people over 50
\(\begin{array}{|c|c|} \hline 94 & 109 & 99 & 95 & 113 & 88 & 110\\ \hline 79 & 115 & 100 & 89 & 114 & 85 & 96\\ \hline \end{array}\)
(i) Use a calculator to calculate \(\displaystyle\overline{{x}}_{{1}},{s}_{{1}},\overline{{x}}_{{2}},{\quad\text{and}\quad}{s}_{{2}}.\) (Round your answers to two decimal places.)
(ii) Assume that the hay fever rate in each age group has an approximately normal distribution. Do the data indicate that the age group over 50 has a lower rate of hay fever? Use \(\displaystyle\alpha={0.05}.\)
(a) What is the level of significance?
State the null and alternate hypotheses.
\(\displaystyle{H}_{{0}}:\mu_{{1}}=\mu_{{2}},{H}_{{1}}:\mu_{{1}}<\mu_{{2}}\)
\(\displaystyle{H}_{{0}}:\mu_{{1}}=\mu_{{2}},{H}_{{1}}:\mu_{{1}}>\mu_{{2}}\)
\(\displaystyle{H}_{{0}}:\mu_{{1}}=\mu_{{2}},{H}_{{1}}:\mu_{{1}}\ne\mu_{{2}}\)
\(\displaystyle{H}_{{0}}:\mu_{{1}}>\mu_{{2}},{H}_{{1}}:\mu_{{1}}=\mu_{{12}}\)
(b) What sampling distribution will you use? What assumptions are you making?
The standard normal. We assume that both population distributions are approximately normal with known standard deviations.
The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations,
The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations,
The Student's t. We assume that both population distributions are approximately normal with known standard deviations,
What is the value of the sample test statistic? (Test the difference \(\displaystyle\mu_{{1}}-\mu_{{2}}\). Round your answer to three decimalplaces.)
What is the value of the sample test statistic? (Test the difference \(\displaystyle\mu_{{1}}-\mu_{{2}}\). Round your answer to three decimal places.)
(c) Find (or estimate) the P-value.
P-value \(\displaystyle>{0.250}\)
\(\displaystyle{0.125}<{P}-\text{value}<{0},{250}\)
\(\displaystyle{0},{050}<{P}-\text{value}<{0},{125}\)
\(\displaystyle{0},{025}<{P}-\text{value}<{0},{050}\)
\(\displaystyle{0},{005}<{P}-\text{value}<{0},{025}\)
P-value \(\displaystyle<{0.005}\)
Sketch the sampling distribution and show the area corresponding to the P-value.
P.vaiue Pevgiue
P-value f P-value
The following observations are lifetimes (days) subsequent to diagnosis for individuals suffering from blood cancer ("A Goodness of Fit Approach to the Class of Life Distributions with Unknown Age," Quality and Reliability Engr. Intl., \(2012: 761-766): 115, 181, 255, 418, 441, 461, 516, 739, 743, 789, 807, 865, 924, 983, 1025, 1062, 1063, 1165, 1191, 1222, 1222, 1251, 1277, 1290, 1357, 1369, 1408, 1455, 1278, 1519, 1578, 1578, 1599, 1603, 1605, 1696, 1735, 1799, 1815, 1852, 1899, 1925, 1965.\)
a) can a confidence interval for true average lifetime be calculated without assuming anything about the nature of the lifetime distribution? Explain your reasoning. [Note: A normal probability plot of data exhibits a reasonably linear pattern.]
b) Calculate and interpret a confidence interval with a 99% confidence level for true average lifetime. [Hint: mean \(= 1191.6, s = 506.6\).]
Let's say the widget maker has developed the following table that shows the highest dollar price p. widget where you can sell N widgets. Number N Price p \(200 53.00\)
\(250 52.50\)
\(300 52.00\)
\(35051.50\)
(a) Find a formula for pin terms of N modeling the data in the table.
(b) Use a formula to express the total monthly revenue R, in dollars, of this manufacturer in month as a function of the number N of widgets produced in a month. \(R=\) Is Ra linear function of N?
(c) On the basis of the tables in this exercise and using cost, \(C= 35N + 900\), use a formula to express the monthly profit P, in dollars, of this manufacturer asa function of the number of widgets produced in a month \(p=\) ?
