Answer B)

Question

asked 2021-05-05

The bulk density of soil is defined as the mass of dry solidsper unit bulk volume. A high bulk density implies a compact soilwith few pores. Bulk density is an important factor in influencing root development, seedling emergence, and aeration. Let X denotethe bulk density of Pima clay loam. Studies show that X is normally distributed with \(\displaystyle\mu={1.5}\) and \(\displaystyle\sigma={0.2}\frac{{g}}{{c}}{m}^{{3}}\).

(a) What is thedensity for X? Sketch a graph of the density function. Indicate onthis graph the probability that X lies between 1.1 and 1.9. Findthis probability.

(b) Find the probability that arandomly selected sample of Pima clay loam will have bulk densityless than \(\displaystyle{0.9}\frac{{g}}{{c}}{m}^{{3}}\).

(c) Would you be surprised if a randomly selected sample of this type of soil has a bulkdensity in excess of \(\displaystyle{2.0}\frac{{g}}{{c}}{m}^{{3}}\)? Explain, based on theprobability of this occurring.

(d) What point has the property that only 10% of the soil samples have bulk density this high orhigher?

(e) What is the moment generating function for X?

(a) What is thedensity for X? Sketch a graph of the density function. Indicate onthis graph the probability that X lies between 1.1 and 1.9. Findthis probability.

(b) Find the probability that arandomly selected sample of Pima clay loam will have bulk densityless than \(\displaystyle{0.9}\frac{{g}}{{c}}{m}^{{3}}\).

(c) Would you be surprised if a randomly selected sample of this type of soil has a bulkdensity in excess of \(\displaystyle{2.0}\frac{{g}}{{c}}{m}^{{3}}\)? Explain, based on theprobability of this occurring.

(d) What point has the property that only 10% of the soil samples have bulk density this high orhigher?

(e) What is the moment generating function for X?

asked 2021-05-05

A random sample of \( n_1 = 14 \) winter days in Denver gave a sample mean pollution index \( x_1 = 43 \).

Previous studies show that \( \sigma_1 = 19 \).

For Englewood (a suburb of Denver), a random sample of \( n_2 = 12 \) winter days gave a sample mean pollution index of \( x_2 = 37 \).

Previous studies show that \( \sigma_2 = 13 \).

Assume the pollution index is normally distributed in both Englewood and Denver.

(a) State the null and alternate hypotheses.

\( H_0:\mu_1=\mu_2.\mu_1>\mu_2 \)

\( H_0:\mu_1<\mu_2.\mu_1=\mu_2 \)

\( H_0:\mu_1=\mu_2.\mu_1<\mu_2 \)

\( H_0:\mu_1=\mu_2.\mu_1\neq\mu_2 \)

(b) What sampling distribution will you use? What assumptions are you making? NKS The Student's t. We assume that both population distributions are approximately normal with known standard deviations.

The standard normal. 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 known standard deviations.

The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations.

(c) What is the value of the sample test statistic? Compute the corresponding z or t value as appropriate.

(Test the difference \( \mu_1 - \mu_2 \). Round your answer to two decimal places.) NKS (d) Find (or estimate) the P-value. (Round your answer to four decimal places.)

(e) Based on your answers in parts (i)−(iii), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level \alpha?

At the \( \alpha = 0.01 \) level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

At the \( \alpha = 0.01 \) level, we reject the null hypothesis and conclude the data are statistically significant.

At the \( \alpha = 0.01 \) level, we fail to reject the null hypothesis and conclude the data are statistically significant.

At the \( \alpha = 0.01 \) level, we reject the null hypothesis and conclude the data are not statistically significant.

(f) Interpret your conclusion in the context of the application.

Reject the null hypothesis, there is insufficient evidence that there is a difference in mean pollution index for Englewood and Denver.

Reject the null hypothesis, there is sufficient evidence that there is a difference in mean pollution index for Englewood and Denver.

Fail to reject the null hypothesis, there is insufficient evidence that there is a difference in mean pollution index for Englewood and Denver.

Fail to reject the null hypothesis, there is sufficient evidence that there is a difference in mean pollution index for Englewood and Denver. (g) Find a 99% confidence interval for

\( \mu_1 - \mu_2 \).

(Round your answers to two decimal places.)

lower limit

upper limit

(h) Explain the meaning of the confidence interval in the context of the problem.

Because the interval contains only positive numbers, this indicates that at the 99% confidence level, the mean population pollution index for Englewood is greater than that of Denver.

Because the interval contains both positive and negative numbers, this indicates that at the 99% confidence level, we can not say that the mean population pollution index for Englewood is different than that of Denver.

Because the interval contains both positive and negative numbers, this indicates that at the 99% confidence level, the mean population pollution index for Englewood is greater than that of Denver.

Because the interval contains only negative numbers, this indicates that at the 99% confidence level, the mean population pollution index for Englewood is less than that of Denver.

asked 2021-05-16

Consider the curves in the first quadrant that have equationsy=Aexp(7x), where A is a positive constant. Different valuesof A give different curves. The curves form a family,F. Let P=(6,6). Let C be the number of the family Fthat goes through P.

A. Let y=f(x) be the equation of C. Find f(x).

B. Find the slope at P of the tangent to C.

C. A curve D is a perpendicular to C at P. What is the slope of thetangent to D at the point P?

D. Give a formula g(y) for the slope at (x,y) of the member of Fthat goes through (x,y). The formula should not involve A orx.

E. A curve which at each of its points is perpendicular to themember of the family F that goes through that point is called anorthogonal trajectory of F. Each orthogonal trajectory to Fsatisfies the differential equation dy/dx = -1/g(y), where g(y) isthe answer to part D.

Find a function of h(y) such that x=h(y) is the equation of theorthogonal trajectory to F that passes through the point P.

A. Let y=f(x) be the equation of C. Find f(x).

B. Find the slope at P of the tangent to C.

C. A curve D is a perpendicular to C at P. What is the slope of thetangent to D at the point P?

D. Give a formula g(y) for the slope at (x,y) of the member of Fthat goes through (x,y). The formula should not involve A orx.

E. A curve which at each of its points is perpendicular to themember of the family F that goes through that point is called anorthogonal trajectory of F. Each orthogonal trajectory to Fsatisfies the differential equation dy/dx = -1/g(y), where g(y) isthe answer to part D.

Find a function of h(y) such that x=h(y) is the equation of theorthogonal trajectory to F that passes through the point P.

asked 2021-04-11

Let F = yi + zj + xzk. Evaluate

Double integral \(\displaystyle{F}\cdot{a}{S}\) for each of the following regions W:

a. \(\displaystyle{x}^{{2}}+{y}^{{2}}\) (less than or equal to) z (less thanor equal to) 1

b. \(\displaystyle{x}^{{2}}+{y}^{{2}}\) (less than or equal to) 1 and x (greater than or equal to) 0

Double integral \(\displaystyle{F}\cdot{a}{S}\) for each of the following regions W:

a. \(\displaystyle{x}^{{2}}+{y}^{{2}}\) (less than or equal to) z (less thanor equal to) 1

b. \(\displaystyle{x}^{{2}}+{y}^{{2}}\) (less than or equal to) 1 and x (greater than or equal to) 0

asked 2021-02-14

Dayton Power and Light, Inc., has a power plant on the Miami Riverwhere the river is 800 ft wide. To lay a new cable from the plantto a location in the city 2 mi downstream on the opposite sidecosts $180 per foot across the river and $100 per foot along theland.

(a) Suppose that the cable goes from the plant to a point Q on theopposite side that is x ft from the point P directly opposite theplant. Write a function C(x) that gives the cost of laying thecable in terms of the distance x.

(b) Generate a table of values to determin if the least expensivelocation for point Q is less than 2000 ft or greater than 2000 ftfrom point P.

(a) Suppose that the cable goes from the plant to a point Q on theopposite side that is x ft from the point P directly opposite theplant. Write a function C(x) that gives the cost of laying thecable in terms of the distance x.

(b) Generate a table of values to determin if the least expensivelocation for point Q is less than 2000 ft or greater than 2000 ftfrom point P.

asked 2021-05-22

Find the equation of the tangent plane to the graph of \(\displaystyle{f{{\left({x},{y}\right)}}}={8}{x}^{{{2}}}-{2}{x}{y}^{{{2}}}\) at the point (5,4).

A)z=23x-15y+42

B)z=48x-80y+120

C)0=48x-80y+120

D)0=23x-15y+42

A)z=23x-15y+42

B)z=48x-80y+120

C)0=48x-80y+120

D)0=23x-15y+42

asked 2021-05-18

The student engineer of a campus radio station wishes to verify the effectivencess of the lightning rod on the antenna mast. The unknown resistance \(\displaystyle{R}_{{x}}\) is between points C and E. Point E is a "true ground", but is inaccessible for direct measurement because the stratum in which it is located is several meters below Earth's surface. Two identical rods are driven into the ground at A and B, introducing an unknown resistance \(\displaystyle{R}_{{y}}\). The procedure for finding the unknown resistance \(\displaystyle{R}_{{x}}\) is as follows. Measure resistance \(\displaystyle{R}_{{1}}\) between points A and B. Then connect A and B with a heavy conducting wire and measure resistance \(\displaystyle{R}_{{2}}\) between points A and C.Derive a formula for \(\displaystyle{R}_{{x}}\) in terms of the observable resistances \(\displaystyle{R}_{{1}}\) and \(\displaystyle{R}_{{2}}\). A satisfactory ground resistance would be \(\displaystyle{R}_{{x}}{<}{2.0}\) Ohms. Is the grounding of the station adequate if measurments give \(\displaystyle{R}_{{1}}={13}{O}{h}{m}{s}\) and R_2=6.0 Ohms?

asked 2021-05-10

Hypothetical potential energy curve for aparticle of mass m

If the particle is released from rest at position r0, its speed atposition 2r0, is most nearly

a) \(\displaystyle{\left({\frac{{{8}{U}{o}}}{{{m}}}}\right)}^{{1}}{\left\lbrace/{2}\right\rbrace}\)

b) \(\displaystyle{\left({\frac{{{6}{U}{o}}}{{{m}}}}\right)}^{{\frac{{1}}{{2}}}}\)

c) \(\displaystyle{\left({\frac{{{4}{U}{o}}}{{{m}}}}\right)}^{{\frac{{1}}{{2}}}}\)

d) \(\displaystyle{\left({\frac{{{2}{U}{o}}}{{{m}}}}\right)}^{{\frac{{1}}{{2}}}}\)

e) \(\displaystyle{\left({\frac{{{U}{o}}}{{{m}}}}\right)}^{{\frac{{1}}{{2}}}}\)

if the potential energy function is given by

\(\displaystyle{U}{\left({r}\right)}={b}{r}^{{P}}-\frac{{3}}{{2}}\rbrace+{c}\)

where b and c are constants

which of the following is an edxpression of the force on theparticle?

1) \(\displaystyle{\frac{{{3}{b}}}{{{2}}}}{\left({r}^{{-\frac{{5}}{{2}}}}\right)}\)

2) \(\displaystyle{\frac{{{3}{b}}}{{{2}}}}{\left\lbrace{3}{b}\right\rbrace}{\left\lbrace{2}\right\rbrace}{\left({r}^{{-\frac{{1}}{{2}}}}\right)}\)

3) \(\displaystyle{\frac{{{3}{b}}}{{{2}}}}{\left\lbrace{3}\right\rbrace}{\left\lbrace{2}\right\rbrace}{\left({r}^{{-\frac{{1}}{{2}}}}\right)}\)

4) \(\displaystyle{2}{b}{\left({r}^{{-\frac{{1}}{{2}}}}\right)}+{c}{r}\)

5) \(\displaystyle{\frac{{{3}{b}}}{{{2}}}}{\left\lbrace{2}{b}\right\rbrace}{\left\lbrace{5}\right\rbrace}{\left({r}^{{-\frac{{5}}{{2}}}}\right)}+{c}{r}\)

If the particle is released from rest at position r0, its speed atposition 2r0, is most nearly

a) \(\displaystyle{\left({\frac{{{8}{U}{o}}}{{{m}}}}\right)}^{{1}}{\left\lbrace/{2}\right\rbrace}\)

b) \(\displaystyle{\left({\frac{{{6}{U}{o}}}{{{m}}}}\right)}^{{\frac{{1}}{{2}}}}\)

c) \(\displaystyle{\left({\frac{{{4}{U}{o}}}{{{m}}}}\right)}^{{\frac{{1}}{{2}}}}\)

d) \(\displaystyle{\left({\frac{{{2}{U}{o}}}{{{m}}}}\right)}^{{\frac{{1}}{{2}}}}\)

e) \(\displaystyle{\left({\frac{{{U}{o}}}{{{m}}}}\right)}^{{\frac{{1}}{{2}}}}\)

if the potential energy function is given by

\(\displaystyle{U}{\left({r}\right)}={b}{r}^{{P}}-\frac{{3}}{{2}}\rbrace+{c}\)

where b and c are constants

which of the following is an edxpression of the force on theparticle?

1) \(\displaystyle{\frac{{{3}{b}}}{{{2}}}}{\left({r}^{{-\frac{{5}}{{2}}}}\right)}\)

2) \(\displaystyle{\frac{{{3}{b}}}{{{2}}}}{\left\lbrace{3}{b}\right\rbrace}{\left\lbrace{2}\right\rbrace}{\left({r}^{{-\frac{{1}}{{2}}}}\right)}\)

3) \(\displaystyle{\frac{{{3}{b}}}{{{2}}}}{\left\lbrace{3}\right\rbrace}{\left\lbrace{2}\right\rbrace}{\left({r}^{{-\frac{{1}}{{2}}}}\right)}\)

4) \(\displaystyle{2}{b}{\left({r}^{{-\frac{{1}}{{2}}}}\right)}+{c}{r}\)

5) \(\displaystyle{\frac{{{3}{b}}}{{{2}}}}{\left\lbrace{2}{b}\right\rbrace}{\left\lbrace{5}\right\rbrace}{\left({r}^{{-\frac{{5}}{{2}}}}\right)}+{c}{r}\)

asked 2021-05-14

For the equation (-1,2), \(y= \frac{1}{2}x - 3\), write an equation in slope intercept form for the line that passes through the given point and is parallel to the graph of the given equation.

asked 2021-05-13

Let the continuous random variables X and Y have joint pdf

\(f(x,y)=e^{-x-y}, 0\)

a)\(e^{-y}\)

b)\(e^{-x}\)

c)\(\frac{e^{y}}{e^{-x}}\)