asked 2021-06-26

The analysis of tooth shrinkage by C. Loring Brace and colleagues at the University of Michigan’s Museum of Anthropology indicates that human tooth size is continuing to decrease and that the evolutionary process has not yet come to a halt. In northern Europeans, for example, tooth size reduction now has a rate of 1% per 1000 years.

a. If t represents time in years and y represents tooth size, use the condition that \(\displaystyle{y}={0.99}{y}_{{{0}}}\) when t = 1000 to find the value of k in the equation \(\displaystyle{y}={y}{0}{e}^{{{k}{t}}}\). Then use this value of k to answer the following questions.

b. In about how many years will human teeth be 90% of their present size?

c. What will be our descendants’ tooth size 20,000 years from now (as a percentage of our present tooth size)?

a. If t represents time in years and y represents tooth size, use the condition that \(\displaystyle{y}={0.99}{y}_{{{0}}}\) when t = 1000 to find the value of k in the equation \(\displaystyle{y}={y}{0}{e}^{{{k}{t}}}\). Then use this value of k to answer the following questions.

b. In about how many years will human teeth be 90% of their present size?

c. What will be our descendants’ tooth size 20,000 years from now (as a percentage of our present tooth size)?

asked 2021-03-02

1) In what way is the point unusual? Does it have high leverage, a large residual, or both?

2) Do you think that point is an influential point?

3) If that point were removed, would the correlation be- come stronger or weaker? Explain.

4) If that point were removed, would the slope of the re- gression line increase or decrease? Explain

asked 2020-12-01

The images of the following points under under a \(90^\circ\) rotation counterclockwise about the origin:

I. \((2,\ 3)\)

II. \((-1,\ 2)\)

III, (m,n) interms of m and n

b)To show:

That under a half-turn with the origin as center, the image of a point \((a,\ b)\ \text{has coordinates}\ (-a,\ -b).\)

c) To find:

The image of \(P (a,\ b)\text{under the rotation clockwise by} 90^{\circ}\) about the origin.

asked 2021-02-03

Lily wants to define a transformation (or series of transformations) using only rotations, reflections or translations that takes Figure A to Figure B.

Which statement about the transformation that Lily wants to define is true?

A. It can be defined with two reflections.

B.It can be defined with one rotation and one translation.

C. It cannot be defined because Figure A and Figure B are not congruent.

D.It cannot be defined because the longest side of Figure B is on the bottom.

Which statement about the transformation that Lily wants to define is true?

A. It can be defined with two reflections.

B.It can be defined with one rotation and one translation.

C. It cannot be defined because Figure A and Figure B are not congruent.

D.It cannot be defined because the longest side of Figure B is on the bottom.

asked 2021-02-19

A 10 kg objectexperiences a horizontal force which causes it to accelerate at 5 \(\displaystyle\frac{{m}}{{s}^{{2}}}\), moving it a distance of 20 m, horizontally.How much work is done by the force?

A ball is connected to a rope and swung around in uniform circular motion.The tension in the rope is measured at 10 N and the radius of thecircle is 1 m. How much work is done in one revolution around the circle?

A 10 kg weight issuspended in the air by a strong cable. How much work is done, perunit time, in suspending the weight?

A 5 kg block is moved up a 30 degree incline by a force of 50 N, parallel to the incline. The coefficient of kinetic friction between the block and the incline is .25. How much work is done by the 50 N force in moving the block a distance of 10 meters? What is the total workdone on the block over the same distance?

What is the kinetic energy of a 2 kg ball that travels a distance of 50 metersin 5 seconds?

A ball is thrown vertically with a velocity of 25 m/s. How high does it go? What is its velocity when it reaches a height of 25 m?

A ball with enough speed can complete a vertical loop. With what speed must the ballenter the loop to complete a 2 m loop? (Keep in mind that the velocity of the ball is not constant throughout the loop).

A ball is connected to a rope and swung around in uniform circular motion.The tension in the rope is measured at 10 N and the radius of thecircle is 1 m. How much work is done in one revolution around the circle?

A 10 kg weight issuspended in the air by a strong cable. How much work is done, perunit time, in suspending the weight?

A 5 kg block is moved up a 30 degree incline by a force of 50 N, parallel to the incline. The coefficient of kinetic friction between the block and the incline is .25. How much work is done by the 50 N force in moving the block a distance of 10 meters? What is the total workdone on the block over the same distance?

What is the kinetic energy of a 2 kg ball that travels a distance of 50 metersin 5 seconds?

A ball is thrown vertically with a velocity of 25 m/s. How high does it go? What is its velocity when it reaches a height of 25 m?

A ball with enough speed can complete a vertical loop. With what speed must the ballenter the loop to complete a 2 m loop? (Keep in mind that the velocity of the ball is not constant throughout the loop).

asked 2021-07-05

Regarding linear equations with one independent variable, answer the following questions: a. What is the general form of such an equation? b. In your expression in part (a), which letters represent constants and which represent variables? c. In your expression in part (a), which letter represents the independent variable and which represents the dependent variable?

asked 2020-11-22

Answer true or false to each of the following statements and explain your answers.

a. In using the method of transformations, we should only transform the predictor variable to straighten a scatterplot.

b. In using the method of transformations, a transformation of the predictor variable will change the conditional distribution of the response variable.

c. It is not always possible to fnd a power transformation of the response variable or the predictor variable (or both) that will straighten the scatterplot.

a. In using the method of transformations, we should only transform the predictor variable to straighten a scatterplot.

b. In using the method of transformations, a transformation of the predictor variable will change the conditional distribution of the response variable.

c. It is not always possible to fnd a power transformation of the response variable or the predictor variable (or both) that will straighten the scatterplot.

asked 2021-04-25

A stunt man whose mass is 70 kg swings from the end ofa 4.0 m long rope along thearc of a vertical circle. Assuming that he starts from rest whenthe rope is horizontal, find the tensions in the rope that are required to make him follow his circular path at each of the following points.

(a) at the beginning of his motion N

(b) at a height of 1.5 m above the bottom of the circular arc N

(c) at the bottom of the arc N

(a) at the beginning of his motion N

(b) at a height of 1.5 m above the bottom of the circular arc N

(c) at the bottom of the arc N

asked 2021-01-23

Sketch the graph of the function \(f(x) = -2^x+1 +3\) using transformations. Do not create a table of values and plot points

asked 2021-01-15

Create a new function in the form \(y = a(x-h)^2 + k\) by performing the following transformations on \(f (x) = x^2\).

Give the coordinates of the vertex for the new parabola.

g(x) is f (x) shifted right 7 units, stretched by a factor of 9, and then shifted down by 3 units. g(x) = ?

Coordinates of the vertex for the new parabola are:

x=?

y=?

Give the coordinates of the vertex for the new parabola.

g(x) is f (x) shifted right 7 units, stretched by a factor of 9, and then shifted down by 3 units. g(x) = ?

Coordinates of the vertex for the new parabola are:

x=?

y=?