asked 2021-05-18

From 2000 - 2010 a city had a 2.5% annual decrease in population. If the city had 2,950,000 people in 2000, determine the city's population in 2008.

a) Exponential growth or decay:

b) Identify the initial amount:

c) Identify the growth/decay factor:

d) Write an exponential function to model the situation:

e) "Do" the problem.

a) Exponential growth or decay:

b) Identify the initial amount:

c) Identify the growth/decay factor:

d) Write an exponential function to model the situation:

e) "Do" the problem.

asked 2021-06-02

The table shows the populations P (in millions) of the United States from 1960 to 2000.
Year 1960 1970 1980 1990 2000 Popupation, P 181 205 228 250 282

(a) Use the 1960 and 1970 data to find an exponential model P1 for the data. Let t=0 represent 1960. (c) Use a graphing utility to plot the data and graph models P1 and P2 in the same viewing window. Compare the actual data with the predictions. Which model better fits the data? (d) Estimate when the population will be 320 million.

(a) Use the 1960 and 1970 data to find an exponential model P1 for the data. Let t=0 represent 1960. (c) Use a graphing utility to plot the data and graph models P1 and P2 in the same viewing window. Compare the actual data with the predictions. Which model better fits the data? (d) Estimate when the population will be 320 million.

asked 2021-04-13

As depicted in the applet, Albertine finds herself in a very odd contraption. She sits in a reclining chair, in front of a large, compressed spring. The spring is compressed 5.00 m from its equilibrium position, and a glass sits 19.8m from her outstretched foot.

a)Assuming that Albertine's mass is 60.0kg , what is \(\displaystyle\mu_{{k}}\), the coefficient of kinetic friction between the chair and the waxed floor? Use \(\displaystyle{g}={9.80}\frac{{m}}{{s}^{{2}}}\) for the magnitude of the acceleration due to gravity. Assume that the value of k found in Part A has three significant figures. Note that if you did not assume that k has three significant figures, it would be impossible to get three significant figures for \(\displaystyle\mu_{{k}}\), since the length scale along the bottom of the applet does not allow you to measure distances to that accuracy with different values of k.

a)Assuming that Albertine's mass is 60.0kg , what is \(\displaystyle\mu_{{k}}\), the coefficient of kinetic friction between the chair and the waxed floor? Use \(\displaystyle{g}={9.80}\frac{{m}}{{s}^{{2}}}\) for the magnitude of the acceleration due to gravity. Assume that the value of k found in Part A has three significant figures. Note that if you did not assume that k has three significant figures, it would be impossible to get three significant figures for \(\displaystyle\mu_{{k}}\), since the length scale along the bottom of the applet does not allow you to measure distances to that accuracy with different values of k.

asked 2021-05-14

Consider the accompanying data on flexural strength (MPa) for concrete beams of a certain type.

\(\begin{array}{|c|c|}\hline 11.8 & 7.7 & 6.5 & 6 .8& 9.7 & 6.8 & 7.3 \\ \hline 7.9 & 9.7 & 8.7 & 8.1 & 8.5 & 6.3 & 7.0 \\ \hline 7.3 & 7.4 & 5.3 & 9.0 & 8.1 & 11.3 & 6.3 \\ \hline 7.2 & 7.7 & 7.8 & 11.6 & 10.7 & 7.0 \\ \hline \end{array}\)

a) Calculate a point estimate of the mean value of strength for the conceptual population of all beams manufactured in this fashion. \([Hint.\ ?x_{j}=219.5.]\) (Round your answer to three decimal places.)

MPa

State which estimator you used.

\(x\)

\(p?\)

\(\frac{s}{x}\)

\(s\)

\(\tilde{\chi}\)

b) Calculate a point estimate of the strength value that separates the weakest \(50\%\) of all such beams from the strongest \(50\%\).

MPa

State which estimator you used.

\(s\)

\(x\)

\(p?\)

\(\tilde{\chi}\)

\(\frac{s}{x}\)

c) Calculate a point estimate of the population standard deviation ?. \([Hint:\ ?x_{i}2 = 1859.53.]\) (Round your answer to three decimal places.)

MPa

Interpret this point estimate.

This estimate describes the linearity of the data.

This estimate describes the bias of the data.

This estimate describes the spread of the data.

This estimate describes the center of the data.

Which estimator did you use?

\(\tilde{\chi}\)

\(x\)

\(s\)

\(\frac{s}{x}\)

\(p?\)

d) Calculate a point estimate of the proportion of all such beams whose flexural strength exceeds 10 MPa. [Hint: Think of an observation as a "success" if it exceeds 10.] (Round your answer to three decimal places.)

e) Calculate a point estimate of the population coefficient of variation \(\frac{?}{?}\). (Round your answer to four decimal places.)

State which estimator you used.

\(p?\)

\(\tilde{\chi}\)

\(s\)

\(\frac{s}{x}\)

\(x\)

\(\begin{array}{|c|c|}\hline 11.8 & 7.7 & 6.5 & 6 .8& 9.7 & 6.8 & 7.3 \\ \hline 7.9 & 9.7 & 8.7 & 8.1 & 8.5 & 6.3 & 7.0 \\ \hline 7.3 & 7.4 & 5.3 & 9.0 & 8.1 & 11.3 & 6.3 \\ \hline 7.2 & 7.7 & 7.8 & 11.6 & 10.7 & 7.0 \\ \hline \end{array}\)

a) Calculate a point estimate of the mean value of strength for the conceptual population of all beams manufactured in this fashion. \([Hint.\ ?x_{j}=219.5.]\) (Round your answer to three decimal places.)

MPa

State which estimator you used.

\(x\)

\(p?\)

\(\frac{s}{x}\)

\(s\)

\(\tilde{\chi}\)

b) Calculate a point estimate of the strength value that separates the weakest \(50\%\) of all such beams from the strongest \(50\%\).

MPa

State which estimator you used.

\(s\)

\(x\)

\(p?\)

\(\tilde{\chi}\)

\(\frac{s}{x}\)

c) Calculate a point estimate of the population standard deviation ?. \([Hint:\ ?x_{i}2 = 1859.53.]\) (Round your answer to three decimal places.)

MPa

Interpret this point estimate.

This estimate describes the linearity of the data.

This estimate describes the bias of the data.

This estimate describes the spread of the data.

This estimate describes the center of the data.

Which estimator did you use?

\(\tilde{\chi}\)

\(x\)

\(s\)

\(\frac{s}{x}\)

\(p?\)

d) Calculate a point estimate of the proportion of all such beams whose flexural strength exceeds 10 MPa. [Hint: Think of an observation as a "success" if it exceeds 10.] (Round your answer to three decimal places.)

e) Calculate a point estimate of the population coefficient of variation \(\frac{?}{?}\). (Round your answer to four decimal places.)

State which estimator you used.

\(p?\)

\(\tilde{\chi}\)

\(s\)

\(\frac{s}{x}\)

\(x\)

asked 2021-05-22

Sheila is in Ms. Cai's class . She noticed that the graph of the perimeter for the "dented square" in problem 3-61 was a line . "I wonder what the graph of its area looks like ," she said to her teammates .

a. Write an equation for the area of the "dented square" if xx represents the length of the large square and yy represents the area of the square.

b. On graph paper , graph the rule you found for the area in part (a). Why does a 1st−quadrant graph make sense for this situation? Are there other values of xx that cannot work in this situation? Be sure to include an indication of this on your graph, as necessary.

c. Explain to Sheila what the graph of the area looks like.

d. Use the graph to approximate xx when the area of the shape is 20 square units.

a. Write an equation for the area of the "dented square" if xx represents the length of the large square and yy represents the area of the square.

b. On graph paper , graph the rule you found for the area in part (a). Why does a 1st−quadrant graph make sense for this situation? Are there other values of xx that cannot work in this situation? Be sure to include an indication of this on your graph, as necessary.

c. Explain to Sheila what the graph of the area looks like.

d. Use the graph to approximate xx when the area of the shape is 20 square units.

asked 2021-06-19

When two targets are presented close together in a rapid visual stream, the second target is often missed. Psychologists call this phenomenon the attentional blink (AB). A study published in Advances in Cognitive Psychology (July 2013) investigated whether simultaneous or preceding sounds could reduce AB. Twenty subjects were presented a rapid visual stream of symbols and letters on a computer screen and asked to identify the first and second letters (the targets). After several trials, the subject's AB magnitude was measured as the difference between the percentages of first target and second target letters correctly identified. Each subject performed the task under each of three conditions. In the Simultaneous condition, a sound (tone) was presented simultaneously with the second target; in the Alert condition, a sound was presented prior to the coming of the second target; and in the No-Tone condition, no sound was presented with the second target. Scatterplots of AB magnitude for each possible pair of conditions are shown below as well as the least squares line for each. a. Which pair of conditions produces the least squares line with the steepest estimated slope? b. Which pair of conditions produces the least squares line with the largest SSE? c. Which pair of conditions produces the least squares line with the smallest estímate of σ?

asked 2021-06-09

The table shows the total number of bacteria in a sample over five hours.

HourNumber of Bacteria 112 2144 31728 420,736 5248,832

Use your calculator to find an exponential equation that models the bacteria data.

HourNumber of Bacteria 112 2144 31728 420,736 5248,832

Use your calculator to find an exponential equation that models the bacteria data.

asked 2021-02-25

We will now add support for register-memory ALU operations to the classic five-stage RISC pipeline. To offset this increase in complexity, all memory addressing will be restricted to register indirect (i.e., all addresses are simply a value held in a register; no offset or displacement may be added to the register value). For example, the register-memory instruction add x4, x5, (x1) means add the contents of register x5 to the contents of the memory location with address equal to the value in register x1 and put the sum in register x4. Register-register ALU operations are unchanged. The following items apply to the integer RISC pipeline:

a. List a rearranged order of the five traditional stages of the RISC pipeline that will support register-memory operations implemented exclusively by register indirect addressing.

b. Describe what new forwarding paths are needed for the rearranged pipeline by stating the source, destination, and information transferred on each needed new path.

c. For the reordered stages of the RISC pipeline, what new data hazards are created by this addressing mode? Give an instruction sequence illustrating each new hazard.

d. List all of the ways that the RISC pipeline with register-memory ALU operations can have a different instruction count for a given program than the original RISC pipeline. Give a pair of specific instruction sequences, one for the original pipeline and one for the rearranged pipeline, to illustrate each way.

Hint for (d): Give a pair of instruction sequences where the RISC pipeline has “more” instructions than the reg-mem architecture. Also give a pair of instruction sequences where the RISC pipeline has “fewer” instructions than the reg-mem architecture.

a. List a rearranged order of the five traditional stages of the RISC pipeline that will support register-memory operations implemented exclusively by register indirect addressing.

b. Describe what new forwarding paths are needed for the rearranged pipeline by stating the source, destination, and information transferred on each needed new path.

c. For the reordered stages of the RISC pipeline, what new data hazards are created by this addressing mode? Give an instruction sequence illustrating each new hazard.

d. List all of the ways that the RISC pipeline with register-memory ALU operations can have a different instruction count for a given program than the original RISC pipeline. Give a pair of specific instruction sequences, one for the original pipeline and one for the rearranged pipeline, to illustrate each way.

Hint for (d): Give a pair of instruction sequences where the RISC pipeline has “more” instructions than the reg-mem architecture. Also give a pair of instruction sequences where the RISC pipeline has “fewer” instructions than the reg-mem architecture.

asked 2021-05-14

When σ is unknown and the sample size is \(\displaystyle{n}\geq{30}\), there are tow methods for computing confidence intervals for μμ. Method 1: Use the Student's t distribution with d.f. = n - 1. This is the method used in the text. It is widely employed in statistical studies. Also, most statistical software packages use this method. Method 2: When \(\displaystyle{n}\geq{30}\), use the sample standard deviation s as an estimate for σσ, and then use the standard normal distribution. This method is based on the fact that for large samples, s is a fairly good approximation for σσ. Also, for large n, the critical values for the Student's t distribution approach those of the standard normal distribution. Consider a random sample of size n = 31, with sample mean x¯=45.2 and sample standard deviation s = 5.3. (c) Compare intervals for the two methods. Would you say that confidence intervals using a Student's t distribution are more conservative in the sense that they tend to be longer than intervals based on the standard normal distribution?

asked 2021-05-12

When a < 0 and b>1,y=abx models negative exponential growth. a. Write an exponential function that models negative growth. b. Give an example of a situation that could be modeled by your function. c. Explain one difference between negative exponential growth and exponential decay.