What does it mean to say that algebra is a written language? How would I express an algebraic expression such as for example, numerator displaystyle{3}{x}^{2}+{5}{y} and 2 as the denominator, in words?

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What does it mean to say that algebra is a written language? How would I express an algebraic expression such as for example, numerator displaystyle{3}{x}^{2}+{5}{y} and 2 as the denominator, in words?

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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.

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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.

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asked 2021-05-05

A golf ball lies 2.00 m directly south of the hole on a levelgreen. On the first putt, the ball travels 3.00 m along astraight-line path at an angle of 5 degrees east of north; on thesecond putt, it travels a straight-line distance of 1.20 m at anangle of 6 degrees south of west.
What would be the displacement ofa third putt that would put the ball in the hole?
The answer in the back of the book is 1.3 m at 43 degreessouth of east. How do I get that?

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asked 2021-03-29

Two stationary point charges +3 nC and + 2nC are separated bya distance of 50cm. An electron is released from rest at a pointmidway between the two charges and moves along the line connectingthe two charges. What is the speed of the electron when it is 10cmfrom +3nC charge?
Besides the hints I'd like to ask you to give me numericalsolution so I can verify my answer later on. It would be nice ifyou could write it out, but a numerical anser would be fine alongwith the hint how to get there.

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asked 2021-05-09

The dominant form of drag experienced by vehicles (bikes, cars,planes, etc.) at operating speeds is called form drag. Itincreases quadratically with velocity (essentially because theamount of air you run into increase with v and so does the amount of force you must exert on each small volume of air). Thus
\(\displaystyle{F}_{{{d}{r}{u}{g}}}={C}_{{d}}{A}{v}^{{2}}\)
where A is the cross-sectional area of the vehicle and \(\displaystyle{C}_{{d}}\) is called the coefficient of drag.
Part A:
Consider a vehicle moving with constant velocity \(\displaystyle\vec{{{v}}}\). Find the power dissipated by form drag.
Express your answer in terms of \(\displaystyle{C}_{{d}},{A},\) and speed v.
Part B:
A certain car has an engine that provides a maximum power \(\displaystyle{P}_{{0}}\). Suppose that the maximum speed of thee car, \(\displaystyle{v}_{{0}}\), is limited by a drag force proportional to the square of the speed (as in the previous part). The car engine is now modified, so that the new power \(\displaystyle{P}_{{1}}\) is 10 percent greater than the original power (\(\displaystyle{P}_{{1}}={110}\%{P}_{{0}}\)).
Assume the following:
The top speed is limited by air drag.
The magnitude of the force of air drag at these speeds is proportional to the square of the speed.
By what percentage, \(\displaystyle{\frac{{{v}_{{1}}-{v}_{{0}}}}{{{v}_{{0}}}}}\), is the top speed of the car increased?
Express the percent increase in top speed numerically to two significant figures.

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asked 2021-05-04

When a gas is taken from a to c along the curved path in the figure (Figure 1) , the work done by the gas is W = -40 J and the heat added to the gas is Q = -140 J . Along path abc, the work done by the gas is W = -50 J . (That is, 50 J of work is done on the gas.)
I keep on missing Part D. The answer for part D is not -150,150,-155,108,105( was close but it said not quite check calculations)
Part A
What is Q for path abc?
Express your answer to two significant figures and include the appropriate units.
Part B
f Pc=1/2Pb, what is W for path cda?
Express your answer to two significant figures and include the appropriate units.
Part C
What is Q for path cda?
Express your answer to two significant figures and include the appropriate units.
Part D
What is Ua?Uc?
Express your answer to two significant figures and include the appropriate units.
Part E
If Ud?Uc=42J, what is Q for path da?
Express your answer to two significant figures and include the appropriate units.

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asked 2021-02-21

How do you solve this problem? I don' t even know whereto begin.
A Ferrari with a mass of 1400 kg approaches a freeway underpassthat is 10 m across. At what speed must the car be moving, inorder for it to have a wavelength such that it might somehow"diffract" after passing through this "single slit"? How dothese conditions compare to normal freeway speeds of 30m/s?

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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?

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asked 2021-04-15

A car initially traveling eastward turns north by traveling in a circular path at uniform speed as in the figure below. The length of the arc ABC is 235 m, and the car completes the turn in 33.0 s. (Enter only the answers in the input boxes separately given.)
(a) What is the acceleration when the car is at B located at an angle of 35.0°? Express your answer in terms of the unit vectors \(\displaystyle\hat{{{i}}}\) and \(\displaystyle\hat{{{j}}}\).
1. (Enter in box 1) \(\displaystyle\frac{{m}}{{s}^{{2}}}\hat{{{i}}}+{\left({E}{n}{t}{e}{r}\in{b}\otimes{2}\right)}{P}{S}{K}\frac{{m}}{{s}^{{2}}}\hat{{{j}}}\)
(b) Determine the car's average speed.
3. ( Enter in box 3) m/s
(c) Determine its average acceleration during the 33.0-s interval.
4. ( Enter in box 4) \(\displaystyle\frac{{m}}{{s}^{{2}}}\hat{{{i}}}+\)
5. ( Enter in box 5) \(\displaystyle\frac{{m}}{{s}^{{2}}}\hat{{{j}}}\)

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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.

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Answer 1

Step 1
To explain the connection (in algebra) between the written and symbolic language
Step 2
Historically, problems (in algebra, or arithmetic or geometry) were expressed completely as word problems in the corresponding languages (Greek, Latin, Arabic,...). It was only much later that symbols were introduced and mathematrical expressions began to be expressed in the compact symbolic form that we are used to. Even operations like addition,multiplication (+, -, * ,/) were expressed only in words (plus, minus,...). In fact , the history of algebraic notation is a fascinating and important subject of research on its own
Step 3
Powers like \(\displaystyle{x}^{3},{x}^{2},{x}^{{\frac{1}{{2}}}}{\left(\square{\sqrt[{o}]{{f}}}{x}\right)}\) were also expressed as words (cubus, quadratum ). , radix quadrata,.
Step 4
ANSWER: Coming to the present problem, the expression displayed would be described in words as "Three times the square of x plus five times y , the whole divided by 2"
\(\displaystyle\frac{{{3}{x}^{2}+{5}{y}}}{{2}}\)

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What does it mean to say that algebra is a written language? How would I express an algebraic expression such as for example, numerator displaystyle{3}{x}^{2}+{5}{y} and 2 as the denominator, in words?

What does it mean to say that algebra is a written language? How would I express an algebraic expression such as for example, numerator displaystyle{3}{x}^{2}+{5}{y} and 2 as the denominator, in words?

Answers (1)

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