A sample of size
=n83
is drawn from a population whose standard deviation is
=σ42
Part 1 of 2
(a) Find the margin of error for a
95%
confidence interval for
μ. Round the answer to at least three decimal places.
The margin of error for a
95%
confidence interval for
μ
is
. Part 2 of 2
(b) If the confidence level were
99%
, would the margin of error be larger or smaller?

Answers

Answer 1

The margin of error would be higher at a 99% confidence level.

Confidence level is the probability, or degree of certainty, that the confidence interval would include the real population parameter when a random sample is drawn numerous times.

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Related Questions

a 2.2 GB game is being downloaded onto your laptop. When you have downloaded half a gigabyte, you notice that your computer has been downloading at a rate of .01GB/min. Write an inequality that represents at least how many minutes it will take to download the whole game.

Answers

The inequality that represents at least how many minutes it will take to download the whole game

is x ≥ (2.2 - 0.5)/0.01

What is an inequality?

Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.

In this scenario, 2.2 GB game is being downloaded onto your laptop and when you have downloaded half a gigabyte, you notice that your computer has been downloading at a rate of .01GB/min.

The inequality will be illustrated. Let the number of minutes be x.

x ≥ (2.2 - 0.5)/0.01

This illustrates the inequality.

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a measurement of how well a child can do certain tasks at a certain time in comparison to other children is a(n) test.

Answers

A(n) IQ test evaluates a child's performance in relation to other kids in terms of how well they can perform specific activities at a specific time.

Each individual IQ exam is made up of a number of smaller questions, and no reading nor writing are required. Some verbal subtests consist of spoken questions with no set time restriction. Other subtests are frequently timed and typically have a visual or spatial focus. It takes one to two hours to give the exam.

115 to 129: Superior or intelligent. 130 through 144: Fairly talented. From 145 through 159: Very talented. Exceptionally talented from 160 to 179.

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A decision maker has five potential independent variables with which to build a regression model to explain the variation in the dependent variable. At step 1, variable x3 enters the regression model. Which of the following indicates which of the four remaining independent variables will be next to enter the model?A) The variable with the highest coefficient of partial determinationB) The variable that has the next highest correlation with the dependent variableC) The variable that will provide the next largest value for the slope coefficientD) Can't be determined without seeing the correlation matrix.

Answers

When building a regression model provided the given information from the four remaining independent variables the variable to be entered next (second) would be variable with the highest coefficient of partial determination. (Option A)

A regression model refers to a function that illustrates the relationship between one or more independent variables and a response, target, dependent variable. The primary uses of regression analysis are forecasting, time series modeling and identifying the cause-and-effect relationship between variables. When building a regression model with five potential independent variables to explain the variation in the dependent variable, at step 1, variable x3 enters the regression model. Of the four remaining independent variables, the variable entered next into the model would be the variable with the highest coefficient of partial determination. A coefficient of partial determination refers to the measurement of marginal (extra) contribution of X variable or percentage of variation in the response variable that can be explained by the explanatory variables and can be used to measure how strongly two variables are related to one another.

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alice walks from the top to the bottom of an escalator that is moving up and counts 150 steps. her friend, bob, walks from the bottom to the top of the escalator and counts 75 steps. if alice's walking speed (in steps per unit of time) is three times bob's walking speed, how many steps are visible on the escalator at a given time? (assume that this value is constant.)

Answers

Based on the information provided, it can be determined that there are 120 steps visible on the escalator at any given time.

Assume that there are x total steps, e for the escalator speed, and b for Bob's pace.

Bob noticed 75 stairs and climbed the entire escalator in the time it took him to ascend it. As a result, the escalator must have added an extra x + 75 steps.

Let e and b be the speeds of the escalator and Bob, respectively.

Alice took 150 steps at a speed of (3b-e) step rate as she descended the stairs.

Bob took 75 steps at a speed of (b+e) each step as he ascended.

Since, Al and Bob were walking the same distance at a time , we have,

150(3b-e) = 75(b+e)  

Solving  these two equation we get ,  e/b = 3/5

Thus while Bob took 75 steps to go up, the escalator contributed an extra

3/5 * 75 = 45 steps

Finally, there is a total of 75+45=120 steps in the length of the escalator.

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why is it inportant to use the order of operations to evaluate algebracic expressions

Answers

Answer:

To get the correct answer.If it isnt followed you will get a number/answer but that is incorrect

can someone please help me solve the systems by graphing?​

Answers

The graphs for the given systems of linear equations are shown below.

From the graph, the solution to the first system is (8, -5)

From the graph, the solution to the second system is (-7, -6)

Graphing system of linear equations

From the question, we are to graph the given system of equations

The given system of equations is

y = 1/4x - 7

y = -1/2x - 1

First, we will plot the graph by using the x-intercepts and the y-intercepts of  the lines

y = 1/4x - 7

Set y = 0 to determine the x-intercept

0 = 1/4x - 7

7 = 1/4x

x = 28

The x-intercept of the equation is 28

Set x = 0 to determine the y-intercept

y = 1/4(0) - 7

y = 0 - 7

y = -7

The y-intercept of the equation is -7

For y = -1/2x - 1

Set y = 0 to determine the x-intercept

0 = -1/2x - 1

1 = -1/2x

-x = 2

x = -2

The x-intercept of the equation is -2

Set x = 0 to determine the y-intercept

y = -1/2(0) - 1

y = 0 - 1

y = -1

The y-intercept of the equation is -1

Using the x-intercepts and y-intercepts, the graph of the system is shown below

For the second system of equations

y = 1/7x - 5

y = 8/7x + 2

For y = 1/7x - 5

Set y = 0 to determine the x-intercept

0 = 1/7x - 5

5 = 1/7x

x = 35

The x-intercept of the equation is 35

Set x = 0 to determine the y-intercept

y = 1/7(0) - 5

y = 0 - 5

y = -5

The y-intercept of the equation is -5

For y = 8/7x + 2

Set y = 0 to determine the x-intercept

0 = 8/7x + 2

-2 = 8/7x

8x = -14

x = -14/8

x = -7/4

The x-intercept of the equation is -7/4

Set x = 0 to determine the y-intercept

y = 8/7(0) + 2

y = 0 + 2

y = 2

The y-intercept of the equation is 2

Using the x-intercepts and y-intercepts, the graph of the system is shown below

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A round shaped wall clock frame is made of a steel rod with length of 1.57m. calculate the radius,in m, of the frame.​

Answers

Check the picture below.

[tex]\textit{Circumference of a circle}\\\\ C=2\pi r ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ C=1.57 \end{cases}\implies 1.57=2\pi r\implies \cfrac{1.57}{2\pi }=r\implies {\Large \begin{array}{llll} \stackrel{meters}{0.25}\approx r \end{array}}[/tex]

an open-top box is to be made by cutting small congruent squares from the corners of a 12- in.-by-12-in. sheet of tin and bending up the sides. how large should the squares cut from the corners be to make the box hold as much as possible? what are the dimensions of the box with the largest volume?

Answers

The squares cut from the corners should be large in width and length 6 to hold the box as much as possible. The dimensions of the box with the largest volume are 6 x 6.

If the squares cut from the corners are h × h inches

The open-top box will have

A height of h

A width of 12 - 2h

and a length of 12 - 2h

So its volume will be

V(h) = h × (12 - 2h) × (12 - 2h)

= 4h³ - 48h² + 144h    (square inches)

dV/dh= 12h² - 96h + 144

Critical points occur when the derivative (dV/dh) is zero.

12h² - 96h + 144 = 0

h² - 8h + 12 = 0

(h − 2)(h − 6) = 0

It is clear that h = 6 is not the crucial point for the maximum as it would produce widths and lengths of zero (and so a volume of zero).

In order to cut out squares measuring 6 × 6 inches from the corners of the bigger sheet, the most volume may be obtained.

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A, B, and C are three landmarks in a national park. Landmarks A and B are 650 meters apart. Landmarks B and C are 822 meters apart. Carla takes 4 minutes to run from Landmark A Landmark B, and another 6 muinutes to run from Landmark B to Landmark C. What is Carla's average speed in meters per minute for the run from Landmark A to Landmark C?

Answers

Carla’s average speed was 174

kal and kara solve this problem in two different ways. the perimeter of a rectangle is 4646 centimeters. its length is 88 centimeters. what is its width? use the drop-down menus to complete the sentences below.

Answers

If the perimeter of the rectangle is 4646 centimeters and its length is 88 centimeters then its width would be 2235 centimeters

What is meant by the term Perimeter?

The perimeter of a form in geometry is defined as the entire length of its border. A shape's circumference is calculated by summing the lengths of all of its sides and edges. Its dimensions are expressed in linear units like centimeters, meters, inches, and feet.

In daily life, people constantly employ the idea of perimeter. For instance, we measure the perimeter of the area to be fenced in or decorated for Christmas to determine how much wire you will need.

We are aware that a regular polygon has equal-length sides.

A regular polygon's perimeter is equal to the product of all of its sides, which is equal to the quantity o sides times the length of a side.

How to solve?

width = 4646 - 2*88 =4470

width of one side = 4470/2 = 2235 centimeters

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how long will it take for the population of a small town with 500 people to double in size if the population increases at a rate of 15% per year

Answers

The small town would take up 5 years to double the population from 500 people.

What is percentage ?

As its sign is "%," the word "percent" implies "for every hundred". Since it is read as a percentage, "x%" should be read as "x percent." So, a percent is a fraction with a denominator of 100. 30%, for instance, equals 30/100 (i.e. 30 parts from 100). You can also write this as 0.30.

Population of small town = 500

Population Growth rate = 15 %

To find :

              Time when the population is doubled.

We will use successive change

500 People after 1 year = 575

575 People after 1 year = 661.25

661.25 People after 1 year = 760.4375

760.4375 People after 1 year = 874.503125

874.503125 People after 1 year = 1005.67859

Hence it will total take the time of 5 years to double the population.

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Which ordered pairs lie on the graph of the exponential function ​f(x)=3(14)x? Select each correct answer. (1, 0.75) (-3,-192) (0,1) (-1,12)

Answers

The ordered pair that lie on the graph of the exponential function ​f(x)=3(14)ˣ is (-1, 12)

What is exponential graph?

A curve that depicts an exponential function is known as an exponential graph.

The curve have a horizontal asymptote and either an increasing slope or a decreasing slope. this is to say that the curve begins as a horizontal line, increases or drops gradually, and then the growth or decay accelerates. It may or may not cut the x-axis, but it always cuts the y-axis at some point.

An exponential graph will almost always have a y-intercept but not necessarily an x-intercept.

The given function was plotted on a graph and the point that lie on the graph is (-1, 12).

the point (-3,-192)  is way out of the graph

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Kaitlynn needs 3 pounds of fruit for a salad.
She already has 3/4 pounds of apples and 1/3 pounds of grapes.

How many more pounds of fruit does she need to buy?

Answers

answer:

1.92 pounds or 23/12 lb

step-by-step explanation:

first convert 3/4 and 1/3 to fractions that have the same denominator such as 9/12 and 4/12. then add the two numbers together and subtract it by 3 to get the answer. hope that helps!

If you earn $0. 25 per quart of berries picked, how much will you earn if you pick 900 quarts?.

Answers

Answer: $225

Step-by-step explanation: .25 x 900 = 225

Answer: $225

Step-by-step explanation:

You earn $.25 for every quart picked. You pick 900 quarts. take 900 and times it by .25. You get 225 so you earn $225

please help!

factor 2x^2-7x-9

Answers

Answer:

(x + 1 ) (2x-9)

Step-by-step explanation:

Break The expression into groups

= ([tex]2x^{2} +2x)+(-9x-9)[/tex]

Factor out 2x from [tex]2x^{2}[/tex] + 2x: 2x (x + 1)

and then you want to factor out the -9x - 9 -9( x + 1 )

and that equals 2x( x + 1 ) [tex]-9(x+1)[/tex]

And now do it again Factor out common term x + 1

and now it " Equals" [tex](x + 1)(2x-9)[/tex]

An online tutoring company charges $25 per session plus an annual membership fee of $45. If a member is charged $545 for the year, how many sessions did they have that year?

Answers

The total number of sessions they did in that year will be equal to 20.

What is an equation?

Equations are mathematical expressions with two algebras on either side of an equal (=) sign. The expressions on the left and right are shown to be similar to one another, demonstrating this relationship. L.H.S. = R.H.S. (left-hand side = right side) is a simple fundamental equation.

As per the data given in the question,

The charge per session = $25

Annual membership charge = $45

Total money paid = $545

Money left after paying for the annual membership = $545 - $45= $500

The total number of sessions in $500 will be,

T = 500/25

T = 20 sessions.  

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(14+ 8²︎) ÷ 2 - 10
Help on this please

Answers

Answer:

29

Step-by-step explanation:

(14+8²︎) ÷ 2 - 10

(14+64) ÷ 2 - 10

(78) ÷ 2 - 10

39 - 10

29

Could you please mark me brainliest for this? Thank you!

a random sample of 1000 car owners in a particular city found 150 car owners who received a speeding ticket this year. find a 95% confidence interval for the true percent of car owners in this city who received a speeding ticket this year.

Answers

The confidence interval for the true percent of car owners in the city  who received a speeding ticket be, (139.27 , 160.73).

Subtract 1 from your sample size. 1000 – 1 = 999. This provides the degrees of freedom.

Subtract the confidence level from 1, and then divide by two.

(1 – .95) / 2 = .025

Now, df = 999 and α = 0.025

from the table at df = 999 we got 2.262.

Divide your sample standard deviation by the square root of your sample size.

150 / √(10) = 4.74

Now, 2.262 × 4.74 = 10.73

So, the confidence interval be,

(150 - 10.73 , 150 + 10.73) = (139.27 , 160.73)

Hence, the confidence interval for the true percent of car owners in the city  who received a speeding ticket be, (139.27 , 160.73).

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create a class to calculate the areas of differents geometrical shapes, the shapes are square, rectangal, triangle. class should methods name area,

Answers

Creation of class to calculate the areas of different geometrical shapes requires to use certain rules which are mentioned in detail here.

How to name a Class?

Developers frequently encounter naming issues. I lost count of the number of hours I've spent considering what to name things and the amount of time it took me to decipher code that had inappropriate names. Whether it was an object, methods, class, or something else is irrelevant. Given that we spend more time reading code than developing it, effective naming is usually beneficial in the long run.

Your code becomes better and cleaner when you use excellent names. It aids in helping you recognize the functions of each piece of code intuitively. It makes your application easier to read in the future by other developers as well as yourself.

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if gear \text{a}astart text, a, end text is rotated by the motor at a rate of 100 \text{ rpm}100 rpm100, start text, space, r, p, m, end text, what is the number of revolutions per minute for gear \text{c}cstart text, c, end text ?

Answers

The number of revolution per minute for Gear C is 200 rpm

It is given that

The gear ratio r:s is ratio of number of teeth of two connected gear

Also , the gear A is rotated at rate of = 100rpm

Since, Gear A has 20 teeth and Gear B has 60

Ratio = r : s

=> 20 : 60

=> 1 : 3

Thus , the ratio of number of revolution per minute for two gear is s:r

=> 3 : 1

Means Gear A turns at 3 rpm , Gear B turns at 1 rpm

Similarly , for Gear B and Gear C

The ratio of rpms for these two will be =>

10 : 60

=> 1 : 6

That is , when Gear B turns at 1rpm , Gear C turns at 6rpms

Therefore, If Gear A turns at 100 rpms

the Gear B turns at = 100/3 rpms

Hence , Gear C turns at = 100/3 × 6

=> 200 rpms

I've answered the question in general as the question is incomplete

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Write the ratio as a fraction in simplest form, with whole numbers in the numerator and denominator.
16 ft to 36 ft

Answers

Answer:

Step-by-step explanation:

The easiest way to do this is to clear the decimal by multiplying the numerator and the denominator by

10

.

You can reduce the fraction later.

40

m

48

m

2) Reduce the fraction to its simplest form

Cancel out

8

from the top and the bottom

5

m

6

m

answer

This answer means that the numerator and denominator of the given fraction

4

m

4.8

m

are in a

5

:

6

ratio relationship with each other.

Check

Is

4

4.8

equal to

5

6

 

?

Cross multiply

(

4

)

(

6

)

should be equal to

(

5

)

(

4.8

)

24

is equal to

24.0

C

h

e

c

k

consider any two numbers a, b with a < b. if x is the uniform distribution on the interval [a, b], what is the variance of x?

Answers

The variance over an interval for a uniform distribution is

V(X) = ( b - a )²/ 12

Here,

a and b are intervals .

By the definition of the variance, V(X) = E[X2] − (EX)2.

On solving ,

V(X)

=(a²+ab+b²)/3−(a²+2ab+b²)/4

=(a²−2ab+b²)/12

=( b - a )²/ 12

A continuous probability distribution is a Uniform distribution and is related to the events which are equally likely to occur. It is defined by two parameters, x and y, where x = minimum value and y = maximum value. It is generally denoted by u(x, y).

A two-parameter family of curves known as the uniform distribution (sometimes known as the rectangle distribution) is famous for having a constant probability distribution function (pdf) between its two bounding parameters.

For values tabulated to a specific number of decimal places, this distribution is suitable for illustrating the distribution of round-off mistakes. Techniques for generating random numbers , like the inversion method, use the uniform distribution.

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x + 2y = −4 please hurry

Answers

Answer:

x = -2y - 4

Step-by-step explanation:

x + 2y = -4

Subtract 2y from both sides.

x = -4 - 2y

Answer:

x = 2

this is the answer hope u pass

sketch the nyquist plot based on the bode plots for each of the following systems , and then compare your results whit that obtained by using the matlab command nyquist : dont be concerned with the details of exactly where the curve goes , but do make sure it crosses the real axis at the right spot , has the correct number of -1 encirclements and goes off to infinity in the correct direction. A). >KG ( s) a= K( s+2 ) / s + 10 B.>KG ( s) = K / ( s + 10 )(s+2)2 C).>KG ( s) = K (s+10)(s+10) / (s+100)(s+2)3 D). Usinng your plots , estimate the range of k for which each system is stable , and qualitatively verif your result by using a rough sketch of a root locus plot.

Answers

Sketching the nyquist plot based on the bode plots for the mentioned systems require a certain understanding of bode plots explained in detail.

What do you understand by bode plots?

In reality, Bode plots are a collection of graphs that display a system's frequency response. This system might be any system (not simply a circuit!) that changes its behavior when its frequency (cycles per second) changes.

Frequency Response simply describes how our system will alter in response to a specific input frequency. This collection of notes will be referred to as our input frequency.

Bode charts often have two graphs. We'll refer to one as the magnitude plot and the other as the phase angle plot.

We'll need something initially called a transfer function. Typically represented as H(s) or H(j). A transfer function often equates to the ratio of the output to the input.

A). >KG ( s) a= K( s+2 ) / s + 10 B.>KG ( s) = K / ( s + 10 )(s+2)2 C).>KG ( s) = K (s+10)(s+10) / (s+100)(s+2)3 D)

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best answer gets brain award thing!

Answers

Look at the point in which the x-value is equal to -1

k(-1) = 7

a circle has a radius of 8 what is its circumference do not round

Please help me!

Answers

Answer:

C = 50.27

Step-by-step explanation:

Hope this helps!

Answer:

C = 16 pi

Step-by-step explanation:

The circumference of a circle is given by

C = 2 * pi * r

C = 2 * pi * 8

C = 16 pi

if a woman's first child is a girl and her second child is also a girl, what is the probability that her third child would be a girl?

Answers

The probability that her third child would be a girl is 50%.

Probability:

In math probability means the possible of happening a particular event amount the total number of event.

Given,

Here we need to find if a woman's first child is a girl and her second child is also a girl, what is the probability that her third child would be a girl.

We already know that, there are two sex chromosomes X and Y.

And in the humans are diploid having two sex chromosomes, in females a pair of the X chromosome is found while in males an X and Y chromosome is present.

So, there is  50% chance that the subsequent child is going to be a girl because it entirely depends upon the chromosome of the sperm which fertilizes the ovum.

For each pregnancy features a  50% chance of leading to a boy or girl and this doesn't include the likelihood of multiples.

Here already having 2 girls previously doesn't affect the probabilities of any resulting pregnancy.

Therefore, the prospect of getting a girl remains at  50%.

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please help me asap it would help alot

Answers

X = 60

Adding x and 2x makes a line which is 180 degrees. 180/3 is 60.
This x is 60

Write the rule for the mapping, x =,1,2,3,4 and y= 1,3,5,7

Answers

Answer: y=2x-1

Step-by-step explanation:

(1,1) (2,3) (3,5) (4,7)
1=2(1)-1
3=2(2)-1
5=2(3)-1
7=2(4)-1

2.66 as a fraction in simplest form

Answers

Answer:

133/50

Step-by-step explanation:

2.66 as a fraction in simplest form

(2.66 × 100)/100 =

266/100 =

133/50

-----------------

check

133 : 50 = 2.66

the answer is good

Other Questions
at a certain temperature, the solubility of strontium arsenate, sr3(aso4)2, is 0.0500 g/l. what is the Ksp of this salt at this temperature? Which characteristic is a sign of healthy peer relationships? honestyjealousyinsecuritycompetitiveness. 1. Consider the supply contract problem scenario that we discussed in class (and in Chapter 4). That is, the seller (supplier) is MTO; the seller pays a fixed cost of $100,000 to produce, and its per unit production cost is $35; the buyer pays the seller $80 per item purchased, and sells the items, for which there is a demand, for $125; the residual price is $20. As discussed, the globally optimal solution which maximizes the combined expected profit, is for the buyer to purchase Q* = 16,000 items. This results in a combined expected profit of $1,014,500. Suppose that the buyer and seller do not share any information beyond that given in the following contract: Suppose that the buyer and seller have a revenue sharing contract with Chew being the new cost per unit for the buyer in exchange for x% revenue sharing. Suppose Chew = CM = 35. Does there exist a value of x that will both: yield both the maximum combined expected profit and equally split it between the buyer and the seller? If so, determine this value of x. If not, explain why no such value exists. suppose that as a project manager, you provide detailed plans and frequent project updates to both the team and stakeholders. what project management value does this represent? 1 point a runner is participating in half marathon he has run 12 of the 15 miles course what percent of the course has he run so far? If a person agrees that resources should be paid based upon the value of their creation, then income payments based on marginal revenue product provide a fair and distribution of society's income.equitable, equitible, or equal after a reciprocal translocation occurs between chromosome ii and iv, what will be the chromosome contents for these two chromosomes in the nucleus? as theorists point out, a good deal of the competition for valued resources takes place along racial lines in the united states. a client has a decreased secretion of erythropoietin from the kidneys due to end-stage kidney disease. the nurse explains that the decrease in erythropoietin will have what effect? Solve each of the following equations using the Principle of Zero Products and match it to its correct pair of solutions on theright. Each pair on the right will be used once.(x-9)(3x + 4) = 0(x-4) (9x + 1) = 0(x+9)(3x-4)= 0(x+4)(9x-1)=0x = -4 or x =x = -9 or x =x = 9 or x = -x = 4 or x=-1 a nurse is caring for a client who uses a hearing aid for amplifying sound. during the rinne test for checking the bone conduction of the sound, where should the nurse place the stem of the vibrating tuning fork? anthropologist oyeronke oyewumi holds a postmodern view of gender. she reports that the yoruban society of west africa was a genderless society prior to the arrival of western researchers, if that is indeed the case, why did the researchers find evidence of a gender system upon their arrival? calculate the pressure due to the ocean, in atmospheres, at the bottom of this trench. given that its depth is 11.0 km and assuming the density of seawater is a constant 1.025 x 103 kg/m? all the way down according to einsteins second postulate, if you are moving 10.0 m/s on a bike with headlight on, what is the speed of the light from the bike? Why should you include both reasons and evidence in a literary analysis? A. Readers will need both before deciding whether to accept your interpretation. B. Evidence is meaningless without reasons to back it up. C. Evidence and reasons make it appear as if you have researched your topic. D. Readers will expect your literary analysis to look just like other such essays. An atom has three protons and one neutron in its nucleus. How many electrons will it have; if it is a stable atom? How do you know?When you combine vinegar and baking soda, a gas is produced. Why is the gas considered evidence that a chemical reaction occurred?How can you use a graduated cylinder, water, and an electronic balance to find the density of water?Please answer all 3:) a nurse has decided to specialize in the care of the aging individuals in both illness and health. what is the term for this nursing specialty? signs that use blue, white and red colors and have the interstate number located on the middle of the sign are: a) regulatory signs b) warning signs c) guide signs d) interstate signs mauro and his wife just found out that their infant has a birth defect in his heart that will require heart surgery. which of the following is the best label for the heart defect? ten points labeled a, b, c, d, e, f, g, h, i, j are arranged in a plane in such a way that no three lie on the same straight line. (a) how many straight lines are determined by the ten points?