Shirley is drawing triangles that have the same area. The base of each triangle varies inversely with the height. What are the possible base and height of a second triangle if the first triangle's base is 12 and its height is 8?.

Answers

Answer 1

The possibile base and height of second triangle is option 4: 16 and 6.

We are given the height and base are inversely proportional for the triangle. Based on this, the area of triangle is given by the formula -

Area = 1/2 × base × height

Keep the values in formula to find the area of first triangle -

Area = 1/2 × 12 × 8

Area = 6 × 8

Area = 48

Now, option a in the choices is incorrect, because there is no variation seen in the two values. Trying the other three options to find the dimensions of same area.

Option 2: 60 and 36

Area = 1/2 × 60 × 36

Area = 30 × 36

Area = 1080

Option 3: 120 and 80

Area = 1/2 × 120 × 80

Area = 60 × 80

Area = 4800

Options 4: 16 and 6

Area = 1/2 × 16 × 6

Area = 8 × 6

Area = 48

Hence, option 4 16 and 6 are correct base and height.

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The complete question is attached in the figure.

Shirley Is Drawing Triangles That Have The Same Area. The Base Of Each Triangle Varies Inversely With

Related Questions

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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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

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

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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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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(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!

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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a rectangular block of mass m has dimensions as shown. in terms of m, a, b and c, find the rotational inertia of the block about an axis of rotation through one of the corners of the block which is perpendicular to the large faces. b. let m

Answers

The rotational inertia of the block about an axis of rotation through one of the corners of the block which is perpendicular to the large faces will be M(a²+b²)/3.

What is rotational inertia?

Any item that can be rotated has the property of rotational inertia. It is a scalar value that indicates how challenging it is to alter an object's rotational velocity around a certain rotational axis. The role of mass in linear mechanics is analogous to that of rotational inertia in rotational mechanics. Because it measures moment of inertia as it is rotating, this property is also known as rotational inertia. A measurement of an object's resistance to changes in its angular velocity is called rotational inertia. Imagine turning an item with a specific torque. As the torque is being applied, measure the angular acceleration. The rotational inertia of the item increases as the resultant angular acceleration decreases.

Here,

The major calculations are attached in image.

Moment of Inertia of plate passing through O is I = Ma²/12

and, ly = Mb²/12

by perpendicular axis theorem I2 = Ma²/12+Mb²/12

The distance of edge and the center is d = √(a²+b²)/4

So by parallel axis theorem, IA = Ma²/12+ Mb²/12 + Md² = M(a²+b²)/3

M(a²+b²)/3 is the rotational inertia of the block about a rotating axis passing through one of its corners and perpendicular to its large faces.

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ways 3 people can divide a 10 segment into a equal amount of shares

Answers

The number of ways to divide the shares into 10 equal segments is 120

How to determine the to divide the shares into equal segments?

from the question, we have the following parameters that can be used in our computation:

Total number of segments, n = 10

Numbers to people, r = 3

The number of ways of dividing the segment is then calculated using the following combination formula

Total = ⁿCᵣ

Where

n = 10 and r = 3

Substitute the known values in the above equation, so, we have the following representation

Total = ¹⁰C₃

Apply the combination formula

ⁿCᵣ = n!/(n - r)!r!

So, we have the following representation

Total = 10!/7!3!

Evaluate the quotient

Total = 120

Hence, the number of ways is 120

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Which represents a side length of a square that has an area of 450 square inches?15 startroot 2 endroot inches in. 16 startroot 3 endroot inches in. 112. 5 in. 115. 5 in.

Answers

Using the area formula of the square we know that (A) 15√2 in inches represents a side length of a square that has an area of 450in².

What is the area?

A shape's area can be calculated by contrasting it with squares of a known size.

The square meter (abbreviated as m2), which is the area of a square whose sides are one meter long, is the common unit of area in the International System of Units (SI).

Three such squares would be the same size as a form with a three-square-meter area.

The area of any other shape or surface is a dimensionless real number, and the unit square is defined in mathematics to have area one.

So, the area of the square:

A = b²

Where B is the square's long side.

A = 450in²

A = b²

b² = 450

b = √450

b = 15√2 in

Therefore, using the area formula of the square we know that (A) 15√2 in inches represents a side length of a square that has an area of 450in².

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Correct question:
Which represents a side length of a square that has an area of 450 square inches?

a. 15 start root 2 end root inches in.

b. 16 start root 3 end root inches in.

c. 112. 5 in.

d. 115. 5 in.

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!!! Needs done by tomorrow

Answers

The population of the small town in 2025 is 22234

How to determine the population in 2025?

The given parameters in the question are

Initial population =24597Rate of decay = 2%

These parameters can be represented as

a = 24597

r = 2%

The equation of the function can be represented as

P(t) = a(1 - r)^t

So, we have

P(t) = 24597 * (1 - 2%)^t

In 2025, we have

Year = 2025

This means that

t = 2025 - 2020

So, we have

t = 5

Substitute t = 5 in P(t) = 24597 * (1 - 2%)^t

P(5) = 24597 * (1 - 2%)^5

Evaluate the expression

P(5) = 22234

Hence, the population is 22234

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a right triangle has legs measuring 20 inches and 21 inches. what is the length of the hypotenuse, in inches?

Answers

Answer: 29 inches.

Step-by-step explanation:

The formula to find the hypotenuse is a^2 + b^2 = c^2.

20^2= 400, and 21^2=441. Together, it was 841. Square root that, and your answer is 29.

-

a^2 + b^2 = c^2

20^2 + 21^2 = c^2

400 + 441= c^2

881 = c^2

29=29

Use the Distributive Property to write an expression equivalent to 0.4(-5-7y-13.8).​

Answers

Answer:

-2.8y-7.52

Step-by-step explanation:

multiply 0.4 by each of the numbers in the parentheses then simplify

Answer: -2.8y-7.52

Step-by-step explanation:

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

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

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

Find the radius of a right circular cylinder of maximum volume that can be inscribed in a sphere of radius 12.

Answers

A right circular cylinder with the largest volume that can fit inside a sphere with a radius of 12 has a radius of √7238/πh units.

What is a right circular cylinder?

The right circular cylinder is a cylinder with circular bases that are parallel to one another.

Three dimensions make up its form.

The two bases of the cylinder are joined at their centers by the cylinder's axis.

Sphere:

A sphere is a geometrical object that resembles a two-dimensional circle in three dimensions. In three-dimensional space, a sphere is a collection of points that are all located at the same distance from a single point.

The radius of the right circular cylinder will be:

The formula for the volume of a sphere: V = 4/3πr²

Now, substitute r = 12 as shown:

V = 4/3πr²

V = 4/3π12²

V = 4/3π144

V = 7238.22947

Rounding off: 7238 units³

Nw, the formula for the volume of a right circular cylinder:

V = πr²h

Substitute V = 7238 and calculate for r as follows:

V = πr²h

7238 = πr²h

r² = 7238/πh

r = √7238/πh

Therefore, a right circular cylinder with the largest volume that can fit inside a sphere with a radius of 12 has a radius of √7238/πh units.

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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!

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 circle with radius of 2 cm sits inside a 7 cm x 11 cm rectangle

Answers

I believe the answer you seek would be that the area of the shaded region would be [tex]64.43 cm^2[/tex].

Hope this helps!

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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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

During a certain period of time, 2,000 penguins had an annual growth rate of 19%. What will the population of penguins be after 5 years?

Answers

1 year is 19% increase
19% of 2000 : 19x2000/100: 380
5y : (380x5) + 2000
: 3900?

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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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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write the general antiderivative. (use c for the constant of integration. remember to use absolute values where appropriate.) 1 8 x 1 8x 1 8 x dx

Answers

The integration of the given function is as follows.

What is anti derivative?

In calculus, an antiderivative, inverse derivative, primitive perform, primitive integral or integral of a perform f could be a differentiable perform F whose spinoff is adequate to the initial perform f. this could be explicit symbolically as F' = f

Main body:

f (x) = x/8 +1/8x + (1/8)^x

to find the anti derivative , we need to integrate the function;

apply sum rule:

[tex]\int\ f{(x)} + g (x)\, dx[/tex] = [tex]\int\ f {(x)} \, dx + \int\ g {(x)} \, dx[/tex]

[tex]\int\ {(x/8)} \, dx[/tex] = x² /16

[tex]\int\ f {(1/8x)} \, dx[/tex] = 1/8 ln|x|

[tex]\int\ f {(1/8^x)} \, dx[/tex] = [tex]-\frac{1}{3\ln \left(2\right)\cdot \:8^x}[/tex]

hence

[tex]\int \frac{x}{8}+\frac{1}{8x}+\frac{1}{8^x}dx[/tex]= [tex]\frac{x^2}{16}+\frac{1}{8}\ln \left|x\right|-\frac{1}{3\ln \left(2\right)\cdot \:8^x}+C[/tex]

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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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best answer gets brain award thing!

Answers

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

k(-1) = 7

how do you calculate degrees of freedom for goodness-of-fit chi-square tests versus chi-square tests for independence and homogeneity?

Answers

The degrees of freedom for goodness-of-fit chi-square tests are calculated with the formula: df=bins(or categories)−1−number of parameters of the distribution and the degrees of freedom for the chi-square are calculated using the following formula: df = (r-1)(c-1) .

In the given question we have to calculate degrees of freedom for goodness-of-fit chi-square tests versus chi-square tests for independence and homogeneity.

When a categorical variable has more than two levels, a chi-square goodness-of-fit test can be performed. A one proportion z test may be performed if there are precisely two categories. There must be no overlap between those category variable's levels. To put it another way, every situation must fall into exactly one group.

The degrees of freedom in this case are calculated with the formula:

df=bins(or categories)−1−number of parameters of the distribution.

The degrees of freedom for the chi-square are calculated using the following formula:

df = (r-1)(c-1)

where r is the number of rows and c is the number of columns.

The null hypothesis can be rejected if the observed chi-square test statistic is higher than the crucial value.

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Liz loses her well-paid executive position in a round of corporate downsizing. She spends the evening becoming intoxicated in a seedy bar across town. Liz is demonstrating _____ coping.emotion-focused T/F: In countries with high malnutrition rates, both personal and national economies decline as productivity ceases. with a limited range of emotion, individuals with schizotypal personality disorder are often indifferent to criticisms or praises of others and appear not to be affected by what others think of them. Write a rule for g(x)=f(x+2) when f(x)=x+1. when the labor market is in equilibrium, the quantity demanded of labor equals the quantity supplied of labor, so the unemployment rate is zero the nurse is creating a plan of care for a client that is reporting an inability to sleep and rest. what outcome criterion will the nurse address for a goal that the client will demonstrate physical signs of being rested? the time is 11:06 in 2 hours it will be please someone answer this, i cant find it anywhere and I keep getting 6725 a straight wire segment that is 0.65 meters long has a current of 1.4 amps. the wire segment is oriented so that the current us travelling in the y direction. the wire is placed in a uniform magnetic field of strength 0.65 tesla in the z direction. find the force acting on the wire. give an example of a cell found in the human body that meets one of these criteria. explain how that unique shape is tied to the function that those cells perform. how does international expansion provide companies with a competitive advantage? (select all that apply.) an unknown gas q effuses 1.75 times as fast under the same conditions as xe gas. what is the molar mass (g/mol) of q? true or false? the sea star die-off of 2013 is currently the most extensive marine-disease event ever documented. an image of the lateral skull taken at 68 kvp, 20 mas and is repeated. if the kvp is increased to 78 kvp, what should be the new mas? What type of corporation is formed for the purpose of doing a public service instead of making money?. 1.consider the following list: 5, 12, 25, 32, 38, 46, 58, 62, 85, 90, 97, 105, 110 using the binary search as described in this chapter, how many comparisons are required to find whether the following items are in the list? show the values of first, last, and middle and the number of comparisons after each iteration of the loop.a. 32b. 20 what is the producer surplus if there is a $5 per unit transaction cost? (do not include the dollar sign $ in your answer) a patient is learning to cope with a newly diagnosed chronic illness. to help the patient adjust, which actions should the nurse take? for the periodic review inventory model presented in the textbook, it is assumed that a special replenishment order will be placed in the event of a stock-out between review points. true false what element is undergoing oxidation (if any) in the following reaction? ch4(g) 2 o2(g) co2(g) 2 h2o(g)