How do you find the mirror image of a curve with respect to a line?

Answers

Answer 1

Finding the mirror image of a curve with respect to a line is a relatively straightforward task.

What is mirror image?

Mirror image is an exact reflection of an object or an image as seen in a mirror. It is an image that is flipped from left to right, with the left side of the image becoming the right side and vice versa. This type of reflection is also known as a lateral inversion. In art and photography, mirror images are often used for aesthetic purposes and to create symmetry.

Firstly, you need to determine the line of reflection. This can be identified by using the angle bisector of the two lines that form the curve. Once you have identified the line of reflection, draw a line perpendicular to it. This is the axis of symmetry.

Next, draw a line parallel to the axis of symmetry. This line will serve as the mirror line. Now, you can start plotting the points of the curve with respect to the mirror line. To do this, take the midpoint of the curve and reflect it across the mirror line. Then, take the points on either side of the midpoint, and reflect them across the mirror line as well. Repeat this process for all the points on the curve.

Finally, connect the reflected points to form the mirror image of the curve. This will give you the same curve, just flipped across the mirror line. It is important to note that the mirror image of the curve will be a mirror reflection of its original shape, but its orientation may be different.

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Related Questions

ANSWER PLS!! NEED ASAP!!


Angela baked an apple pie that had a radius of 6 inches. She wants to cut the pie into eight equal slices. How wide will each piece of pie be at the outer edge?

A- 5.2 in.
B- 4.7 in.
C- 4.4 in.
D- 4.2 in.

Answers

Answer:

Angela baked A-5.2 inches of baked apple pie.

Step-by-step explanation:

PLEASE HELP!! 40 POINTS!!

A gymnast joined a yoga studio to improve his flexibility and balance. He pays a monthly fee and a fee per class he attends. The equation y = 20 + 10x represents the amount the gymnast pays for his membership to the yoga studio per month for a certain number of classes.

Which graph represents this situation?

graph with the x axis labeled number of classes and the y axis labeled monthly amount in dollars and a line going from the point 0 comma 20 through the point 1 comma 30

graph with the x axis labeled number of classes and the y axis labeled monthly amount in dollars and a line going from the point 0 comma 20 through the point 1 comma 10

graph with the x axis labeled number of classes and the y axis labeled monthly amount in dollars and a line going from the point 0 comma 10 through the point 1 comma 30

graph with the x axis labeled number of classes and the y axis labeled monthly amount in dollars and a line going from the point 0 comma 10 through the point one half comma zero

Answers

Answer:

the second option

Step-by-step explanation:

y=mx+c

therefore y=10x+20

20 is the y intercept, 10 is the gradient

enter in the missing numbers to create equivalent ratios i need helpppppp i don’t understand

Answers

Answer:

[tex]8....on \: the \: first \: box \: and \\ 64......on \: the \: second \: box[/tex]

Step-by-step explanation:

Greetings!!!

so first let's see how it comes by changing it into ratios

[tex] \frac{1}{4} ....the \: first \\ \frac{2}{8} cancel(simplify) = \frac{1}{4}...the \: second [/tex]

Thus, following the same order

[tex] \frac{8}{32} simplify = \frac{1}{4} \\ \frac{16}{64} simplify = \frac{1}{4} [/tex]

so we get the same ratios.

If any questions tag it on the comments.

Hope it helps!!!

Notice a pattern:

The first number in each ratio is 1/4 of the second number, because a ratio can be written as a fraction.

1/4 of 4 = 1
1/4 of 8 = 2

So for the next ratio:

? : 32 = 8: 32

We just need to divide 32 by 4 to find 1/4 of it: 32/4 = 8

And 16 : ? = 16 : 64
Because 1/4 of 64 is 16, so 16 x 4 = 64

Hope you understand!

if you can solve this that would be great

Answers

Answer:

I wish you luck

Step-by-step explanation:

Probability of being a senior or white

Answers

The probability of being a senior citizen and white is: (0.63)(0.3) = 0.189.

What is probability?

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can vary from 0 to 1, with 0 being an impossibility and 1 denoting a certainty.

Given that the probability of identifying white is 0.63.

Then the probability of not white is:

1 - 0.63 = 0.37

Given that the probability of being a senior citizen is 0.3.

Then the probability of not a senior citizen is:

1-0.3 = 0.7

Hence, the probability of being a senior citizen and white is:

(0.63)(0.3) = 0.189

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What is true about exponential functions with a base between 0 and 1?

Answers

Answer:1 always rise to the left and approach 0 to the right.

Step-by-step explanation:

1. Bennet is getting in shape for football season. He runs 400 yards 3 times a day for 5 days. How many feet did he run in 5 days?

2. The Russel family is keeping track of the milk they drink each week:

- The first week they drank 2 gallons, 1 quart and 1 cup of milk
- the second week they drank 3 gallons of milk

which week did they drink more milk?

Answers

1) 400x3x5x1,7

Football season, he runs 400 yards three times a day, so 400 yards three times a day for five days, which shows the correct way to find the number of miles Bennett will run in five days. So you would have to multiply, um, all of them. So it would be this first expression.
the second week he drank more milk

how many radians are there in 3 circles

Answers

Answer:

There are 6

Step-by-step explanation:

There are two within each circle.

Answer: 18.84 radians

Step-by-step explanation:

P(x<15) round 2 decimal places

Answers

When rounded to two decimal places, numbers like 0.7035 and 2.836220364, for instance, become 0.70 and 2.84, respectively.

What is Round to Two Decimal Places?

To simplify their interpretation and use in calculations, decimal numbers are frequently rounded off.

The hundredths place, which is the second place to the right of the decimal point, is where a decimal number is rounded to when it is rounded to two decimal places.

When rounded to two decimal places, numbers like 0.7035 and 2.836220364, for instance, become 0.70 and 2.84, respectively.

If you look closely, you will see that instead of 2.83, we have increased the digit in the first number's hundredths position by 1.

We did not, however, add 1 to the digit in the hundredths place for the second number (i.e 0).

The Complete Question is two decimal places.

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Complete question:

Round the function P(x<15) to 2 decimal places.

f(x)= 2x^2+3x-5
f(f(2))

Answers

Answer:

[tex]f(f(2))=184[/tex]

Step-by-step explanation:

[tex]f(x)=2x^2+3x-5\\f(2)=2(2)^2+3(2)-5=2(4)+6-5=8+1=9\\f(f(2))=f(9)=2(9)^2+3(9)-5=2(81)+27-5=162+22=184[/tex]

Amelia is making a hair bow that requires
one yard of ribbon. The ribbon that she
needs is sold by the meter. Will one meter
of ribbon be enough to make the bow?
Explain.

Answers

Yes, one meter of ribbon will be enough to make the bow because one meter is equal to  1.094 yards.

How to determine if  one meter of ribbon be enough to make the bow?

One meter is equal to  1.094 yards. So, one meter is longer than one yard.

Since Amelia needs one yard of ribbon to make the bow, and she can only find ribbon sold by the meter, which is longer than a yard, one meter of ribbon will be enough to make the bow.

Thus, She can purchase one meter of ribbon to make the bow.

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Which equation has infinitely many solutions?
• A 3x - 2 - 2 - 3х
B. x+3x+6=6+4x
C 2x+7x-5=-9x+5
D 4x-5x+3= -5x + 4x -3

Answers

Answer: i think its A

Answer:

B. x+3x+6=6+4x

Step-by-step explanation:

B)

x+3x+6=6+4xx+3x+6-6=6+4x-6x+3x=4x4x=4x

Since both sides are equal, there are infinitely many solutions.

-Hope this helps!

A ferris wheel can accommodate 40 people in 20 minutes. How many people could ride the ferris wheel in 5 hours? What was that rate per hour?​

Answers

Answer:

600 people

Step-by-step explanation:

40 people in 20 minutes => 120 people per hour. 5 hours, so 5 x 120 = 600 people.

What are the 4 properties of subtraction?

Answers

There are various properties of subtraction , out of which four of them are ,

Commutative propertyAssociative property Identity propertyDistributive property

Subtraction means to reduce one number or quantity from another.  It is one of the most common mathematical operations which are present as well as it is represented by the symbol , " - " .

The associative property does not apply to subtraction which are performed between  whole-number. The order of subtraction is significant.

The distributive property helps to simplify the difficult algebraic expression. As a result, the distributive property favors multiplication over subtraction. The property states that subtracting any number from the same number results in the number 0.

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How do you identify the base and exponent in an exponential notation?

Answers

We can identify the base and its exponent as the exponent indicates the number of times the base is used as a factor in an exponential notation.

What is Exponent ?

An exponent is the number of times a number has been multiplied by itself. For instance, the phrase 2 to the third, which is represented as 23, means 2 x 2 x 2 = 8, not 23, and 2 x 3 = 6, respectively. Remember that every number multiplied by one is equal to itself.

Exponents are a technique of expressing extremely large numbers in terms of powers. The number of times a number has been multiplied by itself is the exponent, so to speak. For instance, the result of multiplying the number 6 by itself four times is 6 6 6 6. This can be expressed as 6⁴. Here, the exponent and base are 4 and 6, respectively.

An exponential number takes the shape of a, where an is multiplied by itself n times. The simple example is 8=23=222. In exponential notation, A is referred to as the base, whereas n is referred to as the power, exponent, or index. In scientific notation, 10, which is a specific illustration of exponential numbers, is typically always used as the base number.

Exponential notation make it easy to express powers succinctly. The exponent displays the base's multiplicative power. It can be written as 2 2 2 2=25 for the integer 32 because 2 is the "base" and 5 is the "exponent." The correct translation of this phrase is "two to the fifth power."

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which of the following is not the solution of 3x+6y=12?A) (-4,4) B) (0,2)C) (8,-2)D) (3,1)​

Answers

(3,1) is not the solution of the equation 3x + 6y = 12. So the option D is correct.

In the given question, we have to check which of the following is not the solution of 3x+6y=12.

To check which is not the solution of the given equation, we put the value of x and y from the given point. If for any point the condition is true then that point is the solution of the given equation. If that point doesn't satisfy the condition then that point is not the solution of the given equation.

The given equation is 3x+6y=12.

Firstly we check for the point (-4,4), where x = -4, y = 4

3(-4) + 6(4) = 12

-12 + 24 = 12

12 = 12(True)

Now we check for the point (0,2), where x = 0, y = 2

3(0) + 6(2) = 12

0 + 12 = 12

12 = 12(True)

Now we check for the point (8,-2), where x = 8, y = -2

3(8) + 6(-2) = 12

24 - 12 = 12

12 = 12(True)

Now we check for the point (3,1), where x = 3, y = 1

3(3) + 6(1) = 12

9 + 6 = 12

15 = 12(False)

Hence, (3,1) is not the solution of the equation 3x + 6y = 12. So the option D is correct.

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How do you find a prime number multiples?

Answers

A prime number is a natural number greater than 1 that is not a product of two smaller natural numbers. A prime number can only be divided evenly by 1 and itself.

To find the multiples of a prime number, you can use the following steps:

Start with the prime number itself. This is the first multiple of the prime number.Multiply the prime number by 2. This will give you the second multiple of the prime number.Multiply the prime number by 3. This will give you the third multiple of the prime number.Repeat step 3 for larger and larger integers (4,5,6,7,8....) until you reach the desired number of multiples.

For example, if the prime number is 5, the multiples of 5 are 5, 10, 15, 20, 25, and so on.

It's important to note that a prime number only has two divisors: 1 and itself. This means that a multiple of a prime number will never be a prime number.

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20.25- (-5) - 11.75 + 15.

Answers

Answer:

28.5

20.25 - (-5) = 25.25

25.25 - 11.75 = 13.5

13.5 + 15 = 28.5

Step-by-step explanation:

Sorry it took so long. Hope it helps! =D

A touchdown in football count for 6 point. If n tand for the number of touchdown, which equation repreent how many point n touchdown are worth

Answers

A touchdown in football count for 6 point. If n and for the number of touchdown, then the equation which represents number of points in n touchdown y = [tex]6n[/tex]

Given that,

A touchdown in football count for 6 point.

If n and for the number of touchdown,

We are given that a touchdown in football counts for 6 points.

We have to find an equation which represents number of points in n touchdown.

In order to find the number of points in n touchdown we will multiply 6 with n.

Number of points in one touchdown y = 6

Number of points in n touchdown y = [tex]6*n[/tex]

Number of points in n touchdown y = [tex]6n[/tex]

Therefore,

A touchdown in football count for 6 point. If n and for the number of touchdown, then the equation which represents number of points in n touchdown y = [tex]6n[/tex]

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In two or more complete sentences, compare the number of x-intercepts in the graph of f(x) = x2 to the number of x-intercepts in the graph of g(x) = x2 +1. Be sure to include the transformations that occurred between the parent function f(x) and its image g(x).

Answers

Answer: The graph of f(x) = x^2 will have only one x-intercept (0,0) since it is a parabola that opens upward and its vertex is at the origin. On the other hand, the graph of g(x) = x^2 +1 is a transformation of the parent function, the graph of f(x) = x^2, where the function was shifted up by 1 unit. Therefore this function g(x) = x^2 +1 will not have any x-intercept because when x=0 the y value becomes 1 so the x-intercept will not be on the x-y plane.

In summary, the graph of f(x) = x^2 has one x-intercept, while the graph of g(x) = x^2 +1 has no x-intercepts due to the transformation of the parent function.

Step-by-step explanation:

What circles are drawn on the score sheet at the end of a set?

Answers

In light of this, the scorer circles the S on the scorecard at the end of a set to designate the team that would serve first after a coin flip.

Following are the circles that are drawn at the end of a set on the NCAA women's volleyball scorecard:

who has the first opportunity to serve:

Based on our existing knowledge of how NCAA Women's Volleyball functions, we can see that each period is divided into sets and that there is a scorecard where each team's points are given. In light of this, the scorer circles the S on the scorecard at the end of a set to designate the team that would serve first after a coin flip.

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A candy store sells Nerds in two different sizes. Which is the best buy?

14 oz. for $4.20 OR 18 oz. for $5.04

Answers

Answer: 18oz

Step-by-step explanation:

Can someone help me with this ? Please

Answers

Value of gof(-1) is 2. The solution has been obtained by applying the multiplication operation on the given functions.

What are operations on functions?

Just like we add, subtract, multiply and divide the terms in a function, the functions can also be added, subtracted, multiplied or divided in a similar way.

Suppose there are two functions f(x) and g(x). The notations are as follows:

For Addition: (f+g)(x) = f(x) + g(x)For Subtraction: (f-g)(x) = f(x) - g(x)For Multiplication: (f×g)(x) = f(x) × g(x)For Division: (f/g)(x) = (f(x))/(g(x))

Now, gof= g(f) = 3-f

We are given f = 2+x

So, f(-1) = 2+(-1) = 1

Now, substituting the value of f(-1) in g(f) , we get

gof(-1)= 3-1=2

Hence, the value of gof(-1) is 2.

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In 2006, the U.S. Population (or persons) per square mile of land area was 85. In 2014, the persons per square mile was 89.48.

a. Write an equation describing the relationship between year and persons per square mile. Use ordered pairs of the form (years past 2006, persons per square mile)

b. Use equation on question 7 to predict the persons per square mile in 2023. Round to the nearest whole person.

Answers

In 2006 we have 93.3 people per sq mile .

What is linear equation ?

Linear equation can be defined as equation in which highest degree is one.

In order to determine the equation for this relationship, we need to first find the slope between these two values. There are two ways to do this:

1. Create a graph

*Create a graph with the x-axis representing the years past 2000 (so 2000 would be 0 and 2003 would be 3 and so on)

*Use the fact that slope=rise/run to get slope=2.7/3 (because we rise 87-84.3=2.7 and run 3 (from 2000 to 2003), and 2.7/3=27/30=9/10

*Plug this and the point (0, 84.3) into the formula y=mx+b to find the y-intercept of your equation

--> 84.3=(9/10)(0)+b --> b=84.3

So, your equation can be written now as y=(9/10)x+84.3

[Note: To check, if you plug in 3 you should get 87, and you do, so it works!]

2. Use the slope formula

Alternatively, you could have did slope=(y2-y1)/(x2-x1)=(87-84.3)/(3-0)=2.7/3=9/10

The process here would be the same as above

b) Here, just plug 10 into the equation above (since 10 is the number of years 2010 is after 2000, or 2010-2000=10). Doing this we get:

y=(9/10)(10)+84.3=9+84.3=93.3

So, in 2006 we have 93.3 people per sq mile

Therefore, In 2006 we have 93.3 people per sq mile .

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In ΔTUV, t = 70 inches, mm∠T=99° and mm∠U=53°. Find the length of u, to the nearest inch.

Answers

The length of u is 56.60 inches. The nearest inches it is 57 inch

What is a triangle?

A triangle is a three-edged polygon with three vertices. It is a fundamental shape in geometry. Triangle ABC denotes a triangle with vertices A, B, and C. In Euclidean geometry, any three non-collinear points define a unique triangle and, by extension, a unique plane.

Given that ΔTUV is a triangle with m∠T=99° and m∠U=53°.

The length of t is 70 inches.

The opposite side of ∠T is t, the opposite side of ∠U is u, and the opposite side of ∠V is v.

Sine rule of ΔABC:

a/sin A = b/sin B = c/sin C

Apply sine law in  ΔTUV:

t/sin T = u/sin U = v/sin V

Putting ∠T=99°, ∠U=53°, and t = 70.

70/ sin 99° = u/sin 53°

u = (70sin 53°)/ sin 99°

u =  56.60 inches

The digit after the decimal point is greater than 5, thus add 1 with the 56 to get the nearest inch.

u = 57 inches

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Find the coordiantes of the vertices for the figure after the given transformation
Dilation of 2.

Answers

Answer:

[tex]I'(-2,-4), J'(-4,4), K'(4,4)[/tex]

Step-by-step explanation:

Assuming the dilation is centered at the origin, it is known that for a dilation of scale factor [tex]k[/tex] centered at the origin, [tex](x,y) \to (kx,ky)[/tex].

What is a 30% residual?

Answers

A $50,000 car with a 30% ($15,000) residual value is financed over five years. In this case, the loan is repaid in full in five years for $35,000, with the final $15,000 being paid as a balloon payment.

What is residual?

In statistical or machine learning models, the differences between actual and expected data values are referred to as residuals.

They act as a diagnostic instrument for assessing the caliber of a model. They are also known as errors.

The primary column, Inflation, of the table below provides details on US inflation for each month of 2017. Forecasts from a model that seeks to predict the rate of inflation are shown in the Predicted column.

Following are the calculations for the residuals: Residual is equal to predicted inflation.

The Residual column contains them.

The model predicted 1.8% for the data for January 2017, while the actual inflation rate was only 0.5%, leaving a residual of -1.3%.

Hence, A $50,000 car with a 30% ($15,000) residual value is financed over five years. In this case, the loan is repaid in full in five years for $35,000, with the final $15,000 being paid as a balloon payment.

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Classify this pair of events: A flavor of ice cream is selected at random; A
topping for the ice cream is selected at random.
A. independent
B. dependent

Answers

A A flavor of ice cream is selected at random; A topping for the ice cream is selected at random. This is B. dependent events.

What are dependent event?

Events that are dependent upon prior events are called dependent events. The results of earlier events have an impact on these current ones. For example, two or more events that are interdependent are referred to as dependent events.

If one event is accidentally altered, another is probably going to be different.

If two events are interdependent, then the result of the first event will influence the result of the second even more.

The ice cream in this case represented dependent event.

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Is it possible to have a triangle with sides 2cm 2cm and 5cm justify your answer?

Answers

Answer:

No, it is not possible to have a triangle with sides of 2cm, 2cm, and 5cm. This is because a triangle's sides must adhere to the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. In this case, 2cm + 2cm (4cm) is not greater than 5cm, so it is not possible to form a triangle with these side lengths.

Step-by-step explanation:

Answer:

Yes u can

Step-by-step explanation:

U can create a triangle with that because 2+2 is 4 which is less than 5 meaning it would work as a triangle

Fatoumata is going to invest in an account paying an interest rate of 1.7% compounded continuously. How much would Fatoumata need to invest, to the nearest hundred dollars, for the value of the account to reach $6,300 in 5 years?

Answers

Fatoumata requires an investment of $4390.24

What is basic interest or amount?

The process of figuring out how much interest will accrue on a given principal sum of money is known as simple interest.

Rate r= 1.7%

Total A is $6300.

t = 5 years

Primary P =????

A=P(1+r)^t

6300= P(1+0.017)^5

6300= P(1.017)^5

6300= P(1.435)

P= 6300/1.435

P = 4390.24

Should be the answer. if I'm right can I get Brainiest if I'm wrong then it's fine

Answer:

$5786.63

Step-by-step explanation:

the equation for interest compounded continuously is A=Pe^rt

6300=Pe^.017(5)

then in your calculator put e raised to the .085 (which is .017 times 5)

then divide that by 6300

and P=5786.62739

Other Questions
the first stage of developing romantic relationships in adolescence happens at about 11 to 13 years of age. which of the following is a characteristic of this stage? Research by Italian sociologist Mauro Valeri indicates that racism in Italian soccera. has increased in multiple forms in recent years.b. tends to decrease with higher rates of immigration to Italy.c. is a problem among spectators but not among players.d. is not expressed in stadiums for fear of police actions Which of the following terms indicate infection of the eye? Select all that apply.AmblyopiaExophthalmosKeratitisConjunctivitisStye the dominant, or prestige dialect of a language, is often called this kind of dialect: researchers can neither anticipate nor control maturation or history effects. therefore, such threats to internal validity should be noted in what section of a published article? Which products and services type consists of products the company buys but does not track the quantities?A. ServiceB. Non InventoryC. BundleD. Inventory if you had 4 linked genes each with 2 alleles, how many different haplotypes could there be T/F. Helping at the nest is an altruistic behavior that is usually found in birds. Helping behavior has been well studied in the white-fronted bee-eater, a native species in East and central Africa, with one of the most complex family-based social systems found in birds. An interesting parent-offspring conflict arises when fathers coerce their sons, which are old enough to breed on their own, into helping to raise their siblings. On average, each helper is responsible for an additional 0.47 offspring being raised. In comparison, each parent at a nest unaided by helpers is able to raise 0.51 offspring. From the helper's point of view, for a first-time breeder, the fitness payoff from breeding on its own is only slightly greater than the fitness payoff of helping (0.51 offspring vs. 0.47 offspring). From the parent's point of view, harassing a son tips the balance by increasing his cost of rearing young. Therefore, helping becomes a more favorable strategy for the son than breeding on his own. Suppose that adult bee-eaters could raise only 0.3 more offspring with a helper than without a helper. We would expect that male bee-caters tend to fight off their fathers. suppose f ( x ) = 5 x 2 1091 x 70 . what monomial expression best estimates f ( x ) for very large values of x ? A lamina occupies the part of the disk x2 + y2 < 16 in the first quadrant and the density at each point is given by the function p(x, y) = 5(x2 + y2). A. What is the total mass? 32pi B. What is the moment about the x-axis? 1024/5 C. What is the moment about the y-axis? 1024/5 D. Where is the center of mass? ( 1024/5 1024/5 . 1024/5 ) E. What is the moment of inertia about the origin? 1024/3 An NMOS transistor with k'-800 A/V, W/L=12, Vh=0.9V, and X=0.07 V-1, is operated with VGs=2.0 V.1. What current Ip does the transistor have when is operating at the edge of saturation? Write the answer in mA the nurse is preparing to identify the angle of louis prior to a thoracic assessment. which landmark should the nurse use to identify this structure? a. Clavicle b. Sternum c. First rib d. Vertebral column. A shift of the money-demand curve from MD1 to MD2 could be a result ofa. an increase in government spending.b. a decrease in taxes.c. an increase in the price level.d. All of the above are correct. Find the surface area of the right prism. Round your result to two decimal places. Some people say that business reports never contain footnotes. If you were writing your first report for a business and you did considerable research, what would you do about documenting your sources? he principle of using one's own culture as a means or standard by which to evaluate another group or individual, leading to the view that cultures other than one's own are abnormal or inferiorT/F Suppose that Suadi Arabia sent extra crude oil tankers to the United States. Which of the following best describes the above situation considering the market for crude oil? O a. A shortage leading to an increase in the price b. A surplus leading to a decrease in the price: OC A shortage leading to a decrease in the price Od A surplus leading to an increase in the price how many different boolean functions f (x, y, z) are there such that f (x, y, z) = f ( x, y, z) for all values of the boolean variables x, y, and z? In the first situation (series connection), which of the two bulbs glows the brightest? Two light bulbs have resistances of 400 and 800. Which of the following statements about political appointees is LEAST accurate?Although women and minorities are regularly appointed to head less visible departments like HUD, prestigiouspositions such as Secretary of State or Secretary of Labor remain the exclusive preserve of white men.