Suppose that (a,n) : = if and only if 1. Prove that a¹ = a^(mod n) b = c(mod ord,(a)).

Answers

Answer 1

We have proved that a^1 ≡ a^(mod n) and b ≡ c (mod ordₙ(a)).

To prove the given statements, we will use the properties of congruence and the concept of the order of an element modulo n.

Statement 1: a^1 ≡ a^(mod n)

Let's consider a positive integer k such that k ≡ 1 (mod φ(n)), where φ(n) represents Euler's totient function. By Euler's theorem, we know that a^φ(n) ≡ 1 (mod n). Therefore, we can rewrite k as k = 1 + mφ(n), where m is an integer. Now, we can raise both sides of the congruence to the power of a, yielding a^k ≡ a^(1+mφ(n)) (mod n). By applying the properties of congruence, we have a^k ≡ a^1 ⋅ (a^φ(n))^m ≡ a (mod n). Hence, a^1 ≡ a^(mod n).

Statement 2: b ≡ c (mod ordₙ(a))

Let ordₙ(a) denote the order of a modulo n. By definition, ordₙ(a) is the smallest positive integer k such that a^k ≡ 1 (mod n). Since b ≡ c (mod ordₙ(a)), we can express b as b = c + k⋅ordₙ(a), where k is an integer. Then, we have a^b ≡ a^(c+k⋅ordₙ(a)) ≡ a^c ⋅ (a^(ordₙ(a)))^k ≡ a^c ⋅ 1^k ≡ a^c (mod n), which implies b ≡ c (mod ordₙ(a)).

In conclusion, we have proved that a^1 ≡ a^(mod n) and b ≡ c (mod ordₙ(a)).

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Related Questions

A rectangular prism has a volume of 900 cubic units. The prism has a length of 25 units and a width of 12 units. Which equation could be used to find h, the height of the prism?

Answers

Answer:

52 cubic units

Step-by-step explanation:

got it right on edg

Answer:

37h 900

Step-by-step explanation:

PLEASE HELP ME!!!! In each diagram AB is tangent to C at B. Find the value of x.​

Answers

Answer is 9

Step by step explanation
As CB is radius CB=3, CA=3+7=10
X^2=(7+3)^2-3^2=100-9=81
X=9

1 point
Finish the similarity statement. (Note: your answer will be the 3 letters of
the other triangle. You must place them in the correct order and use
CAPITAL letters!) APQR-4
R
4 in
6 in
VA
8 in
4 in
3 in
2 in

Answers

YOUR ANSWER IS ANGLE BAC

approximate the area under the curve graphed below from x = 2 x=2 to x = 5 x=5 using a left endpoint approximation with 3 subdivisions.

Answers

The approximate area under the curve from x = 2 to x = 5, using a left endpoint approximation with 3 subdivisions, is 13.5 square units.

To approximate the area under the curve, we divide the interval from x = 2 to x = 5 into three equal subdivisions, each with a width of (5 - 2) / 3 = 1. The left endpoint approximation involves using the leftmost point of each subdivision to approximate the height of the curve.

In this case, we evaluate the function at x = 2, x = 3, and x = 4, and use these values as the heights of the rectangles. The width of each rectangle is 1, so the areas of the rectangles are calculated as follows:

Rectangle 1: Height = f(2) = 2, Area = 1 * 2 = 2 square units.

Rectangle 2: Height = f(3) = 4, Area = 1 * 4 = 4 square units.

Rectangle 3: Height = f(4) = 7, Area = 1 * 7 = 7 square units.

Finally, we add up the areas of the three rectangles to obtain the approximate area under the curve: 2 + 4 + 7 = 13 square units. Therefore, the approximate area under the curve from x = 2 to x = 5 using a left endpoint approximation with 3 subdivisions is 13.5 square units.

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Evaluate the expression when b=4 and x=-2 .

b-4x

Answers

Answer:

12

Step-by-step explanation:

b-4x

Plug in 4 as b and -2 as x

= (4)-4(-2)

Multiply 4 and 2

= 4-(-8)

Two negatives make a positive

= 4+8

= 12

I hope this helps!

Yes, the answer above me is correct.

Identify the location of the point (6, -2). A. P B. Q C. R D. S

Answers

Answer:

Step-by-step explanation:

What should be done to both sides of the equation in order to solve y - 4.5 = 12.2?

Answers

Subtract 4.5 from each side so that there’s only y=7.6 left.

To solve the equation y - 4.5 = 12.2 we have to add 4.5 on both sides of the equation.

What is Equation?

Two or more expressions with an Equal sign is called as Equation.

The given equation is y - 4.5 = 12.2

y minus four point five equal to twelve point two.

In the equation y is the variable and minus is the operator in the equation.

To solve the equation we have to isolate the variable y.

To isolate the variable y we have to add 4.5 on both sides of the equation

y-4.5+4.5=12.2+4.5

y=16.7

Hence, to solve the equation y - 4.5 = 12.2 we have to add 4.5 on both sides of the equation.

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Does anyone know how to work this out step by step?

Answers

Answer:

[tex]2x^{3} +10[/tex]

Step-by-step explanation:

[tex]x*2x*x+10=2x^{3} +10[/tex]

Does the equation 3(2x−1)+5=6(x+1) have one, none, or an infinite amount of solutions?

Answers

Answer: No solutions

Step-by-step explanation: If you solve the problem all the way, you get 0 = 4 which is not valid so there is simply no solution

The given equation 3(2x−1)+5=6(x+1) has no solution. Option B is correct.

What is simplification?

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Given equation ⇒

⇒= 3(2x−1)+5=6(x+1)

Simplify the above expression,
⇒ 6x - 3 + 5 = 6x + 1
⇒    2 ≠ 1

Thus, the given equation has no solution.

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Find the general solution of the following second order differential equation. y" + 6y' +9y = e^-3x Inx.

Answers

General solution of the second order differential equation:

-6Ae^(-3x) / x + 9Bxe^(-3x) * ln(x) - Be^(-3x) / x^2

To find the general solution of the given second-order differential equation: y" + 6y' + 9y = e^(-3x) * ln(x)

We will use the method of undetermined coefficients to find a particular solution and then combine it with the complementary solution to obtain the general solution.

Step 1: Finding the particular solution

Since e^(-3x) * ln(x) is a product of exponential and logarithmic functions, we assume a particular solution in the form of:

yp = (A + Bx) * e^(-3x) * ln(x)

where A and B are constants to be determined.

Step 2: Find the first and second derivatives of yp.

yp' = (Ae^(-3x) * ln(x) - 3(A + Bx)e^(-3x) * ln(x) + (A + Bx) * e^(-3x) / x

yp" = (Ae^(-3x) * ln(x) - 3(A + Bx)e^(-3x) * ln(x) + (A + Bx) * e^(-3x) / x)'

yp" = (-9(A + Bx)e^(-3x) * ln(x) + 3(A + Bx)e^(-3x) * ln(x) - 3(A + Bx)e^(-3x) / x + (A + Bx) * (-e^(-3x) / x^2 + e^(-3x) / x))

Simplifying, we have:

yp" = -9(A + Bx)e^(-3x) * ln(x) - 6(A + Bx)e^(-3x) / x + (A + Bx) * (-e^(-3x) / x^2 + e^(-3x) / x)

Step 3: Substitute yp, yp', and yp" into the original differential equation to find the values of A and B.

yp" + 6yp' + 9yp = e^(-3x) * ln(x)

Substituting the expressions we found for yp and its derivatives:

(-9(A + Bx)e^(-3x) * ln(x) - 6(A + Bx)e^(-3x) / x + (A + Bx) * (-e^(-3x) / x^2 + e^(-3x) / x))

6((Ae^(-3x) * ln(x) - 3(A + Bx)e^(-3x) * ln(x) + (A + Bx) * e^(-3x) / x))

9((A + Bx) * e^(-3x) * ln(x))

= e^(-3x) * ln(x)

Expanding and simplifying, we get:

-9Ae^(-3x) * ln(x) + 3Bxe^(-3x) * ln(x) - 6Ae^(-3x) / x + 6Bxe^(-3x) / x + Ae^(-3x) / x - Be^(-3x) / x^2 + Be^(-3x) / x + 9Ae^(-3x) * ln(x) + 9Bxe^(-3x) * ln(x)

= e^(-3x) * ln(x)

Combining like terms, we have:

-6Ae^(-3x) / x + 9Bxe^(-3x) * ln(x) - Be^(-3x) / x^2

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Peter is making an "X marks the spot" flag for a treasure hunt. The flag is made of a square white flag with sides of 12 centimeters. He will make the "X" by stretching red ribbon diagonally from corner to corner.

Answers

Answer:

33.94 cms of ribbon

Step-by-step explanation:

Because you need two diagonals to form the x, therefore the amount  of ribbon needed is the sum of the distance of both diagonals.

When crossing the diagonal, a rectangular angle is formed, where the diagonal would be the hypotenuse, we know that the distance of the hypotenuse can be calculated by means of the legs, which we know its value (12):

d ^ 2 = a ^ 2 + b ^ 2

a = b = 12

d ^ 2 = 12 ^ 2 + 12 ^ 2

d ^ 2 = 288

d = 288 ^ (1/2)

d = 16.97

16.97 cm is what it measures, a diagonal, therefore tape is needed:

16.97 * 2 = 33.94

A total of 33.94 cms of ribbon is needed

Answer from jmonterrozar

2.46 strong association but no correlation. here is a data set that illustrates an important point about correlation: corr x 25 35 45 55 65 y 10 30 50 30 10 (a) make a scatterplot of y versus x. (b) describe the relationship between y and x. is it weak or strong? is it linear? (c) find the correlation between y and x. (d) what important point about correlation does this exercise illustrate?

Answers

a. In the picture we can see that the scatterplot is given for the data in the given table.

b. It is not linear as we can see from scatterplot.

c. The correlation between y and x is 0.

d. when r = 0 there is no relationship between x and y.

Given that,

The data is given in the table.

We know that,

a. We have to make a scatterplot of y versus x.

In the picture we can see that the scatterplot is given for the data in the given table.

b. We have to describe the relationship between y and x.

When x increases y increases upto certain point after that y start to decrease but x is increases only

Therefore, it is not linear as we can see from scatterplot.

c. We have to find the correlation between y and x.

The formula for the correlation coefficient is

r = [tex]\frac{n\times \sum XY-\sum X \times\sum Y}{\sqrt{[n\sum X^2 - (\sum X)^2][n\sum Y^2 - (\sum Y)^2]} }[/tex]

Now we find summation of all X, Y and XY, [tex]X^2[/tex] and [tex]Y^2[/tex]

X          Y           XY            [tex]X^2[/tex]            [tex]Y^2[/tex]

25        10         250         625          100

35        30        1050        1225         900

45        50        2250       2025        2500

55        30        1650        3025        900

65        10          650        4225        100

Now, ∑X = 225

∑Y = 130

∑XY = 5850

∑[tex]X^2[/tex] = 11125

∑[tex]Y^2[/tex] = 4500

Now, Substitute the values in the formula

r = [tex]\frac{5\times 5850-225 \times130}{\sqrt{[5\times 11125 - (225)^2][5\times 4500 - (130)^2]} }[/tex]

r = 0

Therefore, The correlation between y and x is 0.

d. We have to find what important point about correlation does this exercise illustrate.

Therefore, when r = 0 there is no relationship between x and y.

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sara bought x pounds of chocolate covered raisins, which sell for $1.50 a pound, and y pounds of yogurt covered raisins, which sell for $1.20 a pound. sara bought a total of 40 pounds of the two types of raisins for a total of $51.90." help me write a system of equations to model this scenario

Answers

x+y=40
1.50x+1.20y=51.90

i don't think u need me to solve it but ill do it anyway, so there's 3 methods: graphing, elimination, and substitution

substitution's my fave so that's what imma do

x+y=40
-x -x
y=40-x

1.50x+1.20(40-x)=51.90
1.50x+48-1.20x=51.90
.30x+48=51.90
-48 -48.00
.30x=3.9
divide both sides by .30
x=13 so 13 pounds of chocolate covered raisins

bring back the other equation
x+y=40
13+y=40
-13 -13
y=27 so 27 pounds of yogurt covered raisins

a manufacturer knows that their items have a normally distributed lifespan, with a mean of 4.4 years, and standard deviation of 1.2 years.the 7% of items with the shortest lifespan will last less than how many years?

Answers

Using the standard deviation, mean, and z-score, the 7% of items with the shortest lifespan will last less than approximately 1.59 years.

What is 7th percentile of items with the shortest lifespan?

To find the number of years that the 7% of items with the shortest lifespan will last, we need to determine the z-score corresponding to the 7th percentile of the normal distribution.

Step 1: Convert the given percentile to a z-score using the standard normal distribution table or a statistical calculator. The 7th percentile corresponds to a z-score of approximately -1.405.

Step 2: Use the formula for z-score to find the corresponding value in terms of years:

x = μ + z * σ

where x is the value we are looking for, μ is the mean, z is the z-score, and σ is the standard deviation.

Plugging in the values:

x = 4.4 + (-1.405) * 1.2

x = 1.59 years

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Solve the differential equation (D^2 + 4)y=6 sin2x +3x^2 =

Answers

The solution to the differential equation (D^2 + 4)y = 6 sin(2x) + 3x^2 is y = (3/4)x^2 + A sin(2x) + B cos(2x).

To solve the given differential equation (D^2 + 4)y = 6 sin(2x) + 3x^2, where D represents the derivative operator, we can use the method of undetermined coefficients.

First, we find the general solution to the homogeneous equation (D^2 + 4)y = 0. The characteristic equation is r^2 + 4 = 0, which has complex roots ±2i. Therefore, the general solution to the homogeneous equation is y_h = A sin(2x) + B cos(2x), where A and B are constants.Next, we find a particular solution to the non-homogeneous equation. By inspection, we can guess that y_p = (3/4)x^2 is a particular solution.Finally, the general solution to the non-homogeneous equation is the sum of the homogeneous and particular solutions:

y = y_h + y_p

y = A sin(2x) + B cos(2x) + (3/4)x^2

Here, A and B are arbitrary constants that can be determined by applying initial or boundary conditions, if given.

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Regan cycles 78 miles in 6 hours. His average speed for the first 30 miles is 15 miles per hour. Work out Regan's average speed for the last 48 miles.

Answers

Answer:

12 mph

Step-by-step explanation:

Given that:

Total distance traveled = 78 miles

Time taken, t = 6 hours

Average speed for first 30 miles = 15 mph

Time taken = distance / speed

Time taken = 30 / 15

Time taken = 2 hours

Average speed for last 48 miles = x

Time taken to travel last 48 miles = (6 - 2) = 4 hours

Average speed for last 48 miles :

Distance traveled / time taken

48 miles / 4 hours

= 12 mph

What is the slope and y-intercept of 9x - 3y = 15?
NO FILES PEOPLE!

Answers

slope is 3

y-intercept is 0,-5

This is confusing can you help? NO LINKS!!!

Answers

Answer:

huh?

Step-by-step explanation:

did you forget a pic?

Answer:

whatdo u need help with love?

Step-by-step explanation:


If sin A=0.7986, then the measure of Đ A, to the nearest degree is?

Answers

Answer:

B

Step-by-step explanation:

A will equal the sine inverse (arc sine or sin^-1 ) of 0.3571. Using a calculator, sin^-1(0.3751) = 22.03 degrees (B)

Given that coule.us) - EILE DE M2)]. lajure the linearity rule and & (c) = c. to derive the equation for constate) in ternis of EA), Mj and H2(erive expression for cours, 34%, and 22 are independent random vartolus. f(x)= [ (x for 2 exc4 = 56) o elsewhere for a continuon ona random variable &. (a) Compute. P/2 ex <3). (6) Compute Elx), the mean of t. (8) Given (6) For some other random variable & My (t) = e. Determine the mean Ele) for this other random variable. (5* +32+) P.

Answers

(a) The probability that X is less than 3, P(X < 3), is 0.

(b) The mean of X, denoted as E(X), is 71/24, which is approximately 2.9583 when rounded off to four decimal places.

(c) Given Y = e^X, the mean of Y, denoted as E(Y), is approximately 15.75 when rounded off to two decimal places.

(a) It is required to compute P(X<3). Since the range for which f(x) is not equal to 0, is the interval from 2 to 4 for f(x), the probability that X is less than 3 is 0.

Similarly, for X > 4, P(X > 4) = 0.

P(2 ≤ X ≤ 4) = ∫f(x)dx from 2 to 4= ∫ (x/24 - 7/3) dx from 2 to 4= [x^2/(2 × 24) - 7x/3] from 2 to 4= 1/4 - 28/3 + 8/(2 × 24) + 14/3= 71/24= 2.9583(rounded off to four decimal places)

(b) The mean of X can be computed as follows:

E(X) = ∫xf(x)dx from -∞ to ∞= ∫ (x/24 - 7/3) dx from 2 to 4= [x^2/(2 × 24) - 7x/3] from 2 to 4= 1/4 - 28/3 + 8/(2 × 24) + 14/3= 71/24= 2.9583(rounded off to four decimal places)

(c) Y = e^X

The mean of Y can be computed as follows:

E(Y) = E(e^X)= ∫ e^x f(x) dx from -∞ to ∞= ∫ e^x (x/24 - 7/3) dx from 2 to 4= [e^x (x - 31)/(24)] from 2 to 4= (e^4/6 - 31e^4/24 - e^2/6 + 31e^2/24) ≈ 15.75(rounded off to two decimal places).

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PLEASE HELP ILL GIVE BRAINLIEST
WHATS THE PERCENT CHANGE SHOW WORK

Answers

Answer:

34.55556%

Step-by-step explanation:

Identify the values of A, B, and C
5x2 + x - 18 = - 9x + 3x2
A=2, B=10, C=-18
A=2, B=9, C=-18
A=5, B=1, C=-18
A=8, B=-8, C=-18

Answers

Answer:

A=2, B=10, C=-18

The answer is the first one.

Step-by-step explanation:

[tex]5x^{2} -3x^{2} +x+9x-18=0[/tex]

[tex]2x^{2} +10x-18=0[/tex]

Formula: [tex]f(x)=ax^{2} +bx+c[/tex]

Solve for x. Please help me I am confused.

Answers

Answer:

72

Step-by-step explanation:

Multiply all the numbers, and you get the answer

Which set of numbers is infinite?
A) integers between -4 and 7

B) whole numbers between 1 and 17

C) natural numbers between 5 and 10

D) irrational numbers between 10 and 30

Answers

Answer:

D). irrational numbers between 10 and 30

Which of the following represents y < 2x - 3?


help a girl out please

Answers

Answer:

A

Step-by-step explanation:

the y intercept (where x is 0) should be -3 because of y<3x-3

The water used by the 12 students during the experiment was poured from a beaker after the water was poured 1/4 gallon of water was left in the beaker What was the total number of fluid ounces of water in the beaker before the water was poured by the 12 students

Answers

Answer:

128 fluid ounces

Step-by-step explanation:

We were told that:

During the experiment was poured from a beaker after the water was poured 1/4 gallon of water was left in the beaker

Hence, this means that the total gallon of water in the beaker is 1 gallon

Convert 1 gallon to fluid ounces

1 gallon =128 fluid ounces

Therefore, the total number of fluid ounces of water in the beaker before the water was poured by the 12 students is 128 fluid ounces.

Question 3 of 10
Which of the following are exterior angles? Check all that apply.
6
DA. 26
B. 24
C. 23
OD. 22
OE. Z1
O F. 25

Answers

Answer:

I believe the answer to be 5 and 4

The exterior angles of the given triangle are angles 4 and 5

What is triangle?

A triangle is a polygon with three sides, angles and vertices.

Given that, a triangle, with angles, 1, 2, 3, 4, 5 we need to find the exterior angles,

An exterior angle of a polygon is the angle that lies outsides of the polygon,

Here, we can see, that only two angles 4 and 5 lies outsides of the triangles

Therefore, the exterior angles are 4 and 5

Hence, the exterior angles of the given triangle are angles 4 and 5

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Find the product.
-7(-a 2)(-5)

Answers

Answer:

3

5

(

2

)

Step-by-step explanation:

Simplify then multiple the numbers

HELP ASAP, due today.

Answers

Answer:

(A) B h(x)= -2x-5.5

(B) The y intercept is (0,-5.5)

(C) The rate of change is -2

(D) The x intercept is (-2.75,0)

Simplify. simplify simplify ​

Answers

The answer to your question is 16/81

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{(\dfrac{4}{9})^2}[/tex]

[tex]\mathsf{= \dfrac{4}{9}\times\dfrac{4}{9}}[/tex]

[tex]\mathsf{= \dfrac{4^2}{9^2}}[/tex]

[tex]\mathsf{\dfrac{4\times4}{9\times9}}[/tex]

[tex]\mathsf{4 \times 4 = \bold{16}\leftarrow \underline{Numerator}}[/tex]

[tex]\mathsf{9\times9 = \bf 81}\leftarrow\mathsf{\underline{Denominator}}[/tex]

[tex]\boxed{\boxed{\large\textsf{Answer: \boxed{{\bf \dfrac{16}{81}}}}}}\huge\checkmark[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Other Questions
Selected Stock Transactions Alpha Sounds Corp, an electric guitar retaler, was organized by Michele Kirty, Paul Glenn, and Gretchen Northway The charter authorized 1,000,000 shares of common stock with a par of $1. The following transactions affecting stockholders' equity were completed during the first year of operations Journalize the entries to record the transactions. a. Issued 100,000 shares of stock at par to Paul Glenn for cash. If an amount box does not require an entry, leave it blank. Cosb - 100,000 100,000 Common- stock b. (1) Issued 3,000 shares of stock at par to Michele Kirby for promotional services provided in connection with the organization of the corporation, and (2) issued 45,000 shares of stock at par to Michele Kirby for cash. If an amount box does not require an entry, leave it blank. (1) Organizational 3,000 Expense coob 15,000 3,000 cash 45,000 178 Chmmba 45,000 stock c. Purchased land and a building from Gretchen Northway in exchange for stock issued at par. The building is mortgaged for $160,000 for 20 years at 6%, and there is accrued interest of $5,200 on the mortgage note at the time of the purchase. It is agreed that the land is to be priced at $60,000 and the building at $225,000 and that Gretchen Northway's equity will be exchanged for stock at par. The corporation agreed to assume responsibility for paying the mortgage note and the accrued interest. If an amount box does not require an entry, leave it blank. (2) suppose we observe the following rates 1r1=8, 1r2=12 and e(2r1) = 14. if the liquidity premium theory of the term structure of interest rates holds, what is the liquidity premium for year 2 The table below provides the total variable cost for a firm. Quantity of Output Total Variable Cost 0 $0 $50 $60 $75 4 $100 If the fixed cost is $60, what is the average total cost of the 3rd unit? $45 0 $25 $35 $135 $75 1 2 3 Sphere A, of mass 0. 600 kg, is initially moving to the right at 4. 00 m/s. Sphere B, of mass 1. 80 kg, is initially to the right of sphere A and moving to the right at 2. 00 m/s. After the two spheres collide, sphere B is moving at 3. 00 m/s in the same direction as before. (a) What is the velocity (magnitude and direction) of sphere A after this collision? (b) Is this collision elastic or inelastic? (c) Sphere B then has an off-center collision with sphere C, which has mass 1. 60 kg and is initially at rest. After this collision, sphere B is moving at 19. 0 to its initial direction at 1. 60 m/s. What is the velocity (magnitude and direction) of sphere C after this collision? (d) What is the impulse (magnitude and direction) imparted to sphere B by sphere C when they collide? (e) Is this second collision elastic or inelastic? (f) What is the velocity (magnitude and direction) of the center of mass of the system of three spheres (A, B, and C) after the second collision? No external forces act on any of the spheres in this problem What is Pelotons strategy? Assess Pelotons strategy in terms of (a) its fit with its business environmentparticularly in relation to its customers needs and preferences and competitors offerings; (b) its fit with internal resources/capabilities) Suppose that two consumers, you and I, have the same homothetic tastes over goods A and B. My endowment of the two goods is Em = (emA, emB) and your endowment of the two goods is Ey = (exA, eyB). Assume that emA + emB = emB+ eyB and that whenever A = B, the MRS= -1. (a) If goods A and B are not perfect substitutes, explain where the contract curve will lie and what it shows, making sure you refer to the shape of the Edgeworth Box and the MRS in your answer. (6 marks) (b) If goods A and B were instead perfect substitutes for both consumers who continue to have the same tastes, how will this change the contract curve? (6 marks) (c) 'If we have non-convex tastes in a general equilibrium economy, then this may mean that a competitive equilibria cannot exist. But if an equilibrium does exist, we will have Pareto efficiency. It is only when tastes are convex that there will always be some way of redistributing resources to make any Pareto efficient allocation into a competitive equilibrium.' Evaluate the above statement, commenting on whether you think it is an accurate reflection of the first and second welfare theorems. You have a special lightbulb with a very delicate wire filament. The wire will break if the current in it ever exceeds 1.20 A, even for an instant.What is the largest root-mean-square current you can run through this bulb? _______A Consider the two-period model in our lecture. A student collects some data as follows: y = 4, y2 = 6 G = 1, G = 1 The student is unable to find any information concerning t1, 12. He assumes that the government's lifetime budget is balanced. The interest rate r is determined by market clearing (denoted by r**). Let the utility function be log(c) + log(c2) so that the discount factor is 1. What is the equilibrium * ? Is it indeterminate? Consider a single crystal of nickel oriented such that a tensile stress is applied along a [001] direction. If slip occurs on a (111) plane and in a [Consider a single crystal of nickel oriented such01] direction, and is initiated at an applied tensile stress of 13.9 MPa (2020 psi), compute the critical resolved shear stress. Oriole Company issues $2,000,000, 10-year, 7% bonds at 98, with interest payable each January 1. Prepare the journal entry to record the sale of these bonds on January 1, 2022. On January 1, 2020, Sandhill Company leased equipment to Flynn Corporation. The following information pertains to this lease. 1. The term of the non-cancelable lease is 6 years. At the end of the lease term, Flynn has the option to purchase the equipment for $2,000, while the expected residual value at the end of the lease is $5,000. Equal rental payments are due on January 1 of each year, beginning in 2020. 2. 3. The fair value of the equipment on January 1, 2020, is $165,000, and its cost is $120,000. 4. The equipment has an economic life of 8 years. Flynn depreciates all of its equipment on a straight-line basis. 5. Sandhill set the annual rental to ensure a 6% rate of return. Flynn's incremental borrowing rate is 8%, and the implicit rate of the lessor is unknown. 6. Collectibility of lease payments by the lessor is probable. Both the lessor and the lessee's accounting periods end on December 31. Prepare all the necessary journal entries for Flynn for 2020. The following information are obtained: A portfolio contains two types of policies. Type A policies have no deductible and a policy limit u. A total of 50 losses that are less then u were recorded on Type A, y1 , y2 , , y50, and a total of 50 losses that exceed u were also recorded on Type A. Type B have a deductible of u and no policy limit. Losses that are less than u are not recorded on Type B policies. A total of 50 losses that exceed u were recorded on Type B policies, z1 , z, , z50 . The random variable X for the underlying losses for both types of policies has density function (x;theta) and (x;theta). Provide the likelihood function, L, that is used to find the MLE of theta. one affect of the demands for greater profits in news media, have been the proliferation of in _____ local news broadcastsa) deep, investigative pieces b) sensationalistic pieces focusing on violent crime c) minority voices d) virtual newscasts e) thoughtful, guest editorializing f) puff pieces and infotainment g) Both (a) and (e) calculate the volume in liters of 72.3 g of carbon dioxide gas at 22.00 degrees and 875 mmhg. Both isohyetal and Thession polygon methods estimate A A/ A A/ A/ is the term used to describe how heavy it rains. A Question 3 (Mandatory) (1 point) 1) Listen Non-recording raingauge measures of the rainfall. method is to draw equal lines with equal rainfall depth, and in order to draw accurate lines, are desired. A Snow survey measures a snow pack by and A A/ A/ Briefly comment any similarities between the 4Ps marketing mixes About sports shoes Calculate the pH for an aqueous solution of pyridine that contains 2.15 10 M hydroxide ion. What is a good prediction of future occurrences in global markets? Which statement is true about displaying open Client Retainers in QBO?(A)Creating the Client Retainers report starts with the Balance Sheet(B)You can reconcile the Client Retainers account to clear out partially used retainers(C)The Client Retainers report should use the current period only(D)The Client Retainers account can be reconciled automatically using Bank feeds2. Which statement is true about displaying open Client Retainers in QBO?(A)Creating the Client Retainers report starts with the Balance Sheet(B)You can reconcile the Client Retainers account to clear out partially used retainers(C)The Client Retainers report should use the current period only(D)The Client Retainers account can be reconciled automatically using Bank feeds If you were a dictator for the standard OLG model economy, a. What would be your problem to solve? Write down what you think and explain. b. Can you solve for the necessary FOC of the problem that you have defined in part a? Explain?