Write a net ionic equation to show that aniline, C6H5NH2, behaves as a Bronsted-Lowry base in water

Answers

Answer 1

The behavior of aniline as a Bronsted-Lowry base is shown by the equation; C6H5NH2(aq) + H2O(l) ----> C6H5NH3^+(aq) + OH^-(aq).

What is a base?

By way of definition, a Bronsted-Lowry base is any substance that accepts hydrogen ions in water. In other words, a Bronsted-Lowry base is a proton acceptor. Aniline is a Bronsted-Lowry base.

The  net ionic equation to show the behavior of aniline as a  Bronsted-Lowry base is; C6H5NH2(aq) + H2O(l) ----> C6H5NH3^+(aq) + OH^-(aq).

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Related Questions

2x + 3 < -9
PLease ANSWER

Answers

Answer:

Inequality form: x<-6

Interval Notation: (-∞, -6)

Step-by-step explanation: Isolate the variable by dividing each side by factors that do not contain the variable.

I hope this helps you out!

What is the value of the missing segment? there is a ? , 4., 5 and 10​

What is the value of the missing segment? there is a ? , 4., 5 and 10

Answers

Step-by-step explanation:

I assume the ? is the left leg of the left triangle.

the middle line (right leg of the smaller left triangle, and the left leg of the larger right triangle) bisects the top angle of the main large triangle (because the top angles left and right from the middle line are equal).

that means per the angle bisector theorem

5 / 4 = 10 / ?

5 = 10×4/? = 40/?

?×5 = 40

? = 40/5 = 8

at a certain university in the u.s., all phone numbers are 7-digits long and start with either 824 or 825. 1) how many different phone numbers are possible?

Answers

There are 20,000 different phone numbers possible that is 7-digits long and start with either 824 or 825.

Fundamental Principle of Counting, also called the counting rule, is the method to count how many ways multiple independent events can occur.

Based on the given information, all phone numbers are 7-digits long and starts with either 824 or 825. Hence, the four last digits will be the combination of numbers from 0 to 9.

Thus, by Fundamental Principle of Counting, the number of possible outcomes is 20,000.

= (number of phone numbers starting with 824) + (number of phone numbers starting with 825)

= (10 x 10 x 10 x 10) + (10 x 10 x 10 x 10)

= 20,000

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Solve: 2x+1= 2X - 1

A) No Solution

B) x = 0

C) Infinitely Many Solutions

Answers

Answer:

A) No Solution

Step-by-step explanation:

2x+1=2x-12x-2x=-1-10 = -2

Thus, it has no solution

6x + 1 - 5x = 2
What is x=

6x + 1 - 5x = 2What is x=

Answers

Answer:

X=1

Step-by-step explanation:

You want to start by collecting like terms (6x and 5x) which creates:

x+1=2

Move the constant to the right hand side and change the sign:

x=2-1

Calculate

x=1

Answer:

x=1

Step-by-step explanation:

Let's solve your equation step-by-step.

6x+1−5x=2

Step 1: Simplify both sides of the equation.

6x+1−5x=2

6x+1+−5x=2

(6x+−5x)+(1)=2(Combine Like Terms)

x+1=2

x+1=2

Step 2: Subtract 1 from both sides.

x+1−1=2−1

x=1

Answer:

x=1

What is the constant term in the polynomial expression, and what does it represent?

Answers

Aconstant term is a term in an algebraic expression that has a value that is constant or cannot change, because it does not contain any modifiable variables. For example, in the quadratic polynomial

x
2
+
2
x
+
3
,

x^{2}+2x+3
the 3 is a constant term.

What is the weight of a 24 square foot 2 inch thick aluminum plate with a unit weight of 15 lbs?

Answers

Weight of a 24 square foot, 2 inch thick aluminum plate will be: 720 lbs.

What is unitary method?

A single unit's value can be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary method.

Given:

Weight of 1 square foot, 1 inch thick plate = 15 lbs.

To find: weight of a 24 square foot, 2 inch thick aluminum plate

Finding:

By unitary method, we get:

Weight of 1 square foot aluminum plate = 15 lbs.

Weight of 24 square foot aluminum plate = 15(24) lbs = 360 lbs.

Again, by unitary method, we get:

Weight of 1 square foot, 1 inch thick aluminum plate = 15 lbs.

Weight of 24 square foot, 1 inch thick aluminum plate = 15(24) lbs = 360 lbs.

Weight of 24 square foot, 2 inch thick aluminum plate = 360(2) lbs = 720 lbs.

Hence, Weight of 24 square foot, 2 inch thick aluminum plate = 720 lbs.

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how to find the area of a cricle

Answers

Answer:

A=πr2

Step-by-step explanation:

radius is half a circle and pi is 3.14

can you solve this in 3 min?

can you solve this in 3 min?

Answers

The dot plot of the data values is added as an attachment

How to create the dot plot

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

85,88,75,100,90,90,88,72,72,79,88,85

Next, we create a frequency table

So, we have

Values   Frequency

72             2

75             1

79             1

85            2

88            3

90           2

100          1

Total      12

Using the frequency table above, we create the dot plot

See attachment for the dot plot

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can you solve this in 3 min?


Claire and Malia are training for a race.
a. Claire runs 10 km in 1 hour. How many kilometers does she run in half an hour? in 2 1/2 hours?

b. Malia runs 5 miles in 1 hour. How many miles does she run in half an hour? in 2 1/2 hours?
c. On Tuesday, Claire and Malia both ran for 2 1/2 hours. Who ran the farther distance?

Answers

Answer: hello ima say first off Malia is my name lucky me my name is being used but for more serious matters... hope this helpssss

b)Claire runs 10km in 1 hour. In 2-1/2 hours, she runs (2-1/2 x 10) = 25 km.

c) Malia runs 5 miles in 1 hour

Step-by-step explanation:

I need to get the answer to 10 divided by 2 1/2 but I can’t figure it out

Answers

10 divided by 2 1/2 is 4.

What is Division?

The division is one of the basic arithmetic operations in math in which a larger number is broken down into smaller groups having the same number of items. The answer thus derived is the quotient and the left over number is the remainder.

10 divided by 2 1/2 but I can’t figure it out.

It can be written as 10÷2 1/2

convert mixed fraction to improper fraction we get,

\(2\frac{1}{2}= \frac{5}{2}\)

Then divided 10 by 5/2 we get\(\frac{10}{\frac{5}{2} } = 10*\frac{2}{5} = 4\).

Hence, 10 divided by 2 1/2 is 4.

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1. What is the equation for the following graph
use photo for graph ​

1. What is the equation for the following graph use photo for graph

Answers

x = 4 is the answer because the y coordinate is zero and at x axis it intersects at 4..

please mark it as brainliest ❤️❤️ and follow me..

Answer:

x=5 is the answer

Step-by-step explanation:

hope this helped

PLZ HELP I REALLY NEED HELP
which one is written in scientific notation
90 x 10 EXP2 ,
9 x 10 EXP2,
90 x 10EXP 1,
9 x 10EXP1

Answers

1) 9,000
2) 900
3) 90
4) 9
Answer:1) 9,0002) 9003) 904) 9Step-by-step explanation:mark brainliest plzs and have u finished the story plzs ask a question with that in the question but plzs finish it and mark brainliest

A rectangle has a width of 2xy3 and a length of 4x5y6. What is the area of the rectangle?

Answers

Answer:

6x²5y²6 cm²

Step-by-step explanation:

(2xy3) x (4x5y6)

(2x) x (4x) = 6x²

(y) x (5y) =5y²

6x²5y²6 cm²

You are going to buy a house for $400,000. You have enough cash that you can use either an 80% or a 90% LTV mortgage. You talk to your lender and are given the following options: a. You can get an 80% loan at 3.5% for 30 years b. You can get a 90% loan for 4% for 30 years. What is the incremental cost of financing the marginal 10% if you take the second loan, assuming that you will stay in the loan for all 30 years

Answers

To calculate the incremental cost of financing the marginal 10% with the second loan, we need to compare the total interest paid over the 30-year period for both loans. The difference in total interest paid will represent the incremental cost. Using a mortgage calculator, we calculate the total interest paid over the 30-year period for this loan.

a) For the 80% loan at 3.5%:

Loan amount = 80% of $400,000 = $320,000

Interest rate = 3.5%

Loan term = 30 years

Using a mortgage calculator, we can determine the total interest paid over the 30-year period for this loan.

b) For the 90% loan at 4%:

Loan amount = 90% of $400,000 = $360,000

Interest rate = 4%

Loan term = 30 year

To find the incremental cost of financing the marginal 10%, we subtract the total interest paid for the 80% loan from the total interest paid for the 90% loan. By comparing the two options, we can determine the additional interest cost incurred by financing the additional 10% with the second loan.

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how many possible 5 card poker hands with at least 3 aces can be dealt from a standard deck of 52 cards?

Answers

There are 6 probability  5 card poker hands with at least 3 Aces that can be dealt from a standard deck of 52 cards.

A standard deck of 52 cards contains 4 Aces, so the maximum number of Aces that can be dealt in a 5 card hand is 3. To determine the number of possible 5 card poker hands with at least 3 Aces, we must first consider the different combinations of 3 Aces in a 5 card hand. There are 6 possible combinations: AAAxx, AAxxA, AxxAA, xAAAX, xAxxA, and xxAAA. This means that there are 6 possible 5 card poker hands with at least 3 Aces that can be dealt from a standard deck of 52 cards. To calculate this, we first counted the number of Aces in the deck and then calculated the number of possible combinations of 3 Aces in a 5 card hand. Finally, we multiplied this number by the number of remaining cards in the deck (48) to get the total number of possible hands.

4 Aces x 6 combinations = 24

24 x 48 remaining cards = 1,152

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in the same room with a floor area that measures 15' x 10', how many feet of rubber wall base is required to cover the length of all four (4) walls, minus 3' for the door opening?

Answers

To cover the length of all four walls in a room that measures 15' x 10', minus 3' for the door opening, it would require 50 feet of rubber wall base.

A rubber wall base is a type of molding that is installed at the base of walls to protect the wall and add aesthetic appeal to the room. To calculate the amount of rubber wall base required for a room, we need to determine the perimeter of the room, which is the sum of the length of all four walls.

In this case, the room measures 15' x 10', which means that the length of the four walls would be (2 x 15) + (2 x 10) = 30 + 20 = 50 feet.

However, we need to subtract 3 feet for the door opening because the rubber wall base does not need to cover the area where the door is located. Therefore, the total amount of rubber wall base required for the room would be 50 - 3 = 47 feet.

But, we need to add some extra footage for corner pieces and cuts. Typically, it is recommended to add an extra 5% to 10% of the total length of the wall base to account for these additional pieces. So, adding 5% of 47 feet, we get an additional 2.35 feet, which we can round up to 3 feet.

Therefore, the final answer is 47 + 3 = 50 feet.

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(3.4+6.6)x (1.8+2.7)

Answers

Answer:

Step-by-step explanation:

17.98 don't ask

Answer:

45

Step-by-step explanation:

1. 3.4 + 6.6 can be simplified to 3 + 6 and 0.4 + 0.6

2. 3 + 6 = 9

3. 0.4 + 0.6 = 1

4. 9 + 1 = 10  (3.4 + 6.6 = 10)

1. 1.8 + 2.7 can use the same thing

2. 1 + 2 = 3

3. 0.8 + 0.7 = 1.5

4. 3 + 1.5 = 4.5 (1.8 + 2.7 = 4.5)

 

End: 10 x 4.5 = 45!

Hope this helped!

Which values from the given replacement set make up the solution set of the inequality?

5n>24 ; {2, 3, 4, 5, 6}


{2, 3}

{3, 4}

{4, 5, 6}

{5, 6}

Answers

Answer: 5,6

Step-by-step explanation:

Substitute the numbers for n

Which values from the given replacement set make up the solution set of the inequality?5n&gt;24 ; {2,

Answer: {5, 6}

Step-by-step explanation:

1. Find the length of each leg.
R
Q
30⁰
4
60%
P

1. Find the length of each leg.RQ30460%P

Answers

Answer:

QP = 2

QR = 2√3

Step-by-step explanation:

This is a special right triangle with angle measures as follows:

30° - 60° - 90°

And side lengths represented with:

x - x√3 - 2x respectively to angle measures.

The side length that sees angle measure 90, hypotenuse, is given as 4 so the legs would be:

2 and 2√3

Suppose you are given the following information regarding several investments:
Utility Formula Data
Investment Expected Return E(r) Standard Deviation σ
1 .12 .30
2 .15 .50
3 .21 .16
4 .24 .21
U = E(r) − 1/2Aσ^2
(a) On the basis of the utility formula above, which investment would you select if you were risk averse with A = 4?
(b) On the basis of the utility formula above, which investment would you select if you were risk neutral?
(c) The variable (A) in the utility formula represents the:
a. investor’s return requirement.
b. investor’s aversion to risk.
c. certainty equivalent rate of the portfolio.
d. p

Answers

a. On the basis of the utility formula above,  if you were risk-averse with A = 4, you would select either investment 3 or investment 4.

b. If you were risk-neutral, you would select investment 4 with an expected return of 0.24.

c.  The variable (A) in the utility formula represents the investor's aversion to risk. The correct answer is B

To determine the optimal investment based on the utility formula, we need to calculate the utility value for each investment option and compare them.

Investment 1:

Expected Return (E(r)) = 0.12

Standard Deviation (σ) = 0.302

Investment 2:

Expected Return (E(r)) = 0.15

Standard Deviation (σ) = 0.503

Investment 3:

Expected Return (E(r)) = 0.21

Standard Deviation (σ) = 0.164

Investment 4:

Expected Return (E(r)) = 0.24

Standard Deviation (σ) = 0.21

Utility formula: U = E(r) - 1/2Aσ^2

(a) Risk-Averse (A = 4):

To calculate the utility value for each investment:

Investment 1:

U1 = 0.12 - 1/2 * 4 * (0.302)^2

U1 ≈ 0.02

Investment 2:

U2 = 0.15 - 1/2 * 4 * (0.503)^2

U2 ≈ 0.02

Investment 3:

U3 = 0.21 - 1/2 * 4 * (0.164)^2

U3 ≈ 0.20

Investment 4:

U4 = 0.24 - 1/2 * 4 * (0.21)^2

U4 ≈ 0.20

Since investments 3 and 4 have the highest utility values of approximately 0.20, if you were risk-averse with A = 4, you would select either investment 3 or investment 4.

(b) Risk-Neutral (A = 0):

When an investor is risk-neutral (A = 0), the utility formula simplifies to U = E(r). In this case, we only consider the expected return.

Comparing the expected returns of the investments:

Investment 1: 0.12

Investment 2: 0.15

Investment 3: 0.21

Investment 4: 0.24

Based on expected returns alone, if you were risk-neutral, you would select investment 4 with an expected return of 0.24.

(c) The variable (A) in the utility formula represents the

b. investor's aversion to risk.

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Graph the function. Label the vertex and axis of symmetry. g(x)=4x^2-48x+7

Answers

Vertex: (3,-65) axis of Symmetry: x = 3
Graph the function. Label the vertex and axis of symmetry. g(x)=4x^2-48x+7

I’m dead help me
67. A swimming pool holds 6200 L of water.
The water drains at a rate of 20 L/min. How
long will the pool take to empty?

Answers

Answer:

310

Step-by-step explanation:

The answer for this question is 310

g(x) = 3x -1. Find x such that g(x)= 2​​0​.
g​(x)= 3x+1. Find x ​​​such that g(x)= 22​​​​.​

g(x)= ​2x-5. Find g(1/2) and g(a)=9​​​​​​9.
g(x)=x+5/2. Find g(3), g(0), g(-3) and g(x)=0​​​​​​​​​​

Please solve this quickly. I need it right now​​​​​. No silly answer will not be allowed.

Answers

Step-by-step explanation:

i. 3x-1=20

or, 3x= 21

x= 7

ii. 3x+1= 22

3x= 21

x= 7

iii. 2x-5=99

2x= 104

x=52

iv. g(3)= 3+5/2= 11/2

g(0)= 0+ 5/2=5/2

g(-3)= -3+5/2 = -1/2

x+5/2= 0

so, x= -5/2

Can someone help me please

Can someone help me please

Answers

Ratio = pages:days

Proportion

48/3 = 192/?

Or vice versa

Answer: 12 days

Step-by-step explanation:

Divide 48 by 3 to find out how many pages she reads on in one day.

She reads 16 pages a day

Multiply 16•12 to see if the number you get will be 192

She will need 12 more days to finish her book

(X+2) (x+8)
expand and simplify

Answers

Answer:

X+2=2x

x+8=8x

(2x).(8x)=16x

If the price of an apple is $0.50, the marginal utility per dollar spent on the fifth apple is: ________
a) 20
b) 30
c) 40

Answers

The marginal utility per dollar spent on the fifth apple is 60. The correct option is D.

What is marginal utility?

The marginal utility simply refers to the change or extra satisfaction derived from the change in consumption.

Hence, the marginal utility of the fifth apple equals :

Difference /change or extra satisfaction derived by consuming one more than 4 apples = (total utility of 5th apple - total utility of 4th apple)

= (250 - 220) = 30

Hence, marginal utility per dollar: Marginal utility/price per apple

Price per apple = $0.5

Marginal utility of 5th apple = 30

Marginal utility of 5th apple = 30 / 0.5

Marginal utility of 5th apple = 60

Therefore, the marginal utility per dollar spent on the fifth apple is 60. The correct option is D.

Complete question :

If the price of an apple is $0.50, the marginal utility per dollar spent for the fifth apple is:

a) 20

b) 30

c) 40

d) 60

Number of apples ____total utility

2__________________130

3__________________180

4__________________220

5__________________250

6__________________270

7__________________280

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Graph the system of equations on graph paper to answer the question.Please help me with this problem so I can help my son to understand better. {y=−3x+9y=−x−5}What is the solution for the system of equations?Enter your answer by filling in the boxes. (__,___)

Graph the system of equations on graph paper to answer the question.Please help me with this problem

Answers

Given the following system of equations:

y = -3x + 9

y = -x - 5

For us to be able to graph each of the equations, let's first determine the coordinates of its x and y-intercepts.

We get,

For y = -3x + 9,

At x = 0,

y = -3x + 9

y = -3(0) + 9

y = 9

Point 1 = 0, 9

At y = 0

y = -3x + 9

0 = -3x + 9

3x = 9

3x/3 = 9/3

x = 3

Point 2 = 3, 0

For y = -x - 5,

At x = 0,

y = -x - 5

y = 0 - 5

y = -5

Point 1 = 0, -5

At y = 0,

y = -x - 5

0 = -x - 5

x = -5

Point 2 = -5, 0

Let's now plot the two equations:

From the graph, it shows that the graph of the two equations intersects at 7, -12.

This point of intersection is also the solution for the system of equations.

Therefore, the answer is 7, -12.

Graph the system of equations on graph paper to answer the question.Please help me with this problem

write a linear function that shows the linear relationship in the table below.

write a linear function that shows the linear relationship in the table below.

Answers

Answer:

y=1/2x+7

Step-by-step explanation:

First find the slope of the function

Use slope formula:

10-9/6-4 =1/2

M= 1/2x

Find y-intercept:

9=1/2(4)+b

B=7

The Cauchy stress tensor components at a point P in the deformed body with respect to the coordinate system {x_1, x_2, x_3) are given by [sigma] = [2 5 3 5 1 4 3 4 3] Mpa. Determine the Cauchy stress vector t^(n) at the point P on a plane passing through the point whose normal is n = 3e_1 + e_2 - 2e_3. Find the length of t^(n) and the angle between t^(n) and the vector normal to the plane. Find the normal and shear components of t on t he plane.

Answers

The Cauchy stress vector \(t^n\) on the plane passing through point P with a normal vector \(n = 3e_1 + e_2 - 2e_3 \: is \: t^n = [3; 12; 1] \: MPa.\)

The angle between \(t^n\) and the vector normal to the plane is approximately 1.147 radians or 65.72 degrees.

The normal component of \(t^n\) on the plane is approximately 5.08 MPa, and the shear component is [-2.08; 6.92; 1] MPa.

To determine the Cauchy stress vector, denoted as \(t^n\), on the plane passing through point P with a normal vector

\(n = 3e_1 + e_2 - 2e_3\), we can use the formula:

\(t^n = [ \sigma] · n\) where σ is the Cauchy stress tensor and · denotes tensor contraction. Let's calculate \(t^n\)

\([2 5 3; 5 1 4; 3 4 3] · [3; 1; -2] = [23 + 51 + 3*(-2); 53 + 11 + 4*(-2); 33 + 41 + 3*(-2)] = [3; 12; 1]\)

Therefore, the Cauchy stress vector \(t^n\) on the plane passing through point P with a normal vector \(n = 3e_1 + e_2 - 2e_3 \: is \: t^n = [3; 12; 1] \: MPa.\)

To find the length of \(t^n\), we can calculate the magnitude of the stress vector:

\(|t^n| = \sqrt((3^2) + (12^2) + (1^2)) = \sqrt(9 + 144 + 1) = \sqrt(154) ≈ 12.42 \: MPa.\)

The length of \(t^n\) is approximately 12.42 MPa.

To find the angle between \(t^n\) and the vector normal to the plane, we can use the dot product formula:

\(cos( \theta) = (t^n · n) / (|t^n| * |n|)\)

The vector normal to the plane is \(n = 3e_1 + e_2 - 2e_3\)

So its magnitude is \(|n| = \sqrt((3^2) + (1^2) + (-2^2)) = \sqrt (9 + 1 + 4) = \sqrt(14) ≈ 3.74.\)

\(cos( \theta) = ([3; 12; 1] · [3; 1; -2]) / (12.42 * 3.74) = (33 + 121 + 1*(-2)) / (12.42 * 3.74) = (9 + 12 - 2) / (12.42 * 3.74) = 19 / (12.42 * 3.74) ≈ 0.404

\)

\( \theta = acos(0.404) ≈ 1.147 \: radians \: or ≈ 65.72 \: degrees\)

The angle between \(t^n\) and the vector normal to the plane is approximately 1.147 radians or 65.72 degrees.

To find the normal and shear components of t on the plane, we can decompose \(t^n\) into its normal and shear components using the following formulas:

\(t^n_{normal} = (t^n · n) / |n| = ([3; 12; 1] · [3; 1; -2]) / 3.74 ≈ 19 / 3.74 ≈ 5.08 \: MPa \\ t^n_{shear} = t^n - t^n_{normal} = [3; 12; 1] - [5.08; 5.08; 0] = [-2.08; 6.92; 1] \: MPa\)

The normal component of \(t^n\) on the plane is approximately 5.08 MPa, and the shear component is [-2.08; 6.92; 1] MPa.

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y = 4x + 6y + 4x = 6 Find using systems of equation by elimination.A. One SolutionB. Infinitely Many SolutionsC. No Solution In an environment of experimentation and spirited camaraderie, _________, the first _________ jazz style, was born. It changed jazz from popular dance music to intellectual art music. describe the regional precipitation pattern you would expect for the portion of mexico and central america indicated on the map. justify your answer. The measures of two complementary anglesare in the ratio 7:3. What is the measure of thesmaller angle? What is the measure of thelarger angle? Micaela deposited $2000 in a retirement account that offers5% interest compounded annually. She makes no additionaldeposits or withdrawals. Which amount is closest to theinterest Micaela earned at the end of 2 years? What was the most important learning you gained from this article? Seriously help Im about to submit this: A researcher wishes to estimate the percentage of adults who support abolishing the penny what size sample should be obtained if he wishes the estimate to be within three percentage points with a 95% confidence if he:A: uses a previous estimate of 26%?B: he does not use any prior estimates? f(x) = -x - 14Find x if f(x) = -2 The angle between two nonzero vectors V = (2, 2, 0) and w = (1, -2, 2) is 45. a) True b) False What is the best anime to seeA Nartuo B MHAC AOTD black clover A letter to Father tell him what I need for Four coming birthday what is a downside of using job boards? they fail to inform you about the kinds of jobs that are available. they frequently contain outdated listings. they fail to provide job-search information. Using the initial concentration and volume values from Trial 1 of Table 1, fill in the following chart of new concentration values (in Molarity) for the following reactants: [BrO3-], [I-], [H+]. What is the slope of the line that passes through (-4,6) and (5,-3)? All atoms of the same element must have the same number of ________A. protons.B. neutrons.C. compounds.D. electrons. in what direction does the object accelerate when released with initial velocity upward? which of the following can not lead to increase in coupling between two classes a and b? A string of lights in a series circuit is not working. Which of the following is most likely the cause?A light bulb burned out and opened the circuit.A light bulb burned out and closed the circuit.One of the light bulbs is dimmer than the others.One of the light bulbs is brighter than the others. Los elementos reales de La cripta de Kaua? Finding the Walrasian Demand Function Consider a consumer with Cobb-Douglas utility function u(x 1 ,x 2 )=x 1 x 2 1/2 over two goods x 1 and x 2 . Assume the consumer's income is I and the prices of those two goods are p 1 and p 2 , respectively. (a) Using the Lagrangian method to find out the Walrasian demand function (i.e., x 1 (p 1 ,p 2 ,I) and x 2 (p 1 ,p 2 ,I)) and indirect utility function (i.e., v(p 1 ,p 2 ,I)). (b) What restrictions on would ensure that the consumer demands strictly positive amounts of the goods (interior solution)?