Prove that if p is a prime and P is a subgroup of Sp of order p, then |NSp(P)|=p(p-1)

Answers

Answer 1

If a p is a prime number and P is a subgroup of group G = Sₚ of order p (denotes it's oder is prime) then |NSₚ(P)|= p(p-1).

We have provide that p is a prime and P is a a subgroup of a group, Sp of order p. We have to prove that |NSₚ(P)| = p(p−1).

Now, as know every group with a prime order is cyclic group. Here, P is subgroup that means it is a group with prime order so, P is a cyclic subgroup of order p. This cyclic group is generated by a p-cycle. For every a, b ∈ P, a, b are conjugate, that for an another element g∈ P, then a = gbg⁻¹, since they have the same cycle type. Now, every conjugate of P contains exactly (p - 1 ) p-cycles and use the formula for the number of p-cycles to compute the index of NG(P) in Sp. Now, if p−1 = |Sₚ|/|NG(P)|

=> |NG(P)| = (p - 1) |Sp|

=> |NG(P)| = p(p - 1).

Hence, proved, |NSₚ(P)| = p(p-1).

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Related Questions

Felix’s Feed Mill sells chicken feed for $8. 00 per bag. This price is no longer high enough to create a profit. Felix decides to raise the price. He is considering four different plans. Plan A: Raise the price by $0. 10 each week until the price reaches $12. 0. Plan B: Raise the price by 10 percent each week until the price reaches $12. 0. Plan C: Raise the price by the same amount each week for 8 weeks, so that in the eighth week the price is $12. 0. Plan D: Raise the price by $0. 25 each week until the price reaches $12. 0. Which plan will result in the price of the feed reaching $12. 00 fastest? plan A plan B plan C plan D.

Answers

The plan will result in the price of the feed reaching $12.00 fastest is Plan B because it reaches within 5 weeks.

What is decision-making?

The process of making choice is by identifying the correct decision, gathering information, and assessing alternative solutions.

Felix’s Feed Mill sells chicken feed for $8. 00 per bag.

This price is no longer high enough to create a profit.

Felix decides to raise the price. He is considering four different plans.

The plan will result in the price of the feed reaching $12.00 fastest will be

Plan A: Raise the price by $0. 10 each week until the price reaches $12. 0.

⇒ $0.10 × 20 = $2

This plan will take 20 weeks to reach at a price of $12.

Plan B: Raise the price by 10 percent each week until the price reaches $12.0. The price of this plan will be in t weeks is

\(12 = 8 *1.1^t\\\\t = 4.25 \approx 5\)

This plan will take less than 5 weeks.

Plan C: Raise the price by the same amount each week for 8 weeks, so that in the eighth week the price is $12.0. The amount will be

Amount = 2/8 = $0.25

Plan D: Raise the price by $0.25 each week until the price reaches $12. 0.

⇒ 0.25 × 8 = $2

This will take 8 weeks.

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write an a expression to represent

the sum of seven and the quotient of a number x and eight ​

Answers

Answer:

7 + x/8

Step-by-step explanation:

sum of 7 and Q(quorient)

7 + Q

quotient of x and 8

x/8

plus 7

7 + x/8

Answer:

n/8 + 7 = x

Step-by-step explanation:

Please help me by finding the value of x!

Please help me by finding the value of x!

Answers

The value of the angle x found using the trigonometric ratios for sines, and rounded to the nearest degree is; x ≈ 53°

What are trigonometric ratios?

Trigonometric ratios are functions that relates the ratio of two of the sides of a right triangle to an interior angle of the right triangle.

The rectangular angle mark in the diagram, indicates that the specified triangle in the figure is a right triangle.

The required angle measure in the figure = x°

The length of a leg in the right triangle opposite to the angle x° = 12 units

The length of the hypotenuse side of the right triangle = 15 unis

The trigonometric ratios of sines indicates that we get;

sin(θ) = (Length of the opposite side to the angle θ)/(Length of the hypotenuse side of the triangle)

Therefore;

sin(x°) = (Length of opposite side to x)/(Length of the hypotenuse side)

sin(x°) = 12/15 = (3 × 4)/(3 × 5)

sin(x°) = (3 × 4)/(3 × 5) = 4/5

sin(x°) = 4/5 = 0.8

The value of the angle x can be calculated using a calculator as follows;

x° = arcsine(0.8) ≈ 53°

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HELPPPPP WILL MARK BRAINLIEST SHOW WORK TOO

HELPPPPP WILL MARK BRAINLIEST SHOW WORK TOO

Answers

Answer:

area=3/5      

length=7/8    

width=?

so  3/5=7/8 times ?

multiply both sides by 8/7 to clear fraction (7/8 times 8/7=56/56=1 and 1 times ?=? so)

24/35=?  

the width= 24/35 mile

What is the volume of a rectangular prism that has a side length of 1/2 units and a base length of 16 1/4 units squared

Answers

Answer:

Step-by-step explanation:

81 square yards

Jessica is buying roses to sell at a fundraiser for school. She needs to purchase the roses at the lowest price per rose to allow for the highest profit margin. The roses are sold in bunches of 4, 6, 8, or 12. The chart below shows the prices for the different bunches of roses. Roses in Bunch Price 4 $7.98 6 $8.50 8 $10.25 12 $12.25 Based on the information in the chart, which size bunch would be the least expensive per rose? A. 4 B. 6 C. 8

Answers

Answer:

how do i comment

Step-by-step explanation:

Rebecca is given two triangles, ABC and DEF. At first glance, she thinks
that the triangles are congruent. How can she use what she knows about
rotations and triangle congruence to prove the triangle congruence? I need it fast plz

Rebecca is given two triangles, ABC and DEF. At first glance, she thinksthat the triangles are congruent.

Answers

Answer: Side Angle Side

Answer:

B.

She can rotate triangle DEF 180and then compare the angles and sides. She will see that the triangles are congruent by the Side Angle Side theorem.

Step-by-step explanation:

Rebecca is given two triangles, ABC and DEF. At first glance, she thinksthat the triangles are congruent.

At Caesar's Palace Casino in Vegas, there were three poker players, Alice, Bernie and Craig. At the beginning of the night the amount of money each had was split in the ratio 7 : 6 : 5, with Alice starting with the most and Craig the least. At the end of the night, Alice was still ahead and Craig still last, but the money was divided according to the ratio 6 : 5 : 4.

This meant that one of the players was up by $12.

What were the combined assets of the players at the beginning of the evening, in dollars?

Answers

The combined assets of the players at the beginning of the evening was $ 180.

Since at Caesar's Palace Casino in Vegas, there were three poker players, Alice, Bernie and Craig, and at the beginning of the night the amount of money each had was split in the ratio 7: 6: 5, with Alice starting with the most and Craig the least, and at the end of the night, Alice was still ahead and Craig still last, but the money was divided according to the ratio 6: 5: 4, with which one of the players was up by $ 12, To determine what were the combined assets of the players at the beginning of the evening, in dollars, the following calculation must be performed:

6: 5 = 12 difference 1 x 6 = 12 x 6 = 72 72 + 60 + 48 = 180

Therefore, the combined assets of the players at the beginning of the evening was $ 180.

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i need help please!!

i need help please!!

Answers

Answer:

Step-by-step explanation:

do the thing times 2

Do the graph two times

An employee is 25 years old and starting a 401k plan. The employee is going to invest $150 each month. The account is expected to earn 5.5% interest, compounded monthly. What is the account balance, rounded to the nearest dollar, after two years? a. $3,976 b. $3,796c. $6,675 d. $6,765

Answers

Rounding to the nearest dollar, we get an account balance of $3,796. Therefore, the answer is (b) $3,796. Option b is Correct.

A financial repository's account balance represents the amount of money there is at the end of the current accounting period. It is the sum of the balance carried over from the previous month and the net difference between the credits and debits that have been recorded during any particular accounting cycle.

The future value of an annuity with monthly contributions:

FV = \(P * ((1 + r/12)^{n - 1}) / (r/12)\)

Here FV is the future value, P is the monthly payment, r is the annual interest rate, and n is the number of months.

In this case, P = $150, r = 5.5%, and n = 24 months (2 years * 12 months/year). Plugging in these values, we get:

FV =\(150 * ((1 + 0.055/12)^24 - 1) / (0.055/12)\)

≈ $3,795.88

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There is no context as to how this should be answered

There is no context as to how this should be answered

Answers

Answer:

x = 148

Step-by-step explanation:

( Note that ∠DPB = 32° and ∠CPB is x )

∠DPB and ∠CPB are supplementary angles.

Supplementary angles add up to 180°

This means that ∠DPB + ∠CPB must equal 180

If ∠DPB = 32° and ∠CPB = x , then 32 + x = 180

( Note that we've just created an equation that we can use to solve for x )

We now solve for x using the equation we just created

x + 32 = 180

* subtract 32 from both sides *

we're left with x = 148

below the paraboloid z = 18 − 2x2 − 2y2 and above the xy-plane

Answers

Answer:

y

2

=−

2

z

+7

Steps for Solving Linear Equation

z=18−2×2−2y2

Multiply 2 and 2 to get 4.

z=18−4−2y

2

Subtract 4 from 18 to get 14.

z=14−2y

2

Swap sides so that all variable terms are on the left hand side.

14−2y

2

=z

Subtract 14 from both sides.

−2y

2

=z−14

Divide both sides by −2.

−2

−2y

2

=

−2

z−14

Dividing by −2 undoes the multiplication by −2.

y

2

=

−2

z−14

Divide z−14 by −2.

y

2

=−

2

z

+7

Step-by-step explanation:

the given equation defines a paraboloid that lies below the plane z=0. Specifically, it is situated above the xy-plane, which means that the z-values of all points on the surface are greater than or equal to zero.

we can break down the equation z=18-2x^2-2y^2. This equation represents a paraboloid with its vertex at (0,0,18) and axis of symmetry along the z-axis. The first term 18 is the z-coordinate of the vertex and the last two terms -2x^2 and -2y^2 determine the shape of the paraboloid.

Since the coefficient of x^2 and y^2 terms are negative, the paraboloid is downward facing and opens along the negative z-axis. Therefore, all points on the paraboloid have z-values less than 18. Additionally, since the paraboloid is situated above the xy-plane, its z-values are greater than or equal to zero.

the paraboloid defined by the equation z=18-2x^2-2y^2 is situated below the plane z=0 and above the xy-plane. Its vertex is at (0,0,18) and it opens along the negative z-axis.

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select all that are equal to

select all that are equal to

Answers

Answer:

5³ x 5⁻⁷ = 1/625

Step-by-step explanation:

1/5⁴

5⁻⁴

Determine the zero solution
f(x)=3x^(2)+5x-12

Answers

Answer:

x= -3 or 4/3

Step-by-step explanation:

3x²+5x-12 =0

3x²+9x-4x-12=0

3x(x+3) -4(x+3) =0

(3x-4)(x+3)=0

x=-3 or 4/3

A prism is completely filled with 64 cubes that have edge lengths of 12 in. What is the volume of the prism? Enter your answer in the box

Answers

Answer:

answer;8

Step-by-step explanation:

I took the test and got it right

Answer:

110592 in^3

Step-by-step explanation:

12x12x12=1728

1728x64=110592

I need help asap the question is in the picture.​

I need help asap the question is in the picture.

Answers

Answer:

The second one between 2 and 3

Step-by-step explanation:

Sq root of 7 = 2.65

Answer:

2nd number line represents √7 best

Step-by-step explanation:

Method 1

√7 ≈ 2.65

Therefore, the 2nd number line represents √7 best

(the one with the dot between 2 and 3)

Method 2

√1 = 1

√4 = 2

√9 = 3

Therefore, as √7 is between √4 and √9, the solution is somewhere between 2 and 3.

LOGIC Show that (3.8.x)=67.47.77.
B
1
U
!!!
ETT

Answers

Answer:

= 17.75526315

Step-by-step explanation:

Combine multiplied terms into a single fraction

(3.8) = 67.47

\(\frac{(19x)}{5}\) = 67.47

Remove parentheses

\(\frac{19x}{5}\) = 67.47

more steps but it will take to to read but the answer is

= 17.75526315

what geometric shape forms the hole that fits an allen wrench

Answers

Answer:

A hexagon

Step-by-step explanation:

A hexagon - - - the allen wrench has 2 hexagonal heads. See attached pic.

what geometric shape forms the hole that fits an allen wrench

The geometric shape that forms the hole that fits an allen wrench is a hexagon, which is a six-sided polygon with straight sides and angles.

The geometric shape hexagon-shaped hole in an allen wrench, also known as a hex key, is designed to fit tightly over the hexagonal socket of a screw or bolt head. A hexagon is a six-sided polygon, meaning it has six straight sides and angles. In the case of an allen wrench, the hexagon has internal angles of 120 degrees and opposite sides that are parallel.

The hexagonal shape of the hole in the wrench allows for a tight and secure fit onto the corresponding hexagonal socket of the screw or bolt head. This design ensures that the wrench can apply a significant amount of torque to the fastener without slipping, which is essential for many applications in construction, mechanics, and other industries.

The use of a hexagonal shape also allows for greater precision and control when turning the screw or bolt, making it easier to achieve the desired level of tightness. Overall, the hexagon is an ideal shape for the hole in an allen wrench due to its strength, stability, and precision.

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Actividad a desarrollar:
ayudaa plisss

Actividad a desarrollar:ayudaa plisss

Answers

Answer:

a) AUB = { 1 ,2 , 3, 4, 5, 6, 8, 10}

b) A∩ B =  { 2, 4, 6 }

c) A-B = { 8 , 10}

Step-by-step explanation:

Step(i):-

Given that the sets

      U = { 1,2,3,4,5,6,7,8,9,10}

      A = { 2,4,6,8,10}

     B = { 1,2,3,4,5,6}

AUB = { 2,4,6,8,10} U  { 1,2,3,4,5,6}

AUB = { 1 ,2 , 3, 4, 5, 6, 8, 10}

Step(ii):-

A∩ B = {  2 ,4, 6, 8,10} ∩ { 1,2,3,4,5,6} = { 2, 4, 6 }

A-B = { 2,4,6,8,10} - { 1,2,3,4,5,6} = { 8 , 10}

Final answer:-

a) AUB = { 1 ,2 , 3, 4, 5, 6, 8, 10}

b) A∩ B =  { 2, 4, 6 }

c) A-B = { 8 , 10}

what is the full from of MICR ​

Answers

The full form of MICR is:-magnetic ink character recognition

U can search the defention in Gogle

Hope it helps

Name the triangle with the following charcteristics. sides: 5cm, 6 cm, 7cm; Angles: 75°, 60°, and 45° A. Obtuse scalene triangle B. Acute isosceles triangle C. Acute scalene triangle D. Right isosceles triangle​

Answers

Answer:

C.  Acute scalene triangle

sides 5; 6; 7; - NO sides equal

all 3 angles are less than 90 degrees - they are ALL acute

Step-by-step explanation:

Answer:

2 3 6 yw

Step-by-step explanation:

2.) Below are the number of calories in one serving of various cereals:110 98 140 145 150 90 150. 140 120Construct a 95% confidence interval for the average number of calories in cereal. Can we say that the average is 115 calories? Why?3.) Construct a 99% confidence interval for the standard deviation of calories in #2.

Answers

If the number of calories in one serving of various cereals are 110, 98, 140, 145, 150, 90, 150, 140 and 120, then the 95% confidence interval for the average number of calories in cereal is (109.2457, 144.7544).

As per the question statement, the number of calories in one serving of various cereals are 110, 98, 140, 145, 150, 90, 150, 140 and 120,

And we are required to determine the following:

(a) 95% confidence interval for the average number of calories in cereal

(b) If the average is 115 calories or not.

Here, given that sample size, (n = 9)

And we know that, [Mean (M) = {(Σx)/n}],

That is, Mean [(M) = (1143/9)],

Or, [(M) = 127]

Also, we know that, Standard Deviation (s) = [{√Σ(xi - M)²}/(n - 1)]

Or,  (s) = [{√Σ(xi - 127)²}/(9 - 1)]

Or, [(s) = 23.0976]

Now solving for part (a) at 95% confidence interval,  (α = 0.05)

Or, [d = (n - 1) = (9 - 1) = 8]

And, (t-critical) = t[(α/2),d] = t(0.025, 8)

Also, (t-critical) = (±2.306)... [given in the students t-distribution table]

Therefore, the 95% confidence interval (CI) for (μ) goes as,

CI = [(M) ± {(t-critical) * (s/√n)}]

Or, CI = [127 ± {(2.306) * (23.0976/ √9)}]

Or, [CI = (127 ± 17.7543)]

Or, [CI = (109.2457, 144.7544)]

And for part (b), since 115 lies in the range of 95% confidence interval for the average number of calories in our concerned cereal, we cannot reject 115 calories as the average.

Confidence Interval: In Frequentist Statistics, a Confidence Interval, refers to the probability that an unknown population parameter will fall between a set of values for a certain proportion of times, and is based on the mean and standard deviation.

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ATTENTION!!! NEED HELP NOW!!! WILL MARK BRAINLEST!!!!!!!!!!!!!!!!!!!!

ATTENTION!!! NEED HELP NOW!!! WILL MARK BRAINLEST!!!!!!!!!!!!!!!!!!!!

Answers

Answer:

29.7263957575

Step-by-step explanation:

hope this answer help you (:

plss helpp this is urgent hurry

plss helpp this is urgent hurry

Answers

A. Equation: x + 48 +  52 = 180

B. x = 80°.

What is an angle addition postulate?

According to the Angle Addition Postulate, an angle's measure is equal to the sum of the measures of any two adjacent angles. The Angle Addition Postulate can be used to determine the measurement of a missing angle or to determine the angle produced by two or more other angles.

Given:

Two parallel line a and b are cut by a traversal line.

By the alternate exterior angles and angle addition postulates,

x + 48 +  52 = 180

This is the equation for Part A.

And x = 80°.

Therefore, the value of x is 80°.

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A man set off in his friend’s car on a 200-km journey at 10.30 a.m. The car broke down after it had travelled 150 km at an average speed of 50 km/h. Twenty minutes later, the man was given a lift by a motorist who brought him to his destination at an average speed of 100 km/h. Calculate
a) The time at which he arrived at his destination,
b) The average speed at which he travelled for the whole journey
Can someone help me in this question please I am confused

Answers

Answer:

b) The average speed at which he travelled for the whole journey

Step-by-step explanation:

If he had travel 200- km/h and had broke down by which was at 10:30 a.m  you would have to subtract 200 km/h to 10:30  your answer would be 189.7 when they back on the road also the speed slowed down a bit about 50 km/h so you would add 50 km/h to 20 mins you would get 70km/h they were traveling by, then you add all of the numbers up by 100 you would get 640 so your answer would be 640

True or false: These key features were used to sketch the graph of f(x):


nonlinear

increasing for x > 2

y-intercept located at (0, –4)

x-intercept located at (–1, 0) and (5, 0)

End behavior: as x → ∞, y → ∞

True or false: These key features were used to sketch the graph of f(x):nonlinearincreasing for x >

Answers

Answer:

I think its true .

Step-by-step explanation:

The relationship between numbers in List X and List Y follows the rule y = x + 2.05 . Which diagram shows this relationship?

Answers

The given rule y = x + 2.05 represents a linear relationship between the numbers in List X and List Y. This means that for every increase in x by 1, y increases by a constant value of 1.

Therefore, we can expect the points in List X and List Y to lie on a straight line. Thus, we need to choose the diagram that shows a linear relationship between the points.

The diagram that shows this relationship is (B). It depicts a set of points that are arranged in a straight line passing through the origin and have a positive slope. This indicates that as x increases, y also increases at a constant rate of 1. The other diagrams either show a nonlinear relationship or do not have a constant rate of increase between the x and y values.

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What is the difference between different types of integer models
namely total integer model, 0-1
integer model & mixed integer model, explain briefly in our own
words?

Answers

Different types of integer models refer to different formulations and restrictions applied to the variables in mathematical optimization problems. Here are brief explanations of three commonly used types of integer models: total integer model, 0-1 integer model, and mixed integer model.

1. Total Integer Model: In a total integer model, all variables are required to take integer values. This means that the solution must consist of only whole numbers, without any fractional or decimal values. For example, if a variable represents the number of units to produce, a total integer model would ensure that only whole units can be produced.

2. 0-1 Integer Model: In a 0-1 integer model, the variables are binary and can only take two values: 0 or 1. This formulation is often used for decision variables that represent choices or binary decisions, such as selecting or not selecting a particular option. For example, in a facility location problem, a 0-1 integer variable can represent whether a facility is open (1) or closed (0).

3. Mixed Integer Model: A mixed integer model allows a combination of integer and continuous variables in the optimization problem. Some variables can take fractional or decimal values (continuous), while others must take integer values. This formulation is useful when there is a need to model both discrete decisions and continuous quantities in the same problem. For example, in a production planning problem, the number of machines (integer) and the amount of raw material used (continuous) can be decision variables in a mixed integer model.

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a process in which a number is changed, such as by adding, subtracting, dividing, or multiplying.answer choicesoperationsmartsuper cool

Answers

A process in which a number is changed, such as by adding, subtracting, dividing, or multiplying is called Mathematical Expression.

When we combine numbers and variables in a valid way, using operations such as addition, subtraction, multiplication, division, exponentiation, and other operations and functions as yet unlearned, the resulting combination of mathematical symbols is called a Mathematical Expression.

Addition is adding two or more numbers to find their sum.

Subtracting is finding the difference between two or more numbers.

Division is finding the quotient of two number by dividing the both numbers.

Multiplying is finding the product of two or more numbers.

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One hundred people line up to board an airplane. Each person has a boarding pass with an assigned seat. However, the first person to board has lost his boarding pass and takes a random seat. After that, each person takes their assigned seat if it is unoccupied, or one of the unoccupied seats at random if it is occupied. What is the probability that the last person to board gets to sit in their assigned seat

Answers

The probability that the last person to board gets to sit in their assigned seat is 1/50 or 0.02, which is 2%.

How to calculate the probability of the last person sitting in their assigned seat?

The probability that the last person to board gets to sit in their assigned seat can be determined by analyzing the possible seating scenarios.

Let's break down the problem step by step:

1. The first person, who has lost their boarding pass, chooses a random seat. There is a 1/100 probability that they choose their assigned seat correctly.

2. Now, there are two possibilities:

a. If the first person occupies their assigned seat, everyone else will also sit in their assigned seats, resulting in the last person sitting in their assigned seat. The probability of this scenario is 1/100.

b. If the first person occupies someone else's seat, we move to the next step.

3. From the second person onwards, if a person finds their assigned seat unoccupied, they will sit in it, ensuring that the last person also gets their assigned seat. This scenario has a probability of 1/100.

4. If a person finds their assigned seat occupied, they will choose another seat at random from the remaining unoccupied seats. This will continue until the last person boards.

Analyzing all the possible scenarios, we can see that either the first person sits in their assigned seat (1/100 probability) and everyone follows suit, or the first person sits in someone else's seat (99/100 probability), leading to a chain of random seat changes. In this case, the last person will only get their assigned seat if they happen to be the last person who needs to change their seat.

Since there are 99 people in between the first and the last person who need to change seats, the probability that the last person gets their assigned seat in this scenario is 1/99.

Combining the two possibilities:

Probability = (1/100) + ((99/100) * (1/99))

Probability = 1/100 + 1/100

Probability = 2/100

Probability = 1/50

Therefore, the probability that the last person to board gets to sit in their assigned seat is 1/50 or 0.02, which is 2%.

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the speed of light in a certain medium is 2.2 x 10 8 m/s. what is the index of refraction of this medium? The citizens of a certain community were asked to choose their favorite pet. The pie chart below shows the distribution of the citizens' answers. If there are 130,000citizens in the community, how many chose Cats, Dogs, or Birds Zinc reacts with Hydrochloric Acid in a single replacement reaction. If you have 8 g of of zinc metal, what mass of each product would you produce? What is the Japanese word for "real world", where thevalue-adding activities to satisfy the customer are carriedout?a)Kaizenb)Gembac)Gembutsud)Ser Stages of mitosis?? 20 points!!!Not sure what goes with what its like a matching game please help heeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeelp how might subjectivity and the social context of a sociologist influence what they study/see and how they interpret what they see? The width of a box in the shape of a rectangular prism is 4 inches more than the height h . The length is the difference of 9 inches and the height. A. Write a polynomial that represents the volume of the box in terms of its height (in inches). B. The volume of the box is 180 cubic inches. Please help ASAP!! DUE TOMORROW!!describe how the boundaries between earth's tectonic plates compared with the location of most of the earthquakes What meaning is revealed through the narrator'stone?DONEI started to clean everything up, and that waswhen I noticed else something weird. In themiddle of all of that glass was a littleenvelope, about the size of a wireless Internetcard. What the? I opened it up, and insidethere was a key. What the, what the? It was aweird-looking key, obviously to somethingextremely important, because it was fatterand shorter than a normal key. I couldn'texplain it: a fat and short key, in a littleenvelope, in a blue vase, on the highest shelfin his closet.-Extremely Loud and Incredibly Close,Jonathan Safran Foer The Cartesian equation, y = 4, is equivalent to the polar equationr = 4/sinr^2 = 4 sin r = 4/sin Which public health strategy for reducing risk factors related to disease best explains the following example: Those with blood sugar levels that satisfy the criteria for diabetes are aggressively treated? What are the 5 functions of political parties ?. If sin A=4/5,find the value of 5cos A + 3tan A Kai bought his younger sister, Loni, a sticker book and 12 stickers. Each week he gives his sister two new stickers. Let w represent the number of weeks that Loni collects stickers, and let s represent the total number of stickers she has collected. a. Determine the independent and dependent variables. The number of weeks, w, is the ? variable. The total number of stickers, s, is the ? variable. Missy rode her bike 20 miles in 150 minutes. If she rode at a constant rate, how many miles did she ride in an hour? the affinity of hemoglobin for oxygen group of answer choices increases as the height above sea level increases is greater than the affinity for carbon monoxide. is decreased in response to increased metabolic rate Based on the classical view, a) Unemployment never occurs. b) Cyclical unemployment might occur temporarily. c) All goods produced are always purchased at an unchanging price. d) Persistent unemployment might be a problem. What are your reasons for occupation or resistance to occupation? Be sure to use evidence. Ikkita avtomobil ikki shahardan bir vaqtda bir biri tomon yo'lga chiqdi . Birinchi avtomobil 1 soatda 90 km , ikkinchisi esa 1 soatda 80 km yo'l bosmoqda . Agar ikki shahar orasidagi masofa 1304 km bo'lsa , 2 soatdan keyin ular orasida necha kilometr masofa qoladi ?The two cars drove from the two cities towards each other at the same time. The first car travels 90 km per hour and the second 80 km per hour. If the distance between the two cities is 1304 km, how many kilometers will be left between them after 2 hours?