Mathematics High School

## Answers

**Answer 1**

Based on the information in the **graph**, it can be inferred that the variable of belonging to a **tenth** grade and the variable of **preferring** **pizza** are independent.

What information does the graph show?

The **graph** shows the information about the preference of tenth and ninth grade students between **pizza** and hamburger. This table shows the data of 2,500 students, of which 1,050 prefer hamburgers and 1,450 prefer pizza.

Are preference for pizza and belonging to grade 10 dependent variables?

No, the variables of belonging to a grade (ninth or **tenth**) and the variables of preference for a product (**pizza** or hamburger) are independent because the number of members of each grade does not change if the student prefers one or the other product . Also, the number of students who prefer pizza or hamburger does not depend on what grade each student is in.

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## Related Questions

Khan Academy

We want to find the zeros of this polynomial:

p(x) = (x + 2)(2x - 3)(x − 3)

Plot all the zeros (x-intercepts) of the polynomial in the interactive graph.

### Answers

All the **zeros **of the **polynomial function **p(x) = (x + 2)(2x - 3)(x − 3) are

x = -2, x = 2/3 and x = -3

How to find the zeros of the polynomial function

The zeros of the **polynomial function **is solved by equating each term in parenthesis to zero.

for the function, p(x) = (x + 2)(2x - 3)(x − 3)

firstly, x + 2 = 0

x = -2

secondly, (2x - 3)

2x - 3 = 0

2x = 3

x = 3/2

thirdly, (x + 3)

x + 3 = 0

x = -3

the **zeros **are x = -2, x = 2/3 and x = -3

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What are the functions of interest groups for the political system ?

### Answers

**Interest groups**, also known as special interest groups or pressure groups, are organizations that seek to influence public policy by promoting specific causes or by representing the interests of a particular group of people. There are many functions that interest groups serve in a **political system **including advocacy, information, mobilization, representation and coordination.

**Advocacy**: Interest groups advocate for the causes or issues that they support by lobbying politicians, running public awareness campaigns, and participating in the policymaking process.

**Information**: Interest groups provide information and research about the issues they care about to policymakers, the media, and the general public.

**Mobilization**: Interest groups mobilize their members and supporters to take action on issues, such as contacting politicians or participating in demonstrations.

**Representation**: Interest groups represent the interests of their members or the groups they serve by advocating for policies that benefit those groups.

**Coordination**: Interest groups can coordinate the efforts of individuals and organizations that share similar goals or values, helping to build a unified movement around a particular issue.

Overall, interest groups play an important role in a** political system** by providing a voice for groups of people or causes that may not otherwise be represented in the policymaking process.

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After a 65% reduction, you purchase a new sofa on sale for $252. What was the original price of the sofa?

### Answers

The **original price** of the sofa was $388.46, which was **reduced** by 65% to $252.

The original price of the** sofa** can be calculated by multiplying the sale price by 100 and then dividing it by 65. **Mathematically**, this can be expressed as:

Original Price = (Sale Price x 100) ÷ 65

Therefore, the **original price** of the sofa can be calculated as:

Original Price = (252 x 100) ÷ 65

Original Price = $388.46

**Therefore**, the original price of the sofa was $388.46, which was reduced by 65% to $252.

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Three boys, Peter, John and Joseph, are given $140 to share among themselves. They have to divide the money so that John will get two times as much as Peter and Joseph will have $8 less than John.

Form an equation and answer the following.(Start with giving Peter x dollars)

Peter gets $

John gets $

Joseph gets $

show working pls

### Answers

The amounts that each people will get of the $140 are given as follows Peter gets $37.60,John gets $75.20 and Joseph gets $67.20.

How to obtain the amounts for each people?The amounts for each people are obtained using a system of equations, for which the variables are given as follows:

**Variable** x: amount that Peter gets.

Variable y: amount that John gets.

Variable z: amount that Joseph gets.

In total, they are given $140, hence:

x + y + z = 140.

John gets two times as much as Peter, hence:

y = 2x.

Joseph will have $8 less than John, hence:

z = y - 8.

z = 2x - 8.

Then the last two** expressions** can be replaced into the first equation to obtain the amount that Peter gets, as follows:

x + y + z = 140.

x + 2x + 2x - 8 = 180

5x = 188

x = 188/5

x = $37.60.

Then the amount that John gets is given as follows:

y = 2x = 2(37.60) = $75.20.

The amount that Joseph gets is calculated as follows:

z = y - 8 = 75.20 - 8 = $67.20.

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The **amounts** that each people will get of the $140 are given as follows Peter gets $37.60,John gets $75.20 and Joseph gets $67.20.

How to obtain the amounts for each people?

The amounts for each people are obtained using a system of equations, for which the variables are given as follows:

**Variable** x: amount that Peter gets.

Variable y: amount that John gets.

Variable z: amount that Joseph gets.

In total, they are given $140, hence:

x + y + z = 140.

John gets two times as much as Peter, hence:

y = 2x.

Joseph will have $8 less than John, hence:

z = y - 8.

z = 2x - 8.

Then the last two **expression** can be replaced into the first equation to obtain the amount that Peter gets, as follows:

x + y + z = 140.

x + 2x + 2x - 8 = 180

5x = 188

x = 188/5

x = $37.60.

Then the amount that John gets is given as follows:

y = 2x = 2(37.60) = $75.20.

The amount that Joseph gets is calculated as follows:

z = y - 8 = 75.20 - 8 = $67.20.

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What is responsible for digestion and absorption?

### Answers

**Small intestine** is responsible for the continuous breaking-down process which is digestion and absorption.

What is the function of small intestine?The duodenum, jejunum, and ileum are the three sections of the small intestine. It aids in the further **digestion **of stomach-born meals. It takes in water, vitamins, minerals, carbs, lipids, and proteins from meals so that the body can utilize them.In terms of digestion, the **duodenum and jejunum** are where proteins and carbs are absorbed. The majority of fats are also absorbed via the jejunum. Vitamin B12, bile salts, and all other digestive products that were not absorbed in the duodenum and jejunum are all absorbed in the ileum.Your small intestine's walls allow water and nutrients that have been digested to enter your circulation. The digestive system's waste materials travel into the big intestine while peristalsis proceeds.

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Please help me! Ignore the answer I put, I know it’s wrong

### Answers

**Answer:**

y = - x - 2

**Step-by-step explanation:**

Perpendicular definition is two slopes multiply each others and equal to -1, can be expressed in equation as:

[tex] \displaystyle{m_1m_2 = - 1}[/tex]

m represents the slope value. To find another slope that is perpendicular to each other, we find another m-value. We know our first slope is given in the question which is 1 (y = x has slope of 1). Therefore:

[tex] \displaystyle{1m_2 = - 1} \\ \\ \displaystyle{m_2 = - 1}[/tex]

Therefore, another slope that is perpendicular to 1 is -1. We know the slope perpendicular, we substitute in the equation y = mx + b:

[tex] \displaystyle{y = - 1x + b} \\ \\ \displaystyle{y = - x + b}[/tex]

Next, we find the y-intercept (b). We are given the point that the perpendicular line passes through, (-4,2). Substitute x = -4 and y = 2 in the equation above:

[tex] \displaystyle{ 2 = - ( - 4) + b} \\ \\ \displaystyle{2 = 4 + b} \\ \\ \displaystyle{2 -4 = b} \\ \\ \displaystyle{ - 2 = b}[/tex]

Therefore, b = -2, substitute in:

[tex] \displaystyle{y = - x - 2}[/tex]

Therefore, the equation that is perpendicular to y = x and also passes through (-4,2) is **y ****=**** ****-**** ****x ****-**** ****2**

the number n can be expressed as the product of four prime numbers, exactly three of which are the same. how many different positive divisors does n have, including n and 1 ?

### Answers

**Answer:**

8

**Step-by-step explanation:**

Give a **prime factorization** consisting of **two primes**, with one of them **cubed**, you want to know the **number of positive integer divisors**.

Divisors

The number of divisors is the product of the exponents of the prime factorization, each increased by 1.

Application

Your number is ...

n = (a^3)(b^1)

so the number of positive divisors is ...

(3+1)(1+1) = 4·2 = 8

**The number ****n**** has 8 different positive divisors**.

__

*Additional comment*

The divisors are ...

1, a, b, a², ab, a³, a²b, a³b

Example: 24 = 2³·3 has divisors ...

1, 2, 3, 4, 6, 8, 12, 24

joseph's meal came to $18.35 and jayden's meal

came to $21.40. jayden paid for both meals and

left a 15% tip. what is the total cost of both

meals, including tip?

### Answers

the solution of the question is as follows,

joseph's meal is of = $18.35

jayden's meal is of = $21.40

total **bill** for both the meals = joseph meal cost + jayden meal cost

= $18.35 + $21.40

= $39.75

now calculate the amount of tip given 15 **percent, **

amount paid as a **tip **= 15% of bill

= 15/100 X $39.75

= 596.25/100

= $5.962

total cost of both meals, including tip = total bill + amount paid as tip

= $39.75 + $5.962

**= $45.712**

so, **total cost** of both meals, including tip is $45.712.

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How much would $500 invested at 8% interest compounded annually be worth after 3 years? Round your answer to the nearest cent.

### Answers

The** amount **$500 invested at 8% **interest compounded annually** be worth after 3 years is $ 629.86

How to find the amount after 3 years?

Since we have $500 invested at 8% **interest compounded annually**, we need to find the worth after 3 years.

Using the **compound interest formula**, the amount

A = P(1 + r)ⁿ where

P = present value, r = interest rate and n = time

Given that

P = $500, r = 8% **compounded annually **= 0.08 and n = 3 years

So, substituting the values of the variables into the **equation,** we have that

A = P(1 + r)ⁿ

A = $500(1 + 0.08)³

A = $500(1.08)³

A = $500 × 1.259712

A = $ 629.856

A ≅ $ 629.86

So, the amount is $ 629.86

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given that x=3 is a zero of the function, find all the zeros of f(x)= x^4 -6x^3 -12x +18

### Answers

**Answer:3 zeros**

**Step-by-step explanation:**

Solve for x in the equation x squared 20 x 100 = 36.

### Answers

The **solution **of the **equation **are; x = -16 or x = -4. so option A is correct.

**What is a quadratic equation?**

A quadratic equation is the second-order **degree **algebraic expression in a variable. the standard form of this expression is ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.

Given equation;

x²+ 20 x + 100 = 36.

x²+ 20 x + 100 - 36 = 0

x²+ 20 x + 64 = 0.

x²+ (16 + 4)x + 64 = 0.

x²+ 16x + 4x + 64 = 0.

x(x + 16) +4 (x + 16) = 0.

(x+ 4) (x + 16) = 0

Thus, the solution of the equation are; x = -16 or x = -4.

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HELP!!!!!!!!!!!!!!!!!

pls can someone answer/explain these quick algebra questions involving mean median and mode?

### Answers

The statements that are true about the **box plot** are:

A. The **Interquartile Range (IQR) **is 1.2 goals per game

E. The **median** is 3.6 goals per game.

G. The maximum is 5.6 goals per game.

How to Find the Median and Quartile of a Data on a Box Plot?

To find the **median **and **quartiles **of a data set that is displayed on a box plot, follow these steps:

Locate the box on the **box plot**. The box represents the middle 50% of the data and is bounded by the lower quartile and upper quartile.Find the vertical line inside the box. This line represents the median of the data.Locate the lower and upper bounds of the box. These bounds represent the lower quartile and upper quartile, respectively.You can also find the minimum and maximum values of the data set by looking for the "whiskers" on the plot. These are the lines extending from the box that show the range of the data. The minimum value is at the bottom end of the lower whisker, and the maximum value is at the top end of the upper whisker.If you need to find the **interquartile range (IQR),** simply subtract the lower quartile from the upper quartile. The IQR is a measure of the spread of the middle 50% of the data.

Therefore:

Median of the data = 3.6.

**Interquartile Range (IQR) **= Q3 - Q1 = 4 - 2.8 = 1.2.

Minimum value = 2.4

Maximum value = 5.6

Therefore, the correct options are:

A. The **Interquartile Range (IQR) **is 1.2 goals per game

E. The **median** is 3.6 goals per game.

G. The maximum is 5.6 goals per game.

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What basic trigonometric identity would you use to verify that sin x cosxtanx = 1 - cosx?

a.

sinx

c. Sin x = cos x tan x

tanx =

COSX

b.

d. 1+tan²x = secºx

sinx

cosa

X=

tan x

### Answers

**Option A **is the correct answer. The identity used to verify the equation is** tanx=sinx/cos x.**

The trigonometric ratios which are **related **to each other by equations called **trigonometric identities**.

There is a basic **formula **in trigonometric to solve this equation:

**sin²x+cos²x=1.**

consider the given equation:

sin x. cos x.tanx=1-cos²x

Now, we have another formula which is

**tanx=sinx/cos x **

So, on substituting tan x in the left-hand side of the given equation we get:

**sin x. cos x.sin x/cos x**

Cancel common term from **denominator **and **numerator **which is cos x we get:

sin²x

And we have an identity:

sin²x+cos²x=1.

⇒**sin²x=1-cos²x**

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What is the distance between (8, -3) and

(4, -7)?

### Answers

**Answer:**

10.770

**Step-by-step explanation:**

1. naima has $40 to spend on refreshments

for herself and her friends at the movie

theater. each popcorn x is $5, and a small

drink y is $2. write an equation to model the

situation.

### Answers

If the price of each popcorn is $5 and small drink is $2 , then the **equation **to model the situation is 5x + 2y = 40 .

The amount that Naima spent on **refreshments** at movie theater = $40 ,

let the number of **popcorn **be = x ,

the price of each popcorn is = $5 ,

let the number of **small drink** is = y ,

the price of each small drink is = $2 ,

The situation can be represented by the equation ,

**Amount** = (price of popcorn)×(number of popcorn) + (price of small drink)×(number of small drink),

substituting the values ,

we get ,

5x + 2y = 40 .

Therefore , the equation that models the above situation is 5x + 2y = 40 .

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The table has two functions, one given by an equation and the second represented by a graph. Let's find the unit rates and y-intercepts of the

two functions and compare them.

Part A

What are the unit rates for function I and function II?

### Answers

**Answer:**

the greater unit rate is 2 and the greater y-intercept is 6

**Step-by-step explanation:**

did the test

What does Squealer symbolize?

### Answers

Squealer is a character in George Orwell's novel "**Animal Farm**," and he symbolizes the propaganda and manipulation of information that is used by those in power to maintain control and deceive the public.

**Squealer** is a pig who serves as a spokesperson for the pig leaders of the animal rebellion on the farm. He is skilled at using language and rhetoric to persuade the other animals to accept the decisions of the pigs, even when those decisions go against their own interests.

Squealer is able to convince the animals that the pigs are acting in their best interests and that any apparent contradictions or inconsistencies in their actions are necessary for the good of the farm. In this way, Squealer **symbolizes **the way that propaganda and manipulation of information can be used to justify and maintain oppressive systems.

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Why does a green leaf appear green in day light but dark in red light?

### Answers

A **green leaf** can only reflect green **wavelength**. when it put on red light it appears **dark** because in red light leaf is not able to reflect any light so it looks dark.

In the day light the** green leaf** absorbs all constituents light colors of white except green. It means the leaf absorbs all **wavelengths **of colors that are violet, indigo, blue, yellow, orange, red but not green. Since the green light alone is reflected thus leaf appears green. Under the red light all colors including the green are absorbed in the red color. Hence the leaf appears as dark. in the **red light**, the leaf will absorb the light and it appears dark. All the objects absorb all the colors present in the sunlight or from any source of white light and reflect the color ray of particular color of the object. It is the property of all the colored objects. So all the objects appear in some color. here green leaf absorbs the colors from sunlight.

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Can somsone help me with the questin fast?!?!?!

### Answers

**Answer:**

3rd option: 118 < 0.20p + 18 < 218

**Step-by-step explanation:**

The answer is between 118 and 218:

a=answer

118 < a < 218

Now solve fo a:

Since the charge is $18 plus $0.20/kilowatt hour, the result cost is

18 + 0.20p ==> p=kilowatt hour and 0.20p is the cost per kilowatt hour

Hence, a=18 + 0.20p

Hence, the answer is 118 < 18 + 0.20p < 218 ==> plugin 18 + 0.20p for a

118 < 18 + 0.20p < 218 ==> **118 < 0.20p + 18 < 218**

If a mixture of ne and ar has a total pressure of 1. 5 atm at 296 k in a 0. 5 l container, what is the partial pressure of ne if ar is present in a mole fraction of 0. 34?.

### Answers

The **partial pressure** of ne in the mixture is approximately 0.99 atm.

The partial pressure of a gas in a mixture is equal to the total pressure of the mixture multiplied by the **mole fraction** of the gas.

The mole fraction of a gas in a mixture is equal to the number of moles of the gas divided by the total number of **moles** of all the gases in the mixture.

The partial pressure of a gas is the pressure that the gas would exert if it were alone in the container at the same temperature as the mixture. The total pressure of a mixture of gases is equal to the sum of the partial pressures of the individual gases.

In this case, the mole fraction of ne is (1 - 0.34) = 0.66, since the mole fraction of ar is 0.34.

The partial pressure of ne is therefore given by:

Pne = Ptotal × Xne

= 1.5 atm × 0.66

= 0.99 atm

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What does the positive (+) charge indicate (mention specific subatomic particles in your answer)?.

### Answers

An atom is** positively charged **and therefore is referred to as a cation if one or more of its electrons have been lost. The charge of protons is positive (+).

Explain the term subatomic particles?

A particle that is smaller than just an atom is what is known as a subatomic particle.

Protons, electrons, as well as neutrons are the three subatomic particles that make up an atom in most cases.Because they are the tiny particles which it make up atoms, protons, neutrons, and electrons are collectively referred to as **subatomic particles. **"Sub" stands for beneath or lesser. These subatomic particles are shorter than atoms because they are classified as such. Protons and neutrons are bound together to form the nucleus of an atom.

An atom is positively charged and thus is referred to as a** cation** if one or more of its electrons have been lost. The charge of protons is positive (+).

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Which of the following statements is true about the product of the sum and difference of two binomials?

a. The product is the square of the first term plus the square of the second term

b. The product is the square of the first term minus the square of the second term

c. The product is twice the product of the first term plus twice the product of the second term

d. All of the above

### Answers

The** product of the sum** and difference of** two binomials **is given by the formula (a+b)(a-b) = a^2 - b^2. This means that all three statements (a, b, and c) are true.

The **product of the sum **and **difference** of **two binomials** (a+b)(a-b) can be expanded as follows:

a+b = (a + b)

a-b = (a - b)

(a + b)(a - b) = a^2 - b^2

This can be rewritten as:

The product is the square of the first term plus the square of the second term (a^2 + b^2)

The product is the** square of the first term** minus the square of the second term (a^2 - b^2)

The product is twice the product of the first term plus twice the product of the second term (2ab)

Therefore, all three statements are true, making the correct answer D. All of the above.

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What is a solution n+8.3+n-7.53

### Answers

**Answer:**

It is not clear what equation or problem you are trying to solve. Could you please provide more context or clarify what you are asking?

Are you trying to find the solution to the equation "n + 8.3 + n - 7.53 = 0"? If so, the solution would be the value of n that makes the equation true. To find this value, you can simplify the equation by combining like terms and solving for n.

Simplifying the equation gives: 2n + 0.77 = 0

Subtracting 0.77 from both sides gives: 2n = -0.77

Dividing both sides by 2 gives: n = -0.385

So the solution to the equation is n = -0.385.

**Step-by-step explanation:**

What is the range of the given function {( 2 0 4 3 2 9 0 5 5 7 )}?

### Answers

The range of the given **function **is from 0 to 9, as the highest value is 9 and the lowest **value **is 0.

The **range **of the given function is determined by subtracting the lowest value from the highest value. In this case, the highest value is 9 and the **lowest value** is 0, giving us a range of 9 - 0 = 9. This means the range of the given function is from 0 to 9. This makes sense since all of the values in the function are between 0 and 9. It is important to note that the range of a function is determined by the **extreme values,** not necessarily the average value of the function. Therefore, even if the values in the **function **are more clustered around a certain point, the range will remain the same as long as the extreme values remain the same. Understanding the range of a function is an important concept in mathematics that can help us better understand the behavior of functions.

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A greeting card has a perimeter of 80 centimeters and an area of 384 square centimeters what are the dimension of the greeting card

### Answers

If the perimeter of the **greeting card** is 80cm and area 384 cm² , then the **dimensions **of the greeting card is 24 cm by 16 cm .

The **Perimeter **of the greeting card is = 80 cm ,

the **area **of the greeting card is = 384 cm² ,

let the **length **of the greeting card be = l ,

and **width **of the greeting card be = w ,

So , by perimeter , the equation is ⇒ 2(l + w) = 80 ,

and l×w = 384 ⇒ l = 384/w ,

on substituting the value ,

we get ,

384/w + w = 40

384 + w² = 40×w

w² - 40w + 384 = 0

On solving the quadratic equation ,

we get ,

w = 24 and w = 16

Substituting w = 24 , we get l = 384/24 = 16 ,

Substituting w = 16 , we get l = 384/16 = 24 ,

Therefore , the dimensions of the greeting card is length = 24 cm and width = 16 cm .

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A sample of n sludge specimens is selected and the ph of each one is determined. the one-sample t test will then be used to see if there is compelling evidence for concluding that true average ph is less than 7. 0. what conclusion is appropriate in each of the following situations?.

### Answers

The **average pH** is equal to **7**, according to the question.

What do you mean by average pH?

A good **balance** of acidity and alkalinity is something that the human body is designed to do on its own. A **crucial part **of this **process** is played by the kidneys and lungs. On a scale of 0 to 14, where 0 is the most **acidic** and 14 is the most basic, a normal blood **pH** level is between 7.35 and 7.45.

**According to the question,**

Here **null hypothesis** is given,

H0= Hph = 7.0

Ha= Hph < 7.0

a) n= 6, t=-2.9, ∝=0.05

t>tc

Here **statistic** is greater than the absolute critical value

Hence, H0 is **rejected**

b) n=19 t=-3.5 ∝=0.01

t0.01,18 = -2.552

|t| > tc

True average ph>7

Here again absolute value of t is greater than **critical value**

Hence, H0 is **rejected**

c) t0.05,18 =-1.734

|t|> tc

Here, **modulus** is greater

Hence, H0 is **rejected**

d) n=5 t=0.9 ∝=0.05

t0.05,4= -2.132

|t|<tc

Here, **absolute value** is less than the critical value

Hence, **H0** is accepted

Therefore, **Average** pH=7

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Two parents who are both bb for a gene are crossed. what will the genetic makeup of all offspring be? (use the punnett square if needed)bbxbb punnett square question 4 options: bb bb bb ab.

### Answers

The parents' offspring's **genetic makeup** All BB x BB progeny will be BBs. When two parents with both BB genes are crossed, the result is an offspring with the BB genotype.

What is genotype ?An organism's **genotype **is made up of all of its genetic components. The alleles or variations that an individual carries in a specific gene or genetic region are also referred to as the genotype.A gene is a small DNA fragment. Genes instruct the body on how to produce particular proteins. Each cell in the human body contains roughly 20,000 genes. Together, they form the structure and operation of the human body. A person's genotype is their unique genetic composition.A **blood **genotype reveals the complete genetic composition of a person's blood. There are typically five unique blood genotype types. Your genotype serves as a set of instructions for how your body will grow and develop.

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What were the 2 sides and who belonged to each side in WWI?

### Answers

During **World War I**, the two main sides were the Allies (a coalition of countries including France, Great Britain, Russia, Italy, the United States, and Japan) and the Central Powers (a coalition of countries including Germany, Austria-Hungary, and the Ottoman Empire). Other countries, such as Belgium and Serbia, were also involved in the war but were not formally allied with either side.

World War I was a global conflict that took place from 1914 to 1918. The two main sides in the war were the Allies and the **Central Powers**.

The Allies were a coalition of countries that included:

FranceGreat BritainRussia (until 1917)Italy (from 1915)United States (from 1917)Japan (from 1914)

The Central Powers were a coalition of **countries** that included:

GermanyAustria-HungaryOttoman Empire (now Turkey)There were other countries that were not formally allied with either side but were involved in the war, such as Belgium and Serbia.

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The width of our local galactic group, which includes our very own milky way galaxy and the other 52 galaxies "nearby," is 4 * 10 the the 22nd meters. the estimated width of the universe is roughly 9 * 10 the the 26th meters. about how much wider is the universe than our local galactic group?

### Answers

**Universe** is** ****2.25 × **[tex]10^4[/tex] times much **wider** than our local **galactic group**

What is milky way?

The** Milky Way** galaxy, that includes our **solar system**, gets its name from how it looks in the night sky from **Earth**: a hazy band of light composed of **stars** that are too near together to be seen individually.

Given data:

Width fo **galactic group** = 4 * [tex]10^2^2[/tex] meters .

Width of **universe** = 9 * [tex]10^2^6[/tex] meter

let the width our **galactic group** be x times than that of **universe**

so x * Width fo** galactic group** = Width of **universe **

=> x * 4 * [tex]10^2^2[/tex] meters = 9 * [tex]10^2^6[/tex] meters

=> x = 9/4 * [tex]10^2^6^-^2^2[/tex]

=> x = **2.25 * **[tex]10^4[/tex]** **

so **universe** is **2.25 * **[tex]10^4[/tex] times greater than our local **galactic group.**

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(a b)2 = 1a2 2ab 1b2 (a b)3 = 1a3 3a2b 3ab2 1b3 how are binomial expansions related to pascal’s triangle?

### Answers

The **binomial expansions** for the given expressions [tex](a-b)^{2} = 1a^{2} + 2ab + 1b^{2} and (a-b)^{3} = 1a^{3} + 3a^{2}b+ 3ab^{2} + 1b^{3}[/tex] are related to the pascal's triangles 3rd and 4th rows.

What is binomial expansion?

An expression that has been raised to any** finite power **can be expanded using the binomial theorem known as binomial expansion. A useful expansion technique with applications in probability, probability theory, and algebra is the binomial theorem.

Who is pascal's triangle named after?

The triangle is named after the French mathematician and philosopher Blaise Pascal (1623–1662) who, in his dissertation Traité du triangle arithmétique (Treatise on Arithmetical Triangle), published the first structured study on the characteristics and uses of the triangle in 1653.

Pascal's triangle is a triangular array of numbers that can be used to help expand binomials. Each number in the triangle is the sum of the two numbers directly above it. The first row of the triangle consists of a single 1, and each subsequent row begins and ends with a 1, with the other numbers being the sum of the two numbers directly above it.

For example, the first few rows of Pascal's triangle look like this:

1

1 1

1 2 1

1 3 3 1

1 4 6 4 1

To use Pascal's triangle to expand a binomial, you can start by writing out the terms of the binomial, with a blank space for each coefficient. Then, you can fill in the blanks using the numbers from Pascal's triangle. For example, to expand (a + b)^3, you can write out the terms like this:

(a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3

Then, you can fill in the blanks using the numbers from Pascal's triangle:

(a + b)^3 = 1a^3 + 3a^2b + 3ab^2 + 1b^3

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**Answer:**

**The coefficients of the terms come from rows of the triangle.If the exponent isn, look at the entries in rown.**

**Step-by-step explanation:**