Divide using synthetic division

[tex]x^4-3x^3-7x+1[/tex]÷[tex]x+2[/tex]

The **quotient **and **remainder** are x³ -5x² + 10x - 17 and 55.

What is **Synthetic division**?

When the divisor is a** linear factor**, synthetic division is a technique used to carry out the division operation on **polynomials**.

Here, (x+2) is a **linear factor **which indicates that synthetic division can be applied.

So, we will **divide **the x^4 - 3x^3 - 7x + 1 by x+2.

(refer the attached solution)

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What is the median of 35 27 51 31 28 19 33?

**Answer:**

31

**Step-by-step explanation:**

What is the median of 35 27 51 31 28 19 33?

Median: center most value when values are arranged in numerical order so:

19 , 27 , 28 , **31** , 33 , 35 , 51

How do you know if an equation is consistent and independent consistent and dependent or inconsistent?

Now, when a system has at least one solution, it's called **consistent**. When it has only one solution, it's called **independent**. otherwise inconsistent

The classification which best describes the **system **of equations is; Consistent and dependent

A linear or **nonlinear **system of equations as the case may be is termed consistent if there is at least one set of values for the unknowns that satisfies each equation in the system. In essence, when substituted into each of the equations, they make each equation hold true.

Additionally, the system of **equations **is dependent because the value of each variable is dependent on the others.

Now, when a system has at least one solution, it's called consistent. When it has only one solution, it's called **independent**.

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Cuánto es?

35

— –1

10

**Answer:**

145

**Step-by-step explanation:**

Cuánto es means what is the answer

35 - (-110)

Two negative signs equal a positive sign

35 + 110 = 145

How do you find the domain of A?

Take the function y = f(x), with the independent variable x as well as the dependent variable y, to determine the **domain **of a. If a value for x successfully enables the creation of a single value y using another value for x, it is said to be in the domain of the function f.

The collection of all potential inputs for a function is its domain.

For instance, the domain of f(x)=x2 and g(x)=1/x are all real integers with the exception of x=0.

The set of numbers x for which a function is defined in a valid manner is known as the domain of the **function**.

A function's domain is referred to as a closed interval if it is specified across the interval a ≤ x ≤ b.

So, to find the domain of a, consider the function y = f(x), which has the independent variable x and the dependent variable y.

A value for x is said to be in the domain of a function f if it successfully allows the production of a single value y using another value for x.

Therefore, take the function y = f(x), with the independent variable x as well as the dependent variable y, to determine the domain of a. If a value for x successfully enables the creation of a single value y using another value for x, it is said to be in the domain of the function f.

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How do you check the function is continuous or discontinuous?

A function is **continuous **if it is defined for all values of the independent variable and there are no breaks, jumps, or gaps in its graph. In other words, a function is continuous if you can draw its graph without lifting your pen from the paper.

To check whether a function is continuous at a particular point, you can use the following methods:

The two-part definition of **continuity**: A function is continuous at a point if the following two conditions are met:

The limit of the function as it approaches the point from the left and the right exists and is equal to the function's value at that point.

The **function **is defined at the point.

The Epsilon-Delta definition of **continuity**: A function is continuous at a point if, for every epsilon (a small positive number) there exists a delta (also a small positive number) such that, for all points x within delta units of the point in question, the function's value at x is within epsilon units of the function's value at the point.

The **graph **of the function: You can also check the continuity of a function by looking at its graph. If the graph is a continuous curve with no breaks or jumps, then the function is continuous. If the graph has breaks or jumps, then the function is discontinuous.

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The Epsilon-Delta definition of continuity states that a function is continuous at a point if there is an epsilon (a small positive number) and a delta (also a small positive number) such that the value of the function at x is within epsilon units of the value of the function at the point for all points x within delta units of the point in question.

The function's graph: Additionally, you can examine a function's graph to see whether it is continuous. The function is continuous if the graph displays a continuous curve without any interruptions or leaps. The function is discontinuous if the graph has breaks or jumps.

How do you find a prime number?

A prime number is a **positive **integer greater than one that has no positive integer divisors other than one and itself. To find if a number is prime or not, if a number is divide by any other positive number other than 1 and itself it is not a prime number.

A **whole number** higher than one that cannot be divided exactly by any other whole number than itself and one is a prime number.

Complete numbers, the range of numbers that includes zero and natural numbers and not a decimal or fraction.

8 is not a prime number because 8 is divided by 2 and 4 other than 1 and itself.

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A ditributor of computer oftware want to obtain ome cutomer feedback concerning it newet package. Three thouand cutomer have purchaed the package. Aume that 600 of thee cutomer are diatified with the product. Twenty cutomer are randomly ampled and quetioned about the package. Let X denote the number of diatified cutomer ampled. (a) Find the denity for X. (b) Find E[X] and Var X. (c) Set up the calculation needed to find P[X ? 3]. (d) Ue the binomial table to approximate P[X ? 3]

(a) The distribution of X is binomial with parameters n = 20 and p = 600/3000 = 1/5 since we are randomly selecting 20 clients without replacement and interested in the proportion of happy consumers. Given below is the probability density function for this **binomial distribution**.

f(x) is equal to (n pick x) * p * x * (1-p) (n-x)

Where p and 1-p are the probability of success and failure, respectively, and n pick x is the binomial coefficient, which is equal to n!/(x! * (n-x)!).

(b) The formula for the anticipated value of X, or E[X], is

E[X] = **np **= 20 * (1/5) = 4

Var X, the variance of X, is defined as follows:

Var X = np(1-p) = 20*1/5*4/5=3.2

(c) The **cumulative distribution function** of the binomial distribution's formula can be used to get P[X >= 3]:

Sum(i=3 to n) f for P[X >= 3] (i)

Summarizing from I = 3 to 20 and substituting the values from the density function, we obtain:

Sum(i=3 to 20) = P[X >= 3] [(20 pick I (1/5)*i*4/5*(20-i)]

(d) We must determine the value of the **cumulative distribution function** at x = 3, which is equivalent to the likelihood of receiving three or fewer successes out of 20 trials, in order to approximate P[X >= 3] using the binomial table. By using n = 20 and p = 1/5 to calculate the value of the cumulative distribution function at x = 3 in the binomial table, it is possible to determine this probability. P[X >= 3]'s estimated value is 0.586.

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Is 8 a multiple yes or no?

Therefore , the solution to this problem is yes 8 has **multiple** which are 16,24,32 etc.

A multiple in mathematics refers to the product produced by multiplying two numbers or **variable**. In this instance, the number 7 is multiple by 56.

The **expression** is termed as multiple .Fun Facts is an additional example of multiples. 0 is a multiple of all numbers since it produces zero when multiplied by any other number.

Here,

There are eight multiples: 8, 16, 24, 32, 40, 48, 56, 64, 72, and so on.

There are two consecutive results in this sequence, and there is an 8-digit gap between each subsequent number and the one before it.

The results of multiplying any integer by other natural numbers are known as multiples.

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Can a 4 year old count to 100?

Yes, a 4 year old can typically **count** to 100.

Counting is the process of determining the number of elements in a given set or group of objects. Counting is a basic **numerical skill** that is used in mathematics and other fields. It involves recognizing patterns and comparing numbers to identify how many items are in a given set. Counting is an important part of early childhood education, as it introduces children to the concepts of number and quantity.

Depending on the child's exposure to numbers, they may be able to count even higher. Counting to 100 is a fundamental skill that can be developed through practice and repetition. Teaching a 5 year old to count to 100 can be done through activities such as counting **objects**, counting steps, and playing counting games.

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Which is a graph of y 3x âˆ’ 1?

The graph of y=3x-1 will be a **straight **line that does not passes through origin.

A line is a geometry object that extends on both sides and is defined by zero width. Simply put, a straight line is a line devoid of bends. A straight line is one that has no **curves **and continues to infinity on both sides.

ax+by=c is the standard form of straight line.

A straight line serves as the visual representation of a linear function's graph.

The given function is as follows:

y=3x-1

A linear function looks like this:

y=mx+c

Where:

m=3: the slope

c=-1: the y-intercept

So given function has a different y-intercept than 0.

So, the resulting graph o does not cross through the origin.

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What is an example of an inverse variation equation?

y = 3/x **equation** is an example of** inverse variation **between the variables x and y .

Now, According to the question:

The **equation** with the inverse variation between the variables 'x' and 'y' .

Inverse variation is the relationships between **variables** that are represented in the form of y = k/x, where x and y are two variables and k is the constant value.

y = 3/x is an example of inverse variation.

Hence, y = 3/x equation is an **example** of inverse variation between the variables x and y .

Let's know:

What is an** Inverse variation **equation?

Inverse variation is the relationships between variables that are represented in the form of y = k/x, where x and y are two variables and k is the constant value. It states if the value of one quantity increases, then the value of the other quantity **decreases**.

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What is the value of b2 4ac for the following equation 2x2 2x 1 0 4120?

The **value **of b2 - 4ac for the **equation **2x2 + 2x - 1 = 0 is 12.

The equation 2x2 + 2x - 1 = 0 can be written in the form ax2 + bx + c = 0, where a = 2, b = 2 and c = -1. The formula for **calculating **b2 - 4ac for this equation is

[tex]b2 - 4ac = (b2) - (4)(a)(c)= (2)2 - (4)(2)(-1)= 4 - (-8)= 12[/tex]

Therefore, the** value** of b2 - 4ac for the equation 2x2 + 2x - 1 = 0 is 12.

To calculate this value, the formula first finds the value of b2, which is the square of the **coefficient** of the x-term (2). Then it multiplies the coefficient of the x2-term (2) by the constant term (-1), and multiplies the result by 4. Finally, it subtracts the result of this **multiplication** from the value of b2.

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simplify 2√12+3√48-75

To simplify this expression, we can start by simplifying the **square roots**:

2√12 + 3√48 - 75

= 2√(12) + 3√(48) - 75

= 2√(43) + 3√(412) - 75

= 2√4 * √3 + 3√4 * √12 - 75

= 2 * √3 + 3 * √12 - 75

We can then combine like terms:

= 2 * √3 + 3 * √12 - 75

= (2 * √3 + 3 * √12) - 75

= 5 * √12 - 75

Finally, we can simplify the expression to get our final answer:

= 5 * √12 - 75

= 5 * 2√3 - 75

= 10√3 - 75

= -75 + 10√3

= -75 + 10√3

So the simplified expression is **-75 + 10√3.**

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The equation P = 0.00892t^2 + 1.1149t + 78.4491 models the

United States population, P, in millions since 1900. If t

represents the number of years after 1900, then what is

the estimated population in 2025 to the nearest tenth of a

million?

343.9

219.0

356.9

217.8

The **estimated** **population** in 2025 is 356.9

**What is estimation ?**

In math, **estimating** can be used to roughly calculate an answer (getting a "rough response") or to verify its **accuracy** (getting the "proper answer"). Even when **estimating** large **numbers** or decimal **numbers**, you shouldn't need to utilize a calculator or other documented techniques.

**Estimation** is frequently performed by sampling, which involves counting a small sample of a given thing and **extrapolating** that **number** to a wider **population**. Calculating the **number** of sweets of a particular size that are contained in a glass jar serves as an illustration of **estimation**.

There are 125 years from after 1900 to 2025

P = 0.00892t^2 + 1.1149t + 78.4491

P= (0.0089x125x125)+(1.1149x125)+78.4491

=139.0625+139.3625+78.4491

=356.87

=356.9

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boulder is flung out of the top of a 3,000 m tall volcano. The bouIders height, y, in meters, is a function of the horizontal distance it travels, x, in meters. The slope of the line representing the volcano's hillside is -5/3 At what height above the ground will the boulder strike the hillside?

Using the **linear function** y = -5/3x + 3000, the boulder will touch the ground at 1800m

A** linear function** has one independent variable and one dependent variable. The independent variable is x and the dependent variable is y.

A model of a linear function is given as y = mx + c

where m is the slope or rate of change of the function and c is the constant value or **y - intercept**

In this function;

The** slope **is - 5/3 and the constant is 3000

The** linear function** can be written as

y = -5/3x + 3000

The height at which the boulder will strike the ground, the value of y = 0

0 = -5/3x + 3000

5/3x = 3000

x = 1800

The point is at 1800m

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What is the y-intercept of y =- 5x?

**Y- intercept** for the line y = 5x is 0. This can be get from the standard equation for a line.

For the The **standard equation** for a line is,

** y = ax + b **

y is called the dependent variable because its value depends on the value of x

a is the **slope** of the line

x is called the independent variable because it can be any value

b is the y-intercept

Here y is a **function** of x. You could simply write it as y = 5x. Thus if we compare to the standard form equation y = ax + b, a=5 and b=0. Thus the y-intercept is zero. The reason that this is the case is that when you set x=0 the value is plotted on the** y axis** because the equation for the y axis is the line defined by x=0. Any value in the x, y plane where x is equal to zero plots on the vertical line going through (0,0) or in other words the** **y axis.

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A water pail in your backyard has a small hole in it. You notice that it has drained a total of 2.5 liters in 4 days. What is the average change in water volume each day?

The average change in water volume is (answer here)iter(s) per day.

The **average change** in the volume of water per day is **obtained **as 0.625 litres.

The **rate change **of **volume **is the change of volume with **respect **to **time**.

For **instantaneous **change the **derivative **of the **expression **of volume can be taken.

The average **change **in the **volume **of **water **can be obtained as follows,

Average change = Volume of water ÷ Number of days

= 2.5 ÷ 4 = 0.625

Hence, the average change in **water** **volume **is given as 0.625 **liters **per **day**.

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Find the indicated z-scores shown in the graph The graph is bell shaped, both ends are shaded. The number on the right is 0.0322 and the number on the left is 0.0322. The z-scores are (____,_____) use comma to seperate answers as needed. Round to two decimal places as needed

The z-**scores **are (-1.85, 1.85)

An **illustration **of a standardised score is the z-**score**. A z-score calculates how far a **data **point **deviates **from the **distribution's **mean by standard deviation.

If a Z-score is 0, it indicates that the data **point's **score is **identical **to the **mean **score

Given:

If we look at the z score table we will get the value of z- score.

The value 0.0322 lies in **horizontal **row 1.8 and **column **0.05.

Then, for **left **value 0.0322 is -1.85

and, for **right **value 0.0322 is 1.85.

Hence, the z-**scores **are (-1.85, 1.85)

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23.From the following information, prepare trading account for the year ended 31st March, 2013 Cash purchases Rs. 4,50,000; credit purchases Rs. 27,00,000; returns inward Rs. 60,000; cash sales Rs. 4,80,000; credit sales Rs. 33,00,000; returns outward Rs. 30,000; freight inwards Rs. 9,000; carriage inwards Rs. 9,000; wages and salaries Rs. 12,000; opening stock Rs. 4,50,000; closing stock Rs. 2,64,000 but its market value is Rs.2,52,000

The **table **showing trading account is given below

he trading **account **gives details of total sales, total purchases and direct expenses relating to** purchase** and sales. Trading account format for the year **contains** Particulars, Amount, Dr., Cr., Purchases, Sales, etc.

Given here,

Particulars Amount

**Cash** purchases Rs.4,50,000

**Credit** purchases Rs.27,00,000

**Returns **inwards Rs.60,000

**Cash** sales Rs.4,80,000

**credit** sales Rs.33,00,000

**Returns** outward Rs.30,000

**freight** inwards Rs.9000

**carriage** inwards Rs.9000

**Wages** and salaries Rs.12000

**Opening** stock Rs. 4,50,000

**closing** stock Rs. 2,64,000

**Market **value Rs.2,52,000

Hence the trading **account** for the year ended 31st March, 2013 is given above

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Calculate. Then, write a situation to match this expression and explain what 48.78 ÷ 0.9 the quotient means in your situation.

**Answer:**

Calculate: **48.78/0.9 = 54.2**

Write a situation: **Richard has 48.78 ounces of grape juice that he wants to ration out for his friends at his birthday party. Each cup the friends get can hold 0.9 ounces of grape juice. **

What does the quotient mean: **The quotient, 54.2, means that Richard had given 54.2 ounces of grape juice to all of his friends combined.**

determine the 2.5th percentile of the normal distribution with a mean of 72.5 and a standard deviation of 15 as a decimal rounded to the nearest tenth.

**Answer:**

43.1

**Step-by-step explanation:**

2.5 % = .025 look for this value on the z-score table to find this corresponds to z = - 1.96 Standard Deviations

72.5 - 1.96 * 15 = 43.1

Olivia is going on a 490 mile journey. So far, she has travelled 1% of her journey. How many miles has she travelled

**Answer:**

4.9 miles

**Step-by-step explanation:**

(.01)(490)=4.9

What is the function of f and G?

**Answer:**

f(x) and G(x)

**Step-by-step explanation:**

When you want to write a function of something, you can write it as the letter followed by "(x)"

How can you determine if the two angles are congruent by AAS A?

By using the the application of **ASA **we can determine the two angles are **congruent **by AAS.

AAS stands for Angle-Angle-Side. When two angles and a non-included side of a **triangle **are equal to the corresponding **angles **and sides of another triangle, then the triangles are said to be **congruent**.

AAS congruence can be proved in easy steps.

Suppose we have two triangles ABC and DEF, where,

Diagram attaches at the end of the solution.

∠B = ∠E [Corresponding angles]

∠C = ∠F [Corresponding angles]

AC = DF [Adjacent sides]

By angle sum property of triangle, we know that;

∠A + ∠B + ∠C = 180 ………(1)

∠D + ∠E + ∠F = 180 ……….(2)

From equation 1 and 2 we can say;

∠A + ∠B + ∠C = ∠D + ∠E + ∠F

∠A + ∠E + ∠F = ∠D + ∠E + ∠F [Since, ∠B = ∠E and ∠C = ∠F] ∠A = ∠D

Hence, in **triangle **ABC and DEF,

∠A = ∠D

AC = DF

∠C = ∠F

Hence, by **ASA congruency**, (AAS: the application of ASA)

Δ ABC ≅ Δ DEF

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for a ride on a rental scooter, bob paid an fee to start the scooter plus cents per minute of the ride. the total bill for bob's ride was . for how many minutes did bob ride the scooter?

The **total **cost for Bob's ride is C = x + m and no. of **minutes **of the ride is

m = C - x.

What is a numerical expression?A mathematical statement expressed as a string of numbers and **unknowable variables **is known as a numerical expression. Statements can be used to create numerical expressions.

Given, A ride on a rental scooter, bob paid a fee to start the scooter plus cents per minute of the ride.

Let, '**x**' be the fee in cents to start the scooter and '**m**' be the no. of minutes of riding.

Therefore, The total bill(C) for Bob's ride is,

**C = x + m**.

The no. of minutes Bob ride the scooter is simply,

**m = C - x**.

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The probability that a person has immunity to a particular disease is 0.8. Find the mean number who have immunity in samples of size 17

The ** mean number** who have immunity in samples of size 17 is 13.6

Sample Size =17

Immunity to a Particular disease=0.8

=17*0.8

=13.6

The average of the numbers is the mean. Calculating is simple: add up all the numbers, then divide by the total amount of numbers. To put it another way, it is the total divided by the number. In mathematics and statistics, the concept of mean is crucial. The most typical or average value among a group of numbers is called the mean.It is a statistical measure of aTo learn more about **Mean** refer to:

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Which of the following equations represents a proportional relationship? A. x=2.9 B. x+y=2.9 C. y=2.5/x D. y/x=2.5

The equation that represents a **proportional relationship** is **y/X = 2.5.** That is **option D.**

A **proportional relationship** is the type of relationship that exist when between two variables which can be represented as y and x where a constant of proportionality exists between the two variables as k.

The relationship between these two variables can either be **directly proportional** or indirectly proportional.

The **relationship** that exists between X and y is a direct proportional relationship with a constant of proportionality of 2.5.

y = 2.5 X

= y/X = 2.5. Where 2.5 is the constant.

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How do you find the length of a rectangle when given the area?

we will find the length of rectangle when area is divided by** the breadth **of rectangle.

Some properties are rectangle are stated below:

1. rectangle has four right angles

2. rectangles has four sides and equal opposite sides which are parallel to each other.

3.rectangle has two diagonals which are similar in length.

which is the formula for finding the length?The bigger side lengths are called length and the smaller sides are called breadth of rectangle.

if area of rectangle is given, we can find length when area is divided by its **breadth.**

** **length = area/breadth

hence, length of rectangle is determined from the value of area and breadth.

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what is the biggest number to mankind?

**Answer:**

googolplex

**Step-by-step explanation:**

it just is

**Answer:**

A Googolplex

**Step-by-step explanation:**

It is written as 10^googol and 10^10^100

What is * in a math problem?

**Answer:**

it means multiply like the × symbol

**Step-by-step explanation:**

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