What are the quotient and remainder when 3x^(4)-x^(2) is divided by x^(3)-x^(2)+2?

Answer:

The two teachers are 26 meters apart. To calculate this, you can use the Pythagorean Theorem, which states that the distance between two points is equal to the square root of the sum of the squares of the differences between the coordinates of the two points. In this case, the coordinates of the math teacher are (10, 0) and the coordinates of the science teacher are (0, 24), so the distance between them is the square root of [(10-0)^2 + (0-24)^2] = √(100 + 576) = √676 = 26 meters.

We can use the Pythagorean theorem to solve this problem. Let's draw a diagram:

A (Amy)

/|

/ |

/ |10 meters

/ |

/____|

B C (science teacher)

We have a right triangle ABC, where AB = 10 meters and BC = 24 meters. We want to find the length of AC, which is the distance between the two teachers.

Using the Pythagorean theorem:

AC^2 = AB^2 + BC^2

AC^2 = 10^2 + 24^2

AC^2 = 676

AC = sqrt(676)

AC = 26 meters

Therefore, the two teachers are 26 meters apart.

Therefore , the solution of the given problem of function comes out to be the limit may not exist, if the function is not continuous at x = 0.

The mathematical discipline encompasses arithmetic, symbols, and their divisions, as well as histology, construction, and both real and imagined geographic places. A function describes the connections between various elements, which all have an associated outcome. A function is composed of an array of different parts that, when combined, result in particular outcomes for each input.

Here,

We must be aware of the precise function or expression under consideration in order to respond to this query.

The action as x moves towards zero from the negative direction can change depending on the function.

If a function is continuous at x = 0, then in general, if the function has a limit as x gets smaller from the downward direction, however this limit will be the same as the limit as x reaches zero from the positive direction.

The limit as x approaches zero from the downward direction may vary from the limit as x approaches zero from the better way, or the limit may not exist, if the function is not continuous at x = 0.

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The perpendicular line connecting points F and G results in the formation of a triangle with a 14 square unit surface area.

In mathematics, a coordinate is a set of numbers or symbols that describes an object's position or location in a geometric space. The most popular coordinate system is the Geographic coordinate system, which creates a grid on a surface or in three dimensions using a series of perpendicular lines. Each location on the plane or in space is then uniquely identified by an ordered pair or set of three numbers, respectively, that represent a point's distance from the origin along each of the coordinate system's axes.

Given that points F and G share the same x-coordinate, the line connecting them is perpendicular. A degenerate triangle with negative area will be formed by any point H that shares the same x-coordinate as F and G.

D = √((2-2)2 + (6-(-1),2) = √(49), which =  7.

distance(FH)/7  = 2/7.

distance(GH)/7  = 4/7

Distance(FH) / Distance(GH)  = 1 / 2.

The distance between any two points H(x, y) and F(2,6) or G(2,-1) can be calculated using the distance formula as follows:

distance(FH) is  =  √((x-2) + (y-6)).

Distance (GH) is  =  √((x-2) + (y+1)).

By changing the aforementioned values, we obtain:

√((x-2)**2**y+1**2)/7) = 4/7

(x-2)² + (y+1)² = 16

(x-2)² + (y-6) (y-6)² = 1/4 ((x-2)² + (y+1)²)

By condensing and extending, we obtain:

3(x-2)² + 13(y-6)² = 196

5(x-2)² + 25(y+1)² = 784

7(x-2)² + (y-6)² = 1

A triangle with a 14 square unit surface area is created when the perpendicular line joining F and G.

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Because it only covers those who are entering the sports centre, the survey will be prejudiced.

This means that the survey will only reflect the opinions of those who are likely to have positive perceptions of the sports facilities and who are interested in using them. It does not include the viewpoints of those who do not use or hold a poor opinion of the sporting facilities.

Those who don't use the facilities, for instance, could have bad perceptions of the sports centre if it is renowned for being pricey or challenging to get to. The survey will miss important information if it simply polls visitors to the sports centre.

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Without evaluating the expression, the sum of given expression is 80 is this why its even number.

Using letters or alphabets to represent numbers without giving their exact values is the idea behind algebraic expressions. The fundamentals of algebra taught us how to express an unknown value using letters like x, y, and z. These letters are referred to here as variables.

In an algebraic expression, both constants and variables can be used. Any amount that is added before a variable and then multiplied by it is referred to as a coefficient.

An algebraic expression in mathematics is one that contains variables, constants, and algebraic operations (addition, subtraction, etc.). Expressions are built upon terms.

Calculate the power: 81

Calculate the sum or difference: 81 - 1

Answer is 80

Thus, here we know that 80 is an even number.

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Answer:

y = (4/3)x + 2/3

The y-intercept is the value of y when x is equal to zero. So we can substitute x = 0 into the equation and solve for y:

y = (4/3)(0) + 2/3 = 2/3
The y-intercept of the line y = (4/3)x + 2/3 is 2/3.

Step-by-step explanation:

Answer:

The y-intercept is (2/3)

Step-by-step explanation:

I will assume that the equation is missing the "x," and will rewrite is as:

 y = (4/3)x + (2/3)

This is in standard form of y = mx + b, where m is the slope and b is the y-intercept.

The slope is (4/3) and the y-intercept is (2/3)

a) 6% of 34 is 2.04
b) 17 is 50% of 34

c) 18 is 30% of 60

d) 7% of 49 is 3.43.

a. To find 6% of 34, you can multiply 34 by 0.06 (which is the decimal equivalent of 6%): 34 * 0.06 = 2.04. So 6% of 34 is 2.04.

b. To find what percent 17 is of 34, you can divide 17 by 34 and then multiply by 100 to convert the decimal to a percentage: (17/34) * 100 = 50%. So 17 is 50% of 34.

c. To find what number 18 is 30% of, you can divide 18 by 0.30 (which is the decimal equivalent of 30%): 18 / 0.30 = 60. So 18 is 30% of 60.

d. To find 7% of 49, you can multiply 49 by 0.07 (which is the decimal equivalent of 7%): 49 * 0.07 = 3.43. So 7% of 49 is 3.43.

8. Unfortunately, I cannot see the number line that you are referring to, so I cannot provide an answer for this part of the question.

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The cost of admission for a group of 5 people is $200 dollars.

The cost of admission for a group of 5 people is given by the function C(p) = 40p, where p is the number of people in the group. To find the cost for a group of 5 people, we simply plug in 5 for p and solve for C:

C(5) = 40(5)
C(5) = 200

Therefore, the cost of admission for a group of 5 people is $200 dollars.

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A) The probability of at least one red ball being obtained is 1 - the probability of no red balls being obtained.

The probability of no red balls being obtained is (7/17)*(6/16)*(5/15)*(4/14)*(3/13) = 0.0096. Therefore, the probability of at least one red ball being obtained is 1 - 0.0096 = 0.9904.

B) The probability of two red balls and three black balls being obtained is (10/17)*(9/16)*(7/15)*(6/14)*(5/13) = 0.0909. The probability of one red ball and four black balls being obtained is (10/17)*(7/16)*(6/15)*(5/14)*(4/13) = 0.0216.
C) The probability of getting k red balls and (5-k) black balls is (10 choose k)*(7 choose (5-k))/(17 choose 5). This can be calculated for each value of k from 0 to 5 and summed to find the total probability.

For example, when k=0, the probability is (10 choose 0)*(7 choose 5)/(17 choose 5) = 0.0096. When k=1, the probability is (10 choose 1)*(7 choose 4)/(17 choose 5) = 0.0909. The total probability is the sum of these individual probabilities.

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The mean waiting time for these customers is 18.33 minutes.

The mean waiting time can be calculated by multiplying each waiting time by its frequency, summing up these products, and then dividing by the total number of customers.

In mathematical terms, the mean waiting time is:

Mean = (x1 * f1 + x2 * f2 + ... + xn * fn) / (f1 + f2 + ... + fn)

Where x1, x2, ..., xn are the waiting times, and f1, f2, ..., fn are the corresponding frequencies.

Using the data from the table, we can plug in the values and calculate the mean waiting time:

Mean = (5 * 2 + 10 * 4 + 15 * 6 + 20 * 8 + 25 * 10) / (2 + 4 + 6 + 8 + 10)

Mean = (10 + 40 + 90 + 160 + 250) / 30

Mean = 550 / 30

Mean = 18.33 minutes

Therefore, the mean waiting time for these customers is 18.33 minutes.

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Answer:

To divide £300 in the ratio of 10:20, we need to first add the two parts of the ratio to find the total number of parts:

10 + 20 = 30

This means that the ratio can be expressed as 10/30 and 20/30.

Next, we can use these ratios to find the amount of money for each part of the ratio:

10/30 x £300 = £100

20/30 x £300 = £200

Therefore, the amount of money for the parts of the ratio 10:20 would be £100 and £200 respectively.

The algebraic equation "4x = 22.2 - 1.9" could be used to find the price of one tire patch.

Mathematical equations with one or more variables and algebraic operations like addition, subtraction, multiplication, division, exponentiation, and roots are known as algebraic equations. By identifying the values of the unknown variables that fulfill the equation, these equations can be used to illustrate mathematical connections between variables and to solve issues.

Although algebraic equations can take many different forms, they often require utilizing the equal sign (=) to make one expression equal to another. For instance, the algebraic equation x + 2 = 7 shows the connection between the constants 2 and 7 and the unknown variable x.

The equation that could be used to find the price of one tire patch is:

4x = 22.2 - 1.9

This equation represents the total cost of the four tire patches (4x) subtracted from the initial balance on Rhyan's gift card ($22.20) and the remaining balance after the sale ($1.90).

Simplifying the equation, we get:

4x = 20.3

Dividing both sides by 4, we get:

x = 5.075

So the price of one tire patch is $5.075.

Therefore, the equation "4x = 22.2 - 1.9" could be used to find the price of one tire patch. None of the other equations listed would lead to the correct answer.

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Answer:

yo

Step-by-step explanation:

C and E

Answer:

Step-by-step explanation:

[tex]\angle 2,\angle AEG, \angle GEB[/tex]

The value οf the annuity after 120 depοsits is $1,059,780.64.

Cοmpοund interest is interest that is earned nοt οnly οn the principal amοunt but alsο οn any interest earned οn that principal amοunt οver time.

Tο determine the value οf the annuity, we can use the fοrmula fοr the future value οf an annuity:

[tex]A = P \times \dfrac{(1 + r/n)^{(nt)} - 1)}{(r/n)}[/tex]

where A is the future value οf the annuity, P is the mοnthly depοsit amοunt, r is the annual interest rate, n is the number οf times the interest is cοmpοunded per year, and t is the tοtal number οf depοsits.

In this case, P = $100, n = 2 (since interest is cοmpοunded semi-annually), t = 120, and r is the interest rate per year, sο we need tο find r. Tο dο this, we can use the fοrmula:

[tex]A = P\times (1 + r/n)^{(nt)[/tex]

where A is the future value of the annuity after t depοsits.

Substituting the given vaIues, we have:

[tex]\$100 \times (1 + r/2)^{(2\cdot120)[/tex] = A

SimpIifying, we get:

[tex](1 + r/2)^{240} = A/100[/tex]

Taking the natural lοgarithm of both sides, we get:

[tex]ln(1 + r/2)^{240} = ln(A/100)[/tex]

240*ln(1 + r/2) = ln(A/100)

ln(1 + r/2) = ln(A/100)/240

Solving for r, we get:

[tex]$r = 2 \times \frac{e^{(ln(A/100)}}{240) - 1}[/tex]

Substituting the given vaIues, we get:

r = 0.4902 or 49.02%

Now we can plug in all the values into the original fοrmula for the future value οf the annuity:

[tex]A = $100\times \dfrac{(1 + 0.4902/2)^{(2\cdot 120) - 1)}}{0.4902/2}[/tex]

SimpIifying, we get:

A = $1,059,780.64

Therefοre, the value οf the annuity after 120 depοsits is $1,059,780.64.

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The scale unit that James used to create scale drawing of school library is 1 inch = 6 feet.

A measurement scale used to represent actual dimensions in a model or drawing. Scales include units of measurement such as inches, feet, and meters, scale unit. A scale used to represent actual dimensions on a drawing or map. 

A scale map is a two-dimensional representation of a real-world object or place. Maps and floor plans are examples of scale drawings. The scale shows what the length on the scale drawing represents in actual length .

According to the question:

Given, 78 feet length of library is represented by 13 inch

Let, "x" be the number of feet that 1 inch represents.

∴ 13x = 78 feet

  ⇒x = 78/13

  ⇒x = 6

So, 1 inch equals 6 feet.

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Answer:

the answer would be 1 inch = 6 feet

Step-by-step explanation:

What is scale unit?

A measurement scale used to represent actual dimensions in a model or drawing. Scales include units of measurement such as inches, feet, and meters, scale unit. A scale used to represent actual dimensions on a drawing or map.

What is scale drawing?

A scale map is a two-dimensional representation of a real-world object or place. Maps and floor plans are examples of scale drawings. The scale shows what the length on the scale drawing represents in actual length .

Solution:

Given, 78 feet length of library is represented by 13 inch

Let, "x" be the number of feet that 1 inch represents.

∴ 13x = 78 feet

 ⇒x = 78/13

 ⇒x = 6

So, 1 inch equals 6 feet.

The option E. (3/2, - 1/2, - 3) is not a solution to the system of linear equations.

The system of linear equations given is:

3x + y + z = 1
2x + y - 4z = 2

The answer that is not a solution to this system is option. To check this, we can substitute (3/2, - 1/2, - 3) into the system and solve:
3*(3/2) + (-1/2) + (-3) = 1
2*(3/2) + (-1/2) - 4*(-3) = 2

After simplifying, we get 9/2 - 1/2 + 9/2 ≠ 1 and 9 - 1 - 12 ≠ 2, so option E. (3/2, - 1/2, - 3) is not a solution to the system of linear equations.

A system of equations is a set of two or more equations in which we will find unknowns.

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The function (fg)(x) is the product of the function f(x) and g(x) which is (fg)(x) = 24x² - 16x.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout calculation and are essential for the development of significant links.

The two functions are given below.

f(x) = 8x

g(x)= 3x - 2

The function (fg)(x) is calculated as,

(fg)(x) = f(x) · g(x)

(fg)(x) = (8x) × (3x - 2)

(fg)(x) = 24x² - 16x

The function (fg)(x) is the product of the function f(x) and g(x) which is (fg)(x) = 24x² - 16x.

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To solve the inequality -3 > (x)/(4) - 1, we need to isolate the variable x on one side of the inequality. We can do this by following these steps:

Step 1: Add 1 to both sides of the inequality to eliminate the constant term on the right side.
-3 + 1 > (x)/(4) - 1 + 1
-2 > (x)/(4)

Step 2: Multiply both sides of the inequality by 4 to eliminate the fraction on the right side.
-2 * 4 > (x)/(4) * 4
-8 > x

Step 3: Rewrite the inequality with the variable on the left side.
x < -8

Therefore, the solution to the inequality is x < -8.

Note: When multiplying or dividing an inequality by a negative number, the inequality symbol must be reversed. However, in this case, we multiplied by a positive number (4), so the inequality symbol remains the same.

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a) The probability of rolling a Yahtzee is 0.00077

b) The probability of rolling either a small straight or a large straight is 0.1389

Given data:

(a)

To calculate the probability of rolling a Yahtzee on the first round, we need to determine how many outcomes correspond to a Yahtzee and divide it by the total number of possible outcomes when rolling five dice.

A Yahtzee occurs when all five dice show the same number. There are 6 possible outcomes (each number from 1 to 6), and each outcome has only 1 way of occurring. So, there are 6 ways to roll a Yahtzee.

The total number of possible outcomes when rolling five dice is 6^5 (since each die has 6 sides).

Probability of rolling a Yahtzee = (Number of Yahtzee outcomes) / (Total number of outcomes)

[tex]= \frac{6} {6^5}[/tex]

≈ 0.00077 (rounded to 5 decimal places)

(b)

In the second round, you have (2, 3, 4, 6, 6). In the third round, you choose to re-roll both sixes.

A small straight is when you have four consecutive numbers among the dice (e.g., 1, 2, 3, 4, or 2, 3, 4, 5, or 3, 4, 5, 6).

There are three possible small straights: (2, 3, 4, 5), (3, 4, 5, 6), and (1, 2, 3, 4). Each of these outcomes has only one way of occurring.

A large straight is when all five dice are in a row (e.g., 1, 2, 3, 4, 5 or 2, 3, 4, 5, 6).

There are two possible large straights: (1, 2, 3, 4, 5) and (2, 3, 4, 5, 6). Each of these outcomes has only one way of occurring.

Total favorable outcomes (small straights + large straights) = 3 + 2 = 5

Total number of possible outcomes when re-rolling two dice = 6^2 = 36

Probability of rolling either a small straight or a large straight = (Number of favorable outcomes) / (Total number of outcomes)

[tex]=\frac{5}{36}[/tex]

≈ 0.1389 (rounded to 4 decimal places)

Hence, the probability that you roll either a small straight or a large straight after re-rolling the dice is approximately 0.1389.

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It will take 4 years for an investment to double if it is continuously compounded at 18% per year.

The time it takes for an investment to double if it is continuously compounded at 18% per year can be calculated using the formula:
T = ln(2)/r

Where T is the time in years, ln(2) is the natural logarithm of 2, and r is the annual interest rate.

Substituting the given values into the formula, we get:
T = ln(2)/0.18
T ≈ 3.85 years

Therefore, to the nearest year, it will take approximately 4 years for the investment to double if it is continuously compounded at 18% per year.

A neperian logarithm or also known as a natural logarithm, refers to that logarithm that has e as its base, which is worth: 2.718281828.

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Answer: 119.32 centimeters

Step-by-step explanation:

Circumference = diameter x π

C = 38 (3.14)

C = 119.32

The circumference is 119.32 centimeters

Hope this helps!

Answer:

1. [tex]75[/tex]

2. [tex]4x^{8}[/tex]

3. [tex]128[/tex]

Step-by-step explanation:

[tex]\frac{3*5^9}{5^7}=\frac{3*5^2*5^7}{5^7}=3*5^2=75[/tex]

[tex]\sqrt{16x^{16}}=4\sqrt{x^{16}} =4x^8[/tex]

[tex]\frac{(-5)(2^8)}{-6+1}/2=\frac{(-5)(2^8)}{(-5)(2)}=\frac{2^8}{2}=2^7=128[/tex]

81-100. ------2

1-20----------2

21-40---------4

41-60----------1

61-80----------1

Answer: A: 20,40,120

Step-by-step explanation:

Angle A is smaller than Angle B as it is less than 1 time as big as it.

The list of angles from smallest to largest is C, A, and B.

120 x (1/3) = 40

20 < 40

Hope this helps!

Answer:

hi

Step-by-step explanation:

this is the answer

hope this helps

good luck;)

According to the above, the statement that is true about the expression can be inferred: Since the factor of 5/6 is less than 1, the product of 8 * 5/6 will be less than 8. Additionally, the measure of the giant mouse would be 0.76 meters.

To find the correct statement about the fractions we must analyze each of the statements and check it according to the multiplication information. According to the above, we can establish that the factor of 5/6 is less than one because the division of these two numbers results in a number less than 1.

So each number that we multiply by this fraction will give a result less than the same number. In this case if we multiply 8 by this fraction it would give us 6.66

On the other hand, if we want to know the height of the giant mouse, we must establish what the size of the Chihuahua is. So we develop the fraction 2 1/3 = 2.33

To find the height of the giant mouse we must divide the height of the chihuahua by 3.

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a. The polyhedron that can be constructed using the net made of squares is a cube.

b. The polyhedron that can be constructed using the net made of squares is also a cube.

c. The polyhedron that can be constructed using the net made of a regular hexagon and isosceles triangles is a hexagonal pyramid.

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The future value of the loan is $18,358.16. This means that after 8 months, the loan will have grown to $18,397.54 due to the interest.

To find the future value of this loan, we can use the formula FV = PV(1 + r)^t, where FV is the future value, PV is the present value, r is the interest rate, and t is the time period in years.

In this case, we have PV = $17,592, r = 6.6%, and t = 8 months or 0.667 years (8/12).

Plugging these values into the formula, we get:
FV = $17,592(1 + 0.066)^0.667
FV = $17,592(1.066)^0.667
FV = $18,358.16

Therefore, the future value of the loan is $18,358.16. This means that after 8 months, the loan will have grown to $18,397.54 due to the interest.

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Answer:

To solve for x, we need to isolate it on one side of the equation by performing inverse operations.

11x - 10 + 80 = 180

First, we combine the constant terms on the left side of the equation:

11x + 70 = 180

Next, we isolate the variable term by subtracting 70 from both sides:

11x = 110

Finally, we solve for x by dividing both sides by 11:

x = 10

Therefore, the solution to the equation 11x - 10 + 80 = 180 is x = 10.

They are not the same as the upper and lower limits used in other statistical calculations.

A accumulation of numerical data that has been methodically gathered, arranged, and examined is referred to as statistical data. Numerous phenomena, including economic patterns, demographic traits, health outcomes, and more, are described and measured using this data. Numerous techniques, such as surveys, experiments, observations, and administrative documents, can be used to gather statistical data. After being gathered, the data can be examined statistically to reveal patterns, connections, and trends that can be used to guide policy development and decision-making.

given

This is a histogram showing the frequency distribution of the weights of 30 students. Each bar represents a weight range, and the height of the bar represents the frequency of students in that weight range.

To find the upper and lower boundaries for each weight range, we can use the following formula:

Lower bound = midpoint of the previous range + 0.5

Upper bound = midpoint of the current range - 0.5

For example, the lower bound of the first range (60-64) is:

Lower bound = midpoint of previous range + 0.5

= 57

Upper bound = midpoint of current range - 0.5

= 61.5

We can apply the same formula to find the upper and lower bounds for the other ranges in the histogram. The results are:

60-64: lower bound = 57, upper bound = 61.5

65-69: lower bound = 62, upper bound = 66.5

70-74: lower bound = 67, upper bound = 71.5

75-79: lower bound = 72, upper bound = 76.5

80-84: lower bound = 77, upper bound = 81.5

85-89: lower bound = 82, upper bound = 86.5

90-94: lower bound = 87, upper bound = 91.5

95-99: lower bound = 92, upper bound = 96.5

They are not the same as the upper and lower limits used in other statistical calculations.

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