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The 3rd term of the linear sequence above is 14.

Mathematically, the nth term of an arithmetic sequence can be calculated by using this expression:

aₙ =  a₁ + (n - 1)d

Where:

Next, we would determine the common difference as follows.

Common difference, d = a₂ - a₁

Common difference, d = 18 - 22

Common difference, d = -4

For the third term, we have:

a₃ =  a₁ + (n - 1)d

a₃ = 22 + (3 - 1)-4

a₃ = 22 - 8

a₃ = 14.

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[tex]3x^3 + x^2 = 6x[/tex], which is option B, is the right response as Option C,[tex]3x^3 + x^2 = 0[/tex], does not equal the supplied expression.

Using just the methods of addition, elimination, and multiplication as well as ou pas integer exponents, a polynomial is a mathematical equation made up of variables and coefficients. A polynomial, for instance, is 3x2 - 2x + 5, where x has been the component and 3, -2, and 5 are now the coefficients. This polynomial's highest exponent is 2, which also happens to be its degree. Polynomials can have coefficients that are either constants or other polynomials, as well as many variables. Due to their usage in representing a variety of mathematical relations and functions, polynomials play a significant role in mathematics. Several disciplines, including algebra, algebra, geometry, and physics, make extensive use of them.

given

To make [tex]5x^2-x-8x^2 + 3x^3[/tex]simpler, we can rearrange the terms and join comparable terms:

[tex]0 + 3x^3 - x - 3x^2 = 5x^2 - 8x^2 + 3x^3 - x[/tex]

The following step is to factor the final three terms to remove a common factor of x:

[tex]3x^3 - x - 3x^2 = x\\(3x^2 - 1 - 3x)[/tex]

Hence, the abbreviated form is:

[tex]3x^2 - 1 - 3x^3 = 5x^2-x-8x^2 + 3x^3.[/tex]

Due to the fact that Option C,[tex]3x^3 + x^2 = 0[/tex], does not equal the supplied expression, it is incorrect.

Due to their failure to simplify to the specified formula, options A,      [tex]-5x^3+ x^2 = 0,[/tex] and D, [tex]3x^3 -3x^2 =6x[/tex], are likewise incorrect.

[tex]3x^3 + x^2 = 6x[/tex], which is option B, is the right response.

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The complete question is:-  

Simplify: [tex]5x^2-x-8x^2 + 3x^3 = 5x[/tex]

OA.-5x3x2 = 0

B. 3x3 + x2 = 6x

C. 3x3 + x2 = 0

D. 3x3 3x26x

-

Reset Selection

After 6 years, the first accοunt with simple interest earn mοre amοunt.

The interest that is calculated using bοth the principal and the interest that has accrued during the previοus periοd is called cοmpοund interest. It differs frοm simple interest in that the principal is nοt taken intο accοunt when determining the interest fοr the subsequent periοd with simple interest.

Here In first bank account ,

Principal P = $1000

Time N = 6

Rate οf interest = 7%

Interest = [tex]\frac{PNR}{100}[/tex]

=> I = [tex]\frac{1000\times7\times6}{100}[/tex] = $420

Tοtal amount = $1000+$420 = $1420.

Now in secοnd bank account,

Principal P = $1000

Times N= 6

Rate οf interest = 6%

Tοtal amount A = [tex]P(1+\frac{R}{100})^N[/tex]

=> A = [tex]1000(1+\frac{6}{100})^6[/tex]

=> A = $1418.00

Now cοmparing bοth account amounts , In first bank have earned more amount that second bank,

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Answer: 5x/5 = -6/5 + y/5

Step-by-step explanation:

x = -6 + y/5

and then x = -2 +y

Answer:

To show that two fractions are reciprocals, you can multiply them together and check if the product is equal to 1. That is, if we have two fractions a/b and b/a, their product is:

(a/b) * (b/a) = ab / ba = 1

Therefore, if the product of two fractions is equal to 1, they are reciprocals of each other.

For example, let's say we have the fractions 2/5 and 5/2. We can multiply them together to check if they are reciprocals:

(2/5) * (5/2) = 1

Since the product is equal to 1, we can conclude that 2/5 and 5/2 are reciprocals of each other.

Answer:

yes

no

yes

no

no

Step-by-step explanation:

An integer is a positive or negative whole number or zero.

Examples of integers:

-1000, 993, 12, -19, 1000000, -79, 0, 1, 221

Examples of numbers that are not integers:

-5/4, -223.25, 1000.1, 45.2, 1000000.45, 32/7

Is 12 a integer   yes

and is 55.3 a integer   no

and is 18 over 2 a integer = 9, so yes

and is -260.43 a integer   no

and is 12 over 17 a integer =0.70588..., so no

Answer: A=490

Step-by-step explanation:

Formula - A = 2 ( wl + hl + hw)

2(7•14+7•14+7•7) = 490

(a)  40.4° or 139.6°

(b)  137.6° or 222.4°

(c)  124.2° or 304.2°

(a) sinθ=0.6264:θ=40.4° or 139.6°

(b) cosθ=-0.6405:θ=137.6° or 222.4°

(c) tanθ=-1.5519:θ=124.2° or 304.2°.What is interval? An interval is a set of real numbers with the property that every number that lies between two numbers in the set is also included in the set. Let's look at some of the most popular sets of numbers: the integers, the real numbers, and the natural numbers. What is an angle? An angle is a figure formed by two rays starting at a common endpoint called the vertex. The rays are known as sides of the angle, and the point of their intersection is known as the vertex. Angles are usually classified based on their size: acute angles, right angles, obtuse angles, and straight angles are examples. The following is how to solve the problem; 1. In each of the cases given, use the inverse function of sin, cos, or tan to calculate the value of the angle.2. Ascertain if the angle you've calculated is in the required interval.3. Since this question asks for an approximation to the nearest 0.1 degrees, express your solutions to one decimal point.Let's look at the following options:(a) sinθ=0.6264θ = 40.4° or 139.6°(b) cosθ=−0.6405θ = 137.6° or 222.4°(c) tanθ=−1.5519θ = 124.2° or 304.2°.Therefore, to the nearest 0.1 degrees, all angles θ in the interval [0˚, 360˚) that meet the equation are 40.4°, 139.6°, 137.6°, 222.4°, 124.2°, and 304.2°.

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Answer:

$43,200

Step-by-step explanation:

The amount of money you make a year depends on various factors, such as your monthly expenses, debt obligations, and tax liabilities.

To get a rough estimate of your annual income based on the range of affordable rent provided, you can use the rule of thumb that suggests spending no more than 30% of your gross income on housing expenses. Assuming you are willing to spend between $900 and $1080 per month on rent, we can calculate the range of annual incomes that would allow you to meet this guideline:

$900/month rent x 12 months = $10,800/year rent

$10,800/year rent / 0.3 = $36,000/year gross income

$1080/month rent x 12 months = $12,960/year rent

$12,960/year rent / 0.3 = $43,200/year gross income

Therefore, based on the assumption that you can afford rent between $900 and $1080 per month, your estimated annual gross income would need to be in the range of $36,000 to $43,200. However, this is only a rough estimate and may not take into account all of your individual financial circumstances.

Answer:

2.50 p + 1.50p

Step-by-step explanation:

if you buy an item x amount of times you would times the two to figure out the total cost of that type of item then add with the other

The sales price of the item after deduction of percentage discount is: $18

The regular price is defined as the price at which similar goods or services are regularly sold on the market.

The discount is defined as an amount or perhaps percentage deducted from the normal selling price of something.

The sales price is defined as the actual amount for which a good is sold after deduction of discount if any.

The parameters given are:

Regular Price = $20

Percentage Discount = 10%

Thus:

Discount = 10% * 20

Discount = $2

Thus:

Sales Price = $20 - $2

= $18

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Answer:

C. Simplify

Step-by-step explanation:

1. Subtract 7 from both sides

4x +7 -7 < 15 -7

4x < 8

2. divide both sides by 4

4x/4 < 8/4

answer: x < 2

hope this helps

Answer:

6/100=3/50

Step-by-step explanation:

The first bag contains the numbers 1 through 10, which is a total of 10 numbers. The second bag contains the numbers 5 through 14, which is also a total of 10 numbers.

The probability of picking the same number from both bags is the number of ways of picking the same number divided by the total number of possible outcomes. There are 10 possible outcomes in each bag, so the total number of possible outcomes is 10 × 10 = 100.

To count the number of ways of picking the same number, we can simply count the number of numbers that appear in both bags. There are six numbers that appear in both bags: 5, 6, 7, 8, 9, and 10.

Therefore, the probability of picking the same number from both bags is:

6/100

Simplifying this fraction by dividing both the numerator and denominator by 2 yields:

3/50

So the probability of picking the same number from both bags is 3/50.

Conner worked 5 hours on Monday.

Let's use the letters "m" and "f" to denote the number of hours Conner worked on Monday and Friday, respectively.

Conner worked a total of 12 hours, and since we know this from the issue statement, we may write:

m + f = 12

Also, we are aware that Conner received $81 and charged $5 on Mondays and $8 on Fridays. Hence, we can write:

5m + 8f = 81

To determine one of the variables in terms of the other, we can utilise the first equation. To solve for "f," we obtain:

f = 12 - m

We can now solve for "m" by substituting this expression for "f" in the second equation:

5m + 8(12 - m) = 81

After simplifying and finding "m," we obtain:

5m + 96 - 8m = 81

-3m + 96 = 81

-3m = -15

m = 5

Conner spent 5 hours at work on Monday as a result.

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An equation that represents this situation include the following: D. y = -2x + 9.50.

In order to write a linear equation to describe this situation, we would assign variables to the cost of the drinks and the cost of the popcorn respectively, and then translate the word problem into a linear equation as follows:

Since Ben purchased 2 drinks and a bag of popcorn at the movie theater, for a total cost of $9.50, a linear equation that models the situation is given by this mathematical expression:

2x + y = 9.50

By making y the subject of formula, we have:

y = -2x + 9.50

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The marginal revenue when 100 units are sold is approximately $17.12. Selling one additional unit at this point would yield approximately $17.12 in additional revenue.

To find the marginal revenue, we first need to find the derivative of the total revenue function with respect to x, which is the definition of marginal revenue:

R(x) = 2200x/(ln(9x+9))

Using the quotient rule, we get:

R'(x) = (2200(ln(9x+9)) - 2200x(1/(9x+9))(1/(9x+9)))/(ln(9x+9))^2

Simplifying this expression, we get:

R'(x) = 2200(9x)/(9x+9)^2ln(9x+9)^2

Substituting x=100, we get:

R'(100) = 2200(9(100))/((9(100)+9)^2ln(9(100)+9)^2 = $9.77 (rounded to the nearest cent).

Interpretation: The marginal revenue when 100 units are sold is $9.77. This means that selling one additional unit of the product will increase the total revenue by approximately $9.77.

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Complete question:

The total revenue, in dollars, from the sale of x units of a product is given by R(x)=2200x/(ln(9x+9)). Find the marginal revenue when 100 units are sold. (Round your answer to the nearest cent.) Interpret your result.

The  steps taken to design a contingency contract are valuating the potential outcomes, consequences and agree on terms of contract.

Identify the potential outcomes. Party A thinks that there is an 80% chance that the car will not break down in the first year, while Party B thinks that there is an 80% chance that it will. These are the two potential outcomes that need to be identified.

Determine the consequences of each outcome. Next, the consequences of each outcome should be determined. For example, if the car breaks down in the first year, then Party A may have to pay for repairs or reimburse Party B for the purchase price of the car. If the car does not break down, then no consequences need to be determined.

Agree on the terms of the contract. Finally, both parties need to agree on the terms of the contract. This may include how much Party A will have to pay if the car breaks down, how long Party B has to wait for reimbursement if the car does break down, and any other terms that are relevant to the situation. Once the terms have been agreed upon, the contingency contract can be signed by both parties, and they can proceed with the sale of the car.

A contingency contract could be designed to help them avoid an impasse over the issue of the car's breakdown. The contingency contract is a contract that is triggered by a specific event or circumstance, such as the car breaking down in the first year. This contract outlines what will happen if the event or circumstance occurs, and both parties agree to the terms in advance.

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The probability of at least 2 people having the same birthday in a group of 23 people is 0.5073.

The probability of at least 2 people having the same birthday in a group of 23 people can be calculated using the rule for complements. The complement of this event is that all 23 people have different birthdays. We can calculate the probability of this event and then subtract it from 1 to find the probability of at least 2 people having the same birthday.

The probability of the first person having a different birthday from the others is 1. The probability of the second person having a different birthday from the first is 364/365, since there are 364 days left that are not the first person's birthday. The probability of the third person having a different birthday from the first two is 363/365, and so on.

The probability of all 23 people having different birthdays is:

1 * (364/365) * (363/365) * ... * (343/365)

This simplifies to:

364! / (36522 * 341!)

Using a calculator, we find that this is approximately 0.4927.

Therefore, the probability of at least 2 people having the same birthday is:

1 - 0.4927 = 0.5073

So, the probability of at least 2 people having the same birthday in a group of 23 people is 0.5073.

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In a group of 23 persons, the probability that at least two of them share the same birthday is around 0.5073, or 50.73%.

The probability that at least 2 people in a group of 23 have the same birthday, can be calculated by using the rule for compliments. First, we can calculate the probability that no two people share a birthday in a group of  23.

The first individual will have any birthday, however the 2nd individual have to have a distinct birthday, which has a probability of 364/365 (since there are 365 days in a year and one day has already been "used" by the first person). The probability that the third individual will have a different birthdate from the previous two is 363/365. Continuing in this way,

The probability that all 23 people have different birthdays is:

(365/365) x (364/365) x (363/365) x ...

Since the probabilities of all conceivable outcomes must sum up to 1, subtract the likelihood that at least two persons will have the same birthdate from one:

P(at least 2 people have the same birthday) = 1 - (365/365) x (364/365) x (363/365) x ... x (344/365)

P(at least 2 people have the same birthday) = 0.5073

Therefore, the probability that at least 2 people in a group of 23 have the same birthday is approximately 0.5073 or 50.73%

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The transformation as a whole is given by P → Q → R → S. A rotation through angle, about the intersection point of the lines, results from the combination of reflections in lines that meet at angle /2.

Two reflections across intersecting lines have the same composition as one rotation with the junction point as the centre of rotation.

By (0,-1/2), the initial translation is provided.

Given by is the reflection along the x-axis (x,-y)

By (0,1/2), the final translation is indicated. Hence, the transformation as a whole is provided by

(x,y) → (x,-y) → (x,-y+1/2) → (x,y+1)

This demonstrates that the resulting isometry moves the values of (x,y) by one unit in the positive y-direction to (x,y+1).

The whole transformation is provided by:

P → P + (0,d/2) → Q → Q - (0,d/2)

The total transformation is given by:

P → P + (d/2,0) → (x,-y) → (x,y) → Q

where Q is positioned (x,y). Adding the two transformations together, we obtain:

P → P + (0,d/2) → Q → Q - (0,d/2) = P + (d,0)

This demonstrates that a translation across distance d, in the direction perpendicular to the lines of reflection, results from the combination of reflections on parallel lines spaced d/2 apart.

The total transformation is given by:

P → Q → R → S

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Answer:

To rewrite a mixed number as an improper fraction, you need to multiply the whole number by the denominator of the fraction, then add the numerator. The resulting sum is the numerator of the improper fraction, while the denominator remains the same.

For example, to rewrite the mixed number 3 1/2 as an improper fraction, you would:

Multiply the whole number 3 by the denominator 2: 3 x 2 = 6

Add the numerator 1 to the product: 6 + 1 = 7

Write the sum 7 as the numerator of the improper fraction, with the denominator 2: 7/2

So, the improper fraction equivalent of the mixed number 3 1/2 is 7/2.

Step-by-step explanation:

We can round each figure to one decimal place to represent a percentage to the nearest tenth: Lemonade: 28%, Grape juice: 14%, Honey: 1.8% and  Sparkling water: 56.2%. So, the lemonade contributes approximately 28% to the punch mixture.

Calculate the total volume of the combination, divide it by the total volume, and then express the result as a percentage to determine the amount of each ingredient in the punch mixture.

1 quart = 4 cups

1/2 gallon = 8 cups

4 tablespoons = [tex]\frac{1}{4}[/tex] cups

So the total volume of the mixture is:

4 cups (lemonade) + 2 cups (grape juice) + [tex]\frac{1}{4}[/tex] cups (honey) + 8 cups (sparkling water) = [tex]\frac{57}{4}[/tex] cups

Now, we can calculate the percentage of each ingredient in the mixture:

Lemonade:  [tex]\frac{4}{(\frac{57}{4})}*100[/tex] ≈ 28%

Grape juice: [tex]\frac{2}{(\frac{57}{4})}*100[/tex] ≈ 14%

Honey: [tex]\frac{(\frac{1}{4})}{(\frac{57}{4})}*100[/tex] ≈ 1.8%

Sparkling water: [tex]\frac{8}{(\frac{57}{4})}*100[/tex] ≈ 56.2%

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its b

i have covid and want to know what to do

The area of the circle which contains the 45° sector as required to be determined is; 345.4 cm².

As evident from the task content; A 45° sector in a circle has an area of 13.75π cm².

Hence, since the sector is 45° and the sum of angles in the circle would be 360°; it follows that the area of the circle is; 360/45 = 8 times the area of the sector.

Area of circle = 8 × 13.75π

= 8 × 13.75 × 3.14

= 345.4 cm².

Ultimately, the area of the circle is; 345.4 cm².

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The area of shaded region is 45 square units.

The complete question is added as an attachment

The area of the shaded region is calculated as

Shaded region =Area of rectangle - Area of triangle

Using the above as a guide, we have the following:

Area of rectangle = 8 * 6 = 48

Area of triangle = 1/2 * 2 * 3 = 3

Substitute the known values in the above equation, so, we have the following representation

Shaded region = 48 - 3

Evaluate the difference

Shaded region = 45

Hence, the shaded region is 45 square units.

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We need to look at the element in the second row, second column of C, which is -3. Therefore, C₂₂ = -3.

In mathematics, a matrix is a rectangular array of numbers, symbols, or expressions arranged in rows and columns. Matrices are used to represent linear transformations, as well as to solve systems of linear equations.

A matrix with m rows and n columns is called an m x n matrix. The individual entries of a matrix are denoted by a subscript, with the first subscript indicating the row and the second subscript indicating the column. For example, the entry in the second row and third column of a matrix A would be denoted by A[2,3].

Matrices can be added, subtracted, multiplied, and divided (by a scalar). Addition and subtraction of matrices is done element-wise, while matrix multiplication involves taking the dot product of rows and columns. Multiplying a matrix by a scalar involves multiplying every entry in the matrix by that scalar.

To find B - 2A, we need to multiply every element of A by 2 and then subtract the resulting matrix from B:

2A = [(-4)*2 (-3)*2 ; (-2)*2 (-3)*2 ; (-3)2 32 ; (-2)2 42] = [-8 -6 ; -4 -6 ; -6 6 ; -4 8]

B - 2A = [6 -9 ; 7 12 ; -3 -3 ; 2 -7] - [-8 -6 ; -4 -6 ; -6 6 ; -4 8] = [14 -3 ; 11 18 ; 3 9 ; 6 -15]

So C = B - 2A = [14 -3 ; 11 18 ; 3 9 ; 6 -15]

To find C₂₂, we need to look at the element in the second row, second column of C, which is -3. Therefore, C₂₂ = -3.

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I. The measure of angles DEC is: 60°

II. The theorems used are corresponding angles and triangle sum theorems.

We are given the following:

m∠BAC = 64°

m∠CBA = 56°

AB║CD

BC║DE

Considering triangle ABC, we have:

m∠BCA = 180 - m∠BAC - m∠CBA [triangle sum theorem]

Substitute:

m∠BCA = 180 - 64 - 56

m∠BCA = 60°

Therefore, based on the corresponding angles theorem,

m∠DEC = m∠BCA

Substitute:

m∠DEC = 60°

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In the given functions  [tex]5^x[/tex] function is increasing because 5>1.

Let's first define functions so that we may better comprehend the monotonicity and rising and decreasing functions. In its simplest form, a function is a relationship between input and output in which each input is associated with exactly one outcome.

To better understand monotonicity and rising and decreasing functions, let's first define what a function is. A function, in its most basic form, is a relationship between input and output in which each input is connected to precisely one result.

During the duration of their whole domain, functions might alter, growing, shrink, or stay the same. Functions are both continuous and differentiable in the defined intervals.

Functions can change over the course of their entire domain, either increasing, decreasing, or remaining constant. In the specified intervals, functions are both continuous and differentiable.

We have all the functions that are exponential

So when we shall check all the given function

We observe that we have functions of the form:

f (x) = A[tex]b^x[/tex]

When

b > 1 The function grows

b <1 Function decreases

Hence [tex]5^x[/tex] function is increasing.

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Answer:

Since the fish is swimming down at a constant rate of 12 ft per hour for 6 hours, the distance it travels can be found by multiplying its speed by the time:

distance = speed x time

distance = 12 ft/hour x 6 hours

distance = 72 ft

Therefore, the fish will end up 72 feet down from the surface.