Gastonia’s population of 15,000 in 2020 was expected to grow exponentially by 12% each DECADE for the rest of the century…

-------------------------------------------------

What will be the population in 2030?

ANSWER: people

-------------------------------------------------

What will be the population in 2040?

ANSWER: people

Answer:

<b> <i>

Step-by-step explanation:

The probability distribution that X has is a binomial distribution, and the expected score on the exam is 20.

a. The correct probability distribution is a binomial distribution.

This is because the multiple-choice exam consists of 100 questions with 5 possible responses to each question.

The discrete probability distribution of the number of successes in a series of n independent experiments, each asking a yes-or-no question and each with its own Boolean-valued outcome, is known as the binomial distribution with parameters n and p in probability theory and statistics: success (with probability p) or failure (with probability q= 1 - p)

Therefore, this is a classic example of a binomial distribution where there are two outcomes in each trial (success and failure) and the trials are independent of each other.

(b) The expected score on the exam

The expected value of X is given by the formula;

Expected value (E) = np

n is the number of trials (100)

p is the probability of getting the correct answer (1/5).

Therefore, Expected value (E) = np

= 100 × (1/5) = 20

So, your expected score on the exam is 20.

A score of 50 is z = 6 standard deviations above the mean.

Therefore, it is extremely unlikely that you would score over 50 on this exam.

In conclusion, a binomial distribution is the probability that X has. Meanwhile, 20 is the expected score.

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Aiden would need to buy one 4-gallon jug, which would give him 15.14 liters.

First, we need to convert the gallons to liters to have a consistent unit of measurement:

2 gallons = 7.57 liters

3 gallons = 11.36 liters

4 gallons = 15.14 liters

7 gallons = 26.50 liters

Next, we can calculate the cost per liter for each jug:

2-gallon jug: $4.28 / 7.57 liters = $0.57 per liter

3-gallon jug: $5.92 / 11.36 liters = $0.52 per liter

4-gallon jug: $6.56 / 15.14 liters = $0.43 per liter

7-gallon jug: $12.98 / 26.50 liters = $0.49 per liter

Based on these calculations, the cheapest option per liter is the 4-gallon jug, which costs $0.43 per liter.

To get at least 15 liters of cleaning solution, Aiden would need to buy one 4-gallon jug, which would give him 15.14 liters.

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Your question is incomplete. Your complete question is:

Aiden needs 15 liters of cleaning solution. He can buy a 2-gallon jug ($4.28) a 3-gallon jug ($5.92) a 4-gallon jug ($6.56) a 7-gallon jug ($12.98). Which jug should he purchase to get at least 15 liters of cleaning solution and spend the least amount of money?

The exponential function that represents the population in the next six years is given as follows:

[tex]39366(1.028)^6[/tex]

The standard definition of an exponential function is given as follows:

[tex]A(t) = A(0)b^{\frac{t}{n}}[/tex]

The parameters of the exponential function are given as follows:

In 2010, the population of Belvedere was estimated to be 39,366 people, hence the parameter a is given as follows:

a = 39366.

The yearly increase rate is of 2.8%, hence the parameter values for b and n are given as follows:

b = 0.028, n = 1.

Then the expression giving the population after t years is of:

[tex]P(t) = 39366(1.028)^t[/tex]

After six years, the expression is given as follows:

[tex]39366(1.028)^6[/tex]

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The length of AN is equal to: C. 32 units.

In Mathematics and Geometry, a perpendicular bisector can be defined as a type of line that bisects or divides a line segment exactly into two (2) equal halves and forms an angle that has a magnitude of 90 degrees at the point of intersection.

Based on the information provided about the triangles, we can logically deduce that the perpendicular bisector of FN is AB. Therefore, we can calculate the length of AN by equating the length of AN to the length of A-F as follows;

5r - 3 = r + 25

5r - r = 25 + 3

4r = 28

r = 28/4

r = 7.

For the length of AN, we have:

AN = r + 25

AN = 7 + 25

AN = 32 units.

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Answer:

0.33

Step-by-step explanation:

To solve this, you first write the problem as an algebra equation as follows: 3x + 4 = 5

Then you solve the equation by subtracting 4 from both sides, and then divide both sides by 3. Here is the math to illustrate better:

3x + 4 = 5

3x + 4 - 4 = 5 - 4

3x = 1

3x/3 = 1/3

x = 0.33

Answer = 0.33

Therefore, you would be more likely to win the game by choosing option (2) - winning if the spinners do not match.

Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 indicates that the event is impossible, and 1 indicates that the event is certain. The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. Probability is used in many areas of mathematics, science, engineering, finance, and other fields to model and analyze uncertain situations. It helps to make predictions, to assess risks and opportunities, and to make informed decisions based on available information. Probability theory provides a foundation for statistical inference, which is used to draw conclusions from data and to test hypotheses about the underlying population.

Here,

In the "Two Spinner Game", there are two possible outcomes for each spin - a match or a non-match. The probability of the spinners matching is the probability of both spinners landing on the same color. Let's say that there are 3 red sections, 3 blue sections, and 2 green sections on each spinner.

The probability of the first spinner landing on red is 3/8, and the probability of the second spinner landing on red is also 3/8. Therefore, the probability of both spinners landing on red (a match) is (3/8) x (3/8) = 9/64.

Similarly, the probability of both spinners landing on blue (another match) is (3/8) x (3/8) = 9/64, and the probability of both spinners landing on green (a match) is (2/8) x (2/8) = 4/64.

The probability of the spinners not matching is the probability of them landing on different colors. There are 3 different pairs of colors that are not a match: red-blue, red-green, and blue-green. The probability of each of these pairs is (3/8) x (3/8) = 9/64.

So, there are 6 possible outcomes, and the probability of winning by a match is 9/64 + 9/64 + 4/64 = 22/64, or about 34.4%. The probability of winning by a non-match is 3 x 9/64 = 27/64, or about 42.2%.

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Answer:

Step-by-step explanation:

2(-4) - 3(-2) = -2

 -8 + 6 = -2

   -2 = -2

The solution to the equation (3√x) - √(9x-17) = 1 is x = 9.

Given the equation in the question (3√x) - √(9x-17) = 1.

To solve for x in the given equation:

(3√x) - √(9x-17) = 1

We can start by isolating the square root term on one side of the equation. Adding √(9x - 17) to both sides, we get:

(3√x) = √(9x - 17) + 1

Squaring both sides of the equation, we get:

(3√x)² = (√(9x - 17) + 1)²

9x = -16 + 2√(9x - 17) + 9x

Solve for 2√(9x - 17)

2√(9x - 17) = 16

36x - 68 = 256

Add 68 to both sides

36x - 68 + 68 = 256 + 68

36x = 324

x = 324/36

x = 9

Therefore, the solution is x = 9.

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Answer:

Step-by-step explanation:

[tex]\angle R+\angle S+ \angle T =180[/tex]       (angle sum of a triangle is 180°)

[tex]2x+11+3x+23+x+42=180[/tex]

                              [tex]6x+76=180[/tex]

                                      [tex]6x=104[/tex]

                                        [tex]x=17.667[/tex]

[tex]\text{So we get: } \angle R= 46.33,\angle S=76,\angle T=59.667[/tex]

In ascending order:

   [tex]\angle R= 46.33,\angle T=59.667,\angle S=76[/tex]

The length of the side labeled x is 75.3 when rounded to the nearest tenth which can be determined by using Pythagorean theorem.

The Pythagorean theorem states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

To find the length of the side labeled x, we will first need to calculate the length of the other two sides.

For the first triangle, the hypotenuse is equal to the side labeled x, so the length of the side labeled x can be calculated using the formula:

x = √(35² + 42²) = 50.1

For the second triangle, the hypotenuse is the side opposite the right angle, which is equal to the side labeled x. We can calculate the length of the side labeled x using the formula:

x = √(60² + 50²) = 75.3

For the third triangle, the hypotenuse is the side opposite the right angle, which is equal to the side labeled x. We can calculate the length of the side labeled x using the formula:

x = √(28² + 34²) = 39.6

Therefore, the length of the side labeled x is 75.3 when rounded to the nearest tenth.

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The rounded value of x in the triangles is:

25) x ≈ 76

27) x ≈ 21

29) x ≈ 104

All trigonometric identities are based on six trigonometric ratios. Sine, cosine, tangent, cosecant, secant, and cotangent. All these trigonometric ratios are defined using the sides of a right triangle as follows: Adjacent side, opposite side, and hypotenuse side.

25) Since, Sinθ = Opposite side/hypotenuse

Sin35° = 39/hypotenuse

hypotenuse = 39/Sin35°

Sin35° = 0.57

hypotenuse = 39/0.57

hypotenuse = 68.42

Now, using Pythagoras theorem:

hypotenuse² = base² + perpendicular²

68.42² = 39² + perpendicular²

4681.29 - 1521 = perpendicular²

4681.29 - 1521 = perpendicular²

3160.29 = perpendicular²

√3160.29 = perpendicular

56.21 = perpendicular

For the calculation of x:

Cosθ = Adjacent side/hypotenuse

Cos42° = 56.21/x

0.74 = 56.21/x

x = 56.21/0.74

x = 75.95

x ≈ 76

27) Cosθ = Adjacent side/hypotenuse

Cos60° = 14/hypotenuse

0.5 = 14/hypotenuse

hypotenuse = 14/0.5

hypotenuse = 28

Now, using Pythagoras theorem:

hypotenuse² = base² + perpendicular²

28² = 14² + perpendicular²

784 - 196 = perpendicular²

588 = perpendicular²

√588 = 24.24

perpendicular = 24.24

For the calculation of x:

Sinθ = Opposite side/hypotenuse

Sin50 = 24.24/hypotenuse

0.76 = 24.24/hypotenuse

hypotenuse = 24.24/0.76

hypotenuse = 31.89

Using Pythagoras theorem:

hypotenuse² = base² + perpendicular²

31.89² = x² + 24.24²

1016.97 = x² + 587.57

x² = 1016.97 - 587.57

x² = 429.4

x = √429.4

x = 20.72

x ≈ 21

29) Sinθ = Opposite side/hypotenuse

Sin28° = 44/hypotenuse

0.46 = 44/hypotenuse

hypotenuse = 44/0.46

hypotenuse = 95.65

Using Pythagoras theorem:

hypotenuse² = base² + perpendicular²

95.65² = 44² + perpendicular²

perpendicular² = 9148.92 - 1936

perpendicular² = 7212.92

perpendicular = √7212.92

perpendicular = 84.92

For the calculation of x:

Cosθ = Adjacent side/hypotenuse

Cos34 = 84.92/x

x = 84.92/0.82

x = 103.56

x ≈ 104

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The correct answer is three squares. To represent 3/5, 3 out of 5 squares need to be shaded.

Fractions written using a numerator (the number on top) and a denominator (the number on the bottom) that indicate how many parts make up the whole.

This can be seen visually if you draw 5 squares in a row and shade in 3 of them. Since fractions are a representation of the part-whole relationship, the numerator of the fraction (3) indicates the number of parts of the whole (5) that are shaded.

Fractions can be used to represent a variety of ratios, from unit fractions (1/2 or 1/3) to more complex fractions (3/5 or 7/9). To answer the question, "How many squares would need to be shaded to represent 3/5?", it is important to understand that the numerator of the fraction (3) indicates the number of parts of the whole (5) that are shaded.

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We need to shade 3/5 or 60% of the small squares in the bigger square which is 54 small squares.

Fractions written using a numerator (the number on top) and a denominator (the number on the bottom) that indicate how many parts make up the whole.

For this problem, we need to shade 3/5 or 60% of the small squares in the bigger square.

To calculate the number of small squares that need to be shaded, we must first calculate the total number of small squares within the bigger square.

We can do this by multiplying the number of squares in the rows(10) by the number of squares in the columns(9), which in this case is

10 x 9 = 90.

Now that we know the total number of small squares, we can calculate the number of small squares that need to be shaded.

To do this, we need to multiply the total number of small squares (90) by  by the fraction we are trying to represent (3/5).

90 x 3/5 = 54.

This means that 54 small squares need to be shaded to represent 3/5.

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Answer:

720

Step-by-step explanation:

20% of 600 is 120, so add them together and you get 720

The smallest value of `n` for which `S_n` has an element of order greater than or equal to 100 is 101.

To determine the smallest value of n for which S_n has an element of order greater than or equal to 100, we can use the formula

S_n = n!/r!(n - r)!,

where n is the number of elements in the set, and r is the number of elements being chosen at a time.

Given, S_n has an element of order greater than or equal to 100. The smallest value of n should be determined.

The formula for the number of permutations in a set with n elements is given by, `S_n = n!/r!(n - r)!`

where `n` is the number of elements in the set and `r` is the number of elements being chosen at a time.

The element of order `n` in `S_n` is an `n` cycle. For `n = 100`, we have an element of order 100.

This element can be expressed as `(1 2 3 ... 99 100)`. Thus, `r = 100`.

Substituting these values in the formula of S_n we get, S_n = n!/r!(n - r)! => n!/(100!(n - 100)!)

Now, we have to find the smallest value of n for which S_n has an element of order greater than or equal to 100. If we substitute `n = 100`, then we will have an element of order 100. But the question asks for the smallest value of n. So, if we substitute `n = 101`, we will have an element of order `101`. Hence, the smallest value of `n` for which `S_n` has an element of order greater than or equal to 100 is 101.

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Step-by-step explanation:

it is completely vertical.

the slope is the ratio

y coordinate change / x coordinate change

when going from one point on the line to another.

but in such a case x is not changing at all. x is a constant for all y values.

so the slope is

y difference / 0

this is undefined (or in some ways described as infinity).

The slοpe οf the flagpοle in the figure is nοt defined.

Here, the pοle is similar tο the Y-axis οf the graph.

Angle the pοle makes with Y-axis = 90 degree

( as it is vertically standing straight )

Thus, the slοpe οf the pοle

= [tex]tan90[/tex]

= not defined

Hence, the slope of the given flag pole is not defined.

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Complete question;

What is the slope of the flagpole in the image shown below? _________

There are 15C5 or 3003 possible combinations in the sample space.There are 20C5 or 15504 possible combinations in the sample space.

A number is a mathematical object used to count, measure, and label. Numbers can be represented in many different forms such as natural numbers, integers, real numbers, and complex numbers. They can also be classified as scalar numbers (which have a magnitude or value only) or vector numbers (which have both magnitude and direction). Numbers can be used to represent many different things, including measurements, distances, money, and quantities.

A) Sample Space: The sample space for selecting a set of 5 questions from a set of 15 questions is the set of all possible combinations of 5 questions from 15 questions. There are 15C5 or 3003 possible combinations in the sample space.

B) Sample Space: The sample space for forming a committee of 5 from a membership of 20 is the set of all possible committees that can be formed from 20 members. There are 20C5 or 15504 possible combinations in the sample space.

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The original price of the pearl was 52 euros.

Price is the monetary value of a product, service, or asset. It is one of the most important factors in a customer's decision to purchase something. Price also determines the amount of profit a business makes on a particular product or service. Price is a key component of the marketing mix, and it can be used to create a sense of value for customers. Price can also be used to differentiate a product from competitors, as well as to indicate quality levels and to create loyalty.

a) One of the cheapest pearls costs 41 euros.

b) This necklace costs 2153 euros, which is the sum of all the pearls.

c) The pearl with the crack originally cost 52 euros. The price was reduced by 1/5, which is 10.4 euros, making the price of the pearl 41.6 euros. The decrease in price of the necklace was 6.5 euros, which means the reduction in price of the pearl was 6.5 euros. Therefore, the original price of the pearl was 52 euros.

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(x-bar) refers to the sample means in statistics. It is the average of all the data values in a sample. It is calculated by dividing the sum of all the data values by the sample size.

The distribution of (x-bar) follows a normal distribution, and its expected value is equal to the population mean. The standard error of (x-bar) is calculated by dividing the population standard deviation by the square root of the sample size. It is used to estimate how much the sample mean varies from the population mean.

Sample mean (x-bar) is a statistical concept used to calculate the average of a sample, and standard error is a measure of the variability of the sample mean. The distribution of the sample mean is a normal distribution with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.

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Using the equation [tex]y = $7.32(1.04)^t[/tex], the amount of time after which the employee will be earning $10.00 is about 9.64 years, or approximately 9 years and 8 months.

What is an equation?

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").

We can start by setting up the equation for the employee's hourly wage y after t years -

[tex]y = $7.32(1.04)^t[/tex]

We want to find the amount of time t after which the employee will be earning $10.00 per hour, so we can set y equal to 10 and solve for t -

[tex]10 = $7.32(1.04)^t[/tex]

Dividing both sides by $7.32, we get -

[tex]1.367 = 1.04^t[/tex]

Taking the natural logarithm of both sides, we get -

[tex]ln(1.367) = ln(1.04^t)[/tex]

Using the property of logarithms that [tex]ln(a^b) = b ln(a)[/tex], we can simplify the right-hand side -

ln(1.367) = t ln(1.04)

Dividing both sides by ln(1.04), we get -

t = ln(1.367)/ln(1.04) ≈ 9.64

Therefore, the employee will be earning $10.00 per hour after about 9.64 years.

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The p-value for the Box-Ljung Q test of returns is greater than 5%, which means that we do not reject the null hypothesis and find no evidence of volatility clustering in the raw returns.

In statistics, p-value is a measure of the strength of evidence against the null hypothesis. It is defined as the probability of obtaining the observed results, or results more extreme, assuming that the null hypothesis is true.

The null hypothesis is a statement that assumes there is no significant difference or relationship between two groups or variables being compared. The alternative hypothesis is the statement that there is a significant difference or relationship.

Given by the question.

Based on the information provided, we can conclude that there is evidence of volatility clustering in the IBM data using 15 lags. This is indicated by the p-value being less than 5% for the Box-Ljung Q test of squared returns. Therefore, we reject the null hypothesis and find evidence of volatility clustering.

However, since the test is conducted on squared returns, it is the p-value for this test that is more relevant in assessing volatility clustering.

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Answer:

$11.22

Step-by-step explanation:

20% of 56.09 = 1/5 of 56.09

Now, we divide 56.09 by 5 to get our answer which when rounded becomes 11.22.

Answer:

$11.22

Step-by-step explanation:

20% = 0.2

We Take

56.09 x 0.2 = $11.218

Round $11.218 will be $11.22

So, the tip amount is $11.22

The calculated value of x in the similar triangles is 14 and it is calculated from the ratio 10 : x = 20 : 28

Given the triangle

The triangle is a superset of similar triangles

So, we have the following equivalent ratio that can be used to determine teh value of x

The set up of teh ratio is

10 : x = 10 + 10 : 28

Evaluating the like terms, we get

10 : x = 20 : 28

So, we have

x/10 = 28/20

Multiply both sides by 10

x = 14

Hence, the value of x is 14

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Step-by-step explanation:

20% off means you pay 80 % of the original price for two books

80% * ( 2 x 19.95 ) = .8 ( 39.90) = $ 31.92

The given expression is

[tex]15 + c = 17.50[/tex]

We can use this expression to model the cost for a service.

Let's say that your gardener charges an initial amount of $15, and an additional per hour. If the gardener worked only for one hour, and the total cost charged was $17.50, how much was the additional cost?

So, the given expression models this real life situation, we can answer the problem by just solving the equation for [tex]c[/tex]

[tex]15 + c = 17.50[/tex]

[tex]c=17.50-15[/tex]

[tex]c=2.50[/tex]

Answer: Well C equals 2.5. You could use...

You have 3 sticks. one stick is 15 inches long and the other is 17.50. You want to get a small stick to add to the first one so that the first and last stick is equal to the 2nd stick.  C is the third stick.  15+C = 17.50. What is the length of C?

Step-by-step explanation:

EASY

Move all terms not containing C to the right side of the equation. C = 2.5

The following characteristics of racional decimal number abstraction apply: Conmutative property: The order of the remaining rational decimal numbers has no bearing on the operation's outcome,

Proprietary property: The racional decimal numbers may remain in various groups without affecting the operation's ultimate outcome, i.e., (a - b) - c = a - (b - c). Distributive property: Subtracting one racional decimal number from a sum of racional decimal numbers equals the sum of the subtractions of each one of them, or a - (b + c) = a - b - c. Neutral element: If a racional decimal number is left at zero, the outcome is the same number, i.e., a - 0 = a. Estas propiedades son útiles para simplificar y realizar cálculos más complejos con números racionales decimales.

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4x - 4/4x² + x is the value of linear equation.

What in mathematics is a linear equation?

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.  

                                   Equations with power 1 variables are known as linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.

28x³ - 28x²/28x⁴ + 7x³

= 28x²( x - 1 )/7x³( 4x + 1)

= 4( x - 1)/x( 4x + 1)

= 4x - 4/4x² + x

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The required perimeter of the trapezoid is22 units.

The given vertices of the trapezoid are (1,3), (4,7), (9,7), and (9,3). To find the perimeter of the trapezoid, we need to add up the lengths of all four sides.

We can use the distance formula to find the length of each side of the trapezoid:

[tex]{Side 1: }&(1,3) \text{ to } (4,7) \&d = \sqrt{(4 - 1)^2 + (7 - 3)^2} = \sqrt{9 + 16} = 5 \\\text{Side 2: }&(4,7) \text{ to } (9,7) \&d = \sqrt{(9 - 4)^2 + (7 - 7)^2} = \sqrt{25} = 5 \\\text{Side 3: }&(9,7) \text{ to } (9,3) \&d = \sqrt{(9 - 9)^2 + (3 - 7)^2} = \sqrt{16} = 4 \\\text{Side 4: }&(9,3) \text{ to } (1,3) \&d = \sqrt{(1 - 9)^2 + (3 - 3)^2} = \sqrt{64} = 8\end{align*}[/tex]

Therefore, the perimeter of the trapezoid is:

[tex]$\begin{align*}P &= \text{Side 1} + \text{Side 2} + \text{Side 3} + \text{Side 4} \&= 5 + 5 + 4 + 8 \&= 22\end{align*}[/tex]

Thus, the perimeter of the trapezoid is22 units.

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These limitations are represented by the inequalities x 500 + 2y and 35x + 50y > 225002.

How do equations work?

An equation is an expression that shows the relationship between two or more numbers and variables. Numerical constants, symbolic names, mathematical operators, functions, and conditional expressions are all examples of components that can be included in expressions.

If x stands for the quantity of product A and y for the quantity of product B, then:

x ≤ 500 + 2y (1) (1)

Also:

35x + 50y > 22500² (2) (2)

These limitations are represented by the inequalities x 500 + 2y and 35x + 50y > 225002.

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The angle BOC on the line AOC is found to be 47 degrees in magnitude.

When two straight lines or rays intersect at a single endpoint, an angle is created. The vertex of an angle is the location where two points come together.

Hence, AOC is a straight angle, BOC is equal to 6x+29°, and AOB is equal to 3x+124°.

It is common knowledge that a straight angle measures 180 degrees.

As the angle ∠BOC+∠AOB=∠AOC is essentially a straight line, we are assuming that it is 180 degrees, which also satisfies the requirement that all angles on the line add to 180 degrees.

6x+29°+3x+124°=180°

9x+153°=180°

9x=27°

x=3°

Hence, ∠BOC=6x+29°

=6×3+29°

= 47°

So, the value of ∠BOC is 47°.

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The net sales in the department during the month of april is $15960.

Sell-thru perecentage rate = Units sold / Units recieved

In our case:

Net sales = (Sell-thru rate)*(opening inventory)

Net sales = (0.28)*($57000)

= $15960

Net sales refer to the total amount of revenue generated by a company from its primary business operations, minus any returns, allowances, and discounts. This figure reflects the actual revenue earned by a company after accounting for any deductions and is a critical metric for evaluating the financial performance of a business.

Net sales are reported on a company's income statement and are a key component of the top line, which also includes other sources of revenue, such as interest income or gains from the sale of assets. Understanding a company's net sales is essential for assessing its growth potential, profitability, and overall financial health. Investors, creditors, and other stakeholders use net sales as a metric to evaluate a company's ability to generate revenue from its core operations, as well as its ability to compete effectively in its industry.

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