An astronomer knows the distances from herself to stars AAA and BBB, as well as the distance between them. The distances are 450450450, 400400400, and 909090 light years (\text{l. Y. }l. Y. Start text, l, point, y, point, end text) respectively.

If the astronomer's telescope is currently pointed at star AAA, how many degrees must she rotate her telescope to see star BBB?

Do not round during your calculations. Round your final answer to the nearest degree

Answer: (1) The scenario represents an arithmetic sequence because each time an omelet is made, the number of remaining eggs decreases by the same amount.

(2) Let's denote the number of remaining eggs after making the n-th omelet by a_n. We can see from the problem statement that the difference between any two consecutive terms in the sequence is constant. Let d be a common difference. Then, we have:

a_{n+1} = a_n - d

Using the information from the problem statement, we can find the value of d:

a_2 - a_1 = 174 - 177 = -3

a_3 - a_2 = 171 - 174 = -3

Since the difference is the same in both cases, we have d = -3. Therefore, the recursive formula is:

a_{n+1} = a_n - 3, with a_1 = 177.

(3) To find an explicit formula, we can use the recursive formula to derive a general expression for a_n. Starting with the recursive formula, we have:

a_2 = a_1 - 3

a_3 = a_2 - 3 = a_1 - 23

a_4 = a_3 - 3 = a_1 - 33

a_5 = a_4 - 3 = a_1 - 4*3

We can see that the general expression for a_n is:

a_n = a_1 - (n-1)*3

Substituting a_1 = 177, we get:

a_n = 180 - 3n

Therefore, the explicit formula for the number of remaining eggs after making the n-th omelet is a_n = 180 - 3n.

(4) To find the number of eggs Joe will have left after making 42 omelets, we can simply substitute n = 42 into the explicit formula:

a_{42} = 180 - 3*42 = 54

Therefore, Joe will have 54 eggs left after making 42 omelets.

Step-by-step explanation:

Coefficients and indeterminates are both parts of polynomials. The polynomial  [tex]x^{2}[/tex] - 15x + 36 has the components (x-3) (x-12).

To factor the polynomial  [tex]x^{2}[/tex]- 15x + 36, we need to find two numbers whose product is 36 and whose sum is -15. These numbers are -3 and -12,

=[tex]x^{2}[/tex] -12x -3x + 36

now, we'll use x as the common term between the first two terms and 3 as the common term between the next two terms.

=x(x-12)-3(x-12)

=(x-12)(x-3)

so we can write the polynomial as (x - 3)(x - 12). This is the factored form of the polynomial.

To verify this, we can expand the expression (x - 3)(x - 12) using the distributive property, which gives us  [tex]x^{2}[/tex]- 15x + 36. This confirms that the factored form is correct.

Factoring polynomials is an important skill in algebra as it helps simplify expressions and solve equations more easily. By factoring a polynomial, we can often find its roots, which are the values of x that make the polynomial equal to zero. This is useful in solving various types of problems in mathematics and science.

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When the p-value is less than alpha, reject H_0.

When you conduct a two-tailed hypothesis test, you check if the sample falls outside of the two critical regions. You make use of a two-tailed test if you are required to check both sides of the data.

For example, in a two-tailed hypothesis test, suppose the null hypothesis is that a coin is fair. This means that you expect the coin to be heads half of the time and tails half of the time.

The alternative hypothesis is that the coin is biased. This means that it will be heads more than half of the time or tails more than half of the time.If you get a p-value that is less than your alpha, you can reject the null hypothesis.

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[tex]\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &50000\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ t=years\\ \end{cases} \\\\\\ A = 50000(1 + 0.05)^{t} \implies A=50000(1.05)^t \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{in 2017, 7 years later}}{A=50000(1.05)^7\implies A\approx 70355} \\\\\\ \stackrel{\textit{in 2020, 10 years later}}{A=50000(1.05)^{10}\implies A\approx 81444} \\\\\\ \stackrel{\textit{in 2030, 20 years later}}{A=50000(1.05)^{20}\implies A\approx 132664}[/tex]

Sonya is approximately 47 feet away from Thomas. And

height of the kite above the ground is approximately 43 feet.

How to find the height?

To find the height of the kite above the ground, we can use trigonometry. Let's draw a diagram:

       /|

      / |

     /  | height (h)

    /   |

   /    |

/θ___|___

 distance (d)

We know that the angle θ is 25°, the hand height is 3 feet, and the distance from the hand to the kite is 100 feet. We want to find the height of the kite above the ground, which we'll call h.

Using trigonometry, we can write:

tan(θ) = h / d

where tan(θ) is the tangent of the angle θ, and d is the distance from the hand to the kite. Solving for h, we get:

h = d * tan(θ)

Substituting the known values, we get:

h = 100 * tan(25°) ≈ 43.1 feet

So the height of the kite above the ground is approximately 43 feet.

2.Let's draw a diagram:

        Sonya

          |

          |

 66°      |       48°

          |    

          |

-----------o----------- Balloon

          |

          |

        Thomas

We want to find the distance between Sonya and Thomas, which we'll call x. We know that the height of the balloon above the ground is 126 feet. We also know the angles of elevation from Sonya and Thomas to the balloon.

Let's first find the distance from Sonya to the balloon. We can use trigonometry again:

tan(66°) = 126 / d

where d is the distance from Sonya to the balloon. Solving for d, we get:

d = 126 / tan(66°) ≈ 50.5 feet

Now let's find the distance from Thomas to the balloon:

tan(48°) = 126 / (x + d)

where x + d is the total distance from Thomas to the balloon (the sum of the distances from Thomas to the point directly below the balloon, and from that point to the balloon). Solving for x + d, we get:

x + d = 126 / tan(48°) ≈ 97.5 feet

Finally, we can solve for x:

x = (x + d) - d ≈ 97.5 - 50.5 ≈ 47 feet

So Sonya is approximately 47 feet away from Thomas.

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The length of the ladder can be calculated using trigonometry as 31/sin 78.

The length of the ladder can be calculated using trigonometry. First, use the given information to draw a diagram. The angle of 78 degrees forms the angle of the ladder relative to the ground, and the side opposite of this angle is the length of the ladder. The side adjacent to the angle is the height of the electric box, which is given as 31 feet.

Now, use the sine function to calculate the length of the ladder. The sine function relates the ratio of the opposite side to the hypotenuse, so the equation is 31/sin 78.

Plugging this equation into a calculator will give the length of the ladder as approximately 51.7 feet.

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Rowan should get the ice cream in a cup as the cup holds 26.2 in3 more ice cream than the cone.

First, we need to find the volume of ice cream that the cone holds:

we can use the formula for volume, we get:

Volume = π × r² × h/3

when we put the values in the formula, we get:

Volume = 3.14 × 2.5² × 5/3

solving the problem, we get:

Volume =32.7 inches³

Now we need to find the volume of ice cream that the cup holds,

we use the formula of volume, we get:

Volume = π × r² × h

Diameter = 5 inches ⇒ Radius = 2.5 inches

(since we know that the radius is the exact half of the diameter)

when we put the values in the formula, we get:

Volume = 3.14 × 2.5² × 3

Volume =58.9 inches³

Now that we have both the values, we can easily find the difference:

Volume of the cup - volume of the cone = 58.9 - 32.7 = 26.2 inches³

The cup holds 26.2 in³ more ice cream than the cone.

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Clara is earning money at a faster rate than Tiffany, with a difference of $4 per hour.

A graph in x-y axis plot is a visual representation of mathematical functions or data points on a Cartesian coordinate system.

To determine who is earning money at a faster rate, we need to calculate the hourly earnings for each person.

For Tiffany, the hourly earnings can be calculated as follows:

Hourly earnings = Earnings / Time

Hourly earnings = 40 / 5 = 8

Hourly earnings = 80 / 10 = 8

Hourly earnings = 120 / 15 = 8

So, Tiffany's hourly earnings are a constant $8 per hour.

For Clara, we can estimate her hourly earnings from the graph. The graph shows that Clara earns $60 for 5 hours of work, $120 for 10 hours of work, and $180 for 15 hours of work. Therefore, her hourly earnings can be calculated as follows:

Hourly earnings = Earnings / Time

Hourly earnings = 60 / 5 = 12

Hourly earnings = 120 / 10 = 12

Hourly earnings = 180 / 15 = 12

So, Clara's hourly earnings are a constant $12 per hour.

Thus, Clara is earning money at a faster rate than Tiffany, with a difference of $4 per hour.

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Complete question-

a) The accumulated amount or future value of investing $150 on the first day of each month at 6% compounded monthly for 40 years is $274,152.43.

b) , The future value of the investment after 40 years at an annual interest rate of 4%, compounded semi-annually, is $9,054.60.

a)

N = 40 years * 12 months = 480 months

I% = 6% per year / 12 months = 0.5% per month

PV = $0 (since we are not investing any money initially)

PMT = $150

FV = ?

P/Y = 1 (payments made monthly)

C/Y = 12 (compounded monthly)

Using the formula for future value of an annuity:

FV = PMT * ((1 + I%)^(N) - 1) / I%

FV = $150 * ((1 + 0.5%)^(480) - 1) / 0.5%

FV = $274,152.43

Therefore, the accumulated amount or future value of investing $150 on the first day of each month at 6% compounded monthly for 40 years is $274,152.43.


b)
Given information:

PV (present value) = $900

I% (annual interest rate) = 4%

P/Y (payments per year) = 1 (since the investment is compounded semi-annually)

C/Y (compounding periods per year) = 2

N (number of periods) = 40 years * 2 (since interest is compounded twice a year) = 80

Using the compound interest formula:

FV = PV * (1 + (I%/C/Y))^(N*C/Y)

FV = $900 * (1 + (4%/2))^(80*2)

FV = $900 * (1.02)¹⁶⁰

FV = $900 * 10.06

FV = $9,054.60


Therefore, the future value of the investment after 40 years at an annual interest rate of 4%, compounded semi-annually, is $9,054.60.

PMT (payment per period) cannot be calculated since no periodic payments are mentioned in the given information.

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If the new number is four times the reciprocal of the original number, then  the original number is 0.02.

Let us assume the original positive decimal number is = "x".

When we move the decimal point of x four places to the right,

We get,  "10000x", which is four times the reciprocal of x.

So, equation can be written as;

⇒ 10000x = 4(1/x),

On simplifying the equation,

We get,

⇒ 10000x² = 4,

Dividing both sides by 10000,

We get,

⇒ x² = 0.0004,

Simplifying further,

We get,

⇒ x = 0.02

Therefore, the original positive decimal number is 0.02.

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Answer:

USA Volleyball specifies a minimum ceiling height of 23′ for nationally sanctioned competition.

Step-by-step explanation:

its height regulation of how tall the ceiling should be

The inequality x/6.2 ≥ -2 is solved by multiplying both sides by 6.2 to get x ≥ -12.4, which means x is greater than or equal to 12.4.

To solve the inequality x/6.2 ≥ -2, we want to find all possible values of x that make the inequality true.

First, we can isolate x by multiplying both sides of the inequality by 6.2 (which is positive, so we do not need to flip the inequality sign):

x/6.2 * 6.2 ≥ -2 * 6.2

Simplifying, we get:

x ≥ -12.4

This means that any value of x that is greater than or equal to -12.4 will make the inequality true.

To see why this is the case, we can substitute a few values for x and see if they satisfy the inequality. For example, if we let x = 12.4, then:

x/6.2 = 12.4/6.2 = 2

And we can check that 2 is indeed greater than or equal to -2. Therefore, x = 12.4 is a valid solution.

Similarly, if we let x = 20, then:

x/6.2 = 20/6.2 ≈ 3.23

And we can check that 3.23 is also greater than or equal to -2. Therefore, x = 20 is also a valid solution.

However, if we let x = -15, then:

x/6.2 = -15/6.2 ≈ -2.42

And we can see that -2.42 is not greater than or equal to -2. Therefore, x = -15 is not a valid solution.

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Maxima set is {(6, 9)}.

To find the maxima set from the given set of points, we need to identify the points with the highest y-values.

Step 1: Examine the y-values of the given points.

(7, 2), (3, 1), (9, 3), (4, 5), (1, 4), (6, 9), (2, 6), (5, 7), (8, 6)

Step 2: Identify the highest y-value among the points.

In this case, the highest y-value is 9.

Step 3: Find the points with the highest y-value.

There is one point with a y-value of 9: (6, 9)

Step 4: Create the maxima set.

The maxima set consists of the point(s) with the highest y-value: {(6, 9)}

So the maxima set is {(6, 9)}.

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The statement "The value is decreasing $207 per year" best explains how the value is changing. This is because the function shows that the value is decreasing linearly with time, at a rate of $82 per year. Therefore, over t years, the value will decrease by 82t dollars. For example, after one year, the value will decrease by $82, and after two years, it will decrease by $164.

Now check

Answer:

1080°

Step-by-step explanation:

Let n = the number of sides    

(n-2)180

(8-2)180

6(180) =  1080

Helping in the name of Jesus.                        

87.6  is the difference between the mean of the warmest and coldest days recorded.

What is the mean called in statistics?

By summing all the numbers in a data collection and dividing by the total number of values in the set, one can determine the mean (average) of the data set. When a data collection is ranked from least to greatest, the median is the midpoint. 

WARMEST: 98, 97, 102, 98, 97

                = 97, 97 , 98 , 98 , 102

               = 97 + 97 + 98 + 98 + 102/5

                 = 492/5 = 98.4

COLDEST: 12, 14, 9, 7, 12

               = 7 , 9 , 12 ,12,  14

              =  54/5

               = 10.8

the difference between the mean of the warmest and coldest days recorded    =   98.4 - 10.8

                  =  87.6

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Answer:

x ≤ 40

Step-by-step explanation:

-75-6x+13x ≤ 200

-75 is the cost of the booth a day

-6 is the intial cost of the paintings for Chris

x is the amount of paintings

13 is the price Chris sells the paintings for

200 is the profit needed

First thing you do is add like terms -75-6x+13x ≤ 200

add -6x and 13x

-75+7x ≤ 200

Now add 75 to both sides

7x ≤ 275

Now divide both sides by 7

x≤ 275

x≤ 39.2857142857

round up to x≤ 40   (because 39 paintings is not enough, 40 gives him $205 in profit while 39 only gives him $198 in profit)

Therefore, we need to add approximately 0.0526 gallons of water (which is equivalent to about 6.63 fluid ounces) to 1 gallon of pure antifreeze to obtain a solution that is 95% antifreeze.

In mathematics, an equation is a statement that asserts the equality of two expressions. An equation typically consists of one or more variables, coefficients, and constants, and it can include mathematical operations such as addition, subtraction, multiplication, and division. The expressions on both sides of the equation are separated by an equal sign, indicating that they have the same value. The goal of solving an equation is to determine the value of the variables that make the equation true. Equations are used in many areas of mathematics and science to model real-world phenomena and solve problems.

Here,

Let's assume that we need to add x gallons of water to 1 gallon of pure antifreeze to obtain a solution that is 95% antifreeze. We know that the final solution will contain 1 gallon of antifreeze, and that this will be 95% of the total solution (the remaining 5% will be water). So, we can write:

1 gallon of antifreeze = 95% of (1 gallon of antifreeze + x gallons of water)

We can simplify this equation by converting 95% to a decimal:

0.95 × (1 gallon of antifreeze + x gallons of water) = 1 gallon of antifreeze

Now we can solve for x by isolating it on one side of the equation. First, let's distribute the 0.95:

0.95 gallons of antifreeze + 0.95x gallons of water = 1 gallon of antifreeze

Next, let's isolate x by subtracting 0.95 gallons of antifreeze from both sides:

0.95x gallons of water = 0.05 gallons of antifreeze

Finally, we can solve for x by dividing both sides by 0.95:

x = 0.05 gallons of antifreeze ÷ 0.95

x ≈ 0.0526 gallons of water

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The solution for the equation given would be x = 2 and x = -1.

To solve the equation 2[x² + 2x + 1] - x² - 4x + 4 = x² - 3x, we can simplify and rearrange the terms as follows:

2x² + 4x + 2 - x² - 4x + 4 = x² - 3x

x² - 3x + 6 = x² - 3x

2x² - 2x - 6 = 0

Dividing both sides by 2, we get:

x² - x - 3 = 0

We can then solve for x by factoring or using the quadratic formula. Factoring gives:

(x - 2)(x + 1) = 0

So, the solutions are x = 2 and x = -1.

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Answer:

What is the median of - 11, 31, 17, 22, 18, 25, 25, 10, 15, 12, 30, 12, 29, 25, 21, 32, 30, 25?

10, 11, 12, 12, 15, 17, 18, 21, 22, 25, 25, 25, 25, 29, 30, 30, 31, 32

25 + 25

50 ÷ 2

Step-by-step explanation:

You're welcome.

Answer:

To determine the number of outcomes for Nikia's random selection of a team card and a character card for a role-playing game, we can use a tree diagram, table, or list.

There are four possible teams: air, fire, land, and water. Once a team card is selected, there are three possible character cards: healer, spy, and thief. Therefore, the total number of outcomes is the product of the number of options for each selection, which is:

4 (number of team options) x 3 (number of character options) = 12

So there are 12 possible outcomes for Nikia's random selection of a team card and a character card. However, since Nikia has specified that her favorite team is air and her favorite character is spy, the number of outcomes that would satisfy her preferences is:

1 (air team) x 1 (spy character) = 1

Therefore, only one outcome would satisfy Nikia's preferences.

The graph of x=5 is a line parallel to the y-axis, with x-coordinate 5 at all points.

What is the vertical line?

A vertical line is a straight line that is perpendicular to the horizontal line and goes straight up and down in a two-dimensional coordinate system.

The graph of the equation x=5 is a vertical line passing through the point (5, y) for all values of y.

This is because no matter what value y takes, x will always be equal to 5.

Here's in image example of what the graph of x=5 would look like:

As you can see in the image attached, the line is vertical and intersects the x-axis at x=5.

Therefore, the graph of x=5 is a line parallel to the y-axis, with x-coordinate 5 at all points.

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Therefore, Jozef had 15 dimes and 27 quarters in his piggy bank.

An equation is a mathematical statement that shows that two expressions are equal. It typically consists of variables, constants, and mathematical operations. Equations can be solved by manipulating the expressions to find the value of the variables that satisfy the equation. Equations can be used to model real-world situations, and they are an important tool in many fields, including mathematics, physics, engineering, and economics.

Here,

Let's use the following variables to represent the number of dimes and quarters in Jozef's piggy bank:

d: the number of dimes

q: the number of quarters

We know that Jozef has a total of 42 dimes and quarters, so we can write the equation:

d + q = 42

We also know that the total value of the coins is $8.25. We can express this value in cents as:

10d + 25q = 825

We can simplify this equation by dividing both sides by 5:

2d + 5q = 165

Now we have two equations with two variables:

d + q = 42

2d + 5q = 165

We can use the first equation to solve for one of the variables in terms of the other. For example, we can solve for q:

q = 42 - d

Now we can substitute this expression for q into the second equation:

2d + 5(42 - d) = 165

Simplifying and solving for d, we get:

2d + 210 - 5d = 165

-3d = -45

d = 15

So Jozef had 15 dimes in his piggy bank. We can use the first equation to find the number of quarters:

15 + q = 42

q = 27

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Answer:

Step-by-step explanation:

For vectors a = {4, 5, 0} and b = {1, 0, 3}, you want the cross product and verification that the cross product is orthogonal to both 'a' and 'b'.

The cross product of 4i+5j+0k and 1i+0j+3k is the determinant ...

  [tex]\left|\begin{array}{ccc}i&j&k\\4&5&0\\1&0&3\end{array}\right|=15i-12j-5k[/tex]

As a list of coefficients, the cross product is c = {15, -12, -5}.

Vectors are orthogonal if their dot product is 0.

  a·c = {4, 5, 0}·{15, -12, -5} = (4·15) -(5·12) +(0·(-5)) = 60 -60 = 0

  b·c = {1, 0, 3}·{15, -12, -5} = (1·15) +(0·(-12)) +(3·(-5)) = 15 -15 = 0

The dot products are both zero, so the cross product is orthogonal to both of the vectors that created it.

The cross product of vectors a and b is 15i - 12j - 5k. To verify if it is orthogonal to both a and b, we calculate the dot products and find that they both equal zero.

The cross product of vectors a and b is given by:

a ⨯ b = (aybz - azby)i + (azbx - axbz)j + (axby - aybx)k

Calculating the cross product of a and b using the given values:a ⨯ b = (5)(3) - (0)(0)i + (0)(1) - (4)(3)j + (4)(0) - (5)(1)k = 15i - 12j - 5k

To verify if the cross product is orthogonal to both a and b, we calculate the dot products:

(a ⨯ b) · a = (15)(4) + (-12)(5) + (-5)(0) = 0

(a ⨯ b) · b = (15)(1) + (-12)(0) + (-5)(3) = 0

Since both dot products equal zero, we can conclude that the cross product a ⨯ b is orthogonal to both a and b.

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Answer:

x=56 feet

Step-by-step explanation:

This problem uses trigonometry.

Tangent of an angle equals opposite/adjacent.

Tan(35)=(x/80)

(.700)=(x/80)

(80)(.700)=x

56.0166=x

Using the idea of the angle of elevation as it could be applied to the problem, the height of the statue is 182 ft

When gazing up at an object or point, the angle of elevation is the angle formed between the horizontal plane and the observer's line of sight. It is, in other words, the angle at which the line of sight of an observer is tilted upward from the horizontal plane.

The angle of elevation is an important concept in geometry and trigonometry and is used to calculate the height of objects, such as buildings, towers, or trees, or to measure the distance between two points.

We know that;

Tan 34 = x/270

x = 270 tan 34

x = 182 ft

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You will need 0.75 cups of milk when quadrupling the recipe.

When quadrupling the recipe, you would need 12 tablespoons of milk. To make the calculations easier, it is more efficient to convert the tablespoons to cups. So, the question is how many cups of milk will you need? We know that there are 16 tablespoons in a cup. Therefore, we can find how many cups of milk you will need as follows:

12 tablespoons = (12/16) cups

12 tablespoons  =  0.75 cups

So, you would need 0.75 cups of milk when quadrupling the recipe.

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Answer:

-17

Step-by-step explanation:

1st step =7-4 X 6

2nd step =7-24

3rd step =-17

The function F(x)'s valid domain is therefore (-, -3), (-3, -2), and (-2, ).

We enter each value of x into the function and simplify as follows in order to evaluate the function F(x) at the values of the supplied domain:

[tex]F(-3) = (2(-3) + 6)/((-3)^2 + 5(-3) + 6) = 0/0[/tex] (undefined) (undefined)

[tex]F(-2) = (2(-2) + 6)/((-2)^2 + 5(-2) + 6) = 0/0[/tex](undefined) (undefined)

[tex]F(0) = (2(0) + 6)/(0^2 + 5(0) + 6) = 1[/tex]

[tex]F(2) = (2(2) + 6)/(2^2 + 5(2) + 6) = 2/3[/tex]

[tex]F(3) = (2(3) + 6)/(3^2 + 5(3) + 6) = 2/4 = 1/2[/tex]

The function is undefined at x=-3 and x=-2 because the fraction's

denominator is zero at these points, and division by zero is undefined, as can be seen from the aforementioned evaluations. All real numbers, with the exception of -3 and -2, fall inside the given function's valid domain.

The function F(x)'s valid domain is therefore (-, -3), (-3, -2), and (-2, ).

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The pricing for purchasing apples from the orchard, stating that for the first 10 pounds, the price is $2 per pound, and for each additional pound, the price is $1 per pound.

What is the unit price?

In order to find the unit price of a certain item, we just need to divide the total price paid (or total cost) by the amount of items bought.

If Anne buys less than or equal to 10 pounds of apples from David's Apple Orchard, then she will pay $2 per pound.

If she buys more than 10 pounds, then she will pay $1 per pound for each additional pound after the first 10 pounds.

To buy apples from David's Apple Orchard, Anne has to follow these rules

For the first 10 pounds of apples, she will pay $2 per pound.

For each additional pound of apples after the first 10 pounds, she will pay $1 per pound.

Hence, the pricing for purchasing apples from the orchard, stating that for the first 10 pounds, the price is $2 per pound, and for each additional pound, the price is $1 per pound.

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