What is the value of p in the equation?

One-fourth (8 minus 4 p) + 2 p = 12
–20
–2
5
10

Answer:

12

Step-by-step explanation:

pitcher plant consumes one insect at a time so total number of pitcher plants used for insects consumption according to the given data set will be 12

Their house will be worth approximately $240,154.57 in 8 years.

Non of the options is correct.

To determine how much their house will be worth in 8 years, we can substitute the value of t = 8 into the exponential equation:

y = 150,000(1.004)^(12t)

y = 150,000(1.004)^(12*8)

y = 150,000(1.004)^96

Using a calculator or computer software to evaluate the exponential expression, we find:

y ≈ 150,000 * 1.601030475

y ≈ 240,154.57

None of the provided answer choices match the calculated value. However, we can examine the available options and make an estimation:

A) $240,000: This option is very close to the calculated value of $240,154.57 and is a reasonable estimate.

B) $220,000: This option is significantly lower than the calculated value and is not a close estimate.

C) $1,258,884: This option is significantly higher than the calculated value and is not a close estimate.

D) $14,457,600: This option is extremely higher than the calculated value and is not a realistic estimate.

Based on the provided answer choices, option A) $240,000 is the closest estimate to the calculated value of $240,154.57. However, please note that the actual value may vary depending on the specific calculations and rounding methods used.

Non of the options is correct.

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The ordered triple (p, q, r) that satisfies the given system of linear equations is (7, 2, 2).

To solve the given system of equations:

Start with the first equation: p - 2q = 3.

Multiply this equation by 2 to eliminate the coefficient of q: 2p - 4q = 6.

Next, we'll combine this equation with the second equation: q - 2r = -2.

Add the two equations together: (2p - 4q) + (q - 2r) = 6 + (-2).

Simplifying, we get: 2p - 3q - 2r = 4.

Now, let's consider the third equation: p + r = 9.

Rearrange this equation: p = 9 - r.

We can substitute this value for p in the equation we obtained in step 3:

2(9 - r) - 3q - 2r = 4.

Simplify the equation: 18 - 2r - 3q - 2r = 4.

Combining like terms, we have: -4r - 3q = -14.

We now have a system of two equations with two variables:

-4r - 3q = -14, (Equation 1)

q - 2r = -2. (Equation 2)

To solve this system, we can use various methods such as substitution or elimination. Here, we'll use the substitution method.

From Equation 2, we can solve for q:

q = 2r - 2.Substituting this value for q in Equation 1, we have:

-4r - 3(2r - 2) = -14.

Simplify and solve for r:

-4r - 6r + 6 = -14,

-10r = -20,

r = 2.

Now, substitute the value of r back into Equation 2 to solve for q:

q - 2(2) = -2,

q - 4 = -2,

q = 2.

Finally, substitute the values of q and r into Equation 3 to solve for p:

p + 2 = 9,

p = 7.

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Answer:

Annette should plan to spend 2.25 hours walking back.

Step-by-step explanation:

To solve this problem, we can use the formula:

Time = Distance / Speed

Let's assume the distance of the race is D miles.

Annette spends her time running the distance of the race, which takes:

Time running = D / 9 hours

She then walks back the same distance, which we need to find the time for:

Time walking = D / 3 hours

Since Annette has a total of 3 hours for her training, the sum of the running time and walking time should equal 3 hours:

D / 9 + D / 3 = 3

To simplify the equation, we can multiply all terms by 9 to eliminate the denominators:

D + 3D = 27

Combining like terms:

4D = 27

Dividing both sides of the equation by 4:

D = 6.75

So, the distance of the race is 6.75 miles.

To find the time Annette should spend walking back, we substitute the distance into the time-walking formula:

Time walking = D / 3 = 6.75 / 3 = 2.25 hours

Therefore, Annette should plan to spend 2.25 hours walking back.

These are the four solutions for each given equation within the range of -360 degrees to 360 degrees.

To find the solutions for the given equations involving tangent (tan) functions, we need to solve for the angle (x) that satisfies each equation. Keep in mind that angles in trigonometry are typically measured in degrees.

tan(x) = 0.781:

To find the angle x that satisfies this equation, we can use the inverse tangent function (arctan or tan^(-1)). Taking the inverse tangent of both sides, we have:

x = arctan(0.781)

Using a calculator or a trigonometric table, we find that:

x ≈ 38.08 degrees

Since tangent is a periodic function with a period of 180 degrees, we can add or subtract multiples of 180 to find the other solutions:

x ≈ 38.08 degrees + 180n, where n is an integer

So, the four solutions for tan(x) = 0.781 are approximately:

x ≈ 38.08 degrees, 218.08 degrees, 398.08 degrees, -141.92 degrees

tan(x) = -1.036:

Similarly, using the inverse tangent function, we have:

x = arctan(-1.036)

Using a calculator or a trigonometric table, we find that:

x ≈ -45.14 degrees

Again, considering the periodicity of tangent, we can add or subtract multiples of 180 to find the other solutions:

x ≈ -45.14 degrees + 180n, where n is an integer

The four solutions for tan(x) = -1.036 are approximately:

x ≈ -45.14 degrees, 134.86 degrees, 314.86 degrees, 494.86 degrees

tan(x) = 2.145:

Using the inverse tangent function, we have:

x = arctan(2.145)

Using a calculator or a trigonometric table, we find that:

x ≈ 65.64 degrees

Considering the periodicity of tangent, we can add or subtract multiples of 180 to find the other solutions:

x ≈ 65.64 degrees + 180n, where n is an integer

The four solutions for tan(x) = 2.145 are approximately:

x ≈ 65.64 degrees, 245.64 degrees, 425.64 degrees, -114.36 degrees

These are the four solutions for each given equation within the range of -360 degrees to 360 degrees.

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The volume of the larger can is approximately 3308.56 cubic inches.

To find the volume of the larger can, we can use the formula for the volume of a cylinder, which is given by V = πr²h, where V represents the volume, r represents the radius, and h represents the height.

Let's assume that the radius of the smaller can is r, and the height is h. According to the problem, the larger can has a radius and height that are both three times longer than the corresponding dimensions of the smaller can. Therefore, the radius of the larger can would be 3r, and the height would be 3h.

Given that the volume of the smaller can is 35.28 in³, we can substitute the values into the formula to solve for the volume of the larger can:

V_small = πr²h

35.28 = πr²h

To find the volume of the larger can, we need to calculate V_large = π(3r)²(3h):

V_large = π(3r)²(3h)

V_large = π(9r²)(3h)

V_large = 27πr²h

Since we know that 35.28 = πr²h from the volume of the smaller can, we can substitute this into the equation for the volume of the larger can:

V_large = 27πr²h

V_large = 27π(35.28)

V_large ≈ 3308.56 in³

Therefore, the volume of the larger can is approximately 3308.56 cubic inches.

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Answer:

7606.62

Step-by-step explanation:

Start by finding how much you will have through the annuity. The question isn't that clear, so i will just assume it's an annuity due.

[tex]p(\frac{(1+i)^n-1}{i})*(1+i)\\i=.035/12= .0029166667\\n=10*12=120\\p=75 (given)\\75\frac{(1+.0029166667)^{120}-1}{.0029166667}*(1+.0029166667)= 10788.814149\\[/tex]

Now just equate this to a time 0 payment at the same rate

[tex]10788.814149=(1+.0029166667)^{120}*x\\x= 7606.6228603=7606.62[/tex]

As a quick note, if you were supposed to assume that your annuity was an annuity immediate the answer would be 7584.50.

The interviewer should provide clear and concise feedback on the candidate's performance in the interview, and ensure that the feedback is related to the job requirements.

In addition, the interviewer should ask relevant questions to get an idea about the interviewee's knowledge, skills, and abilities.Overall, the interviewer should strive to be fair and objective throughout the interview process, to minimize the risk of Unbiased Errors.

An interviewer officer selects a person not suitable for the job, this error is known as Unbaised Error.What is an Unbiased Error?An Unbiased error happens when you make an incorrect judgment regarding the interviewee, which may occur when the interviewer is unable to assess the interviewee objectively.

There are many factors that could contribute to an Unbiased Error, such as the interviewer's opinions and preconceptions, their biases or prejudices, the interviewer's inadequate understanding of the job requirements, or the applicant's inadequate preparation for the interview.In an unbiased interview, the interviewer does not have any preconceived ideas or predetermined judgments about the interviewee's knowledge, skills, or abilities.

The interviewer should be able to provide equal chances for all applicants, regardless of their gender, ethnicity, or any other factors that are not related to the job requirements.The interviewer should also assess the interviewee objectively, with no favoritism or bias.

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[tex]\tan(x )=\cfrac{\stackrel{opposite}{18}}{\underset{adjacent}{11}} \implies \tan^{-1}(~~\tan( x )~~) =\tan^{-1}\left( \cfrac{18}{11} \right) \\\\\\ x =\tan^{-1}\left( \cfrac{18}{11} \right)\implies x \approx 58.6^o[/tex]

Make sure your calculator is in Degree mode.

Answer:

x =  58.6°

Step-by-step explanation:

Because this is a right triangle, we're able to find the measure of angle x using one of the trigonometric ratios.  

When angle x is the reference angle, the side that is 18 units long is the opposite side and the side that is 11 units long is the adjacent side.

Thus, we can use the tangent ratio, which is given by:

tan (θ) = opposite / adjacent, where

Thus, we have tan (θ) = 18 / 11

In order to find angle measures we use inverse trigonometry:

tan^-1 (18 / 11) = x

58.57043439 = x

58.6 = x

Thus, the measure of angle x is about 58.6°

S received $1050, J received $0, and the ratio of the money shared between S and J is 0:1. A received 23.33% of the total amount.

Step 1: Determine the amount A received.

We know that A received 1/2 of the total amount, which is $1050. Therefore, the total amount can be calculated by multiplying A's portion by 2: 1050 * 2 = $2100.

Step 2: Calculate the amount J received.

To find the amount J received, we need to subtract A's and S's amounts from the total.

From Step 1, we know that the total is $2100. S received the same amount as A, which is $1050.

Therefore, we subtract A's and S's amounts from the total: 2100 - 1050 - 1050 = $0.

Since J received the remainder, we see that J did not receive any amount from the initial sum of $4500.

Step 3: Calculate the amount S received.

To find the amount S received, we need to subtract S's amount from the total.

Again, from Step 1, we know that the total is $2100. S received the same amount as A, which is $1050.

Therefore, we subtract S's amount from the total: 2100 - 1050 = $1050.

Step 4: Calculate the ratio in which the money was shared between S and J.

Since J did not receive any amount, the ratio of the money shared between S and J is 0:1.

Step 5: Calculate the percentage of the total amount that A received.

To find the percentage, we divide A's amount by the total and multiply by 100: (1050/4500) * 100 = 23.33%.

Therefore, S received $1050, J received $0, and the ratio of the money shared between S and J is 0:1.

A received 23.33% of the total amount.

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The temperature at x = 4, y = 3.2, estimated through linear interpolation from the given data points, is approximately 46.744.

To find the temperature at x=4, y=3.2 using linear interpolation, first of all, determine the values at the surrounding grid points and interpolate between them.

From the given table, we can identify the following surrounding points:

Point A: (x=4, y=3)

Point B: (x=4, y=4)

Point C: (x=6, y=3)

Point D: (x=6, y=4)

Next, interpolate along the x-axis at y=3 to find the temperature at x=4:

Temperature at x=4, y=3 = Interpolate(A, B)

Also, we have to interpolate along the x-axis at y=4 to find the temperature at x=4:

Temperature at x=4, y=4 = Interpolate(A, B)

Next, we'll interpolate between the temperatures obtained above along the y-axis at y=3.2:

Temperature at x=4, y=3.2 = Interpolate(Temperature at x=4, y=3, Temperature at x=4, y=4)

Let's calculate these values step by step:

Interpolate along the x-axis at y=3:

Temperature at x=4, y=3 = Interpolate(A, B)

= 80.00 + (4-4)/(4-4) * (80.00 - 80.00)

= 80.00

Interpolate along the x-axis at y=4:

Temperature at x=4, y=4 = Interpolate(A, B)

= 38.43 + (4-4)/(4-4) * (35.03 - 38.43)

= 38.43

Interpolate between temperatures along the y-axis at y=3.2:

Temperature at x=4, y=3.2 = Interpolate(Temperature at x=4, y=3, Temperature at x=4, y=4)

= 80.00 + (3.2-3)/(4-3) * (38.43 - 80.00)

= 80.00 - 0.8 * 41.57

= 80.00 - 33.256

= 46.744

Therefore, the temperature at x=4, y=3.2 is approximately 46.744.

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Answer:

the amount of metal required to make the can is 352.8π square centimeters.

Step-by-step explanation:

To calculate the amount of metal required to make the can, we need to find the surface area of the can.

The can consists of two circular ends (top and bottom) and a cylindrical body.

1. Surface Area of the Circular Ends:

The circular ends can be considered as two circles. The surface area of each circular end can be calculated using the formula for the area of a circle:

A_end = πr^2

Given the diameter of the can is 14 cm, the radius (r) is half the diameter, so r = 14 cm / 2 = 7 cm.

A_end = π * 7^2 = 49π cm^2 (for each circular end)

2. Surface Area of the Cylindrical Body:

The cylindrical body of the can can be represented as a rectangle that is rolled into a cylinder. The surface area of the cylindrical body can be calculated using the formula for the lateral surface area of a cylinder:

A_body = 2πrh

Given the height (h) of the can is 18.2 cm and the radius (r) is 7 cm, we can calculate the surface area of the cylindrical body:

A_body = 2π * 7 * 18.2 = 254.8π cm^2

3. Total Surface Area:

To calculate the total surface area of the can, we add the surface areas of the circular ends and the cylindrical body:

Total Surface Area = 2 * A_end + A_body

                 = 2 * 49π + 254.8π

                 = 98π + 254.8π

                 = 352.8π cm^2

Therefore, the amount of metal required to make the can is 352.8π square centimeters.

The range of the given sample data is 94 - 1 = 93.

To find the range of the given sample data, we need to calculate the difference between the maximum value and the minimum value in the data set.

The given sample data is: 4, 94, 37, 50, 46, 75, 5, 69, 1, 44, 35.

To find the range, we first need to determine the maximum and minimum values in the data set:

Maximum value: 94

Minimum value: 1

Now we can calculate the range by subtracting the minimum value from the maximum value:

Range = Maximum value - Minimum value

= 94 - 1

= 93

Therefore, the range of the given sample data is 93. The range represents the spread or the difference between the highest and lowest values in the data set.

The range tells us the extent of the variability in the data. In this case, the range of 93 indicates that the jersey numbers of the 11 randomly selected players from the football team have a relatively wide spread. The highest jersey number is 94, and the lowest jersey number is 1, with a difference of 93 between them.

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We can conclude that points, planes, lines, and other undefinable terms are important concepts in geometry. They are essential building blocks of geometric shapes and are used in mathematical calculations and problem-solving.

Geometry is a field of mathematics that deals with the study of shapes, sizes, relative positions, and properties of space. It involves understanding the properties of lines, points, planes, and other shapes in space. Undefinable terms are important concepts in geometry that are not defined or are difficult to define. Some statements that are true regarding undefinable terms in geometry are as follows: A point has no length or width.

A point is one of the fundamental concepts of geometry, and it is an essential building block of other geometric shapes. A point has no length or width; instead, it indicates a specific location in space. Points are represented as dots in geometry.A plane has one dimension, length. A plane is a flat, two-dimensional surface that extends infinitely in all directions. It has only one dimension, length.

A plane is a surface that has no thickness or depth, but it has an infinite number of points.A plane consists of an infinite set of lines. A plane is made up of an infinite number of lines that are parallel to each other. All of these lines extend in both directions, so they never meet. When a plane is intersected by a line, it creates a point where the two meet.

A line has a definite beginning and end. A line is a geometric object that extends infinitely in both directions. It has no width or thickness, but it has a definite beginning and end. A line is usually represented as a straight line that extends infinitely in both directions. A line is made up of an infinite number of points.

A line consists of an infinite set of points. A line is an infinite set of points that are aligned in a straight line. A line has no thickness or width, but it is infinitely long. The points on a line have no beginning or end, but they are considered to be in a specific order.

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We reflect each vertex of triangle ABC across this line of reflection. After the reflection, A' will be (-2, 2), B' will be (-2, 4), and C' will be (-6, 2).

The reflected diagram will have triangle A'B'C' in the same orientation as triangle XYZ, with vertices A'(-2, 2), B'(-2, 4), and C'(-6, 2).

o place triangle ABC into the same orientation as triangle XYZ, we can perform a reflection across a line that preserves the shape and size of the triangles. In the given diagram, we can observe that the vertices of triangle ABC are labeled A(2, 1), B(4, 4), and C(6, 2), while the vertices of triangle XYZ are labeled X(5, 1), Y(7, 4), and Z(9, 2).

To find the line of reflection, we can draw a line that connects the midpoint of AB with the midpoint of XY. The midpoint of AB is ((2+4)/2, (1+4)/2) = (3, 2.5), and the midpoint of XY is ((5+7)/2, (1+4)/2) = (6, 2.5). Therefore, the line connecting these midpoints is a horizontal line with the equation y = 2.5.

Please note that the diagram provided is a rough representation, and the exact positions and orientations may vary based on the precise coordinates of the vertices.

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The function for the velocity is v(t) = 12t² – 12t – 72.

The velocity is zero at t = 3 and t = -2.

The function for the acceleration is a(t) = 24t – 12.

To find the velocity function v(t), we need to take the derivative of the position function s(t) with respect to time.

Given that s(t) = 4t³ – 6t² – 72t, we can differentiate it to obtain the velocity function v(t):

v(t) = s'(t) = d/dt (4t³ – 6t² – 72t)

To differentiate each term, we can apply the power rule of differentiation:

v(t) = 12t² – 12t – 72

Therefore, the function for the velocity is v(t) = 12t² – 12t – 72.

To find when the velocity equals zero, we set v(t) = 0 and solve for t:

12t² – 12t – 72 = 0

We can factor out a common factor of 12:

12(t² – t – 6) = 0

Now, we can solve the quadratic equation t² – t – 6 = 0 by factoring or using the quadratic formula:

(t – 3)(t + 2) = 0

This gives us two possible values for t when the velocity equals zero: t = 3 and t = -2.

Therefore, the velocity is zero at t = 3 and t = -2.

To find the function for acceleration a(t), we need to take the derivative of the velocity function v(t):

a(t) = v'(t) = d/dt (12t² – 12t – 72)

Differentiating each term:

a(t) = 24t – 12

Therefore, the function for the acceleration is a(t) = 24t – 12.

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The water source will provide 144 dal (or 1440 liters) more in 12 minutes compared to the initial 120 dal (or 1200 liters) in 10 minutes.

A water source provides 120 dal (decaliters) of water in 10 minutes. To determine how many additional liters it will provide in 12 minutes, we can convert the units and calculate the difference.

1 dal is equal to 10 liters. So, 120 dal is equal to 1200 liters.

In 10 minutes, the source provides 1200 liters of water.

To find out how many more liters it will provide in 12 minutes, we can set up a proportion:

10 minutes corresponds to 1200 liters

12 minutes corresponds to x liters

Using the proportion, we can cross-multiply:

10 * x = 12 * 1200

10x = 14400

x = 14400 / 10

x = 1440

Therefore, the water source will provide an additional 1440 liters in 12 minutes.

Converting back to decaliters, 1440 liters is equal to 144 dal.

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The volume of the triangular prism that is given above would be = 6cm³. That is option B.

To calculate the volume of the triangular prism, the formula that should be used would be given below as follows;

Volume of triangle prism = ½×b×h×l

base length = 12 mm = 1.2cm

height = 2.5cm

length = 4cm

Volume = 1/2 × 1.2× 2.5× 4

= 6 cm³

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The simplified form of 2i^68 is the value of 2^34.

To simplify 2i^68, we need to use the properties of imaginary numbers and the exponent rules. Here are the steps to simplify it:

Recall that i is defined as the square root of -1.

Since i^2 equals -1, we can rewrite the expression as (2i^2)^34.

Simplify the exponent by applying the rule that (a^m)^n equals a^(mn). In this case, we have (2i^2)^34 = 2^34 * (i^2)^34 = 2^34 * i^(234).

Simplify the terms. 2^34 is a large number, but we can still calculate it. i^(2*34) can be further simplified as i^68.

Determine the value of i^68 by noting that i follows a pattern: i^1 = i, i^2 = -1, i^3 = -i, i^4 = 1. The pattern repeats every four powers of i.

Since 68 is divisible by 4, i^68 equals 1.

Plug in the simplified values: 2^34 * i^(2*34) = 2^34 * i^68 = 2^34 * 1 = 2^34.

Calculate the value of 2^34 using a calculator or by applying exponent rules.

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The percent increase in enrollment from 1980 to 2004 is 125%.

To calculate the percent increase in enrollment from 1980 to 2004, we can use the following formula:

Percent Increase = ((Final Value - Initial Value) / Initial Value) * 100

Given that the number of students in 1980 was 4,000 and the number of students in 2004 was 9,000, we can substitute these values into the formula:

Percent Increase = ((9,000 - 4,000) / 4,000) * 100

Simplifying the numerator:

Percent Increase = (5,000 / 4,000) * 100

Performing the division:

Percent Increase = 1.25 * 100

Calculating the final result:

Percent Increase = 125%

Therefore, the percent increase in enrollment from 1980 to 2004 is 125%.

This means that the number of students increased by 125% over the 24-year period. In other words, the enrollment more than doubled during this time frame.

It is important to note that the percent increase indicates the relative change in enrollment from the initial value. In this case, the enrollment increased by 125% compared to the enrollment in 1980.

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The line of best fit for the given data is represented by equation C, which is y= 0.95x + 12.

To find the line of best fit, the data points are plotted on a graph, and the line is drawn so that the distance between each data point and the line is minimized.

This is done using various statistical methods, such as the least squares method, to determine the equation of the line that best represents the data.
The equation of the line of best fit can then be used to make predictions or estimations about future values of the dependent variable based on the independent variable.

In this case, the line of best fit represents the relationship between x and y, and can be used to predict the value of y for a given value of x.
In conclusion, the line of best fit for the data is represented by equation C, y= 0.95x + 12.

This line provides the closest approximation to the data points and can be used to make predictions about future values of the dependent variable based on the independent variable.

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The swimming pool can hold a volume of 3.456 cubic meters of water.

The volume of water that the swimming pool can hold can be calculated by multiplying the base area of the pool by its depth. In this case, the base area is given as 192 m² and the depth is 1.8 cm.

However, it is important to note that the depth should be converted to meters before performing the calculation.

To convert 1.8 cm to meters, we divide it by 100 (since there are 100 centimeters in a meter):

Depth = 1.8 cm ÷ 100 = 0.018 m

Now we can calculate the volume of water using the formula:

Volume = Base Area × Depth

Substituting the given values, we get:

Volume = 192 m² × 0.018 m = 3.456 m³

Therefore, the swimming pool can hold a volume of 3.456 cubic meters of water.

In the explanation, we use the formula for calculating the volume of a rectangular prism, which is given by multiplying the base area by the depth. We convert the depth from centimeters to meters and then substitute the given values into the formula to find the volume of water that the swimming pool can hold, which is 3.456 cubic meters.

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The house will be worth approximately $1,258,884.83 in 8 years.

The correct answer is C: $1,258,884.

To find the worth of their house in 8 years, we need to substitute the value of t as 8 into the exponential equation:

y = 150,000(1.004)^(12t)

Plugging in t = 8:

y = 150,000(1.004)^(12*8)

Simplifying:

y = 150,000(1.004)^96

Using a calculator or a computer, we can evaluate the exponential expression:

y ≈ 1,258,884.83

Therefore, the house will be worth approximately $1,258,884.83 in 8 years.

The correct answer is C: $1,258,884.

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The ways to select the first 6 places be taken by the 3 schools​ is 20

From the question, we have

Total number of teams, n = 6

Numbers to schools, r = 3

The number of ways of selection could be drawn is calculated using the following combination formula

Total = ⁿCᵣ

Where

n = 6 and r = 3

Substitute the known values in the above equation

Total = ⁶C₃

Apply the combination formula

ⁿCᵣ = n!/(n - r)!r!

So, we have

Total = 6!/(3! * 3!)

Evaluate

Total = 20

Hence, the number of ways is 20

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An x-y coordinate table is the appropriate table to use when graphing a piece of a function. This table helps you to determine the corresponding y-values for different x-values and plot the points on a graph.

To graph a piece of a function, you would typically use an x-y coordinate table, also known as a Cartesian coordinate system. This table consists of two columns: one for the x-values (also called the input values) and one for the corresponding y-values (also called the output values). Each row in the table represents a point on the graph.
To graph a piece of a function, you would need to identify the domain (the set of possible x-values) for that specific piece. Once you have the domain, you can choose values from that domain and calculate the corresponding y-values using the function.
For example, if you have a piece of a linear function, such as y = 2x + 3, you could create a table by choosing various x-values and calculating the corresponding y-values. Let's say we choose x-values of -2, 0, and 2. Plugging these values into the equation, we find the corresponding y-values: -1, 3, and 7.
So the table for this piece of the linear function would look like this:
x    |   y
--------------
-2  |  -1
0    |   3
2    |   7
Once you have the x-y coordinate table, you can plot the points on a graph and connect them to create the graph of the piece of the function.

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The scale factor used is 1/4, which is equivalent to one fourth.

The first quadrilateral labeled D has side lengths of 6, 8, 6, and 8.

The second quadrilateral labeled D' has side lengths of 9, 12, 9, and 12.

To determine the type of dilation and the scale factor used, we can compare the corresponding side lengths of the two quadrilaterals.

The ratio of the corresponding side lengths is as follows:

9/6 = 12/8 = 1.5

Since the corresponding side lengths are in a constant ratio of 1.5, this indicates an enlargement.

Therefore, the type of dilation shown is an enlargement, and the scale factor used is 1.5.

Polygon ABCD with vertices at A(-4, 6), B(-2, 2), C(4, -2), D(4, 4) is dilated using a scale factor of three fourths to create polygon A'B'C'D'.

To find the vertices of polygon A'B'C'D', we multiply the coordinates of each vertex by the scale factor (3/4).

A' = (-4 * 3/4, 6 * 3/4) = (-3, 4.5)

B' = (-2 * 3/4, 2 * 3/4) = (-1.5, 1.5)

C' = (4 * 3/4, -2 * 3/4) = (3, -1.5)

D' = (4 * 3/4, 4 * 3/4) = (3, 3)

Therefore, the vertices of polygon A'B'C'D' are A'(-3, 4.5), B'(-1.5, 1.5), C'(3, -1.5), and D'(3, 3).

The triangle labeled D has side lengths of 3.6, 4.8, and 5.2. The second triangle labeled D' has side lengths of x, 1.2, and 1.3.

To determine the scale factor used, we can compare the corresponding side lengths of the two triangles.

The ratio of the corresponding side lengths is as follows:

x/3.6 = 1.2/4.8 = 1.3/5.2

Simplifying the ratios, we have:

x/3.6 = 1/4 = 1/4

Therefore, the scale factor used is 1/4, which is equivalent to one fourth.

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Line d shows the correct result of the dilation, with line XY being 2 units long.

We are given that segment XY is dilated using a scale factor of two-thirds through point P, which is the center of dilation.

To determine the correct result of the dilation, we need to find the segment that satisfies the given conditions.

Starting from point P, we have line a located 4 units away from point P.

From line a, we have line b located 2 units away.

Similarly, from line b, we have line c located 2 units away.

Continuing this pattern, from line c, we have line d located 2 units away.

Finally, from line d, we have line XY located 2 units away.

Considering the dilation scale factor of two-thirds, we need to find the segment that is two-thirds the length of the previous segment.

Calculating the lengths, we find that line a is 4 units, line b is 2 units, line c is 2 units, line d is 2 units, and line XY is 2 units.

The length of line XY is already two-thirds the length of line d, satisfying the given conditions.

Therefore, line d shows the correct result of the dilation, with line XY being 2 units long.

Marking line d as the correct segment, we can now return our answer.

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