Help me… it’s so hard!

By mathematical induction, the given formula holds for all natural numbers n:

S(n) = 36 + 324 + 900 + ... + (12n - 6)² = 12n(4n² - 1)

To demonstrate our point, mathematical induction can be employed.

We want to prove that the given formula holds for all natural numbers n:

S(n) = 36 + 324 + 900 + ... + (12n - 6)² = 12n(4n² - 1)

Using mathematical induction:

Step 1: Base case (n=1)

S(1) = 6² = 36

12 * 1 * (4 * 1² - 1) = 36

Since S(1) holds true, the base case is proven.

Step 2: Inductive step (Assume it's true for n=k, and show it's true for n=k+1)

Assumption: S(k) = 36 + 324 + 900 + ... + (12k - 6)² = 12k(4k² - 1)

We follow the exhaustive process to prove:

= 12(4k³ + 12k² + 11k + 3)

Since both expressions for S(k+1) are equal, the inductive step is proven.

Thus, by mathematical induction, the given formula holds for all natural numbers n:

S(n) = 36 + 324 + 900 + ... + (12n - 6)² = 12n(4n² - 1)

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The characteristics that shows that the graph is a proportional relationship is: D. The line connecting the points passes through the origin.

A graph of a proportional relationship is a straight line that passes through the origin (0, 0) on a coordinate plane, where the points on the line represent pairs of values that are in direct proportion to each other.

From the graph shown above, if we connect the points together, the line will pass through the origin, therefore, the correct answer is: D. The line connecting the points passes through the origin.

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The characteristics that tell you that the graph shows a proportional relationship are: A straight line can be drawn through the points and The line connecting the points passes through the origin. Option B and D are the correct answer.

A proportional relationship is a relationship between two variables where the ratio of their values is constant. This means that if we multiply one of the values by a constant, the other value also gets multiplied by the same constant.

The graph of a proportional relationship is a straight line that passes through the origin. This is because the ratio of the x- and y-values is constant, so the points can be plotted as a straight line.

The ordered pairs all have the same x- and y-values means that the two variables are perfectly correlated. This is not necessary for a proportional relationship, but it is a common characteristic.

The line connecting the points does not need to pass through the origin for the relationship to be proportional. However, if the line does pass through the origin, then the two variables are directly proportional. Option B and D are the correct answer.

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Answer: f(3) = g(6)

Step-by-step explanation: if you plug them in we see that f of 3 on the y axis intercept g of x so we then go up and see that g of 6 intercepts f of 3 so therefore that is the answer

Jill's annual earnings can be calculated by multiplying her weekly pay by the number of weeks in a year: $298/week x 52 weeks/year = $15,496/year. Her earnings to date are $14,900, so she has earned an additional $596 in the current week.

Social Security is taxed at 6.2%, so the amount deducted from her pay each week is 6.2% of her gross weekly pay. That's 0.062 x $298 = $18.48.

Our square yard calculator allows you to easily find the total area of a surface. Additionally, if you wish to cover that surface with some material or to do some construction work, such as painting or gardening, it gives you an estimation of your material cost and labor cost.

The square yard calculator also allows you to use different units (imperial and metric) and seamlessly convert between the two. Want to enter your measurements in feet and get your area in square yards or square meters? We've got you covered. You can easily switch between units and get answers to questions like "How to convert from feet to yards?" or "How many square feet in a square yard?"

Answer:

I think that people found difficult to accept zero as a number because people think that zero doesn't have any value. In a way yes Zero doesn't have value but zero is also a very important number because sometimes we need to solve some questions and we need to add value but if we need to add that particular value we should even subtract that value which makes it zero. So I think the reason is people don't think zero has any value. But in my point if view zero has many values.

Answer:

Jasper should use the median to make an inference about the house values in his neighborhood because there is an outlier that affects the mean. The outlier in this case is the house with a value of $2,500,000, which is significantly higher than the other house values in the sample. The mean is sensitive to outliers, which means that the outlier can significantly affect the value of the mean. In contrast, the median is not affected by outliers, which makes it a better measure of central tendency for this data set. Therefore, Jasper should use the median because it is in the center of the data and is not affected by the outlier. Answer: He should use the median because there is an outlier that affects the mean.

Answer:

The answer to your problem is, C. He should use the median because there is an outlier that affects the mean. &;  A & E $150,000 ‘n’ $200,000

Step-by-step explanation:

The outlier is represented as ‘ E ‘ the highest price value and lowest between, $150,000 to $200,000.

But since ‘ E ‘ is represented highest it is an outlier making ‘ E ;

$150,000 ‘n’ $200,000

So ‘ E ‘ is represented as, $150,000 ‘n’ $200,000

The second option for ‘ 10 points ‘ is He should use the median because there is an outlier that affects the mean, being the ‘ Option C ‘

Thus the answer to your problem is, C. He should use the median because there is an outlier that affects the mean. &;  A & E $150,000 ‘n’ $200,000

If new equation of this line be after it is rotated 90° counterclockwise around the origin, the equation of the new line after rotation is y = (-5/6)x

To find the new equation of a line after it is rotated 90° counterclockwise around the origin, we need to use the following formula:

(x', y') = (-y, x)

where (x, y) are the coordinates of a point on the original line, and (x', y') are the coordinates of the corresponding point on the new line after rotation.

We can start by finding the slope of the original line, which is given by:

y = (6x/5)

Rearranging this equation, we get:

x = (5/6)y

This tells us that the slope of the original line is 5/6.

To find the equation of the new line after rotation, we need to apply the formula above to two points on the original line. Let's choose two easy points to work with, such as (0,0) and (5,6).

Using the formula, we can find the new coordinates of these points after rotation:

(0', 0') = (-0, 0) = (0,0)

(5', 6') = (-6, 5)

Now we can find the slope of the new line using these two points:

slope = (6' - 0') / (5' - 0') = 5/-6 = -5/6

In summary, to find the new equation of a line after rotating 90° counterclockwise around the origin, we can use the formula (x', y') = (-y, x) to find the new coordinates of two points on the original line, and then use these points to find the slope of the new line. In this case, the new equation of the line is y = (-5/6)x.

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If Point A is located at (1, 2) and Point B is located at (4, 6), the length of the line between points A and B is 5 units.

To determine the length of the line between points A and B, we can use the distance formula, which is a formula used to calculate the distance between two points in a coordinate plane. The distance formula is:

d = √((x₂ - x₁)² + (y₂ - y₁)²)

where (x₁, y₁) and (x₂, y₂) are the coordinates of the two points and d is the distance between them.

Using the coordinates of points A and B, we can substitute their values into the distance formula to find the length of the line between them:

d = √((4 - 1)² + (6 - 2)²)

d = √(3² + 4²)

d = √(9 + 16)

d = √25

d = 5

Rounded to the nearest whole number, the length of the line is also 5 units.

In conclusion, we can use the distance formula to find the length of the line between two points in a coordinate plane. The distance formula uses the coordinates of the two points to calculate the distance between them. The resulting distance can be rounded to the nearest whole number, if needed.

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The steps for the construction are given below:

A new line can be created connecting the points where these two circles intersect using just a simple ruler.

Now that you have succeeded in this task, feel free to experiment and manipulate the astonishing construction you've completed using the same innovative tools.

While this is only an elementary blueprint, there are numerous advanced constructions that can be produced by taking advantage of both GeoGebra and traditional paper/pencil/ruler/compass techniques.

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No, y=2x+X+1 is not a linear function because it contains a term with an exponent of 1 and a term with an exponent of 0. Linear functions are functions of the form y = mx + b, where m and b are constants, and x is the independent variable. The graph of a linear function is a straight line.

In the given function, the term X is not multiplied by a constant, so it does not have a fixed rate of change. Therefore, the graph of this function is not a straight line. Instead, it is a quadratic function, which has a parabolic graph.

Answer:6

Step-by-step explanation:

7w-6 + 8w+6 = 90

15w=90

w=90/15

w=6

Answer:

To solve for C in the formula V = CLS, we need to isolate C on one side of the equation.

Starting with the given formula:

V = CLS

Divide both sides of the equation by LS:

V/LS = C

Therefore, the formula for C is:

C = V/LS

Based solely on the information provided in the table, spending approximately 3-4 hours per customer would give Julie the best chance of a returning customer. So, correct option is C.

To determine the amount of time Julie should spend per customer to have the greatest probability of a returning customer, we need to find the time interval with the highest probability of return. Looking at the table, we see that the probability of return is highest for the 3-4 hour time interval with a probability of 7/8.

Therefore, Julie should spend 3-4 hours designing each customer's garden to have the greatest probability of a returning customer.

So, correct option is C.

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Complete question is:

Julie designs gardens for a living. For a year she kept track of the amount of time she spent designing the garden and whether or not the customer returned. She recorded the time and probability that a customer returned.

To have the greatest probability of a returning customer, what amount of time should Julie spend per customer?

TIME DESIGNING PROBABILITY OF RETURN

1-2 Hours 5/8

2-3 Hours 5/9

3-4 Hours 7/8

4-5 Hours 3/4

5-6 Hours 1/2

6-7 Hours 3/7

7-8 Hours 2/9

A. 1-2 Hours

B. 2-3 Hours

C. 3-4 Hours

D. 4-5 Hours

Answer:

Answer is A

Step-by-step explanation:

A) y = -1/2x represents a proportional relationship because the equation can be written in the form y = kx, where k is a constant. In this case, k = -1/2, which means that y is proportional to x with a constant of proportionality of -1/2.

B) y = 2x - 4 does not represent a proportional relationship because the equation cannot be written in the form y = kx. If we try to write it in this form, we get y/x = 2 - 4/x, which means that y/x is not constant. Therefore, y is not proportional to x with a constant of proportionality.

Answer:

The expected value in this situation can be calculated as follows:

E(X) = P(X) * V(X), where X is the random variable representing the profit of the construction company, P(X) is the probability of X, and V(X) is the value of X.

In this case, the profit of the construction company if the bid is accepted is $96,000 - $1,100 = $94,900, and the probability of the bid being accepted is 1/10. Therefore, we have:

E(X) = (1/10) * $94,900 = $9,490

The expected value of $9,490 means that in the long run, the construction company would expect to earn this amount on average per bid. Therefore, the correct answer is option A: "In the long run, the construction company would expect to earn this amount on average per bid."

Answer:

linear

Step-by-step explanation:

have a good day God bless :)

The amount of paint needed for the soup can is 409.77 cm².

Jacque is using an unopened soup can for a school project and wants to paint it.

The can is 10 cm tall and has a diameter of 9 cm. Therefore, the square centimetres of paint required to paint the soup is as follows:

Therefore,

surface area of a cylinder = 2πr(r + h)

where

Therefore,

r = 9 / 2 = 4.5 cm

h = 10 cm

surface area of a cylinder = 2 × 3.14 × 4.5(4.5 + 10)

surface area of a cylinder = 28.26(14.5)

surface area of a cylinder = 409.77 cm²

Therefore,

amount of paint needed = 409.77 cm²

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The missing side lengths for triangle ABC are 4, 4√3, and 8.

Based on the given information, it seems that the triangle is a right-angled triangle with angles of 30°, 60°, and 90°. Let's find the missing side lengths for triangle ABC using the given lengths and angles.
Identify the triangle type.
Since we have angles of 30°, 60°, and 90°, we are working with a 30-60-90 right-angled triangle.
Determine the ratio of side lengths.
In a 30-60-90 triangle, the ratio of the sides is 1:√3:2.
Find the corresponding side lengths.
Using the given lengths and the 1:√3:2 ratio, we can determine the side lengths for triangle ABC:
- If the shortest side (opposite the 30° angle) is 4, then the other sides would be 4√3 (opposite the 60° angle) and 8 (hypotenuse, opposite the 90° angle).

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Answer:

To find the coordinates for all three possible locations of the fourth vertex, we need to consider the three different ways that a parallelogram can be formed on a 9 by 9 grid.

Method 1: The fourth vertex is directly below the first vertex.

In this case, the coordinates of the fourth vertex are (5, 9), as shown below:

Y 9 8 7 6 5 4 3 2 1 0

X 1 2 3 4 5 6 7 8 9

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . X

Method 2: The fourth vertex is directly to the right of the first vertex.

In this case, the coordinates of the fourth vertex are (1, 5), as shown below:

Y 9 8 7 6 5 4 3 2 1 0

X 1 2 3 4 5 6 7 8 9

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

X . . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

Method 3: The fourth vertex is diagonal to the first vertex.

In this case, the coordinates of the fourth vertex are (5, 5), as shown below:

Y 9 8 7 6 5 4 3 2 1 0

X 1 2 3 4 5 6 7 8 9

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . X . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

Therefore, the coordinates for all three possible locations of the fourth vertex are (5, 9), (1, 5), and (5, 5).

The ratio of gregarious that lived in the valley is 126,00

Ratio is  the comparison of two quantities of the same kind or for comparing two or more quantities that are measured in the same units. It is also  is a relationship between two things when it is expressed in numbers or amounts.

How to determine this

The total who lived in valley = 15,300

The ratio of Reclusive = 3

The ratio of Gregarious = 14

And the ratio of reclusive gregarious = 3 : 14

The total ratio = 3 + 14 = 17

To calculate the total amount of gregarious

= 14/17 * 15,300

= 12,600

Therefore, the total amount of gregarious is 12,600

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The probabilities of the the team are 0.7, 0.9, 0.6 and 0.4

Given that

a) not win

This means that

P = 1 - P(win)

So, we have

P = 1 - 0.3

P = 0.7

b) not draw

This means that

P = 1 - P(draw)

So, we have

P = 1 - 0.1

P = 0.9

c) lose

This means that

P = 1 - P(win) - P(draw)

So, we have

P = 1 - 0.3 - 0.1

Evaluate

P = 0.6

d) not lose

This means that

P = 1 - P(lose)

So, we have

P = 1 - 0.6

P = 0.4

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The real solution is 0, and the imaginary solution is 0.5 ±  0.866i.

The solutions of the equation is calculated as follows;

4x(x² - x + 1) = 0

This equation is satisfied when either 4x = 0 or x² - x + 1 = 0.

If 4x = 0, then x = 0 is a solution,

To find the solutions of x² - x + 1 = 0, we will use formula method;

x = [ -(-1) ± √((-1)² - 4(1)(1)) ] / (2(1))

x = [ 1 ± i√3 ] / 2

x = 0.5 ±  0.866i

Thus, the solutions of the cubic equation involves both real and imaginary solution.

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USD 438

Step-by-step explanation:If we add 20% to the gross amount of USD 365, the total amount would be:USD 365 + 20% of USD 365 = USD 365 + (0.20 * USD 365) = USD 365 + USD 73 = USD 438

If the gross amount is USD 365, then the net amount after adding 20 percent is USD 438.

Net amount refers to the final total after deductions or additions have been made whereas gross amount refers to the total amount before any deductions or additions have been made.

Us the formula:

Net Amount = Gross Amount + (Gross Amount x Percentage)

Given that,

Gross amount = $365

The given percentage = 20%

We can write 20% = 20/100

So, 20% = 0.2

Now put the values into the formula

Net amount  = 365 + (365 x 0.2)

Net amount  = 365 + 73

Net amount  = 438

Hence,

The net amount is USD 438.

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Carleigh, Inc. should separate the organ meats from the residual and sell them abroad, as it would increase their total revenue by $17,150 per week.

To determine whether Carleigh, Inc. should separate the organ meats and sell them abroad, we need to calculate the incremental revenue and incremental costs associated with this decision.

The incremental revenue would be the revenue generated from selling the organ meats abroad, which is $52,000 per week. The incremental cost would include the cost of further processing ($27,500 per week), transportation cost ($12,100 per week), and the increase in resource spending for other activities ($3,120 per week).

Therefore, the incremental cost would be $42,720 per week. Subtracting this from the incremental revenue of $52,000, we get an incremental profit of $9,280 per week.

However, this decision would also decrease the value of the residual from $9,800 to $2,650 per week. Therefore, we need to subtract this decrease in value from the incremental profit. This gives us a net increase in profit of $17,150 per week ($9,280 - $7,130).

Thus, it would be beneficial for Carleigh, Inc. to separate the organ meats and sell them abroad.

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Answer: -1 1/2

Step-by-step explanation:

You simplify -3/2, which becomes -1 1/2!

The area of this​ trapezoid is 14.42 square yards.

To compose the trapezoid into a parallelogram, we need to add a triangle to the top of the trapezoid, so that the top and bottom sides are parallel. The area of the triangle is equal to half the product of the base and height.

First, we need to convert the mixed numbers to improper fractions:

Base 1: 6 1/3 yd = 19/3 yd

Base 2: 8 1/5 yd = 41/5 yd

Height: 3 3/4 yd = 15/4 yd

The length of the top side of the triangle is equal to the difference between the two bases:

Top side = 41/5 - 19/3 = (123 - 95)/15 = 28/15

Now we can calculate the area of the triangle:

Triangle area = (1/2) x (28/15) x (15/4) = 7/4

The trapezoid can now be composed into a parallelogram, with base 1 as one side and base 2 as the other side. The height of the parallelogram is the same as the height of the trapezoid, which is 15/4 yd.

The area of a parallelogram is equal to the product of its base and height, so the area of the trapezoid is:

Parallelogram area = (19/3 + 41/5) x (15/4) = 865/60 = 14.42

Therefore, the area of the trapezoid is 14.42 square yards.

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If owner of car paid $780 as annual premium, then the cost of the accident is $26540 more expensive than what car owner paid in premiums, correct option is (d).

The car owner paid a total of $780 per year for 7 years, which means that the total amount paid in premiums is:

⇒ Total premiums paid = $780 × 7 years = $5460,

When the owner caused an accident, the amount of damage claimed by other driver is $32000.

This means that cost of accident was : $32000 - $5460 = $26540 more expensive than what the "owner" had invested in his insurance policy.

Therefore, Option(d) is correct.

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The given question is incomplete, the complete question is

A car owner pays an annual premium of $780 for automobile insurance, including liability coverage of up to $100,000. The car owner pays this for seven years without needing to file a

single claim. Then the car owner causes an accident for which the other driver is claiming $32,000 in damages. How much more expensive were the costs of the accident than what the car owner paid in premiums?

(a) $37,460

(b) $100,000

(c) $5,460

(d) $26,540

In 2006, the population will reach 109 million.

The correct answer is an option (d)

Here function [tex]f(x)=100(1.0153)^x[/tex] represents the population (in millions) x years after 2000

We need to find the year x when the population will reach 109 million.

i.e., for f(x) = 109, we need to find the value of x.

Consider function f(x),

[tex]f(x)=100(1.0153)^x[/tex]

Substitute f(x) = 109

⇒ [tex]109=100(1.0153)^x[/tex]

⇒ [tex](1.0153)^x=1.09[/tex]

Taking logarithm on both the sides.

⇒ x ln(1.0153) = ln(1.09)

⇒ x = ln(1.09) / ln(1.0153)

⇒ x = 5.675

⇒ x ≈ 6

So, the required year would be,

2000 + 6 = 2006

Therefore, the correct answer is an option (d)

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