Write the statements “If you take away 6 from 6 time a number, you get 60”in the form of equations:.

A. The area decreases by a factor of about 0.6565 after 10 years. B. The area decreases by a factor of about 0.0197 each month.

A. To find the factor by which the area decreases after 10 years, we need to compare the initial area (at t=0) to the area after 10 years (at t=10). We can use the formula for A(t) to calculate these values:

A(0) = 11 square kilometers (initial area)

A(10) = 11 ×(0.98)¹⁰ ≈ 7.22 square kilometers (area after 10 years)

The factor by which the area decreases after 10 years is the ratio of A(10) to A(0):

A(10) / A(0) ≈ 7.22 / 11 ≈ 0.6565

So the area decreases by a factor of about 0.6565 after 10 years.

B. To find the factor by which the area decreases each month, we need to first find the annual rate of decrease, and then convert it to a monthly rate. We know that the area decreases by 2 percent each year, so the annual rate of decrease is 0.02. To find the monthly rate of decrease, we can use the formula:

r = (1 + i)^(1/n) - 1

where:

r is the monthly rate of decrease

i is the annual rate of decrease (0.02 in this case)

n is the number of months in a year (12)

Plugging in the values, we get:

r = (1 + 0.02)^(1/12) - 1 ≈ 0.00165

So the area decreases by a factor of approximately:

(1 - r)¹² ≈ (1 - 0.00165)¹² ≈ 0.0197 each month. Therefore, the area decreases by a factor of about 0.0197 each month.

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Answer:

\(A_X=\frac{15x^2}{16}\)

Step-by-step explanation:

From the question we are told that:

Base of Flower bed \(b=\frac{x}{2}\)

Height of Flower bed \(h=\frac{x}{4}\)

Generally the equation for Area of garden left A_X is mathematically given by

 \(A_X=Area\ of\ Garden\ A_g\ - Area\ of\ flower\ bed\ A_f\)

Where

 \(A_f=b*h\)

 \(A_f=\frac{1}{2}*\frac{x}{2}*\frac{x}{4}\)

 \(A_f=\frac{x^2}{16}\)

Therefore

 \(A_X= A_g - A_f\)

 \(A_X=x^2-\frac{x^2}{16}\)

 \(A_X=\frac{15x^2}{16}\)

Answer: quadrant III  

Step-by-step explanation: srry if am wrong

Answer:F(x)=-x2-3

Step-by-step explanation:We are given a function:

The graph of  is also shown in the given question figure.

It is a parabola with vertex at (0,0).

Sign of  is positive, that is why the parabola opens up.

General equation of parabola is given as:

Here, in G(x), a = 1

Vertex (h,k) is (0,0).

As seen from the question figure,

The graph of F(x) opens down that is why it will have:

Sign of  as negative. i.e.

And vertex is at (0,-3)

Putting the values of a and vertex coordinates,

Hence, the equation of parabola will become:

The expression for \(f(x) = -(x-3)^{2}-2\) represents the red curve.

In this question we know that \(g(x) = x^{2}\) and an unknown \(f(x)\), whose expression can be derived by using the following rigid transformations:

Then, the expression for \(f(x) = -(x-3)^{2}-2\) represents the red curve. \(\blacksquare\)

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Answer:

h(x) = -4 x –7

h(3) = -4(3) —7

h(3) = –12 –7

h(3) = – 19

The fastest possible algorithm to search for the player with the highest score in a listing of 5,000 players could be to use a sorting algorithm like quicksort or mergesort to sort the list in descending order based totally on the players' scores, after which simply return the first player inside the sorted list, which would have the highest score.

The time complexity of quicksort and mergesort algorithms is O(n log n), this means that they can sort a listing of 5,000 players exceptionally fast. once the listing is sorted, finding the player with the highest score is a constant time operation, as it absolutely involves returning the first player in the listing.

Consequently, using a sorting algorithm to sort the listing in descending order and returning the first participant would be the quickest possible set of rules to look for the player with the highest rating in a list of 5,000 players.

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Answer: 6

Step-by-step explanation:

Answer:

5.44 yards

Step-by-step explanation:

The limit exists and equals 0, the sequence an = n²e^(-3n) converges with a limit of 0.

Hi! Based on your given sequence an = n²e^(-3n), we need to determine whether the sequence converges or diverges, and if it converges, find the limit.

To check for convergence, we can examine the behavior of the sequence as n approaches infinity. For this, we can use the limit test:

lim (n -> ∞) an = lim (n -> ∞) n²e^(-3n)

To evaluate this limit, we can apply L'Hôpital's Rule to the transformed limit:

lim (n -> ∞) (n² / e^(3n))

Taking derivatives of numerator and denominator, we get:

lim (n -> ∞) (2n / (3 * e^(3n)))

We can apply L'Hôpital's Rule again:

lim (n -> ∞) (2 / (9 * e^(3n)))

As n approaches infinity, the denominator grows exponentially, causing the limit to approach 0:

lim (n -> ∞) (2 / (9 * e^(3n))) = 0

Since the limit exists and equals 0, the sequence an = n²e^(-3n) converges with a limit of 0.

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The sketch of the solid whose volume is given by the iterated integral is given below.

To sketch the solid, we can first look at the limits of integration. The limits of x are from 0 to 1, and the limits of y are from 0 to 1-x. This means that the solid is a right triangular pyramid with base vertices at (0,0), (1,0), and (0,1), and height h given by the function h(x,y) = 101(7-x-5y).

The solid has a straight side along the x-axis and two straight sides along the y-axis, and a curved side for the hypotenuse of the base triangle.

The highest point of the top of the solid occurs at the vertex opposite the base triangle, which is at (x,y,z) = (1/3,1/3,200/3).

The lowest point of the top of the solid occurs at the vertex of the base triangle at (x,y,z) = (0,0,707/3).

Thus, the sketch of the solid is prepared.

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Answer:

Let x be your original weight.

The weight loss of 4-8 kg can be represented as a range: 4 kg ≤ x ≤ 8 kg.

We also know that this weight loss is equal to 6% of your original weight:

6% of x = 4 kg

To find the lower end of the range, we use 4 kg:

0.06 * x = 4 kg

Solving this equation for x:

x = 4 kg / 0.06

x ≈ 66.67 kg

Therefore, your original weight was approximately 66.67 kg.

-6.75  is a rational number.

Let us understand about natural, whole, integer, rational, and irrational numbers one by one.

Natural number:

Natural numbers are numbers that start from 1 and end at infinity. These are non-negative numbers.

Whole number:

Whole numbers are numbers that start from 0 and end at infinity.

We can also natural numbers including 0 is known as whole numbers.

These are non-negative numbers.

Integer:

An integer is a number with no decimal or fractional part and it includes negative and positive numbers, including zero.

Rational number:

A rational number is a number that can be expressed as the quotient or fraction p/q of two integers, a numerator p, and a non-zero denominator q.

Also, the decimal representation of the rational number is terminating and recurring.

Irrational number:

An irrational number is a number that can not be expressed as the quotient or fraction p/q of two integers, a numerator p, and a non-zero denominator q.

Also, the decimal representation of the irrational number is non-terminating and non-recurring.

The given number is -6.75.

The decimal form is terminating.

So, it is a rational number.

Thus, -6.75  is a rational number.

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Synergy is obtained when the value created by two divisions operated separately and independently is greater than the value that would be created by two divisions cooperating. The given statement is False.

The statement is false. Synergy is a term used to describe the benefits that can be achieved when two or more parts of a business work together to create more value than they could on their own. In other words, when two divisions cooperate and work together, the combined value they create is greater than the value that would be created if they worked independently and separately.

For example, if a company has a marketing division and a sales division, these two divisions could work independently to achieve their goals. However, if they work together and share information, resources, and expertise, they can create more value by developing more effective marketing strategies that lead to increased sales. In this case, the combined value of the marketing and sales divisions working together is greater than the value they could create if they worked independently.

Therefore, it is incorrect to say that synergy is obtained when two divisions operate separately and independently to create greater value than they would if they cooperated.

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Answer:

I don't know if you believe in religion but I am a christian, and I go to God. If not, you may take comfort in loved ones. My sister passed a while ago in a car accident, and I was in it. I broke my back, collar bone, and neck. I was only 6 years old! So, I understand hard times, and maybe you should write just how much your family and that teacher means to you.

-Michael

Answer:

0.0207

Step-by-step explanation:

Answer:

The total is -4.

Step-by-step explanation:

Pair 1: -7 + 3 = -4

Pair 2: -5 + 1 = -4

Pair 3: -3 + (-1) = -4

Storekeepers in electronics companies deal with various types of materials. Five classes of materials include electronic components, raw materials, finished products, packaging materials, and maintenance supplies.

Electronic Components: Storekeepers are responsible for managing a wide range of electronic components such as resistors, capacitors, integrated circuits, connectors, and other discrete components. These components are essential for assembling electronic devices and are typically stored in organized bins or cabinets for easy access.

Raw Materials: Electronics companies require various raw materials for manufacturing processes. Storekeepers handle materials like metals, plastics, circuit boards, cables, and other materials needed for production. These materials are usually stored in designated areas or warehouses and are monitored for inventory levels.

Finished Products: Storekeepers are also responsible for storing and managing finished products. This includes fully assembled electronic devices such as smartphones, computers, televisions, and other consumer electronics. They ensure proper storage, tracking, and distribution of these products to customers or other departments within the company.

Packaging Materials: Packaging plays a crucial role in protecting and shipping electronic products. Storekeepers handle packaging materials such as boxes, bubble wrap, foam inserts, tapes, and labels. They ensure an adequate supply of packaging materials and manage inventory to meet packaging requirements.

Maintenance Supplies: Electronics companies often require maintenance and repair supplies for their equipment and facilities. Storekeepers handle items like tools, lubricants, cleaning agents, safety equipment, and spare parts. These supplies are necessary to support ongoing maintenance activities and ensure the smooth operation of machinery and infrastructure.

Overall, storekeepers in electronics companies deal with a diverse range of materials, including electronic components, raw materials, finished products, packaging materials, and maintenance supplies. Effective management of these materials is crucial to ensure smooth operations, timely production, and customer satisfaction.

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Answer:

Step-by-step explanation:

\(4x^2-16x-9.\\Writ -16x - as -a -difference\\ 4x^2 +2x-18x -9 \\Factor -out- common- terms\\2x(2x+1)-9(2x+1)\\ Factor -out (2x+1)\\(2x+1)(2x-9)\)

I Hope It Helps :)

Answer:

\( \boxed{\sf (2x - 9)(2x + 1)} \)

Step-by-step explanation:

\( \sf Factor \: the \: following: \\ \sf \implies 4 {x}^{2} - 16x - 9 \\ \\ \sf Factor \: the \: quadratic \: 4 {x}^{2} - 16 x - 9. \\ \sf The \: coefficient \: of \: {x}^{2} \: is \: 4 \: and \: the \: constant \\ \sf term \: is \: - 9. \: The \: product \: of \: 4 \: and \: - 9 \: is \\ \sf - 36. \: The \: factors \: of \: - 36 \: which \: sum \: to \\ \sf - 16 \: are \: 2 \: and \: - 18. \\ \sf So, \\ \sf \implies 4 {x}^{2} - (18 - 2)x - 9 \\ \\ \sf \implies 4 {x}^{2} - 18x + 2x - 9 \\ \\ \sf \implies 2x(2x - 9) + 1(2x - 9) \\ \\ \sf Factor \: 2x - 9 \: from \: 2x(2x - 9) + 1(2x - 9) : \\ \sf \implies (2x - 9)(2x + 1)\)

Answer:

15 cubic centimeters

Step-by-step explanation:

The figure is in the shape of a rectangular and the formula for volume of such a rectangular box is

V=lwh, where V is the volume, l is the length, and h is the height.

Since each cube is 1 cm, we see that the length is 5 cm (1 cm cube * 5 = 5 cm), the width is 3 cm (1 cm cube * 3 = 3 cm), and the height is 1 cm (1 cm cube * 1 = 1 cm).

Thus, we the product of our length, width, and height will give us the volume of the figure:

V = 5 * 3 * 1

V = 15 cubic centimeters

Answer:

c=6

Step-by-step explanation:

f(x)=5x-9

c=x

f(x)=f(c)=21

5x-9=21

5x=21+9

5x=30

x=6

c=6

The length of the third side in terms of quadratic equation will be equal to -11x^2 + 8x - 4.

Since it is already given that the length of the two sides of a triangle are (-5-3x+5x^2) and (9+3x+12x^2) and the perimeter of the triangle is (6x^2+8x), so the length of the third side can be determined by simple arithmetic equation. The perimeter refers to the length of the boundary of the polygon (or a closed figure).

It is equal to the sum of the sides of the polygon. In the given polygon that is triangle, the sum of the sides will be equal to the length of the perimeter.

Sum of sides = Perimeter of triangle

(-5 - 3x + 5x^2) + (9 + 3x + 12x^2) + (Side3) = (6x^2 + 8x)

17x^2 + 4 + (Side3) = 6x^2 + 8x

Side3 = (6x^2 + 8x) - (17x^2 + 4 ) = (-11x^2 + 8x - 4)

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Refer to complete question below:

The perimeter of a triangle is 6x^2+8x and the measure of two sides is -5-3x+5x^2 and 9+3x+12x^2. What will be the measure of the third side?

Answer:

2

Step-by-step explanation:

y would be the first number in the equation on the left side of the equal sign. This looks lik the y=mx+b formula, so m, being slope, would be 7, -3 would be x, and b would be 4.

The values of the inverse functions are f-¹ (3) = -1 and f-¹ (8) = 7

From the question, we have the following parameters that can be used in our computation:

x   f(x)

-1   3

1     6

2    5

3    7

7   8

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

f-¹ (x) means that we calculate the value of x from the table when y = x in the function notation

So, we have

f-¹ (3) = -1 and f-¹ (8) = 7

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The yield point of iron increases from 135 MPa to 260 MPa as the grain diameter decreases from 0.05 mm to 0.008 mm. To achieve a yield point of 205 MPa, the grain diameter would need to be interpolated between these two values.


The given information suggests an inverse relationship between grain diameter and yield point in iron. As the grain diameter decreases from 0.05 mm to 0.008 mm, the yield point increases from 135 MPa to 260 MPa. To find the grain diameter corresponding to a yield point of 205 MPa, we can interpolate between the two known points.

By calculating the proportional change in yield point relative to the change in grain diameter, we can determine the ratio of the difference between 205 MPa and 135 MPa to the difference between 260 MPa and 135 MPa. This ratio can then be used to determine the corresponding change in grain diameter. The interpolated grain diameter is the point where the yield point would be 205 MPa.

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Answer:

The answer is 13 hope it helps!<3

Step-by-step explanation:

The second step when evaluating the given expression is to subtract 6 from 18, simplifying the expression within the parentheses to 12.

The second step when evaluating the expression 3 + (18 - 6) + 20 + 4 is to perform the operation within the parentheses, specifically the subtraction inside the parentheses.

Let's break down the expression step by step:

1. Start with the expression: 3 + (18 - 6) + 20 + 4

2. The expression inside the parentheses is 18 - 6. To simplify this, we subtract 6 from 18, which equals 12.

3. Now, we rewrite the expression with the simplified part: 3 + 12 + 20 + 4

4. At this point, the expression consists of addition operations only. When evaluating an expression with multiple addition operations, we start from the left and work our way to the right, performing the addition operation between two numbers at a time.

5. The first addition operation is between 3 and 12. Adding these two numbers gives us 15.

6. We rewrite the expression again, replacing the addition of 3 and 12 with the result: 15 + 20 + 4

7. Now, we perform the next addition operation between 15 and 20, resulting in 35.

8. We rewrite the expression once more: 35 + 4

9. Finally, we perform the last addition operation between 35 and 4, resulting in 39.

Therefore, the second step when evaluating the given expression is to subtract 6 from 18, simplifying the expression within the parentheses to 12.

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Answer:

There are at least 7 M&M's in the bag, since if there were only 1 green M&M, there would be 2.5 blue M&Ms, which is impossible.

Step-by-step explanation:

Given that the ratio of green M&M's to yellow is 2: 5, if there are only green and yellow M&M's in the bag, to determine what is the smallest number of M&M's possible, the following calculation must be performed:

5/2 = 2.5

2/5 = 1 / 2.5

Therefore, there are at least 7 M&M's in the bag, since if there were only 1 green M&M, there would be 2.5 blue M&Ms, which is impossible.