Identify the transformations of the graph of f(x) = x^2 that result in the graph of g shown. What rule, in vertex form, can you write for g(x)?

The mass of the original sample was approximately 1592.5 grams.

The half-life of an element is the time it takes for half of a given sample of that element to decay.

Let's assume that the original mass of the sample was x grams.

After the first half-life of 8 years, the mass of the sample would be x/2 grams.

After the second half-life (16 years total), the mass would be x/4 grams.

After the third half-life (24 years total), the mass would be x/8 grams.

We can continue this pattern until we get to 100 years (which is 12.5 half-lives):

Mass after 100 years = x/2^12.5

We also know from the problem that the mass after 100 years is 10 grams:

x/2^12.5 = 10

Solving for x:

x = 10 x 2^12.5

x ≈ 1592.5 grams

Therefore, the mass of the original sample was approximately 1592.5 grams.

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a. The two companies charge the same for 14 tons of sugar.

b. The cost when the two companies charge the same is $7953.50.

a. Let's represent the amount of sugar as x, and the total cost as C. Then we can set up the following equations for each company:

Company 1: C = 5143 + 200.75x

Company 2: C = 5500 + 175.25x

To find the amount of sugar for which the two companies charge the same, we can set the two equations equal to each other and solve for x:

5143 + 200.75x = 5500 + 175.25x

25.5x = 357

x = 14

So the two companies charge the same for 14 tons of sugar.

b. To find the cost when the two companies charge the same, we can plug in x = 14 into either equation. Let's use Company 1's equation:

C = 5143 + 200.75x

C = 5143 + 200.75(14)

C = 5143 + 2810.50

C = 7953.50

Therefore, the cost when the two companies charge the same is $7953.50.

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The value of secθ in simplest radical form is:

[tex]sec\theta = -\frac{\sqrt{61} }{5}[/tex]

If the point is given on the terminal side of an angle, then:

Calculate the distance between the point given and the origin:

[tex]r = \sqrt{x^{2} +y^2}[/tex]

Here, x = -5 and y = -6

The secant can be found by the following trigonometric relation:

[tex]sec\theta = \frac{1}{cos\theta}[/tex]

[tex]sec\theta = \frac{1}{\frac{x}{r} }\\ \\sec\theta = \frac{r}{x}\\ \\sec\theta = \frac{\sqrt{x^{2} +y^2} }{x}\\ \\sec\theta =\frac{\sqrt{(-5)^2+(-6)^2} }{-5}\\ \\sec\theta = -\frac{\sqrt{61} }{5}[/tex]

The secant function ‘or’ Sec Theta is one of the trigonometric functions apart from sine, cosine, tangent, cosecant, and cotangent. In right-angled trigonometry, the secant function is defined as the ratio of the hypotenuse and adjacent side.

Now , the secθ functions:

[tex]sec\theta = -\frac{\sqrt{61} }{5}[/tex]

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The given question is incomplete, complete question is:

If θ is an angle in standard position and its terminal side passes through the point (-5,-6), find the exact value of secθ in simplest radical form.

Therefore , the solution of the given problem of unitary method comes out to be  it is consistently a constant proportion or percentage of the preceding value.

The task can be completed using the well-known minimalist technique, actual variables, and any essential components from the very first Diocesan specialised question. In response, customers can be given another opportunity to use the item. If not, significant effects on our comprehension of algorithms will disappear.

Here,

According to the students' responses, all instances of exponential decay share the following characteristics:

They begin with a baseline value. (y-intercept).

They get smaller with time. (or successive periods).

They get closer to a horizontal asymptote, which stands for the function's minimum or limit value.

The graphs also demonstrate that, although the rate of decay—or the rate at which values decrease—can vary from circumstance to circumstance,

it is consistently a constant proportion or percentage of the preceding value.

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The perimeter of the rectangle that is inscribed in a circle of radius 5 cm is 28cm

Let x and y be the side of the rectangle

Diameter of circle = radius × 2

Diameter = 5×2

Diameter = 10

According to the Pythagorean theorem

(Diameter)² = X² + Y²

10² = X² + Y²

X² + Y² = 100

By this equation, possible value of x and y is 6 and 8 respectively only 6 and 8 will satisfy the equation

So, X = 6 and Y = 8

Perimeter = 2(X+Y)

Perimeter = 2(6+8)

Perimeter = 2(14)

Perimeter = 28 cm

perimeter of the rectangle is 28cm

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The theoretical probability of rolling a one or two is 3/5 or 0.6 as a decimal.

The theoretical probability of an event happening is the number of favorable outcomes divided by the total number of possible outcomes.

In this case, Alexandria rolled the number cube 60 times and recorded her results in the table.

Looking at the table, we can see that the number 1 came up 16 times and the number 2 came up 20 times.

So the number of favorable outcomes is 16 + 20 = 36.

And the total number of possible outcomes is 60.

Therefore, the theoretical probability of rolling a one or two is:

P(1 or 2) = favorable outcomes/total outcomes = 36/60

Simplifying the fraction, we get:

P(1 or 2) = 3/5

So the theoretical probability of rolling a one or two is 3/5 or 0.6 as a decimal.

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The amount of paint that he will need to paint all six surfaces of the sandbox is: 68 square feet

Since the image is a rectangular prism

The volume of the box can be obtained by using the formula:

Volume = l * b * h

The box has a dimension of 1ft x 4ft x 6ft

The volume of the box = 1 x 4 x 6 = 24 cubic feet

Therefore, the volume of sand needed to fill the box will be = 24 cubic feet of sand

The surface area of the box can be obtained using the formula:

2(lb + lh + bh)

= 2(1*4 + 1*6 + 4*6)

=2(4 + 6 + 24)

=2 (34)

= 68 square feet

Therefore a total surface area of 68 square feet needs to be painted

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Complete question is:

Your cousin is building a Sandbox for his daughter how much sand will he need to fill the Box? Explain. How much paint will he need to paint all six surface of the sandbox? Explain. 1ft 4ft 6ft not answer choices

The algebraic expression for the volume of the right rectangular pyramid is (x/3) × (units²).

The volume of a right rectangular pyramid is given by the formula;

V = (1/3) × base_area × height

where base_area is area of the base of the pyramid.

In this case, the length and width of the base are given as units and units, respectively. Therefore, the area of the base is;

base_area = length × width

Substituting the given values, we get;

base_area = units × units = units²

The height of the pyramid is given as x units. Therefore, the volume of the pyramid can be expressed as;

V = (1/3) × (units²) × x

Simplifying the expression, we get;

V = (x/3) × (units²)

Therefore, the algebraic expression for the volume of pyramid is (x/3) × (units²).

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Therefore, when you solve this expression (6 + 5) x 2^2 - 4 , the solution is 23.

Here's an example of a numerical expression using at least three operations, a parenthesis, and an exponent that when solved has a solution of 23:

(6 + 5) x 2^2 - 4 = 23

Explanation:

- Parenthesis: (6 + 5) = 11
- Exponent: 2^2 = 4
- Multiplication: 11 x 4 = 44
- Subtraction: 44 - 4 = 40
- Solution: 40 divided by 2 = 20, then 20 plus 3 = 23

Therefore, when you solve this expression, the solution is 23.
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Answer:

11. x = 16

12. x = 26

Step-by-step explanation:

11. ∠1 + ∠2 = 90°

   ∠1 = 42°

   ∠2 = 90° - 42° = 48°

   3x = 48

   x = 16

12. ∠C + ∠D = 180°

∠C = 128°

∠D = 180° - 128° = 52°

2x = 52

x = 26

Carl will be charged 7.84% of the initial loan amount as interest.

When taking out a loan, it's important to understand the interest rate and how it will affect the total amount you will owe. In this case, Carl's loan accrues interest at a flat rate of 1.96% per quarter. This means that every quarter, Carl will be charged 1.96% of the initial loan amount as interest.

To determine the equivalent yearly simple interest rate, we use the formula: Yearly interest rate = Quarterly interest rate x 4. This formula works because there are four quarters in a year, so we can multiply the quarterly interest rate by four to get the annual interest rate.

In this case, the quarterly interest rate is 1.96%. Multiplying this by four, we get an annual interest rate of 7.84%. This means that over the course of a year, Carl will be charged 7.84% of the initial loan amount as interest.

Understanding the interest rate is important because it can significantly impact the total amount that you will owe on a loan. A higher interest rate means that you will pay more in interest over the life of the loan, which can make the loan more expensive overall.

By calculating the equivalent yearly simple interest rate, Carl can better understand how much he will owe in interest over the course of the loan and make an informed decision about whether or not to take out the loan.

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The net change in the stock is $1800

Mario has 40 shares of stick that each lost $75 during half of the year

He also had 24 shares of a different stock that gained $50

The net change can be calculated as follows

-40 × 75

= -3000

= 24 × 50

= 1200

Net change

-3000 + 1200

= -1800

Hence the net change in the stocks is $1800

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The statement "Dilation 2 has a scale factor 2" (option b).

Dilation is a transformation that changes the size of an object but not its shape. It is a type of transformation that enlarges or reduces an object by a certain factor called the scale factor. The scale factor is a ratio of the size of the dilated image to the size of the original image.

Now, let's talk about the scale factor for each dilation you asked about.

For dilation 1, the scale factor is 1. This means that the size of the dilated image is the same as the size of the original image. In other words, there is no change in size. This type of dilation is often referred to as the identity transformation because it doesn't change the shape or size of the original object.

For dilation 2, the scale factor is 2. This means that the size of the dilated image is twice as large as the size of the original image. In mathematical terms, if the original object has a length of 'x', then the length of the dilated image will be '2x'. Similarly, if the original object has a width of 'y', then the width of the dilated image will be '2y'.

For dilation 3, the scale factor is 3. This means that the size of the dilated image is three times as large as the size of the original image. In mathematical terms, if the original object has a length of 'x', then the length of the dilated image will be '3x'. Similarly, if the original object has a width of 'y', then the width of the dilated image will be '3y'.

Hence the correct option is (b).

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Answer:

Dilation 1 has a scale factor between 0 and 1

Dilation 2 has a scale factor greater than 1

Dilation 3 has a scale factor equal to 1

Step-by-step explanation:

The prize wheel's area is approximately 12.56 square yards.

The area of a circle can be calculated using the formula A = πr², where A represents the area, r represents the radius, and π is approximately 3.14. In Lucy's case, the big prize wheel has a radius of 2 yards.

To find the area of the prize wheel, we can plug the radius value into the formula:

A = π(2 yards)²

Squaring the radius (2 yards) gives us:

A = π(4 square yards)

Now, we can multiply by the given value of π (3.14):

A = 3.14 × 4 square yards

Finally, multiplying these values together, we get:

A = 12.56 square yards

Therefore, the area of the prize wheel is approximately 12.56 square yards. This calculation helps us understand the size of the prize wheel, which can be useful for various purposes such as determining the space required for the game show set or designing the prize sections on the wheel.

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The polynomial with roots of 1/4 and +5i in standard form is:

f(x) = x² - (1/4)x² + 25x - (25/4)

To write the polynomial with roots of 1/4 and +5i in standard form, we need to use the fact that the roots of a polynomial are related to its factors. Specifically, if r is a root of a polynomial, then x - r is a factor of the polynomial.

Therefore, if the roots of our polynomial are 1/4 and +5i, then we know that the factors of the polynomial are:

(x - 1/4) and (x - 5i) and (x + 5i)

To get the polynomial in standard form, we need to multiply out these factors and simplify.

(x - 1/4) and (x - 5i) and (x + 5i) = (x - 1/4) and (x² - 25i²)

= (x - 1/4) and (x² + 25)

= x³ + 25x - (1/4)x² - (25/4)

Therefore, the polynomial with roots of 1/4 and +5i in standard form is:

f(x) = x³ - (1/4)x² + 25x - (25/4)

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Answer:

The cost of Ticket = £63Booking Fee = 3% = 63*(3/100) = 1.89 = £ 1.89The total price of the ticket = £63 + £1.89 = £64.89. Therefore, the total price of the ticket is £64.89.

The sample space for Ella's compound event where she rolls a die and then flips a coin can be represented in the table below:

Die: 1 2 3 4 5 6
Coin: H-1 H-2 H-3 H-5 H-6 T-1 T-3 T-4 T-5

The size of the sample space is the total number of possible outcomes, which in this case is the number of rows in the table. We can see that there are 9 rows in the table, so the size of the sample space is 9.

To understand the sample space, we can imagine that each row in the table represents a possible outcome of the compound event. For example, the first row represents the outcome where Ella rolls a 1 on the die and gets heads on the coin. The second row represents the outcome where Ella rolls a 2 on the die and also gets heads on the coin, and so on.

Understanding the sample space is important in probability theory because it allows us to calculate the probability of specific events occurring. By knowing the size of the sample space and the number of favorable outcomes, we can determine the probability of an event happening.

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Surface area of the cylinder in terms of [tex]$\pi$[/tex] is [tex]$5904\pi m^2$[/tex].

The surface area of a cylinder can be calculated by adding the area of the two bases (which are circles) and the lateral area (which is the area of the curved surface).

The radius of the cylinder is given as 36m and the height as 46m. Therefore, the diameter of the cylinder is 72m (twice the radius). Using the formula for the area of a circle, we can calculate the area of each base:

[tex]$A_{base} = \pi r^2 = \pi (36m)^2 = 1296\pi m^2$[/tex]

The lateral area of the cylinder can be calculated using the formula:

[tex]$A_{lateral} = 2\pi r h$[/tex]

Substituting the given values, we get:

[tex]$A_{lateral} = 2\pi (36m) (46m) = 3312\pi m^2$[/tex]

Therefore, the total surface area of the cylinder is:

[tex]$A_{total} = A_{base} + A_{lateral} + A_{base} = 2A_{base} + A_{lateral}$[/tex]

Substituting the values we calculated, we get:

[tex]$A_{total} = 2(1296\pi m^2) + 3312\pi m^2 = 5904\pi m^2$[/tex]

So the surface area of the cylinder in terms of [tex]$\pi$[/tex] is [tex]$5904\pi m^2$[/tex].

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In mathematics, an expression is a combination of numbers, variables, and/or operators that represents a mathematical phrase or equation. Therefore, when b = -3, f(b) = -15.

An expression can contain constants, variables, functions, and/or mathematical operators such as addition, subtraction, multiplication, division, exponentiation, and logarithms.

To find f(b), we need to substitute b for a in the expression for f(a):

f(b) = 15b^2 + 40b - 30

To find the value of f when b = -3, we substitute -3 for b in the expression above:

f(-3) = 15(-3)^2 + 40(-3) - 30

f(-3) = 135 - 120 - 30

f(-3) = -15

Therefore, when b = -3, f(b) = -15.

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Answer:

The present ages of A and B will be 48 and 18 years.

Step-by-step explanation:

Let the coefficient be x.

A's age = 8x

B's age = 3x

Six years hence,

Ages will be 8x+6 and 3x+6.

Now, As per the question,

(8x+6) /(3x+6) = 9/4

32x+24 = 27x+54

5x = 30

x = 6.

The length of the straight line between the school and the fire station is 4.6 miles.

We can form a right-angled triangle with the school at the right-angle.

The distance between the school and the fire station is the hypotenuse of this triangle.

Using the Pythagorean theorem, we can calculate the length of the hypotenuse:

h^2 = 4.3^2 + 1.7^2

h^2 = 21.38

h ≈ 4.62

Rounding to the nearest tenth, the length of the straight line between the school and the fire station is approximately 4.6 miles.

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The area of the square is 16 square units.

The area of the rhombus is 24 square units.

Part 1: Using the distance formula, we can find the lengths of the diagonals:

Diagonal AC = √[tex][(7-1)^2 + (2-10)^2[/tex]] = √(36 + 64) = √100 = 10

Diagonal BD = √[[tex](12-(-4))^2 + (12-0)^2[/tex]] = √(256 + 144) = √400 = 20

Part 2: The area of a rhombus can be calculated using the formula: Area = (diagonal 1 x diagonal 2)/2.

So, for this rhombus, the area = (10 x 20)/2 = 100 square units.

Part 3: The area formulas for a square and rhombus are not interchangeable because they have different ways of computing their areas. A square has all four sides equal in length, while a rhombus has opposite sides equal in length. The diagonals of a square bisect each other at right angles, and each diagonal divides the square into two congruent triangles, so the area of a square is simply side length squared (Area =[tex]s^2[/tex]). However, the diagonals of a rhombus bisect each other at right angles, but they do not necessarily divide the rhombus into congruent triangles. Therefore, the area of a rhombus is calculated using the lengths of the diagonals (Area = (diagonal 1 x diagonal 2)/2).

For example, let's consider a square with side length 4 units and a rhombus with diagonals 6 units and 8 units.

The area of the square = [tex]4^2 = 16[/tex]square units.

The area of the rhombus = (6 x 8)/2 = 24 square units.

As we can see, the formulas are not interchangeable.

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Answer:

To find the radius of the cylinder, we can use the formula for the volume of a cylinder, which is pi*(r1^2)*h, where r1 is the radius and h is the height. Given that the cylinder has a height of 6 centimeters and a volume of 302 cubic centimeters, we can solve for r1 by dividing the volume by pi times the height, and then taking the square root of the result. After rounding to the nearest whole centimeter, the radius of the cylinder is approximately 5 centimeters.

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The most general antiderivative of the function g(v) = 5 cos(v) - 8/√(1-v^2) is 5 sin(v) + 8 arcsin(v) + C, where C is the constant of the antiderivative.

To find the antiderivative of the given function g(v), we can use the basic antiderivative rules. The antiderivative of 5 cos(v) is 5 sin(v), as the derivative of sin(v) is cos(v) and we only need to reverse the process.

Similarly, the antiderivative of -8/√(1-v^2) can be found using the inverse trigonometric function arcsin(v), as its derivative is -1/√(1-v^2). However, we need to include a constant of integration, denoted by C, as the antiderivative is not unique.

So the most general antiderivative of g(v) is 5 sin(v) + 8 arcsin(v) + C, where C represents the constant of the antiderivative. To check the correctness of the answer, we can differentiate it and verify if it gives us the original function g(v) as the result.

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Answer:

  (D)  7/10

Step-by-step explanation:

You want the rate of change of y with respect to x for the relation ...

  (2/5)x -(4/7)y = 3/2

Solving for y, we have ...

  2/5x -3/2 = 4/7y . . . . . . . . . . add 4/7y -3/2

  (7/4)(2/5)x -(7/4)(3/2) = y . . . . multiply by 7/4

  7/10x -21/8 = y . . . . . . . . . . simplify

The rate of change is the coefficient of x: 7/10.

The p-value of 0.416 indicates that there is no significant difference in the proportion of Republicans between the two areas of town. Therefore, we fail to reject the null hypothesis and conclude that there is no evidence of a significant difference in the proportion of Republicans between the two areas of town.

Based on the given information, the p-value is 0.416, which is larger than the conventional level of significance (e.g., 0.05 or 0.01). Therefore, we fail to reject the null hypothesis that there is no significant difference in the proportion of republicans between the two areas of town.

In other words, we cannot conclude that there is a significant difference between the two areas. It is possible that any observed difference could be due to chance.

However, it is important to note that statistical significance does not necessarily mean practical significance, and further investigation may be needed to determine if there are any meaningful differences between the two areas in terms of the proportion of republicans.

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A geometric sequence is a type of sequence where each term is found by multiplying the previous term by a constant factor. This means that each term is a multiple of the one before it. In contrast, an arithmetic sequence is a type of sequence where each term is found by adding a constant value to the previous term.

This means that each term is a sum of the one before it and a fixed value.

To answer your question, whether a geometric sequence will always grow faster than an arithmetic one depends on the values of the constant factor and fixed value in each sequence. In general, if the constant factor in a geometric sequence is greater than 1, the terms will grow at an increasingly faster rate than in an arithmetic sequence.

However, if the constant factor is between 0 and 1, the terms will grow at a decreasing rate, meaning that the sequence will actually grow more slowly than an arithmetic one.

It's important to note that the rate of growth is not the only factor to consider when comparing geometric and arithmetic sequences. The actual values of the terms in each sequence can also differ significantly, depending on the starting term and the values of the common ratio and common difference.

In some cases, an arithmetic sequence may actually have higher values than a geometric one, even if it grows more slowly.

In summary, whether a geometric sequence will always grow faster than an arithmetic one depends on the specific values of each sequence. However, in general, if the constant factor in a geometric sequence is greater than 1, it will grow faster than an arithmetic sequence.

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The rate of change after 5 years is 14.4%, indicating that the percentage of US adults using the internet is increasing at a rate of 14.4% per year.

Based on the provided information, the rate of US adults who use the internet can be modeled by the equation dI/dt = -0.5t + 16.9, where t represents the time in years and I represents the percentage of adults using the internet.

To determine the rate of change at a specific time, we need to substitute the value of t into the equation.

For example, to find the rate of change after 5 years, we would substitute t = 5:

dI/dt = -0.5(5) + 16.9
dI/dt = -2.5 + 16.9
dI/dt = 14.4

Therefore, the rate of change after 5 years is 14.4%, indicating that the percentage of US adults using the internet is increasing at a rate of 14.4% per year.

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