2 1/7 divided by 1 1/4​

We get the composite function for the relationship between area and time as A = π (16t + r )².

We are given that, the wave travels at a rate of 16 feet / sec when George jumps off a tire swing in the circular pond.

So, this means that the radius of the wave increases by 16 feet in every second.

Now, we know that, the area of circle is given by:

A = π r²

Now, r increases by 16 feet every second.

So, the composite function will become:

A = π (16t + r )²

where 16 t represents the increase in area in t seconds.

Therefore, we get the composite function for the relationship between area and time as A = π (16t + r )².

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To estimate the number of new users that would be added during time period 7, we can use the Bass diffusion model, which is commonly used to model the adoption of new products or technologies.

The Bass diffusion model is given by the formula:

\(\[N(t) = \frac{{p \cdot q}}{{q + (p/q) \cdot e^{-((p+q) \cdot t)}}}\]\)

where:

- N(t) represents the cumulative number of adopters at time \(t\).

- p is the innovation parameter, representing the coefficient of innovation.

- q is the imitation parameter, representing the coefficient of imitation.

- e is the base of the natural logarithm.

Given a population size of 67 million, an innovation parameter of 0.005, and an imitation parameter of 0.84 for Color TV, we can substitute these values into the Bass diffusion model and calculate the number of new users added during time period 7.

\(\[N(7) - N(6) = \frac{{p \cdot q}}{{q + (p/q) \cdot e^{-((p+q) \cdot 7)}}} - \frac{{p \cdot q}}{{q + (p/q) \cdot e^{-((p+q) \cdot 6)}}}\]\)

Substituting the given values into the equation:

\(\[N(7) - N(6) = \frac{{0.005 \cdot 0.84}}{{0.84 + (0.005/0.84) \cdot e^{-((0.005+0.84) \cdot 7)}}} - \frac{{0.005 \cdot 0.84}}{{0.84 + (0.005/0.84) \cdot e^{-((0.005+0.84) \cdot 6)}}}\]\)

Evaluating the expression will give us the estimated number of new users added during time period 7.

In LaTeX, the solution can be represented as:

\(\[N(7) - N(6) = \frac{{0.005 \cdot 0.84}}{{0.84 + (0.005/0.84) \cdot e^{-((0.005+0.84) \cdot 7)}}} - \frac{{0.005 \cdot 0.84}}{{0.84 + (0.005/0.84) \cdot e^{-((0.005+0.84) \cdot 6)}}}\]\)

After evaluating this expression, you will obtain the estimated number of new users added during time period 7.

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To find the length of the graph of f(x)=ln(4sec(x)) for 0≤x≤π/3, we first need to compute the derivative of the function.

f(x) = ln(4sec(x))
f'(x) = (1/sec(x)) * (4sec(x)) * tan(x) = 4tan(x)
Next, we use the arc length formula:
L = ∫ [a,b] √[1 + (f'(x))^2] dx
Substituting in the values, we get:
L = ∫ [0,π/3] √[1 + (4tan(x))^2] dx
We can simplify this by using the identity 1 + tan^2(x) = sec^2(x):
L = ∫ [0,π/3] √[1 + (4tan(x))^2] dx
 = ∫ [0,π/3] √[1 + 16tan^2(x)] dx
 = ∫ [0,π/3] √[sec^2(x) + 16] dx
 = ∫ [0,π/3] √[(1 + 15cos^2(x))] dx
 = ∫ [0,π/3] √15cos^2(x) + 1 dx
Using the substitution u = cos(x), we get:
L = ∫ [0,1] √(15u^2 + 1) du
This can be solved using trigonometric substitution, but the details are beyond the scope of this answer. The final result is:
L = 4/3 * √(15) * sinh^(-1)(√15/4) - √15/2
Therefore, the length of the graph of f(x)=ln(4sec(x)) for 0≤x≤π/3 is approximately 3.195 units.

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Answer:

All real numbers are solutions

Step-by-step explanation:

Let's solve your equation step-by-step

3(x+2)=5x+1−2x+5

Step 1: Simplify both sides of the equation

3(x+2)=5x+1−2x+5

(3)(x)+(3)(2)=5x+1+−2x+5(Distribute)

3x+6=5x+1+−2x+5

3x+6=(5x+−2x)+(1+5)(Combine Like Terms)

3x+6=3x+6

3x+6=3x+6

Step 2: Subtract 3x from both sides

3x+6−3x=3x+6−3x

6=6

Step 3: Subtract 6 from both sides

6−6=6−6

0=0

Answer: easy just

let x be 2 years and the flavors would be doubled right so i guess it would be 48

Answer:

C. 116

Step-by-step explanation:

AC= 58*2= 116

Answer:

C

Step-by-step explanation:

The measure of the inscribed angle ABC is half the measure of its interceptrd arc AC, thus

arc AC = 2 × 58° = 116° → C

Answer:

Is

Step-by-step explanation:

The statement which is true of the growth rate of the functions over the interval 0 ≤ x ≤ 1 is that: B. The exponential grows at the same rate as the quadratic.

The rate of change can be defined as a type of function that describes the average rate at which a quantity increases or decreases with respect to another quantity.

Mathematically, the rate of change can be calculated by using this formula;

\(Rate = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Rate = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}\)

From the given interval and graph (see attachment), the data point for the exponential function would be as follows:

Next, we would calculate the rate of change of the exponential function over the given interval:

Rate of change = (2 - 1)/(1 - 0)

Rate of change = 1/1

Rate of change = 1.

From the given interval and graph (see attachment), the data point for the quadratic function would be as follows:

Next, we would calculate the rate of change of the quadratic function over the given interval:

Rate of change = (1 - 0)/(1 - 0)

Rate of change = 1/1

Rate of change = 1.

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Answer:

c: 8   i'm sure

Step-by-step explanation:

Because we count where the line stops is 8 squares which means it's 8

Answer:

I am not so sure about this one.

Step-by-step explanation:

Solution:

Probability of the second outcome occurring is 1-p

Explanation:

In an experiment with only two outcomes, the probabilities of both outcomes must add up to 1.

This means that if the first outcome has a probability of p, the second outcome must have a probability of 1-p.

Therefore, the equation for this situation would be: p + (1-p) = 1Solving for p, we get: p = 1 - (1-p) = 1 - 1 + p = p.

Therefore, the probability of the first outcome occurring is simply p, as given in the question.

The probability of the second outcome occurring is 1-p.

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The probability of the first outcome, p, is equal to the total probability of all outcomes, minus the probability of the second outcome, p2. So, p = 1 - p2.

In an experiment with only two outcomes, the sum of the probabilities of the two outcomes must equal 1. This means that if the first outcome has a probability of p, the second outcome must have a probability of 1-p.

Therefore, the probability of the first outcome, p, can be found by subtracting the probability of the second outcome, p2, from 1:
p = 1 - p2

So, if you know the probability of the second outcome, you can find the probability of the first outcome by subtracting it from 1.

For example, if the probability of the second outcome is 0.3, the probability of the first outcome would be:
p = 1 - 0.3 = 0.7

So the probability of the first outcome is 0.7.

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8/19 or 42.1%

add all values up to a total, then find the percentage from that total.

8 + 2 + 1 + 3 + 5 = 19 balls total

8 tennis valls to 19 total.

8/19 or 42.1%

The maximum value of the sum of the roots of the equation (x−a) (x−b) + (x−b) (x−c) = 0 is 16.5

Given,

The equation; (x−a) (x−b) + (x−b) (x−c) = 0

We have to find the maximum value of the sum of the roots of the equation

Here, a, b and c be three distinct on-digit numbers;

Now,

(x−a) (x−b) + (x−b )(x−c) = 0

2x² − ax − 2bx − cx + ab + bc = 0

2x² − (a + 2b + c) x + ab + bc = 0

According to Vieta's formulae, the sum of the roots in this quadratic equation is just (a+2b+c) / 2. It is obvious that maximizing the 2b term is necessary for this total to be at its highest level. Consequently, b = 9. (the largest one-digit number). Since both of the coefficients of a and c are equal, their values can be either the second-largest one-digit number (8) or the third-largest one-digit number ( 7 ). This is due to the fact that a, b, and c are three separate one-digit numbers.

Then,

(8+2 × 9+7) / 2 = 16.5

That is,

The maximum value of the sum of the roots of the equation (x−a) (x−b) + (x−b) (x−c) = 0 is 16.5

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This is the solution to the given integral using trigonometric substitution. To solve the given integral using trigonometric substitution, follow these steps:

Step 1: Given integral: ∫3(t^2 - 4)dt

Step 2: Substitute t = 2sinθ, then dt/dθ = 2cosθ. The given integral becomes ∫3(4sin^2θ - 4)2cosθ dθ

Step 3: Simplify the given integral: 24 ∫sin^2θ cosθ dθ - 24 ∫cosθ dθ

Step 4: Use the identity sin^2θ = 1 - cos^2θ in the first integral to get: 24 ∫(1 - cos^2θ) cosθ dθ

Step 5: Simplify the first integral: ∫cosθ dθ - ∫cos^3θ dθ

Step 6: Evaluate the integral of cosθ and cos^3θ.

Step 7: Substitute back the value of θ = sin^-1(t/2) in the final answer.

Here's the complete solution:

∫3(t^2 - 4)dt = 24 ∫sin^2θ cosθ dθ - 24 ∫cosθ dθ [∵ t = 2sinθ, dt = 2cosθ dθ]

= 24 [∫cosθ dθ - ∫cos^3θ dθ - ∫cosθ dθ] [using the identity sin^2θ = 1 - cos^2θ]

= 24 [sinθ - (3/4)cosθ - (1/4)cos3θ - sinθ - C1] [simplifying]

= 24 [(3/4)cosθ + (1/4)cos3θ - C1] [simplifying]

Substituting the value of θ = sin^-1(t/2), we get:

= 24 [(3/4)cos(sin^-1(t/2)) + (1/4)cos3(sin^-1(t/2))) - C1]

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Answer:

C. y = 4/5

Step-by-step explanation:

A line that is parallel to the x axis and perpendicular to the y axis will be a horizontal line.

Horizontal lines have a slope of 0, so the equation of the line will not have x in them.

Since horizontal lines will have a constant y value, the equation will have y = in the beginning.

So, C is the correct answer.

Solution

A standard deck of cards has 4 suits: Hearts, Clubs, Spades, and Diamonds

Each suite contains an ace, 2, 3, 4,5,6,7,8,9,10, jack, queen, and king, a total of 13 cards

Therefore a standard pack of cards has 4 x13 cards = 52 cards/elements

An expression for probability is

The question requires us to find the probability of picking an Ace or a Club

No of Aces = 4 across all the suits

No of Clubs = 4 across all suits

Total number of cards = 52

The probability of picking an Ace or a Club is

Answer = 2/13

The question is asking how many pages of a book can be numbered with twice the number of digits used to number a 500-page book. We can enumerate up to 999,999 pages with six digits, but in practical terms, it is not relevant as no book has that many pages.

Let's break this down. To number a 500-page book, we need three digits (from 001 to 500). If we want to number another book with twice the number of digits, we would need six digits (from 000001 to 999999).

Now, we need to figure out how many pages can be numbered with six digits. To do this, we need to find the largest number that can be represented by six digits. The largest six-digit number is 999,999.

So, the answer to the question is that we can enumerate up to 999,999 pages with six digits. However, this is not a practical or realistic scenario as no book has that many pages.

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Answer:

wat da f-u-c-k

Step-by-step explanation:

true

Answer:

false

Step-by-step explanation:

it is 530.93cm cubed

Answer: 4/5x

Step-by-step explanation:

Answer: option c

Answer:30,6

Step-by-step explanation:

Answer:

10/25=×/150

x=60

so 60 students

Answer:

60

Step-by-step explanation:

because I litterly just did the test and got my answers back

Answer:

The rounded answer is 11

Step-by-step explanation:

a-squared + b-squared = c-squared
8-squared + 7-squared = c-squared
64 + 49 = c-squared
area-113 (the check mark symbol thing)

Answer:

  (d)  10.63

Step-by-step explanation:

You want the length of the hypotenuse of a right triangle with legs 7 in and 8 in.

The Pythagorean theorem tell you the relationship between legs a, b, and hypotenuse c of a right triangle is ...

  c² = a² +b²

In this figure, this means ...

  x² = 7² +8² = 49 +64 = 113

  x = √113 ≈ 10.63

The length of x is about 10.63.

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Answer:

the juniors, this is because they are the juniors, which means they are the smaller ones here and the ones who need a speech of inspiration and motivation

Answer:

B cause it same

Step-by-step explanation:

If am wrong correct me thanks

The value of the friction force on the sofa will be 288 N.

The force which opposes the motion of the body is known as friction force.

Ralph wants to move a 60.0 kg sofa.

He applies a force of 480 N.

Under these conditions, the sofa initially moves with an acceleration of 3.20 m/s².

Then the value of the friction force on the sofa will be

We know

ΣF = ma

We have

m = 60 kg

a = 3.2 m/s²

Then the value of friction force will be

480 – f = 60 × 3.2

480 – f = 192

          f = 480 – 192

          f = 288 N

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Answer:

288

Step-by-step explanation:

Answer:

x = 11

z = 86

Step-by-step explanation:

8x + 6 and 10x-16 are vertical angles

Vertical angles are pairs of angles that are opposite each other and have the same vertex, or point of intersection. They are formed when two lines intersect at a point, and are always congruent, or of equal measure.

To solve this equation, we need to isolate the variable x on one side of the equation. To do this, we can start by subtracting 6 from both sides of the equation:

8x + 6 - 6 = 10x - 16 - 6

8x = 10x - 22

Now we can subtract 8x from both sides of the equation:

8x - 8x = 10x - 22 - 8x

0 = 2x - 22

To solve for x, we can add 22 to both sides of the equation:

0 + 22 = 2x - 22 + 22

22 = 2x

Finally, we can divide both sides of the equation by 2 to find the value of x: 22 / 2 = 2x / 2

x = 11

Therefore, the solution to the equation is x = 11.

Now that we have x, z is a supplementary angle to 8x + 6 (or you could do 10x - 16)

Supplementary angles are pairs of angles that add up to 180 degrees. They are formed when two lines intersect at a point, and the angles formed at the intersection are supplementary.

First plug in x, 8x + 6 = 8(11) + 6 = 88 + 6 = 94

180 - 94 = z

z = 86

Answer:

(6,-6)

Step-by-step explanation:

The required coordinates of B is (6,-6).

In geometry, a line segment is a part of a line that is bounded by two end points, and contains every point on the line that is between end points.

Now it is given that,

Midpoint M (x,y) = (2,-7)

Coordinates of A( x₁,y₁) = (-2,-8)

Let the coordinates of B be (x₂,y₂)

Since, midpoint of line segment AB is given as,

{[(x₁+x₂ )/2] , [(y₁+y₂ )/2]}

Therefore,

x = (x₁+x₂ )/2

⇒ 2x = (x₁+x₂)

⇒ x₂ = 2x - x₁

Putting the values we get,

x₂ = 2(2) - (-2)

⇒ x₂ = 4 + 2

⇒ x₂ = 6

Similarly,

y₂ = 2y - y₁

Putting the values we get,

y₂ = 2(-7) - (-8)

⇒ y₂ = -14 + 8

⇒ y₂ = -6

so, the coordinates of B is (6,-6)

Thus, the required coordinates of B is (6,-6).

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The true statements that could be part of the explanation of the statement "tan 40° ≈ 0.84" are: All right triangles with an acute angle of 40° are similar to each other. If you know tan 40° ≈ 0.84 and the length of the leg opposite to the 40° angle, then you can calculate the length of the other leg. The ratio of the opposite side to the hypotenuse in any right triangle with an angle of 40° is always approximately 0.84

In a right triangle, the tangent of an acute angle is defined as the ratio of the opposite side and the adjacent side of that angle. Mathematically, for an acute angle A, tan(A) = opposite/adjacent. In the current case, we are discussing tan 40°. So, if the angle A in a right triangle is 40°, and if the opposite side to that angle is x and the adjacent side is y, then tan 40° = x/y .If we know the value of tan 40°, then we can calculate the value of x/y or y/x .In the following true statements, we will discuss how we can use tan 40° to make some conclusions: The ratio of the opposite side to the hypotenuse in any right triangle with an angle of 40° is always approximately 0.84This statement is true. This is based on the definition of tangent. tan 40° = opposite/adjacent. In a right triangle with an angle of 40°, the hypotenuse is neither the opposite side nor the adjacent side. But, we can write the above equation as opposite/hypotenuse = tan 40°/1. So, the ratio of the opposite side to the hypotenuse in any right triangle with an angle of 40° is always approximately 0.84.

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