Which is shorter 14.75 yards or 52 feet

Option (d) An explicit formula representing the sequence is f(x) = 4(3/2)^x and option (e) The sequence shows exponential growth, are correct for the given geometric sequence.

A geometric sequence is a sequence of numbers where the ratio between any two neighboring terms is a constant. This constant ratio is called the common ratio. If the first term of the geometric sequence is a and the common ratio is r, then the n-th term (the last term) is given by a * r^(n-1). The first term is denoted by a, while the common ratio is denoted by r. Here, we are given that the recursive formula representing the sequence is f(x + 1) = 3/2(f(x )) when f(1) = 4.

By using the formula and considering f(1) = 4, we can find the first few terms in the sequence. So, the first few terms are 4, 6, 9, 27/2, …Now, let’s check each statement one by one.(a) The domain is the set of natural numbers. False.

The domain is {1, 2, 3, …} because the first term of the sequence is given and we need to use the recursive formula to find all the other terms.(b) The range is the set of natural numbers. False.

The range is not just the set of natural numbers as the sequence has decimals and fractions in it.(c) The recursive formula representing the sequence is f(x + 1) = 3/2(f(x )) when f(1) = 4.True.

This is given in the question.(d) An explicit formula representing the sequence is f(x) = 4(3/2)^x. True.

We can find the common ratio by dividing any term by its preceding term, and we get 3/2. Since the first term is 4, we can write the nth term as 4(3/2)^(n-1).(e) The sequence shows exponential growth. True.

The sequence is increasing and the ratio between any two consecutive terms is constant, which means it’s an exponential sequence.

Therefore, the answers are options (d) An explicit formula representing the sequence is f(x) = 4(3/2)^x and (e) The sequence shows exponential growth..

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Answer:

its the first one

Step-by-step explanation:

im in 8th grade and im like a 11th grader bc im smart :)

Answer:

4ft

Step-by-step explanation:

4ft is the answer

i hope this helps BRAINEST PLEASE

As you consider the various factors involved in starting a group, the most important factor you have to judge is the group's purpose or goal.

Step 1: Identify the group's purpose or goal - This is crucial because it will guide all other decisions, including membership criteria, communication methods, and meeting schedules.

Step 2: Assess the needs and resources of potential members - This will help you understand their motivations and ensure the group can support their needs while accomplishing its goal.

Step 3: Establish clear membership criteria and expectations - This will ensure that everyone in the group is on the same page and committed to the same goals.

Step 4: Choose an appropriate communication method - This will facilitate smooth and efficient communication among group members.

Step 5: Develop a meeting schedule that works for all members - Regular meetings help keep the group on track and provide opportunities for collaboration and feedback.

By focusing on the group's purpose or goal, you can create a solid foundation for a successful and productive group.

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The definition of a function is a relationship or expression involving one or more variables.

If each input value leads to only one output value, classify the relationship as a function. If any input value leads to two or more outputs, do not classify the relationship as a function.

After the last cutting, you will have 1,024 pieces of paper.

After cutting the sheet of paper into 4 pieces, each subsequent cut into 4 pieces will multiply the number of pieces by 4. Therefore, after the first cut, you will have 4 pieces.

After the second cut, you will have 4 * 4 = 16 pieces. After the third cut, you will have 16 * 4 = 64 pieces. Continuing this pattern, after the fourth cut, you will have 64 * 4 = 256 pieces.

After the fifth and final cut, you will have 256 * 4 = 1,024 pieces.

Therefore, after the last cutting, you will have 1,024 pieces of paper.

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Answer:

y = - 4x + 13

Step-by-step explanation:

In order to do this problem you would need a whole new equation, but you will use what is given to you:

instead of going with:

x - 4y = 20

Turn it into y = mx + b form, also known as slope-intercept form:

x - 4y = 20

-x       = -x

_________

- 4y = 20 - x

Then divide both sides by - 4:

\(\frac{-4y}{-4} = \frac{-x + 20}{-4}\)

You will then get:

y = \(\frac{1}{4}x - 5\)

From this equation we will only need the slope!

m || = \(\frac{1}{4}\)

(This slope is for parallel)

but if you want perpendicular to the slope, then we need the negative reciprocal!

Negative reciprocal is a flipped version of the value that is negative, for example:

2 = \(-\frac{1}{2}\)

Because \(\frac{2}{1}\) = 2

Now we will find the perpendicular slope which is:

m ⊥ = - 4

Now substitute this slope into slope intercept form:

y = mx + b

(-3) = -4(4) + b

(Take away parentheses)

-3 = -16 + b

(Move - 3 to the other side, by making it positive, but what you do to one side, you do to the other)

= -13 + 6

(Move - 13 to the other side, by make - 13 into +13)

+13 = +13

________

13 = b

(This is you b, also known as you intercept)

Your answer is:

y = -4x + 13

Answer:

1. =−8

2. =4x^6−5x^5+2

Step-by-step explanation:

happy to help ya :)

the diameter of the circle is

D = 16 cm

so the radius is r = D/2 = 16/2 = 8cm

the area of the circle is,

put r = 8 and pi = 3.14

thus the area of the circle is 200.96 centimetres squared.

The meaure of the side length x of the right triangle is approximately 2.02 units.

The figure in the image is a right triangle with one of its internal angle at 90 degrees.

From the image:

Angle θ = 68 degree

Adjacent to angle θ = x

Opposite to angle θ = 5

To solve for the missing side length x, we use the trigonometric ratio.

Note that: tangent = opposite / adjacent

Hence:

tan( θ ) = opposite / adjacent

Plug in the given values and solve for x.

tan( 68° ) = 5 / x

Cross multiply:

tan( 68° ) × x = 5

x = 5 / tan( 68° )

x = 2.02

Therefore, the value of x is 2.02.

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Answer:

20x^4

Step-by-step explanation:

Answer:

3/k = 4/5

k = 3 divided by 4/5

k = 3.75

Step-by-step explanation:

To find the equation of the tangent line to the curve y = 5ex cos(x) at the point (0, 5), we need to find the slope of the tangent line at that point.

First, we find the derivative of y with respect to x:

dy/dx = 5ex (-sin(x)) + 5ex cos(x)

Next, we evaluate the derivative at x = 0:

dy/dx |x=0 = 5e0 (-sin(0)) + 5e0 cos(0) = 5

So the slope of the tangent line at (0, 5) is 5.

Now we use the point-slope form of the equation of a line to find the equation of the tangent line:

y - y1 = m(x - x1)

where m is the slope of the line and (x1, y1) is the given point.

Plugging in the values we have:

y - 5 = 5(x - 0)

Simplifying, we get:

y = 5x + 5

So the equation of the tangent line to the curve y = 5ex cos(x) at the point (0, 5) is y = 5x + 5.

Step 1: Find the derivative of the function y.
Given function y = 5e^x cos(x), we will differentiate it with respect to x using the product rule.

Product rule: (uv)' = u'v + uv'
Let u = 5e^x and v = cos(x).

Step 2: Find u' and v'.
u' = d(5e^x)/dx = 5e^x
v' = d(cos(x))/dx = -sin(x)

Step 3: Apply the product rule.
y' = u'v + uv'
y' = (5e^x)(cos(x)) + (5e^x)(-sin(x))
y' = 5e^x(cos(x) - sin(x))

Step 4: Find the slope of the tangent line at the given point (0, 5).
Substitute x = 0 in the derived equation.
y'(0) = 5e^0(cos(0) - sin(0)) = 5(1)(1 - 0) = 5

Step 5: Use the point-slope form to find the equation of the tangent line.
Point-slope form: y - y1 = m(x - x1)
Given point: (0, 5) => x1 = 0 and y1 = 5
Slope (m) = 5

Step 6: Plug the values into the point-slope form.
y - 5 = 5(x - 0)
y - 5 = 5x

Step 7: Rewrite the equation in slope-intercept form (y = mx + b).
y = 5x + 5

The equation of the tangent line to the curve y = 5e^x cos(x) at the point (0, 5) is y = 5x + 5.

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Option d) {(–3, 2), (–2, 3), (–1, 2), (0, 4), (1, 1)} is the correct answer.

A function is a mathematical relation that maps each element in a set to a unique element in another set.

To determine which relation is a function between the given options, we need to check whether each input has a unique output.

In option a), the input -1 has two outputs, 3 and 2, which violates the definition of a function.

In, Option b) has two outputs for the input 0, violating the same definition.

In, Option c) has two outputs for the input 0, but it also has two outputs for the input -2, which violates the definition of a function as well.

In, Option d) is the only relation that satisfies the definition of a function, as each input has a unique output. Therefore, Option d) is the correct answer.

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Answer:

180 inches.

Step-by-step explanation:

============================

Perimeter of a triangle is:

\(P = a + b + c\\\rule{150}{0.5}\\a, b, c \text{ - given side lengths of a triangle}\)

We would actually need to use another formula before calculating the perimeter.

============================

There is one missing side measure.

Since the triangle given is a right triangle, we can use the Pythagorean Theorem to solve for the third side. Since the third side is opposite the right angle, it will be the hypotenuse. The other sides will be the legs, 'a' and 'b'.

\(a^2 + b^2 = c^2\\\rule{150}{0.5}\\30^2 + 72^2 = c^2\\\\\rightarrow 30^2 = 900\\\rightarrow 72^2 = 5184\\\\5184 + 900 = c^2\\\\6084 = c^2\\\\\sqrt{6084}= \sqrt{c^2}\\\\\boxed{78 = c}\)

Side C is 78 inches.

============================

As mentioned before, the perimeter of a triangle is:

\(P = a + b + c\\\rule{150}{0.5}\\a, b, c \text{ - given side lengths of a triangle}\)

We are given the measurements of 30, 72, and 78 inches.

\(P = a + b + c\\\rule{150}{0.5}\\P = 30 + 72 + 78\\\\\boxed{P = 180}\)

The perimeter of the given triangle should be 180 inches.

============================

Hope this helps!

Answer:

180 in

Step-by-step explanation:

you first find the hypotenuse since we're not given.

using a²+b²= c²

where a is 30 b is 72

30²+72²=c²

c²=6084

c= 78

perimeter is simply the distance round the figure. so it's 78+72+30 which is 180 in.

I hope this helps!

A graph of the solutions of this inequality 3x + 2 ≥ 1/2(x + 5) is shown on the number line attached below.

In this exercise, we would solve the given inequality by making x the subject of formula as follows;

3x + 2 ≥ 1/2(x + 5)

By multiplying both sides of the inequality by 2, we have the following:

(3x + 2) × 2 ≥ 1/2(x + 5) × 2

6x + 4 ≥ x + 5

By rearranging and collecting like terms, we have the following:

6x - x ≥ 5 - 4

5x ≥ 1

x ≥ 1/5

Next, we would use an online graphing calculator to plot the inequality as shown in the graph attached below. Additionally, the circle on the number line (graph) is closed because of the greater than or equal to (≤) symbol.

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Answer:

Step-by-step explanation:

23

Tyron receives a 30% discount on a hat. Calculations of discount percent are provided below.

The discount Percentage is calculated by = \(( Discount / Price )\) × \(100\)

What information do we have,

Usual cost = $28

Discount = $ 8.40

So,

Discount percentage \(= ( 8.40 / 28 )\) × 100

= 30%

Thus, 30% is the correct answer.

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Answer:

f=1.5⋅d or equivalent. The bag will last 140 days since 210÷1.5=140.

Step-by-step explanation:

Answer:

I think this is the right answer but last two signs are incorrect

Hope this will help

Answer:

i dont know

Step-by-step explanation:

A percentage is a way to describe a part of a whole.  The most improbable simulation for this coin is heads are 9.

A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.

To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.

The most improbable simulation for this coin for heads is the frequency of heads coming up out of 20 which is far from the estimated frequency. Since out of these 20 times 75% of the times the head will come up. Therefore, the number of times the head will come up can be written as,

\(75\%\ of\ 20\\\\= \dfrac{75}{100} \times 20\\\\= 15\)

Now it is estimated that at least 15 times out of 20, the head will come up. Thus, the most improbable simulation for this coin is heads are 9.

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Answer:

A coin is biased to display heads 75% of the time. It is tossed 20 times, and the outcomes are recorded. The most improbable simulation for this coin is

9 heads.

Step-by-step explanation:

Answer:

A could finish the whole work in 60 days

Step-by-step explanation:

Both A and B can finish the work in 30 days.

That means both A and B can finish 1/30 part of the work in 1 day.

So in 20 days, both A and B can finish 20/30 = 2/3 part of the work.

Both A and B worked together for 20 days and completed 2/3 part of the work. Now 1/3 part of the work is remaining.

But after 20 days B left the work. Now A finished the remaining 1/3 part of the work alone.

Given A has completed the remaining 1/3 part of the work in 20 days. We are asked to find in how many days A could finish the whole work.

Let A could finish the whole work in x days.

That means A could finish 1/x part of the work in 1 day.

So in 20 days, A could finish 20(1/x) = 20/x part of the work.

But it's given that A finished the remaining 1/3 part of the work in 20 days.

Thus we are able to equate 20/x and 1/3.

\(\longrightarrow\dfrac{20}{x}=\dfrac{1}{3}\)

\(\Longrightarrow\underline{\underline{x=60}}\)

Hence A could finish the whole work in 60 days.

Answer:

I believe the answer is C. I'd have to work this out on paper to be certain, but from what i worked out mentally, i got C. lol

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

It explains all ways he can learn for each topic

Gt= Graph and text

Gv= Graph and vid

(same pattern with the rest)

and at the end

T/V= both text and video

Answer: Hey Love ❤️ It’s B. Associative property

Step-by-step explanation: The person on the top is wrong what a shame

Answer:

I just took the test, it's Associative Property :D

Step-by-step explanation:

Answer:

5.8

Step-by-step explanation:

\( \sqrt{ {5}^{2} } + \sqrt( { - 3}^{2} )\)

\( \sqrt{25 + 9} \)

\( \sqrt{34} \)

5?8

a.we get, `A = √(2α³/π)`.

b.`⟨H⟩ = (3/4)hω - (h²/4ma²)` where `a = α/√(mω/h)`.

c.we can say that the variational principle is valid in this case.

(a) Let's find the normalization constant A.

We know that the integral over all space of the absolute square of the wave function is equal to 1, which is the requirement for normalization.  `∫⟨ψ|ψ⟩dx= 1`

Hence, using the given trial wavefunction, we get, `∫⟨ψ|ψ⟩dx = ∫ |A/(x^2+α²)|²dx= A² ∫ dx / (x²+α²)²`

Using a substitution `x = α tan θ`, we get, `dx = α sec² θ dθ`

Substituting these in the above integral, we get, `A² ∫ dθ/α² sec^4 θ = A²/(α³) ∫ cos^4 θ dθ`

Using the identity, `cos² θ = (1 + cos2θ)/2`twice, we can write,

`A²/(α³) ∫ (1 + cos2θ)²/16 d(2θ) = A²/(α³) [θ/8 + sin 2θ/32 + (1/4)sin4θ/16]`

We need to evaluate this between `0` and `π/2`. Hence, `θ = 0` and `θ = π/2` limits.

Using these limits, we get,`⟨ψ|ψ⟩ = A²/(α³) [π/16 + (1/8)] = 1`

Therefore, we get, `A = √(2α³/π)`.

Hence, we can now write the wavefunction as `ψ(x) = √(2α³/π)/(x²+α²)`.  

(b) Using the wave function found in part (a), we can now determine the expectation value of energy using the time-independent Schrödinger equation, `Hψ = Eψ`. We can write, `H = (p²/2m) + (1/2)mω²x²`.

The first term represents the kinetic energy of the particle and the second term represents the potential energy.

We can write the first term in terms of the momentum operator `p`.We know that `p = -ih(∂/∂x)`Hence, we get, `p² = -h²(∂²/∂x²)`Using this, we can now write, `H = -(h²/2m) (∂²/∂x²) + (1/2)mω²x²`

The expectation value of energy can be obtained by taking the integral, `⟨H⟩ = ⟨ψ|H|ψ⟩ = ∫ψ* H ψ dx`Plugging in the expressions for `H` and `ψ`, we get, `⟨H⟩ = - (h²/2m) ∫ψ*(∂²/∂x²)ψ dx + (1/2)mω² ∫ ψ* x² ψ dx`Evaluating these two integrals, we get, `⟨H⟩ = (3/4)hω - (h²/4ma²)` where `a = α/√(mω/h)`.

(c) Since we have an approximate ground state wavefunction, we can expect that the expectation value of energy ⟨H⟩ should be greater than the true ground state energy.

Hence, the value obtained in part (b) should be greater than the true ground state energy obtained by solving the Schrödinger equation exactly.

Therefore, we can say that the variational principle is valid in this case.

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1.5 is the variance for the given population of scores (5,2,5,4). Thus, the correct answer is option d.

The given data is as follows:

Scores are given =  5, 2, 5, 4,

The mean of the scores is calculated by using the formula,

Mean = (sum of the scores)/Number of scores

Mean = (5+2+5+4)/4

Mean = 16/4 = 4.

Now, we can calculate the Difference between each score and mean:

5-4=1

2-4=-2

5-4=1

4-4=0

The list of the scores generated by the squared differences =  1, 4, 1, 0

The total sum of squared difference = 1+4+1+0 = 6

Variance is calculated by using the formula,

Variance = sum of squared difference/Mean

Variance = 6/4 = 1.5

Therefore, we can conclude that 1.5 is the variance for the given population of scores.

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