Enter a formula using k to connect the two variables.
F is proportional to a.


Please help​

Answer:

$7.10

Step-by-step explanation:

5 = $3.55

to get 10 cans you double the 5 cans

5 × 2 = 10 cans

$3.55 × 2 = $7.10

10 cans = $7.10

Answer:

d

Step-by-step explanation:

Answer:

A:65 grams

Step-by-step explanation:

I got it correct on a quiz I did that had this question.

You can weigh 4 marbles against each other first, then if none are heavier, weigh 3 of the remaining marbles against each other, and if none of those are heavier, weigh the last two marbles against each other to find the heavier one.

An object's power of attraction toward the Earth is measured by its weight. It is the result of multiplying the object's mass by the acceleration caused by gravity.

A scale or balance is a tool used to determine mass or weight. These are also referred to as weight scales, mass scales, weight balances, and mass balances.

To weigh the 12 marbles and find out the heavier one,

This solution will always work because at each step, you are halving the number of marbles you need to check, so you will always be able to find the heavier marble in 3 weighings or less.

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Answer:

\(v = t (5t^{3} - 24)\)

Step-by-step explanation:

We are given an expression to solve for the displacement (x), so in order to find velocity (v), we need to differentiate the function.

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

Solving :

⇒ \(\frac{dx}{dt} = \frac{d}{dx} (t^{5} - 12t^{2} + 9)\)

⇒ \(v = (5)t^{5-1} - (2)12t^{2-1} + 0\)

⇒ \(v = 5t^{4} - 24t\)

⇒ \(v = t (5t^{3} - 24)\)

Using this equation, we can find the velocity if a value of t is given.

The statement that is true in the given is that if BE ≅ BD and AD ≅ CE then, ΔABC is an isosceles triangle.The triangles have three congruent sides, such as SSS (Side-Side-Side). If three pairs of sides are congruent, the triangles are identical (congruent)

.The third pair of angles must be congruent since the triangles are isosceles. CPCTC (Corresponding Parts of Congruent Triangles are Congruent) is the proof method to be used.CPCTC means that the parts of congruent triangles that correspond to one another are also congruent. In this situation, it means that AB is congruent to AC. So, by using the CPCTC theorem, we can conclude that ΔABC is an isosceles triangle with AB ≅ AC. Hence, option (c) CPCTC (Corresponding Parts of Congruent Triangles are Congruent) is the correct answer. The following is an explanation of this:In ΔABE and ΔCBD, we have BE ≅ BD (Given)AB ≅ CB (Common)∠ABE ≅ ∠CBD (Vertically opposite angles)Therefore, by SAS, we haveΔABE ≅ ΔCBDThus, AE ≅ CD (CPCTC)Similarly, in ΔADE and ΔCBE, we haveAD ≅ CEBE ≅ BD∠ADE ≅ ∠CEB Therefore, by SAS, we haveΔADE ≅ ΔCBEThus, AD ≅ CB and AE ≅ CDThus, AB + BC = AD + CDSince AD ≅ CDBut, CD = AE Therefore, AB + BC = AD + AEBut, AD + AE > ABTherefore, AB + BC > ABThus, BC > 0Thus, AB = ACTherefore, ΔABC is an isosceles triangle.

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The correct answer is option (c) CPCTC (Corresponding Parts of Congruent Triangles are Congruent).

Given that BE ≅ BD and AD ≅ CE

To prove that ΔABC is an isosceles triangle.

It can be observed that by adding the two equations given above, we get AD + BE = CE + BD

If we see closely, this equation gives us two sides of the triangle ΔABC.

In other words, AD + BE represents side ABCE + BD represents side AC

Now, if we can show that BC = AB, then we can say that ΔABC is an isosceles triangle.

Now, since AD ≅ CE, it means that ΔABD ≅ ΔCBE (SAS)

Similarly, since BE ≅ BD, it means that ΔCBD ≅ ΔBDA (SAS)

Now, it can be observed that

AB = BD + DA (sum of two sides)

BC = BE + CE (sum of two sides)

Using the fact that BE ≅ BD, and AD ≅ CE and applying CPCTC, we can get BD = BE and CE = AD

Therefore, AB = BD + DA = BE + AD = BC

Therefore, it is proved that ΔABC is an isosceles triangle.

Hence the correct answer is option (c) CPCTC (Corresponding Parts of Congruent Triangles are Congruent).

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For the food bill, each person would owe $31.33 ($156.65 divided by 5). For the alcohol bill, each person would owe $9.90 ($49.50 divided by 5).

To find out how much you owe for each bill, you need to divide the total amount on each bill by the number of people attending the working dinner (5 people).

For the food bill:
1. Total food cost: $156.65
2. Divide by the number of people (5): $156.65 / 5 = $31.33

For the alcohol bill:
1. Total alcohol cost: $49.50
2. Divide by the number of people (5): $49.50 / 5 = $9.90

So, you owe $31.33 for the food bill and $9.90 for the alcohol bill.

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Thus, \(\left[\begin{array}{ccc}-2\\0\\1\end{array}\right]\) , \(\left[\begin{array}{ccc}-3\\1\\0\end{array}\right]\) are the required vectors.

A nonzero vector that is orthogonal to direction vectors of the plane is called a normal vector to the plane.

The image of a function consists of all the values the function takes in its target space. If f is a function from X to Y, then

image(f) = {f : (x : x in X)} = {b in Y : b = f for some x in X}

Consider the system in terms of an equation,

x + 3y + 2z = 0

x = -3y - 2z

When y = 0

\(x =\left[\begin{array}{ccc}-2\\0\\1\end{array}\right]\)

When z = 0

\(x =\left[\begin{array}{ccc}-3\\1\\0\end{array}\right]\)

Thus, \(\left[\begin{array}{ccc}-2\\0\\1\end{array}\right]\) , \(\left[\begin{array}{ccc}-3\\1\\0\end{array}\right]\) are the required vectors.

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To solve the given initial value problem using Laplace transforms, we can apply the Laplace transform to both sides of the differential equation and use initial conditions to determine the transformed equation.

By algebraically manipulating the transformed equation, we can find the Laplace transform of the desired solution. Finally, we can use the inverse Laplace transform to obtain the solution in the time domain. Let's denote the unknown function as x(t). Applying the Laplace transform to both sides of the differential equation yields the transformed equation in terms of the Laplace transform variables s and X(s). By substituting the initial conditions x(0) = 0 and x'(0) = 20 into the transformed equation, we can solve for X(s).

After obtaining the Laplace transform X(s), we can manipulate the equation algebraically to isolate X(s) on one side. This may involve factoring, simplifying, and using partial fraction decomposition if necessary. Once we have the equation in terms of X(s), we can apply the inverse Laplace transform to find the solution x(t) in the time domain.

To find y(t), we follow the same procedure, applying the Laplace transform to both sides of the differential equation involving y(t) and using the given initial condition y(0) = y0. Solving for the Laplace transform Y(s), we can then find y(t) by applying the inverse Laplace transform.

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The 3 d.o.f. torsional finite element has three nodes, with each node having one degree of freedom (d.o.f.) for rotational displacement. To derive the element stiffness matrix (K) and load vector (F) for this element, we consider the equilibrium of torques, assuming GJ is constant and a distributed torque per unit length is present.

For the element stiffness matrix, we apply the torsional spring analogy and use Hooke's Law for torsional deformation: T = GJθ'/L, where T is the torque, GJ is the torsional stiffness, θ' is the angular displacement, and L is the length of the element. The stiffness matrix K is then formed as a 3x3 matrix, relating the torques at each node to their respective angular displacements.
To derive the load vector, we consider the distributed torque per unit length and integrate it over the length of the element. This results in a 3x1 vector, representing the external torque applied at each node.
Combining the stiffness matrix and the load vector, we can solve for the angular displacements of each node and analyze the torsional behavior of the element.

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Answer:

\(sin^2x\)

Step-by-step explanation:

To simplify the expression (1 - cos x)(1 + cos x), we can use the difference of squares identity, which states that \(a^2 - b^2 = (a + b)(a - b).\)

Let's apply this identity to the given expression:

\((1 - cos x)(1 + cos x) = 1^2 - (cos x)^2\)

Now, we can simplify further by using the trigonometric identity \(cos^2(x) + sin^2(x) = 1.\) By rearranging this identity, we have \(cos^2(x) = 1 - sin^2(x).\)

Substituting this into our expression, we get:

\(1^2 - (cos x)^2 = 1 - (1 - sin^2(x))\)

Simplifying further:

\(1 - (1 - sin^2(x)) = 1 - 1 + sin^2(x)\)

Finally, we get the simplified expression:

\((1 - cos x)(1 + cos x) = sin^2(x)\)

To simplify the expression \(\sf\:(1-\cos x)(1+\cos x)\\\), follow these steps:

Step 1: Apply the distributive property.

\(\longrightarrow\sf\:(1-\cos x)(1+\cos x) = 1 \cdot 1 + 1 \cdot \\\)\(\sf\: \cos x -\cos x \cdot 1 - \cos x \cdot \cos x\\\)

Step 2: Simplify the terms.

\(\longrightarrow\sf\:1 + \cos x - \cos x - \cos^2 x\\\)

Step 3: Combine like terms.

\(\longrightarrow\sf\:1 - \cos^2 x\\\)

Step 4: Apply the identity \(\sf\:\cos^2 x = 1 - \sin^2 x\\\).

\(\sf\:1 - (1 - \sin^2 x)\\\)

Step 5: Simplify further.

\(\longrightarrow\sf\:1 - 1 + \sin^2 x\\\)

Step 6: Final result.

\(\sf\red\bigstar{\boxed{\sin^2 x}}\\\)

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\textcolor{red}{\underline{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

(1) One of the six countries sent 41 representatives to the congress --> obviously x6=41x6=41 --> x1+x2+x3+x4+A=34x1+x2+x3+x4+A=34.

Given: x1<x2<x3<x4<A<x6x1<x2<x3<x4<A<x6 and x1+x2+x3+x4+A+x6=75x1+x2+x3+x4+A+x6=75. Q: is A≥10A≥10

Can A≥10A≥10? Yes. For example: x1=2x1=2, x2=3x2=3, x3=8x3=8, x4=10x4=10, A=11A=11 --> sum=34sum=34 (answer to the question YES);

Can A<10A<10? Yes. For example: x1=4x1=4, x2=6x2=6, x3=7x3=7, x4=8x4=8, A=9A=9 --> sum=34sum=34 (answer to the question NO).

(2) Country A sent fewer than 12 representatives to the congress --> A<12A<12.

The same breakdown works here as well:

Can 12>A≥1012>A≥10? Yes. For example: x1=2x1=2, x2=3x2=3, x3=8x3=8, x4=10x4=10, A=11A=11, x6=41x6=41 --> sum=75sum=75 (answer to the question YES);

Can A<10A<10? Yes. For example: x1=4x1=4, x2=6x2=6, x3=7x3=7, x4=8x4=8, A=9A=9, x6=41x6=41 --> sum=75sum=75 (answer to the question NO).

(1)+(2) The given examples fit in both statements and A in one is more than 10 and in another less than 10. Not sufficient.

Answer:i hope this helps

Step-by-step explanation:add all the terms together and divide by the amount of terms given

Answer:100

Step-by-step explanation:perimeter times apothem divided by two

Answer:

k = -5 and i think the other one is k=0

Step-by-step explanation:

Answer:

k=-1 k=0

Step-by-step explanation:

Answer: 4

Step-by-step explanation:

Given: Total girls = 24

Total boys = 20

If each group must be identical, then the maximum number of groups that can be made = GCD(24,20)   [GCD= Greatest common divisor]

Since 24 = 2 x 2 x 2 x 3

20 = 2 x 2 x 5

GCD(24,20)= 2 x 2 = 4

Hence, the maximum number of groups that can be made = 4

Answer:

P = 2 !

Step-by-step explanation:

15p = 31 = 61

        -31   -31

-----------------------

Thus, P = 2. Hope this helps! <3

a) Correlation: -0.9351

b) They all follow a binomial distribution.

c) The regression line minimizes the sum of the squares of the residuals.

d) The slope of the regression line is: Negative

e) H0: β1 = 0

f) Ha: β1 ≠ 0

g) 4 degrees of freedom

h) The probability of committing a Type I Error is:

0.01 or 1%

a. The correlation between price and mileage can be computed using the given data.

Mileage: 37530, 77720, 88800, 105730, 116810, 39210

Price: 16100, 13460, 10290, 7020, 8280, 15430

Using a statistical software or calculator, you can find the correlation coefficient (r) to determine the correlation between price and mileage.

Correlation: -0.9351 (rounded to 4 decimal places)

b. The assumption that is NOT made on the standard regression assumptions is:

c) They all follow a binomial distribution

The standard regression assumptions are:

a) They are all independent of each other

b) They all have the same standard deviation

d) They all have mean (expected value) 0

c) They all follow a binomial distribution is not one of the standard regression assumptions.

c. The statement that is true about the regression line is:

c) The regression line minimizes the sum of the squares of the residuals.

The regression line is chosen to minimize the sum of the squares of the residuals, which represents the deviation of the observed values from the predicted values.

d. The slope of the regression line can be determined by examining the data. Since the correlation coefficient is negative, it suggests a negative relationship between price and mileage.

Therefore, the slope of the regression line is:

b) Negative

e. The null hypothesis for the hypothesis test is:

g) H0: β1 = 0

The null hypothesis assumes that there is no relationship between mileage and price, meaning the slope of the regression line is zero.

f. The alternative hypothesis for the hypothesis test is:

h) Ha: β1 ≠ 0

The alternative hypothesis states that there is a significant relationship between mileage and price, implying that the slope of the regression line is not equal to zero.

g. The t-statistic is used for this hypothesis test. Under the null hypothesis, the t-statistic has a distribution with (n - 2) degrees of freedom, where n is the number of observations (sample size). In this case, n = 6, so the t-statistic has:

4 degrees of freedom

h. The probability of committing a Type I Error for this test is equal to the significance level, which is given as α = 0.01.

Therefore, the probability of committing a Type I Error is:

0.01 or 1%

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Answer:

Step-by-step explanation:

a) The probabilities for X = 0, 1, 2, and 3, and then summing them up, we find that P(X > 3) ≈ 0.019. b) The probability of zero successes is approximately 0.430. c) The length of an interval of time is 1.306 hours.

a) The time between arrivals of small aircraft is exponentially distributed with a mean of one hour. To find the probability that more than three aircraft arrive within an hour, we will use the Poisson distribution, where λ (lambda) represents the average number of arrivals per hour, which is 1 in this case. The probability formula is P(X > 3) = 1 - P(X ≤ 3), where X is the number of arrivals. Using the Poisson formula, we get:

P(X > 3) = 1 - [P(X=0) + P(X=1) + P(X=2) + P(X=3)]

Calculating the probabilities for X = 0, 1, 2, and 3, and then summing them up, we find that P(X > 3) ≈ 0.019.

b) To find the probability that no interval contains more than three arrivals in 30 separate one-hour intervals, we can use the binomial distribution. The probability of success (an interval with more than three arrivals) is 0.019 from part a), and the probability of failure (an interval with three or fewer arrivals) is 1 - 0.019 = 0.981. Using the binomial formula with n = 30 (number of intervals) and p = 0.981, we find the probability of zero successes (i.e., no interval with more than three arrivals) is approximately 0.430.

c) To determine the length of an interval of time (in hours) such that the probability that no arrivals occur during the interval is 0.27, we use the exponential distribution formula:

P(T > t) = e^(-λt), where T is the waiting time between arrivals, t is the time interval, and λ is the average number of arrivals per hour (1 in this case).

We want to find the value of t such that P(T > t) = 0.27. So:

0.27 = e^(-1 * t)

Taking the natural logarithm of both sides, we get:

ln(0.27) = -t

Solving for t, we find that t ≈ 1.306 hours.

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Answer:

60°  and 180°

Step-by-step explanation:

Sum of interior angles of a polygon = (n - 2) × 180°

(where n is the number of sides)

A hexagon has 6 sides

⇒ Sum of interior angles of a hexagon = (6 - 2) × 180° = 720°

Let x = smallest unknown angle

Therefore, 3x = largest unknown angle

Sum the angles and solve for x:

⇒ 114° + 130° + 140° + 96° + x + 3x = 720°

⇒ 480° + 4x = 720°

⇒ 4x = 720° - 480°

⇒ 4x = 240°

⇒ x = 60°

Therefore, smallest unknown angle = 60°

and largest unknown angle = 3 × 60° = 180°

The expression that best estimates 6 3/4 divided by 1 2/3 is 7/2.

What are dividends?

 The number divided by (15) is known as the dividend, and the number divided by (3 in this instance) is known as the divisor. The quotient is the outcome of the division.

Here, we have

6 3/4  divided by 1 2/3 comes out to 4 1/20.

The closest value to this in the options available is 7/2 (or 3.5).

This answer is only .55 away from the correct value, while the rest of the options are far less close.

Hence, the expression that best estimates 6 3/4 divided by 1 2/3 is 7/2.

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The cost of 100 donuts is $ 1 if a dozen of donuts cost 12 cents.

This question is solved using the unitary method. The unitary method is a method in which you find the value of a unit and then the value of the required number of units.

1 dozen refers to a group of 12.

Cost of 1 dozen donuts or 12 donuts = 12 cents

Cost of 1 donut = \(\frac{12}{12}\) = 1 cent

Cost of 100 donuts = 1 * 100 = 100 cents

100 cents = 1 dollar.

Thus, the cost of 100 donuts is 100 cents or 1 dollar.

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Answer:

20kg

Step-by-step explanation:

There are 2.2 pounds in a kg, so we will divide 44 by 2.2 to see how many kg are in 44 pounds  

The first four non-zero terms of the power series representation for f(x) = ln|1 - 5x| are  c₂ * x² / 2, c₃ * x³ / 3, c₄ * x⁴ / 4, c₅ * x⁵ / 5. To find the power series representation of f(x) = ln|1 - 5x|, we'll start with the power series representation of f'(x) and then integrate it.

The power series representation of f'(x) is given by:

f'(x) = ∑[n=1 to ∞] (cₙ₊₁ * xⁿ)

To integrate this power series, we'll obtain the power series representation of f(x) term by term.

Integrating term by term, we have:

f(x) = ∫ f'(x) dx

f(x) = ∫ ∑[n=1 to ∞] (cₙ₊₁ * xⁿ) dx

Now, we'll integrate each term of the power series:

f(x) = ∑[n=1 to ∞] (cₙ₊₁ * ∫ xⁿ dx)

To integrate xⁿ with respect to x, we add 1 to the exponent and divide by the new exponent:

f(x) = ∑[n=1 to ∞] (cₙ₊₁ * xⁿ⁺¹ / (n + 1))

Now, let's express the first four non-zero terms of this power series representation:

f(x) = c₂ * x² / 2 + c₃ * x³ / 3 + c₄ * x⁴ / 4 + ...

The first four non-zero terms of the power series representation for f(x) = ln|1 - 5x| are  c₂ * x² / 2, c₃ * x³ / 3, c₄ * x⁴ / 4, c₅ * x⁵ / 5

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Answer:

x > 15

General Formulas and Concepts:

Pre-Algebra

Step-by-step explanation:

Step 1: Define inequality

5x - 7 > 4x + 8

Step 2: Solve for x

Here we see that any value x that is greater than 15 would work as a solution to this inequality.

Using sampling concepts, the population being studied is all visitors that are flying to the state of Hawaii.

The problem is incomplete, but researching it on a search engine, it asks for us to identify who is the population of this study.

In this problem, a set of visitors traveling to Hawaii were sampled, hence the population being studied is all visitors that are flying to the state of Hawaii.

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Answer:

1.36078

Step-by-step explanation:

the answer would be two (2)

Answer:

8 inches

Step-by-step explanation:

The volume of a hemisphere is half the volume of a sphere.

Therefore, the sum of the volumes of the two hemisphere-shaped scoops of ice cream (with diameters of 4 inches), is equal to the volume of a sphere with diameter of 4 inches.

If the melted ice cream fills the cone exactly to the top without overflowing, the volume of the cone with diameter of 4 inches must be equal to the volume of a sphere with diameter of 4 inches.

As the diameter of a circle is twice its radius, then the radius of the sphere and cone is r = 2 inches.

The formulas for the volume of a cone and the volume of a sphere are:

\(\boxed{\begin{minipage}{4 cm}\underline{Volume of a cone}\\\\$V=\dfrac{1}{3} \pi r^2 h$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\ \phantom{ww}$\bullet$ $h$ is the height.\\\end{minipage}}\)   \(\boxed{\begin{minipage}{4 cm}\underline{Volume of a sphere}\\\\$V=\dfrac{4}{3} \pi r^3$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius.\\\\\end{minipage}}\)

The depth of the cone is its height.

Therefore, to calculate how deep the cone must be so that the melted ice cream will fill the cone exactly to the top without overflowing, set the two equations equal to each other, substitute r = 2, and solve for h (the depth of the cone).

\(\begin{aligned}\textsf{Volume of a cone}&=\textsf{Volume of a sphere}\\\\\dfrac{1}{3} \pi (2)^2 h & = \dfrac{4}{3} \pi (2)^3\\\\\dfrac{1}{3} \pi \cdot 4 h & = \dfrac{4}{3} \pi \cdot 8\\\\\dfrac{4}{3} \pi h& = \dfrac{32}{3} \pi \\\\\dfrac{4}{3} h& = \dfrac{32}{3} \\\\4 h& = 32 \\\\h&=\dfrac{32}{4}\\\\h&=8\; \sf inches\end{aligned}\)

Therefore, the depth of the cone must be 8 inches.

The cone must be at least 8 inches deep in order for the melted ice cream to fill the cone exactly to the top without overflowing.

1. The opening of the ice cream cone has a diameter of 4 inches. This means that the radius of the cone's opening is 4/2 = 2 inches.

2. The two hemisphere-shaped scoops of ice cream have diameters of 4 inches each. This means that the radius of each scoop is 4/2 = 2 inches.

3. When the ice cream melts, it will take up the space between the scoops and fill the cone. In order for the melted ice cream to fill the cone exactly to the top without overflowing, the depth of the cone must be equal to the combined height of the two ice cream scoops.

4. The height of each hemisphere-shaped scoop can be calculated using the formula for the volume of a sphere, which is (4/3)πr³, where r is the radius.

  - For each scoop, the radius is 2 inches, so the height of each scoop is (4/3)π(2)³ = (4/3)π(8) = (32/3)π.

5. Since there are two scoops, the combined height of the two scoops is 2 * (32/3)π = (64/3)π.

6. Therefore, the cone must be at least (64/3)π inches deep in order for the melted ice cream to fill the cone exactly to the top without overflowing. This is approximately equal to 67.03 inches.

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\({ \qquad\qquad\huge\underline{{\sf Answer}}} \)

In the first sequence,

let's take ratio of the next term with its preceding term, so we will get the common ratio ~

\(\qquad \sf  \dashrightarrow \: \cfrac{4}{16} = \dfrac{1}{4} \)

So, we can imply that The next term of the sequence is 1/4 times the previous term.

hence, the unknown term will be 1/4 times of previous term.

Therefore, the next term here is 1

In the second sequence,

Do the same procedure as above, we will get common ratio as :

\(\qquad \sf  \dashrightarrow \: \cfrac{18}{6} = 3\)

So, the next term is 3 times the preceding term, that is :

Therefore, the next term is 162