Option 2: Proof
Can you prove using algebra which tray has more pie in?

Answer:

  $9.50

Step-by-step explanation:

You want Suzie's hourly rate on Saturday if she babysat for 3.5 hours on Friday, earning 8.50 per hour, and for 4.5 hours on Saturday, earning a total of 72.50 from both jobs.

For (hours, rates) of (h1, r1) and (h2, r2), Suzie's total earnings for the two jobs are ...

  earnings = h1·r1 +h2·r2

Filling in the known values, we can find r2:

  72.50 = 3.5·8.50 +4.5·r2

  72.50 = 29.75 +4.5·r2 . . . . . . . simplify

  42.75 = 4.5·r2 . . . . . . . . . . . subtract 29.75

  9.50 = r2 . . . . . . . . . . . . divide by 4.5

Suzie earned $9.50 per hour on Saturday.

__

Additional comment

The steps of the "multistep" problem are ...

Effectively, these are the steps to solving the equation we wrote.

In linear equation, 4,000 guest nights did the hotel have during this period.

What is a linear equation in mathematics?

A linear equation is an algebraic equation of the form y=mx+b. m is the slope and b is the y-intercept. The above is sometimes called a "linear equation in two variables" where y and x are variables. 

According to question,

Guest nights = Number of guests × Number of nights

                       = 2,000 × 2

                       = 4,000

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Thus, the cost to cover all three faces and base of the triangular prism is $12.24.

An elongated pyramid-like 3D shape is a triangular prism. It features three rectangular faces and two bases. A form must have two similar bases, at least three rectangle-shaped faces, and a consistent cross-section over its whole length in order to qualify as a prism. Your shape is a triangular prism if it is also triangular.

Area of the rectangular base A1 = length * width

A1 : 5*2 = 10 ft²

Area of two rectangles faces A2:

A2: 2*3 + 2*4 = 14 ft²

Area of the two triangles faces A3 = 1/2*base*height

Base of triangle: (x)+(x-5)

Using the Pythagorean theorem:

x²+h² = 3²  

h² = 9-x²   ...eq 1

(5-x)²+h²=4²

h²=16-(5-x)²   ...eq 2

Equating eq 1 and eq 2:

9-x² = 16-(5-x)²

9-x² = 16-25-10x-x²

on solving:

x=1.8

Then,

h²=9-(1.8)²------------ >

h=2.4 ft

Area A3 = (5*2.4)*2/2 = 12 ft²

Total Surface area A = A1+A2+A3

A = 10+14+12

A = 36 ft²

Rate of foil:

$0.34 for 1 ft²

For, A = 36 ft²

rate = 36*0.34

rate = $12.24

Thus, the cost to cover all three faces and base of the triangular prism is $12.24.

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complete question:

The figure shown is a triangular prism. How much would it cost to cover the bases and the other three faces with foil that costs $0.34 per square foot?

The number of batches of pancakes made by Hugo using 3 cups of milk is equal to 9 batches.

Number of cups of milk used by Hugo for each batch =  1/3 cup of milk ,

The total amount of milk used for b batches would be,

Total milk = (1/3) × b

The total milk used was 3 cups,

Substitute the value in the equation we have,

⇒ (1/3) × b = 3

Solve for b we get,

Multiply both sides of the equation by the reciprocal of 1/3,

Reciprocal of ( 1/3 ) = 3/1 or simply 3

⇒ (1/3) × b × 3 = 3 × 3

⇒ b = 9

Therefore, Hugo made 9 batches of pancakes.

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The above question is incomplete, the complete question is:

Hugo made a bunch of batches of pancakes for his summer camp. For each batch, Hugo used 1/3 cup of milk. Hugo used a total of 3 cups of milk. Let b represent the number of batches Hugo made . Find the value of b?

The length of the line segment PQ to the nearest tenth is: 16.5\

The formula for the distance between two coordinates is given by:

D(x, y) = √[(y₂ - y₁)² + (x₂ - x₁)²]

In this question , we are given:

P(-10, 2) and Q(6, 6)

Thus:

PQ = √[(6 - 2)² + (6 + 10)²]

PQ = √(16 + 256)

PQ = √272

PQ = 16.49

To the nearest tenth gives:

PQ = 16.5

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The correct option is - D. (1,5). The solution to the system of equations for the given graph is at (1,5).

A collection of values for a variable that simultaneously fulfil each equation is the solution to a system of equations. A system of equations must be solved by identifying all possible sets of variable values that make up the system's solutions.

For the given graph, the solution of the system of equation is obtained as the point where the lines intersect.

The two lines in the graph intersect at the (1,5). Thus, the solution to the system of equations for the given graph is at (1,5).

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The probability that the largest of n random samples is greater than the population median M is bounded above by[tex]1 - F(M)^(n-1) \times F(X(n))[/tex].

Assumptions about the population and the sampling method.

Let's assume that the population has a continuous probability distribution with a well-defined median, and that we are taking independent random samples from this population.

Let [tex]X1, X2, ..., Xn[/tex] be the random samples that we take from the population, where n is the sample size.

Let M be the population median.

The probability that the largest of these random samples, denoted by X(n), is greater than M.

Cumulative distribution function (CDF) of the population distribution to calculate this probability.

The CDF gives the probability that a random variable takes on a value less than or equal to a given number.

Let F(x) be the CDF of the population distribution.

Then, the probability that X(n) is greater than M is:

[tex]P(X(n) > M) = 1 - P(X(n) < = M)[/tex]

Since we are assuming that the samples are independent, the joint probability of the samples is the product of their individual probabilities:

[tex]P(X1 < = x1, X2 < = x2, ..., Xn < = xn) = P(X1 < = x1) \times P(X2 < = x2) \times ... \times P(Xn < = xn)[/tex]

For any x <= M, we have:

[tex]P(Xi < = x) < = P(Xi < = M) for i = 1, 2, ..., n[/tex]

Therefore,

[tex]P(X1 < = x, X2 < = x, ..., Xn < = x) < = P(X1 < = M, X2 < = M, ..., Xn < = M) = F(M)^n[/tex]

Using the complement rule and the fact that the samples are identically distributed, we get:

[tex]P(X(n) > M) = 1 - P(X(n) < = M)[/tex]

= [tex]1 - P(X1 < = M, X2 < = M, ..., X(n) < = M)[/tex]

=[tex]1 - [P(X1 < = M) \times P(X2 < = M) \times ... \times P(X(n-1) < = M) \times P(X(n) < = M)][/tex]

[tex]< = 1 - F(M)^(n-1) \times F(X(n))[/tex]

Probability depends on the sample size n and the distribution of the population.

If the population is symmetric around its median, the probability is 0.5 for any sample size.

As the sample size increases, the probability generally increases, but the rate of increase depends on the population distribution.

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The cardholder will pay an additional $1,471.66 in interest by making monthly payments of $200 until the balance is paid off instead of paying off the current balance in full.

First, we need to calculate the total interest that will accrue on the current balance of $4,528.34. We can do this using the formula

Interest = Balance x (APR/12)

where APR is the annual percentage rate and is divided by 12 to get the monthly interest rate. Plugging in the values, we get:

credit card Interest = $4,528.34 x (22.99%/12) = $87.80

So the total interest that will accrue on the current balance is $87.80.

Next, we need to calculate how long it will take to pay off the balance by making monthly payments of $200. We can use a credit card repayment calculator to do this, but we'll use a simplified formula here

Months = -log(1 - (Balance x (APR/12))/Payment) / log(1 + (APR/12))

where Payment is the monthly payment amount. Plugging in the values, we get

Months = -log(1 - ($4,528.34 x (22.99%/12))/$200) / log(1 + (22.99%/12)) = 29.6 months

So it will take about 30 months (or 2.5 years) to pay off the balance by making monthly payments of $200.

Finally, we can calculate how much more the cardholder will pay in total by subtracting the current balance from the total amount paid over 30 months

Total amount paid = $200 x 30 = $6,000

Total interest paid = $6,000 - $4,528.34 = $1,471.66

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If Alice has $50 and spends 4/5 of her money, she spends $40.

A fraction is a mathematical expression that represents a part of a whole or a ratio between two quantities. Fractions are commonly represented using two numbers separated by a horizontal line, where the top number is called the numerator and the bottom number is called the denominator.

Alice spends 4/5 of her money, which is equivalent to 0.8 of her money.

To find out how much Alice spends, we can multiply her total money ($50) by 0.8

= $50 x 0.8

Multiply the numbers

= $40

Therefore, Alice spends $40.

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I have solved the question in general, as the given question is incomplete.

The complete question is:

Alice has $50 and spends 4/5 of her money. How much does Alice spend?

Answer:

The circumference of a circle is given by the formula:

C = πd

where C is the circumference, d is the diameter, and π is a mathematical constant approximately equal to 3.14.

In this case, the diameter of the circle is given as 12.5 cm.

Substituting this value into the formula, we get:

C = π(12.5)

C = 39.25 cm

Therefore, the circumference of the circle is 39.25 cm.

Hence, the answer is 39.25 cm.

Sue works 5 out of 7 days a week, which implies that she has two days off. We need to discover how numerous conceivable plans there are for her to work on Tuesday or Friday or both.

There are two cases to consider:

1. Sue works on Tuesday as it were, Friday as it were, or both Tuesday and Friday.

2. Sue does not work on Tuesday or Friday.

For the primary case, there are three conceivable outcomes:

1. Sue works on Tuesday as it were and has Friday off.

2. Sue works on Friday as it were and has Tuesday off.

3. Sue works on both Tuesdays and Fridays.

For the moment case, there are two conceivable outcomes:

1. Sue works on one of the other 5 days of the week and has both Tuesday and Friday off.

2. Sue has Tuesday and Friday off.

In this manner, there are added up to 3 + 2 = 5 conceivable plans for Sue to work on Tuesday or Friday or both. 

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The equation of the hyperbola is [tex](x + 3)^2/16 - (y - 5)^2/36[/tex] = 1.

The collection of all points in a plane such that the distance between any point on the curve and two fixed points (referred to as the foci) is constant is known as a hyperbola. Hyperbolas are a sort of conic section. A hyperbola contains two distinct branches and has the appearance of two curving branches that are mirror reflections of one another. A hyperbola's center, vertices, co-vertices, foci, and asymptotes are some of its most important characteristics. The center, which is the point around which the hyperbola is symmetric, is the midway of the line segment connecting the vertices.

Given that, the co-vertices are (1, 5) and (-7, 5).

Now, using the midpoint formula we have:

center = ((1+(-7))/2, (5+5)/2) = (-3, 5)

Now, the distance between center and vertex is a = 4.

Also, the distance between the center and each co-vertex is b = 6.

Now, the equation of the hyperbola is:

[tex](x - (-3))^2/4^2 - (y - 5)^2/6^2 = 1\\(x + 3)^2/16 - (y - 5)^2/36 = 1[/tex]

Hence, the equation of the hyperbola is [tex](x + 3)^2/16 - (y - 5)^2/36[/tex] = 1.

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The volume of the basketball is approximately 4.2x³.

a. The formula for the volume of a sphere is:

V = (4/3)πr³

where r is the radius of the sphere. In this case, the radius is given as x, so we have:

V = (4/3)πx³ ≈ 4.2x³

Therefore, the volume of the basketball is approximately 4.2x³.

b. The volume of a cube is given by:

V = s³

where s is the length of one of its sides. Since the basketball touches all of the sides of the case, the length of one of its sides is equal to the diameter of the basketball plus the length of a side of the basketball. This is equal to 2x + 2x = 4x. Therefore, we have:

V = (4x)³ = 64x³

Therefore, the volume of the box is 64x³.

c. The volume of air in the box is equal to the volume of the box minus the volume of the basketball. We can substitute the formulas we obtained in parts (a) and (b) to get:

V_air = V_box - V_basketball = 64x³ - 4.2x³ = 59.8x³

Therefore, the volume of air in the box is approximately 59.8x³.

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Check the picture below.

let's find the hypotenuse

[tex]\textit{using the pythagorean theorem} \\\\ c^2=a^2+o^2\implies c=\sqrt{a^2 + o^2} \qquad \begin{cases} c=hypotenuse\\ a=\stackrel{adjacent}{8}\\ o=\stackrel{opposite}{15}\\ \end{cases} \\\\\\ c=\sqrt{8^2+15^2}\implies \implies c=\sqrt{289}\implies c=17 ~\hfill \boxed{\sin( \theta )=\cfrac{\stackrel{opposite}{15}}{\underset{hypotenuse}{17}}}[/tex]

Answer: -37.5

Step-by-step explanation: You can simply do this in the calculator by doing 3 times -12.5. the parenthesis is a sign to multiply

Answer:

the answer is -75/2= - 37.5

The most appropriate statistical procedure to answer this research question would be a two-sample t-test for means.

In this particular case, the research question is related to a Star Trek scenario, where two groups of people have different levels of experience with the franchise.

The most appropriate statistical procedure to answer this research question would be a two-sample t-test for means.

This is because the two-sample t-test for means is used when two independent samples are compared to determine if there is a significant difference between the means of the two samples.

This is useful in this scenario, as it will allow us to compare the levels of experience between the two groups and determine if there is a statistically significant difference between them.

The two-sample t-test for means is the most appropriate statistical procedure for this task, as it allows us to compare the means of two independent samples and determine if there is a statistically significant difference between them.

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The correct option is - C. The data for the two population of the weight of squirrels have different skews.

Data that produces an uneven, skewed curve on a graph is referred to as skewed data. In statistics, a data set with a normal distribution has a bell-shaped, symmetrical graph. Skewed data, however, has a "tail" on each side of the graph. Two of the most typical skew types are:

For the given  population of the weight of squirrels:

The data for the two population of the weight of squirrels have different skews.

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Answer:

[tex]y=5-2x[/tex]

Step-by-step explanation:

You have to give the equation in the form [tex]y=mx+c[/tex], where m is the gradient and c is the y-intercept (where the line crosses the y-axis).

From the graph, we can see the line crossed the y-axis at (0,5), so the y-intercept is (0,5), which means c is 5.

We can work out the gradient with the two points (2,1) and (1,3) by doing:

[tex]\frac{change in y}{change in x} =\frac{1-3}{2-1}=-2[/tex]
So the gradient of the line, m, is -2.

Thus the equation of the line is [tex]y=5-2x[/tex].

The function which has range (2, ∞) is,

D) y = 5ˣ + 2

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Now, For a function: y = 5ˣ

Range is,

⇒ ( 0 , + ∞ )

And, we have:

y = 5ˣ + 2 ,

which is translated 2 units up.

So, the range is ( 2, + ∞ ).

Hence, The function which has range (2, ∞) is,

D ) y = 5ˣ + 2

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The solutions to the equation sin(πx/3) = 0 in the interval -5 < x < 5 are x = -3, 0, and 3.

What is Trigonometric equation?

A trigonometric equation is an equation that involves trigonometric functions such as sine, cosine, tangent, or their inverses. Trigonometric equations arise in a variety of mathematical and scientific contexts, from solving geometric problems involving angles and triangles to modeling periodic phenomena in physics, engineering, and other fields.

Solving a trigonometric equation typically involves finding the values of the unknown variable that satisfy the equation within a certain interval. For example, the equation sin(x) = 0 has infinitely many solutions, but if we restrict the interval to [0, 2π], then the solutions are x = 0, π, 2π, which correspond to the x-intercepts of the sine function in that interval.

Here the equation sin(πx/3) = 0 has solutions whenever πx/3 is an integer multiple of π, since the sine function is zero at these values. Thus, we need to find all integers n such that πx/3 = nπ, or equivalently x = 3n for some integer n.

Since -5 < x < 5, we need to find all integers n such that -5 < 3n < 5. Dividing all sides by 3, we get -5/3 < n < 5/3. The only integers in this range are -1, 0, and 1. Therefore, the solutions to the equation sin(πx/3) = 0 in the interval -5 < x < 5 are x = -3, 0, and 3.

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The given statement "The classical model of decision making assumes that managers have all of the information they need in order to make the optimum decision." is false because it is not necessary that they have all information.

The classical decision-making model assumes that managers have access to all the relevant information, but it does not necessarily assume that they have all the information they need to make the optimum decision.

The model also assumes that the decision-maker is rational and logical, able to identify and evaluate all alternatives and select the best one based on a careful analysis of the pros and cons of each option. However, in practice, managers may not have access to all the information they need, or they may be influenced by biases or external pressures that can lead to suboptimal decision-making.

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The answer is B

The internal angles of a triangle have to be 180

IN ΔABC, m∠A=70° and m∠B=35°.

70°+35°+x=180°

105°+x=180°

x=180°-105°

x=75°

Answer B meets the requirements because in ΔPQR m∠P=70° and m∠R=75°

70°+75°+x=180°

145°+x=180°

x=180°-145°

x=35°

The angles of both triangles measure the same

The volume of Preston's new step in rectangular prism shape with given length , width, and height is equals to 2,376 cubic inches

Let us consider l be the length, w is the width, and h is the height.

The volume of a rectangular prism is equal to,

V = l × w × h

In this case,

The length (l) is equals to 11 inches,

The width (w) is equals to 36 inches,

The height (h) is equals to 6 inches.

So, we can plug in these values and calculate the volume,

V = l × w × h

⇒ V = 11 inches × 36 inches × 6 inches

⇒ V = 2,376 cubic inches

Therefore, the volume of Preston's new step for given dimensions is 2,376 cubic inches.

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a) The zero rates for the five maturities are: 1 year is 2.01%, 2 years is 2.48%, 3 years is 2.77%, 4 years is 1.73%, and 5 years is 4.32%.

b) The price of the security is $128.31.

a) To find the zero rates for all 5 maturities, we can use the formula for the present value of a bond:

PV = C / [tex](1+r)^n[/tex]

where PV is the present value,

C is the coupon payment,

r is the zero rate, and

n is the number of years to maturity.

We can solve for r by rearranging the formula:

r = [tex](C/PV)^{(1/n) }[/tex]- 1

Using the bond data given in the question, we can calculate the zero rates for each maturity as follows:

For the 1-year bond, PV = 98 and C = 0, so r = 2.01%.

For the 2-year bond, PV = 101, C = 2.48, and n = 2, so r = 2.48%.

For the 3-year bond, PV = 103, C = 2.91, and n = 3, so r = 2.77%.

For the 4-year bond, PV = 101, C = 2, and n = 4, so r = 1.73%.

For the 5-year bond, PV = 103, C = 5, and n = 5, so r = 4.32%.

Alternatively, we can use linear algebra to find the zero rates. We can write the present value equation in matrix form:

PV = A × x

where A is a matrix of coefficients, x is a vector of unknowns (the zero rates), and PV is a vector of present values.

To solve for x, we can use the equation:

x = ([tex]A^{-1}[/tex]) x PV

where ([tex]A^{-1}[/tex]) is the inverse of matrix A.

Using this method, we can solve for the zero rates as follows:

[2.01% ]

[2.48% ]

[2.77% ] = x

[1.73% ]

[4.32% ]

PV = [tex]A^{-1}[/tex] x  [98]

                   [101]

                   [103]

                   [101]

                   [103]

PV =   [-0.0201]

          [ 0.0248]

          [ 0.0277]

          [-0.0173]

          [ 0.0432]

b) To find the price of the security which pays cash flows of $10 in one year, $25 in two years, and $100 in four years, we can use the formula for the present value of a series of cash flows:

PV = [tex]C1/(1+r)^1 + C2/(1+r)^2 + C3/(1+r)^4[/tex]

where PV is the present value, C1, C2, and C3 are the cash flows, r is the zero rate, and the exponents correspond to the number of years until each cash flow is received.

Using the zero rates calculated in part (a), we can calculate the present value of each cash flow:

PV1 = $10 /(1+2.01 % [tex])^1[/tex] = $9.80

PV2 = $25/(1+2.48%[tex])^2[/tex] = $22.15

PV3 = $100/(1+1.73%[tex])^4[/tex] = $81.36

Then, the price of the security is the sum of the present values:

PV = $9.80 + $22.15 + $81.36 = $128.31

Therefore, the price of the security is $128.31.

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The scale ratio for this map is 0.0000063.

What is scale ratio?

Scale ratio is the ratio between the measurements of an object or distance on a map or drawing and the actual measurements of the object or distance it represents in real life. It allows us to compare and relate the sizes or distances of objects in a drawing or map to their actual sizes or distances in the real world.

The scale ratio can be found by dividing the distance on the map by the corresponding distance in reality:

scale ratio = distance on map / distance in reality

In this case, the distance from Wellspring to Red Creek is 4 inches on the map and 10 miles in reality. So the scale ratio is:

scale ratio = 4 inches / 10 miles

To simplify this ratio, we need to convert the units so that they are the same. Let's convert inches to miles:

1 mile = 63,360 inches

So, we can convert the inches on the map to miles as follows:

4 inches * (1 mile / 63,360 inches) = 0.000063 miles

Now we can rewrite the scale ratio as:

scale ratio = 0.000063 miles / 10 miles

Simplifying this ratio by canceling out the units of miles, we get:

scale ratio = 0.0000063

Therefore, the scale ratio for this map is 0.0000063.

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An airline passenger is planning a trip with three connecting flights from airports A, B, and C.

The least total amount of time the passenger must spend between flights, assuming all flights keep to their schedules, is 55 minutes.

This occurs when the passenger takes the first flight from airport A at 8:00 a.m., arriving at airport B at 10:30 a.m., catches the second flight from airport B at 10:40 a.m., arriving at airport C at 11:50 a.m., and then takes the third flight from airport C at 12:45 p.m.

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Answer:

p = 3, q = 1

Step-by-step explanation:

well, let's think about what (x - p)² actually is.

let's do the multiplication (what a square is) :

(x - p)(x - p) = x² - px - px + p² = x² - 2px + p²

now, we compare the theoretical equation to the actual equation :

x² - 6x + 8 = 0

x² - 2px + p² = q

x² = x² check

-6x = -2px

-6 = -2p

p = -6/-2 = 3

that gives us

x² - 6x + 9 = q

compare this to

x² - 6x + 8 = 0

we subtract the second equation from the first

x² - 6x + 9 = q

- x² - 6x + 8 = 0

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

0 0 1 = q

there you have it.

The friends can form teams in 6 different ways.

If the four friends want to form two teams, we can count the number of ways they can do this using combinations.

The number of ways to choose two people out of four is given by the combination formula,

C(4,2) = 4! / (2! * (4-2)!) = 6

We can list them as follows, where each team is represented by the letters A and B,

AB  |  CD

AC  |  BD

AD  |  BC

BC  |  AD

BD  |  AC

CD  |  AB

This means that there are 6 different ways the four friends can be split into two teams.

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The smallest positive integer divisible by 6 and 2 that can be written using at least one 2 and one 6 is 6.

The smallest positive integer that is divisible by both 2 and 6 is their least common multiple (LCM), which is equal to the product of the highest power of each prime factor that appears in the factorization of 2 and 6.

The prime factorization of 2 is simply 2, while the prime factorization of 6 is 2 × 3. The highest power of 2 that appears in the factorization of 6 is just 2 itself, so the LCM of 2 and 6 is 2 × 3 = 6.

We are asked to write this integer using at least one 2 and one 6. We can do this by simply writing 6, which is the LCM of 2 and 6 and is divisible by both of them. Since 6 contains one 2 and one 6, this meets the requirement of the problem. Therefore, the smallest positive integer divisible by 6 and 2 that can be written using at least one 2 and one 6 is 6.

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