At a farm, four employees harvest 48 pounds of food over a certain number of hours. Each employee works the number of hours shown: Employee A: 6 hours Employee B: 4 hours Employee C: 6 hours Employee D: 8 hours The number of pounds of food harvested by each employee is proportional to the number of hours worked. Fill in the table with the amount of food, in pounds, each employee harvested. Employee A B С D Pounds of Food Harvested​

Answer:

\((B)\dfrac{y+1}{y-1}\)

Step-by-step explanation:

We are to find an equivalent expression for:

\(\dfrac{1+\frac{1}{y} }{1-\frac{1}{y}}\)

Step 1: Combine the terms in the numerator into one fraction. Do the same for the denominator.

\(=\dfrac{\frac{y+1}{y} }{\frac{y-1}{y}}\)

Step 2: Write on a straight line and simplify

\(=\dfrac{y+1}{y} \div \dfrac{y-1}{y}\\=\dfrac{y+1}{y} \times \dfrac{y}{y-1}\\=\dfrac{y+1}{y-1}\)

The correct option is B.

This question is based on the solving the fraction. Therefore, the correct option is B, that is \(= {\dfrac{y+1}{y-1}\) is  equivalent to the following complex fraction.

Given:

Expression:

\(\dfrac{1+\frac{1}{y} }{1-\frac{1}{y} }\)

We need to calculate the expression which is equivalent to given complex fraction.

According to the question,

Firstly, take LCM of numerator and denominator.

We get,

\(= \dfrac{\dfrac{y+1}{y} }{\dfrac{y-1}{y} }\)

Now, above expression can be written as follows. Solve it further,

\(= {\dfrac{y+1}{y} }\times{\dfrac{y}{y-1} }\)

Therefore, we get,

\(= {\dfrac{y+1}{y-1}\)

Therefore, the correct option is B, that is \(= {\dfrac{y+1}{y-1}\) is  equivalent to the following complex fraction.

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The distribution of X follows the characteristics of a normal distribution with a mean of 106 and a standard deviation of 18, reflecting the IQ distribution of the ruling species on the faraway planet. This can be denoted as X ~ N(106, 18), where "N" represents the normal distribution.

The distribution of X, representing the IQ of an individual from the ruling species on the faraway planet, is a normal distribution with a mean (μ) of 106 and a standard deviation (σ) of 18. This can be denoted as X ~ N(106, 18), where "N" represents the normal distribution.

In this distribution, the majority of IQ values will cluster around the mean of 106. The standard deviation of 18 indicates the average amount of variation or dispersion from the mean. The normal distribution is symmetric, which means that the probabilities of IQ values being above or below the mean are equal.

The shape of the normal distribution is bell-shaped, with the highest point being at the mean. As we move away from the mean, the probability of observing extreme values decreases. The spread of the distribution is determined by the standard deviation, where a larger standard deviation indicates a wider spread of IQ values.

the distribution of X follows the characteristics of a normal distribution with a mean of 106 and a standard deviation of 18, reflecting the IQ distribution of the ruling species on the faraway planet.

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On a planet far far away from Earth, IQ of the ruling species is normally distributed with a mean of 106 and a standard deviation of 18. Suppose one individual is randomly chosen. Let X = IQ of an individual.  What is the distribution of X? X ~ N( 106 , 18 )  

There are 360 black counters and 306 white counter in 20:17 ratio.

Let's denote the number of black counters by B and the number of white counters by W. We know that the ratio of black to white counters is 20:17, which means that:

B/W = 20/17

We also know that there are 54 more black counters than white counters, which means that:

B = W + 54

We can use substitution to solve for B. Substituting the second equation into the first equation, we get:

(W + 54)/W = 20/17

Cross-multiplying, we get:

17(W + 54) = 20W

Expanding the left side, we get:

17W + 918 = 20W

Subtracting 17W from both sides, we get:

918 = 3W

Dividing both sides by 3, we get:

W = 306

Now we can use the second equation to find B:

B = W + 54 = 306 + 54 = 360

Therefore, there are 360 black counters in the bag.

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Answer:

x=11

Step-by-step explanation:

It seems that the two angles are supplementary.  Soo they add up to 180

Thus,

15+15x=180

Solve for x...

15x=165

x=11

Hope this helps!!!

Answer:

there are 60 triangles with vertices of different colors that can be formed from the given points.

Step-by-step explanation:

To find the number of triangles with vertices of different colors chosen from the given points, we can consider the combinations of colors.

We have 5 red points, 4 green points, and 3 blue points on the circle.

To form a triangle with vertices of different colors, we need to choose one point from each color group.

The number of possible triangles can be calculated as the product of the number of choices from each color group:

Number of triangles = (number of choices for red points) * (number of choices for green points) * (number of choices for blue points)

Number of triangles = C(5, 1) * C(4, 1) * C(3, 1)

where C(n, r) represents the combination of choosing r items from a set of n items.

Evaluating the expression:

Number of triangles = 5 * 4 * 3 = 60

The probability that a person has the disease given that his test result is positive is approximately 0.166 or 16.6%.

The Bayes theorem's assumption that the prior probabilities are known with certainty is one of its limitations. These probabilities, however, could not be known or be impossible to predict precisely in many real-world settings. Moreover, Bayes' theorem makes the assumption that each occurrence is independent, which may not necessarily be true in real-world circumstances.

Given that,

P(D) = 0.001

P(D') = 1- 0.001 = 0.999

P(T|D) = 0.99 (the test is 99% effective in detecting the disease)

P(T'|D') = 0.995

The Baye's theorem is given as follows:

P(A|B) = P(B|A) * P(A) / P(B)

Substituting the values:

P(T) = (0.99 * 0.001) + (0.005 * 0.999) = 0.00594

P(D|T) = (0.99 * 0.001) / 0.00594 ≈ 0.166

Hence, the probability that a person has the disease given that his test result is positive is approximately 0.166 or 16.6%.

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The complete question is:

a) The sample space for this experiment is {H, TH, TTH, ... so on} . The probability that the coin turns up heads after i tosses is (1/2)^i for i = 1, 2, 3, and so on.

b) Let E be the event that the first time a head turns up is after an even number of tosses, the  set of outcomes belong to this event is {TH, TTTH, TTTTTH, ..... so on}. the probability that event E occurs is 1/3.

a) The sample space for this experiment consists of all possible sequences of tosses that end in a head. This includes the sequence "H" (which is the outcome when the first toss is a head), the sequence "TH" (which is the outcome when the first toss is a tail followed by a head), the sequence "TTH" (which is the outcome when the first two tosses are tails followed by a head), and so on.

The sample space is infinite because there is no limit to the number of tosses that could occur before a head is observed.

The probability that the coin turns up heads after i tosses is (1/2)^i for i = 1, 2, 3, and so on. This is because the probability of getting a head on any given toss is 1/2, and the tosses are independent of each other.

Therefore, the probability of getting a head on the first toss is 1/2, the probability of getting a head on the second toss is (1/2)(1/2) = 1/4, the probability of getting a head on the third toss is (1/2)(1/2)*(1/2) = 1/8, and so on.

b) The set of outcomes that belong to the event E consists of all sequences of tosses that end in a head and where the number of tosses before the first head is even. This includes the sequence "TH" (which has one even-numbered toss before the head), the sequence "TTTH" (which has three even-numbered tosses before the head), and so on.

The probability that event E occurs is given by the sum of the probabilities of all the sequences in E. To calculate this, we can use the formula for an infinite geometric series, which is:

sum = a/(1-r)

where a is the first term of the series, r is the common ratio, and sum is the sum of the series. In this case, a = (1/2)^2 = 1/4 (since the first even-numbered toss occurs on the second toss), and r = (1/2)^2 = 1/4 (since each subsequent even-numbered toss has probability (1/2)^2 of occurring).

Therefore, the sum of the probabilities of all the sequences in E is:

sum = (1/4)/(1-1/4) = (1/4)/(3/4) = 1/3

So the probability that event E occurs is 1/3.

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The probability of drawing all three red marbles is 1/6 or approximately 0.1667.

To calculate the probability of drawing all three red marbles, we need to consider the total number of possible outcomes and the number of favorable outcomes.

Total number of marbles in the bag: 5 red + 5 black = 10 marbles

When we draw the first marble, there are 10 marbles in total, and 5 of them are red. So the probability of drawing a red marble on the first draw is 5/10.

After the first marble is drawn, we have 9 marbles left in the bag, and 4 of them are red. So the probability of drawing a red marble on the second draw, given that the first marble was red, is 4/9.

Similarly, after the first and second marbles are drawn, we have 8 marbles left in the bag, and 3 of them are red. So the probability of drawing a red marble on the third draw, given that the first two marbles were red, is 3/8.

To find the probability of all three marbles being red, we multiply the probabilities of each individual draw:

P(all three marbles are red) = (5/10) * (4/9) * (3/8)

Simplifying the expression, we get:

P(all three marbles are red) = 1/6

Therefore, the probability of drawing all three red marbles is 1/6 or approximately 0.1667.

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The expression 2*(6+7) represents the total cost of the seed packets.

The factor "2" represents the packet cost per unit ($/packet). Then, to find the total cost, we have to multiply that factor by another that represents all the packets he is buying.

This last factor is what is expressed as a sum "6+7".

This sum represents the packets he is buying separated in two terms:

- "6" represents the packets of lettuce seeds.

- "7" represents the packets of pea seeds.

If we look at the expression without the parenthesis, like 2*6+7, it will have a different result than 2*(6+7) because we are changing the order by which operations are solved.

For 2*6+7, we solve 2*6 first and then add 7 to the result.

In the case of 2*(6+7), because of the parenthesis, we first solve the sum whitin the parenthesis and then we multiply the result by 2.

2*6+7 may represent another situation.

We can represent with this equation the following situation: "Martin has 2 bags of 6 kg of sand and one bag that weights 7 kg of sand. The expression 2*6+7 represents the total amount of kg of sand he got".

Answer:

The part in parenthesis shows the sum of 6 and 7.

The sum represents the number of packets of lettuce seeds plus the number of packets of pea seeds.

One of the factors is 2. The other factor is the sum of 6 and 7

The product represents the price per packet times the number of packets Martin bought.

Answer:

Step-by-step explanation:

The part in parenthesis shows the sum of 6 and 7.

The sum represents the number of packets of lettuce seeds plus the number of packets of pea seeds.

One of the factors is 2. The other factor is the sum of 6 and 7

The product represents the price per packet times the number of packets Martin bought.

Answer:

We get -2 < r < 3

Corresponding to the fourth choice

The fourth number line is the correct option

Step-by-step explanation:

-2 < 3r+4 < 13

We have to isolate r,

subtracting 4 from each term,

-2-4< 3r + 4 - 4 < 13 - 4

-6 < 3r < 9

divding each term by 3,

-6/3 < r < 9/3

-2 < r < 3

so, the interval is (-2,3)

or, -2 < r < 3

this corresponds to

The fourth choice (since there is no equality sign)

Answer:

I would say B The x-intercept of function p is less than the x-intercept of function q. tell me if you got it right.

Step-by-step explanation:

The correct answer is option B. The x-intercept of function p is greater than the x-intercept of function q.

The x-intercept is where the curve represented by the equation cuts the x axis. At that point the ordinate should be 0.

\(log_{2} (x-1)=0\)

⇒ x= 2

The x-intercept of p(x) is 2

2^x-1 = 0

⇒x= 0

The x-intercept of q(x) is 0

So, we can see the  x-intercept of p(x) is greater than x-intercept of q(x)

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The equation of the line passing through the points (−2,9) and (8,34) is y = (5/2)x + 23/2 in its simplest form.

To find the slope between the two points (−2,9) and (8,34), we can use the slope formula:

m = (y2 - y1) / (x2 - x1)

Let's substitute the coordinates into the formula:

m = (34 - 9) / (8 - (-2))

= 25 / 10

= 5 / 2

So the slope between the two points is 5/2.

Now, let's use the slope-intercept form of a linear equation, y = mx + b, to find the equation of the line passing through these points.

We'll use one of the points and the slope we just calculated.

Using the point (−2,9) and the slope 5/2, we have:

9 = (5/2)(-2) + b

Now, let's solve for b:

9 = -5/2 + b

9 + 5/2 = b

(18/2) + (5/2) = b

23/2 = b

So the y-intercept (or the value of b) is 23/2.

Now, we can write the equation of the line in slope-intercept form:

y = (5/2)x + 23/2

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The graph best represents a function with a domain of all real numbers greater than or equal to 1 and less than or equal to 2 are area between equation x + y \(\geq\) 1 and x + y \(\leq\) 2 .

The collection of all potential inputs for a function is known as its domain. For instance, the domain of f(x)=x2 is all real numbers, and the domain of g(x)=1/x is all real numbers other than x=0.

The real numbers are all the numbers that make up the real number line, per definition. Thus, all real numbers can be graphed by simply drawing a number line. The number line is a graph of all real numbers since it contains all of the rational numbers.

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Answer: 3, 37

Step-by-step explanation:

Divide by 3, divide by 3 again. 37 is a prime number, so it can't be divided again after that.

Step-by-step explanation:

2a+26°+58°=180°

2a=180-26-58

2a=96

a=48

2*48+26=122

Given :

▪︎Measure of an angle in a parallelogram = 58°

▪︎Measure of the angle opposite this angle = (2x+26)°

We know that :

▪︎Opposite angles in a parallelogram are equal.

Which means :

\( =\tt 2a+ 26 = 58\)

\( =\tt 2a = 58 - 26\)

\( =\tt 2a= 32\)

\( =\tt a = \frac{32}{2} \)

\(\hookrightarrow\color{plum}\tt a = 16\)

Thus, the value of a = 16

Let us now place 16 in the place of a and check whether or not we have found out the correct value of a:

\( =\tt 2 \times 16 + 26 = 58\)

\( = \tt32 + 26 = 58\)

\( =\tt 58 = 58\)

Since the values in both the side match, we can conclude that we have found out the correct value of a.

▪︎Therefore, the value of a = 16

Answer:

A: 45 5/16

B: The present of the area as 83%

Step-by-step explanation:

(a)

35= 3+3+3.2x+3.2x+3.2x+3.2x

35= 6 + 12.8

29/12.8 +12.8x/12.8

X=2.265625 = 2/12/64

1x = 2 17/64 * 4 + 9 1/16

P = 45 5/16

(b)

The present of the area as 83%

35 – the bases or 6 = 29

29/35 + 0.82857142857

0.82857142857 * 100 = 82.8571428571

Rounded to the nearest whole number is 83%

The closest answer is 80 cupcakes per minute, so the correct option is .8. The closest answer is 165 minutes, so the correct option is 165.

The throughput capacity of the icing stage can be calculated by dividing the number of cupcakes in a batch (100) by the time required to process each cupcake (1.25 minutes).

Throughput capacity = Number of cupcakes in a batch / Time to process each cupcake

Throughput capacity = 100 cupcakes / 1.25 minutes

Throughput capacity = 80 cupcakes per minute

The closest answer is 80 cupcakes per minute, so the correct option is .8.

The throughput time for a batch of cupcakes is the time required to process the entire batch, including the setup time.

Throughput time = Time for setup + (Number of cupcakes in a batch * Time to process each cupcake)

Throughput time = 40 minutes + (100 cupcakes * 1.25 minutes per cupcake)

Throughput time = 40 minutes + 125 minutes

Throughput time = 165 minutes

The closest answer is 165 minutes, so the correct option is 165.

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The image is formed behind the mirror, and the image is upright.

Given data: Object height, h = 3.0 cm Image distance, v = ? Object distance, u = -20.0 cmFocal length, f = -60.0 cmUsing the lens formula, the image distance is given by;1/f = 1/v - 1/u

Putting the values in the above equation, we get;1/-60 = 1/v - 1/-20

Simplifying the above equation, we get;v = -40 cm

This negative sign indicates that the image is formed behind the mirror, as the object is placed in front of the mirror.

Hence, the image is virtual and erect. Using magnification formula;M = -v/uWe get;M = -(-40) / -20M = 2Hence, the height of the image is twice the height of the object.

The height of the image is given by;h' = M × hh' = 2 × 3h' = 6 cm Now, let's draw the ray diagram:

Thus, the position of the image is -40.0 cm and the height of the image is 6 cm.

The image is formed behind the mirror, and the image is upright.

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The art teacher can make a maximum of 24 identical kits using all the crayons and drawing paper for proper distribution.

To determine the largest number of identical kits the art teacher can make using all the crayons and drawing paper, we need to find the greatest common divisor (GCD) of the quantities.

The GCD represents the largest number that can divide all the quantities without leaving a remainder.

The GCD of the quantities of crayons can be found by considering the prime factorization:

\(72 = 2^3 * 3^2\\\\48 = 2^4 * 3\\\\48 = 2^4 * 3\\\\48 = 2^4 * 3\\\\\)

The GCD of the crayons is \(2^3 * 3\), which is 24.

Now, we need to find the GCD of the quantity of drawing paper:

120 = \(2^3 * 3 * 5\)

The GCD of the drawing paper is also \(2^3 * 3\), which is 24.

Since the GCD of both the crayons and drawing paper is 24, the art teacher can make a maximum of 24 identical kits using all the crayons and drawing paper.

Each kit would contain an equal distribution of crayons and drawing paper.

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The circumference of the circle in terms of pi is 16π yards.

The circumference of a circle is the distance around the edge or perimeter of the circle. It is the length of a closed curve and can be measured by using a flexible measuring tape or a string to wrap around the circle. The formula for the circumference of a circle is C = 2πr, where C is the circumference, r is the radius of the circle, and π is the mathematical constant pi (approximately equal to 3.14159). The circumference of a circle is proportional to its radius and increases as the radius increases. Therefore, if we know the radius of a circle, we can use the formula to find its circumference, and if we know the circumference, we can use the formula to find the radius. The circumference is an important concept in geometry and is used in many real-world applications, such as calculating the length of a fence needed to enclose a circular garden or the distance traveled by a car moving around a circular racetrack.

Substituting the given value of the radius, we get:

C = 2π(8) = 16π

Therefore, the circumference of the circle in terms of pi is 16π yards.

So the answer is 16pi yards.

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In a Taylor series, the polynomial t3(x) represents the third degree Taylor polynomial of a function. It is an approximation of the function near a specific point, obtained by taking the first three terms of the Taylor series expansion.

The polynomial t3(x) is given by t3(x) = f(a) + f'(a)(x-a) + (f''(a)/2!)(x-a)^2 + (f'''(a)/3!)(x-a)^3, where f(a) is the value of the function at the point a, f'(a) is its first derivative, f''(a) is its second derivative, and f'''(a) is its third derivative.

In the context of Taylor series, polynomial T3(x) refers to the third-degree Taylor polynomial. It is an approximation of a given function using the first four terms of the Taylor series expansion. The general formula for the Taylor series is:

f(x) ≈ f(a) + f'(a)(x-a) + f''(a)(x-a)^2/2! + f'''(a)(x-a)^3/3! + ...

For T3(x), you'll consider the first four terms of the series:

T3(x) = f(a) + f'(a)(x-a) + f''(a)(x-a)^2/2! + f'''(a)(x-a)^3/3!

Here, f(a) represents the function value at the point 'a', and f'(a), f''(a), and f'''(a) represent the first, second, and third derivatives of the function evaluated at 'a', respectively. The T3(x) polynomial approximates the given function in the vicinity of the point 'a' up to the third degree.

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Answer:

x is equal to 12.

Step-by-step explanation:

Because the two lines are parallel to each other, and one is the base of the triangle, that means that the segments of the side lines have the same ratio to each other.

In other words, |AC| / |CE| is equal to |AB| / |BD|.

With that information, we can simply say:

\(\frac{4x + 6}{6} = \frac{3x}{4}\\\\24\times \frac{4x + 6}{6} = 24\times\frac{3x}{4}\\\\4(4x + 6) = 6(3x)\\\\16x + 24 = 18x\\\\2x = 24\\\\x = 12\)

So x is equal to 12

Answer:

Step-by-step explanation:

To solve the system of equations algebraically, we need to substitute the second equation into the first equation and solve for x:

y = 4x – 5 (equation 1)

y = -3 (equation 2)

Substitute equation 2 into equation 1:

-3 = 4x – 5

Add 5 to both sides:

2 = 4x

Divide both sides by 4:

x = 1/2

Now, we can substitute this value of x back into either equation to find y:

y = 4(1/2) – 5 = -3

Therefore, the solution to the system of equations is (1/2, -3).

To verify this solution using the graph, we can plot the two equations on the same set of axes:

y = 4x – 5 (red line)

y = -3 (blue line)

The two lines intersect at the point (1/2, -3), confirming our solution.

Therefore, the answer is (B) (1/2, -3).

Answer

D

Step-by-step explanation:

A ternary Huffman code for the given source with probabilities 0.2, 0.2, 0.15, 0.15, 0.1, 0.1, 0.1 has an average word-length of 1.85 bits.

To construct a ternary Huffman code, we need to arrange the given probabilities in descending order and start combining the two smallest probabilities at each step until we have only one probability left. We then assign 0, 1, and 2 to the three branches at each node in the code tree, representing the three possible symbols in the ternary code.

The following table shows the steps to construct a ternary Huffman code for the given source:

Symbol Probability Codeword

A 0.2 0

B 0.2 1

C 0.15 20

D 0.15 21

E 0.1 220

F 0.1 221

G 0.1 222

The resulting code tree for the ternary Huffman code is as follows:

                   *

                  /|\

                / / \ \

              / / / \ \ \

             A  B  C D EFG

The average word-length for this code can be calculated as follows:

Average word-length = (0.2 x 1) + (0.2 x 1) + (0.15 x 2) + (0.15 x 2) + (0.1 x 3) + (0.1 x 3) + (0.1 x 3)

= 0.2 + 0.2 + 0.3 + 0.3 + 0.3 + 0.3 + 0.3

= 1.85 bits

Therefore, the average word-length for the ternary Huffman code for the given source is 1.85 bits.

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The tent with the assumed parameters is tall enough for the sisters to stand up inside.

Assuming a reasonable height for a typical tent, which is around 6 feet, it should be tall enough for both sisters to stand up inside if they are both over 5 feet tall.

In this case, we can imagine the tent as a triangular prism, with the sloping sides forming a right triangle.

Let's call the height of the tent "h," the length of the base "b," and the length of the sloping side "s."

Using the Pythagorean theorem, we can write:

s^2 = h^2 + (b/2)^2

Since we know that each sister is over 5 feet tall, we can set h = 5 feet. We also know that the base of the tent is usually wider than it is tall, so we can assume a reasonable value for b, such as 8 feet.

Substituting these values into the equation above, we get:

s^2 = 5^2 + (8/2)^2

s^2 = 25 + 16

s^2 = 41

Taking the square root of both sides, we get:

s ≈ 6.4 feet

Since this is greater than the height of both sisters (which is 5 feet), we can conclude that the tent is tall enough for them to stand up inside.

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Answer:

A

Step-by-step explanation:

7d/7=d

-56/7=-8

7(d-8)

Answer:   \(\text{x}^3\text{y}\)

This is the same as writing x^3y

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

Explanation:

When finding the GCF, we look for the smallest exponent for each variable.

The x terms of the given expressions are x^3 and x^5. The smallest exponent here is 3, so x^3 is part of the GCF.

The y terms are y^2 and y. Think of y as y^1, which shows 1 is the smallest exponent. We'll have y as part of the GCF.

-----------

We found that...

The overall GCF is x^3y which can be written as \(\text{x}^3\text{y}\)

Side note: We ignore the coefficients since they are 1 for each monomial.