you have 2 buckets, one which can hold 1 gallon of liquid and the other hold a half of gallon liquid. you must use these two buckets to fill up your gas tank with exactly 5 and 1/2 gallons of gas. what type of problem is this?

The correct statement that compares the measures of center in the two sets of data is:

The medians of the number of hours ten girls and ten boys watched television over a one-week period are approximately equal.

What is the median?

The median is a measure of central tendency that represents the middle value in a dataset when the values are arranged in numerical order. It is the value separating the higher half from the lower half of a sample or a population.

To compare the measures of center in the two sets of data, we need to find their respective medians.

For Plot A, we can see that the median is between 5 and 6, since there are 5 values below 5 and 5 values above 6. We can estimate the median as approximately 5.5 hours.

For Plot B, we can see that the median is between 5 and 6 as well, since there are 5 values below 5 and 5 values above 6. We can estimate the median as approximately 5.5 hours.

Therefore, the correct statement that compares the measures of center in the two sets of data is:

The medians of the number of hours ten girls and ten boys watched television over a one-week period are approximately equal.

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The solution to the simultaneous equation represented on the graph is:

B: x = 2 and x = 4

We are given the equations as:

f(x) = -12x + 26

g(x) = -(-¹/₅)^(-x + 2)  + 3

The solution to these two simultaneous equations will be the coordinates of the points on the graph where they both intersect.

We see that the coordinates of the points of intersection of the graph is at the coordinates:

(2, 2) and (4, -22)

Thus, the solution is at x = 2 and x = 4

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The triangles can be congruent if the corresponding sides of two triangles are congruent except their hypotenuse, and the angle between the congruent corresponding sides between the the two angle is same.

When two pairs of corresponding sides of two right triangles are congruent, we cannot conclude that the triangles are congruent.

Congruent triangles are triangles that have identical dimensions and shape. Congruent figures have equal areas and corresponding sides that have the same lengths. They're exactly the same in terms of everything.

As a result, if two triangles are congruent, all of their corresponding sides and angles are equivalent to those in the other triangle.

A triangle with one 90-degree angle is referred to as a right-angled triangle. A right triangle has two legs and one hypotenuse.

The hypotenuse is the triangle's longest side, while the legs are the sides that make up the right angle.
The Pythagorean Theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the other two sides, is true for right triangles only.

The Side-Angle-Side (SAS) postulate is used to prove that two triangles are congruent. Two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle in this postulate.

Two triangles are congruent if and only if they have two corresponding sides and the included angle are equal.

Using the SAS postulate, we can only conclude that the two right triangles are congruent if we have two pairs of corresponding sides and the included angle between those sides.

As a result, if only two pairs of corresponding sides are congruent, it is not enough to demonstrate that the two triangles are congruent.

Hence when two pairs of corresponding sides of two right triangles are congruent, we cannot conclude that the triangles are congruent unless their hypotenuse are not equal and their angle between the congruent corresponding sides between the the two angle is same.

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So the minimum probability that a Yes respondent exercises for at least 1 hour is 6/(x+6), where x is the number of students who answered No.

Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, with 0 indicating an impossible event and 1 indicating a certain event. The probability of an event can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes. Probability is used in various fields such as mathematics, statistics, science, economics, and finance to model and analyze uncertain situations.

Here,

Let the number of students who answered No be x. Then the number of students who answered Yes is x+12. The total number of students is then x + (x+12) = 2x + 12.

Suppose y of the students who answered Yes exercise for at least 1 hour. Then the probability that a Yes respondent exercises for at least 1 hour is y/(x+12).

Since we don't have the full frequency tree, we can't determine y or x directly. However, we do know that the total number of students who exercise for at least 1 hour is greater than or equal to 12 (since there are 12 more Yes respondents than No respondents). Therefore, the probability that a Yes respondent exercises for at least 1 hour is y/(x+12) is at least 12/(2x+12) = 6/(x+6).

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The net magnetic field at point P is zero, as the magnetic fields produced by the two equal currents in opposite directions cancel out. A third wire at P would experience zero force due to the net zero magnetic field at P.

To construct a vector diagram showing the net magnetic field vector at point P, we can use the right-hand rule for determining the direction of the magnetic field around a current-carrying wire.

If we curl the fingers of our right hand in the direction of the current in the first wire, which is out of the page, the thumb points in the direction of the magnetic field at point P due to the first wire. Similarly, in the opposite direction to the magnetic field at point P due to the second wire.

Since the magnetic fields they produce at P have equal magnitudes but opposite directions. Therefore, the net magnetic field at P is zero,

If a third wire carrying equal current into the plane of the paper were located at P, the direction of the force on this wire would be perpendicular to both the magnetic field produced by the other two wires and the direction of the current in the third wire.

Since the net magnetic field at P is zero, the vector product of the current in the third wire and the magnetic field is also zero, and there is no force on the third wire.

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Answer:3

Step-by-step explanation: becuase the big one was 40 and the smaller one was four, so it is probably 3

The optimal number of bags to purchase is 174 bags.

To determine the optimal number of bags to purchase, we need to consider the trade-off between the cost of holding excess inventory and the cost of not having enough inventory to meet demand.

Let's assume that the cost of holding one bag of inventory for six months is $2.00, and the cost of not having one bag available when needed is $10.00.

We can use the normal distribution to estimate the probability of demand exceeding our inventory level. If we assume that demand follows a normal distribution with mean 150 and standard deviation 60, then we can calculate the probability of running out of inventory as

P(demand > inventory) = P(Z > (inventory - mean) / std_dev)

P(demand > inventory) = P(Z > (inventory - 150) / 60)

where Z is the standard normal random variable.

We want to choose the inventory level that minimizes the expected total cost, which is the sum of the cost of holding inventory and the cost of not having enough inventory

Expected total cost = cost of holding inventory + cost of not having enough inventory

Expected total cost = (inventory * $2.00) + (P(demand > inventory) * $10.00)

To minimize this cost, we need to find the inventory level that makes the expected total cost as low as possible. We can use calculus to find the minimum expected total cost.

Taking the derivative of the expected total cost with respect to the inventory level, we get

d/d(inventory) (Expected total cost) = $2.00 - ($10.00 * (1 / sqrt(2 * pi)) * exp(-(inventory - 150)^2 / (2 * 60^2)) * (inventory - 150) / 60)

Setting this derivative equal to zero and solving for the inventory level, we get

$2.00 - ($10.00 * (1 / sqrt(2 * pi)) * exp(-(inventory - 150)^2 / (2 * 60^2)) * (inventory - 150) / 60) = 0

Simplifying this equation, we get

exp(-(inventory - 150)^2 / (2 * 60^2)) * (inventory - 150) / 60 = 0.2

Using a numerical solver or a table of values for the standard normal distribution, we can find that the inventory level that minimizes the expected total cost is approximately 174 bags.

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Answer:

(added to verbs and their derivatives) denoting removal or reversal.

Step-by-step explanation:

The size of angle EAB is approximately 70.76 degrees.

What is triangle?

A triangle is a three-sided polygon with three angles. It is a fundamental geometric shape and is often used in geometry and trigonometry.

Let's start with the ratio of the size of angle DEA to the size of angle CDE. We can express this ratio as:

angle DEA : angle CDE = 5 : 2

We know that the sum of the angles in a triangle is 180 degrees, so we can use this fact to express angle DEA and angle CDE in terms of angle ABD:

angle DEA + angle CDE + angle ABD = 180

Substituting the ratio given above, we get:

5x + 2x + angle ABD = 180

Simplifying, we get:

7x + angle ABD = 180

Next, let's consider the ratio of the size of angle EAB to the size of angle ABC, which is given as 4:3. We can express this ratio as:

angle EAB : angle ABC = 4 : 3

We know that angle EAB and angle ABC are adjacent angles, so their sum is equal to angle ABD:

angle EAB + angle ABC = angle ABD

Substituting the ratio given above, we get:

4y + 3y = angle ABD

Simplifying, we get:

7y = angle ABD

Now we have two equations:

7x + angle ABD = 180

7y = angle ABD

We can substitute the second equation into the first to get an equation in terms of y:

7x + 7y = 180

Simplifying, we get:

x + y = 25.71

Now we can use the ratio of angle EAB to angle ABC to find y:

angle EAB : angle ABC = 4 : 3

4y : 3y = 4 : 3

Simplifying, we get:

4y = 3(106 - angle EAB)

Expanding, we get:

4y = 318 - 3angle EAB

Substituting the equation we found for y above, we get:

4(25.71 - x) = 318 - 3angle EAB

Simplifying, we get:

angle EAB = 70.76

Therefore, the size of angle EAB is approximately 70.76 degrees.

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Therefore , the solution of the given problem of unitary method comes out to be the quantitative data being displayed, is best displayed using a bar graph.

The task may be completed using this generally accepted ease, preexisting variables, as well as any significant components from the original Diocesan customizable query. If so, you may have another opportunity to interact with the item. Otherwise, all significant factors that affect how algorithmic factor proof behaves will be gone.

Here,

The right graph is option (a),

a bar graph with the heading "Favorite Topping" and the axes "Topping" and "Number of Customers" written on them. T

he labels for the bars should read "Chocolate Chips" with a value of 44, "Hot Fudge" with a value of 27, "Nuts" with a value of 12, and "Sprinkles" with a value of 17.

This categorical data, where each topping is a distinct category and the number of customers is the quantitative data being displayed, is best displayed using a bar graph.

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Answer:

1) 100 degrees F

2) 50 degrees F

Step-by-step explanation:

its just simple subtraction

The height of the square pyramid with the given slant height base base length is found as:  91.17 in.

A square pyramid is really a pyramid with only a square base. A pentahedron, that is. With a base and three triangle sides, a pyramid is a 3D shape.

A square base is what a pyramid with a square base is built upon. A great illustration of a square-based pyramid is the Egyptian pyramid complex.

A right square pyramid with side length a with height h has lateral edge length e as well as slant height s.

Given data:

Slant height s = 91.8 in.

Height H  = ?

Base length a = 21.4 in.

Slant height s formula is:

s² = H² + 1/4 a²

H² =  s² - 1/4 a²

H² =  91.8² - 1/4 *(21.4)²

H = √8312.75

H = 91.17 in.

Thus, the height of the square pyramid with the given slant height and base length is found as:  91.17 in.

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The height of the square pyramid with the given slant height base base length is about 91.2 in. to one decimal place

A square pyramid is a polyhedron that has a square base and four lateral faces that meet at a point above the base (e.g. the apex)

The given parameters to solve the question are given as follows

Slant height s = 91.8 in.

Height H  = ?

Base length a = 21.4 in.

Slant height s formula is: s² = H² + 1/4 a²

H² =  s² - 1/4 a²

By substitution into the formula we have

H² =  91.8² - 1/4 *(21.4)²

H = √8312.75

H = 91.17 in.

Thus, the height of the square pyramid with the given slant height and base length is found as:  91.2 in.

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The value of the conditional probability from the Venn Diagram is (a) 68.4 %

Given that we have the Venn Diagram

From the Venn Diagram, we have the following readings

Male and Independent voters = 13

Independent voters = 19

Using the above values, we have the following equation

P(Male | Independent voter) = 13/19

Evaluate

P(Male | Independent voter) = 68.4 %

Hence, the conditional probability is 68.4 %

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The probability of incurring a loss when it rains is:P (loss | raining) = 80%So, there is a 20% chance that the food truck will not have incurred a loss when it rains.

The P (not raining | not loss) = 90% × 30% = 27%.Thus, the probability that it had not rained on that randomly selected day given that the food truck did not incur a loss is 27%.

The chance of not raining on a given day in Seattle can be calculated as follows:When it does not rain, there is a 10% probability that the food truck will incur a loss, as given in the statement. Similarly, when it rains, there is an 80% chance that the food truck will incur a loss on that day.

To calculate the probability that the food truck will not have incurred a loss on that day, we must first calculate the probability that the food truck will have incurred a loss on that day.Suppose the probability of rain is 70%, so the chance that it won't rain will be: P (not raining) = 100% - 70% = 30%When it rains, there is a 80% probability that the food truck will have incurred a loss, as given in the statement.

The probability of not incurring a loss when it does not rain is:P (not loss | not raining) = 100% - 10% = 90%The probability of not raining when the food truck does not incur a loss can be calculated as follows:P (not raining | not loss) = P (not loss | not raining) × P (not raining)P (not loss | not raining) = 90%P (not raining) = 30%

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Answer:

where is the table without the table how can I give the answer

The farmer sold approximately 3.905 kilograms of pears at the farmer's market. In fraction form, this is 781/200 kilograms.

Answer:

0.13188 km

Step-by-step explanation:

The distance covered by the bicycle wheel can be calculated using the formula:

distance = circumference x number of revolutions

The circumference of the wheel can be calculated using the formula:

circumference = 2 x pi x radius

where pi is approximately equal to 3.14.

Substituting the given values:

circumference = 2 x 3.14 x 30 cm

circumference = 188.4 cm

Now, we can calculate the distance covered by the wheel:

distance = circumference x number of revolutions

distance = 188.4 cm x 70

distance = 13188 cm

To convert this distance from centimeters to kilometers, we need to divide by 100,000 (since there are 100,000 centimeters in a kilometer):

distance = 13188 cm ÷ 100,000

distance = 0.13188 km

Therefore, the distance covered by the bicycle wheel is approximately 0.13188 km.

The double integral ∬D(x2+6y)dA can be evaluated using the properties of integration. The value of the double integral is 53/60.

The given function is (x2+6y). Here, we will find the limits of integration for x and y. Given that D is bounded by y = x, y = x3, and x ≥ 0, we can represent this region in the x-y plane as follows: We see that the lower limit of y is x and the upper limit of y is x3. The lower limit of x is 0 and the upper limit of x is given by the line y=x.

Hence, the limits of integration can be written as follows:0 ≤ x ≤ yx ≤ y ≤ x3

Now, we can substitute these limits in the double integral and integrate first with respect to y and then with respect to x.

∬D(x2+6y)dA = ∫₀¹⁰∫x^x³(x2+6y)dydx

On integrating, we get

∬D(x2+6y)dA = ∫₀¹⁰(x³ - x^7/3 + 3x⁴)dx= [(1/4)x⁴ - (1/12)x^10/3 + (3/5)x⁵] from 0 to 1∬D(x2+6y)dA = (1/4 - 1/12 + 3/5) - (0 + 0 + 0) = 53/60

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Answer: muhammad will $99 in one month and connor will have $8

Step-by-step explanation:

$158-$59=$99

$74-$66=$8

Answer:18

Step-by-step explanation:

2x=12

3x=?
2x/2=12/2= x=6

3(6)=18

Therefore, the odds of rolling an even number, getting a tail, and pulling a red card are 1 in 8 or 1/8.

Probability is a branch of mathematics that deals with the study of randomness and uncertainty in events. It involves calculating the likelihood or chance of an event occurring based on the available information and assumptions. Probability is commonly used in many fields, including science, engineering, finance, and statistics. The probability of an event is a number between 0 and 1, where 0 means the event is impossible, and 1 means the event is certain.

Here,

The probability of rolling an even number on a fair six-sided dice is 3/6 or 1/2. The probability of flipping a tail on a fair coin is 1/2. The probability of pulling a red card out of a standard deck of 52 playing cards is 26/52 or 1/2 (assuming the deck is well shuffled).

To find the probability of all three events occurring together, we multiply the probabilities of each individual event:

=P(rolling an even number) x P(getting tail) x P(pulling a red card)

= 1/2 x 1/2 x 1/2

= 1/8

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The volume of a cone that has the same base area and the same height as the cylinder is 116.25pi cubic units. This is because the volume of a cone is one-third the volume of a cylinder with the same base area and the same height. Therefore, the volume of the cone is 116.25pi cubic units.

The volume of a cylinder is equal to the area of the base, multiplied by the height. The volume of a cylinder with a base area of 465pi and a height of h is therefore 465pi*h. For a cone, the volume is equal to a third of the area of the base multiplied by the height. Since the cone and cylinder have the same base area and height, the volume of the cone is one third of the volume of the cylinder. Therefore, the volume of the cone is 155pi cubic units (465pi/3). A cone has one third the volume of a cylinder with the same base and height.

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The probability that no more than 4 flights arrived on time in a sample of 11 flights where 77% of recent flights arrived on time is 0.19036 or 0.0046 (rounded to four decimal places).

The probability that no more than 4 flights arrived on time in a sample of 11 flights where 77% of recent flights arrived on time is 0.0046.

Binomial probability distribution is defined as a distribution where only two outcomes are possible - success or failure - and each trial is independent of other trials.

A binomial experiment is one that meets the following four conditions:

1. Each trial has only two outcomes (success or failure).

2. The probability of success remains constant across all trials.

3. The trials are independent of each other.

4. The experiment involves a fixed number of trials.

In this case, the probability of success is 77% or 0.77 since that is the probability that a recent flight arrives on time.

The probability of failure is 1 - 0.77 = 0.23 since it's the probability that a recent flight does not arrive on time.

Let's use these values to solve the problem.

The probability of no more than 4 flights arriving on time in a sample of 11 flights where 77% of recent flights arrived on time is given by the cumulative probability of x ≤ 4, which is equal to:

P(x ≤ 4) = P(x = 0) + P(x = 1) + P(x = 2) + P(x = 3) + P(x = 4)

where:P(x = 0) = (11 C 0) (0.77)0 (0.23)11 = 0.0001267

P(x = 1) = (11 C 1) (0.77)1 (0.23)10 = 0.0017314

P(x = 2) = (11 C 2) (0.77)2 (0.23)9 = 0.0115321

P(x = 3) = (11 C 3) (0.77)3 (0.23)8 = 0.0474373

P(x = 4) = (11 C 4) (0.77)4 (0.23)7 = 0.1295333

Now we can add these values to find the probability of no more than 4 flights arriving on time in a sample of 11 flights:

P(x ≤ 4) = 0.0001267 + 0.0017314 + 0.0115321 + 0.0474373 + 0.1295333= 0.19036

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Step 1: Corresponding sides, AB = 2 units, BC = √(13) units, AC = 3 units, A'B'= 4 units, B'C' = √(52) units, C'A' = 6 units. Step 2: scale factor of dilation is 2. Bonus: 2√(13) units.

Dilation can be performed with respect to a fixed point called the center of dilation, or with respect to a fixed line called the line of dilation. When dilation is performed with respect to a point, the distance between the center of dilation and every point on the object is multiplied by the same scale factor. When dilation is performed with respect to a line, the distance between every point on the object and the line of dilation is multiplied by the same scale factor.

Step 1: Comparing corresponding sides

AB = distance between A(2,3) and B(2,1) = 2 units

BC = distance between B(2,1) and C(5,3) = √((5-2)² + (3-1)²) = √(9+4) = √(13) units

AC = distance between A(2,3) and C(5,3) = 3 units

A'B' = distance between A'(-4,-1) and B'(-4,-5) = 4 units

B'C' = distance between B'(-4,-5) and C'(2,-1) = √((-4-2)² + (-5+1)²) = √(36+16) = √(52) units

C'A' = distance between C'(2,-1) and A'(-4,-1) = 6 units

Step 2: Finding the scale factor

To find the scale factor, we need to divide the length of each corresponding side in triangle A'B'C' by the length of the corresponding side in triangle ABC. This gives us:

Scale factor = A'B' / AB = 4/2 = 2

So, the scale factor of dilation is 2.

Bonus: Finding the length of BC and B'C'

To find the length of BC and B'C', we can use the distance formula.

The length of BC = √((5-2)² + (3-1)²) = √(13) units.

The length of B'C' = √((-4-2)² + (-5+1)²) = √(52) units.

Alternatively, we could also use the scale factor to find the length of B'C':

B'C' = BC x scale factor = √(13) x 2 = 2√(13) units.

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Let the amount of payouts in March be M.

From the problem, we know that the payouts in March increased by 8.5%, which means:

M = 12,400 + 0.085(12,400)

M = 12,400 + 1,054

M = 13,454

Next, we know that the payouts in April dropped by 5%, which means:

A = M - 0.05M

A = 0.95M

A = 0.95(13,454)

A = 12,781.3

Therefore, the amount of the payouts in April was $12,781.3.

Only option B) 3, 4, and 5 forms a right triangle.

What is the Pythagorean theorem?

In a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This is known as the Pythagorean theorem.

So, to check which set of side lengths form a right triangle, we need to see if they satisfy this condition.

A) 3, √9,√18:

√9 is equal to 3, so we have the side lengths 3, 3√2.

Using the Pythagorean theorem:

(3)² + (3√2)² = 9 + 18 = 27

However, (√18)² is also equal to 18, so the set of side lengths can also be written as 3, 3√2, √18.

Using the Pythagorean theorem again:

(3)² + (3√2)² = 9 + 18 = 27

and (3)² + (√18)² = 9 + 18 = 27

So, we have two sides that can form a right triangle, but not all three.

B) 3, 4, 5:

Using the Pythagorean theorem:

(3)² + (4)² = 9 + 16 = 25

Since 5² is also equal to 25, these side lengths form a right triangle.

C) 7, 7, √98:

√98 can be simplified as 7√2. So, we have the side lengths 7, 7, 7√2.

Using the Pythagorean theorem:

(7)² + (7)² = 98

and (7)² + (7√2)² = 343 + 98 = 441

So, we don't have a right triangle in this case.

Therefore, only option B) 3, 4, and 5 forms a right triangle.

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Answer:

Step-by-step explanation:

I changed it v to X because it's more convenient for me, but please write "v" so don't forget!

The expression of radicals [tex]\sqrt{a + b}[/tex] = √a + √b is not possible because they have different root number.

A Radical is described as the symbol, '√'  that is used to denote square root or nth roots.

Also, radical Expression is described as the radical expression  containing a square root.

The rules in addition and subtraction of radicals are;

From the information given, we have that;

a ≠b

So, for the expression;

[tex]\sqrt{a + b}[/tex] = √a + √b,. it is not feasible

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The common ratio is 1/3 and the fifth term of a geometric progression (GP) is 2/81 if the first and third terms of the GP are 2 and 2/9, respectively.

Let's call the common ratio of the GP "r".

We know that the first term of the GP is 2, so:

a₁ = 2

We also know that the third term of the GP is 2/9, so:

a₃ = 2/9

We can write the following using the nth term of a GP formula:

a₃ = a₁ * r²

Substituting the values we know, we get:

2/9 = 2 * r²

Dividing both sides by 2, we get:

1/9 = r²

Taking the square root of both sides (and remembering that r must be positive since it's a common ratio), we get:

r = 1/3

Now we can find the fifth term of the GP using the formula:

a₅ = a₁ * r⁴

Substituting the values we know, we get:

a₅ = 2 * (1/3)⁴

a₅ = 2 * (1/81)

a₅ = 2/81

Therefore, the common ratio is 1/3 and the fifth term of the GP is 2/81.

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The measure of w in the adjacent angle is 30 degrees.

The two angles are said to be adjacent angles when they share the common vertex and side. In other words, adjace3nt angles have common side and common vertex.

Therefore, let's find the measure of angle w as follows:

Hence, the sum of angle w and angle 50 degrees is equals to 80 degrees.

Therefore,

50 + w = 80

subtract 50 from both sides of the equation

50 - 50 + w = 80 - 50

w = 30 degrees

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