In your answer sheet , prove the theorem , using the given below . if a quadrilateral is inscribed in a circle , then its opposite angles are supplementary." Given : Quadriateral ABCD is inscribed in OE Prove : ∠ABC and ∠ABC are supplementary ∠DAB and ∠DCB are supplementary

The equivalent expression that combines like terms for the new price of the item is b(0.57).

To write an equivalent expression by combining like terms for the new price of the item with a 43% discount, we can simplify the expression b - 0.43b.

First, let's understand the given expression: b represents the original price of the item, and 0.43b represents the amount of the discount (43% of the original price).

To combine like terms, we can factor out the common term 'b' from both terms in the expression:

b - 0.43b = b(1 - 0.43).

Next, we can simplify the expression within the parentheses:

1 - 0.43 = 0.57.

Finally, substituting the simplified expression back into the original equation, we get:

b - 0.43b = b(0.57).

Therefore, the equivalent expression that combines like terms for the new price of the item is b(0.57).

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3. -38: Sarah's bank account balance is -$38, indicating that she has overdrafted and owes the bank money.

The integer -38 can be represented in a real-life situation where Sarah's bank account balance is negative, indicating an overdraft.

In this scenario, the negative integer -38 represents a negative bank account balance. When Sarah checks her bank account, she sees that her balance is -$38. This means that she has overdrafted her account and owes the bank $38. The negative sign indicates a deficit or debt in this real-life situation. Sarah will need to deposit funds into her account to bring her balance back to positive and clear her debt to the bank.

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The correct option is D, which has the equation (y+13)²/144 - (x+5)²/25 = 1.

The hyperbola x²/16 - y²/9 = 1 has its center at (0, 0), its transverse axis along the x-axis, and its foci at (-c, 0) and (c, 0),

Where c is the distance from the center to the foci.

The formula for the distance from the center to the foci is c = √(a² + b²), Where a is the distance from the center to a vertex on the transverse axis, and b is the distance from the center to a vertex on the conjugate axis.

In this case,

a² = 16, so a = 4, and b² = 9, so b = 3.

Therefore, c = √(16 + 9) = 5.

So, we are looking for a hyperbola with one focus at (-5, 0) or (5, 0).

Option A has a focus at (13, 5) and a focus at (13, -5), so it does not have a focus in common with the given hyperbola.

Option B has a focus at (13, 5) and (13, -5), so it does not have a focus in common with the given hyperbola.

Option C has a focus at (13, 5) and (13, -5), so it does not have a focus in common with the given hyperbola.

Option D has a focus at (-5, -13) and (-5, 13), so it has a focus in common with the given hyperbola. Therefore, the correct answer is D.

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The complete question is:

Which hyperbola has one focus in common with the hyperbola  x²/16 - y²/9 = 1.

The discounted-price of the game system is $154.00, given the original-cost of a video game system is $175 and Raymond works in an electronics store and gets a 12 percent employee discount.

The discounted price, we need to find 12% of $175 which is equal to: [tex]\frac{12}{100}\times175=21[/tex]

The employee discount is $21.

We need to subtract this discount from the original cost:

175 - $21 = 154

So, the discounted price of the game system is $154.00.

Therefore, the correct option is $154.00

The discounted price of the game system is indeed $154.00.

The original cost of the game system is $175, and

Raymond receives a 12% employee discount.

We calculate 12% of $175, which is $21.

By subtracting this discount from the original cost, we get $154.00, which is the final discounted price.

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The scientists compared the saliva and sweat when people did two activities to determine if the brain can smell fear. These activities are skydiving and lying.

The question is about the experiment conducted by scientists to determine if the brain can smell fear. The study was conducted by scientists who measured the saliva and sweat of people who were skydiving and lying to determine if the brain can smell fear. The human brain reacts differently to fear, and scientists wanted to study this reaction by monitoring the reactions of people who were afraid. They discovered that the brain can smell fear by analyzing the chemical changes in the sweat and saliva of people who were afraid. Sweat and saliva are two of the primary ways that the human body releases chemicals, including hormones. The sweat and saliva of people who were skydiving and lying were analyzed to determine if there was a chemical reaction to fear. The scientists discovered that the chemical composition of sweat and saliva changes when a person is scared. This discovery led them to conclude that the brain can smell fear.

The results of this study will help scientists better understand how the human brain reacts to fear and how it can help us to protect ourselves.

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To show that the lorry is traveling below the speed limit, we need to convert its speed from meters per second to kilometers per hour and compare it to the speed limit of 50 km/h.

The lorry's speed is given as 13.6 m/s. To convert this to kilometers per hour, we multiply it by the conversion factor: Speed (km/h) = Speed (m/s) * (3.6 km/h) = 13.6 * 3.6 = 48.96 km/h. Comparing the lorry's speed of 48.96 km/h to the speed limit of 50 km/h, we can see that the lorry is traveling below the speed limit.

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The number of times Felipe's stamp collection is contained within his uncle Carlo's collection is 52.5 times.

Felipe has 36 stamps in his collection, and his uncle Carlo has 1890 stamps in his collection. To determine how many times Felipe's collection fits into Carlo's collection, we can divide the number of stamps Carlo has by the number of stamps Felipe has.

1890 / 36 = 52.5

Therefore, Felipe's stamp collection is contained within his uncle Carlo's collection approximately 52.5 times.

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A combination of the sum of two complex numbers is 15 - 19i

To find the sum of two complex numbers, add their real parts separately and add their imaginary parts separately.Now, we need to find the sum of the following complex numbers.

(-4i) + (10 - 5i) -3

5i -3 - 5i

6 - 4i 6 - 6i

Add the real parts, which are (-4) and 10.

Therefore, the real part is (10 - 4) = 6.

Add the imaginary parts, which are (-5) and (-3).

Therefore, the imaginary part is (-5 - 3) = -8.

Thus, the sum of (-4i) and (10 - 5i) is 6 - 8i.

Now, we need to find the sum of the following complex numbers.

(-3 − 5i) + (6 − 4i) + (6 − 6i)

First, we add (-3 − 5i) and (6 − 4i) to find the sum.

(−3 − 5i) + (6 − 4i) = (3 − 5i)

Then we add (3 − 5i) and (6 − 6i) to find the sum.

(3 − 5i) + (6 − 6i) = 9 − 11i

Therefore, the sum of (-3 - 5i), (6 - 4i) and (6 - 6i) is 9 - 11i.

Now we have to write our answer as a combination of the sum of two complex numbers, which we found earlier.

6 - 8i + 9 - 11i = 15 - 19i

Thus, the final answer is 15 - 19i.

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The total number of pennies on Rows 1-4 (the first 32 squares) is 232. The content loaded formula can be used to calculate the total number of pennies on the Rows 1-4 of the first 32 squares.

formula = 2^(n-1) + 2^(n-2) + 2^(n-3) + 2^(n-4) + 2^(n-5) + ……+ 2^1 + 2^0Where n = the number of rows The first four rows of the chessboard have 2^(4-1) = 8, 2^(4-2) = 4, 2^(4-3) = 2, and 2^(4-4) = 1 pennies respectively .The total number of pennies on the first 32 squares (Rows 1-4) is calculated using the following formula; Total = 8 + 4 + 2 + 1 = 15For the first four rows (the first 32 squares), the total number of pennies is 15. Hence, the correct option is 15.

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The exact value of tangent (19π/12) is option C: StartFraction 3 minus StartRoot 3 EndRoot Over 3 + StartRoot 3 EndRoot EndFraction.

To find the exact value of tangent (19π/12), we can use the trigonometric identity:

tangent (θ) = sin (θ) / cos (θ).

First, let's find the values of sin (19π/12) and cos (19π/12).

Using the unit circle, we can determine that sin (19π/12) = -1/2 and cos (19π/12) = -√3/2.

Now we can substitute these values into the tangent formula:

tangent (19π/12) = sin (19π/12) / cos (19π/12) = (-1/2) / (-√3/2).

Simplifying the expression by multiplying the numerator and denominator by 2/√3:

tangent (19π/12) = (-1/2) * (2/√3) / (-√3/2) = (1/√3).

To rationalize the denominator, we multiply the numerator and denominator by √3:

tangent (19π/12) = (1/√3) * (√3/√3) = √3/3.

Therefore, the exact value of tangent (19π/12) is option C: StartFraction 3 minus StartRoot 3 EndRoot Over 3 + StartRoot 3 EndRoot EndFraction.

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Amilia has 20 times as many toothpicks as Tim. Tim has 3 tooth picks. Amilia has 60 tooth picks.

To determine how many times as many toothpicks Amilia has compared to Tim, we can divide the number of toothpicks Amilia has by the number of toothpicks Tim has.

Amilia has 60 toothpicks, while Tim has 3 toothpicks.

To calculate the ratio, we divide the number of toothpicks Amilia has by the number of toothpicks Tim has:

60 / 3 = 20

Therefore, Amilia has 20 times as many toothpicks as Tim. This means that the number of toothpicks Amilia has is twenty times greater than the number of toothpicks Tim has. It indicates a significant difference in the quantity of toothpicks possessed by the two individuals.

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The average height is 1.4m and the total height of the other three children is given by T = 2.95 m

Given data,

To find the total height of the other three children, we first need to determine the combined height of Nosiku, Naza, and Tom.

Given that the average height of Nosiku, Naza, John, and Tom is 1.4m, and John's height is 1.25m, we can calculate the total height of the other three children as follows:

Total height of the other three children = Average height * Number of children - John's height

Total height of the other three children = ( 1.4m x 3 ) - 1.25m

T = 4.2m - 1.25m

T = 2.95m

Hence , the total height of the other three children (Nosiku, Naza, and Tom) is 2.95 meters.

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Answer:

Precise measurements and calculations are necessary to achieve the desired pH of 12.00.

Step-by-step explanation:

To convert a sodium hydroxide solution with a pH of 13.00 to a pH of 12.00, you would need to decrease the concentration of hydroxide ions (OH-) in the solution. One way to achieve this is by diluting the solution with a neutral solvent, such as water.

Here's a step-by-step process:

Determine the volume of the sodium hydroxide solution you want to prepare with a pH of 12.00. Let's assume you want to prepare 100 mL of the new solution.

Calculate the amount of water needed to dilute the solution. Since you want to decrease the concentration of hydroxide ions, you need to add water. The amount of water needed depends on the desired concentration and the initial concentration.

pH is a logarithmic scale, so the difference in pH values represents a 10-fold difference in concentration. Since the pH is decreasing from 13.00 to 12.00, you need to dilute the solution by a factor of 10.

Therefore, to dilute 100 mL of the sodium hydroxide solution by a factor of 10, you would need to add 900 mL of water.

Mix the sodium hydroxide solution with the calculated amount of water. Ensure thorough mixing to obtain a homogeneous solution.

By diluting the sodium hydroxide solution with water, you decrease the concentration of hydroxide ions, resulting in a lower pH value. However, it's important to note that pH is a logarithmic scale, so small changes in concentration can result in significant changes in pH.

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The Fahrenheit temperature of 100°C is 212°F. So, we can put the given Celsius temperature in the above formula:F = 9/5(100) + 32F = 180 + 32F = 212°FTherefore, the Fahrenheit temperature of 100°C is 212°F.

Given, Celsius temperature c = 100°FTo find Fahrenheit temperature, we can use the formula:F = 9/5C + 32Put the given Celsius temperature into the formula:F = 9/5(100) + 32F = 180 + 32F = 212°F. Therefore, the Fahrenheit temperature of 100°C is 212°F.

We know that the formula for converting Celsius to Fahrenheit is given by:F = 9/5C + 32Where, F is the temperature in Fahrenheit and C is the temperature in Celsius.Water boils at 100°C. So, we need to find the Fahrenheit temperature when Celsius temperature is 100°F.So, we can put the given Celsius temperature in the above formula:F = 9/5(100) + 32F = 180 + 32F = 212°FTherefore, the Fahrenheit temperature of 100°C is 212°F.

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Let's solve the problem step by step:

1. Alexa was riding her motorcycle on a freeway at 480 kilometers north of her exit.

2. She was riding south toward the exit at a constant velocity.

3. It took her 2 hours to get one quarter of the way to her exit.

Let's denote Alexa's velocity as [tex]\(v\)[/tex] (in kilometers per hour) and the total distance to her exit as [tex]\(D\)[/tex] (in kilometers).

According to the information given, Alexa traveled one quarter of the total distance in 2 hours. This can be represented by the equation:

[tex]\(\frac{1}{4} \times D = v \times 2\)[/tex]

Simplifying this equation, we have:

[tex]\(\frac{D}{4} = 2v\)[/tex]

Next, we know that Alexa started 480 kilometers north of her exit. So the total distance to her exit is:

[tex]\(D = 480 + \text{distance traveled}\)[/tex]

Substituting this expression for [tex]\(D\)[/tex] into our equation, we get:

[tex]\(\frac{480 + \text{distance traveled}}{4} = 2v\)[/tex]

Simplifying further:

[tex]\(120 + \frac{\text{distance traveled}}{4} = 2v\)[/tex]

From this equation, we can see that the velocity [tex]\(v\)[/tex] is independent of the distance traveled. Therefore, the velocity [tex]\(v\)[/tex] remains constant.

To determine the exact value of [tex]\(v\)[/tex], we need more information about the distance traveled by Alexa.

Please provide the additional information, such as the distance traveled or the time taken to cover a specific distance, to calculate the velocity accurately.

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The  statement is d) Line segments E'F' and G'H' do not intersect and are the same distance apart as EF and GH.

The figure shows a pair of parallel line segments on a coordinate grid: Line segment GH runs from (-1, -1) to (3, -1), and line segment EF runs from (-1, -2) to (3, -2).

To determine the characteristics of line segments E'F' and G'H' after being translated 2 units to the right, we need to apply the translation to the endpoints of the original line segments.

Applying a translation of 2 units to the right:

Endpoint E: (-1, -2) + (2, 0) = (1, -2)

Endpoint F: (3, -2) + (2, 0) = (5, -2)

Endpoint G: (-1, -1) + (2, 0) = (1, -1)

Endpoint H: (3, -1) + (2, 0) = (5, -1)

Now, let's analyze the statements:

a) Line segments E'F' and G'H' do not intersect and are closer together than EF and GH.

  This statement is false. E'F' and G'H' do not intersect, but they are not closer together than EF and GH. They are actually farther apart.

b) Line segments E'F' and G'H' intersect at (-2, 0) and are two times farther apart than EF and GH.

  This statement is false. E'F' and G'H' do not intersect at (-2, 0). They have different coordinates for their endpoints.

c) Line segments E'F' and G'H' intersect at (0, -2) and are two times closer together than EF and GH.

  This statement is false. E'F' and G'H' do not intersect at (0, -2). They have different coordinates for their endpoints.

d) Line segments E'F' and G'H' do not intersect and are the same distance apart as EF and GH.

  This statement is true. E'F' and G'H' do not intersect, and they have the same distance between them as EF and GH.

Therefore, the correct statement is d) Line segments E'F' and G'H' do not intersect and are the same distance apart as EF and GH.

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Given the figure, we have to find the value of y.Using the angle sum property of a quadrilateral, we know that the sum of angles in a quadrilateral is 360 degrees.

Therefore:

∠A + ∠B + ∠C + ∠D = 360°

We know that

∠A = 600°,

∠B = 120°, and

∠C = 100°

∠A + ∠B + ∠C + ∠D = 360°

600° + 120° + 100° + ∠D = 360°

820° + ∠D = 360°

∠D = 360° - 820°

∠D = -460°

Since angle D is not possible to be negative, we know that there must be a mistake in the diagram. We need to make sure that the figure is correct before we can find the value of y.

Therefore, the value of y cannot be determined with the information given in the figure.

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The calculted ratio of the side lengths is 2 : 3

From the question, we have the following parameters that can be used in our computation:

Using the above as a guide, we have the following:

Ratio = Smaller box : Larger box

So, we have

Ratio = 12 inches : 18 inches

Simplify the ratio

Ratio = 2 : 3

Hence, the ratio is 2 : 3

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Question

A company is experimenting with two new boxes for packaging merchandise. Each box is a cube with the side lengths shown. (smaller box is 12 in, larger box is 18 in.)

What is the ratio of the side lengths of the smaller box to the side lengths of the larger box in lowest terms?

In each round, half of the remaining teams are eliminated.7th round: 2 - 1 = 1 team eliminated The sequence shows the progressive elimination of teams as the tournament progresses.

The sequence that represents the number of teams that have been eliminated in round n of the badminton tournament. This pattern continues until there is only one team left, which becomes the winner of the tournament.

It can be written as follows:

1st round: 128 - 64 = 64 teams eliminated

2nd round: 64 - 32 = 32 teams eliminated

3rd round: 32 - 16 = 16 teams eliminated

4th round: 16 - 8 = 8 teams eliminated

5th round: 8 - 4 = 4 teams eliminated

6th round: 4 - 2 = 2 teams eliminated

7th round: 2 - 1 = 1 team eliminated

In each round, half of the remaining teams are eliminated. This pattern continues until there is only one team left, which becomes the winner of the tournament. The sequence shows the progressive elimination of teams as the tournament progresses.

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If Henry uses 1 1/2 cups of corn grits, he will need 3 cups of water.

The recipe calls for 1/4 cup of corn grits for every 1/2 cup of water. To find out how much water Henry will need if he uses 1 1/2 cups of corn grits, we can set up a proportion.

Let's assume x represents the amount of water needed in cups. The proportion can be written as:

1/4 cup of corn grits / 1/2 cup of water = 1 1/2 cups of corn grits / x cups of water

To solve the proportion, we can cross multiply:

(1/4) × x = (1 1/2) × (1/2)

Simplifying the right side of the equation:

(1/4) × x = (3/2) × (1/2)

x/4 = 3/4

To isolate x, we can multiply both sides of the equation by 4:

x = (3/4) × 4

x = 3

Therefore, if Henry uses 1 1/2 cups of corn grits, he will need 3 cups of water.

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The angle of the sun above the horizon when a person 5.94 ft tall casts a shadow 9.74 ft long is approximately 34.45 degrees.

To find the angle, we can use the concept of similar triangles. The person's height, the length of the shadow, and the distance between the person and the tip of the shadow form a right triangle.

Let's denote the angle of the sun above the horizon as "θ". We can use the tangent function to find the angle:

tan(θ) = opposite/adjacent

In this case, the opposite side is the person's height (5.94 ft) and the adjacent side is the length of the shadow (9.74 ft).

tan(θ) = 5.94/9.74

To find the angle θ, we can take the inverse tangent (arctan) of both sides:

θ = arctan(5.94/9.74)

Using a calculator, we can evaluate this expression to find that θ is approximately 34.45 degrees.

Therefore, the angle of the sun above the horizon when a person 5.94 ft tall casts a shadow 9.74 ft long is approximately 34.45 degrees.

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Adrienne invested $1200 in account A and $1600 in account B.

Let's set up a system of equations to represent the given information. We are given that the total amount invested is $2800, so we have the equation a + b = 2800.

The interest earned from account A is given as 39% of the amount invested in account A, which can be represented as 0.39a.

Similarly, the interest earned from account B is 5% of the amount invested in account B, represented as 0.05b. The total interest earned is $128, so we have the equation 0.39a + 0.05b = 128.

Solving this system of equations can be done using various methods, such as substitution or elimination. One way to solve is by substitution.

From the first equation, we can solve for a in terms of b: a = 2800 - b. Substituting this into the second equation, we get 0.39(2800 - b) + 0.05b = 128.

Simplifying and solving for b, we find b = $1600. Substituting this value back into the first equation, we get a = $1200.

Therefore, Adrienne invested $1200 in account A and $1600 in account B.

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The correct symbol to make the statement true is: -56 < -55

To make the statement true, we need to choose the correct symbol between -56 and -55.

The options are:

-56 > -55 (greater than)

-56 < -55 (less than)

-56 = -55 (equal to)

-56 ≥ -55 (greater than or equal to)

-56 ≤ -55 (less than or equal to)

In this case, the correct symbol to make the statement true is:

-56 < -55

Therefore, the correct statement is: -56 < -55.

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The value of the variable x in the given figure is given by 19.1 ft.

Here in the given picture the given two triangles are similar triangles.

For the similar triangles, the ratios of the similar sides are equal.

So here the side with 9.3 ft of first triangle is similar with the side with x ft and the side of 1.7 ft of first triangle is similar with the side with 3.5 ft.

By the condition then,

x/9.3 = 3.5/1.7

x = 9.3 * (3.5 / 1.7) = 19.1 [rounding off to the nearest first decimal place]

Hence the value of x in the given figure is 19.1 ft.

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The question is incomplete. The complete question will be -

Fats that are highly unsaturated, such as polyunsaturated fats, are most susceptible to rancidity.

Rancidity refers to the deterioration of fats and oils, resulting in undesirable odors and flavors. The stability of fats, or their resistance to rancidity, is influenced by their degree of unsaturation.

1. Fats are composed of fatty acids, which can be classified as saturated, monounsaturated, or polyunsaturated based on the presence of double bonds between carbon atoms in their chemical structure.

2. Saturated fats have no double bonds and are the most stable, as the absence of double bonds makes them less susceptible to oxidation and rancidity.

3. Monounsaturated fats have one double bond, which introduces some susceptibility to rancidity but to a lesser extent than polyunsaturated fats.

4. Polyunsaturated fats have multiple double bonds, making them the most susceptible to rancidity. The presence of multiple double bonds provides more sites for oxidation, leading to increased chemical reactivity and the potential for rancid flavors and odors to develop.

5. Common examples of polyunsaturated fats include vegetable oils such as soybean oil, corn oil, and sunflower oil. These oils are often stored in dark bottles and refrigerated to slow down the oxidation process and extend their shelf life.

In summary, fats that are highly unsaturated, particularly polyunsaturated fats, are the most susceptible to rancidity due to the presence of multiple double bonds, which increase their susceptibility to oxidation and degradation.

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L ≈ 35.8 ,the length of the arc to the nearest tenth is 35.8 units

The formula for calculating the length of an arc intercepted by a central angle is L=, where L is the arc's length,  is the circle's radius, and  is the central angle in radians. The length of the arc to the nearest tenth is 35.8 units. Given, In a circle with radius r = 6.5, an angle measuring  = 5.5 radians intercepts an arc. We know that the formula for calculating the length of an arc intercepted by a central angle is L=, where L is the arc's length,  is the circle's radius, and  is the central angle in radians. Substituting the values in the formula, we get:

L = rL = 6.5(5.5)L = 35.75 ≈ 35.8 (to the nearest 10th)

Therefore, the length of the arc to the nearest tenth is 35.8 units.

In a circle, the length of an arc intercepted by a central angle is determined by the central angle's size and the circle's radius. This is known as the arc's length formula. L=where L is the arc length,  is the radius of the circle, and  is the central angle in radians. We can use this formula to find the length of an arc intercepted by a central angle in a circle. Let's consider the following illustration to understand the concept better. In a circle with a radius of 6.5, an angle of 5.5 radians intercepts an arc. We'll use the arc length formula to find the arc's length, L.L= (Length of arc formula)Substitute the given value of r and  in the formula. L = 6.5 × 5.5L = 35.75The length of the arc is 35.75 units. We'll round this answer to the nearest tenth to get the final answer. L ≈ 35.8Therefore, the length of the arc to the nearest tenth is 35.8 units.

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The value of AB is [76 + 2x]/3.

Given that d is the midpoint of AB and e is the midpoint of AC.

We are to find the value of AB.

Let the length of AB be x.

So, AD = 8 and DB = x - 8.

Also, AE = x - 8 and EC = x + 8. It is given that

BC = 22. So, AC = 2 * EC = 2 (x + 8) = 16 + 2x.

Similarly, AB = 2 * DB = 2 (x - 8) = 2x - 16.

It is also given that AB : school = 2 : 3

Thus, AB/School = 2/3 => School = (3/2) * AB

Also, AB + AC + BC = School + School = 2School

So, x + 16 + 22 = 2 * (3/2) * AB38 + x = 3 * AB/2 => 2(38 + x) = 3 * ABAB = [2(38 + x)]/3AB = [2(38 + x)]/3 = [76 + 2x]/3

Therefore, the value of AB is [76 + 2x]/3.

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Marcus ends up paying $37.70 for the two shirts. To calculate the final price Marcus pays for the shirts, we need to follow these steps:

Calculate the discounted price of each shirt: Since the shirts are on a 30% off rack, the discounted price of the first shirt is 0.70 * $28.99 = $20.29, and the discounted price of the second shirt is 0.70 * $30.29 = $21.20.

Calculate the total cost of the shirts before tax: The total cost of the two shirts is $20.29 + $21.20 = $41.49.Apply the additional 10% off discount: To calculate the final price after the additional discount, we need to subtract 10% from the total cost. 10% of $41.49 is 0.10 * $41.49 = $4.15. Subtracting this amount from the total cost gives us $41.49 - $4.15 = $37.34.

Add the sales tax: To calculate the final price including the 6% sales tax, we need to add 6% of $37.34 to the total cost. 6% of $37.34 is 0.06 * $37.34 = $2.24. Adding this amount to the total cost gives us $37.34 + $2.24 = $39.58.

Rounding to the nearest cent, Marcus ends up paying $39.59 for the two shirts. Therefore, the correct answer is option a. $39.59.

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A 9kg bag of peas would cost $32.22 at the same rate as a 5kg bag based on the given details.

To find the cost of a 9kg bag of peas at the same rate, we can use the concept of direct proportion.

The cost of the peas is directly proportional to the weight of the bag. This means that the cost per kilogram remains the same.

Let's calculate the cost per kilogram of peas:

Cost per kilogram = Total cost / Total weight

= $17.91 / 5kg

Cost per kilogram = $3.58/kg

Now, we can calculate the cost of a 9kg bag of peas:

Cost of 9kg bag = Cost per kilogram * Weight of the bag

= $3.58/kg * 9kg

Cost of 9kg bag = $32.22

Therefore, a 9kg bag of peas would cost $32.22.

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When rolling a number cube four times, the probability of obtaining an even number in three of the four rolls is 1/4.

To calculate the probability that a number cube will land on an even number three out of four rolls, we need to consider the total number of possible outcomes and the number of favorable outcomes.

The total number of possible outcomes when rolling a number cube four times is 6^4, which is equal to 1,296. This is because each roll has six possible outcomes (numbers 1 to 6), and the rolls are independent events, so we multiply the number of outcomes for each roll.

Now, let's consider the favorable outcomes. We want the cube to land on an even number three out of four times. There are two cases that satisfy this condition: either the first, second, and third rolls are even, or the second, third, and fourth rolls are even.

Case 1: First, second, and third rolls are even.

The probability of rolling an even number on a single roll is 3/6, or 1/2 since there are three even numbers (2, 4, and 6) out of six total numbers on the cube.

So, the probability of the first, second, and third rolls being even is (1/2) * (1/2) * (1/2) = 1/8.

Case 2: Second, third, and fourth rolls are even.

Again, the probability of rolling an even number on a single roll is 1/2.

So, the probability of the second, third, and fourth rolls being even is (1/2) * (1/2) * (1/2) = 1/8.

Now, we need to add the probabilities from both cases because we are interested in the probability of either of these events occurring:

1/8 + 1/8 = 2/8 = 1/4.

Therefore, the probability that the cube will land on an even number three out of four rolls is 1/4.

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