Triangle ABC has vertices A(0, 0), B (12, 7), and C(12, 0). If circle O is circumscribed around the triangle, what are the coordinates of the center of the circle?

As the town gets smaller, the population of high school students decreases by 6% each year. The senior class has 160 students now.  7 years will it have about 100 students.

The formula for calculating exponential decay is given by:

P(t) = [tex]P_0 e^{rt}[/tex]

Where,

P(t) = population after t years

[tex]P_0[/tex] = initial populationr = annual decay ratet = time in years

A decay rate refers to the amount of decrease in a population over a given period of time. A negative value indicates that the population is decreasing.

The problem gives that the senior class has 160 students now. In the next year, the population will decrease by 6%. So, the new population will be (1-6%) of the original population.

That is,P(1) = P(0) (1-6%)= P(0) 0.94

Where,

P(0) = 160 is the initial population of the senior class.

P(1) = 160 × 0.94 = 150.4 students in the next year

Similarly, the population after two years is

P(2) = P(1) × 0.94 = 141.4 students

P(3) = P(2) × 0.94 = 133.0 students

P(4) = P(3) × 0.94 = 125.0 students

P(5) = P(4) × 0.94 = 117.5 students

P(6) = P(5) × 0.94 = 110.2 students

P(7) = P(6) × 0.94 = 103.3 students

Since we are interested in the population when it is about 100, it is clear that it will be after 7 years (since it will be less than 100 for the 6th year and more than 100 for the 7th year).

Therefore, the senior class will have about 100 students after 7 years.

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The probability that your survey will provide a sample proportion within 0.05 of the population proportion = 0.8818

Here,  people end up tossing 10% of what they buy at the grocery store

So, the probability of occurance P = 0.1

q = 1 - p

q = 1 - 0.1

q = 0.9

Also, the sample size (n) = 90

Now the standard error of the distribution of sample means would be,

s = [tex]\sqrt{\frac{p\times q}{n} }[/tex]

s = 0.032

We need to calculate the probability that your survey will provide a sample proportion within 0.05 of the population proportion.

z₁ = (-0.05)/(0.032)

z₁ = -1.5625

z₂ = (+0.05)/(0.032)

z₂ = +1.5625

p(z-score between -1.5625 and +1.5625) = 0.8818

Therefore the required probability is 0.8818

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Number of ways to select 8 countries from the United Nations is 48,054,722,400

To solve this problem, we need to use the combination method, which states that if there are m ways to perform one task and n ways to perform another task after the first task is completed, then there are m x n ways to perform both tasks in sequence.

Using this principle, we can break down the selection of 8 countries into three separate tasks

Selecting 3 countries from a block of 52: There are 52C3 ways to do this, where 52C3 is the binomial coefficient "52 choose 3," which can be calculated as follows

52C3 = (52 x 51 x 50) / (3 x 2 x 1) = 22,100

Selecting 2 countries from a block of 64: There are 64C2 ways to do this, where 64C2 is the binomial coefficient "64 choose 2," which can be calculated as follows

64C2 = (64 x 63) / (2 x 1) = 2,016

Selecting 3 countries from a block of 73: There are 73C3 ways to do this, where 73C3 is the binomial coefficient "73 choose 3," which can be calculated as follows

73C3 = (73 x 72 x 71) / (3 x 2 x 1) = 1,082,790

To find the total number of ways to select 8 countries, we simply multiply these three quantities together

22,100 x 2,016 x 1,082,790 = 48,054,722,400

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The length of arc GJ in circle H with m∠GHJ=90 and GH=20 is equal to half of the circumference of the circle.

The length of arc GJ in circle H with m∠GHJ=90 and GH=20 can be calculated using the formula for circumference of a circle. First, find the radius of the circle by using the Pythagorean Theorem. Using the values given, the radius of the circle is 20. Then, use the formula for circumference of a circle (2πr) to find the circumference of the circle, which is equal to 2π(20) = 40π. Finally, divide the circumference of the circle by two to find the length of arc GJ, which is equal to 40π/2 = 20π.

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The correct tiles that complete the pairs of corresponding angles are;

D                  [tex]\longrightarrow[/tex]                  H

G                  [tex]\longrightarrow[/tex]                  C

E                  [tex]\longrightarrow[/tex]                  A

B                  [tex]\longrightarrow[/tex]                  F

Corresponding angles are pairs of angles that are formed by the intersection of two parallel lines and a common transversal. The location of corresponding angles are in matching corners of the intersection such that their measures are equal. Corresponding angles are therefore, congruent.

The corresponding angles in the diagram included in the question are found in matching corners with regards to the common transversal and the parallel lines.

The corresponding angles in the figure are;

Angle ∠A corresponds to angle ∠E

Angle ∠B corresponds to angle ∠F

Angle ∠D corresponds to angle ∠H

Angle ∠C corresponds to angle ∠G

Therefore, we get;

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Answer:

(a) The best answer for residuals plot (a) is:

A. The fanned pattern indicates that the linear model is not appropriate. The model's predicting power decreases as the values of the explanatory variable increases.

A fanned pattern in the residuals plot suggests that the linear model is not appropriate because the variability of the residuals increases as the values of the explanatory variable increases. This indicates that the linear model is not capturing all the important features of the data and may not be the best fit for the data.

(b) The best answer for residuals plot (b) is:

B. The curved pattern in the residuals plot indicates that the linear model is not appropriate. The relationship is not linear.

A curved pattern in the residuals plot suggests that the linear model is not appropriate because the relationship between the variables is not linear. This indicates that the linear model is not capturing all the important features of the data and may not be the best fit for the data.

Answer: The perimeter of the original square is the sum of the lengths of all its sides, which are all equal to 10 units:

Perimeter of original square = 4 x 10 = 40 units

When the square is enlarged by a scale factor of 2.2, all of its sides will be multiplied by 2.2:

New side length = 2.2 x 10 = 22 units

The perimeter of the new square is the sum of the lengths of all its sides, which are all equal to 22 units:

Perimeter of new square = 4 x 22 = 88 units

Therefore, the perimeter of the new square is 88 units.

Step-by-step explanation:

There are different models that can be used to add fractions, but one common model is the area model, which represents fractions as parts of a whole.

To use the area model to add fractions, you can follow these steps:

1. Draw a rectangle to represent the whole. The size of the rectangle can be arbitrary, but it should be divided into equal parts to match the denominators of the fractions you are adding.

2. Divide the rectangle into the appropriate number of equal parts to represent the denominators of the fractions. For example, if you are adding 1/3 and 1/4, divide the rectangle into 12 equal parts (3 x 4 = 12).

3. Shade the appropriate number of parts in each fraction. For example, shade 4 out of 12 parts for 1/3 and 3 out of 12 parts for 1/4.

4. Count the total number of shaded parts in the rectangle. This represents the numerator of the sum of the fractions.

5. Write the sum of the fractions as the total number of shaded parts over the total number of parts in the rectangle.

For example, to add 1/3 and 1/4 using the area model:

1. Draw a rectangle to represent the whole.

```

+---+---+---+---+

| | | | |

+---+---+---+---+

| | | | |

+---+---+---+---+

| | | | |

+---+---+---+---+

```

2. Divide the rectangle into 12 equal parts.

```

+---+---+---+---+

| | | | |

+---+---+---+---+

| | | | |

+---+---+---+---+

| | | | |

+---+---+---+---+

1 2 3 4

```

3. Shade 4 out of 12 parts for 1/3 and 3 out of 12 parts for 1/4.

```

+---+---+---+---+

|###|###|###| |

+---+---+---+---+

|###|###|###| |

+---+---+---+---+

|###|###| | |

+---+---+---+---+

The demand curve is a graphical representation of the relationship between the quantity of a good or service that buyers are willing and able to purchase at various prices. It is based on the law of demand, which states that as the price of a good or service increases, the quantity demanded decreases, and vice versa.

However, there are other factors that can affect demand besides price, such as changes in buyers' incomes, tastes and preferences, the prices of related goods or services, and expectations about future prices or economic conditions. When one or more of these factors changes, the entire demand curve can shift to the right or left, indicating a change in the quantity demanded at every price.

In the case of an increase in buyers' incomes, the demand curve for most goods or services will shift to the right. This means that at every price level, buyers will be willing and able to purchase more of the good or service than before. This can be explained by the fact that when buyers' incomes increase, they have more purchasing power and are able to buy more of everything, including the good or service in question.

For example, if the economy is booming and buyers' incomes are rising, they may be more willing to purchase luxury goods or services that they previously couldn't afford. This could lead to an increase in demand for high-end products such as luxury cars, designer clothing, and high-end restaurants, even though the prices of these goods or services have not changed.

In summary, changes in buyers' incomes are one of several factors that can cause the demand curve to shift to the right or left. When buyers' incomes increase, the demand for most goods or services will increase as well, indicating that buyers are willing and able to purchase more of the good or service at every price.

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The curve shifts to the right if the determinant causes demand to increase. This means more of the good or service are demanded even though there's no change in price. When the economy is booming, buyers' incomes will rise. They'll buy more of everything, even though the price hasn't changed. write a statement according to the context .

The impact of critic reviews and star ratings on one's strategies would depend on the individual and their approach to the game.

Some players may be heavily influenced by reviews and ratings, using them to adjust their strategies in order to please the critics and achieve higher scores.

Others may choose to ignore them altogether and focus on their own personal goals or strategies. Still, others may use the feedback as a tool for improvement, taking the criticism constructively and using it to make changes in their approach to the game.

Ultimately, it is up to the individual player to decide how much weight they place on reviews and ratings and how they choose to use them in their gameplay.

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the solution to the equation is x = 7/3, which is between x=2 and x=3 on the x-axis of the graph. Therefore, the correct answer is A: "The solution is between x = 2 and x = 3".

How to find the solution?

To find the solution to 1/(x - 2) - 3 =0, we need to solve for x such that the equation is satisfied.

Starting with the given equation, we can first add 3 to both sides:

1/(x - 2) = 3

Next, we can invert both sides to get:

x - 2 = 1/3

Adding 2 to both sides yields:

x = 2 + 1/3

So the solution to the equation is x = 7/3, which is between x=2 and x=3 on the x-axis of the graph. Therefore, the correct answer is A: "The solution is between x = 2 and x = 3".

From the graph, we can see that the curve approaches the x-axis as x approaches 2 from the right side and becomes infinitely large as x approaches 2 from the left side. As x moves further to the right of 2, the curve rapidly drops to negative infinity. Hence, the curve never crosses the x-axis, so there are no real solutions to the equation other than x=7/3.

It's important to note that the values in the table provided do not align with the actual values of the function due to the graph's curvature. The table seems to have some errors, such as negative values of y when x is between 0 and 2, which is not possible for the given function.

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The radius οf the circle is apprοximately 1.2 units.

A circle is a twο-dimensiοnal shape that is defined as the set οf all pοints in a plane that are equidistant frοm a fixed pοint called the center. The distance frοm the centre tο any pοint οn the circle is called the radius, and the distance acrοss the circle passing thrοugh the center is called the diameter.

The circumference οf a circle is the distance arοund its οuter edge, and it is equal tο the prοduct οf the diameter and pi (π), a mathematical cοnstant apprοximately equal tο 3.14159. Circles have many prοperties that make them useful in geοmetry and οther areas οf mathematics.

In this prοblem, we are given the angle and the length οf the intercepted arc. Let's call the radius οf the circle "r". Then we can write:

11.8 = r * 9.7

Tο sοlve fοr "r", we can divide bοth sides by 9.7:

r = 11.8 / 9.7

r ≈ 1.2165

Rοunding tο the nearest tenth, we get:

r ≈ 1.2

Therefοre, the radius οf the circle is apprοximately 1.2 units.

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UV is tangent to OT. The ∠v = 44°.

A line that only touches a circle or an ellipse at one point is said to be tangential in geometry. If a line contacts a curve at point P, that point is referred to as the point of tangency.

In other words, it is described as the line that, at that particular location, indicates the slope of a curve.

Given the circle in which the UV and UW are tangent to oT. To find m ∠V

∠v + ∠T = 180

∠v = 180° - 136°

∠v = 44°

Thus, the ∠v = 44°.

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The cost per zinnia plant is $0.04.

What is the cost price?

The precise value that corresponds to the unit price paid is represented by the cost price. In some stock market theories, this value is utilized to establish the value of stock holdings and is used as a key determinant of profitability.

Here, we have

Given: Mrs. Cook purchased 200 zinnia plants for $23. One month later, she purchased 500 zinnia plants for $35.

We have to find the cost per zinnia plant.

To find the cost per zinnia plant, derive two points from the info given which are:

(200, 23) and (500, 35)

The slope = cost per zinnia plant = 35 - 23 / 500 - 200

= 12/300

= $0.04.

Hence, the cost per zinnia plant is $0.04.

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Regularization is a process of adding a penalty term to the error function in order to avoid overfitting in an estimation process.

The addition of a penalty term can prevent model overfitting and improve model generalization. Regularization is a technique that is used in many machine learning models, including regression, neural networks, and SVMs (Support Vector Machines).The regularization parameter, also known as the tuning parameter, controls the extent of the penalty added to the error function. A larger regularization parameter results in more aggressive regularization and a simpler model, while a smaller regularization parameter results in less aggressive regularization and a more complex model. The regularization parameter should be selected carefully to achieve a balance between model complexity and model performance.

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A 95% confidence interval for the true proportion of those from their entire mailing list who may donate is between 0.244 and 0.356 based on a random sample of 500 people where 150 may donate.

To give a 95% confidence interval for the true proportion of those from their entire mailing list who may donate, we need to know the sample proportion and the sample size. Let's assume that a random sample of 500 people from the mailing list was selected, and 150 of them indicated that they may donate.

The sample proportion is:

p = 150/500 = 0.3

To calculate the standard error of the proportion, we use the formula:

SE = sqrt(p(1-p)/n) = sqrt(0.3(1-0.3)/500) = 0.0288

To find the 95% confidence interval, we use the formula:

CI = p ± z*SE

where z is the z-score corresponding to a 95% confidence level, which is 1.96.

Substituting the values, we get:

CI = 0.3 ± 1.96*0.0288

CI = (0.244, 0.356)

Therefore, we can say with 95% confidence that the true proportion of those from their entire mailing list who may donate is between 0.244 and 0.356.

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"Suppose a nonprofit organization is planning a fundraising campaign and has a mailing list of 10,000 potential donors. The organization plans to randomly sample 500 people from the list and ask them to donate. They expect that 20% of those who are sampled will donate. Give a ​%95 confidence interval for the true proportion of those from their entire mailing list who may donate."

The average weight of an adult human brain is about 1.3 kilograms (2.87 pounds). The average weight of an adult human heart is about 300 grams (0.66 pounds) for females and 350 grams (0.77 pounds) for males. Therefore, the total weight of an average man's brain and heart would be approximately 1.65 kilograms (3.63 pounds).

Arithmetic operations helps to determine the total amounts. Here, the total amount of paper, glass, and plastic waste not recovered is equals to the 5.363 × 10⁷ tons.

We have quantities of paper, glass and plastics in tons. See the table carefully present in above figure. The units used here is tons. For paper,

Generated paper quantity = 7.131 × 10⁷ tons

Recovered paper quantity= 4.457× 10⁷ tons

Generated glass quantity = 1.153 × 10⁷ tons

Recovered glass quantity= 0.313× 10⁷ tons

Generated plastics quantity = 3.104 × 10⁷ tons

Recovered plastics quantity= 0.255 × 10⁷ tons

We have to calculate total amount of paper, glass, and plastic waste not recovered. Now, for calculating waste amount we have to use substraction operation,

The amount of paper waste or not recovered = toatal generated amount of paper - recovered amount of paper

= 7.131 × 10⁷ tons - 4.457× 10⁷ tons

= 1.674×10⁷ tons

The amount of glass waste or not recovered = toatal generated amount of glass - recovered amount of glass

= 1.153 × 10⁷ tons - 0.313× 10⁷ tons

= 0.840×10⁷ tons

The amount of plastics waste or not recovered = toatal generated amount of plastics - recovered amount of plastics

= 3.104 × 10⁷ tons - 0.255 × 10⁷ tons

= 2.849×10⁷ tons

Total amount of paper, glass, and plastic waste not recovered = 1.674×10⁷ tons + 2.849×10⁷ tons + 0.840×10⁷ tons =5.363 × 10⁷ tons. Hence, required amount value is 5.363 × 10⁷ tons.

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Complete question:

The above figure completes the question.

What is the total amount of paper, glass, and plastic waste not recovered

The average score of Adrian’s favorite team relative to its opponent using the observations Adrian made during the game is -0.3333.

What is data set?

A data set is a group of related data. In the case of tabular data, a data set relates to one or more database tables, where each row refers to a specific record in the corresponding data set and each column to a specific variable.

Here, we have

Given: Adrian kept an eye on the basketball game score by looking online every 10 minutes. Over 2 hours, 4 times Adrian’s favorite team was ahead by 3 points, and 4 times Adrian’s favorite team was behind by 4 points. All the other times, the two teams were tied.

The mean of a data set is given by the sum of all observations divided by the number of observations.

Adrian looked at the scores every 10 minutes in 2 hours, thus 12 times, as

= (2×60)/10 = 12

4 times ahead by 3 points, thus 4×3 = 12

4 times behind by 4 points, thus -4×4 = -16

At the other moments, the game was tied, thus the observation is 0.

Thus, the mean is of:

M = (12 - 16 = 0)/12 = -4/12 = -0.333

Hence, The average score of Adrian’s favorite team relative to its opponent using the observations Adrian made during the game is -0.3333.

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a. The probability that exactly 125 km of track need to be tested before a defect is found is approx 0.005186, or about 0.52%,

b. Before a defect is discovered, 100 1-km segments of railroad track need to be tested.

a. To compute the probability that exactly 125 km of track need to be tested before a defect is found, we can use the geometric distribution. The geometric distribution models the number of independent and identically distributed trials needed to achieve the first success. In this case, a success is finding a defective 1-km segment of track.

The probability of finding a defect on any given 1-km segment is 0.01, so the probability of not finding a defect on any given segment is 0.99. Therefore, the probability of finding the first defect on the 125th 1-km segment tested is:

P(X = 125) = (0.99)^124 * 0.01

Where X is the number of 1-km segments tested before the first defect is found.

Using a calculator, we can evaluate this probability to be approximately 0.005186, or about 0.52%.

b. The expected value of the geometric distribution is given by:

E(X) = 1/p

Where p is the probability of success on any given trial. In this case, p = 0.01, so:

E(X) = 1/0.01 = 100

Therefore, on average, 100 1-km segments of railroad track need to be tested before a defect is found.

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The length of PRQ is 2, expressed as a fraction times .

A circle is a two-dimensional shape defined by the set of points on a plane which are equidistant from a fixed point known as the center. Circles are one of the most basic shapes in geometry, and they are found in nature, architecture, and many other areas. They have many properties, including a circumference, a diameter, a radius, and an area. Circles are used in mathematics, science, engineering, and other fields.

Let θ denote the central angle of the shaded sector. Then, the area of the shaded sector is
Area of shaded sector = (1/2)r²θ = 8
where r is the radius of the circle.
Therefore, r²θ = 16
Since OP = 8, the radius of the circle is 8. Hence,

r²θ = 16
(8)²θ = 16
θ = 16/64

Now, PRQ is an arc of the circle. Let s denote the length of the arc PRQ. Then,

s = θr = (16/64)8 = 2

Hence, the length of PRQ is 2, expressed as a fraction times .

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Answer:

42.6%

Step-by-step explanation:

Initial price of the iPhone = $938.99

Final price of the iPhone = $538.99

Decrese in price = $(938.99 - 538.99 )

= $ 400 .

We can calculate decrease in percentage by ,

= Decrease / Initial price * 100

= $400/938.99 * 100

= 42.59%

= 42.6% ( nearest tenth)

Hence the required answer is 42.6% .

The ratio of h:m:t in its simplest form is 15:12:8.To find the ratio of h:m:t, we need to use the given ratios h:m = 5:4 and m:t = 3:2 and simplify them to express them in terms of h, m, and t.

From the ratio h:m = 5:4, we can write:

m = (4/5)h

Similarly, from the ratio m:t = 3:2, we can write:

t = (2/3)m

Substituting the value of m from the first equation into the second equation, we get:

t = (2/3)(4/5)h

Simplifying this expression, we get:

t = (8/15)h

Therefore, the ratio of h:m:t can be expressed as:

h : m : t = h : (4/5)h : (8/15)h

Simplifying this ratio by multiplying all the terms by the least common multiple of the denominators (15), we get:

h : m : t = 15h : 12h : 8h

Simplifying further by dividing all the terms by the greatest common factor (h), we get:

h : m : t = 15 : 12 : 8

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The probability of winning the board game Monopoly is 32.5% if you move first. If you play 20 games of monopoly where you move first, the probability that you win at least 10 out of 20 times is 0.334.

          Monopoly is a game of chance where the probability of winning changes depending on the variables. When you move first in a game of Monopoly, the probability of winning is 32.5%. If you play 20 games of Monopoly where you move first, you need to determine the probability of winning at least ten games.

       We can determine this by using a binomial distribution. A binomial distribution is used to determine the probability of the number of successes or failures in a fixed number of independent trials.

The formula for the binomial distribution is:

      P(X=k) = C(n,k) * p^k * (1-p)^(n-k)

Where:

P(X=k) = probability of k successes
n = number of trials
k = number of successes
p = probability of success
(1-p) = probability of failure
C(n,k) = the number of combinations of n things taken k at a time.

Using this formula, we can determine the probability of winning at least ten games of Monopoly out of twenty. We need to find the probability of winning exactly ten games, eleven games, twelve games, and so on, up to twenty games. We can then add these probabilities together to get the probability of winning at least ten games.

     P(X>=10) = P(X=10) + P(X=11) + P(X=12) + ... + P(X=20)

     P(X=k) = C(20,k) * 0.325^k * 0.675^(20-k)

Therefore, the probability that you win at least 10 out of 20 times is:

         P(X>=10) = 0.334

    Hence, the answer is 0.334.

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The probability that something other than between 1 and 5 seconds will elapse between arrivals is 0.917.

There are three parts to this question. First, you need to know the arrival rate which is 15 cars per minute. Second, you need to know the probability of a car arriving between 1 and 5 seconds which is 0.083.

Third, you need to know the probability that something other than between 1 and 5 seconds will elapse between arrivals which can be calculated as follows:

P (something other than 1 to 5 seconds elapse) = 1 - P (1 to 5 seconds elapse)

P (1 to 5 seconds elapse) = 0.083

P (something other than 1 to 5 seconds elapse) = 1 - 0.083 = 0.917

Therefore, the probability that something other than between 1 and 5 seconds will elapse between arrivals is 0.917 .

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Answer:

22

Step-by-step explanation:

To find out how much the other pizzas cost you need to do 7-1 because that is the other 6 pizzas not including the 1st pizza. Then multiply 6 x 6 because that is the total cost for the other pizzas after the first pizza bought. This means that the pizzas cost 36 dollars without the first pizza. Then do 58-36 for the first pizza cost which is 22 dollars. Therefore the regular price of the first large pizza is 22 dollars. If you were to write it in slope intercept form it would be Y=6x+16 {x[tex]\geq[/tex]1} with Y representing the cost and x representing the pizza. You would need a domain as if you were to buy 0 pizza it wouldn't mean that it would cost you 16 dollar. Which is why you want the domain to be greater than or equal to 1 because if you bought 1 pizza it would cost 22 dollars

An experiment can show that all angles of a rectangle are equal and angles.

To verify experimentally that all angles of a rectangle are equal and right angles, you can perform the following steps:

Through these steps, you can verify experimentally that all angles of a rectangle are equal and right angles.

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Answer:

4 hours

Step-by-step explanation:

riding the bus. sidney rode on a bus for 2 1/4 hours + another 1 3/4 hours.

together, this is 4 hours.

Answer:

a₄₀=340

Step-by-step explanation:

Sₙ=[(a₁+aₙ)/2]*n

a₁=8 n=40 S₄₀=6960

S₄₀=[(a₁+a₄₀)/2]*40

6960=[(8+a₄₀)/2]*40   /:40

174=(8+a₄₀)/2   /*2

348=8+a₄₀

a₄₀=340