A proportional relationship exist between x and y. When x = 16 the value of y is 28. Write an equation for v in terms of x.

The correct answer is 'statement missing.'Causation refers to the relationship between an event and a possible cause that is inferred from the past events or historical records.

Statements of causation are one of the several types of causal relationships.Jewelers consider weight, cut grade, color, and clarity when pricing diamonds. In researching jewelry prices, Yvonne makes the following statements based on her observations.No statement has been given in the question.The given statements are missing.Therefore, it is impossible to determine the statements of causation.In simple words, no information has been given regarding any statement. Hence, the correct answer is 'statement missing.'

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To increase their win percentage from 70% to 80%, the basketball team needs to win a specific number of remaining games.

Let's first determine the number of games the team has won out of the 20 games played. Since they have won 70% of the games, we can calculate that as 0.7 * 20 = 14 games won.

Now, let's assume the team has to play 'x' remaining games to achieve an 80% win percentage. If they win all the remaining games, they will have a total of 20 + x games played and 14 + x games won.

To find the win percentage, we divide the total number of games won by the total number of games played and set it equal to 80% or 0.8:

(14 + x) / (20 + x) = 0.8

We can solve this equation to determine the value of 'x':

0.8 * (20 + x) = 14 + x

16 + 0.8x = 14 + x

0.8x - x = 14 - 16

0.2x = -2

x = -2 / 0.2

x = -10

Since we cannot have a negative number of remaining games, it is not possible for the team to increase their win percentage to 80% by winning all their remaining games.

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The volume of the given right rectangular prism is 0.0126 m³.

The volume of a right rectangular prism can be calculated using the formula:

V = l × w × h,

where l, w, and h are the dimensions of the prism.

The given dimensions of the right rectangular prism are 0.25m, 0.36m, and 0.14m.

Volume of the prism = l × w × h

= 0.25 × 0.36 × 0.14

= 0.0126 m³

Therefore, the volume of the prism is 0.0126 m³.

We have used the formula:

V = l × w × h to find out the volume of the prism.

This is because the given prism is a right rectangular prism.

The formula for finding the volume of a right rectangular prism is

V = l × w × h,

where l, w, and h are the dimensions of the prism.

A right rectangular prism is a three-dimensional figure with six rectangular faces.

It has three pairs of congruent faces that are parallel to each other.

The opposite faces of the right rectangular prism are identical in size and shape.

The right rectangular prism is a type of prism, which is a three-dimensional figure with two identical and parallel faces called bases.

A prism can be named by the shape of its base. In this case, the right rectangular prism has a rectangular base.

Conclusion: The volume of the given right rectangular prism is 0.0126 m³, which was found using the formula V = l × w × h.

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Using the equation E = hf, where f = 2.9 × 10^(-16) Hz and h = 6.63 × 10^(-34) J·s, the energy of the photon is approximately 1.9 × 10^(-49) J.

To calculate the energy of a photon, you can use the equation:

E = hf

where E is the energy of the photon, h is Planck's constant, and f is the frequency of the photon.

Given:

Frequency (f) = 2.9 × 10^(-16) Hz

Planck's constant (h) = 6.63 × 10^(-34) J·s

Now, substitute the values into the equation:

E = (6.63 × 10^(-34) J·s) × (2.9 × 10^(-16) Hz)

Multiply the values:

E = 1.9207 × 10^(-49) J

To the nearest tenths place, the energy of the photon is approximately 1.9 × 10^(-49) J.

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Once the check has cleared, Alli has $17.55 in her savings account. Finally, the amount of money Alli has in her savings account after the check has cleared is $25, so the answer is option A: $17.55.

Initial amount in Alli's checking account = $382.45

Initial amount in Alli's savings account = $450

Amount Alli withdrew from checking account = $400

Amount the bank withdrew from Alli's savings account = $25

Total cost of the check = 400+25

=425

Since the initial amount in her checking account was insufficient, the bank automatically withdrew $25 from her savings account to cover the cost of the check. This means that Alli has a total of $425 - $400 = $25 left in her savings account.After the withdrawal from her savings account, Alli's remaining savings balance is $450 - $25 = $425. However, she spent $400 to cover the check, so her final savings balance is $425 - $400 = $25.

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we would need a total of 5 buses to accommodate all the students and teachers on the trip.To determine the number of buses needed, we divide the total number of students and teachers by the capacity of each bus, which is 58 people.

238 students + 10 teachers = 248 people

To calculate the number of buses needed, we divide 248 people by 58 people per bus:

248 people ÷ 58 people/bus ≈ 4.276 buses

Since we cannot have a fraction of a bus, we round up to the nearest whole number. Therefore, we would need a total of 5 buses to accommodate all the students and teachers on the trip.

It's important to note that rounding up ensures that there are enough buses to accommodate all the individuals, even if there are some empty seats on each bus.

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If Vangs drives for 2 hours at a speed of 65 miles per hour, we can calculate how far he will be from Fort Worth. Vangs will be 125 miles away from Fort Worth.

Given that Vangs drives at a speed of 65 miles per hour for 2 hours, we can calculate the distance traveled using the formula Distance = Speed × Time.

Distance = 65 miles/hour × 2 hours = 130 miles.

Since Vangs started 185 miles away from Fort Worth and traveled a distance of 130 miles, we subtract the distance traveled from the initial distance to find how far he will be from Fort Worth.

Distance from Fort Worth = Initial distance - Distance traveled = 185 miles - 130 miles = 55 miles.

Therefore, Vangs will be 55 miles away from Fort Worth after driving for 2 hours at a speed of 65 miles per hour.

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If the sum of the fractions is less than 1, the denominator could be any number greater than 10. If the sum is equal to 1, the denominator must be 10. If the sum is greater than 1, the denominator must be less than 10.

To find a denominator that satisfies the given conditions, we can consider the fractions with numerators 8 and 2. If the sum of these fractions is less than 1, the denominator could be any number greater than 10. If the sum is equal to 1, the denominator must be 10. If the sum is greater than 1, the denominator must be less than 10.

To determine the possible denominators that satisfy the conditions, we need to consider the given numerators of 8 and 2. Since the fractions have the same denominator, let's denote it as 'd'. The fractions can be written as 8/d and 2/d.

If the sum of these fractions is less than 1, we have:

8/d + 2/d < 1

Combining the fractions, we get:

(8 + 2)/d < 1

Simplifying, we have:

10/d < 1

To satisfy this inequality, the denominator 'd' can be any number greater than 10. For example, if we choose d = 11, the fractions become 8/11 and 2/11, and their sum is 10/11, which is less than 1.

If the sum of the fractions is equal to 1, we have:

8/d + 2/d = 1

Combining the fractions, we get:

10/d = 1

Solving for 'd', we find that the denominator must be 10. For example, if we choose d = 10, the fractions become 8/10 and 2/10, and their sum is 10/10, which is equal to 1.

If the sum of the fractions is greater than 1, we have:

8/d + 2/d > 1

Combining the fractions, we get:

10/d > 1

To satisfy this inequality, the denominator 'd' must be less than 10. For example, if we choose d = 9, the fractions become 8/9 and 2/9, and their sum is 10/9, which is greater than 1.

In summary, if the sum of the fractions is less than 1, the denominator could be any number greater than 10. If the sum is equal to 1, the denominator must be 10. If the sum is greater than 1, the denominator must be less than 10.

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To calculate the perimeter, add the lengths of sides AB, BC, and AC. The area can be found using Heron's formula. To find the angles, use the law of cosines.

1. **Perimeter and area of triangle ABC**

To find the perimeter and area of triangle ABC, we need to use the given information about its sides and angles.

Let's assume that side AB has a length of "a", side BC has a length of "b", and side AC has a length of "c". The given angles are angle A, angle B, and angle C.

The perimeter of a triangle is the sum of the lengths of its sides. Therefore, the perimeter P of triangle ABC is given by: P = a + b + c.

To find the area of triangle ABC, we can use Heron's formula, which states that the area A of a triangle with side lengths "a", "b", and "c" is given by: A = √(s(s - a)(s - b)(s - c)), where s is the semi-perimeter of the triangle, given by: s = (a + b + c) / 2.

Once we have calculated the area, we can use the law of cosines to find the measures of the angles. The law of cosines states that for a triangle with side lengths "a", "b", and "c", and opposite angles A, B, and C, the following relationships hold:

cos(A) = (b^2 + c^2 - a^2) / (2bc)

cos(B) = (a^2 + c^2 - b^2) / (2ac)

cos(C) = (a^2 + b^2 - c^2) / (2ab)

Using these formulas, we can calculate the measures of the angles A, B, and C.

To find the exact values of the perimeter, area, and angles, we would need the specific lengths of the sides and the measures of the angles. Please provide those values, and I can assist you with the calculations.

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The answers are:Square root of 1/961 is 1/31Explanation:We can write the square root of 1/961 as √1/961. Simplifying this,

we get:√1/961=√1/√961=1/31Therefore, the main answer is 1/31.Square root of -361 is not real:As we know, the square root of a negative number is not real.

herefore, the square root of -361 is not real. Hence, the main answer is "not real".Square root of 625 is 25:We can write the square root of 625 as √625. Simplifying this, we get:√625=25Therefore, the main answer is 25.

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To determine Gunther's weight after 10 weeks, we can use a linear equation. Given that he plans to lose 2 pounds each week, we can represent his weight after 10 weeks as a linear function of time. Therefore, Gunther's weight after 10 weeks would be 268 pounds.

1. The equation would be: weight = starting weight - (rate of weight loss * number of weeks). Substituting the given values, we find Gunther's weight after 10 weeks.

2. Gunther's weight after 10 weeks can be determined using a linear equation. Let's denote Gunther's starting weight as W₀ and the rate of weight loss as R. Since he plans to lose 2 pounds each week, the rate of weight loss R is -2 (negative because it represents a decrease in weight).

3. The equation for Gunther's weight after 10 weeks would be: weight = W₀ - (R * number of weeks).

Substituting the given values, we have weight = 248 - (-2 * 10).

4. Simplifying further, weight = 248 + 20 = 268. Therefore, Gunther's weight after 10 weeks would be 268 pounds.

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250 pins would be knocked down.

In bowling, a single bowler would knock down all ten pins in every frame; thus, a total of 10 frames will result in 100 knocked down pins for each bowler. So, five bowlers each knocking down 100 pins would result in a total of 500 pins knocked down. Consequently,  all 50 pins would be knocked down in total (100 pins per bowler × 5 bowlers), which amounts to 250 knocked down pins.

Therefore, the main answer is 250 pins would be knocked down.

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The percent increase in iron content after the recipe change for the cereal is approximately 35.56%.

To calculate the percent increase in iron content, we need to find the difference between the new iron content (1.8 mg) and the original iron content (1.21 mg). The difference is 1.8 - 1.21 = 0.59 mg. Then, we divide this difference by the original iron content (1.21 mg) and multiply by 100 to get the percentage increase: (0.59 / 1.21) × 100 ≈ 35.56%.

This means that the iron content of the cereal increased by approximately 35.56% after the recipe change. To calculate the percent increase, we compare the difference between the new and original values to the original value. In this case, the original iron content was 1.21 mg, and the new iron content is 1.8 mg. The difference between these two values is 1.8 - 1.21 = 0.59 mg. To find the percentage increase, we divide this difference (0.59 mg) by the original value (1.21 mg) and multiply by 100.

The resulting value, 0.59 / 1.21 ≈ 0.4876, represents the proportion of increase. Multiplying it by 100 gives us the percentage increase, which is approximately 48.76%. Therefore, the iron content increased by approximately 48.76% after the recipe change.

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When trade barriers such as quotas and tariffs are removed between two nations, the most likely outcome is an increase in international trade and economic integration. Here are some key potential outcomes:

Increased Exports and Imports: Removal of trade barriers allows businesses in both nations to freely export and import goods and services, leading to an expansion of trade volume between the two countries. Economic Growth: Increased trade often leads to economic growth as businesses have access to larger markets, enabling them to increase production, create jobs, and generate more revenue. Consumer Benefits: Removal of trade barriers can result in greater consumer choice and lower prices. With increased competition from foreign markets, domestic industries may need to become more efficient and offer competitive prices and quality to attract customers.

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The regression equation is given asp = 0.02b + 2366Where, p is the profit in dollars and b is the number of bulbs sold. It can be seen that the coefficient of b is 0.02 i.e., the profit per bulb is $0.02.

The problem states that the profit required is $3000, therefore,3000 = 0.02b + 2366b = (3000 - 2366)/0.02b = 31700Therefore, approximately 31,700 bulbs need to be sold to make a profit of $3000.The profit margin for Larry's Light Bulbs in 2006 can be determined using the regression equation p = 0.02b + 2366, where p is the profit in dollars and b is the number of bulbs sold. The coefficient of b is 0.02, which implies that the profit per bulb is $0.02.Let us assume that Larry's Light Bulbs requires a profit of $3000. This means that p = 3000. Using the regression equation, we get,3000 = 0.02b + 2366Solving for b, we get,b = (3000 - 2366)/0.02b = 31700Therefore, approximately 31,700 bulbs need to be sold to make a profit of $3000.Hence, option A, i.e., 32,000 is the closest option to the answer. Thus, the correct option is A, i.e., 32,000.

The regression equation p = 0.02b + 2366, where p is the profit in dollars and b is the number of bulbs sold is given. The profit required is $3000. The profit per bulb is $0.02. Therefore, approximately 31,700 bulbs need to be sold to make a profit of $3000. Since 31,700 is the closest option to 32,000, option A is the correct answer.

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There are 32 ounces are in a quart

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

128 ounces in a gallon

Also, we have

4 quart in a gallon

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

128 ounces = 4 quart

Divide both sides by 4

So, we have

32 ounces = 1 quart

Hence, there are 32 ounces are in a quart

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It is percentage decrease by 43 percent.

Given that, the original cost of item = $175.00 and the sale price of item = $99.75.

Percentage increase or decrease = (Original Price - Sale Price)/Original Price ×100

= (175.00-99.75)/175.00 ×100

= 75.25/175.00 ×100

= 0.43×100

= 43%

Therefore, it is percentage decrease by 43 percent.

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The value of function at x = 36 is 34.12.

To find the cost of mailing an object that weighs 36 pounds, we can substitute the value of x into the function f(x) = 5.32 + 0.80x.

The function f(x) = 5.32 + 0.80x represents a linear relationship between the weight of the object (x) and the cost (f(x)) with a base cost of $5.32 and an additional cost of $0.80 per pound. By plugging in the value of 36 into the function, we can calculate the specific cost for that weight.

Plugging in x = 36, we have:

f(36) = 5.32 + 0.80 * 36

Simplifying the expression:

f(36) = 5.32 + 28.8

f(36) = 34.12

Therefore, f(36) is equal to 34.12. This means that it would cost $34.12 to mail an object weighing 36 pounds according to the given function.

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The correct arrangement is 4.5%, 0.3, and 1/7.

To order the percent, decimal, and fraction from least to greatest, we need to find the appropriate value for each of the blanks using the numbers 0-7 exactly once.

Starting with the percent, we can see that 4.5% is the smallest possible value. Moving to the decimal, 0.3 is the next smallest value. Finally, for the fraction, the only remaining option is 1/7.

Therefore, the correct arrangement from least to greatest is 4.5%, 0.3, and 1/7.

It's important to note that the order may not be unique since there could be other valid combinations using the numbers 0-7. However, based on the given information, 4.5% is the smallest, followed by 0.3, and then 1/7.

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The height is equal to the radius, the height of the cone to the nearest tenth of a centimetre is 14.98 cm. A cone with equal height and radius has volume 1234 cm³. To find the height of the cone, we will use the formula for the volume of a cone: V = 1/3πr²h

A cone with equal height and radius has volume 1234 cm³. To find the height of the cone, we will use the formula for the volume of a cone: V = 1/3πr²h

where: V is the volume of the cone, π is pi (3.14), r is the radius of the cone, h is the height of the cone

We are given that the height and radius of the cone are equal, so we can substitute r for h. Also, we know the volume of the cone is 1234 cm³. So:

1234 = 1/3πr²h

1234 = 1/3πr²(r)

1234 = 1/3πr³ (since r = h)

Now we can solve for r: 1234 * 3 / π = r³

3747.22 = r³

r ≈ 14.98 cm

Since the height is equal to the radius, the height of the cone to the nearest tenth of a centimetre is 14.98 cm.

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The given equation is I = -2OD where I is the intensity of light, O is the aperture of the lens and D is the distance between the lens and the object. This equation is known as the Inverse Square Law of Light.

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"t" is the independent variable representing the number of minutes since Willie started firing the retro-rocket, while "d" is the dependent variable representing the distance from the surface of Mars

The independent variable "t" represents the number of minutes since Willie started firing the retro-rocket. It is the variable that Willie has control over and chooses to manipulate. By changing the value of "t," Willie can observe how it affects the dependent variable "d," which is the distance from the surface of Mars. The independent variable is typically the input or the cause in a relationship or function.

On the other hand, the dependent variable "d" represents the distance from the surface of Mars. It depends on the value of "t" and is influenced by the independent variable. As Willie changes the number of minutes, the distance "d" changes accordingly. The dependent variable is usually the output or the effect in a relationship or function.

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To calculate Stephanie Ambrose's annual base premium, we need to sum up the costs of her bodily injury, property damage, comprehensive, and collision insurance.

Given that the bodily injury limits are $100/300 and the property damage limits are $100,000, we can calculate the cost of bodily injury and property damage insurance. The cost for bodily injury insurance is $100 for every $100,000 of coverage, and the cost for property damage insurance is $100 for every $100,000 of coverage.

For bodily injury insurance, the cost is calculated as:

(100/300) * 100 = $33.33

For property damage insurance, the cost is:

(100,000/100,000) * 100 = $100

Adding up the costs of bodily injury, property damage, comprehensive, and collision insurance:

Base premium: $292.50

Comprehensive insurance: $75.90

Collision insurance: $225.79

Bodily injury insurance: $33.33

Property damage insurance: $100

Total annual base premium = Base premium + Comprehensive insurance + Collision insurance + Bodily injury insurance + Property damage insurance

Total annual base premium = $292.50 + $75.90 + $225.79 + $33.33 + $100 = $727.52

Therefore, Stephanie Ambrose's annual base premium is $727.52.

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Therefore, Janine spends 4/5 of an hour doing these activities.

To determine the fraction of an hour that Janine spends doing the given activities, we need to convert the given times to fractions of an hour. We know that 1 hour is equivalent to 1 whole, which means that half an hour would be equivalent to half of a whole.

Similarly, one-fifth of an hour would be equivalent to 1 ÷ 5, which is 0.2, and one-tenth of an hour would be equivalent to 1 ÷ 10, which is 0.1.

Now, let's add the three times together to find the total time:

1/10 hour making the bed + 1/5 hour getting dressed + 1/2 hour eating breakfast = 1/10 + 2/10 + 5/10= 8/10 (which can be simplified to 4/5).

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The area is then calculated as (1/2) * base * height, resulting in approximately 39.375 square feet.

To find the area of the actual banner, we need to scale up the dimensions from the drawing to real-world measurements. We are given that 1 inch on the drawing is equivalent to 1.5 feet on the actual banner.

The base of the triangle on the drawing is 5 inches, so the base of the actual triangle will be:

5 inches * 1.5 feet/inch = 7.5 feet

Similarly, the height of the actual triangle will be:

7 inches * 1.5 feet/inch = 10.5 feet

Now that we have the base and height of the actual triangle, we can calculate its area using the formula for the area of a triangle:

Area = (1/2) * base * height

Area = (1/2) * 7.5 feet * 10.5 feet

Area ≈ 39.375 square feet

Therefore, the area of the actual banner will be approximately 39.375 square feet.

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Let's represent the amount of money Justin has as [tex]\(x\).[/tex]

According to the given information, Trey has 3 times what Justin has, so Trey has [tex]\(3x\)[/tex] dollars.

Leila has 10 dollars more than Justin, so she has [tex]\(x + 10\)[/tex] dollars.

The sum of the amounts of money they have is 125 dollars:

[tex]\(x + 3x + (x + 10) = 125\)[/tex]

Combining like terms, we have:

[tex]\(5x + 10 = 125\)[/tex]

Subtracting 10 from both sides:

[tex]\(5x = 115\)[/tex]

Dividing both sides by 5:

[tex]\(x = 23\)[/tex]

So Justin has 23 dollars.

Trey has 3 times that amount:

[tex]\(3 \times 23 = 69\)[/tex]

Leila has 10 dollars more than Justin:

[tex]\(23 + 10 = 33\)[/tex]

Therefore, Justin has 23 dollars, Trey has 69 dollars, and Leila has 33 dollars.

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The probability of selecting a pediatrician or a cardiologist at a medical convention can be found by adding the probabilities of selecting each. The probability is 12/19 or approximately 0.63.

The total number of participants at the medical convention is 7 + 5 + 3 + 4 = 19.

The probability of selecting a pediatrician is 7/19, since there are 7 pediatricians out of 19 participants.

The probability of selecting a cardiologist is 5/19, since there are 5 cardiologists out of 19 participants.

Since we are looking for the probability of selecting a pediatrician or a cardiologist, we can add these probabilities together:

P(pediatrician or cardiologist) = P(pediatrician) + P(cardiologist)

P(pediatrician or cardiologist) = 7/19 + 5/19

P(pediatrician or cardiologist) = 12/19

Therefore, the probability of selecting a pediatrician or a cardiologist is 12/19, or approximately 0.63 (rounded to two decimal places).

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The correct polynomial product is indeed Option B: 6y^3 + 17y^2 + 22y + 15.

Let's break down the options to see why Option B is correct:

Option A: 15y^3 + 17y^2 + 22y + 15

This option does not match the given product as it includes an additional term, 15y^3, that is not present in the correct polynomial product.

Option B: 6y^3 + 17y^2 + 22y + 15

This option matches the given polynomial product exactly. It includes all the terms and coefficients mentioned: 6y^3, 17y^2, 22y, and 15.

Option C: 6y^3 + 20y^2 + 22y + 15

This option differs from the correct product in the coefficient of the second term. It includes 20y^2 instead of 17y^2.

Option D: 6y^3 + 17y^2 + 22y + 25

This option differs from the correct product in the coefficient of the last term. It includes 25 instead of 15.

Therefore, Option B, 6y^3 + 17y^2 + 22y + 15, is the correct polynomial product based on the given information.

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(a) The road distance between Wrexham and Oswestry is 15 miles.

(b) The number of miles Sarah travels to and from work each week is 330 miles.

Given a chart of the road distances between various towns and cities.

(a) From the chart,

Distance the corresponds to Wrexham and Oswestry = 15 miles

Road distance between Wrexham and Oswestry is 15 miles.

(b) Distance between Ruthin and Oswestry = 33 miles

Total distance travelled to and from work in a day = 33 × 2 = 66 miles

She works 5 days a week.

Total distance travelled for 5 days = 66 × 5 = 330 miles

Hence, the number of miles travelled by Sarah in a week is 330 miles.

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The chart is given below.

"Your question is incomplete, probably the complete question/missing part is:"

The chart shows the distances, in miles, between some towns and cities.

Toby lives in Wrexham and works in Oswestry.

Wrexham

18

Ruthin

a) Use the chart to find the road distance

between Wrexham and Oswestry.

15

21

12

Corwen

15

33

23

Oswestry

Sarah lives in Ruthin and works in Oswestry for

5 days a week. Each day she travels to and

from work using the route shown on the map.

MOLD

ROTHEN

WRESTHAM

b) How many miles, in total, does she travel to

and from work each week? 231 miles

CORNEN

OSWESTRY

Choose CI​

Based on Amadou's measurements, the height of the skyscraper is approximately 97.2 meters.

Amadou measures the angle of elevation from his eye to the top of the skyscraper as 44 degrees. To determine the height of the skyscraper, we can use trigonometry. The tangent of an angle is defined as the ratio of the opposite side to the adjacent side.

In this case, the opposite side represents the height of the skyscraper, and the adjacent side represents the horizontal distance from Amadou to the base of the skyscraper. We are given that the adjacent side is 164 meters and the angle of elevation is 44 degrees.

Using the tangent function, we can set up the following equation:

tan(44 degrees) = height of skyscraper / 164 meters

To solve for the height of the skyscraper, we rearrange the equation:

height of skyscraper = tan(44 degrees) * 164 meters

Using a scientific calculator or trigonometric table, we find that tan(44 degrees) is approximately 0.9659. Multiplying this value by 164 meters gives us the height of the skyscraper:

height of skyscraper ≈ 0.9659 * 164 meters ≈ 97.2 meters

Therefore, based on Amadou's measurements, the height of the skyscraper is approximately 97.2 meters.

Learn more about angle of elevation:

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