Sam’s brother is 4 years older than him. Their mother is 3 times older than Sam. Their ages together total 74 years. How old are the family members?

Right triangle, the hypotenuse is the longest side and is opposite the right angle. The length of the hypotenuse of the right triangle is approximately 31.6 in.

In a right triangle, the hypotenuse is the longest side and is opposite the right angle. To find the length of the hypotenuse, we can use the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the two legs.

Let's denote the length of the legs as a = 18 in and b = 26 in. The Pythagorean theorem can be written as:

c^2 = a^2 + b^2

Substituting the values, we have:

c^2 = 18^2 + 26^2

= 324 + 676

= 1000

Taking the square root of both sides, we find:

c = √1000

≈ 31.6

Therefore, the length of the hypotenuse is approximately 31.6 in, rounded to the nearest tenth.

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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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The daily revenue (R) is given by R = 4.15x, and the daily cost (C) is given by C = 3.20x + 798, where x is the number of scoops served in a day.

In more detail, the given equations represent a linear relationship between the number of scoops served (x) and both the revenue (R) and cost (C). The coefficient of x in the revenue equation, 4.15, represents the revenue generated per scoop served. Similarly, the coefficient of x in the cost equation, 3.20, represents the cost incurred per scoop served. The constant term 798 in the cost equation represents additional fixed costs.

To determine the daily profit, we can subtract the cost from the revenue: Profit = R - C = 4.15x - (3.20x + 798) = 0.95x - 798. This equation allows us to calculate the profit based on the number of scoops served.

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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 correct inequality that shows Annika's spending in terms of h is 35h + 180 ≤ 400.To express Annika's spending in terms of h, the number of hours the DJ can be at the party, we can set up an inequality by considering the total cost.

Let's represent Annika's spending on the DJ as 35h, where h is the number of hours. Additionally, we know Annika plans to spend $180 on decorations. Therefore, the total cost should be no more than $400.

The inequality can be written as:

35h + 180 ≤ 400

This inequality states that the cost of hiring the DJ (35h) plus the cost of decorations ($180) should be less than or equal to $400.

Therefore, the correct inequality that shows Annika's spending in terms of h is 35h + 180 ≤ 400.

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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.

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To find the amount of the payment that goes towards interest at the 12th payment, you should multiply the balance at the 12th payment by the interest rate which is 8%.

The balance of the loan after 12 payments is $4159.90.

Thus the amount of the payment that goes towards interest at the 12th payment is:

4159.90 × 0.08 = $332.79

The principal amount paid at the 12th payment is the difference between the monthly payment of $187.80 and the amount of interest paid of $332.79.

The principal amount paid at the 12th payment

= $187.80 − $332.79

= −$144.99

The negative answer means that the amount paid is the interest.

To find the balance of the loan after the 35th payment, we will subtract the monthly payment from the balance after the 34th payment.

Therefore, the balance of the loan after the 35th payment is:

380.60 − 187.80 = $192.80

To find the amount of the payment that goes towards interest at the 35th payment, you should multiply the balance at the 35th payment by the interest rate which is 8%.

The balance after the 34th payment is $380.60, so the interest payment at the 35th payment is:

380.60 × 0.08 = $30.44

The principal amount paid at the 35th payment is the difference between the monthly payment of $187.80 and the amount of interest paid of $30.44.

The principal amount paid at the 35th payment

= $187.80 − $30.44

= $157.36

Therefore, the balance of the loan after the 35th payment is:

192.80 − 157.36 = $35.44.

The balance of the loan after the 35th payment is $35.44.

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The sum of the geometric series with 12 terms, starting from 10 and with a common ratio of 2, is 40,950.

To find the sum of a geometric series, we can use the formula:

S = a * (1 - r^n) / (1 - r)

Where:

S is the sum of the series,

a is the first term of the series,

r is the common ratio,

n is the number of terms in the series.

In this case, the first term (a) is 10, the common ratio (r) is 2, and the number of terms (n) is 12.

Plugging in the values into the formula, we have:

S = 10 * (1 - 2^12) / (1 - 2)

Simplifying further:

S = 10 * (1 - 4096) / (1 - 2)

S = 10 * (-4095) / (-1)

S = 10 * 4095

S = 40,950

Therefore, the sum of the geometric series with 12 terms, starting from 10 and with a common ratio of 2, is 40,950.

The correct answer is D) 40,950.

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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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"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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1/10 of the baker's total cost for 100 pounds of chocolate sprinkles is 10x dollars.

To find 1/10 of the baker's total cost for 100 pounds of chocolate sprinkles, we need to determine the cost per pound of chocolate sprinkles.

Let's assume the cost per pound of chocolate sprinkles is 'x' dollars.

Since it is mentioned that chocolate sprinkles cost as much per pound as sugar, we can assume that the cost per pound of sugar is also 'x' dollars.

Now, let's calculate the total cost for 100 pounds of chocolate sprinkles:

Total cost = Cost per pound * Number of pounds

Total cost = x * 100

Total cost = 100x dollars

To find 1/10 of the total cost, we multiply the total cost by 1/10:

1/10 of total cost = (1/10) * (100x)

1/10 of total cost = 10x

Therefore, 1/10 of the baker's total cost for 100 pounds of chocolate sprinkles is 10x dollars.

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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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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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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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The value of the variables for which ABCD must be a parallelogram include the following:

x = 4.

y = 5.

In order for any quadrilateral to be considered as a parallelogram, two pairs of its parallel sides must be equal (congruent). This ultimately implies that, the diagonals of a parallelogram would bisect one another only when their midpoints are the same:

Line segment AC = Line segment BD

Next, we would write an equation to model the length of the diagonals of this parallelogram as follows;

4x - 2 = 3y - 1  .........equation 1.

3y - 3 = 3x       .........equation 2.

From equation 2, we have the following:

y - 1 = x       .........equation 3.

By substituting equation 3 into equation 1, we have:

4(y - 1) - 2 = 3y - 1

4y - 4 - 2 = 3y - 1

4y - 3y = 6 - 1

y = 5.

For the value of x, we have:

x = y - 1

x = 5 - 1

x = 4

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Complete Question:

Find values of x and y for which ABCD must be a parallelogram.

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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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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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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Tommy walks 2 miles to school each morning, and he sees a billboard every 1/5 of a mile.

To find out how many billboards he sees, we can divide the total distance he walks (2 miles) by the distance between each billboard (1/5 of a mile).

Number of billboards = Total distance / Distance between billboards

= 2 miles / (1/5 mile)

= 2 miles * (5/1)

= 10 billboards

Therefore, Tommy sees 10 billboards each morning.

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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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He travels: (i) C is 4 km north of A. (ii) C is 6 km east of A.

(i) North of A:

The northward component from A to B is 8 km on a bearing of N30°E. To find the northward distance, we can use trigonometry. Since the bearing is N30°E, we can split it into two right-angled triangles: one facing north and one facing east.

In the northward triangle:

Opposite side = 8 km * sin(30°)

Opposite side = 8 km * 0.5

Opposite side = 4 km

Therefore, C is 4 km north of A.

(ii) East of A:

The eastward component from B to C is 6 km due East. Since this distance is directly east, it does not change the eastward position of C relative to A. Therefore, C is 6 km east of A.

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The solution to the system of equations is (x, y) = (2, 1).

Given equations are,1. 1/4x + 1/2y = 5/82. 3/4x - 1/2y = 27/8 - 3/8

Now we will solve these two equations by elimination method:

Multiplying equation 1 by 3 and equation 2 by 2,3/4x + 3/2y = 15/8  -------------- (3)

3/2x - y = 6/8 -------------- (4)

Simplifying equation 3,3/4x + 3/2y = 15/8 -------------- (5)

Multiplying equation 4 by 3,4.5x - 3y = 3 -------------- (6)

Now, we will add equation 5 and equation 6,

3/4x + 3/2y = 15/8 -------------- (5)

4.5x - 3y = 3 -------------- (6)

______________15/4x + 0y = 39/8

Therefore, x = 2.Now, substituting x=2 in equation 4,3/2(2) - y = 6/8-3y = -3/8

Therefore, y = 1.

Hence, the solution to the system of equations is (x, y) = (2, 1).

We are given 2 equations as follows:1/4x + 1/2y = 5/8 ...(i)3/4x - 1/2y = 27/8 - 3/8 ...(ii)

Multiplying equation (i) by 3 and equation (ii) by 2,3/4x + 3/2y = 15/8...(iii)3/2x - y = 6/8 ...(iv)We can write equation (iii) as follows: y = (3/2x - 6/8)/-1 = 3/2x - 6/8Now we substitute this value of y in equation (i)1/4x + 1/2(3/2x - 6/8) = 5/8Simplifying,3/4x - 3/8 = 5/8 => 3/4x = 5/8 + 3/8 => 3/4x = 1 => x = 4/3

Now we substitute this value of x in equation (iv):y = 3/2(4/3) - 6/8 = 2/1 = 2

Therefore, the solution to the system of equations is (x, y) = (4/3, 2).

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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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The correct statement is given as follows:

The can of pringles has a z-score close to zero, which means it's more likely to happen.

The z-score formula is given as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

In which:

The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, and can be positive(above the mean) or negative(below the mean).

The z-score table is used to obtain the p-value of the z-score, and it represents the percentile of the measure represented by X in the distribution.

The z-score for pretzels is given as follows:

Z = (25 - 23)/1.2

Z = 1.67.

The z-score for pringles is given as follows:

Z = (40 - 34)/4

Z = 1.5. -> closer to zero -> more likely to happen.

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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 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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7,875 lbs.

Old furniture weighs = 1,123 lbs.

Combined weight of furniture and truck = 8,122 lbs.

New items = 876 lbs.

First, subtract the weight of the old furniture from the combined weight:

8,122 lbs - 1,123 lbs. = 6,999 lbs.

Then, add the weight of the new items:

6,999 lbs + 876 lbs. = 7,875 lbs.

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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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​