The reed family bought a case of Apples. Paula ate 3/10 of the apples. Kyle ate 21% of the apples. Wendy ate 0.34 of the apples,and Ron ate the rest. What percent of the apples did Ron eat?

To create a 40 L solution with a 45% acid concentration, a chemist combines a 25% acid solution and a 50% acid solution. Therefore, the chemist used 32 L of the 50% acid solution and (40 - 32) = 8 L of the 25% acid solution to create the 40 L solution with a 45% acid concentration.

Let's assume the chemist uses "x" liters of the 50% acid solution. Since the total volume of the mixture is 40 L, the remaining volume will be (40 - x) liters of the 25% acid solution.

The acid content in the 50% solution is 0.5x, while the acid content in the 25% solution is 0.25(40 - x).

To find the acid content in the final 45% solution, we multiply the acid concentration (0.45) by the total volume (40):

0.45 * 40 = 0.5x + 0.25(40 - x)

Simplifying the equation:

18 = 0.5x + 10 - 0.25x

Combining like terms:

0.25x = 8

Dividing both sides by 0.25:

x = 32

Therefore, the chemist used 32 L of the 50% acid solution and (40 - 32) = 8 L of the 25% acid solution to create the 40 L solution with a 45% acid concentration.

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When working together, it will take Angela and Brandon about 3 hours and 12 minutes to paint the school rock.

The answer is 3

Let's first assume that Angela can paint the school rock in x hours, then Brandon would be able to paint the school rock in y hours.Angela’s work rate: \frac{1}{x} of the rock per hour .

So, Angela’s work rate = [tex]$\frac{1}{5.5}$[/tex]and Brandon’s work rate = \frac{1}{7} Working together, Angela and Brandon’s work rate will be: \frac{1}{5.5} + \frac{1}{7} of the rock per hour [tex]$\frac{1}{5.5} + \frac{1}{7}$ = $\frac{0.1818 + 0.1429}{1}$ = $\frac{0.3247}{1}$[/tex] Working together, they will paint the rock in \frac{1}{0.3247} hours = 3.08 hours. Rounding off to the nearest minute, it will take them about 3 hours and 12 minutes .

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The selling price for Calvin's badminton kit, with a desired profit of 25%, is ₹450.

To determine the selling price for Calvin's badminton kit, including a desired profit of 25%, we need to calculate the cost price and add the profit margin.

The cost price of the badminton kit consists of two rackets worth ₹140 each and a shuttlecock worth ₹80. Let's calculate the total cost price:

Cost Price = (2 * ₹140) + ₹80 = ₹280 + ₹80 = ₹360

To find the selling price with a 25% profit margin, we need to add 25% of the cost price to the cost price:

Profit = 25% of ₹360 = (25/100) * ₹360 = ₹90

Selling Price = Cost Price + Profit = ₹360 + ₹90 = ₹450

Therefore, the selling price for Calvin's badminton kit, with a desired profit of 25%, is ₹450.

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To find which fractions are equivalent, we need to simplify each fraction. the fractions that are equivalent are 12/24 and 1/2.

The fractions 26/12 and 14/36 cannot be simplified since both already are in their simplest form. Hence 26/12 and 14/36 are not equivalent.14 and 36The fractions 26/12 and 14/36 cannot be simplified since both already are in their simplest form. Hence 26/12 and 14/36 are not equivalent.26 and 14The fractions 26/12 and 14/36 cannot be simplified since both already are in their simplest form.

Two fractions are equivalent if they represent the same part of a whole. To find which fractions are equivalent, we can simplify each fraction by dividing the numerator and denominator by their greatest common factor. The simplified fractions will represent the same part of a whole as the original fraction and will be equivalent fractions.

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1. Vertical stretch: f(x) = 2(2x-4)

2. Horizontal stretch: f(x) = 2(x/2-4)

3. Vertical shift up: f(x) = 2x-4+3

4. Vertical shift down: f(x) = 2x-4-3

1. Vertical stretch: To vertically stretch the function, we multiply the function by a constant outside the parentheses. In this case, multiplying f(x) by 2 results in f(x) = 2(2x-4).

2. Horizontal stretch: To horizontally stretch the function, we divide the input variable (x) by a constant inside the parentheses. In this case, dividing x by 2 gives us f(x) = 2(x/2-4).

3. Vertical shift up: To vertically shift the function upward, we add a constant to the function. Adding 3 to f(x) results in f(x) = 2x-4+3.

4. Vertical shift down: To vertically shift the function downward, we subtract a constant from the function. Subtracting 3 from f(x) gives us f(x) = 2x-4-3.

These transformations modify the original function f(x)=2x-4 in different ways, stretching it vertically, horizontally, and shifting it vertically up or down.

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The result of dividing [tex]x^3 - 3x^2 - 10x + 24[/tex] by [tex]x - 2[/tex] is [tex]x^2 + 2x - 6[/tex] with a remainder of 12.

To divide the polynomial [tex]x^3 -3x^2 - 10x + 24[/tex] by x - 2, we can use polynomial long division.

Write the polynomial in descending order of powers of x, filling in missing terms with zeros.

[tex]x^3 - 3x^2 - 10x + 24[/tex] becomes[tex]x^3 + 0x^2 - 3x^2 - 10x + 24[/tex].

Divide the first term of the dividend (x^3) by the first term of the divisor (x) to get the quotient.

The quotient is x^2.

Multiply the divisor [tex](x - 2)[/tex] by the quotient [tex](x^2)[/tex] and write the result below the dividend.

[tex](x - 2) \times (x^2) = x^3 - 2x^2[/tex].

Subtract the result from the dividend.

[tex]x^3 + 0x^2 - 3x^2 - 10x + 24 - (x^3 - 2x^2) = 2x^2 - 10x + 24[/tex].

Bring down the next term from the dividend, which is -10x.

Repeat steps 2-5 with the new dividend [tex](2x^2 - 10x + 24)[/tex].

Divide the first term of the new dividend [tex](2x^2)[/tex] by the first term of the divisor (x) to get the next term of the quotient.

The next term of the quotient is 2x.

Multiply the divisor (x - 2) by the new term of the quotient (2x) and write the result below the new dividend.

[tex](x - 2) \times (2x) = 2x^2 - 4x[/tex]

Subtract the result from the new dividend.

[tex]2x^2 - 10x + 24 - (2x^2 - 4x) = -6x + 24[/tex].

Bring down the last term from the new dividend, which is 24.

Repeat steps 2-5 with the new dividend [tex](-6x + 24)[/tex].

Divide the first term of the new dividend (-6x) by the first term of the divisor (x) to get the final term of the quotient.

The final term of the quotient is -6.

Multiply the divisor [tex](x - 2)[/tex] by the final term of the quotient (-6) and write the result below the new dividend.

[tex](x - 2) \times (-6) = -6x + 12[/tex].

Subtract the result from the new dividend.

[tex]-6x + 24 - (-6x + 12) = 12[/tex].

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The side lengt of the square is approximately 1839 feet.

To find the length in feet of the side of a square with an area of 1.00 acre, we need to convert the acreage to square feet.

Given:

1 acre = 640 acres/mile² (640 acres in a square mile)

1 mile = 5280 feet (conversion factor from miles to feet)

To convert acres to square feet, we can multiply by the conversion factor:

1 acre = 640 acres/mile² * 1 mile² * 5280 feet

Simplifying the units:

1 acre = 640 * 5280 square feet

Now, to find the length of the side of the square, we can take the square root of the area:

Side length = √(1 acre * 640 * 5280 square feet)

Calculating:

Side length ≈ √(1 * 640 * 5280) ≈ √3379200 ≈ 1839.29 feet

Rounding to the nearest foot, the length of the side of the square with an area of 1.00 acre is approximately 1839 feet.

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The volume of the right circular cone with a height of 13.8ft and a base radius of 7.8ft is approximately 672.59 cubic feet.

1. The formula for the volume of a right circular cone is V = (1/3)πr²h, where V represents the volume, π is a mathematical constant (approximately 3.14159), r is the radius of the base, and h is the height of the cone.

2. Plug in the given values into the formula: V = (1/3)π(7.8ft)²(13.8ft).

3. Calculate the volume: V = (1/3)π(60.84ft²)(13.8ft).

4. Simplify the expression: V ≈ 7.484π(13.8ft).

5. Use the approximation π ≈ 3.14159: V ≈ 7.484(3.14159)(13.8ft).

6. Calculate the volume: V ≈ 293.48ft³.

7. Round the result to two decimal places: V ≈ 672.59 cubic feet.

Therefore, the volume of the given right circular cone is approximately 672.59 cubic feet.

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Therefore, the answer rounding to the nearest tenth is d. 5.3.

To convert 1 gallon to liters, we multiply by the conversion factor of 3.79 L/gal.

1 gal. * 3.79 L/gal = 3.79 L

Now, to find the equivalent of 20 liters, we can set up a proportion:

1 gal / 3.79 L = x gal / 20 L

Cross-multiplying and solving for x, we get:

x = (1 gal / 3.79 L) * 20 L = 20 / 3.79 gal

Rounding to the nearest tenth, we have:

x ≈ 5.3

Therefore, the answer is d. 5.3.

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Emily can walk 3/4 of a mile in 1/4 of an hour. At the same rate, time taken to walk 1 mile =1/3 of an hour.

Mathematical representation

We know that, Emily can walk 3/4 of a mile in 1/4 of an hour.

Meaning,

Time taken to walk 3/4 of a mile = 1/4 of an hour

Distance covered = 3/4 mile

We need to find the time taken by Emily to walk 1 mile.

The rate is defined as the distance covered in unit time. So,

                        Rate = Distance / Time

We know that Rate of Emily = 3/4 ÷ 1/4

                                              = 3/4 × 4/1

                                              = 3 miles/hour

The rate of walking is 3 miles/hour.

Now we can find the time taken to walk 1 mile using rate formula.

             Distance = Rate × Time

We have to walk 1 mile and the rate of walking is 3 miles/hour.

             Time = Distance / Rate

Time taken to walk 1 mile = 1 / 3 = 1/3 hour.

So, the answer is option C.

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The fraction that shows how the height of Elijah's and Riley's game pieces are related is 4/7.

The model that shows how the height of the game pieces are related is a fraction. Elijah's game piece, the dragon, is about 1 2 inch tall, and Riley's game piece, the cat, is about 7 8 inch tall.

To represent this situation using a fraction, the numerator of the fraction is the height of the dragon, and the denominator is the height of the cat.

Therefore, the fraction that shows how the heights of the game pieces are related is:1/2 ÷ 7/8To divide fractions, we multiply by the reciprocal of the divisor, which is flipping the divisor over so that the denominator becomes the numerator and the numerator becomes the denominator.

Hence,1/2 ÷ 7/8 = 1/2 x 8/7 = 8/14 = 4/7

Thus, the fraction that shows how the heights of Elijah's and Riley's game pieces are related is 4/7.

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The two villages are approximately 225 kilometers apart.

The scale on the map is given as 1:250000, which means that 1 unit on the map represents 250,000 units in reality.

If the distance between the villages on the map is 9 cm, we can set up the following proportion:

1 cm / 250,000 km = 9 cm / x km

Cross-multiplying, we have:

1 * x km = 9 cm * 250,000 km

x km = 2,250,000 km / 1 cm

Simplifying the expression, we find:

x km = 225 km

Therefore, the two villages are approximately 225 kilometers apart.

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I agree with Rita. Jeremy is incorrect in claiming that there is only one possible additional rope length for Rita to form a triangle.

To form a triangle, the sum of the lengths of any two sides must be greater than the length of the third side. In this case, Rita has two rope lengths of 9 feet and 1 foot. For a triangle to be formed, the sum of the two shorter sides must be greater than the longest side. However, in this case, 1 foot + 9 feet is greater than 9 feet, which satisfies the triangle inequality. Therefore, Rita can form a triangle with these two rope lengths.

Rita's disagreement is valid as there are multiple possible additional rope lengths she can obtain to form a triangle, not just one.

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Cindy has scores of 72, 82, 83 and 89 on her Biology tests. Cindy must score between 68 and 89 on her final exam to earn a C in Biology.

Cindy's current average score in Biology is:

(72 + 82 + 83 + 89) / 4 = 81.5

Since the final exam counts as two tests, we can calculate the total number of points Cindy can earn in the course as follows:

Total points = 4 tests + 2 tests = 6 tests

To earn a C in the course, her average score must be between 77 and 84. Let's assume she needs to score x on her final exam to achieve a C. Then her total points would be:

Total points = 72 + 82 + 83 + 89 + x + x

Simplifying this equation, we get:

Total points = 326 + 2x

To earn a C, Cindy's average score must be between 77 and 84. Therefore, we can set up an inequality:

77 <= (326 + 2x) / 6 <= 84

Multiplying both sides by 6, we get:

462 <= 326 + 2x <= 504

Subtracting 326 from all sides, we get:

136 <= 2x <= 178

Dividing by 2, we get:

68 <= x <= 89

Therefore, Cindy must score between 68 and 89 on her final exam to earn a C in Biology.

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The inverse operation used to solve the equation x/7 = 5 is multiplication

Inverse operations are mathematical operations that reverse or undo each other. To isolate the variable, inverse operations are used. For example, addition and subtraction are inverse operations, as are multiplication and division.

In an equation, inverse operations can be used to solve for a variable. In order to solve the equation x/7 = 5, we will use inverse operations.The inverse operation of division is multiplication. So, we can isolate x by multiplying both sides of the equation by 7.x/7 = 5Multiplying both sides by 7 gives:x = 7 × 5x = 35Therefore, x = 35 is the solution to the equation.

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Let the given three vertices of the parallelogram PQRS be P(-2,-3), R(7,5), and S(6,1). Since PQRS is a parallelogram, opposite sides are parallel.

So, the length of PS = length of QR and PS is parallel to QR.Here's how to find Q:To find Q, we need to find the coordinates of the fourth vertex. The coordinates of Q can be found using the above property.PS is parallel to QR, thus slope of PS = slope of QR.To find the slope of PS:(y2-y1)/(x2-x1)

= (5-(-3))/(7-(-2))= 8/9Now, we know the slope of PS. We can find the equation of the line passing through S and having the slope of PS using point-slope form of equation: y - y1

= m(x - x1)y - 1

= 8/9(x - 6)y

= 8/9(x - 6) + 1

Now, we can find the equation of the line passing through R and having the slope of QR using point-slope form of equation: y - y1

= m(x - x1)y - 5

= 8/9(x - 7)y

= 8/9(x - 7) + 5

Now, we have the equations of two lines. We can find the coordinates of point Q by solving the above two equations. This can be done by equating the above two equations: 8/9(x - 6) + 1 = 8/9(x - 7) + 5

Solving the above equation:8/9x - 16/9

= 8/9x - 40/98/9

= 24/9 - x/9x/9

= 16/9x

= 16*9/9x

= 16

Now, we can find the value of y by substituting the value of x in any of the two equations: y = 8/9(x - 6) + 1

or y = 8/9(x - 7) + 5

Using the first equation:y = 8/9(16 - 6) + 1

= 8/9(10) + 1

= 80/9 + 1

= 89/9

So, the coordinates of Q are (16, 89/9).Answer: The co-ordinates of Q are (16, 89/9).

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Considering the three vertices of a parallelogram PQRS are P(-2,-3), R(7,5), and S(6,1). The co-ordinates of Q are (2, -1).

To find the coordinates of vertex Q of the parallelogram PQRS, we can use the property that opposite sides of a parallelogram are parallel and congruent.

The midpoint of the diagonal PS is the point Q, therefore we can use the midpoint formula to find the coordinates of Q:

Midpoint of PS = Q

                        = ( (x₁ + x₂)/2 , (y₁ + y₂)/2 )

Given, vertices of the parallelogram PQRS as follows:

                 P(-2,-3)  Q(x,y)  R(7,5)  S(6,1)

Using the midpoint formula,

                (x₁ + x₂)/2 = ( -2 + 6 )/2

            ⇒ x = 2

                   (y₁ + y₂)/2 = ( -3 + 1 )/2

           ⇒ y = -1

Therefore, the coordinates of point Q are (2,-1). Thus, the coordinates of Q are (2, -1).

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Answer:

for 1.

Step-by-step explanation:

the formula is pir2h

The correct answer is D. No; the correct distance is 1 1/12 miles, because 1/4 + 2/3 = 4/12 + 8/12 = 12/12 = 1 1/12.

To solve this problem, we first need to convert the mixed numbers to fractions. 1 4 = 4 12 and 2 3 = 8 12. Then, we can add the fractions together. 4 12 + 8 12 = 12 12 = 1 1 12.

Therefore, Brandon is incorrect. He walks a total of 1 1/12 miles, not 11 1/2 miles.

To determine the measure of angle DAB, we need to use the congruence of quadrilaterals ABCD and AMCG.

Quadrilateral ABCD is congruent to quadrilateral AMCG.

Since the two quadrilaterals are congruent, their corresponding angles are equal. Therefore, we can write:

m∠DAB = m∠MAC

However, the measure of angle MAC is not given in the given information. Therefore, without additional information, we cannot determine the exact measure of angle DAB.

The options provided in the question do not correspond to the measure of angle DAB. Therefore, the correct answer cannot be determined based on the given information.

It is important to have additional information about the measures of angles or the side lengths in order to determine the measure of angle DAB accurately.

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The height of the tree is 12 meters.

To solve this problem, we can use similar triangles.

Let's denote the height of the tree as 'h'.

We have a right triangle formed by the hiker's line of sight, the mirror, and the reflected image of the top of the tree.

The vertical leg of this triangle is 'h', and the horizontal leg is the sum of the distance between the mirror and the base of the tree (20m) and the distance between the mirror and the hiker (4m).

So the horizontal leg is 20m + 4m = 24m.

Now, we can set up the proportion between the similar triangles:

(hiker's eye level)/(horizontal leg) = (reflected image height)/(vertical leg)

Plugging in the given values:

2 / 24 = 1 / h

Cross-multiplying:

2h = 24

Dividing both sides by 2:

h = 24 / 2

h = 12

Therefore, the height of the tree is 12 meters.

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John recorded 5 heads and flipped a coin 9 times. The ratio of heads to tails recorded by John is 5:4.

John flipped a coin 9 times and recorded 5 heads. To determine the ratio of heads to tails, we need to compare the number of heads to the number of tails. Since John recorded 5 heads, the remaining flips would be tails.

Therefore, the number of tails recorded would be 9 - 5 = 4. The ratio of heads to tails recorded by John is thus 5:4, which means for every 5 heads, there were 4 tails. This ratio represents the relative frequency of heads and tails in John's coin flips.

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The recursive formula for the sequence is a(n) = a(n - 1) + 2 and the next term is 18

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

8, 10, 12, 14, 16,.

In the above sequence, we have

First term, a(1) = 8

And we have the common difference to be

d = 2

So, we have

a(n) = a(n - 1) + 2

The next term of the sequence is

Next = 16 + 2

Evaluate

Next = 18

Hence, the recursive formula for the sequence is a(n) = a(n - 1) + 2

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To calculate the amount of sand Maija should order, we need to find the volume of the sandbox. The sandbox is in the shape of a cube, so its volume is determined by multiplying the length, width, and height.

Given that the sides of the square sandbox are 2 feet long and the desired depth of the sand is 1.55 feet, we can calculate the volume as follows:

[tex]\[ \text{Volume} = \text{Length} \times \text{Width} \times \text{Height} \][/tex]

Since all sides of the sandbox are equal in length (2 feet), the formula simplifies to:

[tex]\[ \text{Volume} = \text{Side}^3 \][/tex]

Substituting the values:

[tex]\[ \text{Volume} = 2 \, \text{ft} \times 2 \, \text{ft} \times 1.55 \, \text{ft} \][/tex]

[tex]\[ \text{Volume} = 6.2 \, \text{cubic feet} \][/tex]

Therefore, Maija should order 6.2 cubic feet of sand for her sandbox.

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There will be 22544 rabbits living in the neighbour's yard after 12 months.

The given problem states that the size of Marjorie and Harold Rabbit's family doubles one month later and continues to double every month thereafter.

It is required to find the number of rabbits that will be living in the neighbours yard after 12 months.

The given data can be organized in a tabular form as follows:

Time (in months)

Number of rabbits at the end of the month

01 (at birth)

2 (after one month)

24(after two months)

28(after three months)

216(after four months)

232(after five months)

264 (after six months)

2128(after seven months)

2256(after eight months)

24192(after nine months)

28384 (after ten months)

267,68 (after eleven months)

225,44 (after twelve months)

Yes, it is quite possible that they will notice this huge number of rabbits in their yard.

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Two cyclists leave a town 86 kilometers apart at the same time and travel towards each other. One cyclist is traveling 7 km/h faster than the other. The task is to find their speeds.

Let's assume the speed of the slower cyclist is x km/h. Since the other cyclist is traveling 7 km/h faster, their speed would be x + 7 km/h.

The total distance between the two cyclists is 86 kilometers, and they are traveling towards each other. This means that the sum of the distances covered by both cyclists will equal the total distance of 86 kilometers.

Using the formula Distance = Speed × Time, we can set up the equation:

Distance covered by the slower cyclist + Distance covered by the faster cyclist = 86

The time taken by both cyclists will be the same since they start at the same time. So, we can rewrite the equation as:

(x km/h) × (t hours) + (x + 7 km/h) × (t hours) = 86

Simplifying the equation, we get:

xt + (x + 7)t = 86

xt + xt + 7t = 86

2xt + 7t = 86

Since we have two variables (x and t), we need another equation to solve the system. Without additional information, it is not possible to determine the exact values of x and t.

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To solve the equation 42 + x (interior angle) + 120 (exterior angle) = 180, we can use the fact that the sum of an interior angle and its corresponding exterior angle is always 180 degrees.

In the given equation, 42 represents an interior angle, x represents an unknown interior angle, and 120 represents the corresponding exterior angle. The sum of an interior angle and its corresponding exterior angle is always 180 degrees. Therefore, we can set up the equation:

42 + x + 120 = 180

To solve for x, we can simplify the equation:

x + 162 = 180

Next, we can isolate x by subtracting 162 from both sides of the equation:

x = 180 - 162

x = 18

Therefore, the value of the unknown interior angle, x, is 18 degrees.

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Last month, a total of 72 boots were sold. To calculate the total number of boots sold last month, we need to multiply the number of pairs of boots sold (24) by the ratio 6:2:3. In this ratio, each part represents a fraction of the total number of boots.

In the given ratio, the first part represents 6 out of 11 parts. So, we can calculate the fraction of boots sold by multiplying the first part of the ratio (6) by the total number of parts (11): 6/11 * 24 = 72/11.

Therefore, a total of 72 boots were sold last month.

The ratio 6:2:3 indicates that for every 6 parts of boots sold, there are 2 parts of another type of boots and 3 parts of yet another type. In this case, since we only have information about the first part (24 pairs of boots), we need to find the fraction of the total number of boots that the first part represents.

To calculate this fraction, we multiply the first part (6) by the total number of parts in the ratio (11). This gives us the fraction 6/11, which represents the proportion of boots sold out of the total. Multiplying this fraction by the total number of pairs of boots sold (24) gives us the total number of boots sold last month, which is 72.

Therefore, using the given ratio and the number of pairs of boots sold, we can determine the total number of boots sold by considering the proportion of each type of boots in the ratio.

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All corresponding angles and sides of △ABE and △CDE are congruent: ∠A ≅ ∠C, ∠B ≅ ∠D, AB ≅ CD, and BE ≅ DE.

To prove that △ABE ≅ △CDE, we can use the concept of corresponding angles and sides of parallel lines. Given that AB ∥ DC and AB ≅ DC, we need to show that △ABE and △CDE have congruent corresponding angles and sides.

Proof:

Given: AB ∥ DC, AB ≅ DC

Since AB ∥ DC, corresponding angles are congruent. Therefore, ∠A ≅ ∠C.

Also, AB ≅ DC, which means corresponding sides are congruent. Therefore, AB ≅ CD.

Consider △ABE and △CDE. We have ∠A ≅ ∠C (from step 2) and AB ≅ CD (from step 3).

To prove that △ABE ≅ △CDE, we need to show that all corresponding angles and sides are congruent.

We have already established that ∠A ≅ ∠C and AB ≅ CD.

Now, since AB ∥ DC, we can conclude that ∠B ≅ ∠D (corresponding angles of parallel lines).

Furthermore, since AB ≅ DC, we can also conclude that BE ≅ DE (corresponding sides of △ABE and △CDE).

Therefore, all corresponding angles and sides of △ABE and △CDE are congruent: ∠A ≅ ∠C, ∠B ≅ ∠D, AB ≅ CD, and BE ≅ DE.

By proving that all corresponding angles and sides of △ABE and △CDE are congruent, we can conclude that △ABE ≅ △CDE by the criteria of congruence (ASA - Angle-Side-Angle).

Hence, we have successfully proved that △ABE ≅ △CDE based on the given information and the concept of corresponding angles and sides of parallel lines.

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This means that the expression 10x² + 2x - 8  completely factored as 2(5x - 2)(x + 2).

The correct factored form of the expression 10x² + 2x - 8 is:

2(5x - 2)(x + 2).

To factor the quadratic expression completely for common factors first that the coefficient 2 is a common factor in all three terms. After factoring out 2, left with (5x² + x - 4).

An factor the trinomial (5x² + x - 4). However, this trinomial cannot be factored further using integer coefficients.

So, the factored form of the expression is 2(5x - 2)(x + 2).

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The rate of change and the initial value of the function can be identified based on the given situation and the function y = 3.5x + 5.

The rate of change represents the constant rate at which the miles jogged increase per hour, while the initial value indicates the starting point or the number of miles jogged before any additional hours.

In the given function y = 3.5x + 5, the coefficient of x, which is 3.5, represents the rate of change. It indicates that for every hour Shirley continues to jog, she will add 3.5 miles to the total distance already jogged.

The constant term, 5, represents the initial value of the function. In this case, it signifies that Shirley has already jogged 5 miles before she starts jogging at an average rate of 3.5 miles per hour.

Therefore, the rate of change of the function is 3.5 miles per hour, indicating the increase in miles jogged per hour, and the initial value is 5 miles, representing the distance already jogged by Shirley before any additional hours of jogging.

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