What is the value of x?

Therefore, the possible values for x are 1, 4, and 5.

First, let's use long division to factor the polynomial 3x³-16x²+31x-20, which represents the area of the trapezoidal desktop, by x²-5x+x-5:

           ____________________________

[tex]x^{2} -5x+x-5 | 3x^{3} - 16x^{2} + 31x - 20[/tex]

[tex]- (3x^{3} - 15x^{2} + 3x^{2} - 15x)[/tex]

           ____________________________

                  [tex]- x^{2} + 31x - 20[/tex]

                    [tex]-(- x^{2} + 5x - 5)[/tex]

                     ________________

                          [tex]26x - 15[/tex]

The result of the long division is x - 5 with a remainder of 26x - 15.

Therefore, we can rewrite the polynomial as:

[tex]3x^{3} - 16x^{2} + 31x - 20 = (x - 5)(x^{2} - 5x + 4) + (26x - 15)[/tex]

Now, let's use the formula for the area of a trapezoid to set up an equation using the polynomial above:

[tex]area = 1/2h(b_1 + b_2)[/tex]

We know that the bases of the trapezoid are represented by the expressions x + 5 and x² - 5x, so we can substitute them in the formula:

[tex]3x^{3} - 16x^{2} + 31x - 20 = 1/2h((x + 5) + (x^{2} - 5x))[/tex]

Simplifying the expression:

[tex]3x^{3} - 16x^{2} + 31x - 20 = 1/2h(x^{2} - 4x + 5)[/tex]

Multiplying both sides by 2:

[tex]6x^{3} - 32x^{2} + 62x - 40 = h(x^{2} - 4x + 5)[/tex]

Now, we can substitute the remainder of the long division we did earlier (26x - 15) for h:

[tex]6x^{3} - 32x^{2} + 62x - 40 = (x - 5)(x^{2} - 5x + 4) + (26x - 15)[/tex]

[tex]6x^{3} - 32x^{2} + 62x - 40 = (x - 5)(x^{2} - 5x + 4) + h[/tex]

[tex]6x^3 - 32x^2+ 62x - 40 = (x - 5)(x^2 - 5x + 4) + (26x - 15)[/tex]

Simplifying the expression again:

[tex]6x^3 - 32x^2 + 36x - 25 = (x - 5)(x^2 - 5x + 4)[/tex]

Now we have a quadratic equation that we can solve for x:

[tex]x^3 - 5x^2 + 4x + 5x^2 - 25x + 20 = 0[/tex]

[tex]x^3 - 21x + 20 = 0[/tex]

[tex](x - 1)(x - 4)(x - 5) = 0[/tex]

Therefore, the possible values for x are 1, 4, and 5.

Now we can substitute these values in the expression we derived for h:

[tex]h = (6x^3 - 32x^2 + 62x - 40)/(x^2 - 4x + 5)[/tex]

For x = 1:

[tex]h = (6(1)^3 - 32(1)^2 + 62(1) - 40)/2\\h = 6-32+62-40/2\\h = 68-72/2\\h = -4/2\\ h= -2[/tex]

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Using strategy 1 (in your head), divide 60m by 10m to get 6, then multiply that number by one to get 6cm. the length on drawing is 6cm

Procedure 2 (proportions)

Create a proportion first.

We know that 1 cm equals 10 metres, so we place them on a fraction (the operation is unaffected by the denominator or numerator). However, we don't know how many cm equal 10m, so we make that into a variable, in this case x.

1cm x cm

——— ———

100m 60m

Go diagonally to where the variables have already been put in to solve a proportion. You are unable to calculate 60 metres and x centimetres because you are unsure of x. Yet you can travel 60m. Start by multiplying 1 by 30 to reach the number 60. The result of multiplying 60 by 10m is x. This will equal 6.

Thus, your response is 6.

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Answer:

--------------------------------

A mixed number is the number in the format a b/c, where a - whole number and b/c - the fraction part.

Show the given as a mixed number:

The number of horizontal square of D over the number of vertical

squares  = 3 : 2

What is square in math?

A planar shape with four equal sides and four right (90°) angles is referred to as a square in geometry. An equilateral rectangle is a specific sort of square, while a parallelogram is a special kind of square (an equilateral and equiangular one). All four of the sides and all four of the angles make up the regular quadrilateral known as the square. The square's angles are 90 degrees apart from each other or at right angles. The square's diagonals are also equal and split at an angle of 90 degrees.

the number of horizontal squares of A, B , and C over the number of vertical square = 2 : 3

  the number of horizontal square of D over the number of vertical

squares  = 3 : 2

                       6 : 4 = 3 : 2

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The expected product from the intramolecular aldol condensation of 3-methylheptane dial is a cyclic α,β-unsaturated ketone with a seven-membered ring.

3-methylheptane dial is a 7-carbon compound with two carbonyl groups, one at each end of the molecule. Intramolecular aldol condensation occurs when one carbonyl group reacts with the other within the same molecule. The carbonyl group acts as an electrophile, while the enolate formed from the other carbonyl group acts as a nucleophile.

In the case of 3-methylheptane dial, intramolecular aldol condensation can occur between the carbonyl group at the 3-position and the enolate formed from the carbonyl group at the 6-position. The resulting intermediate undergoes dehydration to form a cyclic α,β-unsaturated ketone.

The product of the reaction will have a cyclic structure with a double bond between the α and β carbons. The exact structure of the product will depend on the stereochemistry of the starting material and the reaction conditions. However, the product is expected to have a seven-membered ring and to be an α,β-unsaturated ketone.

Therefore, the expected product from the intramolecular aldol condensation of 3-methylheptane dial is a cyclic α,β-unsaturated ketone with a seven-membered ring.

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The population in 2026 according to the exponential growth function will be approximately 54,515.

Given,

The population in 2001 = 26,100

Annual growth rate = 4%

Population growth function can be written as,

[tex]P(t) = P0e^rt[/tex]

Where,P(t) = Population after t years

P0 = Population at time t = 0

r = Annual growth rate (in decimal form)

t = Time (in years)

According to the given question,In the year 2026, the number of years from 2001 is,2026 – 2001 = 25 years

Therefore,t = 25 years

r = 4% = 0.04

Using these values in the population growth function,

[tex]P(t) = P0e^rt[/tex]

Population in 2026 = P(25)

[tex]P(25) = 26,100e^(0.04 x 25)[/tex]

P(25) = 26,100e

P(25) ≈ 54,515

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The coordinates of the graph when reflected over x-axis is given as A' (7, -8) and B' (2, -3).

The transformation, or f: X X, is the name given to a function, f, that maps to itself. After the transformation, the pre-image X becomes the picture X. Any operation, or a combination of operations, such as translation, rotation, reflection, and dilation, can be used in this transformation. A function can be moved in one way or another using translation, rotation, reflection, and dilation. A function can also be scaled using rotation around a point. Two-dimensional mathematical figures move about a coordinate plane according to transformations.

The mapping of reflection over the x-axis is depicted as follows:

(x, y) to (x, -y)

The coordinates of A and B are:

A (7, 8)

B (2, 3)

After the reflection over x-axis the coordinates are transformed as follows:

A' = (7, -8)

B' = (2, -3)

Hence, the coordinates of the graph when reflected over x-axis is given as A' (7, -8) and B' (2, -3).

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The statement that describes a linear relationship between time and population is 3. The population increases by 2000 people each year.

A linear relationship is an association between two variables, for example, time and population.

In a linear relationship, there is a straight-line relationship between the two variables, which can be expressed graphically or as a mathematical equation, y = mx + b.

There is a positive linear relationship when the slope is positive such that as the independent variable increases, the dependent variable increases.

A negative linear relationship exists when one increases while the other variable decreases.

Finally, a linear relationship can show a neutral relationship when the slope is 0, then as one variable increases, the other remains constant.

Thus, the linear relationship between time and population is best described by Option 3.

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Answer:

x>3

Step-by-step explanation:

The length of each side of the square is 5√2 inches

The diagonal of a square divides it into two 45-45-90 right triangles. In such triangles, the hypotenuse (which is the diagonal of the square) is √2 times as long as each leg. Let x be the length of each side of the square. Then we have

x√2 = 10

Solving for x, we get

x = 10 /√2

To simplify this expression, we can multiply both the numerator and denominator by √2

x = 10 /√2 × √2 /√2

Multiply the numbers

= 10√2 / 2

Divide the numbers

= 5√2 inches

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The expression to represent the p pages David has read is: p = 18 + (1/4)x, where x is the total number of pages in the book.

David has read 18 pages more than 1/4 pages of a book. The expression to represent the p pages that David has read would be: p = 18 + (1/4)x, where x is the total number of pages in the book. The reasoning behind this is as follows:

David has already read 18 pages more than 1/4 of the book, so we have to add 18 pages to whatever the pages of the book are. Since we don't know what the actual number of pages are, we'll call that x. Therefore, David read 1/4 of the book (or 1/4 of x) plus 18 pages.

Hence, the expression is: p = 18 + (1/4)x.

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Answer:

Commutative property of addition

Step-by-step explanation:

The property being used in this equation is the commutative property of addition. This property states that when two numbers are added, the order in which they are added does not change the sum. So, in this case, we can rearrange the terms 5/6 and 7/12 and still get the same result.

Answer:

Erica teaches 32.33 or 32 classes

Bo teaches 10.67 or 10 classes

Step-by-step explanation:

B + E = 43

E - 11 = 2B

B + E = 43

E = 43 - B

E - 11 = 2B

(43 - B) - 11 = 2B

B = 10.67 = 10

B + E = 43

(10.67) + E = 43

E = 32.33 = 32

The letter O has the experimental probability that is closest to its theoretical probability.

Probability is an area of statistics that deals with the study of random events and their likelihood of occurrence.

The theoretical probability of drawing a particular letter is the number of balls of that letter divided by the total number of balls in the game. For each letter, the theoretical probability is:

B: 15/75 = 0.2

I: 15/75 = 0.2

N: 15/75 = 0.2

G: 15/75 = 0.2

O: 15/75 = 0.2

The experimental probability of drawing a particular letter is the number of times that letter was actually drawn divided by the total number of draws. For each letter, the experimental probability is:

B: 247/1250 = 0.1976

I: 272/1250 = 0.2176

N: 238/1250 = 0.1904

G: 241/1250 = 0.1928

O: 252/1250 = 0.2016

Compare the differences between the theoretical and experimental probabilities for each letter. The letter with the smallest difference is the one whose experimental probability is closest to its theoretical probability.

Here, the differences between the theoretical and experimental probabilities for each letter are:

B: 0.2 - 0.1976 = 0.0024

I: 0.2 - 0.2176 = 0.0176

N: 0.2 - 0.1904 = 0.0096

G: 0.2 - 0.1928 = 0.0072

O: 0.2 - 0.2016 = 0.0016

Based on these calculations, we can see that the letter O has the smallest difference between its theoretical and experimental probabilities, with a difference of only 0.0016.

Therefore, the letter O has the experimental probability that is closest to its theoretical probability.

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Three equations that can be seen in the graph for each type of function are x = -6, y = 1.5x  -2.5 and y = x² + 6x + 10

Function 1: Constant

A constant function is a mathematical function that always returns the same output value regardless of its input.

A constant function with the equation x = -6 exist on the graph with the following features: x = -6 as domain and [0, 4] as the range

Function 2: Linear

A linear function is a type of mathematical function where the output varies linearly with the input.

From the graph, we have the points

(4, 3.5) and (5, 5)

Using a graphing tool, the equation is

y = 1.5x  -2.5

And the identities are [4, 5] as the domain and [3.5, 5] as the range

Function 3: Quadratic

This is a function of the form y = a(x - h)² + k or y = ax² + bx + c

From the graph, we have

(h, k) = (-3, 1) and (x, y) = (-2, 2)

Using a graphing tool, the equation is

y = x² + 6x + 10

And the identities are [-4, -2] as the domain and [1, 2] as the range

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The two shorter sides of a right triangle measure 15 inches and 3 feet and the length of the longest side also known as the hypotenuse is 3.269557 feet.

It is given to us that the two shorter sides of a right triangle measure 15 inches and 3 feet.

Let us say that side a is 3 feet and side b is 15 inches and we need to find side c, that is the longest side also known as the hypotenuse,

A right-angled triangle is one in which only one angle is precisely 90 degrees. Since the total of all the angles in a triangle is always 180°, the other two angles will be obviously smaller than the right angle.

We define the sides of a right-angled triangle in a unique manner. The hypotenuse of a triangle is the edge that faces the right angle and is always the largest.

Pythagorean formula. Pythagoras' theorem says that: a² + b² = c². in a right triangle with cathetus a and b and with hypotenuse c.

Take the square root of both sides to find c = √(b²+a²). This Pythagorean theorem expansion can be thought of as a "hypotenuse formula."

Therefore, with this formula we can solve for hypotenuse:

side a = 15 inches = 1.3 feet

side b = 3 feet

a² + b² = c²

1.3² + 3² = c²

1.69 + 9 = c²

10.69 = c²

c = 3.269557 feet

Therefore, we can say that the two shorter sides of a right triangle measure 15 inches and 3 feet and the length of the longest side also known as the hypotenuse is 3.269557 feet.

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The price of a pound of carrots this month is $3.183.

The price of one pound of carrots last month was $2 1/12. To add $1 1/10 to this price, we need to convert both prices to twelfths of a dollar to make the addition easier.

$2 1/12 = 25/12

$1 1/10 = 11/10

Adding these two prices together gives us:

= 25/12 + 11/10

= 3.18333333333

= $3.183.

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I remember doing this but I don’t seem to remember sorry

Answer:

220-8pi

Step-by-step explanation:

(7)  The two polygons are congruent since we can obtain a congruent image of DEF by applying a translation or a rotation.

(8) The two polygons are congruent since we can obtain a congruent image of JKLM by applying a translation or a rotation.

To determine whether the two polygons are congruent, we can apply a series of transformations to one of them to see if it can be mapped onto the other.

(7) Let's first label the polygons: ABCD is the first polygon and DEF is the second polygon.

Translation: We can translate DEF four units to the right and two units down to obtain the image of DEF, which is congruent to ABCD.

Rotation: We can rotate DEF about the point (0, 1) by 180 degrees to obtain the image of DEF, which is congruent to ABCD.

Since we can obtain a congruent image of DEF by applying a translation or a rotation, we can conclude that the two polygons are congruent.

(8) Let's label the two polygons: JKLM is the first polygon and NOPQ is the second polygon.

Translation: We can translate JKLM six units to the right and three units down to obtain the image of JKLM, which is congruent to NOPQ.

Rotation: We can rotate JKLM about the point (-4, 4) by 180 degrees to obtain the image of JKLM, which is congruent to NOPQ.

Since we can obtain a congruent image of JKLM by applying a translation or a rotation, we can conclude that the two polygons are congruent.

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the relationship between the diameter of the pizza and its cost per square inch is non-proportional.

The relationship between the diameter of the pizza and its cost per square inch is non-proportional.

If the relationship were proportional, then the cost per square inch of the pizza would remain constant as the diameter changes. However, in this case, we see that as the diameter of the pizza increases, the cost per square inch decreases. This is because the area of a circle increases more rapidly than its diameter, so the cost must be spread out over a larger area, resulting in a lower cost per square inch.

Therefore, the relationship between the diameter of the pizza and its cost per square inch is non-proportional.

the complete question is :

would relationship between the dilation factor k and the resulting volume of a solid best be described as proportional or non proportional? justify your answer

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The relationship between the central angle and interior angle is Central angle = 2 * Interior angle.

The internal angle is the angle created by two adjacent sides of a polygon within the circle, whereas the central angle is the angle formed by two radii of a circle that intersect at its centre. Since one of the sides of the polygon opposing the interior angle is opposite the central angle, the two angles are connected by the following formula:

central angle = 2 * Interior angle.

As the number of sides in a polygon increases, the measure of each interior angle decreases while the measure of each central angle remains constant.

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The value of the function q and r are as follows (q ° r )(7) = 22 and (r ° q)(7) = 8.

The process of integrating two or more functions into one function is known as composition of functions. A function is an example of labour. Take making bread as an example. Let x be the flour, let g(x) be the function that the food processor performs to prepare the dough using the flour, and let f(x) be the function that the oven does to bake the bread. The output of g(x) should be sent into the function f(x) to make bread (i.e., the prepared dough should be placed in the oven). The outcome is represented by the symbol f(g(x)), and it is made up of the functions f(x) and g. (x).

The function q and r are as follows:

q(x) = x² + 6

r(x) = √(x + 9)

The value of:

(q ° r )(x) = q(r(x))

Here, substitute the value of x in q(x) with the value of r(x):

q(r(x)) = (√(x + 9))² + 6

q(r(x)) = x + 9 + 6

Substitute x = 7:

q(r(7)) = 7 + 9 + 6 = 22

Now, (r ° q) = r(q(x))

r(q(x)) = √(x² + 6 + 9)

= √(x² + 15)

Substitute x = 7:

r(q(7)) = √(7² + 15) = √(49 + 15) = √64 = 8

Hence, the value of the function q and r are as follows (q ° r )(7) = 22 and (r ° q)(7) = 8.

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The cheaper price for the 12 orchid is the 8.60 pounds for 4 orchid.

The cheaper price for the 12 orchid can be calculated as follows;

Therefore, for the first Orchid:

4 orchid = 8.60 pounds

12 orchid = ?

cross multiply

cost for 12 orchid = 8.60 × 12 / 4

cost for 12 orchid = 103.2 / 4

cost for 12 orchid = 25.8 pounds

For the second orchid:

5.40 pounds for each.

Now, 1 / 3 off,

Therefore,

1 / 3 ×5.40 = 1.8

Therefore,

5.40 - 1.8 = 3.6 pounds for each

Therefore,

12 orchid = 12 × 3.6 = 43.2 pounds

Therefore, the cheaper price is 8.60 pounds for 4 orchid.

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Answer:

2/5

Step-by-step explanation:

same denominator so ignore it.

2 + 2 = 4

2/5 + 2/5 = 4/5

simple way.

The length of the second arc is 8 feet.

The rope is swinging in such a way that the length of the arc is decreasing geometrically.

If the first arc is 18 feet long and the third arc is 8 feet long,

The length of the second arc :

In order to find the second arc length, we need to use the formula of the geometric sequence.

We have to understand what is given and what is required.

Given : First arc = 18 feet

Third arc = 8 feet.

To Find : Length of the second arc.

The formula of the geometric sequence is :

[tex]a_n[/tex] = [tex]a_1[/tex] × rn − 1

where, r = Common ratio [tex]a_1[/tex] = First term [tex]a_n[/tex] = [tex]n^{th}[/tex] term

Here, the length of the first arc is [tex]a_1[/tex] = 18.

The length of the third arc is [tex]a_3[/tex] = 8.

We have to find the length of the second arc, which is [tex]a_2[/tex]

Using the formula of the geometric sequence, we can find the [tex]a_1[/tex]: r= [tex]a_3[/tex] / [tex]a_2[/tex]

We know that [tex]a_1[/tex]= 18 and [tex]a_3[/tex]= 8

Substitute the values: r= 8 / [tex]a_2[/tex]

Now, we can rewrite the formula of the geometric sequence: an=[tex]a_1[/tex]×rn−1an= [tex]a_1[/tex] x r(n-1)

The length of the first arc is [tex]a_1[/tex] = 18 feet.

Substituting the value of r, we get:

8 / [tex]a_2[/tex] = r18 x r(n-1) = [tex]a_2[/tex]

We are given that the length of the third arc is 8 feet,

thus : 8 = 18 x r(3-1)8

= 18 x [tex]r_2[/tex][tex]r_2[/tex]

= 8 / 18[tex]r_2[/tex]

= 4 / 9r

= √(4/9)

Using this value of r, we can find the length of the second arc :

[tex]a_2[/tex] = 18 x (4/9) (2-1) [tex]a_2[/tex]

= 18 x (4/9)[tex]a_2[/tex]

= 8

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The population will be equal to one-half of the limiting value after 4.67 months.

Model for the population p(t) in a suburb of a large city is given by the initial-value problem dp/dt= 5 p(1021−2×1027p), p(0) = 5000. Now we are to find out the limiting value of the population and the time when the population will be equal to one-half of the limiting value.Limiting value of the populationThe limiting value is the population value when the population grows until it levels off. In other words, we can say that it is the maximum population that can be sustained by the resources available.

We can find the limiting value by considering what would happen if the rate of change of the population became zero. This can occur only when p=0 or 1021−2×1027p =0.Solving this equation, we get p = 0 and p = 5.1 × 10⁷/2 = 2.55 × 10⁷Thus, the limiting value of the population is 2.55 × 10⁷.We know that the population is given by p(t) and we have to find the time when the population will be equal to one-half of the limiting value. To find t, we need to solve the differential equation dp/dt= 5 p(1021−2×1027p).

Separating variables, we getdp/p(1021−2×1027p) = 5 dtOn integrating, we get-1/2 ln|1021−2×1027p| = 5t + CWhere C is the constant of integration.Using the initial condition p(0) = 5000, we getC = -1/2 ln|1021−2×1027(5000)|Solving for C, we getC ≈ -2.97Solving for p, we get1021−2×1027p = ±e^(-10t+2.97)Multiplying both sides by -1/2, we get-0.5(1021−2×1027p) = ±0.5e^(-10t+2.97)Taking the negative sign, we getp = 0.5(1021 + 0.5e^(-10t+2.97))/1027Substituting p = 1.275 × 10⁷, we get1.275 × 10⁷ = 0.5(1021 + 0.5e^(-10t+2.97))/1027Multiplying both sides by 1027 and simplifying, we get1.32 × 10^4 = 1021 + 0.5e^(-10t+2.97)Solving for e^(-10t+2.97), we gete^(-10t+2.97) = 2 × (1.32 × 10^4 - 1021)Taking the natural logarithm, we get-10t + 2.97 = ln[2 × (1.32 × 10^4 - 1021)]Solving for t, we gett ≈ 4.67 months.

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Answer:

54

Step-by-step explanation:

the angle measures of any triangle add up to 180 degrees, so we need to add all of the given measures and set it equal to 180.

(x) + (40) + (2x - 22) = 180

3x + 18 = 180

3x = 162

x = 54

Answer:20.25

Step-by-step explanation:

Answer:

If the shopkeeper sold the radio for 336 rs and gained a 5% profit, then the cost price (c.p.) of the radio can be calculated as follows:

Let x be the cost price of the radio. Since the shopkeeper gained a 5% profit, we can write the equation: x + 0.05x = 336 Solving for x, we get: x(1 + 0.05) = 336 x = 336/1.05 x = 320

So, the cost price (c.p.) of the radio is 320 rs.

Step-by-step explanation:

On average, a person weighing 150 pounds can burn approximately 80 to 90 extra calories by slowly walking at a pace of 1.7 miles per hour for one hour instead of sitting.

The number of extra calories a person would burn by slowly walking instead of sitting for one hour depends on various factors, such as the person's weight, height, age, and gender. However, on average, a person weighing 150 pounds can burn approximately 80 to 90 calories by walking at a slow pace of 1.7 miles per hour for an hour.

This number may vary slightly based on individual differences and other factors, such as incline or terrain. Walking is a low-impact form of exercise that can help increase calorie burn and improve overall health, making it a great option for those looking to lead a more active lifestyle.

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