Translate the following verbal statement into an algebraic equation and then solve:

Use x for your variable.

The quotient of four more than a number and seven is ten.

Answer:

The common difference is -12

Step-by-step explanation:

Finding the common difference:

11, - 1, - 13, - 25, . . .

The difference between the first and second terms

-1 -11 = -12

The difference between the second and third terms

-13 - -1 = -13 + 1 = -12

The common difference is -12

The solutions to the equations are

a) The percentage of quokkas that weigh over 15.5 pounds is 2.1 %

b) The percentage of quokkas that weigh uncer 11.9 pounds is 75.9 %

c) Percentage of quokkas that weigh between 15.5 and 11.9 pounds 22.0 %

The relationship between a value and the mean of a set of values is expressed numerically by a Z-score. The Z-score is computed using the standard deviations from the mean. A Z-score of zero indicates that the data point's score and the mean score are identical.

The Z-score is calculated using the formula:

z = (x - μ)/σ

where z: standard score

x: observed value

μ: mean of the sample

σ: standard deviation of the sample

Given data ,

The weights of the quokkas are described by the normal model as

N ( 10 , 2.7 )

So , the mean μ = 10

And , the standard deviation σ = 2.7

a)

The percentage of quokkas that weigh over 15.5 pounds is given by the equation P ( x > 15.5 )

On simplifying the equation , we get

From the z-score formula ,

P ( z > ( 15.5 - 10 ) / 2.7 )

P ( z > 2.037 ) = 0.020825

0.020825 = 2.0825 %

Hence , the percentage of quokkas that weigh over 15.5 pounds is 2.1 %

b)

The percentage of quokkas that weigh uncer 11.9 pounds is  given by the equation P ( x < 11.9 )

On simplifying the equation , we get

From the z-score formula ,

P ( z < ( 11.9 - 10 ) / 2.7 )

P ( z < 0.7037 ) = 0.020825

0.75919 = 75.919 %

Hence , the percentage of quokkas that weigh uncer 11.9 pounds is 75.9 %

c)

Percentage of quokkas that weigh between 15.5 and 11.9 pounds is

P ( 11.9 < x < 15.5 )

On simplifying the equation , we get

From the z-score formula ,

P ( 11.9 < x < 15.5 ) = 1 - P ( x < 11.9 ) - P ( x > 15.5 )

P ( 11.9 < x < 15.5 ) = 1 - 0.020825 - 0.75919

P ( 11.9 < x < 15.5 ) = 0.219985

P ( 11.9 < x < 15.5 ) = 22.0 %

Hence , the equations are solved using z-score

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Answer: [tex]4\sqrt{3}[/tex]

Step-by-step explanation:

We can use the pythagorean theorem to solve this.

We will call the length of the unknown side x for now.

Using the theorem, we will get to:
[tex]8^2-4^2=x^2[/tex]

[tex]64 - 16 = x^2[/tex]

[tex]48 = x^2[/tex]

[tex]x = \sqrt{48}[/tex]

In simplest radical form, it will be:

[tex]4\sqrt{3}[/tex]

Answer:

4[tex]\sqrt{3}[/tex]

Step-by-step explanation:

using Pythagoras' identity in the right triangle.

the square on the hypotenuse is equal to the sum of the squares on the other 2 sides.

let x represent the third side, then

x² + 4² = 8²

x² + 16 = 64 ( subtract 16 from both sides )

x² = 48 ( take square root of both sides )

x = [tex]\sqrt{48}[/tex] = [tex]\sqrt{16(3)}[/tex] = [tex]\sqrt{16}[/tex] × [tex]\sqrt{3}[/tex] = 4[tex]\sqrt{3}[/tex]

As a result, the actual interest rate is 5.06% since Nolan purchases a $12,000 13-week treasury bill at 5%.

To calculate simple interest, divide the original by the loan rates, the length of time, and other variables. The marketing equation is simple gain = principal + interested + hours. It is easier to compute interest with this system. The method that is most frequently used to calculate this is as a percentage of the principle amount. If someone borrows $100 from a buddy and promises to return him with 5% interest, he may only pay his portion of the 100% interest. $100 (0.05) = $5. You must pay interest on any further borrowings as well as any loans you put out. Interest is frequently calculated as a measure of the entire amount of the loan. This percentage represents the loan's interest rate.

given that,

Simple interest = $12,000 × 0.05 × 13/52 = $150

Simple discount note = ($12,000 - $150) × 13/52 = $2962.5

Effective rate of interest = $150 / $2962.5

Effective rate of interest = 0.0506 or 5.06%

As a result, the actual interest rate is 5.06% since Nolan purchases a $12,000 13-week treasury bill at 5%.

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Answer:

B

Step-by-step explanation:

12 long 9 wide = 12*9 =108 sqft

$5/sqft

so she'll need 108*5 =540

but she rounded to 100 sqft

Answer:

63, 69, 75, 81

Step-by-step explanation:

to find the first 4 terms substitute n = 1, 2, 3, 4 into the explicit rule.

a₁ = 63 + (1 - 1) × 6 = 63 + 0 × 6 = 63 + 0 = 63

a₂ = 63 + (2 - 1) × 6 = 63 + 1 × 6 = 63 + 6 = 69

a₃ = 63 + (3 - 1) × 6 = 63 + 2 × 6 = 63 + 12 = 75

a₄ = 63 + (4 - 1) × 6 = 63 + 3 × 6 = 63 + 18 = 81

the first four terms are 63, 69, 75, 81

The function below that models the location of the car if it is d miles from the garage h hours after starting towards the garage is option a d = 26 - 35h.

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input. A function is typically represented as y = f. (x).

The distance travelled by the car is given as:

26 miles away from its destination. Let d be the destination the we have the distance in miles as:

26 - d

The formula of the speed is:

Speed = distance / time

35 = (26 - d) / h

Rearranging the equation, we have:

d = 26 - 35h

Hence, the function below that models the location of the car if it is d miles from the garage h hours after starting towards the garage is option a d = 26 - 35h.

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Ella will have 1.0 lbs of 50% syrup, 9.5 lbs of 5% syrup, 0.83 lbs of 75% syrup, and 33.5 lbs of 1.5% syrup

To determine how much water Ella should add to make a specific concentration of syrup, you need to use the formula:

Syrup Concentration = (Mass of Sugar) / (Mass of Sugar + Mass of Water)

50% syrup: In this case, the syrup concentration is 0.50, so you can use the formula as follows:

0.50 = (0.5 lbs of sugar) / (0.5 lbs of sugar + Mass of Water)

Rearranging the formula, we get:

Mass of Water = (0.5 lbs of sugar) / 0.5 - 0.5 lbs of sugar

Mass of Water = 0.5 lbs

The total amount of syrup will be 0.5 lbs of sugar + 0.5 lbs of water = 1.0 lbs

5% syrup: In this case, the syrup concentration is 0.05, so you can use the formula as follows:

0.05 = (0.5 lbs of sugar) / (0.5 lbs of sugar + Mass of Water)

Rearranging the formula, we get:

Mass of Water = (0.5 lbs of sugar) / 0.05 - 0.5 lbs of sugar

Mass of Water = 9 lbs

The total amount of syrup will be 0.5 lbs of sugar + 9 lbs of water = 9.5 lbs

75% syrup: In this case, the syrup concentration is 0.75, so you can use the formula as follows:

0.75 = (0.5 lbs of sugar) / (0.5 lbs of sugar + Mass of Water)

Rearranging the formula, we get:

Mass of Water = (0.5 lbs of sugar) / 0.75 - 0.5 lbs of sugar

Mass of Water = 0.33 lbs

The total amount of syrup will be 0.5 lbs of sugar + 0.33 lbs of water = 0.83 lbs

1.5% syrup: In this case, the syrup concentration is 0.015, so you can use the formula as follows:

0.015 = (0.5 lbs of sugar) / (0.5 lbs of sugar + Mass of Water)

Rearranging the formula, we get:

Mass of Water = (0.5 lbs of sugar) / 0.015 - 0.5 lbs of sugar

Mass of Water = 33 lbs

The total amount of syrup will be 0.5 lbs of sugar + 33 lbs of water = 33.5 lbs

So, to summarize, Ella will have 1.0 lbs of 50% syrup, 9.5 lbs of 5% syrup, 0.83 lbs of 75% syrup, and 33.5 lbs of 1.5% syrup.

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Answer:

Step-by-step explanation:

Ella will have 1.0 lbs of 50% syrup, 9.5 lbs of 5% syrup, 0.83 lbs of 75% syrup, and 33.5 lbs of 1.5% syrup

Calculatng  lbs of  syrup

To determine how much water Ella should add to make a specific concentration of syrup, you need to use the formula:

Syrup Concentration = (Mass of Sugar) / (Mass of Sugar + Mass of Water)

50% syrup: In this case, the syrup concentration is 0.50, so you can use the formula as follows:

0.50 = (0.5 lbs of sugar) / (0.5 lbs of sugar + Mass of Water)

Rearranging the formula, we get:

Mass of Water = (0.5 lbs of sugar) / 0.5 - 0.5 lbs of sugar

Mass of Water = 0.5 lbs

The total amount of syrup will be 0.5 lbs of sugar + 0.5 lbs of water = 1.0 lbs

5% syrup: In this case, the syrup concentration is 0.05, so you can use the formula as follows:

0.05 = (0.5 lbs of sugar) / (0.5 lbs of sugar + Mass of Water)

Rearranging the formula, we get:

Mass of Water = (0.5 lbs of sugar) / 0.05 - 0.5 lbs of sugar

Mass of Water = 9 lbs

The total amount of syrup will be 0.5 lbs of sugar + 9 lbs of water = 9.5 lbs

75% syrup: In this case, the syrup concentration is 0.75, so you can use the formula as follows:

0.75 = (0.5 lbs of sugar) / (0.5 lbs of sugar + Mass of Water)

Rearranging the formula, we get:

Mass of Water = (0.5 lbs of sugar) / 0.75 - 0.5 lbs of sugar

Mass of Water = 0.33 lbs

The total amount of syrup will be 0.5 lbs of sugar + 0.33 lbs of water = 0.83 lbs

1.5% syrup: In this case, the syrup concentration is 0.015, so you can use the formula as follows:

0.015 = (0.5 lbs of sugar) / (0.5 lbs of sugar + Mass of Water)

Rearranging the formula, we get:

Mass of Water = (0.5 lbs of sugar) / 0.015 - 0.5 lbs of sugar

Mass of Water = 33 lbs

The total amount of syrup will be 0.5 lbs of sugar + 33 lbs of water = 33.5 lbs

So, to summarize, Ella will have 1.0 lbs of 50% syrup, 9.5 lbs of 5% syrup, 0.83 lbs of 75% syrup, and 33.5 lbs of 1.5% syrup.

The solution of x in the equation is (-5.855, 2.435)

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

sec(3x - 15) = csc(14x + 3)

Next, we split the equation as follows

y = sec(3x - 15)

y = csc(14x + 3)

Next, we solve the equation graphically

When the graph is plotted, we have one of the points of intersection to be:

(x, y) = (-5.855, 2.435)

Hence, the solution is (-5.855, 2.435)

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Answer:

It might be "C"

Step-by-step explanation:

Answer:

To find Sally's yearly salary, we can use the information that her budget for food is 1/8 of her yearly salary and her total food bill for the year is $12,500. Let's call Sally's yearly salary "S".

Since 1/8 of Sally's yearly salary is dedicated to food, we can write:

S * 1/8 = $12,500

To solve for S, we can divide both sides of the equation by 1/8:

S = $12,500 * 8 = $100,000

So, Sally's yearly salary is $100,000.

Step-by-step explanation:

For the equation [tex]8^{2x-y} = 5^{x-y+8}[/tex], the value for sum of integers x and y is option A: 24.

What is integer?

The Latin term "Integer," which implies entire or intact, is where the word "integer" first appeared. Zero, positive numbers, and negative numbers make up the particular set of numbers known as integers.

The given equation is [tex]8^{2x-y} = 5^{x-y+8}[/tex].

The first step is to make the base same-

Multiply the left-hand side with 5 and right-hand side with 8.

[tex]5(8)^{2x-y} = 8(5)^{x-y+8}\\40^{2x-y} = 40^{x-y+8}[/tex]

Since, the bases are same, the power values can be taken into consideration -

2x - y = x - y + 8

Collect the like terms -

2x - x = - y + y + 8

x = 8

Substitute the value of x in any one side of the equation -

2x - y = 0

2(8) - y = 0

16 - y = 0

-y = -16

y = 16

So, now the value of expression x + y is -

8 + 16 = 24

Therefore, the final value is obtained as 24.

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36/25 scoops needed for the recipe if the we have a scoop that holds 2/5 cup, and a recipe calls for 3 3/5 cups of water.

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

We have given that baker has 2/5 cup, and a recipe calls for 3 3/5 cups of water

3 3/5 = 18/5

we only has a 18/5 cup water.

Scoops we will need for the recipe = (18/5)/(2/5) = 36/25

Thus, we will need 36/25 scoops for the recipe.

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9  scoops would we need to use.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

2/5 cup of water can be hold by a scoop.

So, 1 cup of water hold 5/2 scoop

and, 18/5 cup of water can be hold by

=5/2 x 18/5

=18/2

= 9 scoops

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Probability that it is Saturday is 1/2 as it is on weekend. We can calculate this using Conditional Probability formula.

Given that a day of the week is randomly selected and that it is on the weekend, the probability of it being Saturday can be calculated as follows:

There are two days in a week that are on the weekend: Saturday and Sunday.

If we know that a day is on the weekend, the probability of it being Saturday is equal to the number of Saturdays on the weekend divided by the total number of weekend days. This is because there are two equally likely outcomes for the weekend (Saturday and Sunday), and we are interested in only one of them.

We can find this out by using formula:

P(A|B) = P(A and B) / P(B), where A and B are two events.

So, the probability of selecting Saturday, given that it is on the weekend, is 1/2. In other words, if we randomly select a day of the week and it is on the weekend, there is a 50% chance that it will be Saturday.

This can be written as P(Saturday|Weekend) = 1/2.

Therefore, probability = 1/2

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Answer: Y = 23

Step-by-step explanation: -5 x -4 = positive 20 then add 3 which equals 23. 23 is the value of y

Step-by-step explanation:

a=3, u= 5, t=7 (given)

v=u+at

v = 5+ 3×7 = 5+21= 26

v=26

The substitute a = 3, u = 5, t = 7 into the formula v=u+at. The value of V would be 26.

Given, a = 3, u = 5, t = 7

To find, v=u+at or v = u + (a × t)

= 5 + (3 × 7)

= 5 + 21

= 26

Thus, v = 26.

By substituting a = 3, u = 5, t = 7 into the formula v=u+at the value of V would be 26.

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Answer:

The perimeter of the triangle is 30.5.

Step-by-step explanation:

To find the perimeter of the triangle, we need to find the length of the other leg.

We can use the equation of the line that defines the hypotenuse, y = 3x + 2, to find the coordinate of the endpoint of the shorter leg. The endpoint has x-coordinate equal to 3 (since the length of the leg is 3), and the y-coordinate can be found by substituting x = 3 into the equation:

y = 3x + 2

y = 3 * 3 + 2

y = 11

So the endpoint of the shorter leg is (3, 11).

Next, we can use the Pythagorean theorem to find the length of the other leg:

a^2 + b^2 = c^2

where a is the length of the shorter leg (which we know is 3), b is the length of the other leg, and c is the length of the hypotenuse (which is also on the line y = 3x + 2).

We can use the coordinates of the endpoint of the shorter leg to find the length of the hypotenuse:

c = √((3 - 0)^2 + (11 - 2)^2)

c = √(3^2 + 9^2)

c = √(9 + 81)

c = √90

So the length of the hypotenuse is √90.

Using the Pythagorean theorem, we can now find the length of the other leg:

3^2 + b^2 = (√90)^2

9 + b^2 = 90

b^2 = 81

b = 9

So the length of the other leg is 9.

Finally, the perimeter of the triangle is 3 + 9 + √90, which is approximately 12 + 9 + 9.5 = 30.5.

Answer:

6 scarves

Step-by-step explanation:

So he has $90 and spends $35 so: [tex]90-35=55[/tex]

The scarves cost 8 dollars each so we need to divide: [tex]55[/tex]÷[tex]8=6.875[/tex]

You can't buy have .875 of the scarves so he can only buy 6 scarves

Answer: 6

Step-by-step explanation: 90-35=55  55-8-8-8-8-8-8=7

In this case, the optimal solution occurs at X1 = 40 and X2 = 0, which gives a maximum value of Z = 200.

An inequality is a relation which makes a non-equal comparison between two numbers or mathematical expressions.

here, we have,

aX1 + bX2 ≤ c

where a, b, and c are constants.

The first constraint, 1.5X1 + 2.5X2 ≤ 80, is already in standard form.

The second constraint, 2X1 + 1.5X2 ≤ 70, can be rewritten in standard form as follows:

-2X1 - 1.5X2 ≤ -70

You can now write the problem in the following standard form:

Maximize Z = 5X1 + 4X2

Subject to:

1.5X1 + 2.5X2 ≤ 80

-2X1 - 1.5X2 ≤ -70

X1, X2 ≥ 0

In this case, the optimal solution occurs at X1 = 40 and X2 = 0, which gives a maximum value of Z = 200.

This means that if you produce 40 units of X1 and 0 units of X2, you will achieve the highest possible value of Z.

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Answer:

Tip=7.47

Total bill=57.24

Step-by-step explanation:

tip=15/100×49.77=7.47(to nearest cent)

total bill=115/100×49.77=57.24(to nearest cent)

Answer:

see below

Step-by-step explanation:

1. XZ = √(200²+200²) =√2*200 = 282.8m

2. if the man started from 0,0 point & walks 120° meaning he's walking towards the northwest, so he'll be 400m west and 400√3 = 693m north from his starting point, because 120° -90° = 30° you are basically solving a problem of 3 sides length of a special straight triangle with an angle of 30. this type of triangle has a property of shorter side = 1/2 of the long side.  2nd shorter side = √3/2 of the long side.  this, you should memorize.  which will make lots of problems a piece of cake. good luck

Answer:

1. XZ = √(200²+200²) =√2*200 = 282.8m

2. Not sure

Step-by-step explanation:

The region has a 318.0863 square foot size, as stated in the sentence.

The diameter or extent of a circular is its circumference. A straight line connecting a spot on one length of the circular to a position at the other end, going through the middle, is the diameter.

Diameter of the circle is 26 feet , so radius of the circle is r

= 26/2

= 13 feet

Central angle of the sector is [tex]\frac{5 \pi}{8} \text { radians. }[/tex]

We know that area of a sector of circle of radius r and central angle θ is

[tex]A=\frac{1}{2} \theta r^2[/tex]

Therefore, area of the sector is

A = 1/2 × 5π/8 × 13² = 318.0863 square feet

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For the Propositional Function each proposition ∀x∀y P(x,y) is false.

What is a function?

In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.

It is given that Propositional function -

P(x,y) : x ≥ y

Universal quantifier x Universal quantifier y Propositional function

∀x∀y P(x,y)

For every positive integer = every positive integer ≥ every positive integer

But this is false.

Example - x = 1 and x = 2

x < y

Therefore, the given statement is false.

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Let P(x,y) be the propositional function x≥y. The domain of discourse is Z+×Z+. Tell whether each proposition is true or false.

∀x∀yP(x,y)

The amount of paper, he will need for the bulletin board is 30.875 square feet.

The required amount of ribbon is 22.5 feet.

The whole distance that a rectangle's borders, or its sides, the cover is known as its perimeter. Given that a rectangle has four sides, the perimeter of the rectangle will be equal to the total of its four sides.

Given:

Kyle puts ribbon around his rectangular bulletin board and covers it in a paper board measuring 4[tex]\frac{3}{4}[/tex] feet by 6[tex]\frac{1}{2}[/tex].

That means,

the perimeter of the paper board = the perimeter of the rectangular bulletin board

The perimeter of the rectangular bulletin board = 2(4[tex]\frac{3}{4}[/tex] + 6[tex]\frac{1}{2}[/tex])

The perimeter of the rectangular bulletin board = 45/2 feet

The perimeter of the rectangular bulletin board = 22.5 feet.

The amount of paper = (4[tex]\frac{3}{4}[/tex] x 6[tex]\frac{1}{2}[/tex]) = 30.875 square feet.

Therefore, the required amount of ribbon is 22.5 feet.

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The sample proportion for successes that estimates the percentage of people who own a tablet computer from Horace's survey of 400 individuals is 48.75%.

The sample proportion shows the percentage or proportion of successes or expected outcomes in a sample.

The sample proportion is given as the quotient resulting from the division operation between the successes (numerator) and sample size (denominator), and multiplied by 100.

The Sample Size = 400

The number of tablet computer owners in the sample = 195

The sample proportion = Number of Success/Sample Size x 100

= 195/400 x 100

= 48.75%

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The runner slides a distance of approximately 0.255 meters or 25.5 centimeters, and the mechanical energy lost due to friction is 140.29 J.

What is the coefficient?

A coefficient is a number multiplied by a variable. Examples of coefficients: In the term 14 c 14c 14c, the coefficient is 14. In the term g, the coefficient is 1.

A) The mechanical energy lost due to friction can be calculated as follows:

Initial kinetic energy of the runner: KE = 0.5 * m * v² = 0.5 * 80 kg * (4.7 m/s)² = 140.29 J

The force of friction acting on the runner is given by:

[tex]friction_{force} = friction_{coefficient} * normal_{force}[/tex]

where,

[tex]friction_{coefficient} = 0.70[/tex]

[tex]and normal_{force} = m * g (g = 9.8 m/s^{2} )[/tex]

The normal force is given by:

[tex]normal_{force} = m * g = 80 kg * 9.8 m/s^{2} = 784 N[/tex]

Therefore, the force of friction acting on the runner is: [tex]friction_{force} = 0.70 * 784 N = 548.8 N[/tex]

The work done by friction is given by:

[tex]W = friction_{force} * distance[/tex]

Since the speed of the runner is reduced to zero, the work done by friction is equal to the change in kinetic energy:

[tex]W = KE_{final} - KE_{initial}[/tex]

= 0 - 140.29 J = -140.29 J

So, the mechanical energy lost due to friction is 140.29 J.

B) The distance the runner slides can be calculated using the work-energy theorem, which states that the work done on an object is equal to its change in kinetic energy.

The work done by friction is given by: W = friction_force * distance

Since the friction force is constant, the work done by friction is equal to the change in kinetic energy:

[tex]W = KE_{final} - KE_{initial}[/tex]

= 0 - 140.29 J = -140.29 J

Rearranging this equation and substituting in the known values, we get:

[tex]distance = -W / friction_{force}[/tex]

= -140.29 J / 548.8 N = 0.255 m or 25.5 cm

Hence, the runner slides a distance of approximately 0.255 meters or 25.5 centimeters, and the mechanical energy lost due to friction is 140.29 J.

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Answer:

m+1p4 =mp5

1p4= mp5-m

m=p5