Ines's younger brother will be home in a half hour. If her garden hose flows at a rate 24​ gal/min, does she have enough time to fill the pool before he gets​ home? Explain. ​

Answer:

To simplify (1/2)³x(1/2)², we can multiply the coefficients and add the exponents with the same base:

(1/2)³x(1/2)² = (1/2)^(3+2) = (1/2)^5

Therefore, (1/2)³x(1/2)² simplified is equal to (1/2)^5, which can also be written as 1/32 in fraction form.

Step-by-step explanation:

In order to multiply we use the formula for indices' multiplication that is

[tex] {n}^{a} \times {n}^{b} = {n}^{a + b} [/tex]

Hence,

[tex]{( \frac{1}{2} )}^{3}( { \frac{1}{2}}^{2}) = {( \frac{1}{2} )}^{5} [/tex]

[tex] ( \frac{{1}^{5} }{{2}^{5} } ) = {2}^{ - 5} [/tex]

The width of the chest shaped like a rectangular prism, to the nearest tenth of an inch is 32.1.

Kenji has made a treasure chest, shaped like a rectangular prism that must hold around 10,368 cubic inches of sand. In the second act of the school play, an actor will stand on the chest.

Therefore, the chest must be 24 inches tall. The length of the chest is twice its width.

To determine the width of the chest, you should first determine the length of the chest.

Then, using the formula for the volume of a rectangular prism, you can solve for the width of the chest.

Length of the chest

The formula for the volume of a rectangular prism is V = lwh

Given that the chest needs to hold around 10,368 cubic inches of sand, we can write 10,368 = lwh

Since the chest is twice as long as it is wide, the length (l) of the chest is equal to 2w.

Substituting 2w for l, we have:

10,368 = (2w)w

hence 5,184 = wh²(5,184/h)

= w*h(5,184/h²) = w

Since the chest must also be 24 inches tall, we can write:

h = 24 feet

Substituting this value into the equation, we have:

(5,184/24²) = w

hence w = 32.1 inches

Therefore, the width of the chest to the nearest tenth of an inch is 32.1 inches.

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Answer:

75%

Step-by-step explanation:

Assume Teresa can vote for herself. 60/80=3/4=75%

Ricky has 23-word hours each week to dedicate to his classes. Homework takes 6.5 hours and each class (c) is 1.5 hours long. Thus, 05 classes Ricky takes every week.

There are 60 minutes in 1 hour. To convert from minutes to hours, divide the number of minutes by 60. For example, 120 minutes equals 2 hours because 120/60 = 2.

According to the Question:

Let us consider

a = hour she dedicates to his classes = 6.5 hours

and

b = hours spend on homework= 1.5 hours

Total hours in a week devoted to his classes = 23/7

Therefore, 23/7 ×1.5

                = 5 classes.

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Answer:

7 over -5

Step-by-step explanation:

Answer:

Step-by-step explanation:The sum of the measures of the angles in a triangle is always 180 degrees. So, we can set up an equation and solve for x:

36 + (6x+3) + 87 = 180

Combine like terms:

126 + 6x = 180

Subtract 126 from both sides:

6x = 54

Divide both sides by 6:

x = 9

Therefore, the value of x is 9.

The 45th term of the sequence is 267.

The 45th term of a sequence can be calculated using the formula:

Tn = a + (n – 1)d

Where,

Tn = the nth term

a = the first term

n = the term position

d = the common difference

In this sequence, the first term is 3, the common difference is 6, and the term position is 45.

Therefore, the 45th term of the sequence is:

T45 = 3 + (45 – 1)6

T45 = 3 + (44)6

T45 = 3 + 264

T45 = 267

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the value of k such that the line through (6, 4) and (k, 2) is parallel to the line y = 2x is k = 5.

How to solve the question ?

To find the value of k such that the line through (6, 4) and (k, 2) is parallel to the line y = 2x, we need to find the slope of the line y = 2x, which is 2.

Since two lines are parallel if and only if they have the same slope, we know that the line through (6, 4) and (k, 2) must also have a slope of 2.

Using the slope formula:

slope = (y₂ - y₁) / (x₂ - x₁)

where (x₁, y₁) = (6, 4) and (x₂, y₂) = (k, 2), we get:

2 = (2 - 4) / (k - 6)

Multiplying both sides by k - 6 gives:

2(k - 6) = -2

Expanding and simplifying gives:

2k - 12 = -2

Adding 12 to both sides gives:

2k = 10

Dividing both sides by 2 gives:

k = 5

Therefore, the value of k such that the line through (6, 4) and (k, 2) is parallel to the line y = 2x is k = 5.

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Answer:

m>22 and m[tex]\leq[/tex]34

Step-by-step explanation:

Answer:

3x + 18

Step-by-step explanation:

3 ( x + 6 )

= 3*x + 3*6

= 3x + 18

Answer:

Step-by-step explanation:

expand 3(x+6)

3(x + 6) =      

3 * x + 3 * 6

3x + 18

A procession typically has one-fourth of the participants with red hair, one-sixth with brown hair, and the remaining participants with black hair. 7/12 of the population has black hair.

We are given that 1/4 of the people have red hair and 1/6 of them have brown hair.

Let's add these fractions together to find the fraction of people who have either red or brown hair:

[tex]\\\frac{1}{4} + \frac{1}{6}\\ =\frac{3+2}{12} \\ =\frac{5}{12}[/tex]

This means that 5/12 of the people have either red or brown hair.

Since the remaining people must have black hair, we can subtract this fraction from 1 to find the fraction of people who have black hair:

1 - 5/12

=12-5/12

= 7/12

Therefore, the fraction of people who have black hair is 7/12.

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Step-by-step explanation:

Don't worry we will take care of everything. It's easy. listen carefully

first of all write your questions carefully.

i think it should be like this-

y= -6x +43 ------ (i)

y= -8x -59---------(ii)

1. We have two unknowns x and y. and two equations .

2. CONCEPT:- there are several ways to solve it like.

ACCORDING TO SUBSTITUTION METHOD:-

Simply, write the equation in term of single variable(unknown). * [ which is already done for us]

second step, substitute the expression of obtained variable in any one equation.

example: substitute the value of y from equation (i) in (ii)

we will obtained equation -

=> y= -8x -59 [ put value of y from (i) ]

=> -6x +43 = -8x -59

(solve and find x)

=> -6x +8x = -59 - 43

=> 2x = -102

=> x = -51

Third step in substitute method is, now substitute this obtained value of x in any equation (i) or (ii) to get unknown y.

y will be = 349

* your questions was wrong so i have made it by myself. if this does not match your question sorry from my side. buti have shown you the concept to solve this type of questions. You will be able to solve this by your self now by applying concepts.

Answer:

The scale factor is 1/2

Step-by-step explanation:

The ordinal length is 8 and the width is 4.

The image has a length of 4 and a width of 2.

Helping in the name of Jesus.

The scale factor is 1/2

A scale factor is when you enlarge a shape and each side is multiplied by the same number. This number is called the scale factor. Maps use scale factors to represent the distance between two places accurately.

here, we have,

given that,

a polygon ABCD with vertices at 6 comma 6, 14 comma 6, 14 comma 10, 6 comma 10 and a second polygon A prime B prime C prime D prime with vertices at 3 comma 3, 7 comma 3, 7 comma 5, 3 comma 5.

so, we get,

The ordinal length is 8 and the width is 4.

and, we have,

The image has a length of 4 and a width of 2.

so, we get,

scale factor for length = 4/8

                                     = 1/2

scale factor for width = 2/4

                                    = 1/2

Hence, The scale factor is 1/2.

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Answer: Using the absolute value function, linear functions and translations, we have that:

9. Vertex (2, 0), Range: {y | 0 ≤ y < ∞}

10. The equation is f(x) = -5x + 100.

11. The correct option is: The slope of f(x) is greater than the slope of g(x).

12. h(-5) = 10.

13. The equation is f(x) = 2x + 5.

14. The graph of y = f(x) will shift right 9 units.

Step-by-step explanation:

The inflection points are at x = -[tex]\sqrt{(1/3)}[/tex] and x = sqrt(1/3), and f is concave up on (-[tex]\sqrt{1/3}[/tex]), [tex]\sqrt{(1/3)}[/tex]), and concave down elsewhere.

(a) To find the intervals on which f is increasing or decreasing, we need to find the first derivative of f and determine its sign.

[tex]f(x) = x^4 - 2x^2 + 3[/tex]

[tex]f'(x) = 4x^3 - 4x[/tex]

Setting f'(x) = 0, we get:

[tex]4x(x^2 - 1) = 0[/tex]

This equation has roots at x = 0, x = -1, and x = 1. We can use the first derivative test to determine the intervals of increasing and decreasing.

When x < -1, f'(x) is negative, so f is decreasing.

When -1 < x < 0, f'(x) is positive, so f is increasing.

When 0 < x < 1, f'(x) is negative, so f is decreasing.

When x > 1, f'(x) is positive, so f is increasing.

Therefore, f is decreasing on (-∞, -1) and (0, 1), and increasing on (-1, 0) and (1, ∞).

(b) To find the local maximum and minimum values of f, we need to look for critical points and evaluate the function at those points.

Critical points occur where f'(x) = 0 or is undefined. We have already found that f'(x) = 0 at x = 0, x = -1, and x = 1.

f(0) = 3, f(-1) = 6, f(1) = 2

Therefore, f has a local maximum at x = -1, with a value of 6, and local minimums at x = 0 and x = 1, with values of 3 and 2, respectively.

(c) To find the intervals of concavity and inflection points, we need to find the second derivative of f and determine its sign.

[tex]f(x) = x^4 - 2x^2 + 3[/tex]

[tex]f'(x) = 4x^3 - 4x[/tex]

[tex]f''(x) = 12x^2 - 4[/tex]

Setting f''(x) = 0, we get:

[tex]12x^2 - 4 = 0[/tex]

[tex]x^2 = 1/3[/tex]

x = ±sqrt(1/3)

We can use the second derivative test to determine the intervals of concavity.

When x < -sqrt(1/3), f''(x) is negative, so f is concave down.

When -sqrt(1/3) < x < sqrt(1/3), f''(x) is positive, so f is concave up.

When x > sqrt(1/3), f''(x) is negative, so f is concave down.

Therefore, the inflection points are at x = -sqrt(1/3) and x = sqrt(1/3), and f is concave up on (-sqrt(1/3), sqrt(1/3)), and concave down elsewhere.

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the total number of days spent in Bolivia by Audrey is 7days.

Audrey spent two weeks in Brazil

that mean

the total number of days spent in Brazil by Audrey = 2x7

= 14 days

This is twice as many days as she spent in Bolivia.

2m = 14

m = 14/2

m = 7

so, the total number of days spent in Bolivia by Audrey = 7days

The term "week" most commonly refers to any span of seven continuous days. The term "week" is also frequently used to describe the seven-day period that runs from Sunday through Saturday (though in some places this may be different, with the week considered to begin on Monday, for example)

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1. This is an example of a minimum wage price floor.

2. This is an example of a price ceiling because it establishes a maximum price at which a gasoline station may sell gasoline.

3.This is an example of a price floor because it sets a minimum amount at which a gasoline station may sell gasoline.

Price Ceilings or Price Floors: A Determination
1. There are many teenagers who would like to work at gas stations, but they are not hired due to minimum-wage laws.
This is an example of a minimum wage price floor.

In a minimum wage, the government sets a minimum wage, and employers are unable to offer their employees less than that amount.

The minimum wage acts as a price floor because it establishes a minimum amount that an employer must pay.

2. The government prohibits gas stations from selling gasoline for more than $2.70 per gallon.
This is an example of a price ceiling because it establishes a maximum price at which a gasoline station may sell gasoline.

A price ceiling is a maximum amount that can be charged for a good or service.
3. The government has instituted a legal minimum price of $2.70 per gallon for gasoline.
This is an example of a price floor because it sets a minimum amount at which a gasoline station may sell gasoline.

A price floor establishes a minimum price that must be charged for a good or service in this scenario.

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Answer:

The first step is to calculate the area of the circle pool:

- The diameter of the pool is 16 ft, which means the radius is 8 ft (half of the diameter).

- The formula for the area of a circle is A = πr^2, where A is the area and r is the radius.

- Plugging in the values, we get A = π(8 ft)^2 = 64π sq ft.

The total area of the yard is 25 ft x 60 ft = 1500 sq ft. To find out how many square feet of the yard will be grass, we need to subtract the area of the pool from the total area of the yard:

- Grass area = Total area - Pool area = 1500 sq ft - 64π sq ft ≈ 1304.43 sq ft.

Therefore, about 1304.43 square feet of their yard will be grass, to two decimal places.

The value of the constant c such that the function f(x) = cx³ is a probability density function is 4.

The given function is f(x) = cx³, where 0 < x < 1. We know that a function f(x) is said to be a probability density function on the interval [a, b] if it satisfies the following conditions: 1. f(x) ≥ 0 for all x ∈ [a, b].2. ∫f(x)dx = 1 over the interval [a, b]. Given that 0 < x < 1, the limits of integration are from 0 to 1.

Now, integrating the given function, we get: ∫₀¹ cx³ dx= [c/4 x⁴]₀¹= c/4 × 1⁴ - c/4 × 0⁴= c/4

Therefore, for the given function to be a probability density function, the value of c should be such that∫₀¹ cx³ dx = 1⇒ c/4 = 1⇒ c = 4

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Answer: Therefore, the height of the light pole is 50 feet.

Step-by-step explanation:

We can use proportions to solve the problem.

Let h be the height of the light pole.

Then, we have:

h / 75 = 8 / 12

To solve for h, we can cross-multiply:

12h = 75 * 8

h = (75 * 8) / 12

h = 50

As per the congruent angles' theorem, the angles ∠3=∠4.

Angles that are identical to one another are said to be congruent. As a result, these angles are proportionally equal to one another.

Angles can be acute, obtuse, exterior, or interior, and their shape has no bearing on whether they are congruent or not.

In the given triangle,

∠5 = ∠6

∠1 = ∠2 as the angles are opposite corresponding angles.

As two of the 3 angles are equal to each other.

So, ∠3=∠4.

The third angles are equivalent to each other as per the congruent angle theorem.

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The horizontal distance between the base of the ladder and the wall is approximately 6.58 feet

We can use trigonometric function to solve this problem. Let's call the horizontal distance we are looking for "x".

First, we can use the fact that the ladder forms an angle of 66° with the ground to find the vertical height it reaches. We know that the ladder is 16 feet long, and we can use the sine function to find the vertical height

sin(66°) = height/16

height = 16×sin(66°) = 15.12 feet (rounded to two decimal places)

Now, we can use the same angle and the cosine function to find the horizontal distance x

cos(66°) = x/16

x = 16×cos(66°) = 6.58 feet (rounded to two decimal places)

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For the rectangle shaped drawing, the area of the scale drawing is 31.25  cm².

What exactly is a rectangle?

A rectangle is a four-sided flat form with four right angles on its four sides (90-degree angles). It is a quadrilateral having two pairs of equal-length parallel sides.  A rectangle's perimeter is the total of the lengths of all four sides, and its area is derived by multiplying the rectangle's length and breadth. A square is a specific instance of a rectangle with four equal-length sides.

Now,

To find the perimeter of the scale drawing, we add the lengths of all four sides. Rounded to the nearest half centimeter, the length is 12.5 cm and the width is 2.5 cm, so the perimeter is:

P = 2(12.5 cm) + 2(2.5 cm) = 25 cm + 5 cm = 30 cm

Therefore, the perimeter of the scale drawing is 30 centimeters.

To find the area of the scale drawing, we multiply the length by the width. Rounded to the nearest half centimeter, the length is 12.5 cm and the width is 2.5 cm, so the area is:

A = (12.5 cm) × (2.5 cm) = 31.25 cm²

Therefore, the area of the scale drawing is 31.25 square centimeters.

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Correct Question :-

Central Park is a rectangular park in New York City. A map of Central Park in New York City. The measured length is 12.5 centimeters. The measured width is 2.5 centimeters. Find the perimeter and the area of the scale drawing of Central Park. Round your measurements for the length and the width to the nearest half centimeter to calculate your answers.

12 7/8 - 56/17 = 1303/136

Company revenue quadratic function.

Angel

The revenue, in billions of dollars, for a company in the year 2002 was $2.7 billion. One year later, in 2003, the revenue had risen to $3.4 billion. In 2005, the revenue climbed to $3.9 billion, before falling to $2.7 billion in 2008. The revenue, r, in billions of dollars, for the company, is a quadratic function of the number of years since 2002, x. what is the vertex of the function?

To find the quadratic function that represents the revenue of the company as a function of the number of years since 2002, we can use the vertex form of a quadratic function:

r(x) = a(x - h)^2 + k

where a is the coefficient of the quadratic term, h is the x-coordinate of the vertex, and k is the y-coordinate of the vertex.

We can use the given revenue values to set up a system of three equations:

2.7 = a(0 - h)^2 + k

3.4 = a(1 - h)^2 + k

2.7 = a(6 - h)^2 + k

Subtracting the first equation from the second, and the first equation from the third, we get:

0.7 = a(1 - h)^2

0 = a(6 - h)^2

Since a cannot be zero (otherwise we wouldn't have a quadratic function), we can divide the second equation by the first to get:

6 - h = 10

which gives us h = -4.

Substituting h = -4 into the first equation, we get:

2.7 = a(0 - (-4))^2 + k

2.7 = 16a + k

Substituting the revenue value for 2005, we get:

3.9 = a(3 - (-4))^2 + k

3.9 = 49a + k

Solving for a and k, we get:

a = -0.1

k = 4.3

Therefore, the quadratic function that represents the revenue of the company as a function of the number of years since 2002 is:

r(x) = -0.1(x + 4)^2 + 4.3

The vertex of this function is at (-4, 4.3).

Angel

What is the sum of the numbers in the sequence 3, −4, 5, −6, . . . , 101?

We can notice that the sequence alternates between adding an odd number and subtracting an even number. The first term is 3, which is odd, so the sequence starts by adding an odd number. The second term is -4, which is even, so the sequence then subtracts an even number. This pattern continues, so the sum of the sequence can be written as:

3 - 4 + 5 - 6 + ... + 101

We can group the terms into pairs:

(3 - 4) + (5 - 6) + ... + (99 - 100) + 101

Each pair of terms adds up to -1, so we can simplify the expression to:

-1 -1 -1 ... -1 + 101

where there are 50 pairs of -1's. The sum of 50 -1's is -50, so the sum of the sequence is:

-50 + 101 = 51

Therefore, the sum of the numbers in the sequence 3, −4, 5, −6, . . . , 101 is 51.

Angel

What is 12 7/8 - 56/17?

To subtract mixed numbers like 12 7/8, we first need to convert it to an improper fraction. We can do this by multiplying the whole number by the denominator of the fraction, and adding the result to the numerator. This gives us:

12 7/8 = (12 × 8 + 7)/8 = 103/8

Now we can subtract 56/17 from 103/8. To do this, we need to find a common denominator for the two fractions. The least common multiple of 8 and 17 is 136, so we can rewrite the fractions with this denominator:

103/8 = (103/8) × (17/17) = 1751/136

56/17 = (56/17) × (8/8) = 448/136

Now we can subtract the two fractions:

1751/136 - 448/136 = (1751 - 448)/136 = 1303/136

We can simplify this fraction by finding a common factor to divide both the numerator and denominator. Since both 1303 and 136 are relatively prime, we cannot simplify it any further. Therefore, the final answer is:

12 7/8 - 56/17 = 1303/136

Answer:

16.8%

Step-by-step explanation:

When fourty percentage of the people in a town are females. 10% of the females are left -handed. Then total 16.8% of peoples in the town are not female and are left-handed.

We have a percentage data of people in a town. Percentage of female peoples in the town = 40 %

Percentage of female left handed = 10 %

Percentage of total left handed = 20.8 %

Percentage is defined as a ratio of a number to 100 or it expressed as a fraction of 100. Let Total population of the town = X

So, female peoples in the town = 40% of X = (40/100) × X

= 0.4X

The peoples who are not female = X - 0.4X = 0.96X

Number of female left-handed = 10% of 0.4X = (10/100)× 0.4X

= 0.04X

Number of all left-handed in the town

= 20.8% of X = (208/100)× X

= 0.208X

Left-handed peoples who are not female

= 0.208X - 0.04X

= 0.168X

The percentage of people who are not female and who are left-handed

= (0.168X /X )×100

= 16.8%

Hence, required percentage is 16.8%.

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The dot plot for the given data is given below with Title Number of hours students watched Netflix in a month. The mode is 21, median is 29.5, mean is 26.92, range is 16.

A dot plot is a simple and effective way to display data graphically. It is a type of chart that uses dots to represent values and shows the distribution of a dataset.

Mode is a statistical term that refers to the value that appears most frequently. In the given data, 21 occurs most frequently, hence the mode is 21.

To find the median first arrange the data in ascending or descending order

18, 18, 21, 21, 21, 22, 29, 30, 31, 32, 33, 33, 34, 34

Hence, the number of observations in the data set are 14, therefore the median is the average of 7th and 8th observation is the arranged data set.

Median = (29 + 30)/2 = 59/2 = 29.5

Mean is the ratio of sum of all observations to the total number of observations.

Mean = (18 + 18 + 21 + 21 + 21 + 22 + 29 + 30 + 31 + 32 + 33 + 33 + 34 + 34)/14 = 26.92

Range is the difference between the highest and lowest number in the data set.

Range = 34 - 18 = 16

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Let's call the speed of the wind "w". When the airship is flying with the wind, its effective speed is 50 + w km/hour. When the airship is flying against the wind, its effective speed is 50 - w km/hour.

Using the formula distance = rate x time, we can write two equations for the round trip:

150 = (50 + w)(t1)

150 = (50 - w)(t2)

where t1 is the time the airship took to fly with the wind and t2 is the time it took to fly against the wind.

We also know that the total round trip took 6 hours and 15 minutes, or 6.25 hours:

t1 + t2 = 6.25

Now we can solve for w. Let's rearrange the second equation to solve for t2:

t2 = 150 / (50 - w)

Substitute this expression for t2 into the third equation:

t1 + 150 / (50 - w) = 6.25

Solve for t1:

t1 = 6.25 - 150 / (50 - w)

Now substitute this expression for t1 into the first equation:

150 = (50 + w)(6.25 - 150 / (50 - w))

Simplify and solve for w:

w = 25 km/hour

Therefore, the speed of the wind is 25 km/hour.

The graph given in this problem represents a proportional relationship with a constant of variation that is equals to -3.

A proportional relationship is a type of relationship between two quantities in which they maintain a constant ratio to each other. This means that if one quantity is multiplied by a certain factor, the other quantity will also be multiplied by the same factor.

The equation that defines the proportional relationship is given as follows:

y = kx.

In which k is the constant of proportionality, representing the increase in the output variable y when the constant variable x is increased by one.

For the graph given, when x increases by 1, y decays by 3, hence the constant is given as follows:

k = -3.

Then the equation is given as follows:

y = -3x.

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If the value of C, the circumference is known, then the diameter is:

D = C/pi

For a circle whose radius is R, the formula for the circumference is:

C = 2*pi*R

Where pi = 3.14

Particularly, we know that the diameter of a circle is twice the radius, os:

D = 2*R

We can rewrite the circumference equation to get:

C = pi*(2*R) = pi*D

So, solving that equation for the diameter, we will get:

D = C/pi

That equation gives the diameter if we know the value of the circumference.

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If 25 tapered pins are machined from a steel rod 15 ft long, then total 15 tapered pins can be made from a steel rod 9 ft long.

The unitary method is a method where you find the value of one unit and then find the value of the number of units you want. The formula for the units method is to find the value of a single unit and then multiply the value of the single unit by the number of units to get the desired value. We have specify that 25 tapered pins can be made up from a steel rod 15 ft long. Let 'x' represent the number of pins that can be made from 9 ft long steel rod. Now, using the unitary method,

number of pins machined from a 15 ft long steel rod = 25

number of pins machined from a 1 ft long steel rod = 25/15

So, number of pins machined from a 9 feet long steel rod, x = (25/15)×9

=> x = 3×5 = 15

Hence, required tapered pins made from a steel rod 9 ft long is equals to the 15 pins.

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