Consider a system with one component that is subject to failure, and suppose that we have 120 copies of the component. Suppose further that the lifespan of each copy is an independent exponential random variable with mean 25 days, and that we replace the component with a new copy immediately when it fails.(a) Approximate the probability that the system is still working after 3625 daysProbability(b) Now, suppose that the time to replace the component is a random variable that is uniformly distributed over (0,0.5). Approximate the probability that the system is still working after 4250 days.Probability

The values in the interval [0, 2π) for which the two points would intersect as required is; Choice C; theta equals 2 times pi over 3 comma 4 times pi over 3.

Recall from the task content; the given functions are;

f (x) = 2cos2θ and g(x) = −1 − 4cos θ − 2cos2θ

Therefore, for intersection; f (θ) and g(θ):

2 cos²θ = −1 − 4cos θ − 2cos²θ

4cos²θ + 4cosθ + 1 = 0

let cos θ = y;

4y² + 4y + 1 = 0

y = -1/2

Therefore; -1/2 = cos θ

θ = cos-¹ (-1/2)

θ = 2π/3, 4π/3.

Ultimately, the correct answer choice is; Choice C; theta equals 2 times pi over 3 comma 4 times pi over 3.

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Answer:

  see attached

Step-by-step explanation:

You want the given triangle dilated by a factor of -3 about point A.

To find the image point corresponding to a pre-image point, multiply the pre-image point's distance from A by the dilation factor. The negative sign means the distance to the image point is measured in the opposite direction.

In the attached figure, the chosen point is 4 units up and 5 units right of A. Its image in the dilated figure is 3·4 = 12 units down, and 3·5 = 15 units left of A.

This same process can be used to locate the other vertices of the triangle's image.

Answer:

$109.99

Step-by-step explanation:

The original price of each tire is [tex]\[/tex][tex]109.99[/tex]

Take the amount saved and divide by 4 to find the amount saved on each tire

[tex]96.16\div4 =24.04[/tex]

Add that to the sale price of each tire to find the original price

[tex]85.95+24.04 =109.99[/tex]

Therefore, The original price is $109.99.

The maximum area of the surfboard correct to 2 places is 0.67 m².

Given that a surfboard is in the shape of a rectangle and a semicircle, and its perimeter is to be 4m. We need to find the maximum area of the surfboard, correct to 2 decimal places.

Let the radius of the semicircle be 'r' and the length and breadth of the rectangle be 'l' and 'b' respectively. Perimeter of the surfboard = [tex]4m => l + 2r + b + 2r = 4 => l + b = 4 - 4r[/tex] -----(1)

Area of surfboard = Area of rectangle + Area of semicircle Area of rectangle = l × b Area of semicircle = πr²/2 + 2r²/2 = (π + 2)r²/2Area of surfboard = l × b + (π + 2)r²/2 -----(2)

We have to maximize the area of the surfboard. So, we have to find the value of 'l', 'b', and 'r' such that the area of the surfboard is maximum .From equation (1), we have l + b = 4 - 4r => l = 4 - 4r - bWe will substitute this value of 'l' in equation (2)

Area of surfboard = l × b + (π + 2)r²/2 = (4 - 4r - b) × b + (π + 2)r²/2 = -2b² + (4 - 4r) b + (π + 2)r²/2Now, we have to maximize the area of the surfboard, that is, we need to find the maximum value of the above equation.

To find the maximum value of the equation, we can differentiate the above equation with respect to 'b' and equate it to zero. d(Area of surfboard)/db = -4b + 4 - 4r = 0 => b = 1 - r Substitute the value of 'b' in equation (1),

we get l = 3r - 3Now, we can substitute the values of 'l' and 'b' in the equation for the area of the surfboard.

Area of surfboard =

[tex]l × b + (π + 2)r²/2 = (3r - 3)(1 - r) + (π + 2)r²/2 = -r³ + (π/2 - 1)r² + 3r - 3[/tex]

[tex]-r³ + (π/2 - 1)r² + 3r - 3 = -0.6685 m² \\[/tex]

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The value of y when x=36 is 31/3.

According to the question,

x varies directly with 3y+5

Thus,

[tex]x = k(3y+5)[/tex]

where K is any positive integer.

Now, from the question,

y=5/3 when x=10

Thus,

[tex]10 = k(3(\frac{5}{3} )+5)\\10 = k(10)\\k = 1[/tex]

Now we can use k to find the value of y when x=36:

[tex]36 = 1(3y+5)\\31 = 3y\\y = \frac{31}{3}[/tex]

In mathematics, an integer is a whole number that can be positive, negative, or zero. Integers are a fundamental concept in number theory and are used in a variety of applications across many fields. Integers can be represented using the symbol "Z" and are denoted by an integer value like -3, 0, 1, 2, 3, etc. They are used to count and measure quantities in real-life situations, such as the number of apples in a basket or the distance between two cities.

Integers are closed under addition, subtraction, and multiplication, meaning that if you add, subtract, or multiply any two integers, the result will also be an integer. However, the division is not always closed under integers, as dividing by zero is undefined, and dividing two integers can result in a non-integer value.

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Complete Question:

If x varies directly with 3y+5 and y=5/3 when x=10, then what is the value of y when x=36

Answer:

y = - 2x + 4

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = [tex]\frac{1}{2}[/tex] x - 9 ← is in slope- intercept form

with slope m = [tex]\frac{1}{2}[/tex]

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{1}{2} }[/tex] = - 2 , then

y = - 2x + c ← is the partial equation

to find c substitute (3, - 2 ) into the partial equation

- 2 = - 2(3) + c = - 6 + c ( add 6 to both sides )

4 = c

y = - 2x + 4 ← equation of perpendicular line

the answer to the problem that you need to is 1024

Answer: 41666666669 / 50000000003

Step-by-step explanation:

The instantaneous velocity of the object at t = 6 is 2.

Suppose that s is the position function of an object, given as s(t) = 2t - 7. We compute the instantaneous velocity of the object at t = 6 as follows. Use exact values. First we compute and simplify (6 + h). s(6 + h) = 2(6 + h) - 7 = 12 + 2h - 7 = 2h + 5Then we compute and simplify the average velocity of the object between t = 6 and t = 6 + h.8(6+h) - s(6) h = 8(6 + h) - (2(6) - 7) h= 8h + 56

Then, to rationalize the numerator in the average velocity. (If it applies, simplify again.)$(6 + h) - $(6) h(h(h) + 56)/(h(h)) = (8h + 56)/h The instantaneous velocity of the object att = 6 is the limit of the average velocity as h approaches zero.s(6 + h) – $(6) v(6) lim h -0s(6 + h) – s(6) v(6) lim h -0Using the above calculation, we get:s(6 + h) – s(6) / h lim h -0s(6 + h) = 2(6 + h) - 7 = 2h + 5So,s(6 + h) – s(6) / h lim h -0(2h + 5 - (2(6) - 7)) / h= (2h + 5 - 5) / h = (2h / h) = 2

Therefore, the instantaneous velocity of the object at t = 6 is 2.

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Answer:

Step-by-step explanation:

see diagram

Answer:

4 apples

Step-by-step explanation:

We know

John had 3 apples, then Dropped 2, found 4, then gave 1 to his friend.

How many apples does he have now​?

3 - 2 + 4 - 1 = 4 apples

So, he has 4 apples now.

Answer:

4 apples

Step-by-step explanation:

We know that John had 3 apples

but then he had dropped 2 of them

he then found 4

then he gave 1 to his friend

3-2=1

1+4=5

5-1=4

The answer is 4

Hope this helps!

The Sale price is C. $260.63.

Selling price is the price at which a product or service is sold by a business or seller to a customer. It is the amount of money that a customer must pay in order to purchase the product or service. The selling price is typically determined by factors such as production costs, competition, supply and demand, and profit margins.

Sale price is the discounted price at which a product or service is sold for a limited period of time. It is usually a lower price than the regular price, and it is offered to customers as an incentive to make a purchase. Sale prices can be determined by applying a discount or markdown to the regular selling price.

In the given question,

To find the sale price, we need to first calculate the amount of the markdown:

Markdown = Regular Price x Markdown Rate

Markdown = $389 x 0.33

Markdown = $128.37

The sale price is then the regular price minus the markdown:

Sale Price = Regular Price - Markdown

Sale Price = $389 - $128.37

Sale Price = $260.63

Therefore, the answer is C. $260.63.

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The probabilities Z > 0.75 is P(Z > 0.75) = 1 - P(Z < 0.75).

The probability of Z > 0.75 is 1 - 0.77337 = 0.22663

The probability of Z < -1.06 from it. P(-1.06 < Z< 2.17) = P(Z < 2.17) - P(Z < -1.06) = 0.98425 - 0.14457 = 0.83968

Suppose Z follows the standard normal distribution. The probabilities using the ALEKS calculator are given below.(a) P(Z < 0.79) = 0.78524. (rounded to 5 decimal places)(b) P(Z > 0.75) = 1 - P(Z < 0.75) = 1 - 0.77337 = 0.22663. (rounded to 5 decimal places)(c) P(-1.06 < Z< 2.17) = P(Z < 2.17) - P(Z < -1.06) = 0.98425 - 0.14457 = 0.83968. (rounded to 5 decimal places). In the standard normal distribution, the mean is equal to zero and the standard deviation is equal to 1. The notation for a standard normal random variable is z. Z is a random variable with a standard normal distribution and P(Z) denotes the probability of the random variable Z. Suppose z follows a standard normal distribution then the probability of Z < 0.79 is P(Z < 0.79) = 0.78524. So, the answer is 0.78524(rounded to 5 decimal places).Suppose z follows a standard normal distribution then the probability of Z > 0.75 is P(Z > 0.75) = 1 - P(Z < 0.75). Therefore, the probability of Z > 0.75 is 1 - 0.77337 = 0.22663(rounded to 5 decimal places).Therefore, the probability of -1.06 < Z< 2.17 can be found by finding the probability of Z < 2.17 and then subtracting the probability of Z < -1.06 from it. P(-1.06 < Z< 2.17) = P(Z < 2.17) - P(Z < -1.06) = 0.98425 - 0.14457 = 0.83968(rounded to 5 decimal places).

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Answer:

The value of t = 18

Step-by-step explanation:

202 = 2t + 5 + t + 3t - 2 + 5t +1  Combine like terms

202 = 11t + 4  Subtract 4 from both sides

198 = 11[tex]\frac{11x}{11}[/tex]x  Divide both sides by 11

[tex]\frac{198}{11}[/tex] = 18

Is the question the value of t or the length of each side?

Each side

2t + 5

2(18) + 5

41

T

18

3T - 2

3(18) - 2

52

5T + 1

5(18) + 1

91

91 + 52 + 18 + 41 = 2002

Helping in the name of Jesus.

Answer: $1,071.54

Step-by-step explanation:

To find the interest refund, first we need to calculate the total interest charged on the loan. We can do this by multiplying the monthly interest by the number of months in the loan:

Monthly interest = Total interest / Number of months

Monthly interest = $2,802 / 35

Monthly interest = $80.06

Total interest charged on the loan = Monthly interest x Number of months

Total interest charged on the loan = $80.06 x 35

Total interest charged on the loan = $2,802.10

Now we need to calculate the interest that would have been charged for the remaining 13 months of the loan:

Interest for remaining 13 months = Monthly interest x Remaining months

Interest for remaining 13 months = $80.06 x 13

Interest for remaining 13 months = $1,040.78

Finally, we can find the interest refund by subtracting the interest for the remaining 13 months from the total interest charged on the loan:

Interest refund = Total interest charged - Interest for remaining months

Interest refund = $2,802.10 - $1,040.78

Interest refund = $1,074.32

Therefore, the interest refund on the loan is $1,074.30.

Answer:

x=1.9

Step-by-step explanation:

[tex]\frac{x}{4.6} =\frac{4.6}{11}[/tex]

[tex]11x=21.16[/tex]

[tex]X=1.9[/tex]

We need 144 men to build the house in 12 days working 13 hours a day.

Let M be the number of men needed to build the house in 12 days working 13 hours a day.

140 x 10 x 16 = M x 13 x 12

Simplifying the equation, we get:

22400 = 156M

Dividing both sides by 156, we get:

M = 144.1

An equation in mathematics is a statement that two expressions are equal. It consists of two sides, the left-hand side (LHS) and the right-hand side (RHS), separated by an equal sign (=). The expressions on either side can be numbers, variables, or combinations of both. The equation expresses that the values of the expressions on both sides are equivalent.

Equations play a fundamental role in many areas of mathematics and are used to model various real-world situations, such as physics, engineering, and finance. They can be solved using various techniques, such as substitution, elimination, or graphing, to find the values of the variables that satisfy the equation.

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The gradient of the chord PQ is 2h + 8

Let's first find the coordinates of points P and Q on the curve y = 2x^2+1.

Point P has an abscissa of 2, so its coordinates are (2, 2(2)^2+1) = (2, 9).

Point Q has an abscissa of 2+h, so its coordinates are (2+h, 2(2+h)^2+1) = (2+h, 2(4+4h+h^2)+1) = (2+h, 8+8h+2h^2+1) = (2+h, 2h^2+8h+9).

The gradient of the chord PQ is given by:

(m) = Δy /Δx

(m) = (2h^2+8h+9 - 9) / (2+h - 2)

(m) = (2h^2+8h) / (h)

(m) = 2h + 8

As h approaches zero, the gradient of the chord PQ approaches 8, because the term 2h becomes negligible compared to 8 when h is small. Therefore, the gradient of the tangent to the curve at point P is 8.

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Answer:

x=5/4 or x=5/9

pls mark me brainliest

Answer:

x=5/4 (for the first x),x=5/9 (for the second x)

The number of students that are in the sixth grade is given as follows:

250 students.

The number of students is obtained applying the proportions in the context of the problem.

We know that all students in the sixth grade either purchased their lunch or brought their lunch from home on Monday, and 24% of the students purchased their lunch, hence 76% of the students brought their lunch from home.

190 students brought their lunch from home, which is equivalent to 76% of the number of students, hence the number of students is given as follows:

0.76n = 190

n = 190/0.76

n = 250 students.

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In Python, to calculate FV (Future Value), you can use the following formula: "FV = PV * (1 + r) ^ n" Here, PV = Present Value, r = interest rate, and n = number of periods. There are different ways to implement this formula in Python, but one possible way is using a function.

Here is an example: function fv(pv, r, n): return pv * (1 + r) ** n

The function takes three arguments: pv, r, and n. Then it returns the future value computed with the formula. In your Python code, you can call the function and pass the required values. For example fv_result = fv(1000, 0.05, 10)print(fv_result)The output will be the future value of $1000 after 10 years with a 5% annual interest rate.

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     |-----|-----|-----|----|-----|-----|--│--|-----|----|-----|

    -5   -4   -3   -2   -1    0    1   │  2    3    4    5

                                            1 1/2

On this number line, the tick mark labeled "1 1/2" is located halfway between the integer values of 1 and 2.

To represent the number 1 1/2 on a number line, we need to draw a horizontal line with evenly spaced tick marks. Each tick mark represents a specific value on the number line. Since 1 1/2 is a mixed number that includes a whole number (1) and a fraction (1/2), we need to locate it between the integer values of 1 and 2. The tick mark for 1 1/2 should be halfway between these two integers, which means it would be located at the midpoint of the line segment that connects the tick marks for 1 and 2. By placing the tick mark for 1 1/2 in the correct position on the number line, we can accurately represent this number visually.

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the given form of the rate function:[tex]tan² (t) + 1 = sec²[/tex](t)

Therefore, we can write the given function as:c (t) dtUsing integration by substitution, we haveu = tan (t) ⇒ du = sec² (t) dt

Therefore,S [tex]π/t tan (t) sec² (t) dt= S u du= ln |tan (t)| + C[/tex]Thus, the equivalent closed form of the given function is:S π/t 4tan (t) dt= 4 ln |tan (t)| + C

a. S π/π/4 5t+4/t² + 1 dt equivalent closed formThe question demands to find an equivalent closed form for each function. So let's find the equivalent closed form for the given functions:a. S π/π/4 5t+4/t² + 1 dt

Hint: begin by writing as a sum of two functionsNow, we need to write the given function as a sum of two functions. Let's first write the numerator of the function as a sum of two functions.

Using the formula, a²-b² = (a+b)(a-b), we have5t + 4 = (2 + √21)(√21 - 2)Therefore, we can write the numerator of the function as follows:5t + 4 = (√21 - 2)² - 17Using this in the given function,

we haveπ/π/4 [(√21 - 2)² - 17]/t² + 1 dtLet's further simplify the numeratorπ/π/4 [21 + 4 - 4√21 - 17t² + 34t - 17] / (t² + 1) dt= π/π/4 [-17t² + 34t + 8 - 4√21]/(t² + 1) dtLet's now find the closed form of this function using the integration formulaS f(x) dx = ln |f(x)| + C Therefore, the equivalent closed form of the function is:

S π/π/4 5t+4/t² + 1 dt= π/π/4 [-17t² + 34t + 8 - 4√21]/(t² + 1) dt= - π/2 ln |t² + 1| + 34 π/2 arctan (t) - 17 π/2 t + 2 π/√21 arctan [(2t-√21)/ √21] + Cb. S π/t 4tan (t) dt equivalent closed formNow, let's find the equivalent closed form of the second given function.b. S π/t 4tan (t)

dtHint: begin by using a trig identity to change the form of the rate function Let's now use the following trig identity to change

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The given expression ((y-b)²/(y-b+1)+(y-b)/(y-b+1) after being reduced to a polynomial, can be represented as y-b.

In order to reduce the given equation to a polynomial, we are required to simplify and combine like terms. First, we can simplify the expression in the numerator by expanding the square:

((y-b)²/(y-b+1) = (y-b)(y-b)/(y-b+1) = (y-b)²/(y-b+1)

Now, we can combine the two terms in the equation by finding a common denominator:

(y-b)²/(y-b+1) + (y-b)/(y-b+1) = [(y-b)² + (y-b)]/(y-b+1)

Next, we can combine the terms in the numerator by factoring out (y-b):

[(y-b)² + (y-b)]/(y-b+1) = (y-b)(y-b+1)/(y-b+1)

Finally, we can cancel out the common factor of (y-b+1) in the numerator and denominator to get the polynomial:

(y-b)(y-b+1)/(y-b+1) = y-b

Therefore, the equation ((y-b)²)/(y-b+1)+(y-b)/(y-b+1)  after being simplified, is equivalent to the polynomial y-b.

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Answer:

We know that A receives R500 less than C, so we can write:

4x = 9x - 500

Solving for x, we get:

5x = 500

x = 100

Now we can calculate the amounts received by each person:

A = 4x = 4(100) = R400

B = 7x = 7(100) = R700

C = 9x = 9(100) = R900

To check our answer, we can verify that the ratios of the amounts received by A, B, and C are indeed 4:7:9:

A:B = 400:700 = 4:7

B:C = 700:900 = 7:9

Therefore, the total amount divided is:

400 + 700 + 900 = R2000

So the amount that is divided is R2000.

Step-by-step explanation:

The total amount of money divided is R2000.

Ratio is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.

We are given that;

The ratio of A, B and C= 4:7:9

Now,

Let's start by assigning variables to the unknowns in the problem. Let's call the total amount of money "T". Then, if A receives 4x, B receives 7x, and C receives 9x, where "x" is some constant, we can write:

4x + 500 = C's share

We can also write an equation to represent the fact that the three shares add up to the total amount:

4x + 7x + 9x = T

Simplifying this equation, we get:

20x = T

Now we can substitute the first equation into the second equation and solve for x:

4x + 7x + (4x + 500) = 20x

15x + 500 = 20x

500 = 5x

x = 100

Now we can find the individual shares by multiplying x by the appropriate ratio factor:

A's share = 4x = 400

B's share = 7x = 700

C's share = 9x = 900

Finally, we can check that these add up to the total amount:

400 + 700 + 900 = 2000

Therefore, by the given ratio the answer will be R2000.

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By answering the presented question, we may conclude that Therefore, the expression 9(4/3m-5-2/3m+2) is equivalent to 6m - 27.

An expression in mathematics is a collection of representations, numbers, and conglomerates that mimic a statistical correlation or regularity. A real number, a mutable, or a mix of the two can be used as an expression. Mathematical operators include addition, subtraction, fast spread, division, and exponentiation. Expressions are often used in arithmetic, mathematic, and form. They are used in the representation of mathematical formulas, the solution of equations, and the simplification of mathematical relationships.

To simplify the expression,

[tex]a(b+c) = ab + ac\\9(4/3m-5-2/3m+2) = 9(4/3m - 2/3m - 5 + 2)\\= 9(2/3m - 3)\\= 6m - 27[/tex]

Therefore, the expression 9(4/3m-5-2/3m+2) is equivalent to 6m - 27.

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Step-by-step explanation:

x<-5 is the answer

1.

6x=-30

2.

x=-5

3.

x<-5

After 6 days, the probability that the stock has its original price is 5/16.

There are two possible scenarios that can take place when the stock price fluctuates from one day to the next. Either the price goes up by 1/8th of a point with probability 1/3 or it goes down by 1/8th of a point with probability 2/3.

The price of the stock after six days can be denoted as S6. The price of the stock after the first day can be represented as S0.

Since the price fluctuates either up or down by 1/8th of a point on each day, the price after six days can be represented as follows:S6 = S0 + (up, up, up, up, up, up), (up, up, up, up, up, down), (up, up, up, up, down, up), ... , (down, down, down, down, down, down)

In order to return to the original price, the stock must go up and down by the same amount. As a result, there must be an equal number of ups and downs in the six-day period.

As a result, we must calculate the probability of obtaining an equal number of ups and downs over six days.

Let's represent an increase in the stock price as 'U' and a decrease as 'D.'

The total number of ways in which the stock can go up and down over six days is [tex]2^6 = 64[/tex].

The total number of ways in which the stock can return to its original price can be calculated as follows: [tex]N(UUUDDD) = 6! / (3! * 3!) = 20[/tex]

The probability of the stock returning to its original price after six days can be calculated as:

[tex]P = N(UUUDDD) / 64 = 20 / 64 = 5 / 16[/tex]

Therefore, the probability that after 6 days the stock has its original price is 5/16.

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a) Measurement of arcCD is 40°

b) Measurement of arcVW is 134°

The Circle identities refer to a set of fundamental identities in trigonometry that relate the six trigonometric functions of an angle in a right-angled triangle.

a) Given that, ∠CED=∠AEC =50°  arcAB=140° we have to find out arcCD

We know the formula for external angle as per given diagram,

∠AEC = [tex]\frac{1}{2} (arcAB-arcCD)[/tex]

50° = [tex]\frac{1}{2} *(140-arcCD)[/tex]

Simplify, arcCD = 140° - 100° = 40°

Therefore, measurement of arcCD is 40°

b) Given that, ∠VYW =36°  arcVX=62° we have to find out arcVW

We know the formula for external angle as per given diagram,

∠VYW = [tex]\frac{1}{2} (arcVW-arcVX)[/tex]

36° = [tex]\frac{1}{2} *(arcVW-62)[/tex]

Simplify, arcVW = 72° + 62° = 134°

Therefore, measurement of arcVW is 134°

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According to the question the a) Measurement of arcCD is 40° and b) Measurement of arcVW is 134°

The Circle identities refer to a set of fundamental identities in trigonometry that relate the six trigonometric functions of an angle in a right-angled triangle.

a) Given that, ∠CED=∠AEC =50°  arcAB=140° we have to find out arcCD
We know the formula for external angle as per given diagram,
∠AEC = 1/2 (arcAB - arcCD)
50° = 1/2*(140 - arccd)
Simplify, arcCD = 140° - 100° = 40°
Therefore, measurement of arcCD is 40°

b) Given that, ∠VYW =36°  arcVX=62° we have to find out arcVW
We know the formula for external angle as per given diagram,
∠VYW = 1/2(arcVW - arcVX)
36° = 1/2*(arcVW - 62)
Simplify, arcVW = 72° + 62° = 134°
Therefore, measurement of arcVW is 134°

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Therefore, the compound inequality for the diameter of the washers is: 3.150 ≤ d ≤ 3.240.

In mathematics, an inequality is a statement that compares two values or expressions, indicating that one is greater than, less than, or equal to the other. The symbols used to represent inequalities are:

">" which means "greater than"

"<" which means "less than"

"≥" which means "greater than or equal to"

"≤" which means "less than or equal to"

Inequalities can be solved by applying algebraic techniques, such as adding, subtracting, multiplying, or dividing both sides of the inequality by the same number. The solution to an inequality is a range of values that satisfy the inequality.

Here,

The formula for the circumference of a circle in terms of its diameter is:

C = πd

where π (pi) is approximately 3.14.

We are given that the acceptable range for the circumference of the washer is 9.9 ≤ C ≤ 10.2 centimeters. Substituting C = 3.14d into this inequality, we get:

9.9 ≤ 3.14d ≤ 10.2

Dividing all sides of the inequality by 3.14, we obtain:

3.15 ≤ d ≤ 3.24

Rounding to three decimal places, the corresponding interval for the diameters of the washers is:

3.150 ≤ d ≤ 3.240

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