Consider a uniformly charged disk with radius R and total charge Q sitting in the xy-plane with its center at the origin. The electric field in the z-direction, Ez, at a distance d from the origin along the z-axis is given by Ez(d) 2kQ R2 1 ਦੇਸ਼ R2 1 where k is Coulomb's constant. For large distances d away from the origin relative to the radius of the disk R, we have d » Ror, R equivalently, < 1. Assuming this is the case, use the binomial approximation to simplify the expression for d Ez(d). Ez(d) ~

The value of the function (f·g)(-9) is 186.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

The given functions f(x)=2x²-4x-15 and g(x)=x+12.

Here, (f·g)(x)=f(x)+g(x)

= 2x²-4x-15+x+12

= 2x²-3x-3

(f·g)(-9)=2(-9)²-3(-9)-3

= 2×81+27-3

= 162+27-3

= 162+24

= 186

Therefore, the value of (f·g)(-9) is 186.

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A midpoint is a point that bisects a line into two equal parts.

Given that  C is the midpoint of AE, hence;

AC + CE = AE ........ 1

Similarly, if C is the midpoint of BD, then;

BC + CD = BD................... 2

If AE = BD, then we will equate 1 and 2 to have:

AC + CE = BC + CD

Also since CE = BC, the equation becomes

AC + CE = CE + CD

AC = CD (Proved)

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Answer:

A

B

C

Step-by-step explanation:

100% correct answers

Answer:

C

Step-by-step explanation:

The value of sin(θ) is approximately 0.921 and the value of cos(θ) is approximately 0.391.

To find the value of each variable using sine and cosine, we need to set up a right triangle with the given information. Let's label the sides of the triangle as follows:

Using the Pythagorean theorem, we can find the length of the hypotenuse:

h2 = s2 + t2

h2 = 31.32 + 13.32

h2 = 979.69 + 176.89

h2 = 1156.58

h = √1156.58

h ≈ 34.0

Now that we know the length of the hypotenuse, we can use sine and cosine to find the values of the variables:

sin(θ) = s / h

sin(θ) = 31.3 / 34.0

sin(θ) ≈ 0.921

cos(θ) = t / h

cos(θ) = 13.3 / 34.0

cos(θ) ≈ 0.391

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Answer:

x=3

y=0

Step-by-step explanation:

To solve this equation you use subistitution method for solve x and y in x^2+y^2=9 and x+y=3

x+y=3

x=3-y ... solving x interms of y and you will substitute in this eq. x^2+y^2=9

x^2+y^2=9

(3-y)^2 + y^2 = 9

y^2 - 6y + 9 +y^2 =9 ... you will squere 3-y

2y^2 + 6y = 0 ... simplify

1/2(2y^2 + 6y = 0 ) ... multiple both side by 1/2 to get

y^2 unit 1

y^2 + 3y = 0 ... y is 0

Y=0

and we are going to solve x

x+y=3

x+0=3

X=3

Answer:

C

Step-by-step explanation:

By using the rule of 3 we wills ee that the percentage of students who play the trumpet is 20%

We know that there are 150 students in the marching band, that will be our 100% in this case, and we know that 30 of them play the trumpet.

These 30 students represent a percentage X that we want to find, so we can write a little system of equations and use the rule of 3.

30  = X

150 = 100%

Taking the quotient between the two equations we get:

(30/150) = X/100%

Solving for X we get:

(30/150)*100% = X = 20%

So we can say that 20% of the students play the trumpet.

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The estimated number of whole cookies of the remaining 60 is 50.  

Estimating is the process of making an approximate calculation or judgment based on incomplete or uncertain information.

It involves using reasoning and previous experience to make an educated guess about a quantity, value, or outcome.

Estimating is often used when exact calculations are not feasible or practical, or when only a rough estimate is needed.

Here we have

Tara made 6 dozen cookies and brought them to the school bake sale in a big container.

She has taken 12 cookies out of the container to give to customers. Of the cookies she has taken out, 2 were broken and 10 were whole.

The total number of cookies Tara made = 6 × 12 = 72 cookies.

She took 12 cookies out of the container i.e 1 dozen

In which broken cookies = 2 i.e 2/12 = 1/6

The whole cookies = 10/12 = 5/6

Hereafter taking 12 cookies, remaining cookies = 72 - 12 = 60

Hence, the estimated number of whole cookies calculated as

the estimated number of whole cookies = (5/6)(60) = 5(10) = 50

Therefore,

The estimated number of whole cookies of the remaining 60 is 50.  

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Answer:

The answer is 900

good luck

Answer:

Step-by-step explanation:

It's a scalene triangle because,

It's all angles are unequal and sides are congruent which means unequal.

a. a² - 26 = a² + 4b² + 2ab√2 - 26 = a² + 4b² is an element of Q(√2). Hence, we have proven that a² - 26 ∈ Q(√2) for any non-zero a ∈ Q(√2).

b. We can conclude that √2 is not an element of Q(√3).

c. Since 2φ(√2) ≠ 2√3, φ cannot preserve the addition operation. Therefore, there cannot exist a function φ: Q(√2) → Q(√3) that is a group isomorphism.

(a) To prove that a² - 26 is an element of Q(√2), we first express a non-zero element a in Q(√2) as a = a + b√2. By squaring a, we obtain a² - 26 = a² + 4b², which shows that a² - 26 is an element of Q(√2). The key point is that 2ab√2 must be irrational unless ab = 0, which leads to the conclusion.

(b) In order to demonstrate that √2 is not an element of Q(√3), we assume the opposite and suppose that √2 ∈ Q(√3). By squaring both sides of the equation √2 = a + b√3, we arrive at 2 = a² + 2ab√3 + 3b². Since √3 is irrational, the only way for 2ab√3 to be rational is if ab = 0. However, this contradicts the assumption that a and b are non-zero rational numbers, implying that √2 cannot belong to Q(√3).

(c) To prove that there cannot exist a function φ: Q(√2) → Q(√3) that preserves the group structure, we consider the element √2 + √2 in Q(√2). If φ is a group isomorphism, it should preserve addition. However, evaluating φ(√2 + √2) and φ(√2) + φ(√2) leads to a contradiction. Hence, there is no function φ that simultaneously preserves the group structures of Q(√2) and Q(√3).

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a) The demand function is x = 16,000,000 / p^2 for x≥5 and p>0.

The demand function is x = k/p^2 where k is a constant of proportionality. Substituting x=16 and p=$1000, we get k=16*1000^2. Therefore, the demand function is x = 16,000,000 / p^2 for x≥5 and p>0.

b) The cost function is C(x) = 10,000 + 250x, where x is the number of units produced.

c) The profit function is P(x) = px - C(x) = xp - 10,000 - 250x. Substituting x = 16,000,000 / p^2, we get P(p) = (16,000,000/p) * p - 10,000 - 250(16,000,000/p^2) = 16,000p - 10,000 - 4,000,000/p.

To find the price that maximizes profit, we take the derivative of P(p) with respect to p and set it equal to zero: dP/dp = 16,000 + 4,000,000/p^2 = 0. Solving for p, we get p = √250.

Therefore, the price that maximizes profit is $500, and we should negotiate with our partner for this price. This is because the profit function is concave down, which means that increasing the price beyond $500 will result in decreasing profits, and decreasing the price below $500 will result in lower profits as well.

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So, the simpler form of the radical expression 4 sqrt 1296 x^16y^12 is 144x^14y^14 sqrt (x) sqrt (y).

To simplify the radical expression 4 sqrt 1296 x^16y^12, we need to first factor the number inside the radical. 1296 can be factored into 36 x 36, which simplifies to 6^4. So, the expression becomes 4 sqrt (6^4 x^16y^12).
Next, we can simplify the expression further by using the property of exponents that says a^m x a^n = a^(m+n). This means that we can combine the exponents of x and y, which gives us 4 sqrt (6^4 x^(16+12) y^(12+16)). Simplifying this, we get 4 sqrt (6^4 x^28 y^28).
Now, we can simplify the radical expression even further by using the property that says sqrt (a x b) = sqrt (a) x sqrt (b). Applying this to our expression, we get 4 x 6^2 x sqrt (x^28) x sqrt (y^28). Simplifying this further, we get 144x^14y^14 sqrt (x) sqrt (y).
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Answer:

1/8 will be 0.125 as a decimal so that is greater than 0.12! so it will be this \(1.8 \geq 0.12\)

Answer:

Step-by-step explanation:

4. 1/8   > 0.12

5. -6/7  < -5/6

6. 3/10 + (-7/10) = -4/10= -2/5

7. -4/9 - 1/9 = -5/9

The equation of the line in slope intercept form is y = (-4/3)x   .

In the question ,

a line graph is given ,

we need to find the equation of that line .

the two points that are given on the line graph are (-3 , 4) and (0 , 0) ,

the equation of the line passing from the points (x₁ , y₁) with slope m  in the slope intercept form is given by

(y - y₁) = m(x - x₁) .

we first need to find the slope .

So , m = (0 - 4)/(0 + 3)

m = -4/3

The equation of the line passing from the points (-3 , 4) with slope -4/3 , in the slope intercept form is

(y - 4) = (-4/3)(x -(-3))

y - 4 = (-4/3)(x + 3)

y - 4 = (-4/3)x - 4

y = (-4/3)x - 4 + 4

y = (-4/3)x

Therefore , The equation of the line in slope intercept form is  y = (-4/3)x  .

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The line integral of xy dx + x^2 dy around the given rectangle is 0.

To evaluate the line integral ∮C (xy dx + x^2 dy) along the given rectangle C with vertices (0, 0), (5, 0), (5, 1), and (0, 1), we can break it down into four line integrals along each side of the rectangle and sum them up.

Along the bottom side:

Parametrize the line segment from (0, 0) to (5, 0) as r(t) = (t, 0), where t ranges from 0 to 5. The differential element along this line segment is dr = (dt, 0). Substituting these values into the line integral, we get:

∫[0,5] (t*0) dt = 0.

Along the right side:

Parametrize the line segment from (5, 0) to (5, 1) as r(t) = (5, t), where t ranges from 0 to 1. The differential element along this line segment is dr = (0, dt). Substituting these values into the line integral, we get:

∫[0,1] (5t0 + 25dt) = ∫[0,1] 25*dt = 25.

Along the top side:

Parametrize the line segment from (5, 1) to (0, 1) as r(t) = (5-t, 1), where t ranges from 0 to 5. The differential element along this line segment is dr = (-dt, 0). Substituting these values into the line integral, we get:

∫[0,5] ((5-t)*0 + (5-t)^2 * 0) dt = 0.

Along the left side:

Parametrize the line segment from (0, 1) to (0, 0) as r(t) = (0, 1-t), where t ranges from 0 to 1. The differential element along this line segment is dr = (0, -dt). Substituting these values into the line integral, we get:

∫[0,1] (0*(1-t) + 0) dt = 0.

Summing up all the line integrals, we have:

0 + 25 + 0 + 0 = 25.

Therefore, the line integral of xy dx + x^2 dy around the given rectangle is 25.

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Answer:

Paranthesis, Exponents, Multipilication, Division, Addition, Subtraction

Step-by-step explanation:

The way I learned it was by saying a phrase that goes like, "Please Excuse My Dear Aunt Sally". I repeated this many times and it got stuck in my mind ever since.

The inequality that represents the amounts in dollars that could be deposited in a new checking account is a ≥ 75.

This inequality states that "a" must be greater than or equal to 75 dollars, which is the minimum deposit required for opening a new checking account.

the inequality "a ≥ 75" represents the amounts in dollars that could be deposited in a new checking account, where "a" is the amount being deposited and must be greater than or equal to $75.

To represent this mathematically, we can use an inequality. An inequality is a statement that compares two values using symbols like "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "! =" (not equal to).

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a. Fe and S4 are not independent.

b. Fe and Σo are independent.

c. S4 and Σo are independent.

d. Fe, S4, and Σo are not mutually independent.

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is.

To determine if the given events are independent, we need to check if the probability of their intersection is equal to the product of their individual probabilities.

(a) Fe and S4:

The event Fe: The first die is even.

The event S4: The second die is 4.

These events are independent if P(Fe ∩ S4) = P(Fe) * P(S4).

P(Fe) = 1/2 (since there are three even numbers out of six possible outcomes for the first die)

P(S4) = 1/6 (since there is only one 4 out of six possible outcomes for the second die)

P(Fe ∩ S4) = 1/12 (since there is only one outcome where the first die is even and the second die is 4)

P(Fe ∩ S4) = 1/12 ≠ (1/2) * (1/6) = 1/12

Therefore, Fe and S4 are not independent.

(b) Fe and Σo:

The event Σo: The sum of the two dice is odd.

These events are independent if P(Fe ∩ Σo) = P(Fe) * P(Σo).

P(Fe) = 1/2 (as mentioned above)

P(Σo) = 1/2 (since there are three odd sums out of six possible outcomes for the two dice)

P(Fe ∩ Σo) = 1/4 (since there are three outcomes where the first die is even and the sum is odd: (2, 1), (2, 3), (2, 5))

P(Fe ∩ Σo) = 1/4 = (1/2) * (1/2) = P(Fe) * P(Σo)

Therefore, Fe and Σo are independent.

(c) S4 and Σo:

The event S4: The second die is 4.

These events are independent if P(S4 ∩ Σo) = P(S4) * P(Σo).

P(S4) = 1/6 (as mentioned above)

P(Σo) = 1/2 (as mentioned above)

P(S4 ∩ Σo) = 1/6 (since there is only one outcome where the second die is 4 and the sum is odd: (1, 4))

P(S4 ∩ Σo) = 1/6 = (1/6) * (1/2) = P(S4) * P(Σo)

Therefore, S4 and Σo are independent.

(d) Fe, S4, and Σo:

To determine if these three events are mutually independent, we need to check if the probability of their intersection is equal to the product of their individual probabilities.

P(Fe ∩ S4 ∩ Σo) = P(Fe) * P(S4) * P(Σo)

P(Fe ∩ S4 ∩ Σo) = P(Fe) * P(S4) * P(Σo) = (1/2) * (1/6) * (1/2) = 1/24

However, there are no outcomes where all three events occur simultaneously. Therefore, P(Fe ∩ S4 ∩ Σo) = 0 ≠ 1/24.

Therefore, Fe, S4, and Σo are not mutually independent.

In summary, the events Fe and Σo are independent, while the events Fe and S4, as well as S4 and Σo, are not independent. Fe, S4, and Σo are not mutually independent.

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Using a system of equations, it is found that:

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the variables are:

From Stan's purchases, we have that:

\(n + 3p + 2m = 7.5\)

From Jan's purchases, we have that:

\(2n + 6p + 5m = 15.50\)

From Fran's purchases, we have that:

\(n + 2p + 2m = 6.25\)

From the third equation:

\(n = 6.25 - 2p - 2m\)

Replacing on the first:

\(n + 3p + 2m = 7.5\)

\(6.25 - 2p - 2m + 3p + 2m = 7.5\)

\(p = 1.25\)

On the second equation, we have that:

\(2n + 6p + 5m = 15.50\)

\(2(6.25 - 2p - 2m) + 6(1.25) + 5m = 15.50\)

\(2(3.75 - 2m) + 5m = 8\)

\(m = 0.5\)

Finally:

\(n = 6.25 - 2(1.25) - 2(0.5) = 2.75\)

Then:

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The overall worst-case time complexity of the algorithm is O(n).

To analyze the worst-case time complexity of the algorithm from exercise 35 of section 3.1, we can follow these steps:

1. Review the algorithm: Recall the algorithm designed in exercise 35, which aims to find the first term of a sequence less than the immediately preceding term.

2. Identify the loop: The main part of the algorithm is a loop that iterates through the sequence of numbers, comparing each term to the previous one.

3. Count the operations: For each iteration of the loop, there are a constant number of operations, such as comparisons and variable assignments.

4. Determine the number of iterations: In the worst-case scenario, the algorithm has to iterate through the entire sequence to find the first term that is less than the immediately preceding term. If the sequence has n elements, the algorithm will have n-1 iterations, since we compare each element with its previous one.

5. Calculate the time complexity: Since each iteration takes a constant amount of time, and there are n-1 iterations in the worst case, the overall worst-case time complexity of the algorithm is O(n). This means that the time complexity grows linearly with the length of the input sequence.

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Answer:

75,582

Step-by-step explanation:

There are 21,168 ways to form a subcommittee of 3 men and 5 women from the given committee.To form a subcommittee of 3 men and 5 women from a committee consisting of 9 men and 10 women, you can use the combination formula.

A combination is a selection of items from a larger set, where the order of items does not matter. The formula for combinations is:

C(n, r) = n! / (r!(n-r)!)

where n is the total number of items in the set, r is the number of items to be chosen, and ! represents the factorial function (e.g., 5! = 5 x 4 x 3 x 2 x 1).

For this problem, you will first find the number of ways to choose 3 men from the 9 men, and then the number of ways to choose 5 women from the 10 women.

For men:
C(9, 3) = 9! / (3!(9-3)!)
C(9, 3) = 9! / (3!6!)
C(9, 3) = 84

For women:
C(10, 5) = 10! / (5!(10-5)!)
C(10, 5) = 10! / (5!5!)
C(10, 5) = 252

To find the total number of ways to choose the subcommittee, you will multiply the number of ways to choose the men by the number of ways to choose the women:

Total ways = 84 (ways to choose men) x 252 (ways to choose women)
Total ways = 21,168

So, there are 21,168 ways to form a subcommittee of 3 men and 5 women from the given committee.

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Answer:

Amount of Niobium-91 initially

= 300/91 =3.2967mol

2040 years = 3 ×680 = 3 half-lives

therefore, amount left = 0.4121mol

mass of Niobium-91 remaining = 0.4121 ×91 =37.5g

Please give brainliest

The answers are :

a. 500 plants will be picked in each random sample.

b. Sample size is 5000. I selected number because quantitative sample sizes larger than the qualitative sample sizes.

c. It is because 5000 plants can be equally divided into 10 parts of 500 each.

d. Number of plants is large enough, each plant has an equal chance of being chosen.

What do you mean by sample size determination ?

The process of selecting the number of observations for a statistical sample is known as sample size determination.

It is given that a public health expert wants to test the plants at the farm.

a.

We know that the appropriate sample size can be obtained by dividing the population by the fixed periodic interval.

In this instance, the fixed periodic interval will be given by n number of plant. It is because there are 5000 plants and there needs to be a random sample of n plants.

So, If n = 10 then ; 500 plants will be picked in each random sample.

b.

The sample size in this case is 5000. We are aware that the qualitative sample sizes are, in fact, lower than the quantitative sample sizes. Here, quantitative sampling is used to make sure that there is a sufficient sample of the plants, meaning that the randomized data acquired is enough to attain statistical significance.

c.

We know that a random sample is known as unbiased representation of larger data. It is considered a fair way of selecting a sample from a large number of data as each one has an equal chance of getting selected.

Here ; if random sample is 10 then , 5000 plants can be equally divided into 10 parts of 500 each.

d.

The number of plants is large enough, each plant has an equal chance of being chosen, the units of the sample are entirely independent, and there is no obvious correlation or attraction between them. This is how random sampling is used.

Therefore , the answers are :

a. 500 plants will be picked in each random sample.

b. Sample size is 5000. I selected number because quantitative sample sizes larger than the qualitative sample sizes.

c. It is because 5000 plants can be equally divided into 10 parts of 500 each.

d. Number of plants is large enough, each plant has an equal chance of being chosen.

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x = -15

Step-by-step explanation:

\(x = \frac{2}{3} x - 5\)

Collect like terms and simplify

\(x - \frac{2}{3} x = - 5 \\ \frac{1}{3} x = - 5\)

Cross multiply

\(x = - 5 \times 3 \\ \\ x = - 15\)

Answer:

57,416

Step-by-step explanation:

50,000 + 7,000 + 400 + 10 + 6

50,000 is in the ten thousands place.

7,000 is in the thousands place.

400 is in the hundreds place.

10 is in the tens place.

6 is in the ones place.

a. The class width for all intervals in this frequency distribution is 3.

b. Calculating the class midpoints for all intervals, we get:

32-35: 33.5

36-39: 37.5

40-43: 41.5

44-47: 45.5

48-51: 49.5

52-55: 53.5

56-59: 57.5

c. Calculating the class boundaries for all intervals, we get:

32-35: 30.5-36.5

36-39: 34.5-39.5

40-43: 38.5-43.5

44-47: 42.5-47.5

48-51: 46.5-51.5

52-55: 50.5-55.5

56-59: 54.5-59.5

The number of full oscillations that any wave element performs in one unit of time is how we determine the frequency of a sinusoidal wave.

To find the class width, class midpoints, and class boundaries for the given frequency distribution, let's analyze the temperature intervals and frequencies:

Temperature (°F)    Frequency

32-35                      1

36-39                      3

40-43                      5

44-47                      11

48-51                      7

52-55                      7

56-59                      1

(a) Class width:

The class width is the difference between the upper and lower boundaries of each temperature interval. In this case, all the intervals have the same width.

Class width = Upper boundary - Lower boundary

For example, in the first interval (32-35), the lower boundary is 32 and the upper boundary is 35.

Class width = 35 - 32 = 3

The class width for all intervals in this frequency distribution is 3.

(b) Class midpoints:

The class midpoint is the average value of the upper and lower boundaries of each interval. It represents the central value of the interval.

Class midpoint = (Upper boundary + Lower boundary) / 2

For example, in the first interval (32-35), the lower boundary is 32 and the upper boundary is 35.

Class midpoint = (35 + 32) / 2 = 33.5

Calculating the class midpoints for all intervals, we get:

32-35: 33.5

36-39: 37.5

40-43: 41.5

44-47: 45.5

48-51: 49.5

52-55: 53.5

56-59: 57.5

(c) Class boundaries:

The class boundaries are the values that separate each interval. They are calculated by adding or subtracting half of the class width from the upper and lower boundaries.

For example, in the first interval (32-35), the lower boundary is 32 and the upper boundary is 35, and the class width is 3.

Lower class boundary = Lower boundary - (0.5 * class width) = 32 - (0.5 * 3) = 32 - 1.5 = 30.5

Upper class boundary = Upper boundary + (0.5 * class width) = 35 + (0.5 * 3) = 35 + 1.5 = 36.5

Calculating the class boundaries for all intervals, we get:

32-35: 30.5-36.5

36-39: 34.5-39.5

40-43: 38.5-43.5

44-47: 42.5-47.5

48-51: 46.5-51.5

52-55: 50.5-55.5

56-59: 54.5-59.5

Note: The class boundaries are inclusive of the lower boundary and exclusive of the upper boundary.

These are the calculations for the class width, class midpoints, and class boundaries for the given frequency distribution.

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To find the class width, subtract the lower class limit from the upper class limit. To find the class midpoints, add the lower and upper class limits and divide by 2. To find the class boundaries, subtract 0.5 from the lower class limit and add 0.5 to the upper class limit.

(a) Class width:

To find the class width, we subtract the lower class limit from the upper class limit. For example, the class width for the first class interval (32-35) is 35 - 32 = 3.

(b) Class midpoints:

To find the class midpoints, we add the lower class limit and the upper class limit and divide the sum by 2. For example, the class midpoint for the first class interval (32-35) is (32 + 35) / 2 = 33.5.

(c) Class boundaries:

To find the class boundaries, we subtract 0.5 from the lower class limit and add 0.5 to the upper class limit. For example, the class boundaries for the first class interval (32-35) are (32 - 0.5) and (35 + 0.5).

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