Please help me with my math!!

An expression equivalent to (a - b)³ is a³ - 3a²b + 3ab² - b³.

The fractions 4/10, 6/15, 8/20, etc. are identical to 2/5. In the reduced form, equivalent fractions have the same value. Explanation: When writing equivalent fractions, the numerator and denominator should be multiplied or divided by the same number.

One way to expand (a - b)³ is to use the binomial formula:

(a - b)³ = C(3,0) * a³ * (-b)^0 + C(3,1) * a² * (-b) + C(3,2) * a * (-b)² + C(3,3) * a * (-b)³

where C(n,k) denotes the number of ways there are to select k objects from a set of n objects, and "n choose k" is the binomial coefficient.

Simplifying the above expression, we get:

(a-b)³ = a³-3a²b+3ab²-b³.

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The formula for f(t) as a sum of Heaviside functions is f(t) = tuc(t) - tuc(t-3) + (2t-3)uc(t-3) - (2t-3)uc(t-4) + 5uc(t-4).

To express f(t) as a sum of Heaviside functions, we break down the function into its respective intervals and use the unit step function or Heaviside function to represent the function in each interval.

f(t) = t, 0 ≤ t ≤ 3

f(t) = 2t - 3, 3 < t ≤ 4

f(t) = 5, 4 < t

Using the Heaviside function uc for the jump at c, we can represent each interval as follows:

f(t) = tuc(t) - tuc(t-3), 0 ≤ t ≤ 3

f(t) = (2t-3)uc(t-3) - (2t-3)uc(t-4), 3 < t ≤ 4

f(t) = 5uc(t-4), 4 < t

Therefore, the formula is f(t) = tuc(t) - tuc(t-3) + (2t-3)uc(t-3) - (2t-3)uc(t-4) + 5uc(t-4)

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A. I and II only true if we use a large sample rather than a small one

sampling model

A sampling model is a statistical model used to describe the behavior of a sample statistic. In other words, it is a model that describes the distribution of a particular sample statistic, such as the mean or standard deviation, as it is repeatedly sampled from a population.

When a sample is drawn from a population that is strongly skewed to the left, a small sample may not accurately represent the true population mean. However, if a large sample is taken, the sample mean is more likely to be normally distributed, due to the central limit theorem. This means that both statement I and II are true.

Statement III is false because as the sample size increases, the variability of the sample means actually decreases. This is because larger samples tend to have less sampling error and are more representative of the population as a whole.

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Answer:

112°

Step-by-step explanation:

Finding the unknown angle in a quadrilateral:

        Sum of all angles of a quadrilateral = 360

                                      a + 49 + 72 + 127 = 360

                                                     a + 248  = 360

                                                                a = 360 - 248

                                                                a = 112°

Answer:

WELL 17

Step-by-step explanation:

60 DIVED BY 5 IS 12

SO 12 DIVIDED BY 204 IS 17 SOOOOOO 17 IS THE ANS

To fill the wooden box with potting soil precisely up to two-thirds of its capacity, Benito requires a volume of 3,584 cubic inches.

The volume of soil that Benito needs to fill the box two-thirds full can be calculated by finding two-thirds of the total volume of the box.

The volume of the box can be calculated by multiplying the width, height, and length:

16 inches (width) x 12 inches (height) x 28 inches (length) = 5,376 cubic inches.

Two-thirds of this volume can be found by multiplying the total volume by 2/3:

5,376 cubic inches x 2/3 = 3,584 cubic inches.

Therefore, Benito needs 3,584 cubic inches of potting soil to fill the box exactly two-thirds full.

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The method used to collect data will depend on the specific research question being asked and the resources available to the researcher.

One common method for collecting data is through experimentation. This involves designing a controlled experiment that allows researchers to manipulate one or more variables while keeping all other factors constant.

Observational data can be particularly useful when it is not possible or ethical to manipulate variables in an experiment.

Surveys and questionnaires are another way to collect data. These methods involve asking people to provide information about their attitudes, beliefs, and behaviors.

Other methods for collecting data include case studies, in which researchers closely examine a single individual or group, and archival research, in which data is collected from existing records, such as census data or medical records.

By carefully selecting the right method for their research, scientists can gather accurate and reliable data that can help to advance our understanding of the world around us.

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The regression result of 0.320, the beta of 0.136, and the p-value of 0.000.

The strongest predictor in the MLRA summary Table is past history of depression. This is shown by the regression result of 0.320, the beta of 0.136, and the p-value of 0.000. This means that past history of depression has a strong and statistically significant influence on predicting depression at wave 2.

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Jada overtakes Elena after 7.5 seconds.

The set of equations that best captures the scenario is =y=15+20x.

Let's establish a coordinate system with Elena's starting point as the origin. Elena's separation from the origin at time x is given by: y=15+20x

y1 = 15 + 20x

Jada's distance from the origin at time x is determined similarly by:

y2 = 22x

Finding the moment x at which Jada overtakes Elena and their distances from the origin are equal is our goal.

y1 = y2

With the formulas for y1 and y2 substituted, we obtain:

15 + 20x = 22x

When we simplify this equation, we obtain:

2x = 15

x = 7.5

Jada therefore overtakes Elena after 7.5 seconds.

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Answer:

Step-by-step explanation:

Overtime Rate = [tex]17.70 \times 1\frac{1}{2}[/tex]

                        [tex]= 17.70 \times \frac{3}{2}[/tex]

                       [tex]=\frac{53.10}{2}[/tex]

                      [tex]=\pounds26.55[/tex]

Pay [tex]=11*26.55=\pounds 292.05[/tex]    (I assume you can use a calculator for this)

Solution: [tex]\pounds 292[/tex]

Answer:

A. Less than

Step-by-step explanation:

Answer:

C. Rachel is saving $5 per week.

Step-by-step explanation:

The initial savings are $10, as it is the y-intercept.

And to obtain the slope we can take 2 points from the graph.

A(0,10)

B(1,15)

m=(y2-y1)/ (x2-x1)

m=(15-10)/ (1-0)

m= 5/1

m= 5 savings in dollars per (1) week

Answer:

6 29 25

Step-by-step explanation:

those are the prime numbers on the 2023 feb calendar

Answer: Below :)

Step-by-step explanation:

A) To find the profit, we first need to calculate the cost of the produce plus the 25% markup.

The markup is 25% of the cost, which is 0.25 * 500 = €125.

So the total cost of the produce plus markup is €500 + €125 = €625.

Now, if the greengrocer sells all the produce, the total revenue will be 100% plus the 25% markup, which is 125% of the original cost.

125% of €500 is 1.25 * 500 = €625, which is the same as the cost plus markup.

Therefore, the profit is the markup, which is €125.

B) To find the total income, we add the profit to the total cost:

Total income = €500 + €125 = €625

Answer:

A)  €125

B)  €625

The value of x in the equation 1/4(4 + x) = 4/3 is x = 4/3.

Multiply both sides of the equation by 4 to eliminate the fraction on the left-hand side:

1/4(4 + x) = 4/3

4 * 1/4(4 + x) = 4 * 4/3

Simplifying:

4 + x = 16/3

Subtract 4 from both sides of the equation:

4 + x - 4 = 16/3 - 4

Simplifying:

x = 16/3 - 12/3

x = 4/3

A fraction is a mathematical concept used to represent a part of a whole or a ratio between two quantities. It is typically written in the form of a numerator (top number) over a denominator (bottom number), separated by a horizontal line. For example, the fraction 1/2 represents one out of two equal parts, or half of a whole. Similarly, the fraction 3/4 represents three out of four equal parts, or three-quarters of a whole.

Fractions are an essential part of mathematics and are used in a wide range of applications, including measurements, cooking, and financial calculations. They can be added, subtracted, multiplied, and divided just like whole numbers, but they require a bit more care in their manipulation due to their unique structure.

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Answer:

3

Step-by-step explanation:

Interval 3 ≤ x ≤ 5 means all f(x) values from x= 3 inclusive  to x = 5 inclusive

At x = 3 f(x) = 2

At x = 5, f(x) = 8

Change in f(x) = Δf(x) = 8 - 2 = 6

Change in x = Δx = 5 - 3 = 2

Average rate of change
= Δf(x)/Δx

= 6/2

= 3

To solve this problem, we can use the Greatest Common Factor (GCF) of 10 and 20.

The GCF is the largest number that divides evenly into both 10 and 20. To find the GCF, we can use a factor tree.

We start with 10 and 20 as our starting numbers.

10 = 2 * 5

20 = 2 * 2 * 5

We can see that both 10 and 20 have a factor of 2 and a factor of 5. The Greatest Common Factor between 10 and 20 is 2 * 5, or 10.

Therefore, the greatest number of portions of trail mix Stanley can make is 10.

Answer: Yes, the Mean Value Theorem can be applied to f(x) = 9x^3 on the closed interval [1, 2].

To find all values of c in the open interval (1, 2) such that f'(c) = (f(b) - f(a))/(b - a), we first find the derivative of f(x):

f'(x) = 27x^2

Then, we can use the Mean Value Theorem to find a value c in the open interval (1, 2) such that:

f'(c) = (f(2) - f(1))/(2 - 1)

27c^2 = 9(2^3 - 1^3)

27c^2 = 45

c^2 = 5/3

c = +/- sqrt(5/3)

Therefore, the values of c in the open interval (1, 2) such that f'(c) = (f(b) - f(a))/(b - a) are:

c = sqrt(5/3), -sqrt(5/3)

Note that these values are not in the closed interval [1, 2], as they are not between 1 and 2, but they are in the open interval (1, 2).

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

First set up the fraction [tex]\frac{9}{40}[/tex] , and next divide 9 ÷ 40 = 0.225. Lastly, multiply 0.225 × 100 = 22.5%.

Hope this helps.

The viewing angle a of a person sitting a distance x from the front wall of a classroom with a blackboard that is 12 ft long and starts 3 ft from the wall they are sitting next to can be calculated as: a = cot-1(x/15) - cot-1(x/3)

To understand this calculation, let's consider a diagram of the classroom.

We can see from the diagram that the blackboard has length 12 ft, starting 3 ft from the wall the student is sitting next to. The student is sitting a distance x from the front wall.

The viewing angle a is the angle between the wall the student is sitting next to and the line from the student to the front wall. This angle can be calculated using the tangent of the opposite side (front wall) and adjacent side (wall the student is sitting next to).

We can therefore write: a = tan-1(12/3) - tan-1(x/3)

Simplifying this equation, we can rewrite it as: a = cot-1(x/15) - cot-1(x/3).

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The probability that a randomly selected finishing time is greater than 87 seconds is 14.08%. This can be calculated using the empirical rule.

The empirical rule states that for any data that is normally distributed, about 68% of the data will fall within one standard deviation of the mean (in this case, within 69 ± 6 seconds). Approximately 95% of the data will fall within two standard deviations (in this case, within 69 ± 12 seconds), and about 99.7% of the data will fall within three standard deviations (in this case, within 69 ± 18 seconds).Given the mean and standard deviation given, we can calculate the probability that a randomly selected finishing time is greater than 87 seconds.

We can do this by subtracting the area under the curve from the mean to the value we are interested in (in this case, 87 seconds). Since the total area under the curve is 1, subtracting the area from the mean to 87 seconds will give us the desired probability.To calculate the area under the curve, we need to calculate the Z-score, which is the number of standard deviations away from the mean a particular value is. In this case, the Z-score is (87 - 69) / 6, which is 2.16. Using a Z-table, the probability of a Z-score of 2.16 or higher is 0.8592. Therefore, the probability that a randomly selected finishing time is greater than 87 seconds is 1 - 0.8592, which is 0.1408. Rounding to two decimal places, this is 14.08%.

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The number of students traveling are 2 students out of the 30 who are traveling out of the country this summer.  If 1/3 of the students are traveling somewhere this summer, then we can calculate the number of students who are traveling by multiplying the total number of students by 1/3:

Number of students traveling = 30 x 1/3 = 10  

Now, we need to find out how many of these 10 students are traveling out of the country. We know that 1/5 of the students who are traveling are going out of the country, so we can find the number of students who are traveling out of the country by multiplying the total number of traveling students by 1/5:

Number of students traveling out of the country = 10 x 1/5 = 2

Therefore, there are 2 students out of the 30 who are traveling out of the country this summer.

It's important to note that fractions can be converted to decimals or percentages to make them easier to work with. For example, 1/3 can be written as 0.33 or 33%, and 1/5 can be written as 0.20 or 20%. This can be particularly useful when dealing with more complex problems or when working with larger numbers.

In summary, by using the information given, we can determine that out of the 30 students in Mr. Hall's class, 10 are traveling somewhere this summer, and out of those 10 students, 2 are going out of the country. This type of problem-solving helps build math skills that are applicable in real-world scenarios, such as budgeting and planning for travel.

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The expression for the marginal revenue function is MR(q) = 600r - 7.

The given product's revenue function is R(q) = - 7q + 600qr.

To find an expression for the marginal revenue function, we can use the following steps:

Step 1: Take the first derivative of the revenue function with respect to q to obtain the marginal revenue function MR(q).

Step 2: Simplify the expression for MR(q) to record the final result.

In other words, the marginal revenue function MR(q) is the derivative of the revenue function R(q) with respect to q. Here, R(q) = - 7q + 600qr.

So, we have to differentiate R(q) with respect to q to get MR(q).

The derivative of - 7q with respect to q is - 7.

The derivative of 600qr with respect to q is 600r because the derivative of q with respect to q is 1.

MR(q) = dR(q) / dq

= (d/dq)(- 7q + 600r)

= (- 7) + (600r)

= 600r - 7

The equation that represents the marginal revenue function is MR(q) = 600r - 7.

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The cookers at healthy Bakery could make 323 bagels in 17 hours, and their rate is 19 bagels according to hour.

To find out how many bagels the cookers could make in 17 hours, we will use the unitary method, which involves finding the rate at which the cookers can make bagels and additionally multiplying that price through the wide variety of hours labored.

Let the rate at which the cookers can make bagels be r bagels in line with hour. We also can set up the subsequent share

190 bagels/ 10 hours = r bagels 1 hour

Simplifying this proportion, we get

r = 190 bagels/ 10 hours

r = 19 bagels/ 1 hour

So the cookers can make 19 bagels in keeping with hour.

To find out how many bagels they could make in 17 hours, we can multiply the rate via the number of hours

19 bagels/ hour × 17 hours = 323 bagels

Therefore, the cookers at healthy Bakery could make 323 bagels in 17 hours, and their rate is 19 bagels according to hour.

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The probability of drawing four red balls in succession, with replacement, is 0.04 or 4%.

Since we are replacing the ball after each draw, the probability of drawing a red ball remains the same for each draw. The probability of drawing a red ball on any given draw is:

P(Red) = Number of Red Balls / Total Number of Balls

P(Red) = 6 / (8 + 6)

P(Red) = 0.4286

So, the probability of drawing four red balls in a row is the product of the probability of drawing a red ball four times in a row:

P(4 Red Balls) = P(Red) * P(Red) * P(Red) * P(Red)

P(4 Red Balls) = 0.4286 * 0.4286 * 0.4286 * 0.4286

P(4 Red Balls) = 0.04 or 4%

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Answer:

circumference=50.24

Step-by-step explanation:

c=2x3.14xr

c=2x3.14x(8)

c=50.24

Answer:

9.5 decimal

espero y te ayude

The publication of three major books on race in chronological order, from earliest to most recent is:

Chronological order is the listing, description, or discussion of when events occurred in relation to time. Essentially, it is similar to looking at a chronology to see what happened initially and what happened after that. For example, if teachers asked their pupils to recount their first day of school, they would expect students to begin by waking up that morning and getting ready. If pupils begin from the time they enter the school, significant information is lost and the listener may become confused due to a lack of knowledge.

Helping pupils grasp what chronological order is and how to use the skill correctly can benefit students ranging from kindergarten to collegiate levels. The concept may appear simple, yet failing to master chronological sequence can cause kids to struggle academically and lack a solid educational foundation.

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X = -80538738812075974, Y = 80435758145817515,

and Z = 12602123297335631 are the values of  x,y,z of whole numbers.

What in mathematics is a whole number?

Complete numbers the sum of all natural numbers plus zero. not a decimal or fraction. {0, 2, 3, 4, 5 6, 7, 8, 9, 10, 11 …} Integer. a negative number, zero, or a counting number.

                            Natural numbers with a starting value of 1 and higher are considered whole numbers. Let's examine a few instances of entire numbers. The alphabet "W" stands for the collection of whole numbers. W = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10,.…}

x3+y3+z3=k, with k being all the numbers from one to 100

X = -80538738812075974,

Y = 80435758145817515,

and Z = 12602123297335631

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