What is the average weight gain for students in their first year in college? Group of answer choices 3 to 4 pounds 8 to 10 pounds 15 to 20 pounds 20 to 25 pounds

The least amount we can charge for each CD to make a $100 profit depends on the number of CDs sold. The revenue per CD will decrease as the number of CDs sold increases.

According to Problem 2, we want to find the minimum amount we can charge for each CD to make a $100 profit. To determine this, we need to consider the cost and revenue associated with selling CDs.

Let's say the cost of producing each CD is $5. We can start by calculating the total revenue needed to make a $100 profit. Since the profit is the difference between revenue and cost, the revenue needed is $100 + $5 (cost) = $105.

To find the minimum amount we can charge for each CD, we need to divide the total revenue by the number of CDs sold. Let's assume we sell x CDs. Therefore, the equation becomes:

Revenue per CD * Number of CDs = Total Revenue
x * (Revenue per CD) = $105

To make it simpler, let's solve for the revenue per CD:
Revenue per CD = Total Revenue / Number of CDs
Revenue per CD = $105 / x

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The approximate probability that you will win a prize is 0.39 or 39%.

If you buy a lottery ticket in 50 lotteries, in each of which your chance of winning a prize is 1/100, the approximate probability that you will win a prize is 0.39 or 39%.

Here's how to calculate it:

Probability of not winning a prize in one lottery = 99/100

Probability of not winning a prize in 50 lotteries = (99/100)^50 ≈0.605

Probability of winning at least one prize in 50 lotteries = 1 - Probability of not winning a prize in 50 lotteries

= 1 - 0.605 = 0.395 ≈0.39 (rounded to two decimal places)

Therefore, the approximate probability that you will win a prize is 0.39 or 39%.

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The correct quadratic polynomial is -8.8473x² + 1.4118x + 7.5, and the correct result of the multiplication is x³ - 3x² - 24x + 30. The connection between the remainder of the division and your friend's error is that the error in determining the constant term led to a non-zero remainder.

To find the quadratic polynomial that your friend used, we need to consider the constant term in the result x³-3x²-24x+30.

The constant term of the result should be the product of the constant terms from multiplying (x+4) by the quadratic polynomial. In this case, the constant term is 30.

Let's denote the quadratic polynomial as ax²+bx+c. We need to find the values of a, b, and c.

To find c, we divide the constant term (30) by 4 (the constant term of (x+4)). Therefore, c = 30/4 = 7.5.

So, the quadratic polynomial used by your friend is ax²+bx+7.5.

Now, let's determine the correct result of the multiplication.

We multiply (x+4) by ax²+bx+7.5, which gives us:

(x+4)(ax²+bx+7.5) = ax³ + (a+4b)x² + (4a+7.5b)x + 30

Comparing this with the given correct result x³-3x²-24x+30, we can conclude:

a = 1 (coefficient of x³)

a + 4b = -3 (coefficient of x²)

4a + 7.5b = -24 (coefficient of x)

Using these equations, we can solve for a and b:

From a + 4b = -3, we get a = -3 - 4b.

Substituting this into 4a + 7.5b = -24, we have -12 - 16b + 7.5b = -24.

Simplifying, we find -8.5b = -12.

Dividing both sides by -8.5, we get b = 12/8.5 = 1.4118 (approximately).

Substituting this value of b into a = -3 - 4b, we get a = -3 - 4(1.4118) = -8.8473 (approximately).

Therefore, the correct quadratic polynomial is -8.8473x² + 1.4118x + 7.5, and the correct result of the multiplication is    x³ - 3x² - 24x + 30.

Now, let's discuss the connection between the remainder of the division and your friend's error.

When two polynomials are divided, the remainder represents what is left after the division process is completed. In this case, your friend's error in determining the constant term led to a remainder of 30. This means that the division was not completely accurate, as there was still a residual term of 30 remaining.

If your friend had correctly determined the constant term, the remainder of the division would have been zero. This would indicate that the multiplication was carried out correctly and that there were no leftover terms.

In summary, the connection between the remainder of the division and your friend's error is that the error in determining the constant term led to a non-zero remainder. Had the correct constant term been used, the remainder would have been zero, indicating a correct multiplication.

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There is no speed for the skater that would allow the cyclist to travel 75 kilometers while the skater travels 45 kilometers in the same amount of time.

To find the speed of the skater, let's denote the speed of the skater as "x" kilometers per hour. Since the cyclist traveled 12 kilometers per hour faster than the skater, the speed of the cyclist would be "x + 12" kilometers per hour.

We can use the formula: speed = distance/time to solve this problem.

For the cyclist:
Speed of cyclist = 75 kilometers / t hours

For the skater:
Speed of skater = 45 kilometers / t hours

Since both the cyclist and the skater traveled for the same amount of time, we can set up an equation:

75 / t = 45 / t

Cross multiplying, we get:
75t = 45t

Simplifying, we have:
30t = 0

Since the time cannot be zero, we have no solution for this equation. This means that the given information in the question is not possible and there is no speed for the skater that satisfies the conditions.

There is no speed for the skater that would allow the cyclist to travel 75 kilometers while the skater travels 45 kilometers in the same amount of time.

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Answer:

20 Dimes and 30 nickels

Step-by-step explanation:

Let n =  the number of nickels

Let d = the number of dimes.

.05n + .1d = 3.50  Multiply through by 100 to remove the decimal

5n + 10d = 350

n = d + 10

Substitute d + 10 for n in the first equation.

5n + 10d = 350

5(d  10) + 10d = 350  Distribute the 5

5d + 50 + 10d = 350  Combine the d's

15d + 50 = 350  Subtract 50 from both sides

15d = 300 Divide both sides by 15

d = 20

The number of dimes is 20.

Substitute 20 for d

n = d + 10

n = 20 + 10

n = 30

The number of nickels is 30.

Helping in the name of Jesus.

We are given two linear equations and we have to solve them and get the solution for m and n . This problem can be solved using the basics of algebra and linear equations. By solving these equations we have got the values of m and b to be 2.5, 3.5 .The correct option is none of the above.

Given equations are: m + 3n = 10 m = n - 2. To find the solution to the set of equations in the form (m, n), we need to solve the above equations. We have the value of m in terms of n, therefore we can substitute it in the other equation to get the value of n as follows: m + 3n = 10m + 3(n - 2) = 10m + 3n - 6 = 10 3n = 10 - m + 6 n = (10 - m + 6)/3 n = (16 - m)/3Now we have the value of n, we can substitute it in the equation for m, we get: m = n - 2m = ((16 - m)/3) - 2 3m = 16 - m - 6 4m = 10 m = 5/2.

Thus, the solution to the set of equations in the form (m, n) is (5/2, 7/2) or (2.5, 3.5).Therefore, the correct option is (none of the above).

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For every inch in the scale drawing, it represents 60 inches in the actual gym.

To determine the scale Jorge used to create the scale drawing of the school gym, we can calculate the ratio of the length in the scale drawing to the length of the actual gym.

In the scale drawing, the length of the gym is 17 inches, while the length of the actual gym is 85 feet.

Since there are 12 inches in a foot, we can convert the length of the actual gym from feet to inches:

85 feet * 12 inches/foot = 1020 inches

Now, we can calculate the scale by dividing the length in the scale drawing by the length of the actual gym:

17 inches / 1020 inches = 1/60

Therefore, the scale that Jorge used to create the scale drawing of the school gym is 1:60.

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To find the left-rectangle approximation of the shaded region.

To find the left-rectangle approximation of the shaded region using 5 rectangles, we can follow these steps:

1. Determine the width of each rectangle. Since we are using 5 rectangles, we divide the total width of the shaded region by 5.
2. Calculate the left endpoint of each rectangle. We start from the leftmost point of the shaded region and add the width of each rectangle to find the left endpoint of the next rectangle.
3. Calculate the area of each rectangle. Multiply the width of each rectangle by the height of the shaded region.
4. Sum up the areas of all the rectangles to find the total approximate area of the shaded region using the left-rectangle approximation.

Please note that without the specific values of the width and height of the shaded region, I cannot provide the numerical answer. However, by following the steps above, you will be able to find the left-rectangle approximation of the shaded region.

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a. When selecting a random sample of 200 employees, we do not expect exactly 60% of the sample to use an FSA because of sampling variability.

b. The standard error for samples of size 200 drawn from this population is approximately 0.0245. To obtain a more precise sample proportion, adjustments such as increasing the sample size, using stratified sampling, and employing random sampling techniques can be made.

a. If a random sample of 200 employees is selected, we do not necessarily expect exactly 60% of the sample to use an FSA. While the population proportion is known to be 60%, the sample proportion may vary due to sampling variability. In other words, the composition of the sample may differ from the population, leading to a different proportion of employees using an FSA. It is more likely that the sample proportion will be close to 60%, but it may not be exactly the same.

b. The standard error for samples of size 200 can be calculated using the formula:

SE = sqrt((p * (1 - p)) / n),

where p is the population proportion (0.60) and n is the sample size (200).

SE = sqrt((0.60 * (1 - 0.60)) / 200) ≈ 0.0245.

To produce a sample proportion that is more precise, several adjustments could be made to the sampling method:

Increase the sample size: A larger sample size reduces sampling variability and provides a more accurate estimate of the population proportion. Increasing the sample size would lead to a smaller standard error.

Use stratified sampling: Dividing the population into different strata based on relevant characteristics (e.g., department, tenure) and then sampling proportionately from each stratum can help ensure a more representative sample.

Employ random sampling techniques: Ensuring that the sample is randomly selected helps to minimize bias and obtain a representative sample.

By implementing these adjustments, the sample proportion would be more precise and provide a better estimate of the population proportion.

The correct question should be :

7.40 Variation in Sample Proportions Suppose it is known that 60% of employees at a company use a Flexible Spending Account (FSA) benefit.

a. If a random sample of 200 employees is selected, do we expect that exactly 60% of the sample uses an FSA? Why or why not?

b. Find the standard error for samples of size 200 drawn from this population. What adjustments could be made to the sampling method to produce a sample proportion that is more precise?

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The inverse function f⁻¹(x) is given by f⁻¹(x) = (4 + x)/x.

To determine the inverse function f⁻¹(x) of the function f(x) = 4/(x - 1), we need to find the value of x when given f(x).

The equation of the function: f(x) = 4/(x - 1).

Replace f(x) with y:

y = 4/(x - 1).

Swap x and y in the equation:

x = 4/(y - 1).

Multiply both sides of the equation by (y - 1) to eliminate the fraction:

x(y - 1) = 4.

Expand the equation: xy - x = 4.

Move the terms involving y to one side:

xy = 4 + x.

Divide both sides by x:

y = (4 + x)/x.

Therefore, the inverse function f⁻¹(x) is f⁻¹(x) = (4 + x)/x.

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Abdul is taking a combined total of 12 credit hours at both Westside Community College and Pinewood Community College. At Westside, the class fee is $98 per credit hour, and at Pinewood, the class fee is $115 per credit hour.

To find the total cost of Abdul's classes, we can multiply the number of credit hours by the respective class fees at each college and then add the results together.

At Westside, the cost of 12 credit hours would be 12 x $98 = $<<12*98=1176>>1176.
At Pinewood, the cost of 12 credit hours would be 12 x $115 = $<<12*115=1380>>1380.

Adding the two totals together, Abdul's combined class fees would be $1176 + $1380 = $<<1176+1380=2556>>2556.

So, the main answer to your question is: The combined total cost of Abdul's classes at Westside Community College and Pinewood Community College is $2556.

In summary, Abdul is taking 12 credit hours at Westside Community College and Pinewood Community College. By multiplying the number of credit hours by the respective class fees at each college, we find that the cost at Westside is $1176 and the cost at Pinewood is $1380. Adding these two totals together, Abdul's combined class fees amount to $2556.

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Leah paid $45 for supplies and incurred additional costs for wrapping each item. She was able to sell $75 worth of baked goods.

Leah's bake sale for her favorite charity had some costs involved. She initially paid $45 for supplies at the grocery store. Additionally, she spent about $0.50 for wrapping each individual item. As for the revenue, Leah was able to sell $75 worth of baked goods at the bake sale.

To calculate the total expenses, we can add the cost of supplies to the cost of wrapping each item. The cost of wrapping can be determined by multiplying the number of items by the cost per item. However, we don't have the exact number of items Leah sold, so we cannot provide an accurate calculation.

To determine the profit or loss from the bake sale, we need to subtract the total expenses from the revenue. Since we don't have the exact total expenses, we cannot determine the profit or loss.

In conclusion, Leah paid $45 for supplies and incurred additional costs for wrapping each item. She was able to sell $75 worth of baked goods. However, without knowing the exact expenses, we cannot calculate the profit or loss from the bake sale.

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The result of dividing (6a³ + a² - a + 4) by (a + 1) using synthetic division is the quotient 6a² + 5a - 4 with a remainder of 4.

To divide the polynomial (6a³ + a² - a + 4) by (a + 1) using synthetic division, we follow these steps:

First, set up the synthetic division table:

  -1   |   6   1   -1   4

Next, bring down the coefficient of the highest power term, which is 6, and place it in the first row of the synthetic division table:

  -1   |   6   1   -1   4

        |__|

Multiply the divisor, -1, by the number in the first row (6) and place the result in the second row of the synthetic division table. Then, add the numbers vertically:

  -1   |   6   1   -1   4

        |__| -6

        |__________

Next, repeat the process. Multiply the divisor, -1, by the number in the second row (-6) and place the result in the third row. Then, add the numbers vertically:

  -1   |   6   1   -1   4

        |__| -6   5

        |__________

              -5

Repeat the process one more time:

  -1   |   6   1   -1   4

        |__| -6   5  -4

        |__________

              -5   4

The numbers in the last row represent the coefficients of the quotient polynomial. Therefore, the quotient is 6a² + 5a - 4.

The remainder is the last number in the synthetic division, which is 4.

Hence, the result of dividing (6a³ + a² - a + 4) by (a + 1) using synthetic division is the quotient 6a² + 5a - 4 with a remainder of 4.

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(n / (n + 1)) × (s / (s - 1)) = n[s / (s - 1)] = (n + 1) / n. This is in conflict with Equation 2. Therefore, we can conclude that the equations provided are not identical.

The given equations,s = n/(n + 1)[s / (s - 1)] = nare not two ways of writing the same formula. Let's analyze why:Equation 1: s = n/(n + 1)Divide both sides by s - 1 to obtain:s / (s - 1) = n / (n + 1)(s / (s - 1)) = (n / (n + 1)) × (s / (s - 1))Equation 2: [s / (s - 1)] = n

The only way to determine if they are the same is to equate them to each other and attempt to derive any sort of conclusion:(n / (n + 1)) × (s / (s - 1)) = n[s / (s - 1)] = (n + 1) / n

This is in conflict with Equation 2. Therefore, we can conclude that the equations provided are not identical.Explanation:The two equations provided are not equivalent to each other because they generate different outcomes. Although they appear to be similar, they cannot be used interchangeably. To verify that two equations are the same, we can replace one with the other and see if they generate the same result. In this case, the two equations do not produce the same results; thus, they are not the same.

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The outstanding balance on the invoice is $47,000. Ralph Corp. received an invoice dated September 9 for $50,000 with terms of 3/10, n/30.

On September 16, Ralph mailed a partial payment of $3,000, leaving a remaining balance of $47,000.

The terms of 3/10, n/30 mean that the buyer (Ralph Corp.) is entitled to a discount of 3% if the payment is made within 10 days of the invoice date, and the full payment is due within 30 days without any discount.

Since Ralph Corp. made a partial payment of $3,000 on September 16, which is within the 10-day discount period, this amount qualifies for the discount. The discount can be calculated as 3% of $50,000, which equals $1,500. Therefore, the effective payment made by Ralph Corp. is $3,000 - $1,500 = $1,500.

To determine the outstanding balance, we subtract the effective payment from the original invoice amount: $50,000 - $1,500 = $47,000. Thus, the outstanding balance on the invoice is $47,000, indicating the remaining amount that Ralph Corp. needs to pay within the designated 30-day period.

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The odds in favor of the event are a/(b - a).

To find the odds in favor of an event, we need to determine the ratio of favorable outcomes to unfavorable outcomes.

In this case, the probability of the event is given as a/b. To find the odds, we need to express this probability as a ratio of favorable outcomes to unfavorable outcomes.

Let's assume that the number of favorable outcomes is x and the number of unfavorable outcomes is y.

According to the given information, the probability of the event is x/(x+y) = a/b.

To find the odds in favor of the event, we need to express this probability as a ratio.

Cross-multiplying, we get bx = a(x+y).

Expanding, we have bx = ax + ay.

Moving the ax to the other side, we get bx - ax = ay.

Factoring out the common factor, we have x(b - a) = ay.

Finally, dividing both sides by (b - a), we find that x/y = a/(b - a).

Therefore, the odds in favor of the event are a/(b - a).

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Answer:

15 m =16.404 yards

Step-by-step explanation:

15 m = 16.404 yards

The quadratic equation with roots 4-3i and 4+3i is x² + 8x + 25 = 0.

To find the quadratic equation with roots 4-3i and 4+3i, we can use the sum and product of roots formulas.

The sum of the roots is given by -b/a, so in this case, -b/a = -8/a = -8/1 = -8.

The product of the roots is given by c/a, so in this case, c/a = (4-3i)(4+3i)/1 = (16-9i²)/1 = (16-9(-1))/1 = (16+9)/1 = 25/1 = 25.

Now, we can use these values to form the quadratic equation. Since a=1, the quadratic equation is:

x² - (sum of roots)x + product of roots = 0

Substituting the values, we have:

x² - (-8)x + 25 = 0

Simplifying further, we get:

x² + 8x + 25 = 0

Therefore, the quadratic equation with roots 4-3i and 4+3i is:

x² + 8x + 25 = 0.

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To find the probability of a company having both a website and a section in the newspaper, we can use the formula for conditional probability.

Let's denote the events as follows:
A: A company has a section in the newspaper
B: A company has a website

We are given the following probabilities:
P(A) = 0.43 (Probability of a company having a section in the newspaper)
P(B|A) = 0.84 (Probability of a company having a website given that it has a section in the newspaper)

The probability of both events A and B occurring can be calculated as:
P(A and B) = P(A) * P(B|A)

Substituting in the values we have:
P(A and B) = 0.43 * 0.84
P(A and B) = 0.3612

Therefore, the probability of a company having both a website and a section in the newspaper is 0.3612 or 36.12%.

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To determine a cubic polynomial with integer coefficients that has [tex]$\sqrt[3]{2} \sqrt[3]{4}$[/tex]as a root, we can use the fact that if $r$ is a root of a polynomial, then $(x-r)$ is a factor of that polynomial.

In this case, let's assume that $a$ is the unknown cubic polynomial. Since[tex]$\sqrt[3]{2} \sqrt[3]{4}$[/tex] is a root, we have the factor[tex]$(x - \sqrt[3]{2} \sqrt[3]{4})$[/tex].
Now, we need to rationalize the denominator. Simplifying [tex]$\sqrt[3]{2} \sqrt[3]{4}$, we get $\sqrt[3]{2^2 \cdot 2} = \sqrt[3]{8} = 2^{\frac{2}{3}}$.[/tex]
Substituting this back into our factor, we have $(x - 2^{\frac{2}{3}})$. To find the other two roots, we need to factor the cubic polynomial further. Dividing the cubic polynomial by the factor we found, we get a quadratic polynomial. Using long division or synthetic division, we find that the quadratic polynomial is [tex]$x^2 + 2^{\frac{2}{3}}x + 2^{\frac{4}{3}}$.[/tex]Now, we can find the remaining two roots by solving this quadratic equation using the quadratic formula or factoring. The resulting roots are Simplifying these roots further will give us the complete cubic polynomial with integer coefficients that has[tex]$\sqrt[3]{2} \sqrt[3]{4}$[/tex] as a root.

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A cubic polynomial with integer coefficients that has [tex]\sqrt[3]{2} \sqrt[3]{4}[/tex] as a root is [tex]x^{3} - 6x^{2} + 12x - 8$[/tex].

To determine a cubic polynomial with integer coefficients that has  [tex]\sqrt[3]{2} \sqrt[3]{4}[/tex] as a root, we can start by recognizing that the expression  [tex]\sqrt[3]{2} \sqrt[3]{4}[/tex] can be simplified.

First, let's simplify [tex]\sqrt[3]{4}[/tex]. We know that [tex]\sqrt[3]{4}[/tex] is the cube root of 4. Therefore, [tex]\sqrt[3]{4} = 4^{\frac{1}{3}}[/tex].

Next, let's simplify [tex]\sqrt[3]{2}[/tex]. This can be written as [tex]2^{\frac{1}{3}}[/tex] since [tex]\sqrt[3]{2}[/tex] is also the cube root of 2.

Now, let's multiply [tex]\sqrt[3]{2} \sqrt[3]{4}[/tex]:
[tex](2^{\frac{1}{3}}) (4^{\frac{1}{3}})[/tex].

Using the property of exponents [tex](a^m)^n = a^{mn}[/tex], we can rewrite the expression as [tex](2 \cdot 4)^{\frac{1}{3}}[/tex]. This simplifies to [tex]8^{\frac{1}{3}}[/tex].

Now, we know that [tex]8^{\frac{1}{3}}[/tex] is the cube root of 8, which is 2.

Therefore, [tex]\sqrt[3]{2} \sqrt[3]{4} = 2[/tex].

Since we need a cubic polynomial with [tex]\sqrt[3]{2} \sqrt[3]{4}[/tex] as a root, we can use the root and the fact that it equals 2 to construct the polynomial.

One possible cubic polynomial with [tex]\sqrt[3]{2} \sqrt[3]{4}[/tex] as a root is [tex](x-2)^{3}[/tex]. Expanding this polynomial, we get [tex]x^{3} - 6x^{2} + 12x - 8[/tex].

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The confidence intervals created using the percentile method and the standard error method are not exactly the same for two reasons:

First, the two methods are based on different assumptions about the population distribution of the sample. Second, the percentile method and the standard error method use different formulas to compute the confidence intervals. The standard error method assumes that the population is normally distributed, while the percentile method does not make any assumptions about the distribution of the population. As a result, the percentile method is more robust than the standard error method because it is less sensitive to outliers and skewness in the data. The percentile method calculates the confidence interval using the lower and upper percentiles of the bootstrap distribution, while the standard error method calculates the confidence interval using the mean and standard error of the bootstrap distribution.

Since the mean and percentiles are different measures of central tendency, the confidence intervals will not be exactly the same.

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By using the given geometric figure and splitting it into three rectangular blocks, we can prove the factoring formula for the sum of cubes, a³+b³=(a+b)(a² - ab+b²).

To prove the factoring formula for the sum of cubes, a³+b³=(a+b)(a² - ab+b²), we can use the geometric figure provided.

First, let's split the figure into three rectangular blocks. One block has dimensions a, b, and a+b, while the other two blocks have dimensions a, b, and a.

Now, let's calculate the volume of the entire figure. We know that the volume is equal to the sum of the volumes of each rectangular block. The volume of the first block is (a)(b)(a+b) = a²b + ab². The volume of the second and third blocks is (a)(b)(a) = a²b.

Adding these volumes together, we have a²b + ab² + a²b = 2a²b + ab².

Next, let's factor out the common terms from this expression. We can factor out ab to get ab(2a + b).

Now, let's compare this expression with the formula we want to prove, a³+b³=(a+b)(a² - ab+b²). Notice that a³+b³ can be written as ab(a²+b²), which is equivalent to ab(a² - ab+b²) + ab(ab).

Comparing the terms, we see that ab(a² - ab+b²) matches the expression we obtained from the volume calculation, while ab(ab) matches the remaining term.

Therefore, we can conclude that a³+b³=(a+b)(a² - ab+b²) based on the volume calculation and the fact that the two expressions match.

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If the product of two polynomials with integer coefficients is a polynomial with even coefficients, not all of which are divisible by 4, then in one of the polynomials all the coefficients are even, and in the other at least one of the coefficients is odd. This statement is proved.

To prove that if the product of two polynomials with integer coefficients is a polynomial with even coefficients, not all of which are divisible by 4, then in one of the polynomials all the coefficients are even, and in the other at least one of the coefficients is odd, we can use proof by contradiction.

Assume that both polynomials have all even coefficients. In this case, every coefficient in each polynomial would be divisible by 2. When we multiply these polynomials, the resulting polynomial will have all even coefficients, as each term in the product will have even coefficients.

However, since not all of the coefficients in the resulting polynomial are divisible by 4, this means that there must be at least one coefficient that is divisible by 2 but not by 4. This contradicts our assumption that all coefficients in both polynomials are even.

Therefore, our assumption is incorrect. At least one of the polynomials must have at least one odd coefficient.

In conclusion, if the product of two polynomials with integer coefficients is a polynomial with even coefficients, not all of which are divisible by 4, then in one of the polynomials all the coefficients are even, and in the other at least one of the coefficients is odd.

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The 95% confidence interval for μ is approximately $144.32 to $175.68.

To find a 95% confidence interval for μ, we can use the formula:
Confidence interval = sample mean ± (critical value * standard error)

Step 1: Find the critical value for a 95% confidence level. Since the sample size is large (n > 30), we can use the z-distribution. The critical value for a 95% confidence level is approximately 1.96.

Step 2: Calculate the standard error using the formula:
Standard error = standard deviation / √sample size

Given that the standard deviation is $64 and the sample size is 64, the standard error is 64 / √64 = 8.

Step 3: Plug the values into the confidence interval formula:
Confidence interval = $160 ± (1.96 * 8)

Step 4: Calculate the upper and lower limits of the confidence interval:
Lower limit = $160 - (1.96 * 8)
Upper limit = $160 + (1.96 * 8)

Therefore, the 95% confidence interval for μ is approximately $144.32 to $175.68.

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The area of circular lid of the CD case is approximately 271.89 cm². This is found by subtracting the surface area of the curved side from the total surface area, using the given height of 10 cm and solving for the radius.

To find the area of the circular lid of the CD case, we need to subtract the surface area of the curved side of the cylinder from the total surface area.

Given:

Surface area of the CD case = 603 cm²

Height of the CD case = 10 cm

The total surface area of the cylinder is given by the formula: 2πr + 2πrh, where r is the radius and h is the height.

Since we want to find the area of the circular lid, we can ignore the curved side and focus on the two circular bases. The formula for the area of a circle is πr².

Let's solve for the radius (r) first.

Total surface area = 2πr + 2πrh

603 = 2πr + 2πr(10)

603 = 2πr + 20πr

603 = 22πr

r = 603 / (22π)

Now we can find the area of the circular lid using the formula for the area of a circle.

Area of the circular lid = πr²

Area of the circular lid = π * (603 / (22π))²

Area of the circular lid = (603² / (22²))

Area of the circular lid ≈ 271.89 cm²

Therefore, the area of the circular lid of the CD case is approximately 271.89 cm².

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The total area of hexagon [tex]$aobcpd$[/tex] is sum of the areas of the triangles that is 36$ square units.

To find the area of hexagon [tex]$aobcpd$[/tex], we can break it down into smaller shapes and then sum their areas.

1. Start by drawing the radii [tex]$\overline{oa} and \overline{op}$[/tex]
2. Since the circles are externally tangent, [tex]$\overline{oa}$ is perpendicular to $\overline{cd}$ and $\overline{op}$ is perpendicular to $\overline{cd}$.[/tex]
3. Connect points a and b to form triangle aob.
4. Similarly, connect points $c$ and $d$ to form triangle $cpd$.
5. The area of triangle $aob$ can be calculated using the formula: Area = (base * height) / 2. In this case, the base is $2$ (since the radius of circle $o$ is $2$) and the height is $4$ (since $\overline{oa}$ is perpendicular to $\overline{cd}$ and $\overline{op}$). So, the area of triangle $aob$ is $(2 * 4) / 2 = 4$.
6. Similarly, the area of triangle $cpd$ can also be calculated as $(4 * 4) / 2 = 8$.
7. Now, we have two triangles with areas 4 and 8.
8. The remaining shape is a rectangle, which can be divided into two triangles: $\triangle bcd$ and $\triangle oap$. Both triangles have equal areas because they share the same base and height. The base is the sum of the radii, which is $2 + 4 = 6$. The height is the distance between $\overline{op}$ and $\overline{cd}$, which is $4$. So, the area of each triangle is $(6 * 4) / 2 = 12$.
9. The total area of hexagon [tex]$aobcpd$[/tex] is the sum of the areas of the triangles: $4 + 8 + 12 + 12 = 36$ square units.

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The probability that exactly 20 customers will arrive in the next 2 hours is 0.070. The average arrival rate of customers at the bakery is 10 customers per hour. So, in 2 hours, there is an expected arrival of 10 * 2 = 20 customers.

We can use the Poisson distribution to calculate the probability that exactly 20 customers will arrive in the next 2 hours. The Poisson distribution is a probability distribution that describes the number of events that occur in a fixed period of time,

given an average rate of occurrence. In this case, the event is a customer arriving at the bakery and the average rate of occurrence is 10 customers per hour.

The formula for the Poisson distribution is: P(X = k) = (λ^k e^(-λ)) / k!

where:

In this case, we want to calculate the probability that there are 20 events (customers arriving at the bakery) in a period of time with an average rate of occurrence of 10 events per hour (2 hours).

So, we can set λ = 10 and k = 20. We can then plug these values into the formula for the Poisson distribution to get the following probability: P(X = 20) = (10^20 e^(-10)) / 20!

This probability is very small, approximately 0.070. In conclusion, the probability that exactly 20 customers will arrive in the next 2 hours at the bakery is 0.070.

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f(x) = (x - 3)/(x + 2)

As the equation is basically a fraction the only thing that can be out of domain is if the denominator is equal to 0, so let's see when the denominator can be 0

x + 2 = 0

x = -2

So -2 is out of domain and all the other numbers are inside the domain.

Answer:

[tex]-2 \implies \sf no[/tex]

 [tex]0 \implies \sf yes[/tex]

 [tex]3 \implies \sf yes[/tex]

Step-by-step explanation:

Given rational function:

[tex]f(x)=\dfrac{x-3}{x+2}[/tex]

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

A rational function is not defined when its denominator is zero.

Therefore, to find when the given function f(x) is not defined, set the denominator to zero and solve for x:

[tex]x+2=0 \implies x=-2[/tex]

Therefore, the domain is restricted to all values of x except x = -2.

This means that the domain of f(x) is (-∞, 2) ∪ (2, ∞).

In conclusion:

To solve this problem, let's break it down step by step: The original area of the paper is [tex]81 cm^2[/tex]. The first strip that is cut off is 1/3 the original area. This means the first strip has an area of [tex](1/3) * 81 cm^2 = 27 cm^2[/tex].

From this first strip, another strip is cut off that is 1/3 the area of the first. So, the second strip has an area of [tex](1/3) * 27 cm^2 = 9 cm^2[/tex]. This process continues indefinitely, with each subsequent strip being 1/3 the size of the previous one.
To find the sum of all the strip areas, we can use the concept of infinite geometric series. The formula for finding the sum of an infinite geometric series is S = a / (1 - r), where a is the first term and r is the common ratio. In this case, the first term (a) is [tex]27 cm^2[/tex] and the common ratio (r) is 1/3. Plugging these values into the formula, we get

[tex]S = (27 cm^2) / (1 - 1/3)[/tex].

Simplifying, we have

[tex]S = (27 cm^2) / (2/3) \\= (27 cm^2) * (3/2)\\ = 40.5 cm^2[/tex].

Therefore, the sum of the areas of all the strips is [tex]40.5 cm^2[/tex]. The sum of the areas of all the strips cut from the original piece of paper is [tex]40.5 cm^2[/tex]. The area of the original piece of paper is [tex]81 cm^2[/tex]. When a strip is cut off that is 1/3 the size of the original area, it has an area of [tex]27 cm^2[/tex]. From this first strip, another strip is cut off that is 1/3 the area of the first, resulting in a strip with an area of [tex]9 cm^2[/tex]. This process continues indefinitely, with each subsequent strip being 1/3 the size of the previous one. To find the sum of all the strip areas, we use the formula for an infinite geometric series: S = a / (1 - r), where a is the first term and r is the common ratio. In this case, the first term is[tex]27 cm^2[/tex] and the common ratio is 1/3. Plugging these values into the formula, we find that the sum of the strip areas is [tex]40.5 cm^2.[/tex]

The sum of the areas of all the strips cut from the original piece of paper is [tex]40.5 cm^2.[/tex]

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Therefore, Isaac should use the arithmetic mean to describe the temperatures recorded at noon during the week.

To describe the temperatures recorded by Isaac during one week, we need to choose an appropriate measure of center. The measure of center provides a representative value that summarizes the central tendency of the data.

In this case, since the temperatures do not contain an extreme value and we want a measure that represents the typical or central value of the data, the most suitable measure of center to use is the arithmetic mean or average.

The arithmetic mean is calculated by summing all the values and dividing the sum by the number of values. It provides a balanced representation of the data as it considers every observation equally.

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