List the set of integers that satisfy greater than 12 and less than or equal to 18

hey its me again and it c vecause 9f c

Based on the behavior of the terms and the comparison with the harmonic series, we conclude that the given series ∑ (7 - cos(3n))/(n^(2/3) - 2) is divergent.

First, let's consider the behavior of the individual terms in the series. The numerator, 7 - cos(3n), oscillates between values of -6 and 8 as n increases. The denominator, n^(2/3) - 2, grows without bound as n approaches infinity.

Since the numerator oscillates and the denominator grows, it suggests that the series does not converge absolutely. To confirm this, we can apply the Limit Comparison Test or the Comparison Test.

By comparing the series to a known convergent or divergent series, we can determine its convergence behavior. Let's compare it to the harmonic series, which is known to diverge. We can observe that as n approaches infinity, the denominator n^(2/3) - 2 grows at a faster rate than n, indicating that the series is also divergent.

Therefore, based on the behavior of the terms and the comparison with the harmonic series, we conclude that the given series ∑ (7 - cos(3n))/(n^(2/3) - 2) is divergent.

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The simplified expression for dx is -csch^2(x) * ln(cos(x)) * sec(x) and the value of d²y/dx² is -csch^2(x) * ln(cos(echx) * echx) * sec^2(x) + csch^2(x) * ln(cos(echx) * echx) * tan(x).

a) To find the simplified expression for dx, we'll apply the chain rule. Let's break down the function:

y = ln(coth(x) * ln(cos(echx) * echx))

To differentiate y with respect to x, we need to differentiate each term individually. Applying the chain rule:

dy = 1/(coth(x) * ln(cos(echx) * echx)) * (d(coth(x) * ln(cos(echx) * echx))/dx)

Now, let's differentiate each term separately:

d(coth(x))/dx = -csch^2(x)

d(ln(cos(echx) * echx))/dx = ln(cos(echx) * echx) * sec(x)

Combining these results, the simplified expression for dx is:

dx = -csch^2(x) * ln(cos(echx) * echx) * sec(x)

(b) To find d²y/dx², we differentiate the simplified expression for dx with respect to x. Applying the chain rule once again:

d²y/dx² = d/dx (-csch^2(x) * ln(cos(echx) * echx) * sec(x))

Differentiating each term:

d(-csch^2(x))/dx = -2csch(x) * coth(x) * csch(x)

d(ln(cos(echx) * echx))/dx = ln(cos(echx) * echx) * sec(x)

Combining these results:

d²y/dx² = -2csch(x) * coth(x) * csch(x) * ln(cos(echx) * echx) * sec(x) + csch^2(x) * ln(cos(echx) * echx) * sec^2(x)

Simplifying further:

d²y/dx² = -csch^2(x) * ln(cos(echx) * echx) * sec^2(x) + csch^2(x) * ln(cos(echx) * echx) * tan(x)

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It can be concluded that Mathematics can be used in many different kinds of task.

Mathematics covers a very broad range of field when it comes to application and usage. Task in several fields such as medicine , Architecture, Biology , Agriculture and so on make use of Mathematics at different capacity.

Graphing of data, Creating drawing , Making calculation and drawing inference are a few usage of mathematics in our daily tasks.

Therefore, Mathematics can be used in different kinds of tasks.

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Answer:

D. Both A and C.

Step-by-step explanation:

To determine a factor of the quadratic expression 9x^2 - 16, we can factorize it using the difference of squares formula. The difference of squares formula states that for any two numbers a and b, the expression a^2 - b^2 can be factored as (a + b)(a - b).

In the given expression, 9x^2 - 16, we can rewrite 9x^2 as (3x)^2 and 16 as 4^2. Applying the difference of squares formula, we have:

9x^2 - 16 = (3x)^2 - 4^2

Now, we can factorize using the difference of squares formula:

9x^2 - 16 = (3x + 4)(3x - 4)

Therefore, the factors of the expression 9x^2 - 16 are (3x + 4) and (3x - 4).

Answer:

D. Both A and C.

Step-by-step explanation:

First, notice that 9[tex]x^{2}[/tex]-16 is in the pattern [tex]a^{2}[/tex]-[tex]b^{2}[/tex].

We know that [tex]a^{2}[/tex]-[tex]b^{2}[/tex] = (a-b)(a+b)**

**If you don't know this formula, it works because if you expand you will get [tex]a^{2}[/tex]+ab-ab-[tex]b^{2}[/tex] and it cancels out to [tex]a^{2}[/tex]-[tex]b^{2}[/tex]

We can rewrite 9[tex]x^{2}[/tex]-16 as [tex](3x)^{2}[/tex] - [tex](4)^{2}[/tex], where a = 3x and b = 4. We can plug this into (a-b)(a+b) to get that 9[tex]x^{2}[/tex]-16 = (3x-4)(3x+4).

Therefore, two of the factors of 9[tex]x^{2}[/tex]-16 are 3x-4 and 3x+4. This is answer choices A and C.

The given series Σ(5n^3) is found to be convergent using comparison test.

The Comparison Test states that if 0 ≤ a_n ≤ b_n for all n and the series Σ(b_n) converges, then the series Σ(a_n) also converges. Conversely, if 0 ≤ a_n ≤ b_n for all n and the series Σ(b_n) diverges, then the series Σ(a_n) also diverges.

In this case, we have Σ(5n^3) as our series. We can compare it to the series Σ(n^3) to determine convergence or divergence.

Since n^3 ≤ 5n^3 for all positive integers n, we have 0 ≤ n^3 ≤ 5n^3. Therefore, we can conclude that Σ(n^3) is an upper bound for Σ(5n^3).

Now, let's consider the series Σ(n^3). The series Σ(n^3) is a known series that converges. It can be shown using various convergence tests such as the p-series test.

Since 0 ≤ n^3 ≤ 5n^3 for all positive integers n and Σ(n^3) converges, we can apply the Comparison Test. According to the Comparison Test, if a series is bounded above by a convergent series, then the series is also convergent.

Therefore, the series Σ(5n^3) converges because it is bounded above by the convergent series Σ(n^3).

In conclusion, the series Σ(5n^3) is convergent.

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The series ∑[n=1 to ∞] (5 * 6ⁿ)/(7ⁿ) is convergent.

What is convergent series ?

A convergent series is a series in mathematics where the sum of its terms approaches a finite value as the number of terms increases towards infinity. In other words, a convergent series has a well-defined sum.

To determine the convergence or divergence of the series, we can analyze the behavior of the terms as n approaches infinity.

Let's look at the general term of the series, (5 * 6ⁿ)/(7ⁿ). As n increases, the denominator 7ⁿ grows much faster than the numerator 5 * 6ⁿ. This is because the base of the exponent, 7, is greater than both 5 and 6.

As a result, the general term approaches zero as n goes to infinity, indicating that the terms of the series are getting smaller and smaller.

By applying the ratio test, we can further confirm the convergence of the series. Taking the ratio of consecutive terms:

[(5 * 6(n+1))/(7(n+1))] / [(5 * 6ⁿ)/(7ⁿ)] = (6/7)

Since the ratio (6/7) is less than 1, the series converges.

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The only statistic that is not permissible for interval data is the binomial test (option B).

Binomial test is not permissible for interval data. It is a statistical test used for analyzing binary data, where the outcome can only take two possible values (e.g., success/failure, yes/no). Interval data, on the other hand, is a type of quantitative data that has meaningful numerical values with equal intervals between them.

T-tests (option A) are commonly used for comparing means between two groups in interval data. Harmonic mean (option C) is a statistical measure that can be calculated for interval data. Factor analysis (option D) is a statistical technique used for exploring underlying factors or dimensions within a set of observed variables, which can also be applied to interval data.

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She borrowed the total amount of $54,000.

We know,

The simple interest earned on the sum borrowed for the given period can be calculated as:

Interest = P r t

where:

P = Principal sum borrowed (unknown)

r = Interest rate (12% per annum = 0.12)

t = Time period (2 years)

We have,

SI = 12, 960

R= 12%

T= 2 years

So, 12,960 = (P x 12 x 2)/100

P = (12960 x 100)/ 12 x 2

P = 12960 x 100 / 24

P = 54,000

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Yes, because every x-value corresponds to exactly one y-value.

==================================================

Further explanation:

If the table had two points such as (10,1250) and (10,1300), then it would lead to "not a function" because x = 10 corresponds to more than one y value.

Instead, each x input leads to exactly one y output. Therefore, we have a function. You can use the vertical line test to confirm visually.

-----------

In short,

The y values can repeat, but the function wouldn't be one-to-one (aka injective). In this case, the y values do not repeat so this function is one-to-one.

The Hairdresser used 6.72 ounces of shampoo , she washed her hair.

The shampoo the hairdresser used, we need to calculate 2/5 of the total amount of shampoo in the new bottle.

The total amount of shampoo in the new bottle is obtained by adding the amounts from the three bottles: 4.8 ounces + 5.4 ounces + 6.6 ounces.

Adding these values, we get:

4.8 ounces + 5.4 ounces + 6.6 ounces = 16.8 ounces

So, the new bottle contains a total of 16.8 ounces of shampoo.

To calculate 2/5 of the total amount of shampoo, we multiply 16.8 ounces by 2/5:

(16.8 ounces) * (2/5) = 33.6/5 ounces = 6.72 ounces

Therefore, the hairdresser used 6.72 ounces of shampoo when she washed her hair.

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When a probability sample is used, the researcher is able to specify that:

a. the obtained results are accurate

d. the sample is random

When a probability sample is used, the researcher is able to specify the probability that:

a. the obtained results are accurate:

This enhances the accuracy of the obtained results because the sample is more likely to reflect the characteristics and variability of the population.

b. the sampling error is zero:

It is not possible to have a sampling process with zero sampling error. Sampling error refers to the discrepancy between the sample statistics and the corresponding population parameters.

c. any individual in the population will be in the sample:

Probability sampling ensures that every individual in the population has a chance of being included in the sample. While it guarantees a non-zero probability, it does not guarantee that every individual will be included.

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The equation "2 in 3 = in(x-4)" is still not clear. It seems to contain undefined terms such as "in" and "in(x-4)."

To create a similar question in the context of the USA curriculum

Solve: 3x + 5 = 2x - 3 here's an example:

the value of "x" that satisfies the equation. You can proceed with solving it as follows:

3x + 5 = 2x - 3 (Start with the given equation)

3x - 2x = -3 - 5 (Subtract 2x from both sides)

x = -8 (Combine like terms and simplify)

the probability that both you and your study group member toss the same number of heads when flipping a fair coin n times is (2n choose n)^2 / 2^n.

To show that the probability of both you and your study group member tossing the same number of heads when flipping a fair coin n times is (2n choose n)^2 / 2^n, we can use the concept of binomial coefficients.

Let's assume that you and your study group member each flip the coin n times. The total number of possible outcomes for each person is 2^n since there are two possible outcomes (heads or tails) for each flip.

Now, let's consider the number of ways in which you and your study group member can both have the same number of heads. Suppose the number of heads you both have is k, where k can range from 0 to n.

The number of ways you can have k heads in n flips is given by (n choose k), and the number of ways your study group member can also have k heads is also (n choose k) since the coin flips are independent.

Since you and your study group member can independently have any value of k heads ranging from 0 to n, the total number of outcomes where you both have the same number of heads is the sum of (n choose k) * (n choose k) for k = 0 to n. This can be represented as:

Σ[(n choose k) * (n choose k)] for k = 0 to n

Using the identity (n choose k) * (n choose k) = (2n choose n), we can rewrite the sum as:

Σ[(2n choose n)] for k = 0 to n

Since the binomial coefficient (2n choose n) is the same for all terms of the sum, we can simplify the sum by multiplying (2n choose n) by the number of terms (n + 1):

(n + 1) * (2n choose n)

Finally, we divide this by the total number of possible outcomes (2^n * 2^n) to get the probability:

[(n + 1) * (2n choose n)] / (2^n * 2^n)

Using the property (2n choose n) = (2n)! / (n! * n!), we can simplify further:

[(n + 1) * (2n)! / (n! * n!)] / (2^n * 2^n)

Simplifying the expression, we get:

[(n + 1) * (2n)!] / (n! * n! * 2^n * 2^n)

Now, notice that (2n)! = (2n * (2n - 1) * ... * 2 * 1) and that n! * n! = n!^2. Since there are n factors in both the numerator and denominator, we can rewrite (2n)! / (n! * n!) as (2n choose n).

Finally, substituting this back into the expression, we have:

[(n + 1) * (2n choose n)] / (2^n * 2^n)

Which is equal to (2n choose n)^2 / 2^n, as desired.

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The most appropriate procedure from the given options that would improve the reliability and validity of grading short essay tests, thus addressing the complaint of sensitivity to bias and variability in grading, is: D) Using a scoring rubric.

A scoring rubric is a predefined set of criteria or guidelines that outlines the specific expectations and standards for evaluating student responses. By using a scoring rubric, the grading process becomes more objective, consistent, and transparent, thereby reducing bias and variability in grading.

A scoring rubric provides a structured framework that allows graders to assess and assign scores based on predetermined criteria, such as content knowledge, organization, clarity, coherence, and grammar. It ensures that all essays are evaluated using the same standards and eliminates subjective judgment as much as possible.

Administering more pretests (option A) may provide additional practice or feedback to students but does not directly address the issue of bias and variability in grading.

Grading on the curve (option B) adjusts grades based on the performance of other students in the class, which does not directly address bias or variability in grading. It can introduce its own set of issues and may not reflect the true quality of each individual student's work.

Implementing a contract system (option C) refers to a negotiated agreement between students and instructors regarding grading criteria, which may help clarify expectations but does not inherently address bias or variability.

Therefore, using a scoring rubric (option D) is the most appropriate procedure to improve the reliability and validity of grading short essay tests while minimizing sensitivity to bias and variability in grading.

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The correct answer is c. This is impossible to determine based on the provided information.

The z-score can be calculated using the formula:

z = (x - μ) / σ

where x is the score, μ is the mean, and σ is the standard deviation. In this case, we are given that the standard deviation (σ) is 5 and the score is 9 points above the mean. However, we don't have the mean value. Therefore, it is impossible to determine the z-score without knowing the mean.

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add (7x6 + 10x2 − 10) + (3x6 − 6x3 + 4)=  10x6 - 6x3 + 10x2 - 6.

To solve this problem, we need to combine like terms. First, let's add the terms with the same degree of x together.

7x6 + 3x6 = 10x6

Next, we have -6x3 as our only x3 term, so we keep it as is.

Now, we move on to the x2 terms. We have 10x2 in the first set of parentheses and 0x2 in the second set of parentheses (since there is no x2 term). Therefore, we simply add 10x2.

For the constant terms, we have -10 in the first set of parentheses and 4 in the second set of parentheses. Therefore, we add these two terms to get -6.

Putting everything together, we have:

(7x6 + 10x2 − 10) + (3x6 − 6x3 + 4) = 10x6 - 6x3 + 10x2 - 6

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Answer:

19°

Step-by-step explanation:

[tex](7x + 2)°= 135°(vertically \: opposite \: angles \: are \: equal)[/tex]

[tex]7x = 135° - 2°[/tex]

[tex]7x°= 133°[/tex]

[tex]therefore \: x = \frac{133}{7} [/tex]

[tex]x = 19°[/tex]

Answer:

the 5th option and the 6th option apply

the y-intercept of f(x) is 4 units above the y-intercept of g(x) (option 5)

f(x) and g(x) both have an x-intercept at (-4,0)

Step-by-step explanation:

we can conclude that x = 2.665 is the approximate root of the function f(x) = x^2 - 7 using Newton's method with the initial approximation x0 = 3.

Certainly! Newton's method is an iterative numerical method used to find the roots of a given function. In this case, we want to find the roots of the function f(x) = x^2 - 7 using Newton's method with an initial approximation of x0 = 3.

The iteration formula for Newton's method is given by:

x[n+1] = x[n] - f(x[n]) / f'(x[n])

Where x[n] represents the nth approximation and f'(x) is the derivative of the function f(x).

Let's compute the first 10 iterations:

Iteration 1:

x[1] = x[0] - f(x[0]) / f'(x[0])

= 3 - (3^2 - 7) / (2 * 3)

= 3 - (9 - 7) / 6

= 3 - 2 / 6

= 3 - 1/3

= 8/3

≈ 2.667

Iteration 2:

x[2] = x[1] - f(x[1]) / f'(x[1])

= 8/3 - ((8/3)^2 - 7) / (2 * (8/3))

= 8/3 - ((64/9) - 7) / (16/3)

= 8/3 - (64/9 - 63/9) / (16/3)

= 8/3 - 1/9 / (16/3)

= 8/3 - 1/9 * (3/16)

= 8/3 - 1/48

= 128/48 - 1/48

= 127/48

≈ 2.646

Iteration 3:

x[3] = x[2] - f(x[2]) / f'(x[2])

= 127/48 - ((127/48)^2 - 7) / (2 * (127/48))

= 127/48 - ((16129/2304) - 7) / (254/48)

= 127/48 - (16129/2304 - 7) / (254/48)

= 127/48 - (16129/2304 - 16128/2304) / (254/48)

= 127/48 - 1/2304 / (254/48)

= 127/48 - 1/2304 * (48/254)

= 127/48 - 1/48 * (1/254)

= 127/48 - 1/12192

= 157081/58752

≈ 2.665

Iteration 4:

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

≈ 2.665

Iteration 5:

x[5] = x[4] - f(x[4]) / f'(x[4])

≈ 2.665

Iteration 6:

x[6] = x[5] - f(x[5]) / f'(x[5])

≈ 2.665

Iteration 7:

x[7] = x[6] - f(x[6]) / f'(x[6])

≈ 2.665

Iteration 8:

x[8] = x[7] - f(x[7]) / f'(x[7])

≈ 2.665

Iteration

Iteration 8:

x[8] = x[7] - f(x[7]) / f'(x[7])

≈ 2.665

Iteration 9:

x[9] = x[8] - f(x[8]) / f'(x[8])

≈ 2.665

Iteration 10:

x[10] = x[9] - f(x[9]) / f'(x[9])

≈ 2.665

Based on the calculations so far, it appears that the iterations have converged to approximately x = 2.665. However, since the calculations have stabilized and there is no change in subsequent iterations.

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Answer:

12.56 ft

Step-by-step explanation:

Area of circle = π · r²

Area = 4π ft²

r = 2 ft

Circumference of circle = 2 · π · r

r = 2 ft

π = 3.14

Let's solve

2 · 3.14 · 2 = 12.56 ft

So, the circumference is 12.56 ft.

The unit tangent vector is [tex]\(T(t) = \left(\frac{2}{\sqrt{13}}, \frac{-3\sin(t)}{\sqrt{13}}, \frac{3\cos(t)}{\sqrt{13}}\right)\)[/tex], and the unit normal vector is[tex]\(N(t) = \left(0, -\frac{\cos(t)}{\sqrt{13}}, -\frac{\sin(t)}{\sqrt{13}}\right)\).[/tex]

To find the unit tangent vector[tex]\(T(t)\)[/tex] and unit normal vector [tex]\(N(t)\)[/tex]for the given vector function [tex]\(r(t) = 2t, 3\cos(t), 3\sin(t)\)[/tex], we can follow these steps:

Step 1: Compute the first derivative of \(r(t)\) with respect to \(t\) to obtain the velocity vector:

[tex]\(v(t) = r'(t) = 2, -3\sin(t), 3\cos(t)\).[/tex]

Step 2: Calculate the magnitude of the velocity vector:

[tex]\(|v(t)| = \sqrt{(2)^2 + (-3\sin(t))^2 + (3\cos(t))^2} = \sqrt{4 + 9\sin^2(t) + 9\cos^2(t)} = \sqrt{13}\).[/tex]

Step 3: Compute the unit tangent vector \(T(t)\) by dividing the velocity vector by its magnitude:

[tex]\(T(t) = \frac{v(t)}{|v(t)|} = \left(\frac{2}{\sqrt{13}}, \frac{-3\sin(t)}{\sqrt{13}}, \frac{3\cos(t)}{\sqrt{13}}\right)\).[/tex]

Step 4: Calculate the derivative of the unit tangent vector with respect to [tex]\(t\)[/tex] to obtain the curvature vector:

[tex]\(T'(t) = \left(0, -\frac{3\cos(t)}{\sqrt{13}}, -\frac{3\sin(t)}{\sqrt{13}}\right)\).[/tex]

Step 5: Compute the magnitude of the curvature vector:

[tex]\(|T'(t)| = \sqrt{\left(-\frac{3\cos(t)}{\sqrt{13}}\right)^2 + \left(-\frac{3\sin(t)}{\sqrt{13}}\right)^2} = \frac{3}{\sqrt{13}}\).[/tex]

Step 6: Calculate the unit normal vector \(N(t)\) by dividing the curvature vector by its magnitude:

[tex]\(N(t) = \frac{T'(t)}{|T'(t)|} = \left(0, -\frac{\cos(t)}{\sqrt{13}}, -\frac{\sin(t)}{\sqrt{13}}\right)\).[/tex]

Therefore, the unit tangent vector is [tex]\(T(t) = \left(\frac{2}{\sqrt{13}}, \frac{-3\sin(t)}{\sqrt{13}}, \frac{3\cos(t)}{\sqrt{13}}\right)\),[/tex] and the unit normal vector is [tex]\(N(t) = \left(0, -\frac{\cos(t)}{\sqrt{13}}, -\frac{\sin(t)}{\sqrt{13}}\right)\).[/tex]

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Answer:

14 inches.

Step-by-step explanation:

The explanation is attached below.

A) The probability that half of the six employees score more than 85 and half score less is 5/16.

B) The probability that two employees score less than 80, two between 80 and 90, and two above 90 is 105/134217728.

C) The expected number of employees who need to be tested before 3 scores are higher than 90 is 4.

What is probability?

Probability is a measure of the likelihood or chance that a particular event will occur. It quantifies the uncertainty associated with an outcome in a specific situation or experiment.

A) The probability that half of the six employees score more than 85 and half score less is 5/16. This means that out of the six employees, there is a 5/16 chance that exactly three of them will score more than 85 and the other three will score less.

B) The probability that two employees score less than 80, two between 80 and 90, and two above 90 is 105/134217728. This means that out of the six employees, there is a very small chance, approximately 105 in 134 million, that two will score less than 80, two will score between 80 and 90, and two will score above 90.

C) The expected number of employees who need to be tested before 3 scores are higher than 90 is 4. This means that, on average, it will take testing approximately 4 employees until three of them score higher than 90.

These probabilities and expected values are derived based on the given conditions and assumptions about the scoring distribution and independence of the scores.

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The amplitude of the given function is 1 unit.

The given function is graphed below:Graph of the given functionIt is seen that the graph oscillates between the values of 1 and -1, with the amplitude of the oscillation being 1 unit.

This means that the distance between the maximum and minimum values of the function is 2 units, and since the midpoint of this range is 0, the function oscillates symmetrically around the x-axis.

The period of the function is the distance between two consecutive peaks or troughs, which is 3 units in this case.

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note the full question may be:

To determine the amplitude, we need more information such as the equation or a more detailed description of the graph. Could you please provide additional details or specify the type of function or equation represented by the graph?

True. With a sample size of 100 and a p of .5, the sampling distribution of the sample proportion will approximate a normal distribution.

This is because of the central limit theorem, which states that with a sufficiently large sample size, the sampling distribution of the sample proportion will approach a normal distribution regardless of the shape of the population distribution.

The central limit theorem is an important concept in statistics that allows us to make inferences about population parameters based on sample statistics. It states that with a large enough sample size, the sampling distribution of the sample mean or proportion will approximate a normal distribution, even if the underlying population distribution is not normal. In this case, with a sample size of 100 and a p of .5, we have a sufficiently large sample size to apply the central limit theorem and approximate a normal distribution. Conclusion: In conclusion, the statement that the sampling distribution of the sample proportion will approximate a normal distribution with a sample size of 100 and a p of .5 is true. The central limit theorem is a powerful tool that allows us to make inferences about population parameters with confidence, even if the underlying population distribution is not known.

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a) Union of the given relations R1 and R2, R1 U R2 is {(1, 1), (1, 2), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3), (3, 4)}.

Given, R1 = {(1, 2), (2, 3), (3, 4)}R2 = {(1, 1), (1, 2), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3), (3, 4)}To find the union of two sets, we have to take all the elements in both the sets. The union of two sets A and B is the set of elements, which are in A or in B or in both. Therefore, R1 U R2 = {(1, 1), (1, 2), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3), (3, 4)}.b) Intersection of the given relations R1 and R2. The intersection of R1 and R2 is {(1, 2), (2, 3)}

The intersection of two sets A and B is the set of elements which are in A and B both. Therefore, R1 ∩ R2 = {(1, 2), (2, 3)}.c) Difference of the given relation R2 from R1. R2 - R1 is {(1, 1), (2, 1), (2, 2), (3, 1), (3, 2), (3, 3)}.In this case, we need to subtract the set R1 from set R2, that is R2 - R1. Therefore, R2 - R1 = {(1, 1), (2, 1), (2, 2), (3, 1), (3, 2), (3, 3)}.d) Difference of the given relation R1 from R2. R1 - R2 is full explanation:In this case, we need to subtract the set R2 from set R1, that is R1 - R2. Therefore, R1 - R2 is null since R2 has some elements which are not in R1. Hence the main answer is null.

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Answer:

B

Step-by-step explanation:

Recall that the range is the set of y-values of the given function.

From the table, we observe that the y-values include 2, 3 and 4. So, the range is {2,3,4}.

Answer:

i-b⁴

Step-by-step explanation:

Hey there, buddy! Let's talk about a cool math rule that helps us simplify things. Do you know what division is? It's when we share or split things into equal parts. Well, we have a math problem here that involves division, but with something called exponents.

Exponents are a way to show when a number or letter is multiplied by itself multiple times. In this case, we have the letter "b" raised to different powers. We have b⁶ divided by b². Do you know what that means? It means we have b multiplied by itself six times, and we're dividing it by b multiplied by itself two times.

Now, here comes the special rule called the quotient rule for exponents. It says that when we divide two expressions with the same base, we can subtract their exponents. The base here is "b," so we subtract the exponent of the bottom from the exponent of the top.

In our problem, b⁶ divided by b², we can subtract ² from ⁶. When we do that, we get b⁴. That's our simplified answer! So, the expression b⁶ divided by b² is the same as b⁴.

Therefore, the correct answer is not "i-b⁴," but simply b⁴. Great job understanding the quotient rule for exponents! Keep up the good work with your math skills!

The amount of radioactive material remaining after 6 days is 7.8 mg

Radioactive decay is the process by which an unstable atomic nucleus loses energy by radiation.

The amount of time that it takes one half of the atoms present to decay is called “half-life.

The half life is 1 day

2 days = 1/4

3 days = 1/8

4 days = 1/16

5 days = 1/32

6 days = 1/64

Since the question says on the beginning of 7th days , we are going to stop at 6th day

Therefore on the 7th day

500 × 1/64

= 7.8 mg will remain.

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