5 ft
8 ft
6:ft
Find the area.
10 ft
5 ft
Remember: A = πr²
A = [?] ft²
Round to the nearest
hundredth.
Use 3.14 for T.

The given sequence an = sin(√n)/√n converges to limit 0 as n approaches infinity

The mentioned nth term of the sequence is an = sin(√n)/√n. To determine the convergence or divergence of the sequence and find its limit, we can use the limit comparison test, which is based on comparing the given sequence with a known sequence whose convergence or divergence is already known.Suppose bn is a known sequence whose convergence or divergence is already known. Then, by the limit comparison test, the given sequence converges or diverges according as the sequence bn converges or diverges.

To apply the limit comparison test, we need to find a suitable sequence bn whose convergence or divergence is known. For this, we observe that sin x ≤ x for all x > 0. Hence, we have 0 ≤ sin(√n)/√n ≤ 1/√n, where the inequality follows by dividing both sides of sin x ≤ x by √n and substituting x = √n. Also, we know that the sequence bn = 1/√n converges to 0 as n approaches infinity. Therefore, by the limit comparison test, the given sequence an = sin(√n)/√n also converges to 0 as n approaches infinity.

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a. In the sample:i. The average value of birth weight for all mothers is 7.17 pounds.

ii. For mothers who smoke is 6.82 pounds.

iii. For mothers who do not smoke is 7.28 pounds.b. i. The difference in average birth weight for smoking and nonsmoking mothers can be estimated using the sample data. The difference is given by the formula:

Difference = X1 – X2, where X1 is the average birth weight of mothers who smoke and X2 is the average birth weight of mothers who do not smoke.Using the sample data, the estimated difference in average birth weight for smoking and nonsmoking mothers is: 7.28 – 6.82 = 0.46 pounds.ii. The standard error for the estimated difference can be calculated using the formula:SE(Difference) = sqrt[(SE1)^2 + (SE2)^2]where SE1 and SE2 are the standard errors of the two sample means.Using the sample data, the standard error for the estimated difference is:SE(Difference) = sqrt[(0.23)^2 + (0.12)^2] = 0.26 pounds.iii. The 95% confidence interval for the difference in average birth weight for smoking and nonsmoking mothers can be calculated using the formula:CI(Difference) = Difference ± (t-value) × (SE(Difference))where (t-value) is the value from the t-distribution table for a 95% confidence level with n1 + n2 – 2 degrees of freedom (where n1 and n2 are the sample sizes for smoking and nonsmoking mothers).Using the sample data, the 95% confidence interval for the difference in average birth weight is:CI(Difference) = 0.46 ± (2.048) × (0.26) = (0.04, 0.88) pounds.

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The correct equation for the given situation is D: 5/x + 3/(x-2) = 1.

Let's assume that Kenny takes x hours to complete the job alone. As per the given information, Jerry works twice as fast as Kenny, which means he can do the job alone in x/2 hours.

Now, Jerry works for 2 hours, which means he completes 2/x of the job. After that, both Jerry and Kenny work together for 3 more hours and complete the remaining (1-2/x) part of the job.

Since they are working together, we can add their rates of work. Jerry's work rate is 1/(x/2) = 2/x and Kenny's work rate is 1/x. Therefore, their combined work rate is 2/x + 1/x = 3/x.

Using the formula "work = rate × time," we get the equation:

2/x × 2 + 3/x × 3 = 1

Simplifying the above equation, we get 5/x + 3/(x-2) = 1.

Therefore, option D is the correct equation for the given situation.

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The option B is the correct option.

Suppose I'm trying to prove that 2 divides n2 - n for any natural number n. If the end/goal of my induction step is 2 divides p2 then my inductive hypothesis must have been 2 divides n2 - n for n = 0,1,...,p-1. The correct option is B.What is natural induction?The concept of natural induction is based on the notion of logical implication, in which the validity of the subsequent statement is demonstrated using the initial statement. Suppose, for example, you want to show that P(2) is valid. A hypothesis is a statement that is proven using induction; it is the statement that P(n) is valid for a natural number n.Suppose I'm trying to prove that 2 divides n2 - n for any natural number n. If the end/goal of my induction step is 2 divides p2 then my inductive hypothesis must have been 2 divides n2 - n for n = 0,1,...,p-1. Therefore, option B is the correct option.

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Answer:

b. 25 in

Step-by-step explanation:

the lateral area is the area of the outside walls (not including the base area).

on a square pyramid there are 4 such outside walls in the form of triangles.

so, each such triangle has an area of 800/4 = 200 in².

the area of a triangle is

baseline × height / 2

the slant height is the height of a wall triangle (not the inner height of the pyramid).

a base edge is nothing else but the baseline of such a wall triangle.

so, we have

200 = baseline × 16 / 2 = baseline × 8

baseline = 200/8 = 25 in

Therefore, the total cost to the buyer, including VAT at 15%, is R73,60.

The term "VAT" usually refers to "Value Added Tax," which is a type of consumption tax that is levied on the value added to goods and services at each stage of production and distribution. It is commonly used by governments around the world as a way to generate revenue and to shift the tax burden from income and sales taxes onto consumption.

by the question.

To calculate the total cost to the buyer including VAT at 15%, you need to add the VAT amount to the original price. Here's how to do it:

Calculate the VAT amount:

VAT = 15% of R64,00

VAT = 0.15 x R64,00

VAT = R9,60

Add the VAT amount to the original price to get the total cost to the buyer:

Total cost = R64,00 + R9,60

Total cost = R73,60

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The number of terms in geometric series with common ratio 0.5 is 5.

A geometric series is a set of integers where each term following the first is created by multiplying the term before it by a predetermined value called the common ratio. To put it another way, each term in the series is created by multiplying the term before it by a set integer.

The sum of a finite geometric sequence is given by the formula:

[tex]S = a(1 - r^n)/(1 - r)[/tex]

Where, S is the sum of the series,

a is the first term,

r is the common ratio, and n is the number of terms.[tex]55.5625 = 28(1 - 0.5^n)/(1 - 0.5)\\\\55.5625(1 - 0.5) = 28(1 - 0.5^n)\\27.5625 = 28 - 28(0.5)^n\\0.4375 = (0.5)^n\\n = log(0.4375)/log(0.5)\\n = 4.17[/tex]

Rounding the numbers, we have n = 5.

Hence, the number of terms in geometric series is 5.

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Answer:

2916 cm^2

Step-by-step explanation:

Area = side x side = 54 x 54 or 54^2 = 2916 cm^2

Answer:

The other guy is right, 2916 cm^2 is the answer

Step-by-step explanation:

Do you need help with any other questions, if so I'm available to help you.

Answer:

A random sample of size 64 is used to test the null hypothesis that for certain age group the mean score on an achievement test is less than or equal to 40 against the alternative that it is greater than 40. The scores are assumed to be normally distributed with variance 0? 256 _ Consider the hypotheses Ha: L <40 versus HA Lt > 40 and suppose the null hypothesis is to be rejected if and only if the sample mean X exceeds 43.5. What is the size of this test? Compute the probability of type Il error at L = 42

Step-by-step explanation:

value of variable x and y in simultaneous equations are 3,1 and 3,-3 respectively.

Several algebraic equations that have the same unknown variables and the same answer are referred to as simultaneous equations. It suggests that there is a single solution to the simultaneous equations. Examples of concurrent equations include: 2x - 4y = 4, 5x + 8y = 3.

Given Simultaneous Equation;

Equation 1 ; y=x²-x+3

Equation 2 ;  y=6-3x

Putting Equation 2 in 1 we get

6-3x=x²-x+3

x²+2x-3=0

x²+3x-x-3=0

x(x+3)-1(x-3)=0

(x-3)(x-1)=0

x=3,1

By entering x values in equation 2, we obtain

y=6-3×3

y=-3

Or y=6-3×1=3

Hence, value of x and y are 3,1 and 3,-3 respectively.

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Answer: r ≈ 3.12

Step-by-step explanation:

The radius is 3.12 cm².

First, isolate the y term on one side of the equation.

-For the first equation: 4x + y = 4

Subtract 4x from both sides of the equation to isolate the y term:

4x + y - 4x = 4 - 4x

y = 4 - 4x

-For the second equation: -6x - 30 + y = -6

Add 6x to both sides of the equation to isolate the y term:

-6x - 30 + y + 6x = -6 + 6x

y = -6 + 6x

Now, set the equations equal to each other to solve for x:

4 - 4x = -6 + 6x

Combine like terms to isolate the x term:

-10x = -10

Divide both sides by -10 to solve for x:

x = 1

Now plug x back into either equation to solve for y:

4 - 4(1) = 4 - 4

y = 0

If increasing the sides of a square field by five feet will increase the area by 245 ft², then the area of the original square is 484 ft².

To find the area of the original square, we can use the following formula:

Area of the original square = x²

where x is the original length of the square field.

Given that the increase in the length and width of the square field is 5 ft, the side length of the new square is (x + 5) ft. Therefore, the area of the new square is (x + 5)² ft².

Given that the area of the new square is 245 ft² more than the area of the smaller square, we can write:

(x + 5)² = 245 + x²

Expanding the left-hand side of the equation and simplifying, we get:

x² + 10x + 25 = 245 + x²

Solving for x, we get:

10x + 25 = 245

x = 22

Plugging x = 22 into the formula, we can find the area of the original square:

Area of the original square = x² = 22² = 484 ft²

Therefore, the area of the original square is 484 ft².

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The answer of  the given question based on the finding the area of the triangle of ABC the answer is the area of triangle ABC is approximately 62.82 square cm.

A triangle is  three-sided polygon with three angles. It is  two-dimensional geometric shape, and one of  basic shapes in geometry. A triangle can be classified based on  length of its sides and  measure of its angles. The sum of the interior angles of  triangle are 180 degrees. Triangles are used in many fields, like mathematics, engineering, architecture, and art.

To find the area of triangle ABC, we can use the formula for the area of a triangle:

Area = (1/2) * base * height

where the base is one side of the triangle and the height is the perpendicular distance from the base to the opposite vertex.

In this case, we know that AB = 11 cm and AC = 17 cm, and angle A is 45 degrees. To find the height of the triangle, we need to use trigonometry.

First, we can find the length of BC using the Law of Cosines:

BC² = AB² + AC² - 2 * AB * AC * cos(A)

BC² = 11² + 17² - 2 * 11 * 17 * cos(45)

BC² = 156 - 265.42

BC² = 109.42

BC = 10.46 cm (rounded to two decimal places)

Now we can use the sine function to find the height of the triangle:

sin(A) = height / BC

height = BC * sin(A)

height = 10.46 * sin(45)

height = 7.39 cm (rounded to two decimal places)

Finally, we can use the area formula to find the area of the triangle:

Area = (1/2) * base * height

Area = (1/2) * 17 * 7.39

Area = 62.82 square cm (rounded to two decimal places)

Therefore, the area of triangle ABC is approximately 62.82 square cm.

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The answer is c): 17 and one-half quarts

To answer the question, we need to find the total amount of juice Sam made by adding the given quantities. However, the given quantities are in different units, which makes the addition difficult. Therefore, we need to convert all quantities to the same unit before adding them.

1 gallon = 4 quarts (since 1 gallon is equal to 128 ounces, and 1 quart is equal to 32 ounces,

thus 1 gallon = 128/32 = 4 quarts)

1 quart = 2 pints

1 pint = 2 cups

Therefore, 3 gallons = 3 x 4 = 12 quarts

2 quarts = 2 x 1 = 2 quarts

4 pints = 4 / 2 = 2 quarts

6 cups = 6 / 4 = 1.5 quarts

Now, we can add all the quantities in quarts to get the total amount of juice that Sam made:

12 + 2 + 2 + 1.5 = 17.5 quarts

Therefore, Sam made 17 and one-half quarts in all. Thus, the correct option is (c) seventeen and one half.

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Answer:

30,000 grams

Step-by-step explanation:

multiply the 30KG by 1,000 (that is the conversion) and you get 30,000g

Answer:

hi I'm really sorry I can't help

As a result, 47 degrees of freedom represent the essential t value ().

Least. To contrast one thing to another, degrees of comparison are employed. One thing or person is described in the positive degree. When comparing two things or people, utilize the comparative degree. Moreover, the exceptional degree is employed to describe groups, individuals, or more than two objects.

The following formula must be used to get the freedom degrees for the crucial t value ():

df = n - 1

where the sample size is "μ". The sample size in this instance is 48, so:

df = 48 - 1

df = 47

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Answer:

Emma had $62.50 in her account when she and Alexis got to the bank.

Step-by-step explanation:

Let's start by assigning variables to the unknowns in the problem. Let's call the amount of money in Emma's account before she made her deposit "E", and the amount of money in Alexis's account before she made her withdrawal "A".

From the problem, we know that:

A = 3E (because Alexis had three times as much money as Emma before making her withdrawal)

After Alexis withdrew $100 and Emma deposited $25, they had the same amount of money in their accounts. So we can set up another equation:

A - 100 = E + 25

Simplifying this equation, we get:

A = E + 125

Now we can substitute the first equation into the second equation, because we know that A is equal to 3E:

3E = E + 125

Subtracting E from both sides, we get:

2E = 125

Dividing both sides by 2, we get:

E = 62.5

So Emma had $62.50 in her account when she and Alexis got to the bank.

Answer:62.50

Step-by-step explanation:

she had 62.50

There is evidence to support the claim of the developers that people who complete the 6-week program will increase their manual dexterity.

To determine if the mean manual dexterity has significantly increased after completing the 6-week training program, we can perform a paired t-test. The null hypothesis is that the mean difference between the before and after the program is zero, while the alternative hypothesis is that the mean difference is greater than zero.

Using the given data, the mean difference is (85.6-81.1)/12 = 0.375, with a standard deviation of 0.753. The t-statistic is then calculated as (0.375-0)/(0.753/sqrt(12)) = 2.35, with 11 degrees of freedom (df = n-1).

Using a significance level of 0.05 and a one-tailed test, the critical t-value is 1.796. Since the calculated t-value (2.35) is greater than the critical t-value (1.796), we can reject the null hypothesis and conclude that the mean manual dexterity has significantly increased after completing the 6-week training program.

However, it is important to note that this conclusion is based on a small sample size and that further research may be needed to confirm these findings.

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The graph of f(x)= 2 square x will look like the graph of f(x)= square x but will shrink it vertically by the factor of 1/2.

The graph of f(x)= 2 square x will look like the graph of f(x)= square x but will stretch it vertically by factor of 2.

Thus, Option B and Option D are correct.

A function is a relationship or expression involving one or more variables.  It has a set of input and outputs.  

A. F(x)= 2 square x has the same domain and range as f(x)= square x.

B. The graph of f(x)= 2 square x will look like the graph of f(x)= square x but will shrink it vertically by the factor of 1/2.

D. The graph of f(x)= 2 square x will look like the graph of f(x)= square x but will stretch it vertically by factor of 2.

Option A is false because multiplying the function by 2 will change the range of the function to include all non-negative real numbers (since the square of any number is non-negative).

Option B is true because multiplying the function by 2 will vertically shrink the graph by a factor of 1/2 (since the output values will be half the size of the original function).

Option C is false because multiplying the function by 2 will not affect the horizontal scale of the graph.

Option D is true because multiplying the function by 2 will vertically stretch the graph by a factor of 2 (since the output values will be twice the size of the original function).

Therefore, Option B and Option D are correct.

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The system of inequalities that represents the number of quarters, x, and the number of dimes, y, that Mai could have is given by:

x + y ≥ 10 and 0.25x + 0.1y < 2

These are the two systems of inequalities that represent the number of quarters, x, and the number of dimes, y, that Mai could have.

Let x be the number of quarters and y be the number of dimes that Mai has. Then, the system of inequalities can be represented as:

Thus, the first inequality is x + y ≥ 10.

Also, Mai has less than $2.00, therefore, the second inequality is 0.25x + 0.1y < 2. The value of x and y are assumed to be non-negative integers.+

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False. A mean difference of zero does not necessarily indicate that the peppers are well distributed between the two groups.

Number is a mathematical object used to count, measure, and label. It is one of the most fundamental concepts in mathematics and is used to describe a wide variety of physical, logical, and abstract objects. Numbers are used to represent quantities, lengths, temperatures, money, and many other measurements. They are also used to represent abstract ideas, such as the number of days in a year or the number of colors in a rainbow.

Although the mean may be equal between the two groups, the distribution of the peppers could be skewed and not evenly distributed. For example, one group could have all large peppers and the other all small peppers and the mean would be equal. This would not be considered well distributed. To ensure the peppers are evenly distributed, one should check the standard deviation or range of the data to see if the peppers are spread across both groups.

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Answer:  A mean difference of zero indicates the peppers

are not well distributed between the two groups.

Why: Part B Answers

What do large differences of the means of each group indicate? Select the correct answer.

The peppers with different weights aren’t properly distributed between the two groups.

So they arent distributed well

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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The required fraction of socks that Bobo the clown has used can be[tex]$\frac{\frac{1}{5}W+\frac{5}{8}B}{W+B}[/tex]

Bobo likes to wear one white sock and one black sock.

Let the number of white socks be W and the number of black socks be B. Bobo changes his socks every day. At the end of several days, he finds that he has used exactly [tex]\frac15[/tex] of his white socks.

So, the number of white socks he has used [tex]=\frac{1}{5}W[/tex]

Also, he has used [tex]\frac58[/tex] of his black socks. So, the number of black socks he has used [tex]=\frac{5}{8}B[/tex]

The total number of socks Bobo has used = number of white socks used + number of black socks used

                                                                [tex]=\frac{1}{5}W+\frac{5}{8}B[/tex]

The fraction of all of Bobo's socks he has used [tex]=\frac{\text{Total number of socks used}}{\text{Total number of socks}}[/tex]

So, we need to find the total number of socks.

Total number of white socks = W

Total number of black socks = B

The total number of socks Bobo has is = Total number of white socks + Total number of black socks [tex]= W + B[/tex]

The fraction of all of Bobo's socks he has used [tex]= \frac{\frac{1}{5}W+\frac{5}{8}B}{W+B}[/tex]

Hence, the required fraction of socks that Bobo the clown has used can be calculated as [tex]$\frac{\frac{1}{5}W+\frac{5}{8}B}{W+B}[/tex]

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Answer:

A

Step-by-step explanation:

The replacement time separating the bottom 30% to the top 70% of CD players is 9.27 to 10.73 years.

A normal distribution refers to a continuous probability distribution in statistics that is symmetric and bell-shaped. It is a statistical distribution that is ideal for data that are continuous and normally distributed in a population.

The central limit theorem states that any large number of independent random variables, each with its own distribution, have their sum distribution approach normality as the number of variables grows large enough.

The formula for z-score is given as:

z = (x - μ) / σ

where x is the random variable, μ is the mean, σ is the standard deviation, and z is the z-score.

Substituting the given values of the mean, standard deviation, and percentiles in the above formula, we get:

For the bottom 30%, the percentile rank is 0.3.

Hence, the z-score is given as:

z = invNorm(0.3) = -0.5244

Substituting the z-score formula we get:

-0.5244 = (x - 10) / √2

Rearranging the above formula we get:

x = -0.5244 * √2 + 10 = 9.27 years

For the top 70%, the percentile rank is 0.7.

Hence, the z-score is given as:

z = invNorm(0.7) = 0.5244

Substituting the z-score formula we get:

0.5244 = (x - 10) / √2

Rearranging the above formula we get:

x = 0.5244 * √2 + 10 = 10.73 years

Therefore, the replacement time separating the bottom 30% to the top 70% of CD players is 9.27 to 10.73 years.

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