Suppose an and bn are series with positive terms and bn is known to be convergent. (a) If an > bn for all n, what can you say about an? Why? O a n converges if and only if an < 2bn. Oman converges by the Comparison Test. O an diverges by the Comparison Test. We cannot say anything about an. o a n converges if and only if an 5 4bn. (b) If an

The area of the shaded region is 36.53 cm^2 and the perimeter of the shaded region is 8π cm.

What is area and perimeter?

The area of a shape or figure is its area, whereas the perimeter of a shape is its outer boundary over a given distance. Area is measured in square units or unit2 while perimeter is measured in the same unit.

The circumference of a shape is known as its perimeter. The lengths of all four sides must be added in order to determine a rectangle's or square's perimeter.

Radius, r = 8 cm

Perimeter of a circle = 2πr

Perimeter of s quarter circle = 2πr/4 = 1/2πr

Perimeter of Shaded part = 1/2 * 2πr

                                          = 1/2 × 2 × π × 8

                                          = 8πcm.

Area of a circle = 2πr²

Area of quarter circle = 2πr²/4 = 1/2πr²

Area of a square = length ²

Area of Shaded part = Area of Quarter-circle - Area of Square

                                  = 0.5π(8)² - 8²

                                   = 0.5π(64) - 64

Area of Shaded part  = 36.53 cm^2

Hence, the area of the shaded region is 36.53 cm^2 and the perimeter of the shaded region is 8π cm.

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Answer:

480ft.it does not matter how much east or west they are.it asks how much"they are apart"

so it should be 480.

The study of mathematical logic can help you in your everyday life by developing your ability to think logically and critically.

Everyday logic and mathematical logic are similar in that they both involve reasoning and drawing conclusions based on evidence or information. However, mathematical logic is a more formal and precise system of reasoning that is used in mathematics, computer science, and other fields. It involves using symbols and formal languages to represent statements and arguments, and it often involves the use of mathematical proofs to demonstrate the validity of a conclusion.

The study of mathematical logic can help you in your everyday life by developing your ability to think logically and critically. It can also help you understand the foundations of computer science and the way that computers process information. Additionally, it can help you become more comfortable with using formal language and reasoning, which can be useful in fields such as law, philosophy, and science.

Thus, the study of mathematical logic can help you in your everyday life by developing your ability to think logically and critically.

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Answer: sometimes

Step-by-step explanation:

The rate of change of the perimeter of the square is 11.2 cm/min when the side length is 6 cm.

Step 1: The area of a square is A = s2, where s is the side length.

Step 2: The rate of change of the area of the square is 28 cm2/min.

Step 3: The perimeter of the square is

P = 4s.

Step 4: Substitute s = 6 into the equation for P to get

P = 24 cm.

Step 5: Differentiate P with respect to time to get the rate of change of

the perimeter:

dP/dt = 4ds/dt.

Step 6: Substitute the rate of change of the area (dA/dt = 28 cm2/min) into the equation for dP/dt to get dP/dt = 4(28 cm2/min)/dt.

Step 7: Simplify the equation to get

dP/dt = 112 cm/min.

Conclusion: The rate of change of the perimeter of the square is 112 cm/min when the side length is 6 cm

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Profit made by each girl Sarah, Lilly and Paula respectivly are R 200 , R 400 and R 600

A ratio displays the multiplicity of two numbers. For instance, if a dish of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six. The ratio of oranges to the overall amount of fruit is 8:14, while the ratio of lemons to oranges is 6:8.

An ordered pair of integers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. For instance, you might express the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls) There are 1 in 4 boys and 3 in 4 girls.

A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. Indicators of proportions include "::" and "=".

The amount of investment done by each girl Sarah, Lily and Paula respectivly is x, 2x and 3x

So, the profit will be

x + 2x + 3x = 1200

⇒6x  =1200

⇒ x = 200

Profit made by each girl respectivly are x = R 200 , 2x = R 400 and 3x = R 600.

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Yes, a 3x3 matrix can have infinite solutions. This is because if the determinant of the matrix is zero, the system of equations has an infinite number of solutions.

A 3x3 matrix is a system of three equations with three unknowns.

For a system of linear equations to have a unique solution, the determinant of the matrix must not be zero. If the determinant of the matrix is zero, then the system of equations has an infinite number of solutions.

Therefore, a 3x3 matrix can have infinite solutions if the determinant of the matrix is zero.

Yes, a 3x3 matrix can have infinite solutions. This is because if the determinant of the matrix is zero, the system of equations has an infinite number of solutions.

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The largest possible quotient of a positive 3-digit number divided by the sum of its digits if the 3 digits must be different is 41

The largest possible quotient of a positive 3-digit number divided by the sum of its digits is obtained when the 3 digits are as large as possible, subject to the constraint that they must be different.

The largest possible 3-digit number is 987, which has digits 9, 8, and 7.

The sum of its digits is 9 + 8 + 7 = 24.

The quotient of 987 divided by 24 is:

987/24 = 41.125

otherwise when expressed as a mixed number is read as 41 whole number 3/24

In conclusion, the largest possible quotient of a positive 3-digit number divided by the sum of its digits, when the 3 digits must be different, is 41.

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Answer: 1: x = 2y - 1 This equation shows that the value of x is always 2 times the value of y minus 1.

2: y = 3x + 3 This equation shows that the value of y is always 3 times the value of x plus 3.

3: y = (x/4) - 1 This equation shows that the value of y is always the value of x divided by 4 minus 1.

4: y = x-5 This equation shows that the value of y is always the value of x minus 5.

A ratio is a comparison of two or more numbers expressed as a fraction, such as 3/4 or 4:5. It is used to compare the size or amount of two or more objects or quantities. Ratios can also be expressed as a percent or as a decimal.

A ratio is a comparison of two or more numbers expressed as a fraction. The ratio is written as two numbers separated by a colon (:), or as a fraction. The numbers in the ratio are compared to each other to indicate the size or amount of the objects or quantities being compared. For example, 3:4 means that for every 3 objects, there are 4 of the other object. This can also be written as a fraction, 3/4, to indicate that for every 3 objects, there are 4 of the other object. Ratios can also be expressed as a percent or as a decimal. For example, 3:4 can be expressed as 75% or 0.75.

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The widths of the three fields are the same and equal to x, since that is the variable used in the expressions for the areas of the fields.

To find the greatest possible width, you need to find the highest value of x that satisfies the given conditions. You can substitute x=3 and y=2 in the expressions for the areas of the fields and compare them.

Area of field 1 = 12x^3y = 12 * 3^3 * 2 = 12 * 27 * 2 = 648 square yards Area of field 2 = 6xy^4 = 6 * 3 * 2^4 = 6 * 3 * 16 = 288 square yards Area of field 3 = 21xy = 21 * 3 * 2 = 126 square yards

All three fields have the same width of x = 3 yards, and the width is the greatest possible width.

The inequality that describes this situation will be 6x + 2s ≤ 76

Inequalities are simply created through the connection of two expressions. In this case, it should be noted that the expressions in an inequality are not always equal. Inequalities implies that the expressions are not equal. Here, they are denoted by the symbols ≥ < > ≤.

x = number of group dance numbers

s = number of solo performances

The inequality will be 6x + 2s ≤ 76

This inequality can be read as "the total duration of the group dance numbers (6 minutes per group dance number) plus the total duration of the solo performances (2 minutes per solo performance) is less than or equal to 76 minutes."

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Answer:

t + c <= 17

Step-by-step explanation:

This inequality states that the total number of tables and chairs sold (t + c) must be less than or equal to 17, in order to satisfy the constraint that the store can ship at most 17 pieces of furniture per day.

The midsegments of AABC, hypotenuse BC  is B. 15.

In a triangle, a midsegment is a line segment that connects the midpoints of two non-adjacent sides of the triangle. In this figure, DE and DF are the midsegments of AABC, which means that they connect the midpoints of the sides AB and AC, respectively. Since DE and DF are parallel, we know the triangle isosceles (both legs are congruent).

Since the angle at A is 122°, we know that the angle at B and C are 78° (180-122=58). Therefore, if we draw the altitude from B to AC, we have a 30-78-72 triangle. We have been given the length of the altitude, 8, and the angle of the base, 72. We can use the Sine Ratio to calculate the hypotenuse, BC.

sin(72) = opposite / hypotenuse = 8/BC

Solving for BC, we get 15

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Company A charges $90 for unlimited mileages, while company B charges $75 initial fee and #0.6 per mile driven. Company A will  charge less than company B if the number of miles driven is greater than 25 miles or m > 25.

To solve the problem, we need to translate the word problem into equations.

Let C(A) and C(B) represent the cost charged by company A and B respectively. Let m = the number of mileages.

Company A charges $90 and allows unlimited mileage, it means the charge is a constant and it is not a function of mileage.

Hence,

C(A) = 90

Company B has an initial fee of $75 and charges an additional $0.60 for every mile driven. Hence,

C(B) = 75 + 0.6 m

The inequality that translate: for what mileages will company A charge less than company B is:

C(A) < C(B)

90 < 75 + 0.6 m

To solve the above inequality, subtract 75 from both sides:

90 - 75 < 75 + 0.6 m - 75

15 < 0.6 m

m > 15/0.6

m > 25

Hence, if the mileages > 25 miles, company A charges less than company B.

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Therefore , the required probability is therefore 1/151200, which is the answer to the probability problem.

The probability that a happening will happen or that the proposition is true is determined by a field of mathematics known as probability theory. A probability is a number between 0 and 1, where 1 represents certainty and 0 roughly represents the likelihood that an event will occur. A probability is a numerical expression of a certain event's likelihood or chance of happening. The percentages 0% - 100% and 0 to 1 can also be used to express probabilities. the percentage of times in an ideal collection of equally likely alternatives that an event occurs compared to all possible outcomes.

Here,

The six numbers can only be chosen in one way if the order chosen must match my phone number.

In 10P6 methods, six random digits from a possible total of ten can be chosen.

So the necessary probability is equal to 1/P. (10,6).

Alternative: Probability = 1/151200

The required probability is therefore 1/151200, which is the answer to the probability problem.

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By taking a difference, we will see that you can save $4.70 if you buy the pack.

To find the savings, we need to take the difference between the cost of the  6 times the cost of 1 bookshelf, and the cost of the 6 bookshelves.

The cost of 1 bookshelf is $14.95, and the cost of 6 together is $85.00, then the savings is given by:

S = 6*$14.95 - $85.00

S = $89.70 - $85.00

S = $4.70

You save $4.70 in total if you buy the pack.

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The probability of success is 0.2. The result is obtained by adding the probability of getting 9 and the probability of getting 10.

Probability of an event can be expressed as

P(A) = n(A) / n(S)

Where

The probability of A or B can be calculated by

P(A or B) = P(A + P(B)

A 10-sided die is rolled. Each side of the die is labeled with a number from 1 to 10. A number of 9 or 10 should be rolled to make a player succeed. Find the probability of success!

The number of each side of die are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.

The probability of success is the probability of getting 9 or 10.

P(9) = 1/10

P(10) = 1/10

P(9 or 10) = P(9) + P(10)

P(9 or 10) = 1/10 + 1/10

P(9 or 10) = 2/10

P(9 or 10) = 1/5

P(9 or 10) = 0.2

Hence, the probability that a player would succeed is 0.2.

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The ratio of 2 or more integers is known as fraction. The answer to the given expression is 10

Fractions are written as a ratio of two integers. Fractions are written in the form a/b

The expression in question is given as 5/8 * 16

Simplified form of the expression

On solving, we will have;

5/8 * 16

5 * 16/8

Since the ratio of 18 to 8 is 2, hence the expression will be further simplified as;

5 * 16/8 = 5 * 2

5 * 16/8 = 10

Hence the answer to the given expression is 10

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Therefore , the solution of the given problem of pie chart comes out to be the amount he spent on living expenditures was $1634.5.

A pie chart, also known as a circle chart, is a visual representation of the various values of a given variable or a way to summarize a set of nominal data (e.g. percentage distribution). This kind of chart consists of a circle with numerous segments. Each segment stands for a specific category.

Here,

living expenses are 35% of the monthly budgeted income of $4670.

Next, we must utilize the rule of four:

4670 $ => 100%

x=> 35%

Clearing x:

=> x=(35/100)*(4670)

=> x=1634.5$

The amount he spent on living expenditures was $1634.5.

Therefore , the solution of the given problem of pie chart comes out to be the amount he spent on living expenditures was $1634.5.  

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According to the given information the standard error for the sample proportion is 0.024.

When determining if two ratios as well as fractions are equivalent, using proportion formula is utilized. By dividing the supplied numbers, we may determine the missing value. One way to express the percentage formula is as a: Whereas a and d are indeed the extremes values and b and c are indeed the mean terms, a: b::c : d = a/b = c/d 

Sample size (n) = 146 participants

The percentage (p) of respondents who said they would be interested in attending the program again is as follows:

[tex]\begin{aligned}& p=\frac{132}{146} \\& p=0.9041\end{aligned}[/tex]

For a sample of size "n" and percentage "p," the standard error is as follows:

[tex]\begin{aligned}& S E=\sqrt{\frac{p *(1-p)}{n}} \\& S E=\sqrt{\frac{0.9041 *(1-0.9041)}{146}} \\& S E=0.024\end{aligned}[/tex]

The sample percentage of viewers who wish to see the show again has a standard error of 0.024.

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Answer: C. [tex]2.8[/tex]

Step-by-step explanation:

Using the distance formula, [tex]\sqrt{(-1-1)^2 +(-1-1)^2} \approx 2.8[/tex].

The value of R for the given expression will be 0.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the expression is 750=1000 x (1-(1/(1.01¹³⁹)))+(R/(1.01¹⁴⁰). The expression for the R will be solved as below,

750=1000 x (1-(1/(1.01¹³⁹)))+(R/(1.01¹⁴⁰)

1000(1 - 1 / 4 + R / 4 ) = 750

1000(4 -1 + R ) / 4 = 750

1000 ( 3 + R ) = 3000

3 + R = 3

R = 3 - 3

R - 0

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Answer:

544

Step-by-step explanation:

34 * 2 = 68

68 *2 = 136

136 * 2 = 272

272 * 2 = 544 (month 12 = 1 year)

If the nth term of an arithmetic progression - ap is 4n + 1, then it's  third term is 13

The term in the third is solved using the rule of the sequence

The the formula for the nth term as

= 4n + 1

for n = position of term = 3

solving for the third term

= 4n + 1

substituting known variables

= 4 * 3 + 1

= 12 + 1

= 13

the third term of the sequence is 13

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To calculate the amount of liquid added, the scientist multiplies 6 drops by 0.14 ml, which results in 0.84 ml. Since 0.84 ml falls between 0 ml and 5 ml, it is the exact position of the liquid in the test tube.

6 × 0.14 ml = 0.84 ml

0.84 ml falls between the 0 ml and 5 ml marks on the test tube.

1. Calculate the amount of liquid added: 6 drops × 0.14 ml = 0.84 ml

2. Determine which marks the liquid will be between: 0 ml and 5 ml

3. Determine the exact position of the liquid in the test tube: 0.84 ml falls between the 0 ml and 5 ml marks on the test tube.

The scientist adds 6 drops of liquid to a test tube that has markings every 5 ml. Each drop has 0.14 ml. To calculate the amount of liquid added, the scientist multiplies 6 drops by 0.14 ml, which results in 0.84 ml. Since 0.84 ml falls between 0 ml and 5 ml, it is the exact position of the liquid in the test tube.

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There is no solution when the lines that make up a system are parallel since the two lines do not share any points.

A linear equation with two variables has the for [tex]ax + by + c = 0[/tex], where variables are belongs to R. An A system of linear equations that cannot be solved is a pair of inconsistent linear equations. We can determine whether a system of linear equations has no solution by comparing the coefficients of the equations in the system.

Take into account the pair of linear equations in x and y:

[tex]a1x + b1y + c1 = 0\\a2x + b2y + c2 = 0[/tex]

There won't be a solution if [tex]\frac{a_1}{a_2}= \frac{b_1}{b_2}=\frac{c_1}{c_2}[/tex].

An inconsistent pair of linear equations is the name given to this kind of equational system. The system of equations cannot be solved if the graph's lines are parallel.

So here, both equations are called no solution line.

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annual salary of the 6 employees of a toy company is given below:

Correct option is: Statements (1) and (2) TOGETHER are not sufficient.

The average, sometimes referred to as the arithmetic mean, is calculated by dividing the total number of variables by their sum. Mean, however, represents the data's average. The mean is the sum of the data divided by the total of observations in statistics.

If the 6 annual salaries were ordered from least to greatest, each annual salary would be $6,300 greater than the preceding annual salary.

x, x + 6300, x + (2 × 6300), x + (3 ×6300), x + (4 × 6300), x + (5 × 6300)

Avg = ( x + ( x + 5 × 6300 )) / 2

Avg = ( 2x + 5 × 6300 ) / 2

The range of the 6 annual salaries is $31,500

Thus, no new information, Statement 2) can be derived from Statement 1) itself.

So, Statements (1) and (2) TOGETHER are not sufficient, this is correct option.

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The complete question is as follows:

What is the average (arithmetic mean) annual salary of the 6 employees of a toy company?

(1) If the 6 annual salaries were ordered from least to greatest, each annual salary would be $6,300 greater than the preceding annual salary.

(2) The range of the 6 annual salaries is $31,500.

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

EACH statement ALONE is sufficient.

Statements (1) and (2) TOGETHER are not sufficient.