Use the Limit comparison test to determine the convergence or divergence of the series.[infinity]∑n=11n√n2+5

The striped wall and the floor intersect at a 90 degrees angle since they are perpendicular.

An angle is formed when two or more lines intersect at a point. Types of angles are acute, obtuse, and right angled.

Two lines are said to be perpendicular if there is a 90 degrees angle between them.

The striped wall and the floor intersect at a 90 degrees angle since they are perpendicular.

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The correct symbol used for a column alias containing spaces is C. " " (quotation marks).

In SQL, when we want to assign a column alias containing spaces, we enclose the alias within double quotation marks. This is done to differentiate the alias from other SQL keywords or to handle cases where the alias includes special characters, spaces, or is case-sensitive.

For example, consider the following SQL query:

SELECT column_name AS "Column Alias"

FROM table_name;

In this query, we are selecting a column named "column_name" from the table "table_name" and assigning it the alias "Column Alias" containing spaces. By enclosing the alias within double quotation marks, we indicate to the database that it should treat the entire string as a single identifier or alias.

Using other symbols such as '', ||, or // will not achieve the desired result of creating an alias with spaces. These symbols have different meanings in SQL.

'' (two single quotation marks) typically represents an empty string or a string literal in SQL.

|| (double vertical bars) is the concatenation operator in some SQL dialects, used to combine strings or values.

// (double forward slashes) is commonly used for comments in various programming languages and does not have any special meaning for column aliases in SQL.

Therefore, the correct symbol to use for a column alias containing spaces is C. " " (quotation marks).

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The statement third is correct, which is the first dashed straight line is horizontal to the y-axis at y = -3. Everything below the line is shaded.

The second solid line has a positive slope and goes through (0, - 4) and (3, -2). Everything above the line is shaded.

It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than, known as inequality.

We have two inequality:

2x – 3y <12

y < –3

If we draw these two inequalities on the graph, we will see:

On a coordinate plane, 2 lines are shown. The first dashed straight line is horizontal to the y-axis at y = negative 3. Everything below the line is shaded.

The second solid line has a positive slope and goes through (0, negative 4) and (3, negative 2). Everything above the line is shaded.

Thus, the statement third is correct, which is the first dashed straight line is horizontal to the y-axis at y = -3. Everything below the line is shaded.

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Answer:

B. 720 ways

Step-by-step explanation:

To solve you would multiple 6x5x4x3x2x1 .

The required number of ways can 6 players be assigned to 6 positions on a baseball team is 720ways.

Given that,

Number of players = 6

Assigned position on a baseball = 6

We have to determine,

In how many ways can 6 players be assigned to 6 positions on a baseball team.

According to the question,

To solve this problem assuming that any player can play any position.

The formula to find \(^nP_r\) is given by:

\(^np_r\) is the permutation of arrangement of 'r' objects from a set of 'n' objects, into an order or sequence.

The formula to find permutation is:

\(^np_r = \frac{n!}{(n-r)!}\)

Where, n = 6 and r = 6

Therefore,

\(^6p_6 = \frac{6!}{(6-6)!} \\\)

     \(= \frac{6\times5\times 4 \times 3 \times 2 \times 1}{0!} \\\\= \frac{720}{1} \\\\= 720 \ ways\)

Hence, The required number of ways can 6 players be assigned to 6 positions on a baseball team is 720ways.

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Answer:

0

Step-by-step explanation:

(5x^2+4x-7) + (-5x^2-4x+7)

= 5x² + 4x - 7 - 5x² - 4x + 7

= 4x - 7 - 4x + 7

= - 7 + 7

= 0

The values of a, b, c are 152°, 28°, 152° respectively.

Angles around a point describes the sum of angles that can be arranged together so that they form a full turn.

The sum of angles at a point will give 360°.

This means that a + b + c + 28 = 360

c +28 = 180° ( angle on a straight line)

c = 180 -28

c = 152°

c = a( alternate angles are equal)

therefore the value of a = 152°

b = 28( alternate angles are equal)

therefore the value of b is 28

therefore the values of a, b, c are 152°, 28°, 152° respectively

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Answer:

Hope this helps :)

Step-by-step explanation:

Because x is an absolute value, the value of y is always greater than or equal to zero. I attached the graph below. As you'll see, when x is a negative number, it was the same value as the positive of that value. When x = 1 or x = -1, y = 5.

Answer: Approximately 6.3876 years

When rounding to the nearest whole number, this rounds up to 7 years.

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

Work Shown:

We'll use the compound interest formula

A = P*(1+r/n)^(n*t)

where,

In this case, we know that,

So,

A = P*(1+r/n)^(n*t)

2P = P*(1+r/n)^(n*t)

2 = (1+r/n)^(n*t)

2 = (1+0.11/4)^(4*t)

2 = 1.0275^(4t)

Ln(2) = Ln(1.0275^(4t))

Ln(2) = 4t*Ln(1.0275)

4t*Ln(1.0275) = Ln(2)

t = Ln(2)/(4*Ln(1.0275))

t = 6.38758965414661

It takes roughly 6.3876 years for the deposit to double. If you need this to the nearest whole number, then round up to 7. We don't round to 6 because then we would come up short of the goal of doubling the deposit.

Answer:

- 3x > -19 -5

- 3x > -24

3x < 24

x < 8

Answer:180 minutes

Step-by-step explanation:

Answer:

Inequality

Step-by-step explanation:

An expression is a mathematical phrase that contains numbers, variables, or both. Expressions never have an equal sign. An equation is a mathematical sentence that says two expressions are equal.

The remainder when the polynomial  P(x)=x3-x2-2x+8 is divided by (x+2) is 0

Remainder Theorem

From the definition of remainder theorem which stated that , if a polynomial f(x) is divided by a binomial (x−a), then the remainder is f(a)

Using the remainder theorem, P(x)=x3-x2-2x+8 is divided by (x+2).

binominal (x-a)

Step 1: We divide  p(x) by (x + 2)            

P(x)=x3-x2-2x+8  and X = -2

therefore, Remainder = p(-2)

Step 2: Substitute the value of the remainder into p(x)

P(-2) =\((-2)^{3}\) -( \(-2^{2}\) ) - 2(\(-2\)) + 8

P(-2) = -8 - 4  + 4 + 8

P(-2) = -12+12

P(-2) =0

Therefore, from the remainder theorem, the remainder when P(x) is divided by (x+2) is 0

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the more appropriate average score for the two groups of adolescents is 3.1 hours.

Average hours of work per week for Child Group 1: 2.6 hours

Average hours of work per week for Group 2: 3.1 hours

The more appropriate average score for the two groups of adolescents can be calculated by adding up all the hours of work for each group, then dividing it by the total number of adolescents in each group.

For Child Group 1, the sum of the hours of work is 2 + 0 + 1 + 0 + 0 + 4 + 4 + 0 + 1 + 4 = 16. The total number of adolescents in this group is 10, so the average hours of work per week is 16/10 = 1.6 hours.

For Group 2, the sum of the hours of work is 0 + 2 + 1 + 0 + 2 + 4 + 4 + 1 + 1 + 4 = 19. The total number of adolescents in this group is 10, so the average hours of work per week is 19/10 = 3.1 hours.

Therefore, the more appropriate average score for the two groups of adolescents is 3.1 hours.

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(a) To diagonalize the matrix A, we need to find its eigenvalues and eigenvectors. The characteristic polynomial of A is given by:

det(A - λI) = |(4-λ) -1|

| 2 (1-λ)|

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Copy code

        = (4 - λ)(1 - λ) + 2 = λ² - 5λ + 6 = (λ - 2)(λ - 3)

Therefore, the eigenvalues of A are λ₁ = 2 and λ₂ = 3.

To find the eigenvectors corresponding to each eigenvalue, we solve the equations:

(A - λ₁I)x₁ = 0, and (A - λ₂I)x₂ = 0

For λ₁ = 2, we have:

(A - 2I)x₁ = 0

⇒ (2 - 2)x₁ - (-1)x₂ = 0

⇒ x₁ + x₂ = 0

So, one eigenvector corresponding to λ₁ = 2 is v₁ = ⟨1, -1⟩.

For λ₂ = 3, we have:

(A - 3I)x₂ = 0

⇒ (4-3)x₁ - (-1)x₂ = 0

⇒ x₁ + x₂ = 0

So, another eigenvector corresponding to λ₂ = 3 is v₂ = ⟨1, -1⟩.

Therefore, the matrix A can be diagonalized as:

A = PDP⁻¹, where

P = |1 1|, and D = |2 0|

|0 1| |0 3|

(b) To find P⁻¹, we need to find the inverse of P. We have:

|1 1|⁻¹ = 1/(11 - 11) | 1 -1| = 1/(-1)|-1 1| = |-1 1|

|0 1| | 0 1| | 0 1|

Therefore, P⁻¹ = |-1 1|

| 0 1|

(c) Using the factorization A = PDP⁻¹, we have:

A⁵ = (PDP⁻¹)⁵ = PD⁵P⁻¹

Since D is a diagonal matrix, we can easily compute its fifth power as:

D⁵ = |(2)⁵ 0| = |32 0|

| 0 (3)⁵| | 0 243|

So, A⁵ = PDP⁻¹ = |1 1| |32 0| |-1 1| = |-32 32|

|0 1| |0 243| | 0 1|

Therefore, A⁵ = |-32 32|

| 0 243|.

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In this problem, descriptive statistics is used because the survey percentage is used to make inference for all business owners.

Descriptive statistics is used when data from a sample, which is a sub-set of a population, is used to make inferences about the entire population.

In this problem, the data 979 business owners sampled is used to make inference about the population, which is composed by all business owners, hence descriptive statistics is used.

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Answer:x = 10

Step-by-step explanation:

13+7=20

2 x 10 = 20

x=10

Answer:

x = 10

Step-by-step explanation:

\(2x-7=13\)

First, add 7 to both sides.

\(2x-7 + 7=13 + 7\)

This cancels the -7 on the left side because \(-7 + 7 = 0\).

\(2x=20\)

Then, we can divide both sides by 2 to isolate one multiple of x.

\(2x=20\\\overline{\ 2\ } \ \ \ \ \overline{\, 2 \: }\)

\(\boxed{x = 10}\)

The system of linear equations which has the rank of coefficient matrix equal to augmented matrix and equal to the number of unknowns, has only one solution called the unique solution.

Two types of system of equations exist- consistent and inconsistent.

Inconsistent means that it has no solution , i.e. the solution does not exist , here

Rank of augmented matrix is not equal to that of coefficient matrix.

Consistent system means a solution of the equation exists i.e.

rank of augmented matrix = rank of coefficient matrix.

Now, a consistent system can be of two types again - It may have a unique solution ,i.e.

rank of augmented matrix = rank of coefficient matrix = no. of unknowns

or an infinite number of solutions, where

rank of augmented matrix = rank of coefficient matrix < no. of unknowns   (here we need to assign an arbitrary value to a free variable to find its solutions).

For e.g. let us consider the system -

x + y+ z = 0

2x + 3y + 4z = 1

Since , (0,0,0) is obviously satisfying the equation and so is a solution to this system , the given system is a consistent system .

Also, for a system to be consistent , either a unique solution exists or an infinite number of solutions exist. There is no particular number of solutions.

Here, we see that (-1,1,0) is also a solution other than the zero solution.

We can clearly see that the number of unknown variables , x,y,z is 3 and the number of equations is 2.

Thus, The system if there are fewer equations than variables has infinite solutions, equal number of equations as the unknowns has the unique solution.

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The amount Anne has is $31.

The amount James has is $66.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

James amount = x

Anne amount = y

x + y = 97

x = y/2 - 2

Now,

y/2 - 2 + y = 97

y/2 + y = 97 + 2

y + 2y = 99 x 2

3y = 198

y = 66

Now,

x = y/2 - 2

x = 66/2 - 2

x = 33 - 2

x =31

Thus,

Anne has $31.

James has $66.

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Answer:

find common denominator

1/5

2/3

common denominator is 15

convert 2/3 into a fraction with a denominator of 15

1/5 —> 3/15

2/3 —> multipky numerator and denominator by 5 —> 10/15 (toddlers)

infants = total - toddlers - preschoolers

infants = 15/15 - 10/15 - 3/15 = 2/15

multipky the fractions by 60 (the total number of students) to find for the number in each age group

(10/15)*60 = 40

(3/15)*60 = 12

(2/15)*60 = 8

Answer:

x = -5

Step-by-step explanation:

7x + 15 = 3x - 5

We want all x's on the left side and all numbers (with no x) on the right side.

Step 1. Since we see 3x on the right side, subtract 3x from both sides.

7x - 3x + 15 = 3x - 3x - 5

4x + 15 = -5

Now subtract 15 from both sides.

4x + 15 - 15 = -5 - 15

4x = -20

Since x is being multiplied by 4, divide both sides by 4.

4x/4 = -20/4

x = -5

Answer: x = -5

Answer:

1/6

Step-by-step explanation:

2/3 divided by 4= 2/3 x 1/4

2/3 x 1/4=2/12

2/12 simplifies to 1/6

The measure of ∠CFE is 40°

To solve for triangle ∠CEF, we know that

Parallel to DE is BC

Arc length BD = 58°

Arc length DE = 142°

We can then draw a diameter across the center of the circle and give it a name as the first step. The diameter in this situation is line ZT.

The arcs BD and DE are split in half by the line ZT.

Which is:

Arc SC = 1/(1/2(arc BC) = 1/(58)

Arc SC = 29°

142 = 1/2(arc DE) + arc TE

Arc TE = 71°

Sum of the angles of a semicircle is 180 degrees: Arc SC + Arc CE + Arc TE

29° + Arc CE + 71° = 180°

Arc CE + 100° = 180°

Arc CE = 180-100

Arc CE = 80°

Angle inscribed equals half of angle intercepted

CFE = 1/2 of Arc CE

<CFE = 1/2(80)

< CFE = 40°

The above answer is based on the full question below;

In circle A shown, BC || DE , mBC=58° and mDE=142°. Determine the measure of ZCFE . Show how you arrived at your answer

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A matroid is one which is Non-empty, has hereditary and exchange property. Since,  (s, ik)  satisfies all three axioms of a matroid, we can say that (s, ik) is a matroid.

To show that (s, ik) is a matroid, we need to verify the following axioms:

Non-empty: The matroid must have at least one subset. Since k ≤ |s|, there is at least one subset of size at most k in s, so the matroid is non-empty.

Hereditary: If B is a subset of A and A ∈ ik, then B ∈ ik. Since A is a subset of s and s is finite, we know that A has at most k elements.

If B is a subset of A, then B also has at most k elements, so B ∈ ik. Therefore, the hereditary property holds.

Exchange property: If A, B ∈ ik with |A| < |B|, then there exists an element x ∈ B \ A such that A ∪ {x} ∈ ik.

Let A and B be two subsets of s with |A| < |B| and A, B ∈ ik. Since A and B are subsets of s, they have at most k elements. Since |A| < |B|, there exists an element x ∈ B \ A, that is, x is an element of B but not of A.

We want to show that A ∪ {x} also has at most k elements. Since A has at most k elements, |A ∪ {x}| ≤ |A| + 1 ≤ k + 1. If |A ∪ {x}| > k, then |A| = k and |A ∪ {x}| = k + 1. But then, |B| = k + 1, which contradicts the assumption that |B| ≤ k.

Therefore, A ∪ {x} has at most k elements, so A ∪ {x} ∈ ik. Thus, the exchange property holds.

Since (s, ik) satisfies all three axioms of a matroid, we can conclude that (s, ik) is a matroid.

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In order to decide the best study locations, the researchers must determine which study location is the most suitable for each student. This ensures that students are able to learn effectively and have the best chance of succeeding.

A randomized study location experiment will help researchers find out which study locations are best suited to each type of learner.

To decide study locations, the researcher should use an objective chance procedure, such as flipping a fair coin. The objective chance procedure will guarantee that each student has an equal chance of being assigned to a specific study location.

The researcher should ensure that both groups are matched as closely as possible in terms of characteristics that may be relevant to study success, such as ACT scores, GPAs, and socioeconomic backgrounds.

This guarantees that any variations in academic performance between the two groups are most likely due to differences in the study location and not to other external factors.

Therefore in order to decide the best study locations, the researchers must determine which study location is the most suitable for each student. This ensures that students are able to learn effectively and have the best chance of succeeding.

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The area of trapezoid EFGH is 46.53 square centimeters.

To find the area of trapezoid EFGH, we can use the formula:

Area = (1/2) (sum of parallel sides) (height)

The sum of the parallel sides can be calculated by adding the lengths of EF and GH:

EF + GH = 8.1 + 11.7 = 19.8 cm

The height of the trapezoid can be determined by finding the perpendicular distance between the parallel sides. In this case, we can use the length of EI:

Height = EI = 4.7 cm

Now, we can calculate the area of the trapezoid:

Area = (1/2) (EF + GH) Height

      = (1/2) × 19.8 × 4.7

      = 46.53 cm²

Therefore, the area of trapezoid EFGH is 46.53 cm².

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The answer to the first question is: Burger Quick, because it has a larger median.

The answer to the second question is: Histogram, because it can show the frequency distribution of the continuous variable "number of carbohydrates" and group the data into intervals.

A histogram is a graphical representation of a distribution of numerical data. It consists of a series of bars, where each bar represents a range of values of the data and the height of the bar indicates the frequency or count of data points falling within that range.

In a histogram, the horizontal axis represents the range of values or intervals of the data, called bins, and the vertical axis represents the frequency or count of data points falling within each bin. The bins can be of equal or unequal width depending on the nature of the data.

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The required cubic polynomial is

f(x) = \(-2x^3-2x^2-28x+48\)

What is a polynomial?

An algebraic expression of the form \(a_0 + a_1x+ .... + a_nx^n\) (\(a_0 \neq 0\)) is called a polynomial of degree n.

The zeroes of the cubic polynomial are -4, 2, 3

Let the cubic polynomial is

f(x) = a(x - (-4))(x - 2)(x - 3)

f(x) = a(x + 4)(x - 2)(x - 3)

If x = -5, f(x) = 112

112 = a(-5 + 4) (-5 - 2)(-5 - 3)

112 = -56a

a = \(-\frac{112}{56}\)

a = -2

f(x) = -2(x+ 4)(x - 2)(x - 3)

\(f(x) = -2(x+ 4)(x^2 -3x -2x +6)\\f(x) = -2(x + 4)(x^2 - 5x + 6)\\f(x) = -2(x^3 - 5x^2+4x^2+6x - 20x+24)\\f(x) = -2(x^3 - x^2 - 14x +24)\\f(x) = -2x^3 -2x^2 - 28x + 48\)

(x +4)(x - 2)(x - 3)

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Based on the given data, the hypothesis testing results suggest that there is enough evidence to reject the null hypothesis and conclude that the average daily per-store theft is less than $1000. The calculated z-value of -4.5 falls within the non-rejection range, indicating a significant difference. Additionally, a 90% confidence interval for the population mean is estimated to be approximately 982.74 to 997.26.

a) Hypothesis Testing:

Hypotheses:

Null Hypothesis (H0): The average daily per-store theft is $1000.

Alternative Hypothesis (Ha): The average daily per-store theft is less than $1000.

Critical value and non-rejection range:

Since we are testing at α = 0.10 (10% significance level) and the alternative hypothesis is one-sided (less than), we need to find the critical z-value that corresponds to the desired significance level. In this case, the critical z-value is approximately -1.28.

Non-rejection range: If the calculated z-value falls within the range greater than or equal to -1.28, we fail to reject the null hypothesis.

Compute test-value (calculated z):

The calculated z-value can be calculated using the formula:

z = (X - μ) / (s / √n)

where X is the sample mean, μ is the hypothesized population mean, s is the sample standard deviation, and n is the sample size.

Substituting the values:

z = (990 - 1000) / (20 / √81)

z = -10 / (20 / 9)

z = -10 * (9 / 20)

z = -4.5

Reject or not reject:

Since the calculated z-value (-4.5) is less than the critical z-value (-1.28) and falls within the non-rejection range, we reject the null hypothesis. There is enough evidence to suggest that the average daily per-store theft is less than $1000.

b) Confidence Interval Estimation (CIE):

To construct a 90% confidence interval for the population mean (μ), we can use the formula:

CI = X ± (z * (s / √n))

where X is the sample mean, s is the sample standard deviation, n is the sample size, and z is the critical value corresponding to the desired confidence level.

Substituting the values:

CI = 990 ± (1.645 * (20 / √81))

CI = 990 ± (1.645 * (20 / 9))

CI ≈ 990 ± 7.26

The 90% confidence interval for the population mean (μ) is approximately 982.74 to 997.26.

Note: The confidence interval estimates the range in which we can be 90% confident that the true population mean falls.

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There are several ways to find the measure of an angle in a triangle, depending on the information given about the triangle and the angles. Some common methods include:

Using the angles in a triangle sum to 180 degrees: If you know the measures of two angles in a triangle, you can use the fact that the angles in a triangle sum to 180 degrees to find the measure of the third angle.

Using the Pythagorean theorem: If you have a right triangle, you can use the Pythagorean theorem to find the measure of the right angle (90 degrees)

Using the Law of Cosines: If you know the measures of two angles and the lengths of all three sides of a triangle, you can use the law of cosines to find the measure of the third angle.

Using trigonometry: If you know the lengths of two sides of a triangle and the measure of one angle, you can use trigonometry to find the measure of the other angles.

It is important to note that in order to find the measure of an angle you need to know at least one angle and the values of the sides of the triangle or two angles.