determine whether the sequence converges or diverges. if it converges, find the limit. (if the sequence diverges, enter diverges.) an = 1 7n2 n 3n2

Answer:

C. c = 10

Step-by-step explanation:

You have to use the Pythagorean theorem:

c² = 6² + 8²

c² = 36 + 64

c² = 100

c = √100

c = 10

Answer:

c = 10

Step-by-step explanation:

Since this is a right triangle, we can use the Pythagorean theorem

a^2 + b^2 = c^2 where a and b are the legs and c is the hypotenuse

6^2 + 8^2 = c^2

36+64= c^2

100 = c^2

Take the square root of each side

sqrt(100) = sqrt(c^2)

10 -c

Using proportions, the estimate of the per capita consumption from 2011 was 29.25 gallons.

A proportion is a fraction of the total amount, the measures are related using a rule of three.

The amount in 2012 was an increase of 5.3% from 2011,

105.3% = 1.053 of x,

The consumption per capita was 30.8 gallons,

hence:

1.053x = 30.8

x = 30.8/1.053

x = 29.25 gallons.

(ii) The sales in 2011

= 9.1 billion gallons in 2011.

(iii) The per capita consumption from 2011

= 9.1 / 11.8

= 0.77 billion

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The absolute value of the elasticity coefficient for Toasty Hands' gloves is 394,265.23.

The elasticity coefficient is calculated as follows:

Elasticity coefficient = (Change in demand)/(Change in price) * (Original price)/(Original demand)

In this case, the change in demand is 540,000 - 440,000 = 100,000 pairs. The change in price is 239 - 279 = -40. The original price is $279, and the original demand is 440,000 pairs.

Plugging these values into the formula, we get:

Elasticity coefficient = (100,000)/(-40) * (279)/(440,000) = -394,265.23

The absolute value of the elasticity coefficient is 394,265.23. This means that the demand for Toasty Hands' gloves is elastic, meaning that a small change in price will lead to a large change in demand.

Here is a more detailed explanation of the calculation:

The change in demand is calculated by subtracting the original demand from the new demand. In this case, the new demand is 540,000 pairs, and the original demand is 440,000 pairs. So the change in demand is 540,000 - 440,000 = 100,000 pairs.

The change in price is calculated by subtracting the original price from the new price. In this case, the new price is $239, and the original price is $279. So the change in price is 239 - 279 = -40.

The original price is $279, and the original demand is 440,000 pairs.

Plugging these values into the formula, we get the elasticity coefficient of -394,265.23.

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Answer:

mean=9

median=9

range=16

Based on the given information we have;

Mean = 9 miles ​

Median = 9 miles ​

Range = 6 miles

The mean is the average value which can be calculated by dividing the sum of observations by the number of observations

Mean = Sum of observations/the number of observations

Median represents the middle value of the given data when arranged in a particular order.

We are given that people in Mr. Kendrick's office drive 10, 3, 17, 1, 8, 6, 12, and 15 miles to work.

Mean= 10 + 3 + 17+ 1 + 8 + 6+ 12 + 15 / 8

Mean= 9

The median=9

The range = maximum - minimum

= 6

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Answer:

This survey was -Not Biased- and -Can- be extended to the general population of the phone company's customers.

Step-by-step explanation: Took the quiz ;3

Answer:

Can I get the pdf?

Step-by-step explanation:

To form a polynomial with given zeros and degree, we need to use the fact that if a polynomial has a zero of x = a, then it can be factored as (x - a) times some other polynomial.

This means that if we know the zeros of a polynomial, we can write it in factored form, and then multiply out the factors to get the polynomial in standard form.

The degree of the polynomial tells us how many factors are necessary. For example, if the degree is 3, we know that the polynomial can be factored into three linear factors, one for each zero.

To illustrate this process, let's say we want to form a polynomial of degree 4 with zeros of x = 2, x = -1, and x = 3. We would start by writing the polynomial in factored form as:

f(x) = (x - 2)(x + 1)(x - 3)(ax + b)

Since the degree is 4, we need to include one more factor. We can use the coefficients a and b to determine this factor. To do so, we can either use the value of the leading coefficient (which is a in this case) or a point on the polynomial (i.e., a value of x and f(x)).

Once we have determined the value of a, we can solve for b by setting a point on the polynomial equal to a known value.

Finally, we can multiply out the factors to get the polynomial in standard form:

f(x) = (x - 2)(x + 1)(x - 3)(2x - 4)

f(x) = 2x^4 - 8x^3 - 13x^2 + 22x - 12

In conclusion, to form a polynomial with given zeros and degree, we need to use the fact that a polynomial can be factored as (x - a) times some other polynomial if it has a zero of x = a.

We can write the polynomial in factored form, determine the missing factor(s) using the degree and coefficients, and then multiply out the factors to get the polynomial in standard form.

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The extremum of the function f(x, y) = 3x² + 4y - 4xy, subject to the constraint x + y = 11, can be found using the method of Lagrange multipliers. The extremum located at (22/3, 17/3) is a minimum.

By setting up the Lagrangian equation L = f(x, y) + λ(x + y - 11), where λ is the Lagrange multiplier, we can solve for the critical points. Taking partial derivatives with respect to x, y, and λ and setting them equal to zero, we can solve the resulting system of equations to find the extremum.

The solution yields a critical point located at (x, y) = (22/3, 17/3). To determine whether it is a maximum or a minimum, we can use the second partial derivative test. By calculating the second partial derivatives of f(x, y) with respect to x and y and evaluating them at the critical point, we can examine the sign of the determinant of the Hessian matrix. If the determinant is positive, the critical point is a minimum. If it is negative, the critical point is a maximum.

In this case, the second partial derivatives of f(x, y) are positive, and the determinant of the Hessian matrix is also positive at the critical point. Therefore, we can conclude that the extremum located at (22/3, 17/3) is a minimum.

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Distance divided by speed equals time. Distance is calculated by subtracting the planets' distances.

The length of the line connecting two points is the distance between them. If the two points are on the same horizontal or vertical line, the distance can be calculated by subtracting the non-identical coordinates.

Distance = speed × time is the formula.

Therefore,

1. Assume that the sun and both planets are in line and that they are on the same side of the sun.

from the sun: Jupiter is 778,300,000

from the sun, Venus is 108,200,000

778,300,000 - 108,200,000 = 670,100,000

It would have to travel 670,100,000/6.701*10 with 8 square kilometers.

2. The three planets that are nearest to the sun are Mercury, Venus, and Earth.

Mercury's distance from the sun is 57,909,000 km.

Venus's distance from the sun is 108,200,000 km.

Earth's distance from the sun is 149,600,000 km.

combined distance between Mercury, Venus, and Earth

57,909,000+108,200,000+149,600,000 = 315,709,000

Because 315,709,000 km is less than 4,503,443,661 km, the distance from the sun to Neptune is less  than the sum of the distances from the sun.

3. Assume that every planet is on the same side of the sun and is in alignment with it.

Earth is equal to Earth at ten solar distances is 149,600,000 km *10.

New distance to Earth = 1,496,000,000km

Earth would be closest to Saturn at its distance from the sun is

1,496,000,000 -  1,296,000,000 =67,000,000

and the two would be 67,000,000 km apart.

4. Notation used in science: with a 7 square kilometer. The space shuttle moves at around 28,000 km/h.

To locate Time

Time =   Distance /speed

1,200,000,000 -28,000 =40,000 hrs.

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Answer:

1st

Step-by-step explanation: i think

Answer:C

Step-by-step explanation:

Answer:

28

Step-by-step explanation:

The expression (18)(-3)(-3) is not equivalent to others.

-7+(-3) is equivalent of the expression -7 - 3.

What is an expression?

A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression. In a mathematical expression, the following terms are used:

An absolute numerical value is referred to as a constant.

Variable: A symbol without a fixed value is referred to as a variable.

Term: A term can be made up of a single constant, a single variable, or a mix of variables and constants multiplied or divided.

Coefficient: In an expression, a coefficient is a number that is multiplied by a variable.

Take the first option:

(-9)(-3 × -6)

= (-9)(18)

= (18)(-9)  [Commutative property]

= -(-18)(-9)

Apply the associative property on (-9)(-3 × -6):

(-9)(-3 × -6)

= (-9× - 3)(-6)

= (27) (-6)

= (-6)(27)   [Commutative property]

The given expression is -7 - 3

Rewrite the above expression:

-7+(-3)

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The value of the given function `limit as x approaches infinity is the square root of (x^2+1)` is √(x^2 + 1).

We have to find the value of the limit as x approaches infinity for the given function f(x) = sqrt(x^2 + 1).

Let's use the method of substitution.

Replace x with a very large value of positive integer 'n'.

Now, let's solve for f(n) and f(n+1) to check the behavior of the function.f(n) = sqrt(n^2 + 1)f(n+1) = sqrt((n+1)^2 + 1)f(n+1) - f(n) = sqrt((n+1)^2 + 1) - sqrt(n^2 + 1)

Let's multiply the numerator and denominator by the conjugate and simplify:

f(n+1) - f(n) = ((n+1)^2 + 1) - (n^2 + 1))/ [sqrt((n+1)^2 + 1) + sqrt(n^2 + 1)]f(n+1) - f(n) = (n^2 + 2n + 2 - n^2 - 1)/ [sqrt((n+1)^2 + 1) + sqrt(n^2 + 1)]f(n+1) - f(n) = (2n+1)/ [sqrt((n+1)^2 + 1) + sqrt(n^2 + 1)]

Thus, we can see that as n increases, f(n+1) - f(n) approaches to 0. Therefore, the limit of f(x) as x approaches infinity is √(x^2 + 1).

Therefore, the value of the given function `limit as x approaches infinity is the square root of (x^2+1)` is √(x^2 + 1).

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Number Line :

In math, a number line can be defined as a straight line with numbers placed at equal intervals or segments along its length. A number line can be extended infinitely in any direction and is usually represented horizontally.

or

A number line is a horizontal line that has equally spread number increments. The numbers included on the line will determine how the number on the line can be answered. The question that goes with the number determines how it will be used, for example, plotting a point.

On a number line, a number on the left is always less than a number on the right. Similarly, a number on the right is always greater than a number on the left.

The Number Line app helps students visualize number sequences and illustrate strategies for counting, comparing, adding, subtracting, multiplying, and dividing. Choose number lines labeled with whole numbers, fractions, decimals, or negative numbers. Or use a custom number line, with or without tick marks, and set your own interval.

Show intervals between points on the line using forward or backward jumps above and below the line. Jumps can also be labeled with their values or left blank. Add custom tick marks to the number line to show equivalence or compare number values.

Basic Number Line Skills:

1. Find the dot marked on a number (and name the dot)

2. Place a dot at the desired location

3. Find the desired number below the number line’s tick mark*

   -17                -11        -2                 0

-----|-----------------|----------|----------------|-----------------------------------------------Number line

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The face of the block that should be in contact with the board to achieve the shallowest angle before sliding is the one with the smallest perpendicular dimension, which is the 1.00 cm by 2.00 cm face.

The block will begin to slide down the board when the component of the gravitational force parallel to the board (i.e., the force that would cause the block to slide) exceeds the maximum force of static friction between the block and the board. The maximum force of static friction is proportional to the normal force, which is greater for faces of the block that are more perpendicular to the board.

In this case, the face of the block that should be in contact with the board to achieve the shallowest angle before sliding is the one with the smallest perpendicular dimension, which is the 1.00 cm by 2.00 cm face.

The general approach of analyzing the forces involved and identifying the relevant factors that determine the outcome can be applied to many types of problems in physics and other sciences. However, the specific solution for this problem is only applicable for uniform, rectangular blocks with the given dimensions and on a wooden board. For other scenarios, the analysis and solution may differ.

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If the sample mean is 12.8, sample standard deviation is 2 and sample size is 20, then the student's t-distribution should be use to perform the hypothesis test

The population mean = 13

The sample mean = 12.8

The standard deviation = 2

The sample size of the population = 20

The given condition is the underlying population is normal.

Here population standard deviation is missing in the given data. So to perform a hypothesis test when the population standard deviation is missing then we have to use the student t-distribution

Therefore, the student's t-distribution should be use to perform the hypothesis test

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He will pick a sample of seniors in this instance.

Given statement,

Dr. Stuart wants to study whether there is a relationship between the number of hours a high school senior spends on social networking sites and their grade point average. he obviously cannot study every 12th grader, so instead, he will select a smaller of seniors to study.

→ In this case he will select a sample of seniors.

→ Dr. Stuart is interested in determining whether there is a correlation between a high school senior's grade point average and the number of hours spent on social networking sites. He will instead choose a smaller sample of seniors to study because he certainly cannot study every student in the 12th grade.

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Let H = Hailey's age and M = Maverick

Hailey is 3 times as old as Maverick: H = 3M

The sum of their ages is 48 years: H + M = 48

Since H = 3M, substitute 3M in place of H in the second equation:

H + M = 48

3M + M = 48

4M = 48

M = 12

Maverick is 12 years old. Hailey = 3M = 3(12) = 36 years old.

Answer:

Order of rotation is the number of times you can rotate the geometric figure so that it looks exactly the same as the original figure.

Step-by-step explanation:

We have the counter and the clockwise rotation where counter you move back in in 90 degrees and clockwise you move forward

The number of degrees of freedom for treatment are 4.

Degrees of freedom is a statistical term that refers to the number of values in a calculation that are free to vary. It is a common concept in statistical inference. In general, degrees of freedom represent the number of observations in a statistical analysis that are free to vary.To find the degrees of freedom for treatment, the formula is (k - 1), where k is the number of treatment groups. In this case, there were 5 treatment groups, so the degrees of freedom for treatment would be (5 - 1) = 4.

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The function f(x) = |x| represents the absolute value parent function, which is Option C.

This parent function is characterized by its V-shaped graph, with a vertex at the origin (0, 0) and two linear branches that form a 45-degree angle with the x-axis.

It is neither an exponential parent function (Option A), which typically has the form f(x) = aˣ, nor the quadratic parent function (Option B), which follows the form f(x) = ax² + bx + c.

The absolute value parent function expresses the distance between a number and zero on the number line, resulting in non-negative values for all input values of x.

Hence the answer of the question is C.

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The results of the expressions involving logarithms are listed below:

Case 1: 1 / 2

Case 2:

Subcase a: 0

Subcase b: 11 / 2

Subcase c: - 11 / 2

In this problem we have a case of an expression involving logarithms that must be simplified and three cases of expressions involving logarithms that must be evaluated. Each case can be solved by means of the following logarithm properties:

㏒ₐ (b · c) = ㏒ₐ b + ㏒ₐ c

㏒ₐ (b / c) = ㏒ₐ b - ㏒ₐ c

㏒ₐ cᵇ = b · ㏒ₐ c

Now we proceed to determine the result of each case:

Case 1

㏒ ∛8 / ㏒ 4

(1 / 3) · ㏒ 8 / ㏒ 2²

(1 / 3) · ㏒ 2³ / (2 · ㏒ 2)

㏒ 2 / (2 · ㏒ 2)

1 / 2

Case 2:

Subcase a

㏒ [b / (100 · a · c)]

㏒ b - ㏒ (100 · a · c)

㏒ b - ㏒ 100 - ㏒ a - ㏒ c

3 - 2 - 2 + 1

0

Subcase b

㏒√[(a³ · b) / c²]

(1 / 2) · ㏒ [(a³ · b) / c²]

(1 / 2) · ㏒ (a³ · b) - (1 / 2) · ㏒ c²

(1 / 2) · ㏒ a³ + (1 / 2) · ㏒ b - ㏒ c

(3 / 2) · ㏒ a + (1 / 2) · ㏒ b - ㏒ c

(3 / 2) · 2 + (1 / 2) · 3 + 1

3 + 3 / 2 + 1

11 / 2

Subcase c

㏒ [(2 · a · √b) / (5 · c)]⁻¹

- ㏒ [(2 · a · √b) / (5 · c)]

- ㏒ (2 · a · √b) + ㏒ (5 · c)

- ㏒ 2 - ㏒ a - ㏒ √b + ㏒ 5 + ㏒ c

- ㏒ (2 · 5) - ㏒ a - (1 / 2) · ㏒ b + ㏒ c

- ㏒ 10 - ㏒ a - (1 / 2) · ㏒ b + ㏒ c

- 1 - 2 - (1 / 2) · 3 - 1

- 4 - 3 / 2

- 11 / 2

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a. When adding two vectors, each of magnitude 1 m, the resultant does not necessarily have a magnitude of 2 m. The magnitude of the resultant vector depends on the angle between the two vectors being added.
b. If vectors A and B satisfy the equation A + B = 0, it means that the vectors have equal magnitudes and opposite directions.

a. When adding vectors, the magnitude of the resultant vector is determined by the vector addition rule, which takes into account both the magnitudes and the directions of the vectors being added. In the case of adding two vectors, each of magnitude 1 m, the resultant vector can have a magnitude ranging from 0 to 2 m, depending on the angle between the vectors. If the vectors are in the same direction, the resultant magnitude is 2 m, and if they are in opposite directions, the resultant magnitude is 0 m.
b. When vectors A and B satisfy the equation A + B = 0, it means that their vector sum is the zero vector. This implies that the vectors have equal magnitudes and opposite directions. The magnitudes of A and B are equal, and their directions are opposite, which means they are collinear and point in opposite directions along the same line. In other words, vector A can be thought of as the negative of vector

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a. When adding two vectors, each of magnitude 1 m, the resultant does not necessarily have a magnitude of 2 m. The magnitude of the resultant vector depends on the angle between the two vectors being added.

b. If vectors A and B satisfy the equation A + B = 0, it means that the vectors have equal magnitudes and opposite directions.

a. When adding vectors, the magnitude of the resultant vector is determined by the vector addition rule, which takes into account both the magnitudes and the directions of the vectors being added. In the case of adding two vectors, each of magnitude 1 m, the resultant vector can have a magnitude ranging from 0 to 2 m, depending on the angle between the vectors. If the vectors are in the same direction, the resultant magnitude is 2 m, and if they are in opposite directions, the resultant magnitude is 0 m.

b. When vectors A and B satisfy the equation A + B = 0, it means that their vector sum is the zero vector. This implies that the vectors have equal magnitudes and opposite directions. The magnitudes of A and B are equal, and their directions are opposite, which means they are collinear and point in opposite directions along the same line. In other words, vector A can be thought of as the negative of vector

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Question 8: The slope of line (m) =  \(\frac{7}{4}\)

The y-intercept will be b = 1

The equation is \(7x-4y +1 =0\)

the equation of a line is a formula that describes the relationship between the x and y coordinates of points on the line. The most commonly used form of the equation of a line is the slope-intercept form: y = mx + b, where m is the slope of the line and b is the y-intercept.

Given: Points \((x_{1}, y_{1} ) and (x_{2}, y_{2} )\) are (4, 8) and (12, 22)

We know the slope of line (m) = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1}}\)

So, the slope of line (m) = \(\frac{22-8}{12-4}\) = \(\frac{14}{8} = \frac{7}{4}\)

the slope of line (m) =  \(\frac{7}{4}\)

Equation of line, y = mx + b,

here b is the y-intercept, y = \(y_{1}\) = 8, and x = \(x_{1}\) = 4,

so,  \(8=\frac{7}{4}*4 +b\)

Therefore, y-intercept by b = 1.

Equation  \(y=\frac{7}{4}x +1\)

Therefore, the equation is \(7x-4y +1 =0\)

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There are 126 ways a student can select 5 questions from an exam containing 9 questions

The given parameters are

Total questions, n = 9

Selected question, r = 5

The number of ways is calculated as

Ways = nCr

This gives

Ways = 9C5

Apply the combination formula

Ways = 9!/5!4!

Evaluate

Ways = 126

Hence, there are 126 ways a student can select 5 questions from an exam containing 9 questions

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The number of school districts in the United States is currently approximately 13,500. This answer is option D in the given choices.

The number of school districts in the United States can vary depending on how they are defined, but according to the National Center for Education Statistics (NCES), there were 13,500 public school districts in the U.S. as of the 2018-2019 academic year. These districts serve approximately 50.7 million students in over 98,000 public schools. It is important to note that this number only includes public school districts and does not include private or charter schools.

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Answer:

i think it's 42

Step-by-step explanation:

60% of 80 is about 48. 70% of 60 is 42. The number of his classmates who like hip-hop is greater than the number of his relatives who like hip-hop.

Using algebraic techniques, you can eliminate the parameter of a parametric equation.

To eliminate the parameter of a parametric equation, you can use algebraic techniques to solve for the variables. For example, given the parametric equation x = 3t + 2 and y = 2t - 1, you can solve for t by subtracting 2 from both sides of the x equation, resulting in x - 2 = 3t. Then, divide both sides by 3, resulting in t = (x - 2)/3. Plugging this value of t into the y equation, you can solve for y: y = 2((x - 2)/3) - 1. Simplifying the equation, you get y = (2x - 4)/3. This equation is now in the form y = mx + b, where m is the slope and b is the y-intercept, and it eliminates the parameter t. Thus, by using algebraic techniques, you can eliminate the parameter of a parametric equation.

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Answer: 2/63

Step-by-

Answer:

Hello,There! I'll be glad to help!

what is 4/2/3 x 1/3/7 ?

\(6\frac{2}{21}\)

Step-by-step explanation:

Rewriting our equation with parts separated

\(4 +\frac{2}{3} + 1 +\frac{3}{7}\)

Solving the whole number parts

\(4 + 1 =5\)

Solving the fraction parts

\(\frac{2}{3}+\frac{3}{7} =?\)

Find the LCD of 2/3 and 3/7 and rewrite to solve with the equivalent fractions.

LCD = 21

\(\frac{14}{21} +\frac{9}{21} =\frac{23}{21}\)

Simplifying the fraction part, 23/21,

\(\frac{23}{21} =1\frac{2}{21}\)

Combining the whole and fraction parts

\(5 + 1+ \frac{2}{21} =6\frac{2}{21}\)

Hence, The answer is \(6\frac{2}{21}\)