Determine the limit of the sequence or state that the sequence diverges. 2 an = 5 n² (Use symbolic notation and fractions where needed. Enter DNE if the sequence diverges.) lim an = n→[infinity]

Similarity of the Angle-Angle (AA) Quadrilateral According to the theorem, two quadrilaterals are similar if they have two pairs of corresponding angles that are congruent.

The following requirements must be satisfied in order to apply the AA Quadrilateral Similarity Theorem:

Thus, under these conditions, there is an Angle-Angle Quadrilateral Similarity Theorem.

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Answer:

Asymptotes can be defined as lines that the curve approaches but never touches or crosses.

Answer:

85.71 %

Step-by-step explanation:

26-14=12

12/14= 0.8571

0.8571x100= 85.71

Answer:

A change from 14 to 26 represents a positive change (increase) of 85.7142857143%

Step-by-step explanation:

Use the formula:

New - Old / Old x 100%

In other words, new(26) minus old(14) divided by old(14) time 100%

14 is the old value and 26 is the new value. In this case we have a positive change (increase) of 85.7142857143 percent because the new value is greater than the old value.

The coefficient on mrate indicates that on average a decrease in the 401(k) plan match rate by 0.2 results in approximately a 0.2 percentage point increase in the 401(k) plan participation rate by workers.

The coefficient on mrate suggests that there is a positive relationship between the 401(k) plan match rate and the participation rate of workers. Specifically, a decrease in the match rate by 0.2 is associated with an approximate increase of 0.2 percentage points in the participation rate.

This implies that as the match rate offered by the plan decreases, there is a slight rise in the likelihood of workers participating in the 401(k) plan. However, it is important to note that this relationship is an average estimate and other factors could also influence the participation rate.

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The question is -

The coefficient on mrate indicates that on average a decrease in the 401(k) plan match rate by 0.2 results in approximately a ______ percentage point ________ in the 401(k) plan participation rate by workers.

Answer: The slope of the line passing through the points (-3, 5) and (4, -1) is -6/7.

Step-by-step explanation:   To find the slope of a line given two points, you can use the formula:

slope = (y2 - y1) / (x2 - x1)

Using the points (-3, 5) and (4, -1), we can substitute the values into the formula:

slope = (-1 - 5) / (4 - (-3))

= (-6) / (4 + 3)

= (-6) / 7

Therefore, the slope of the line passing through the points (-3, 5) and (4, -1) is -6/7.

Answer:  

\(Slope=-\frac{6}{7}\)

Step-by-step explanation:

\(m= \frac{y2-y1}{x2-x1} \\\\m=\frac{-1-5}{4-(-3)} \\\\m=\frac{-6}{7} \\\\Slope= -\frac{6}{7}\)

The chromatic number of the graph K33, which is a complete bipartite graph with 33 vertices, each connected to every vertex in the other set, is 2. This means that the graph can be colored using only two colors.

The chromatic number of a graph represents the minimum number of colors needed to color its vertices such that no adjacent vertices have the same color.

In the case of K33, the graph is a complete bipartite graph, which means it can be divided into two sets of vertices, where each vertex in one set is connected to every vertex in the other set. In this specific graph, we have 33 vertices in each set.

To determine the chromatic number, we observe that in a complete bipartite graph, no vertices within the same set are connected to each other. Therefore, we can assign one color to all the vertices in one set and a different color to all the vertices in the other set.

In K33, we can color one set of 33 vertices, let's say set A, with color 1, and the other set of 33 vertices, set B, with color 2. Since no vertices within the same set are connected, there will be no adjacent vertices with the same color.

Hence, we conclude that the chromatic number of the graph K33 is 2, as it can be colored using only two colors.

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The feasible set for this system of constraints is not convex, and the points (5, 5) and (3, 7) violate the convexity definition.

To determine whether the feasible set for each system of constraints is convex, we need to analyze the constraints individually and examine their intersection.

a) (x1)² + (x2)² > 9

This constraint represents points outside the circle with a radius of √9 = 3. The feasible set includes all points outside this circle.

b) x1 + x2 ≤ 10

This constraint represents points that lie on or below the line x1 + x2 = 10. The feasible set includes all points on or below this line.

c) x1, x2 > 0

This constraint represents points in the positive quadrant, where both x1 and x2 are greater than zero.

Now, let's analyze the intersection of these constraints:

Considering the first two constraints (a and b), we can see that the feasible set consists of all points outside the circle (constraint a) and below or on the line x1 + x2 = 10 (constraint b).

To determine whether the feasible set is convex, we need to check if any two points within the set create a line segment that lies entirely within the set.

If we consider the points (5, 5) and (3, 7), both points satisfy the individual constraints (a) and (b). However, the line segment connecting these two points, which is the line segment between (5, 5) and (3, 7), exits the feasible set since it passes through the circle (constraint a) and above the line x1 + x2 = 10 (constraint b).

Therefore, the feasible set for this system of constraints is not convex, and the points (5, 5) and (3, 7) violate the convexity definition.

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50 would be the reliability of that measure  by standard error.

What is the standard deviation?

A measure that has no random error and no true score (i.e., is only random error) has zero reliability. A measure that has random error.

50 would be the reliability of that measure .

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The rate of the water rising in the tank when the depth of the water is 1 ft is 56.05 ft/min.

The rate of change of volume is-

dV/dt = 11 ft3/min.

Volume of cylindrical cone = (1/3)πr²h

As we're trying to find dh/dt, we need to calculate the volume within terms of just one variable, h.

Diameter =  22 ft

Thus, radius is 11 ft

By using height and radius of a water in the tank, we may calculate h using similar ratios.

11/44 = r/h

1/4 = r/h

r= h/4

Put into volume;

V = (1/3)π(h/4)h²

V = (1/3)(π)h³ / (16)

dV/dt = [(1/3)(3)(π)(h)² / 16](dh/dt)

V = [(π)(h)² / 16](dh/dt)

Solve for (dh/dt) ;

dh/dt = (dV/dt)(16) / [((π)(h)²]

Now, the change in volume is dV/dt = 11 ft³/min

dh/dt = (11 ft³/min)(16) / [((π)(h)²]

For h = 1 ft,

dh/dt = (11 ft³/min)(16) / [((π)(1 ft)²]

dh/dt ≈ 56.05 ft/min

Thus, the rate of the water rising in the tank when the depth of the water is 1 ft is 56.05 ft/min.

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The negative trend pattern exists in the given data.

The Given information is as follows: Month 1 2 3 4 5 6 7

Value 23 15 20 12 18 22 15

To find: What type of pattern exists in the data

The pattern that exists in the given data can be determined by creating a graph between month and value. So, the graph will be as follows: Type of pattern: From the above graph, it is evident that there is a Negative trend pattern in the data. Answer: (d) Negative trend pattern.

Conclusion: Thus, the negative trend pattern exists in the given data.

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Answer:

a) Finding value of y:

8y+4+4y+7=107

12y+11=107

12y =107-11

12y =96

y = 96/12

y = 8

b) RS= 8y+4

= 8(8)+4

= 64+4

= 68

ST= 4y+7

= 4(8)+7

= 32+7

= 39

Answer:

the one thats says add till its 180 degrees i believe

Step-by-step explanation:

Answer:

Determine if the diagonals are congruent

Step-by-step explanation:

I found a quizlet with that same question

hope this helps ^^

Answer:

DEFG = (1/2)a^2

Step-by-step explanation:

tells us ∠FDG = 45° and ∠EGD = 45° and by corresponding angles related to parallel lines ∠FBD = 45°. Then ∠DFB = 90°!

So DFB- (1/2)(DF)(FB)=(1/2)a2

The rate of flow of gasoline while a customer is pumping it into a gas tank can vary and is dependent on factors such as the type of fuel pump, the condition of the gas tank, and other variables.

The rate of flow of gasoline while a customer is pumping it into a gas tank can vary depending on several factors, including the type of fuel pump being used and the condition of the gas tank.

Typically, the rate of flow is measured in terms of volume per unit time, such as liters per minute.

The rate of flow can be influenced by factors such as the size of the nozzle, the efficiency of the pump, and any restrictions or obstructions in the fuel system.

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La razón que indica el avance de un automóvil  a 40,000m en 60 min es  666.67 m/min

Queremos obtener la razón entre la distancia avanzada por un automóvil y el tiempo en el que se avanza esta distancia.

Recordamos que:

velocidad = distancia/tiempo.

Entonces lo que calcularemos es la velocidad, en promedio, del autmóvil.

Tenemos:

Velocidad = 40,000m/60min = 666.67 m/min

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Answer:

Step-by-step explanation:

(x + 2)(x +9)= x*(x +9) + 2*(x +9)

                   = x*x  + x*9  + 2*x + 2*9

                   = x² + 9x + 2x + 18   {Combine like terms}

                    = x² + 11x  +18

Answer:

x^2 + 11x + 18

Step-by-step explanation:

I assume this is asking about (x+2)(x+9), so if it isn't, then I can't be sure this is right.

That said, the distributive property has to do with multiplication of things in parentheses, meaning you must multiply this expression out to get what the question is asking. When it comes to 2 binomials, you can use the common abbreviation First Inside Outside Last, or FOIL.

Multiply the First terms: x * x = x^2

Multiply the Outside terms: x * 9 = 9x

Multiply the Inside terms: 2 * x = 2x

Multiply the Last terms: 2 * 9 = 18

This leaves you with x^2 + 9x + 2x + 18. Combine your like terms (9x and 2x) to get x^2 + 11x + 18 and you're done!

Convenience purchase: Coca-Cola. Shopping purchase: Apple iPhone. Specialty purchase: Rolex. These brand name products correspond to their respective purchase types based on convenience, shopping involvement, and specialty appeal in the consumer marketplace.

Convenience purchases refer to low-involvement purchases made by consumers for everyday items that are readily available and require minimal effort to obtain. These purchases are typically driven by convenience and habit rather than extensive consideration or brand loyalty.

Shopping purchases involve higher involvement and more deliberate decision-making. Consumers invest time and effort in comparing options, seeking the best value or quality, and may consider multiple brands before making a purchase. These purchases often involve durable goods or products that require more consideration.

Specialty purchases are distinct and unique purchases that cater to specific interests, preferences, or hobbies. These purchases are driven by passion, expertise, and a desire for premium or specialized products. Consumers are often willing to invest more in these purchases due to their unique features, quality, or exclusivity.

Three specific brand name products in the consumer marketplace that correspond to these types of purchases are

Convenience Purchase: Coca-Cola (Soft Drink)

Coca-Cola is a widely recognized brand in the beverage industry. It is readily available in various sizes and formats, making it a convenient choice for consumers seeking a refreshing drink on the go.

With its widespread availability and strong brand presence, consumers often make convenience purchases of Coca-Cola without much thought or consideration.

Shopping Purchase: Apple iPhone (Smartphone)

The Apple iPhone is a popular choice for consumers when it comes to shopping purchases. People invest time researching and comparing features, pricing, and user reviews before making a decision.

The shopping process involves considering various smartphone brands and models to ensure they select a product that meets their specific needs and preferences.

Specialty Purchase: Rolex (Luxury Watches)

Rolex is a well-known brand in the luxury watch industry and represents specialty purchases. These watches are associated with high-quality craftsmanship, precision, and exclusivity.

Consumers who are passionate about luxury watches and seek a premium product often consider Rolex due to its reputation, heritage, and unique features. The decision to purchase a Rolex involves a significant investment and is driven by the desire for a prestigious timepiece.

These examples illustrate how different types of purchases align with specific brand name products in the consumer marketplace, ranging from convenience-driven choices to more involved shopping decisions and specialty purchases driven by passion and exclusivity.

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Answer:

Step-by-step explanation:

You can find this answer by simply doing the reverse of the Pythagorean Theorem. The formula for Pythagorean Theorem is a^2+b^2=c^2, so the reverse would be b^2=c^2-a^2. All we have to do is substitute in the numbers and solve.

b^2=c^2-a^2

b^2=36^2-32^2

b^2=272

sqrt(b^2) sqrt(272)

b=16.492

Since we are rounding to the nearest tenth, our answer will be 16.5 meters.

Given that the correlation between two variables is r=0.23. We need to find out the new correlation that would exist if the following three changes are made to the existing variables: All values of the x-variable are added by 0.14. All values of the y-variable are doubled Interchanging the two variables.  the correct option is B. 0.37.

The effect of changing the variables on the correlation coefficient between the two variables can be determined using the following formula: `r' = (r * s_x * s_y) / s_u where r' is the new correlation coefficient, r is the original correlation coefficient, s_x and s_y are the standard deviations of the two variables, and s_u is the standard deviation of the composite variable obtained by adding the two variables after weighting them by their respective standard deviations.

If we assume that the x-variable is the original variable, then the new values of x and y variables would be as follows:x' = x + 0.14 (since all values of the x-variable are added by 0.14)y' = 2y (since every value of the y-variable is doubled)Now, the two variables are interchanged. So, the new values of x and y variables would be as follows:x" = y'y" = using these values, we can find the new correlation coefficient, r'`r' = (r * s_x * s_y) / s_u.

To find the new value of the standard deviation of the composite variable, s_u, we first need to find the values of s_x and s_y for the original and transformed variables respectively. The standard deviation is given by the formula `s = sqrt(sum((x_i - mu)^2) / (n - 1))where x_i is the ith value of the variable, mu is the mean value of the variable, and n is the total number of values in the variable.

For the original variables, we have:r = 0.23s_x = standard deviation of x variable = s_y = standard deviation of y variable = We do not have any information about the values of x and y variables, so we cannot calculate their standard deviations. For the transformed variables, we have:x' = x + 0.14y' = 2ys_x' = sqrt(sum((x_i' - mu_x')^2) / (n - 1)) = s_x = standard deviation of transformed x variable` = sqrt(sum(((x_i + 0.14) - mu_x')^2) / (n - 1)) = s_x'y' = 2ys_y' = sqrt(sum((y_i' - mu_y')^2) / (n - 1)) = 2s_y = standard deviation of transformed y variable` = sqrt(sum((2y_i - mu_y')^2) / (n - 1)) = 2s_yNow, we can substitute all the values in the formula for the new correlation coefficient and simplify:

r' = (r * s_x * s_y) / s_ur' = (0.23 * s_x' * s_y') / sqrt(s_x'^2 + s_y'^2)r' = (0.23 * s_x * 2s_y) / sqrt((s_x^2 + 2 * 0.14 * s_x + 0.14^2) + (4 * s_y^2))r' = (0.46 * s_x * s_y) / sqrt(s_x^2 + 0.0396 + 4 * s_y^2)Now, we can substitute the value of s_x = s_y = in the above formula:r' = (0.46 * * ) / sqrt( + 0.0396 + 4 * )r' = (0.46 * ) / sqrt( + 0.1584 + )r' = (0.46 * ) / sqrt(r' = (0.46 * ) / sqrt(r' = (0.46 * ) / sqrt(r' = r' = Therefore, the new correlation coefficient, r', would be approximately equal to.

Hence, the correct option is B. 0.37.

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Answer:

b

basically 5/8 goes to 1/2 0.8 times which is 4/5

Answer:

114

Step-by-step explanation:

sum of the interior angles in a quadrilateral is 360* so

48 + 112 + 134 + x = 360

294 + x = 360

x = 360 -294

x = 66°

x + y = 180 (angles on a straight line)

66 + y = 180

y = 180-66

y = 114

:) good luck

The measure y in the drawing is 114 degrees.

Any closed figure made by 4 line segments joined end to end in series is called a quadrilateral.

Since we know that the sum of the interior angles in a quadrilateral is 360*

Therefore,

48 + 112 + 134 + x = 360

294 + x = 360

x = 360 -294

x = 66°

Also, it is known that x + y = 180 (angles on a straight line)

66 + y = 180

y = 180-66

y = 114

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Answer:

$972 interest made

Step-by-step explanation:

p x ir x t =interest

800x.0675x18=972

The capital includes :

Any financial contribution made to a business to assist in achieving and advancing its commercial goal is referred to as a capital investment. The phrase may also refer to a long-term purchase made by a company, such as one for land, equipment, businesses, etc.

When a corporation issues securities to equity investors and debt to bondholders, the total amount of debt and capital lease obligations are added to the amount of stock given to investors to determine the overall amount of money raised. This amount is referred to as invested capital. The balance sheet of the business does not include an item for invested capital because debt, capital leases, and stockholders' equity are all stated separately.

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a) The probability that X assumes the value 6 is 0.3.

b) The expected value of X is 4.

c) The variance of X is 2.4.

d) The random variable Y can take the values 1, 1.5, 2, and 2.5.

e) The expected value of Y is 2, and the standard deviation of Y is approximately 0.692.

a) To meet the requirement for a probability function, the sum of probabilities for all possible values of X should equal 1. Therefore, we can find the probability of X assuming the value 6 by subtracting the sum of probabilities of X=2 and X=4 from 1:

P(X=6) = 1 - P(X=2) - P(X=4)

P(X=6) = 1 - 0.3 - 0.4

P(X=6) = 0.3

b) The expected value (E[X]) of a random variable X is calculated by multiplying each value by its corresponding probability and summing them up. In this case:

E[X] = (2 * P(X=2)) + (4 * P(X=4)) + (6 * P(X=6))

E[X] = (2 * 0.3) + (4 * 0.4) + (6 * 0.3)

E[X] = 0.6 + 1.6 + 1.8

E[X] = 4

c) The variance (Var[X]) of a random variable X is calculated by subtracting the expected value squared from the expected value of the square of X:

Var[X] = E[X^2] - (E[X])^2

To calculate E[X^2], we need to find the expected value of X squared:

E[X^2] = (2^2 * P(X=2)) + (4^2 * P(X=4)) + (6^2 * P(X=6))

E[X^2] = (4 * 0.3) + (16 * 0.4) + (36 * 0.3)

E[X^2] = 1.2 + 6.4 + 10.8

E[X^2] = 18.4

Now we can calculate the variance:

Var[X] = E[X^2] - (E[X])^2

Var[X] = 18.4 - (4)^2

Var[X] = 18.4 - 16

Var[X] = 2.4

d) To find the values that Y can take, we substitute the values of X1 and X2 into the expression for Y:

Y = (X1 + X2) / 4

Since X1 and X2 are independent random variables with the same distribution, we can substitute the probabilities:

Y = ((2 + 2) / 4) = 1

Y = ((2 + 4) / 4) = 1.5

Y = ((4 + 2) / 4) = 1.5

Y = ((4 + 4) / 4) = 2

Y = ((6 + 2) / 4) = 2

Y = ((6 + 4) / 4) = 2.5

Therefore, the values that Y can take are 1, 1.5, 2, and 2.5.

e) To calculate the expected value (E[Y]) and standard deviation (σY) of Y, we use the formulas:

E[Y] = (E[X1] + E[X2]) / 4

σY = √(Var[X1] + Var[X2]) / 4

Since X1 and X2 have the same distribution, we can use the values obtained earlier:

E[Y] = (E[X] + E[X]) / 4

E[Y] = (4 + 4) / 4

E[Y] = 2

σY = √(Var[X] + Var[X]) / 4

σY = √(2.4 + 2.4) / 4

σY = √4.8 / 4

σY ≈ 0.692

Therefore, the expected value of Y is 2, and the standard deviation of Y is approximately 0.692.

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Answer:

(1) - C, \((3,\frac{\pi}{6})\)

(2) - B, \((0,-2)\)

Step-by-step explanation:

\(\text{Using the following conversions:}\\\boxed{\left\begin{array}{ccc}\text{\underline{Rect. to Polar:}}\\(x,y)\rightarrow(r, \theta)\\\\r=\sqrt{x^2+y^2}\\\\\theta=\tan^{-1}(\frac{y}{x})\end{array}\right} \ \ \boxed{\left\begin{array}{ccc}\text{\underline{Polar to Rect.:}}\\(r, \theta)\rightarrow(x,y)\\\\x=r\cos \theta\\\\y=r \sin\theta\end{array}\right}\)

Note that when doing these calculations, make sure your calculator is in radians mode.

Question #2:

Given:

\((\frac{3\sqrt{3} }{2} ,\frac{3}{2} ) \ \text{in} \ (x,y)\)

\((\frac{3\sqrt{3} }{2} ,\frac{3}{2} )\\\\\Rightarrow r=\sqrt{(\frac{2\sqrt{2} }{2})^2+(\frac{3}{2})^2} \\\\\Longrightarrow r=\sqrt{\frac{27}{4} +\frac{9}{4} } \\\\\Longrightarrow r=\sqrt{9}\\\\\therefore \boxed{ r=3}\\\\\Rightarrow \theta=\tan^{-1}(\frac{\frac{3}{2}}{\frac{3\sqrt{3} }{2}})\\\\\Longrightarrow \theta=\tan^{-1}(\frac{\sqrt{3} }{3})\\\therefore \boxed{\theta=\frac{\pi}{6} }\)

Thus, the correct option is C.

\(\boxed{\boxed{(3,\frac{\pi}{6})}}\)

Question #3:

Given:

\((2,\frac{3\pi}{2} ) \ \text{in} \ (r,\theta)\)

\((2,\frac{3\pi}{2} ) \\\\\Rightarrow x=(2)\cos(\frac{3\pi}{2})\\\\\Longrightarrow x=(2)(0)\\\\\therefore \boxed{x=0}\\\\\Rightarrow y=(2)\sin(\frac{3\pi}{2})\\\\Longrightarrow y=(2)(-1)\\\\\therefore \boxed{y=-2}\)

Thus, the correct option is B.

\(\boxed{\boxed{(0,-2)}}\)