2. (15 points) For each of the following series, determine whether or not the series converges. Show all of your work, and justify all of your conclusions. (a) Å sin’(n) 2n2 + 5 n=1 (b) (-1)*+1 (In

The standard form of the equation of an ellipse is a useful representation that helps describe its shape and characteristics.

Standard form of the equation of an ellipse is given by:

(x-h)^2/a^2 + (y-k)^2/b^2 = 1

where (h,k) represents the center of the ellipse, 'a' is the length of the semi-major axis, and 'b' is the length of the semi-minor axis.

To find the standard form of the equation, you need the coordinates of the center and the lengths of the semi-major and semi-minor axes. Let's assume the center of the ellipse is (h,k), the length of the semi-major axis is 'a', and the length of the semi-minor axis is 'b'. Then the standard form equation becomes:

(x-h)^2/a^2 + (y-k)^2/b^2 = 1

The standard form of the equation of an ellipse is a useful representation that helps describe its shape and characteristics. By knowing the center and the lengths of the semi-major and semi-minor axes, you can easily write the equation in standard form, allowing for further analysis and calculations.

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Answer:

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gkgkhhkStep-by-step explanation:

Answer:

2.79

Step-by-step explanation:

For this problem the universe is the number of raspberry plants which has a total of 340 possible outcomes. The event of the problem is "The raspberry are ready for picking" and it has 181 favorable outcomes; now, the complement of this event will be "The raspberry are not ready for picking" and to get its outcomes we subtract the number of plants that are ready to the total number of plants:

Therefore, the number of outcomes for the complement is 159

h = -4.9t^2 + vt

In our problem,

v = 12

t = 2

Let's plug our numbers into the equation.

h = -4.9(2)^2 + (12)(2)

h = -19.6 + 24

h = 4.4 m

Answer:

A. 7 divided by 2

Step-by-step explanation:

The computation is shown below;

\(= 6\frac{3}{4} \div 1 \frac{2}{3} \\\\= \frac{27}{4} \div \frac{5}{3}\\\\= \frac{27}{4} \times \frac{3}{5}\\\\= \frac{27\times 3}{4\times 5} \\\\= \frac{81}{20} \\\\= 4 \frac{1}{20}\)

It could be 4.05

So according to the given options, the option 1 is chosen at is closed to 4.05

Hence, the option A is correct

Answer:

On the Y axis

Step-by-step explanation:

Answer:

(0, 7)

Step-by-step explanation:

aight so its set up as (x,y). X on the graph is left and right while y is up and down. "8" means that the X is positive or to the right of the origin. If you go left, essentially you are subtracting. So 8-8=0. Same kind of idea for the Y axis. Up is positive, down is negative. If you're going down 6 from 13 (13-6) then you are at 7. (0,7)

Answer:

9

Solving steps:

=> 6÷2(1+2)

divide 6 by 2

=> 3(1+2)

add values inside the bracket

=> 3(3)

multiply 3 by 3

=> 9

Answer:

9

Step-by-step explanation:

Use parenthesis, exponents, multiplication, division, addition, and subtraction, witch stands for PEMDAS.

1. 1+2 is the first step, since it is in the parenthesis. This gives you 3

2. You do 6÷2, since that is the next step. Since the operations are from left to right  , you move on the next step, witch is divison. This also gives you 3.

3. You do the final step, witch is to multiply, so you do 3 x 3 , witch gives you 9.

Answer:

The number of soldiers that call out a number 3 is 666 soldiers

Step-by-step explanation:

The parameters given are;

Number of soldiers = 2000

Soldiers calling from the left = 1, 2, 3,.....

Soldiers calling from the right = 1, 2, 3,.....

Therefore, since the number soldiers calling out the number 3 are 1 in 3 from the left and 1 in 3 from the right, we split the soldiers into 2 groups of 1000, with one group calling from left and the other group calling from the right;

The number of 3s in called out in the first group from the left is therefore;

1000/3 = 333.33 which is 333 soldiers  or from the 3rd soldier to the 999th soldier

Similarly the number of 3s called out from the second group = 333

Hence the total number of soldiers that call out a number 3 = 333 + 333 = 666 soldiers.

Answer:

y = -2x  - 2

Step-by-step explanation:

Slope intercept form of equation is y = mx + c

c is intercept and m is slope

given that slope is -2

m = -2

thus, equation in slope intercept will be

y = -2x + c

The given line passes through (-1,0)

y = -2x + c

lets substitute y = 0 and x = -1 in the given equation

0 = -2*-1 + c

0 = 2 + c

c = -2

Thus, the complete slope intercept equation after using the value of c as -2

we have

y = -2x  - 2   answer

Answer:

7 shirts

Step-by-step explanation:

The function for producing shirts is

f($) = 50 + 7.5(x), where x is the number of shirt

The function for selling shirts is

f($) = 15(x)

For there to be a profit, he must make more money selling the shirts than he spent on making the shirts

Therefore, 15(x) > 50 + 7.5(x)

15x > 50 + 7.5x

15x - 7.5x > 50

7.5x > 50

x > 6.67 shirts

To make a profit, Juan must sell at least 7 shirts

The correct answer is C. Systematic sampling because it is the mechanical sampling of one unit at a certain number of units in a certain order.

In statistical sampling, there is a methodology called systematic sampling wherein items or individuals are picked from a larger population regularly at predetermined intervals.

The reason this method exists is to analyze the smaller representative sample as it's overly ambitious to assess the entire population. It involves computing the interval at which the samples must be taken.

To compute such an interval, all one has to do is divide the size of the population with the desired sample size to get the answer.

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The volume of a cone can be calculated using the formula \(V = (1/3) * * r2 * h\), where V is a constant roughly equal to 3.14159, r is the radius, and h is the height.

When the required values are substituted, the answer is \(V = (1/3) * 3.14159 * (1.75 feet)2 * 2.1\) feet.

The assessment of this expression yields V = 5.6688 cubic feet. The cone has a radius of 1.75 feet, a height of 2.1 feet, and a volume of approximately 5.6688 cubic feet."Pitch" is the technical word for the rotating movement of an airplane's nose. Pitch describes the rotation of the aircraft's nose around its lateral axis, either upward or downward. A plane is said to be in a positive pitch attitude when its nose is pointing up, and a negative pitch attitude when it is pointing down. Pitch control is essential for maintaining the correct flying path and managing the aircraft's height.

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These are the polynomial equations:

A = x^ (1/4) - ∛x + 4√x - 8x + 16

B = 3x² - 5x⁴ + 2x - 12

C = x³ - 7x² + 9x - 5x⁴ - 20

D = x⁵ - 5x⁴ + 4x³ - 3x² + 2x - 1

These are the non-polynomial equations:

E = 4/x⁴ + 3/x³ - 2/x² - 1

F = x⁻⁵ - 5x⁻⁴ + 4x⁻³ - 3x⁻² + 2x⁻¹ - 1

Polynomials are mathematical expressions that only use addition, subtraction, multiplication, and non-negative exponentiation of the variables, along with coefficients (constants that multiply with the variables), coefficients, and constants.

Some of the elements of an equation are coefficients, variables, operators, constants, terms, expressions, and the equal to sign. An equation must always begin with the "=" sign and have terms on both sides.

Let the polynomial equations be represented by the following letters: A, B, C, D, E, and F.

In the equation, we can solve for other values to obtain:

Moreover, a polynomial equation is not an algebraic equation that has a negative exponent or an exponent that is fractional. Thus, negative exponent expressions are not polynomials.

A = x^ (1/4) - ∛x + 4√x - 8x + 16

This polynomial exists.

B = 3x² - 5x⁴ + 2x - 12

This polynomial exists.

C = x³ - 7x² + 9x - 5x⁴ - 20

This polynomial exists.

D = x⁵ - 5x⁴ + 4x³ - 3x² + 2x - 1

It is a polynomial.

E = 4/x⁴ + 3/x³ - 2/x² - 1

It is not a polynomial.

F = x⁻⁵ - 5x⁻⁴ + 4x⁻³ - 3x⁻² + 2x⁻¹ - 1

A polynomial is not what it is.

The polynomials are thus resolved.

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Answer:

d

Step-by-step explanation:

A. Manager A wants the decision to be 0.4, so they would recommend a decision of 0.4 to the principal.

B. The recommendations in the Nash equilibrium would be rA = 0.4 and rB = 0.7.

(a) If Manager B always truthfully reports the state of the economy (s = 0.7), Manager A would send a recommendation that minimizes their disutility Ua. In this case, Manager A wants the decision to be 0.4, so they would recommend a decision of 0.4 to the principal.

(b) In a Nash equilibrium, both managers strategically make their recommendations based on their own utility. Manager A wants to minimize their disutility Ua, which increases as the decision deviates from 0.4. Manager B wants to minimize their disutility UB, which increases as the decision deviates from 0.7.

To find the Nash equilibrium, we need to consider the recommendations made by both managers simultaneously. Let's denote the recommendations as rA (from Manager A) and rB (from Manager B). The principal's decision, d, would be the average of the recommendations, so d = (rA + rB) / 2.

Given that both managers strategically choose their recommendations, they will aim to minimize their disutility. In this case, Manager A would recommend a decision of 0.4 (as it minimizes Ua), and Manager B would recommend a decision of 0.7 (as it minimizes UB). Therefore, the recommendations in the Nash equilibrium would be rA = 0.4 and rB = 0.7.

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Answer:

remaining length: 5y² + 6y + 12

Explanation:

new length = original length - length cut

solve for new length:

6y² + 6y + 1 - (y² - 11)

6y² + 6y + 1 - y² + 11

6y² - y² + 6y + 11 + 1

5y² + 6y + 12

The transformations to the graph of the quadratic function are given as follows:

A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.

The four translation rules for functions are defined as follows:

Additionally, when the function is multiplied by |a| > 1, it is said that the function is vertically stretched by a factor of a.

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Work Shown:

y = x^2 + 8x + 3 is the same as y = 1x^2 + 8x + 3

It is in the form y = ax^2 + bx + c

a = 1

b = 8

c = 3

Plug the values of a and b into the formula below to get the x coordinate of the vertex (h,k)

h = -b/(2a)

h = -8/(2*1)

h = -8/2

h = -4

Plug this into the original equation to get its paired y value. This will get us the value of k

y = x^2 + 8x + 3

y = (-4)^2 + 8(-4) + 3

y = 16 - 32 + 3

y = -13

This is the smallest y output possible. Therefore it is the minimum. The minimum occurs at the vertex (h,k) = (-4, -13)

We know we are dealing with a minimum because a = 1 is positive forming a parabola that opens upward. If a < 0, then the parabola would open downward to yield a maximum.

To determine the z-value accurately, we would need the actual proportion of voters supporting the governor in the sample (\(\bar p\)) and the assumed population proportion (p).

The null hypothesis is a type of hypothesis that explains the population parameter and is used to examine if the provided experimental data are reliable.

To assess the governor's chances of reelection, we need to conduct a statistical hypothesis test using the z-test.

Let's assume that the null hypothesis (H₀) is that the governor will receive 80% of the vote in the northern section of the state, and the alternative hypothesis (Hₐ) is that he will receive less than 80% of the vote.

Given that the governor plans to survey 2,000 registered voters in the northern section of the state, we need to determine the sample proportion (\(\bar p\)) of voters who support the governor.

Next, we calculate the standard error (SE) using the formula:

SE = √((\(\bar p\)(1-\(\bar p\)))/n)

Where:

- \(\bar p\) is the sample proportion

- n is the sample size (2,000 in this case)

Once we have the standard error, we can calculate the z-value using the formula:

z = (\(\bar p\) - p) / SE

Where:

- p is the assumed population proportion (80% in this case)

Finally, we compare the z-value to the critical value at the desired significance level (usually 0.05) to determine the statistical significance.

Given that we don't have the specific values for \(\bar p\) and p, it is not possible to calculate the exact z-value without additional information. Therefore, none of the provided options (a, b, c, d) can be considered correct.

To determine the z-value accurately, we would need the actual proportion of voters supporting the governor in the sample (\(\bar p\)) and the assumed population proportion (p).

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Step-by-step explanation:

y=-3/4 ÷ -4/3

y=+9/16‌ ‌ ‌ ‌ ‌ ‌ ‌ ‌ ‌ ‌ ‌

Answer:

So we have this equation:

\(\frac{-4}{3y}=\frac{-3}{4}\)

We can multiply both sides by 4 and 3y:

\(\frac{-4*4*3y}{3y}=\frac{-3*4*3y}{4}\)

\(-4*4=-3*3y\)

\(-16 = -9y\)

Now we divide both sides by 9:

\(\frac{-16}{-9}=y\)

And we can remove the minus signs:

\(\frac{16}{9}=y\)

If you mean \(\frac{-4}{3}y=\frac{-3}{4}\):

\(-4y*4=-3*3\)

\(-16y = -9\)

\(y=\frac{9}{16}\)

Answer:

Step-by-step explanation:

Let the common side of the triangles is s.

Use Pythagorean to get the value of s:

and

Compare these equations and solve for x:

Answer: The fact of being correct and without any mistakes:

Step-by-step explanation: Hope this helps!

The study has a confounding variable since the two groups differ in the time they were supposed to report to the testing room. Since the groups differed in terms of sleep deprivation and the time they were supposed to report to the testing room, the effect of sleep deprivation on learning could not be isolated.

The statement that is true is: d. All of these are true.Explanation:A study may have various sources of variability, including participant selection, the setting in which the study is conducted, and the measure used. The following options are as follows:a. The study may be affected by a situational variable.b. The construction noise may contribute to variability in test scores.c. The study has a confounding variable. The groups differ in the time they are to report to the testing room.d. All of these are true.Therefore, all of these options are true. For example, the study may be affected by a situational variable if a natural disaster or other unforeseen event happens that causes the study to be disrupted. In this case, the study was disrupted by a noisy construction crew, which may have contributed to variability in test scores. The study has a confounding variable since the two groups differ in the time they were supposed to report to the testing room. Since the groups differed in terms of sleep deprivation and the time they were supposed to report to the testing room, the effect of sleep deprivation on learning could not be isolated.

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Answer:

\( \frac{4}{5} - \frac{3}{10} = 0.8 - 0.3 = 0.5 = \frac{5}{10} = \frac{280}{x} \\ x = \frac{10 \times 280}{5} = 560\)

Hello,

Answer is 560

Please check the answer for explanation.

✍️ By Benjemin ☺️

Answer:

C)

Step-by-step explanation:

Prime factorization of 420 = 2 × 2 × 3 × 5 × 7 = 22 × 3 × 5 × 7.

If you take...

2 + 2 + 3 + 5 + 7...

You would get 17.

Hope this helps! :) Good Luck!

-kiniwih426

The polynomial expression xp−x has p distinct zeros in Zp, where p is a prime number. This can be concluded from the fact that Zp is a field and every nonzero element in a field has a unique multiplicative inverse.

To show that xp−x has p distinct zeros in Zp, we can start by considering an arbitrary element a∈Zp. We can then evaluate xp−x at a by substituting a for x in the expression. This gives us \(a^p\)−a. By Fermat's Little Theorem, we know that \(a^p\) is congruent to a modulo p. Therefore, \(a^p\)−a is congruent to a−a=0 modulo p. This means that a is a root of xp−x, as \(a^p\)−a is divisible by p.

Since Zp is a field, every nonzero element has a unique multiplicative inverse. Therefore, if we assume that xp−x has more than p distinct zeros in Zp, then there would exist two distinct elements a and b in Zp such that a≠b and \(a^p\)−a≡0(mod p) and \(b^p\)−b≡0(mod p). However, this would imply that a and b are the same element in Zp, which contradicts the assumption that they are distinct.

Therefore, we can conclude that xp−x has exactly p distinct zeros in Zp. Moreover, since the degree of xp−x is p, and we have found p distinct zeros, these must be all the zeros of the polynomial. Hence, xp−x can be factorized as x(x−1)(x−2)⋯(x−(p−1)), where the factors represent the distinct zeros in Zp.

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Answer:

hi

Step-by-step explanation:

sorry cant help you

Answer: he will have $180

Step-by-step explanation: if he spends $120 he will have $180 leftover.