Five students took a quiz. The lowest score was 1, the highest score was 7, and the average (mean) was 4. A possible set of scores for the students is:

1. Series:

[tex]\[\sum_{n=1}^{\infty} \frac{n}{{n^2 + 3}}\][/tex]

To determine the convergence or divergence of this series, we can use the comparison test or the limit comparison test.

Using the comparison test:

We compare the given series with a known series that we know to be convergent or divergent. Let's consider the series  [tex]\(\sum_{n=1}^{\infty} \frac{1}{n}\).[/tex]

As [tex]\(n\)[/tex] approaches infinity, the term  [tex]\(\frac{n}{{n^2 + 3}}\)[/tex]  is always less than or equal to  [tex]\(\frac{1}{n}\).[/tex]

Since the series  [tex]\(\sum_{n=1}^{\infty} \frac{1}{n}\)[/tex]  is a known divergent harmonic series, and the terms of our series are less than or equal to the corresponding terms of the harmonic series, we can conclude that our series is also divergent.

Therefore, the first series is divergent.

2. Series:

[tex]\[\sum_{n=1}^{\infty} \left(\frac{n}{{n^2 + 3}}\right)^n\][/tex]

To test the convergence or divergence of this series, we can use the root test or the ratio test.

Using the root test:

We take the [tex]\(n\)th[/tex] root of the absolute value of the series term and check the limit as [tex]\(n\)[/tex] approaches infinity.

Let's calculate the limit:

[tex]\[\lim_{{n\to\infty}} \left(\frac{n}{{n^2 + 3}}\right)^n = \lim_{{n\to\infty}} \left(\frac{n^n}{{(n^2 + 3)^n}}\right) = \lim_{{n\to\infty}} \left(\frac{n^n}{{n^{2n} + 3n}}\right) = \lim_{{n\to\infty}} \left(\frac{n^n}{{n^{2n}}}\right) = \lim_{{n\to\infty}} \left(\frac{1}{{n^n}}\right) = 0\][/tex]

Since the limit is less than 1, the root test tells us that the series converges.

Therefore, the second series is convergent.

In summary:

1. The first series is divergent.

2. The second series is convergent.

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Answer:

that statement is true

is there some other question?

Answer:

it is true

Step-by-step explanation:

Answer:

y = 0.20x(-38,000) + 38,000

Step-by-step explanation:

y: represents how much the price is now.

x: Represents the number of years passed.

y = 0.20x(-38,000) + 38,000

For example if it's 1 year

y = 0.20(1) (-38,000) + 38,000

y = 0.20(-38,000) + 38,000

y = -7600 + 38,000

y = 30,400

A stem and leaf plot would best display the following data if you wanted to display the numbers which are outliers as well as the mean. Option C is the correct option.

A stem and leaf plot would be the best choice for displaying the given data if the goal is to show outliers as well as the mean. A stem and leaf plot is a simple and effective way to represent the data distribution while preserving the individual data points.

It organizes the data by separating the leading digit (stem) and the trailing digit (leaf). This plot allows for easy identification of outliers as they would be displayed separately from the main distribution. Additionally, the stem and leaf plot can include a line indicating the mean, providing a visual representation of its position relative to the data points.

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The question is -

Which would best display the following data if you wanted to display the numbers which are outliers as well as the mean?

[4, 1, 3, 10, 18, 12, 9, 4, 15, 16, 32]

A. Pie chart.

B. Bar graph.

C. Stem and leaf plot.

D. Venn diagram.

Answer:

20% i believe

Step-by-step explanation:

i looked it up actually lol

Answer:

The percentage change is a 20% increase

Answer:

Part A: There are 6 possible outcomes of this experiment.

Part B: There are 6  possible outcomes of the experiment ;   red, brown, green, white, black, and blue ( equal)

Part C:

Sample Space = { red, brown, green, white, black,  blue }

Part D:

P (blue)= 1/6

Part E:

P (not purple)= 1

Step-by-step explanation:

Part A:

There are 6 possible outcomes of this experiment.

As there are 6 pairs of socks. Each pair is folded together so that the socks cannot be mixed up . There is 1 chance of choosing each pair of socks.

Part B:

The chosen socks can be any of the following  red, brown, green, white, black, and blue so there are 6  possible outcomes of the experiment ;   red, brown, green, white, black, and blue (all have  equal probability) .

Part C:

The sample space contains all the possible outcomes of the event.

Sample Space = { red, brown, green, white, black,  blue }

Part D:

P(blue)= No of favorable outcomes/ Total no  of outcomes

P (blue)= 1/6

Part E:

P (not purple)= 1

As the total probability is always equal to 1 and we want to find the probability of the color which is not given in the list

P( purple) = 0/6= 0

And the probability of not purple is given by the formula

P (not purple) = 1- P (purple)

                         = 1-0= 1

1 indicates that the event of any other color except purple must occur which is equal to the probability of not purple.

This can be solved by complement rule also.

Answer:

Origin

Step-by-step explanation:

Origin is the starting points (0,0)

Hope this helped :)

(2x + 3) (x^2 - 6x + 9)

Given that the vector field F is (3x, 3y) and the region is an annular region between the circles x² + y² = 9 and x² + y² = 16,To calculate the flux of the vector field, we use the formula: flux = ∬F · dS, Where F is the vector field and dS is an elemental vector area.

Using cylindrical coordinates: For the outer circle x² + y² = 16, the limits of θ are from 0 to 2π and the limits of r are from 4 to 4√2. For the inner circle x² + y² = 9, the limits of θ are from 0 to 2π and the limits of r are from 3 to 3√2.The vector normal to the surface at a point (r,θ) is given by n = (cosθ, sinθ, 0).

Hence, the outward normal vector is given by n = (cosθ, sinθ, 0) and the elemental vector area is given by dS = r dr dθ.Therefore, we have, flux = ∬F · dS= ∫_3^3√2 ∫_0^2π (3r cosθ, 3r sinθ) · (r cosθ, r sinθ, 0) r dr dθ+ ∫_4^4√2 ∫_0^2π (3r cosθ, 3r sinθ) · (r cosθ, r sinθ, 0) r dr dθ= 0

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Answer:

Step-by-step explanation:

Answer:

MEEEEEEEEEEEEEE!!!

The polynomial function h(x) has a complex zero at x = 3 – 4i with a multiplicity of one. The given table provides certain values of h(x) for various x-values.

A zero of a polynomial function corresponds to the values of x for which the function evaluates to zero. In this case, the zero is x = 3 – 4i, where 4i represents the imaginary unit multiplied by 4. The multiplicity of one indicates that this zero occurs only once in the function.

The table provides specific values of h(x) for different x-values, which allows us to observe the behavior of the function. However, without knowing the functional form of h(x) or additional information, we cannot determine the complete polynomial equation.

To fully determine the polynomial function h(x) based on the given zero, we need to know all of its zeros, including any real or complex zeros with their respective multiplicities. Additionally, the degree of the polynomial can affect the number of zeros it possesses. With this information, we could reconstruct the polynomial equation using methods such as factoring, synthetic division, or the quadratic formula.

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A polynomial function h(x) has a zero of x = 3 – 4i with a multiplicity of one. Certain values of h(x) are given in the following table.

x h(x)

–5  0

–2  3

–1  0

1  2

4 0

7  6

10  0

If every real x-intercept of h(x) is shown in the table and each has a multiplicity of one, what is the degree of h(x)?

3

4

5

6

Answer:

I would need to see the variables to answer this questions.

Answer: 97/100

Step-by-step explanation:

Answer:

The answer is 0.97 or 97/100

Step-by-step explanation:

9/10 = 0.9

7/100 = 0.07

0.9 + 0.07 = 0.97

Hope this helps!

Please mark as brainliest!

Answer:

Hehe, I get it mate

Step-by-step explanation:

5 + 5 = 10

The flux of the vector field F across the surface S in the indicated direction (away from origin) is 34.

Let's assume that the surface S is the hemisphere of radius 2 centered at the origin. We can represent this hemisphere with the equation x^2 + y^2 + z^2 = 4 and we can use the parameterization given below.

r(θ, φ) = (2sinθcosφ)i + (2sinθsinφ)j + (2cosθ)k for 0 ≤ θ ≤ π/2 and 0 ≤ φ ≤ 2π

The unit normal vector to the surface is:

n = (r_θ × r_φ)/|r_θ × r_φ| = (-4sinθcosφ)i + (-4sinθsinφ)j + (-4cosθ)k

The flux integral can be calculated using the formula below:

∫∫ F·n dS

where F is the vector field given by F = x^2i + y^2j + z^2k.

After computing the dot product and integrating over the parameterization of the hemisphere, the flux of F across S is found to be 34.

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A race car with wheels with diameter 66 cm must turn 1,088,000 times to cover a 300 km race. This is because the circumference of a wheel is equal to its diameter multiplied by pi, which is approximately 3.14.

So, the circumference of a 66 cm wheel is 66 * 3.14 = 208.2 cm. To travel 300 km, the car must turn its wheels 300,000 / 208.2 = 1,445 times.

The circumference of a circle is equal to its diameter multiplied by pi, which is approximately 3.14. So, the circumference of a 66 cm wheel is 66 * 3.14 = 208.2 cm. To travel 300 km, the car must turn its wheels 300,000 / 208.2 = 1,445 times.

In other words, the car must turn its wheels 1,445 times to cover the race distance. This is a lot of turns, but it is possible for a Formula 1 car to do this. The cars are designed to be very efficient and to have very low rolling resistance, which means that they can turn their wheels very quickly without losing too much energy.

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Answer:

Step-by-step explanation

y2-y1 over x2-x1

0-3 = -3

2-0 = 2

So answer is:

-3/2

Answer: The slope is -3/2 or 1 1/2 simplified

Hope it helped :D

Please mark me brainliest

Answer:

One point would be on (0,0) and the other on (1,-5)

Step-by-step explanation:

hope this helped :)

Answer:

its c. 1/4

hope it helps;)

Answer:

1/4

Step-by-step explanation:

1. Look at the numbers on the number line (1,0,-1)

2. See where the point falls in between. (0 & 1)

3. Since the point is closer to 0 you can infer that it is 1/4

Answer:

A

Step-by-step explanation:

got it right on edg

After simplifying the inequality we get 6 < 28 which is true. Hence the given statement is true.

An inequality is a mathematical statement that uses the inequality symbol to indicate the relationship between two expressions. Both sides of an inequality sign have different expressions.

It signifies that the expression on the left should be more or smaller than the expression on the right, or vice versa. Literal inequalities occur when the relationship between two algebraic expressions is defined using inequality symbols.

The given inequality is:

3(2 - b) < 10 - 3(b-6)

Distribute the number inside the bracket,

6 - 3b < 10 - 3b + 18

Add 3n on both sides,

6 < 10 + 18

Simplifying it,

6<28

Hence,

The given statement is true.

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The complete question is:

Check whether the statement is true or false:

3(2 - b) < 10 - 3(b-6)

Answer:

18/25

Step-by-step explanation:

Answer:

x=-9.5

Step-by-step explanation:

1.1x=-8.1-2.35

x=-9.5

Answer:

9%

Step-by-step explanation:

Given :

Principal, P = 400

Time, t = 4 months = 4/12 = 0.33333

Simple interest = 12

Simple interest = (principal * rate * time)

Rate = r

12 = (400 * r * 0.33333)

12 = 133.3333r

r = 12 / 133.3333

r = 0.090000

r = 0.09

rate = 0.09 * 100% = 9%

Answer:

two

Step-by-step explanation:

The exact value of sec(60°) sec ( 60 ° ) is 2 .

Given Allen has 10 different books at home and he would like to arrange them on his book shelves. The total number of ways he can arrange the books on the shelves is: a) 725,760, b) 80640, c) 2,880, d) 103,680.

a) Allen has 10 different books at home and he would like to arrange them on his bookshelves. To find the number of ways can he do this if he would like to arrange all the books on one shelf in a row so that two of the books: "Robinson Cruso" and "C Programming" cannot be next to each other.

Using permutation formula, we can get the total number of ways that he can arrange the books where two books, Robinson Cruso and C Programming, can't be next to each other:

Total number of ways = 10! - (9! x 2!)

= 725,760

b) Allen has 10 different books at home and he would like to arrange them on his bookshelves. To find the number of ways can he do this if he would like to arrange all the books on one shelf in a row so that the book: "Robinson Cruso" cannot be the first nor the last book in the row.

Using permutation formula, we can get the total number of ways that he can arrange the books, where the book Robinson Cruso cannot be the first nor the last book in the row:

Total number of ways = 8! x 2!

= 80640

c) Allen has 10 different books at home and he would like to arrange them on his bookshelves. To find the number of ways can he do this if he would like to arrange the books on two shelves putting 6 books on the top shelf and 4 books on the bottom shelf (in rows) so that the book "War and peace" has to be on the top shelf and "SPSS" has to be on the bottom one.

The book "War and peace" has to be on the top shelf and "SPSS" has to be on the bottom one. We can arrange these 2 books on the shelves in 1 way. There are 5 books remaining that he can arrange in 5! ways on the top shelf and 4 books remaining that he can arrange in 4! ways on the bottom shelf.

Therefore, the total number of ways he can arrange the books on the shelves is:

Total number of ways = 1 x 5! x 4!

= 2,880

d) Allen has 10 different books at home and he would like to arrange them on his bookshelves. To find the number of ways can he do this if he would like to arrange the books on three shelves putting 3 books on the top shelf, 3 books on the middle shelf, and 4 books on the bottom shelf (in rows) so that "C programming" and "SPSS" are both on the top shelf and "Harry Potter" cannot be on the bottom shelf.

Two of the books, "C programming" and "SPSS", are on the top shelf. We can arrange these 2 books in 2! ways.

There are 2 other books that can be arranged on the top shelf in 2! ways.

One of the books, "Harry Potter", cannot be on the bottom shelf. There are 6 books that can be placed on the middle shelf and 3 books that can be placed on the bottom shelf.

Therefore, the total number of ways he can arrange the books on the shelves is:

Total number of ways = 2! x 2! x 6! x 3!

= 103,680

Answer: a) 725,760b) 80640c) 2,880d) 103,680

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Answer:

the lengths of the sides of the yard.

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

this reason is because the sides tell how big your backyard is

One difference between contingency tables and the tables used in factorial designs is

B) The cells in contingency tables hold frequencies, whereas the cells in factorial analysis of variance tables represent means.

Contingency tables and factorial analysis of variance (ANOVA) tables are both used in statistical analysis, but they serve different purposes and have distinct characteristics.

Contingency tables are used to display the distribution of frequencies or counts for two or more categorical variables. The cells in a contingency table contain the frequencies or counts of observations that fall into specific combinations or categories of the variables being studied. The purpose of a contingency table is to examine the relationship or association between the variables and determine if they are independent or related.

On the other hand, factorial ANOVA tables are used to analyze the effects of two or more independent variables (factors) on a continuous dependent variable. The cells in a factorial ANOVA table represent the means of the dependent variable for each combination of levels of the independent variables. The table displays the sources of variation, degrees of freedom, sum of squares, mean squares, F-values, and p-values for the factors and their interactions.

Therefore, the main difference between the two types of tables is that contingency tables contain frequencies or counts in their cells, reflecting the distribution of observations across categorical variables, while factorial ANOVA tables contain means in their cells, representing the average values of the dependent variable for different combinations of the independent variables.

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