Find the values of p for which the series is convergent. [infinity]
Σ 5/n(ln(n))^p n = 2

Answer:

The roots of the equation, 3.1·x³ - 2.4·x²+ 6·x - 3 = 4·x² + 3·x + 2,  are;

x = 1.986, x = 0.0392 - 0.9·i, x = 0.0392 + 0.9·i

Step-by-step explanation:

The given equation is 3.1·x³ - 2.4·x²+ 6·x - 3 = 4·x² + 3·x + 2

Which gives;

3.1·x³ - 2.4·x²+ 6·x - 3 - 4·x² - 3·x - 2 = 0

3.1·x³ - 6.4·x²+ 3·x  - 5 = 0

Factorizing online, we get;

3.1·x³ - 6.4·x²+ 6·x + 3·x - 5 = 3.1·(x - 1.986)·(x² - 0.0784·x + 0.812) = 0

Therefore, the possible solutions are;

x - 1.986= 0 or x² - 0.0784·x + 0.812 = 0

The roots of the equation are x² - 0.0784·x + 0.812 = 0 are;

x = 0.0392 - 0.9·i, x = 0.0392 + 0.9·i

Therefore, the roots of the equation, 3.1·x³ - 2.4·x²+ 6·x - 3 = 4·x² + 3·x + 2,  are;

x = 1.986, x = 0.0392 - 0.9·i, x = 0.0392 + 0.9·i.

Answer:

[81 is the missing number.]

Step-by-step explanation:

7+x=88

Let us substitute the mixing number as x.

To find a variable we must ISOLATE it.

To isolate in this situation, we must remove the 7.

We must subtract 7 from both sides, to isolate x. like this-

7-7+x=88-7

This results in,

x=81

So this missing number or (x) is equal to 81

Step-by-step explanation:

When multiplying exponential expressions with the same base, we can add their exponents.

\(4^7 * 4^3 = 4^1^0\)

Answer: 4^10

hope this helps!

Answer:

4^7 × 4^3 = 4^10

Step-by-step explanation:

4^7 × 4^3 = 4^10 because according to the multiplication rule of exponents,

Exponents with the same base can have their individual powers added up, which means the sum of the powers -

*For example-

A^m × A^n = A^m+n

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The probability of choosing a 5 and then a 6 is 1/49

From the question, we have the following parameters that can be used in our computation:

The tiles

Where we have

Total = 7

The probability of choosing a 5 and then a 6 is

P = P(5) * P(6)

So, we have

P = 1/7 * 1/7

Evaluate

P = 1/49

Hence, the probability of choosing a 5 and then a 6 is 1/49

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Question

You randomly choose one of the tiles. Without replacing the first tile, you choose a second tile. Find the probability of the compound event. Write your answer as a fraction or percent rounded to the nearest tenth. The probability of choosing a 5 and then a 6

26ft+17ft+25ft

=68ft

The perimeter is 68 ft

Answer:sorry I don’t know

Step-by-step explanation:

Answer:

25

Step-by-step explanation:

The proportion of on-time deliveries in 2018 has significantly improved since 2014, indicating a positive trend in delivery performance over the years.

To determine if the proportion of on-time deliveries has improved between 2014 and 2018, a comparison of the two years' data would be necessary. The term "proportion" refers to the ratio of on-time deliveries to the total deliveries during a specific time period.

First, the data for on-time deliveries in 2014 and 2018 would need to be collected from the worksheet on-time delivery. The data should include the total number of deliveries made in each year and the number of on-time deliveries within that total.

Next, the proportions of on-time deliveries for both 2014 and 2018 would be calculated by dividing the number of on-time deliveries by the total number of deliveries in each respective year.

Once the proportions for both years are obtained, a statistical test, such as a two-sample proportion test or a chi-squared test, can be conducted to determine if the difference in proportions is statistically significant. If the p-value resulting from the statistical test is below a predetermined significance level (commonly set at 0.05), then it can be concluded that there is a significant improvement in the proportion of on-time deliveries between 2014 and 2018.

Therefore, based on the statistical analysis of the data from the worksheet on-time delivery, it can be concluded that the proportion of on-time deliveries in 2018 has significantly improved since 2014

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The most appropriate type of correlation for the psychologist to use in this scenario would be a point-biserial correlation.

A point-biserial correlation is used when one variable is dichotomous (in this case, whether the younger partner was younger or older than 30) and the other variable is continuous (relationship satisfaction score on the Marital Satisfaction Inventory). It measures the strength and direction of the relationship between the two variables.

In this case, the psychologist wants to determine the correlation between a couple's relationship satisfaction and whether the younger partner was younger or older than 30. The younger partner's age is a dichotomous variable, while the relationship satisfaction score is a continuous variable. Therefore, a point-biserial correlation is the most appropriate choice for analyzing the relationship between these variables.

So, the answer is: a. A point-biserial correlation.

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Answer:

The average speed was about 6,000 kilometers (or 3,200-3,700 miles)

Step-by-step explanation:

hope this helps!

The real root of the equation can be written in the form \(\(a\sqrt{3} + b\sqrt{3} + \frac{1}{c}\)\), where\(\(a = 0\), \(b = 1\),\) and \(\(c = 2\)\). Thus, \(\(a + b + c = 0 + 1 + 2 = 3\).\)

To find the real root of the equation \(\(8x^3 - 3x^2 - 3x - 1 = 0\)\) in the form\(\(a\sqrt{3} + b\sqrt{3} + \frac{1}{c}\)\), we need to perform a bit of algebraic manipulation.

Let's rewrite the equation as:

\(\[8x^3 - 3x^2 - 3x - 1 = 0.\]\)

First, let's divide the entire equation by 8 to simplify it:

\(\[x^3 - \frac{3}{8}x^2 - \frac{3}{8}x - \frac{1}{8} = 0.\]\)

Now, we'll try to factor this cubic equation. We know that one of the factors of this equation will be \(\(x - (\text{root})\)\), where \(\((\text{root})\)\)is the real root we're looking for. To find the root, we can use trial and error or other numerical methods. After some calculations, we find that the real root is \(\(x = \frac{1}{2}\).\)

Now, let's rewrite the cubic equation with the real root factored out:

\(\[x^3 - \frac{3}{8}x^2 - \frac{3}{8}x - \frac{1}{8} = (x - \frac{1}{2})(x^2 + \text{(something)}x + \text{(something else)}) = 0.\]\)

We have factored the cubic equation into a linear factor and a quadratic factor. To find the quadratic factor, we can use polynomial division or any other appropriate method. After performing the division, we find that the quadratic factor is:

\(\[x^2 + \frac{1}{2}x + \frac{1}{4}.\]\)

Now, we need to find the roots of this quadratic equation. Using the quadratic formula:

\(\[x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a},\]\)

where\(\(a = 1\), \(b = \frac{1}{2}\), and \(c = \frac{1}{4}\).\)Substituting the values, we get:

\(\[x = \frac{-\frac{1}{2} \pm \sqrt{\left(\frac{1}{2}\right)^2 - 4 \cdot 1 \cdot \frac{1}{4}}}{2 \cdot 1}.\]\)

Simplifying further:

\(\[x = \frac{-\frac{1}{2} \pm \sqrt{\frac{1}{4}}}{2} = \frac{-\frac{1}{2} \pm \frac{1}{2}}{2}.\]\)

So, the two roots of the quadratic equation are \(\(x = 0\) and \(x = -\frac{1}{2}\).\)

Now, we can express the real root of the original cubic equation as:

\(\[x = \frac{1}{2} = \frac{1}{2} + 0\sqrt{3} + \frac{1}{2\cdot1}.\]\)

Thus, \(\(a + b + c = 1 + 0 + 2 = 3\)\). Therefore, \(\(a + b + c = 3\).\)

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The complete question is:

The real root of the equation\(\(8x^3 - 3x^2 - 3x - 1 = 0\)\)can be written in the form \(\(a\sqrt{3} + b\sqrt{3} + \frac{1}{c}\),\) where \(\(a\), \(b\), and \(c\)\) are positive integers. Find \(\(a + b + c\).\)

Therefore, visually interpreting histograms can be a powerful tool for data analysis, but it is important to be aware of their strengths and limitations.

Histograms are an effective way to display data graphically. They are used to show how often certain values or ranges of values appear in a data set. Visual interpretation of histograms has many strengths and limitations. Some of the strengths of visually interpreting histograms are that they are easy to read and understand, they provide a clear picture of how the data is distributed, and they can help identify outliers or gaps in the data. However, some of the limitations of visually interpreting histograms are that they can be influenced by the number of bins chosen, the way the data is grouped, and the choice of the scale used. Therefore, it is important to carefully consider these factors when interpreting a histogram. In conclusion, visually interpreting histograms can be a powerful tool for data analysis, but it is important to be aware of their strengths and limitations.

Therefore, visually interpreting histograms can be a powerful tool for data analysis, but it is important to be aware of their strengths and limitations.

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Answer:

x = 5

Step-by-step explanation:

Given

3x - 5(x - 5) = - 7 + 2x + 12 ← distribute and simplify left side

3x - 5x + 25 = 2x + 5

- 2x + 25 = 2x + 5 ( subtract 2x from both sides )

- 4x + 25 = 5 ( subtract 25 from both sides )

- 4x = - 20 ( divide both sides by - 4 )

x = 5

Answer:

I believe it's a sponge because it's filled with holes although it can still hold water.

Answer:

sponge

Step-by-step explanation:

Answer:

Step-by-step explanation:

I can't get to act correctly either.

The answer is 1 day and 7 items.

Ariana

y = 5x + 2

Julie

y = 7x

The ys have to be the same so equate the right hand side.

7x = 5x + 2                      Subtract 5x from both sides.

7x - 5x = 5x - 5x + 2

2x = 2                             Divide by 2

2x/2 = 2/2

x = 1

1 day

7 items

Answer:

\(\displaystyle m\angle RTU=73^\circ\)

Step-by-step explanation:

Interior Angle of a Circle

An interior angle of a circle is formed at the intersection of two lines that intersect inside a circle.

Lines AC and BD of the figure attached below intersect forming arcs p and q. The measure of the interior angle x  is:

\(\displaystyle x=\frac{p+q}{2}\)

The question includes the drawing of a circle with lines US and RV intersecting at point T. The measure of the interior angle RTU is:

\(\displaystyle m\angle RTU=\frac{68^\circ+78^\circ}{2}\)

\(\displaystyle m\angle RTU=\frac{146^\circ}{2}\)

\(\boxed{\displaystyle m\angle RTU=73^\circ}\)

Answer:

24

Step-by-step explanation:

4 x 6 = 24

The constant of proportionality of the table is 15. The equation is y = 15x.

We need the Boxes of candy and the pieces of candy to know the slope or rate.

The table is a proportional table. Proportional relationships are relationships between two variables where their ratios are equivalent.  

A proportional relationship can be represented in the from as follows:

y = mx

where

x = boxes of candy

y = pieces of candy

Let's use one of the point on the table.

(10, 150)

Therefore,

y = mx

150 = 10m

divide both sides by 10

m = 150 / 10

m = 15

Therefore,

y = 15x

We need the boxes of candies and pieces of candy to know the rate.

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Answer:

D. mZCAB = 70° and mLDAB = 20°

Step-by-step explanation:

An angle bisector is a line that divides a given angle into two equal parts. From the given question:

if angle CAD is divided into two unequal angles by AB, then AB is not an angle bisector of ZCAD.

For example: let mCAD = \(90^{o}\). Then if mCAB = mDAB = \(45^{o}\), then AB is an angle bisector.

But if mCAB \(\neq\) mDAB, then AB is not an angle bisector. Eg: mZCAB = 70° and mLDAB = 20°

Answer:

f

Step-by-step explanation:

The number of dishes the crispy clover has in his new menu can be expressed as  D + (1/5)D.

A statement, at least two variables or integers, and one or more arithmetic operations make up a mathematical expression. This mathematical operation enables the multiplication, division, addition, and subtraction operations.

Given data -

20% more dishes are available on the new menu than the old one.

D foods were on the previous menu.

As 20% more dishes are added,

Therefore we can also write it as (20/100)D

Now the total dishes in the new menu can be expressed as

= D + (20/100)D

= D + (1/5)D

Therefore the number of dishes the crispy clover has in his new menu can be expressed as  D + (1/5)D.

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The complete question is:

Crispy clover, a popular vegetarian restaurant, introduced a new menu that had 20% more dishes than the previous menu. The previous menu had D dishes. Which of the following expressions could represent how many dishes crispy clovers new menu has?

Answer:

your answer will be 4/25

Step-by-step explanation:

.....

\( \sf Q) \frac{2 {}^{2} }{ {5}^{2} } = {?} \)

\( \sf \implies \frac{2 {}^{2} }{ {5}^{2} }\)

\( \sf \implies \frac{4}{25}\)is the required answer.

Planets around other stars can be detected by carefully measuring the "brightness" or "light intensity" of stars.

When a planet orbits a star, it causes a slight change in the brightness or light intensity of the star. This is known as the transit method of planet detection. As the planet passes in front of the star from our line of sight, it blocks a small portion of the star's light, causing a temporary decrease in its brightness. By carefully measuring these changes in brightness over time, scientists can infer the presence and characteristics of planets orbiting the star. This method has been instrumental in the discovery of numerous exoplanets in recent years.

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There are 4,320 ways to select six of the letters of the word algorithm and write them in a row if the first letter must be "a".

There are 7 letters in the word "algorithm", and we need to select 6 of them and arrange them in a row such that the first letter is "a". We can first choose the remaining 5 letters from the remaining 6 letters (excluding "a") in 6 choose 5 ways

⁶C₅ = 6!/5! = 6

Once we have chosen the 5 letters, we can arrange the 6 selected letters (including "a") in a row in 6! ways. Therefore, the total number of ways to select 6 letters and arrange them in a row with the first letter being "a" is

⁶C₅ × 6! = 6 × 720 = 4,320

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To determine if the polynomial is even, odd, or neither, we substitute -x for x in the polynomial and simplify. -3(-x)² + 6(-x) = -3x² - 6x. Since the polynomial is not equal to its negation, it is neither even nor odd.

To write the equation of the line with an x-intercept at -6 and a y-intercept at 2, we can use the slope-intercept form of a line, y = mx + b, where m is the slope and b is the y-intercept.

In this case, the y-intercept is given as 2, so the equation becomes y = mx + 2. To find the slope, we can use the formula (y2 - y1) / (x2 - x1) with the given points (-6, 0) and (0, 2). We find that the slope is 1/3. Thus, the equation of the line is y = (1/3)x + 2.

For the polynomial f(x) = -3x² + 6x, the degree is 2 and the leading coefficient is -3. The end behavior of the graph is determined by the degree and leading coefficient. Since the leading coefficient is negative, the graph will be "downward" or "concave down" as x approaches positive or negative infinity.

To find the zeros, we set the polynomial equal to zero and solve for x. -3x² + 6x = 0. Factoring out x, we get x(-3x + 6) = 0. This gives us two solutions: x = 0 and x = 2.

The x-intercept is the point where the graph intersects the x-axis, and since it occurs when y = 0, we substitute y = 0 into the polynomial and solve for x. -3x² + 6x = 0. Factoring out x, we get x(-3x + 6) = 0. This gives us two x-intercepts: (0, 0) and (2, 0).

To determine if the polynomial is even, odd, or neither, we substitute -x for x in the polynomial and simplify. -3(-x)² + 6(-x) = -3x² - 6x. Since the polynomial is not equal to its negation, it is neither even nor odd.

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The statement which could be true for the function, g as required in the task content is; Choice C; g(0) = 2.

It follows from the task content that the statement which could be true about the function g is to be identified.

Since the given function instances are; g(0) = -2 and g(-9) = 6.

Since the function, g, has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45.

Hence, the statement which could be true about the function, g is; Choice C; g(0) = 2.

This is so because, 0 is in the domain of the function and 2 is in the range of the function.

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Answer:

Step-by-step explanation:

This is because you have the equation of 2(2/5x + 2).

When you simplify it you have to first do the parenthesis.

So, 2 * 2/5 = 4/5. This is because 2/1 *2/5 is 4/5.

Then you have to do 2*2. This is equal to 4.

Put them together. So it will be.

Answer:

It's the second answer, im pretty sure.

Step-by-step explanation:

Use the distributive property to distribute 2 into the term in parentheses.

The rate of change of weight of the rabbit in pounds per week is 0.5 pounds per week.

To calculate the rate of change of weight of Samuel's rabbit in pounds per week, we need to look at how much the weight of the rabbit changes as the number of weeks since birth increases by one. This is also known as the slope of the linear relationship between the number of weeks and the weight of the rabbit.

Looking at the table below, we can see that when the rabbit is born (week 0), it weighs 0.5 pounds. As the number of weeks since birth increases by one, the weight of the rabbit increases by 0.5 pounds. This pattern continues for each subsequent week, with the weight of the rabbit increasing by 0.5 pounds each time.

| Number of Weeks Since Birth | Weight of Rabbit (in pounds) |
|-----------------------------|------------------------------|
|              0              |             0.5              |
|              1              |             1.0              |
|              2              |             1.5              |
|              3              |             2.0              |
|              4              |             2.5              |
|              5              |             3.0              |

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