37.5 in scientific notation

Answer:

Step-by-step explanation:

The equation would be y=25x+ 50 which is linear. Radical expressions have a number under the radical sign which this equation doesn't. Rational expressions have fractions containing polynomials in the numerator and denominator and exponential equations have 'x' as the exponent in a function.

The indefinite integral of \(x^4 ln(1 + x)\) can be expressed as a power series with radius of convergence equal to 1.

To find the power series representation of the given integral, we start by using integration by parts with\(u = ln(1 + x)\)  and \(dv = x^4 dx\). This gives us:

integral of \(x^4 ln(1 + x) dx = x^4 (ln(1 + x) - 1) - 4x^3 + 12x^2 - 24x + 24 + C\)

where C is the constant of integration.

Next, we can express ln(1 + x) - 1 as a power series, as follows:

ln(1 + x) - 1 = -Σ\((-1)^n * x^n / n\)   (n=1 to ∞)

Substituting this into the integral expression and simplifying, we get:

integral of \(x^4 ln(1 + x) dx\)= sum from n=1 to ∞ \((-1)^n * x^{n+4} / n(n+4) - 4x^3 + 12x^2 - 24x + 24 + C\)

This is the power series representation of the given integral, with radius of convergence equal to 1 (since the series diverges when |x| > 1).

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Answer:

87 moneys

Step-by-step explanation:

Step-by-step explanation:

2/11 = 0.18181818......

Hope it helps you

Answer:

0. 181818181818181818181818181818181818181818...

Step-by-step explanation:

Hope it helps! Please mark Brainliest! :)

Answer: BC ≈ 6.4 units

Step-by-step explanation: We can use trigonometry to find the length of line segment BC.

Since we know the length of AC and the measure of angle A, we can use the trigonometric function cosine (cos) to calculate BC.

Using the formula: cos(A) = Adjacent / Hypotenuse, we have

cos(34°) = BC / 9.

Solving for BC, we get BC ≈ 6.4 units (rounded to the nearest tenth).

Here is an article on trigonometry basics: https://byjus.com/maths/trigonometry/#:~:text=Trigonometry%20Basics,are%20based%20on%20these%20functions.

The formula for the sum of a finite geometric series, when the common ratio is not equal to 1, is given by\(S = a(1 - r^n)/(1 - r)\), where S is the sum of the series, a is the first term, r is the common ratio, and n is the number of terms in the series.

To derive the formula for the sum of a finite geometric series, let's consider a series with a first term 'a' and a common ratio 'r'. The series can be represented as \(a + ar + ar^2 + ar^3 + ... + ar^(n-1)\), where n is the number of terms in the series.

Now, if we multiply the series by the common ratio 'r', we get\(ar + ar^2 + ar^3 + ... + ar^(n-1) + ar^n.\)

Subtracting the original series from this, we have: \((ar + ar^2 + ar^3 + ... + ar^(n-1) + ar^n) - (a + ar + ar^2 + ar^3 + ... + ar^(n-1)) = ar^n - a.\)

We can observe that most terms in the series cancel out, leaving only \(ar^n\) and -a. Now, if we factor out 'a' from the right side, we get: \(ar^n - a = a(r^n - 1).\)

Dividing both sides by (r - 1), we obtain the formula for the sum of the geometric series: S = \(a(1 - r^n)/(1 - r)\).

By using this formula, we can easily find the sum of a geometric series with a given first term, common ratio, and number of terms.

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There are 5 full square and 6 triangles that are half squares.

      5 + (6)(1/2) = 5 + 3 = 8

You could also break this into smaller shapes (like a big triangle on the top and a smaller triangle and rectangle on the bottom and use area formulas to calculate the area.  But counting works well in this example.

Answer: 8

Step-by-step explanation:

First you split up this shape into two different shapes, a triangle and trapezoid

Put a line through the coordinates (-2,2) to  (-1,2); the top is a triangle and the other is a trapezoid

Area of the trapezoid is A = .5x (base1 + base2) x height

base1 of the trapezoid goes from -4 to -1 which is 3

base2 goes from -2 to -1 which is 1

height is 0 to 2 whcich is 2

A = .5 x (3+1) x 2 = 4

Now area of a triangle is A = .5 x base x height

the base goes from -2 to 2 which is 4

the height goes from 2 to 4 which is 2

A = .5 x (4) x (2) = 4

Area of the Trapezoid + Area of the Triangle = Total Area

4 + 4 = 8

Answer:

i think the answer would be B i think if its wrong i am sorry

Step-by-step explanation:

The values that make the inequality g ≤ -2 true, from the least to the greatest, are: -10, -7, -5, -3, -2.1, -2.01, -2.001, and -2.

An inequality is a mathematical statement that compares two quantities that are unequal, or states how a given scenario is true.

Given the inequality, g ≤ -2, this implies that, all the possible values of g are either -2 or less than -2. This means that g is equal to or less than -2.

All values that make the inequality true are from -2 and below. Values that are above -2 are not included. On a number line, these values are to the left of -2.

Therefore, the values that make the inequality g ≤ -2 true, from the least to the greatest, are: -10, -7, -5, -3, -2.1, -2.01, -2.001, and -2.

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The following parts can be answered by the concept of Sequence.

1.  The sequence converges to: lim an = 3 + 4/5 = 19/5

2. The formula for the general term of the sequence is: an = 3/5 + 4/(5n) - 3/(5(15n + 1)), n ≥ 1.

For the first part of the question:

We can rewrite the sequence as:

an = 3 + (12n²)/(n + 15n²)

As n approaches infinity, the term (12n²)/(n + 15n²) approaches 12/15 = 4/5. Therefore, the sequence converges to:

lim an = 3 + 4/5 = 19/5

So the limit of the sequence is 19/5.

For the second part of the question:

If we look at the first few terms of the sequence, we can notice that:

a1 = 3 + (12×1)/(1 + 15×1) = 3.44

a2 = 3 + (12×2)/(2 + 15×2) = 3.69

a3 = 3 + (12×3)/(3 + 15×3) = 3.86

a4 = 3 + (12×4)/(4 + 15×4) = 3.98

We can observe that the denominator of each term is n + 15n², which can be factored as n(15n + 1). Therefore, we can rewrite the sequence as:

an = 3 + (12n)/(n(15n + 1))

Simplifying this expression, we get:

an = 3/5 + 4/(5n) - 3/(5(15n + 1))

Therefore, the formula for the general term of the sequence is:

an = 3/5 + 4/(5n) - 3/(5(15n + 1)), n ≥ 1.

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Answer:

D.76

Step-by-step explanation:

First, go 2x4x2 for the bottom, and the top of it

Then, for both sides go 5x4x2

Then, for the other sides go 2x5x2

After that, add all of the numbers after you do the equation.

Answer:

-5

Step-by-step explanation:

Divide -10 by 2 and you'll come away with -5

Using a 35-bag sample with a mean of 406.0 grams, a known standard deviation of 25.0 grams, and a level of significance of 0.05, you can perform a one-tailed Z-test to determine whether to reject or fail to reject the null hypothesis.

To test if the potato chip manufacturer's bag filling machine is working correctly at the 411.0-gram setting, we will state the hypotheses using the given terms.

Null Hypothesis (H0): The machine fills bags correctly, with a mean weight of 411.0 grams (µ = 411.0 grams)
Alternative Hypothesis (H1): The machine is underfilling bags, with a mean weight less than 411.0 grams (µ < 411.0 grams)

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In this case, we are given only a partial list of observations. To determine if the process is in control, we would need the complete set of observations to evaluate their values in relation to the control limits.

To construct a control chart and determine if the process is in control, we need to calculate the control limits using the given observations.

Let's start by calculating the average (x(bar)) and standard deviation (σ) of the observations:

Observations: 10, 3, 9, 9, 8, 4

Step 1: Calculate the average (x(bar)):

x(bar) = (10 + 3 + 9 + 9 + 8 + 4) / 6 = 43 / 6 ≈ 7.17

Step 2: Calculate the standard deviation (σ):

1. Calculate the squared deviation for each observation:

\((10 - 7.17)^2, (3 - 7.17)^2, (9 - 7.17)^2, (9 - 7.17)^2, (8 - 7.17)^2, (4 - 7.17)^2\)

= 6.9129, 18.9129, 2.5929, 2.5929, 0.6889, 10.5889

2. Calculate the average of the squared deviations:

(6.9129 + 18.9129 + 2.5929 + 2.5929 + 0.6889 + 10.5889) / 6 ≈ 7.9198

3. Calculate the square root of the average squared deviation:

σ = √(7.9198)

≈ 2.81

Now that we have the average (x(bar)) and standard deviation (σ), we can construct the control chart using two sigma limits. The control limits are calculated as follows:

Upper Control Limit (UCL) = x(bar) + (2 * σ)

Lower Control Limit (LCL) = x(bar) - (2 * σ)

UCL = 7.17 + (2 * 2.81)

≈ 12.79

LCL = 7.17 - (2 * 2.81)

≈ 1.55

Based on the control chart, if any of the observations fall above the UCL or below the LCL, it would indicate an out-of-control process.

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Answer:

  False

Step-by-step explanation:

It is true that term insurance has no value as an investment. However, it is the least expensive type of life insurance. The compound statement is false, because one of the elements of the statement is false.

Answer:

false

Step-by-step explanation:

Answer:

-2x+7(10+18)

Step-by-step explanation:

Hope this helps

Answer:

-1/2, 1/2, -1, -2, 2

Step-by-step explanation:

a_1 = 2

a_2 = -1

a_n+2 = a_n+1/a_n

a_3 = a_2/a_1 = -1/2

a_4 = a_3/a_2 = -1/2 / (-1) = 1/2

a_5 = a_4/a_3 = 1/2 / (-1/2) = -1

a_6 = a_5/a_4 = -1 / (1/2) = -2

a_7 = a_6/a_5 = -2 / (-1) = 2

a_8 = a_7/a_6 = 2/(-2) = -1

a_9 = a_8/a_7 = -1/2

etc.

Answer:

(4x)^2 = x + 15   or

16x^2 = x  + 15  

16x^2 - x - 15 = 0

or x =1    and     x = -0.9375

Make sure next time that you ask a question..

Step-by-step explanation:

This shouldn't really be answered unless we are sure when the answer is there.

4x is the product of a number and 4

(4x)^2 = 16x^2

this will equal x + 15

16x^2 = x + 15

The question is that the answer? I suspect it is.

16x^2 - x - 15 = 0

This might be the answer. It's not clear.

"""""""""""""""""""""""""""""""""""""''''

Believe it or not, this factors without using the quadratic formula

(16x + 15) ( x - 1) = 0

16x + 15 = 0

x = - 15/16 = - 0.9575

x - 1 = 0

x = 1

work it out

Step-by-step explanation:

Jose can plow 7.5 acres of land in an hour. it will take Jose 12 minutes to plow 1.5 acres of land.

To calculate how long will it take Jose to plow 1.5 acres of land, we can use the following steps:

1: Determine the number of acres Jose can plow per minute. Dividing 7.5 acres by 60 minutes will give us the number of acres Jose can plow in 1 minute:7.5 ÷ 60 = 0.125 acres/minute

2. Determine the number of minutes it will take Jose to plow 1.5 acres of land. To calculate the number of minutes, we can divide the number of acres by the acres Jose can plow in 1 minute: 1.5 ÷ 0.125 = 12 minutes

Therefore, it will take Jose 12 minutes to plow 1.5 acres of land.

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No, this set is not a function from R to R. the point (2, 8) also lies in the set, as 2³ = 8 and 8 = 8. Because both of these points are in the set, this set fails the definition of a function, and so it is not a function.

In mathematics, a function is defined as a relation between elements of one set (the domain) and another set (the range) such that each element of the domain is related to exactly one element of the range. In this set, f = © (x 3 , x) : x ∈ r ª , the domain is R, but the range contains both x3 and x, and so each element of the domain (x) is related to more than one element of the range. Therefore, this set is not a function. To demonstrate, consider the point (2, 4). This point lies in the set, as 2³ = 8 and 2 = 2. However, the point (2, 8) also lies in the set, as 2³ = 8 and 8 = 8. Because both of these points are in the set, this set fails the definition of a function, and so it is not a function.

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Answer:

Step-by-step explanation:

Let two consecutive odd integers be x and x+2

Given, their sum is 20.

x+x+2=20

2x=20−2

2x = 18

x=9

Therefore, other number is

x+2=9

9+2=11.

Thus, the numbers are 9,11.

----------------

check

9 + 9 + 2 = 20

20 = 20

the answer is good

The value of the greater integer is 7.

Addition is a way of combining things and counting them together as one large group. ... Addition in math is a process of combining two or more numbers.

here, we have,

The sum of an integer and 2 times the next consecutive integer is 20.

let, the number = x

so, the next consecutive integer = x+1

ATQ, x+2(x+1)=20

    ⇒3x+2=20

    ⇒3x=18

    ⇒x=6

i.e. the greater integer = x+1 = 7

Hence, the value of the greater integer is 7.

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If the conditions for a binomial distribution are met, the variance, given the number of trials (n) and the probability of success(p) is given as:

Given:

n = 170

p = 0.7

Solution

By substituting the given values, the variance is:

Answer: 35.7

Answer:

1/2

Step-by-step explanation:

p(event) = (number of desired outcomes)/(total number of outcomes)

How many different outcomes are there? You can choose 1, 2, 3, 4, 5, 6, 7, 8, 9, or 10, so the total number of possible outcomes is 10.

How many outcomes are desired. The desired outcomes are any outcomes with a number 6 or higher. Which numbers are 6 or higher? 6, 7, 8, 9, 10. There are 5 outcomes that are 6 or higher, so there are 5 desired outcomes.

p(event) = (number of desired outcomes)/(total number of outcomes)

p(event) = 5/10 = 1/2

Answer: 1/2

Answer:

its c

Step-by-step explanation:

easy 23 simple mulitply then add

Quantities that are proportional to each other are,

A) radius and diameter of a circle

B) radius and circumference of a circle

C) radius and area of a circle

D) diameter and circumference of a circle

E) diameter and area of a circle​

A ratio is a comparison between two similar quantities in simplest form.

Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant k and vice versa.

In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.

We know the radius of a circle is r and the diameter of a circle is 2r.

We also know that the circumference of a circle is 2πr and the area of a circle is π(r)².

Now the quantities that will be related to each other are the quantities that are together linked in the formula of circumference and area.

∴ Radius and diameter of a circle, Radius, and circumference of a circle, Radius and area of a circle, Diameter and circumference of a circle, and Diameter and area of a circle​ all are related to each other and are directly proportional.

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The equation x⁴ - 14x² + 49 = 0 can be factored as (x - √7)(x + √7)(x - √7)(x + √7) = 0.

To solve the equation x⁴ - 14x² + 49 = 0 by factoring, we can rewrite it as a quadratic equation in terms of x².

Let's substitute y = x²:

y² - 14y + 49 = 0

This is a simple quadratic equation that can be factored as (y - 7)² = 0. Applying the square root property, we have:

y - 7 = 0

Solving for y, we find that y = 7. Now, let's substitute back x² for y:

x² = 7

Taking the square root of both sides, we get two solutions:

x = √7 and x = -√7

The solutions are x = √7 and x = -√7.

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Report on Commonalities Among Three Chosen Regions

For this assignment, three regions of the world have been selected to identify commonalities among them. The chosen regions are North America, Europe, and East Asia. Through internet research, several commonalities have been identified that are shared among these regions. Below are five commonalities found:

Economic Development:

All three regions, North America, Europe, and East Asia, are characterized by significant economic development. They are home to some of the world's largest economies, such as the United States, Germany, China, and Japan. These regions exhibit high levels of industrialization, technological advancement, and trade activities. Their economies contribute significantly to global GDP and are major players in international commerce.

Technological Advancement:

Another commonality among these regions is their emphasis on technological advancement. They are known for their innovation, research and development, and technological infrastructure. Companies and industries in these regions are at the forefront of technological advancements in fields such as information technology, automotive manufacturing, aerospace, pharmaceuticals, and more.

Cultural Diversity:

North America, Europe, and East Asia are culturally diverse regions, with a rich tapestry of different ethnicities, languages, and traditions. Immigration and historical influences have contributed to the diversity seen in these regions. Each region has a unique blend of cultural practices, cuisines, art, music, and literature. This diversity creates vibrant multicultural societies and fosters an environment of cultural exchange and appreciation.

Democratic Governance:

A commonality shared among these regions is the prevalence of democratic governance systems. Many countries within these regions have democratic political systems, where citizens have the right to participate in the political process, elect representatives, and enjoy individual freedoms and rights. The principles of democracy, rule of law, and respect for human rights are important pillars in these regions.

Education and Research Excellence:

North America, Europe, and East Asia are known for their strong education systems and institutions of higher learning. These regions are home to prestigious universities, research centers, and educational initiatives that promote academic excellence. They attract students and scholars from around the world, offering a wide range of educational opportunities and contributing to advancements in various fields of study.

In conclusion, the regions of North America, Europe, and East Asia share several commonalities. These include economic development, technological advancement, cultural diversity, democratic governance, and education and research excellence. Despite their geographical and historical differences, these regions exhibit similar traits that contribute to their global significance and influence.

Answer:

For this assignment, three regions of the world have been selected to identify commonalities among them. The chosen regions are North America, Europe, and East Asia. Through internet research, several commonalities have been identified that are shared among these regions. Below are five commonalities found:

Economic Development:

All three regions, North America, Europe, and East Asia, are characterized by significant economic development. They are home to some of the world's largest economies, such as the United States, Germany, China, and Japan. These regions exhibit high levels of industrialization, technological advancement, and trade activities. Their economies contribute significantly to global GDP and are major players in international commerce.

Technological Advancement:

Another commonality among these regions is their emphasis on technological advancement. They are known for their innovation, research and development, and technological infrastructure. Companies and industries in these regions are at the forefront of technological advancements in fields such as information technology, automotive manufacturing, aerospace, pharmaceuticals, and more.

Cultural Diversity:

North America, Europe, and East Asia are culturally diverse regions, with a rich tapestry of different ethnicities, languages, and traditions. Immigration and historical influences have contributed to the diversity seen in these regions. Each region has a unique blend of cultural practices, cuisines, art, music, and literature. This diversity creates vibrant multicultural societies and fosters an environment of cultural exchange and appreciation.

Democratic Governance:

A commonality shared among these regions is the prevalence of democratic governance systems. Many countries within these regions have democratic political systems, where citizens have the right to participate in the political process, elect representatives, and enjoy individual freedoms and rights. The principles of democracy, rule of law, and respect for human rights are important pillars in these regions.

Education and Research Excellence:

North America, Europe, and East Asia are known for their strong education systems and institutions of higher learning. These regions are home to prestigious universities, research centers, and educational initiatives that promote academic excellence. They attract students and scholars from around the world, offering a wide range of educational opportunities and contributing to advancements in various fields of study.

In conclusion, the regions of North America, Europe, and East Asia share several commonalities. These include economic development, technological advancement, cultural diversity, democratic governance, and education and research excellence. Despite their geographical and historical differences, these regions exhibit similar traits that contribute to their global significance and influence.

Answer:

Step-by-step explanation:

10

Answer:

-300

Step-by-step explanation:

-21 = 7x/100

-21=7x/2^2*5^2

x=-300