You are downloading songs to your tablet. Th e ratio
of pop songs to rock songs is 5 : 4. You download 40 pop songs. How many rock
songs do you download?

Answer:

c=42

Step-by-step explanation:

#4= -8

#5= 781

#6= 1.34×10(3) (Exponent)

The given series is a divergent p-series, as the exponent of n in the denominator is 1/2, which is not greater than 1.

The given series is a p-series of the form ∑\((1/n^p)\), where n starts from 32 and goes up to 3125, and p is the exponent of n in the denominator. According to Theorem 9.11 (p-series convergence), a p-series converges if p > 1 and diverges if p ≤ 1.

Let's analyze the given series step by step:

The given series is: \(\frac{1}{32\sqrt{2}} + \frac{1}{243\sqrt{3}} + \frac{1}{1024\sqrt{4}} + \frac{1}{3125\sqrt{5}}\)

The denominator of each term is in the form \(n^{p/2}\), where n is the value from 32 to 3125, and p is the exponent.

Using Theorem 9.11, we can determine the convergence or divergence of the series based on the value of p.

Since the exponent of n in the denominator is 1/2, we can rewrite the series as: \(\sum \left( \frac{1}{n^{\frac{1}{2} \cdot 2}} \right)\)

Simplifying, we get: ∑(1/n), which is a p-series with p = 1.

According to Theorem 9.11, a p-series converges if p > 1 and diverges if p ≤ 1.

In this case, p = 1, which is not greater than 1.

Therefore, by Theorem 9.11, the given series diverges.

In conclusion, the given series is a divergent p-series, as the exponent of n in the denominator is 1/2, which is not greater than 1.

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Random assignment and random selection are both important concepts in research methodology, but they refer to different processes.

Random selection refers to the process of selecting individuals or elements from a population to be included in a study. The goal of random selection is to ensure that the sample is representative of the larger population. This helps to increase the generalizability of the findings to the population as a whole. For example, if a researcher wants to study the academic performance of high school students in a particular city, they might use random selection to select a sample of students from different schools in that city. This helps to ensure that the sample represents the diversity of students in the population.

On the other hand, random assignment refers to the process of assigning participants to different groups or conditions in a study. The goal of random assignment is to minimize any pre-existing differences between the groups, making it more likely that any differences observed between the groups can be attributed to the independent variable being studied. For example, if a researcher wants to investigate the effectiveness of a new teaching method, they might randomly assign half of the participants to receive the new method and the other half to receive the traditional method. Random assignment helps to ensure that the groups are comparable at the start of the study, reducing the likelihood of confounding variables.

In summary, random selection is about selecting a representative sample from a population, while random assignment is about assigning participants to groups or conditions in a study. Both processes are important in research methodology to ensure accurate and reliable findings.

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Answer:

The error in his prediction is that he had too small of a sample size for the data to be reliable in how the trend would continue.

Answer:

He did not perform enough trials to compare the theoretical and experimental probabilities.

Step-by-step explanation:

Answer:

Plots that can detect violations in regression assumptions, while response plots help analyse the relationship between the response variable and predictors are Residual plots and scatterplot matrix.

Step-by-step explanation:

There are several graphical plots commonly used to detect violations of regression model assumptions and analyze estimated regression models. Here are a few examples:

Residual plot: A residual plot shows the difference between the observed values of the response variable and the predicted values from the regression model. Patterns in the residuals, such as nonlinearity, heteroscedasticity (unequal variances), or outliers, can indicate violations of assumptions.

Response plot: This plot examines the relationship between the response variable and one of the predictor variables while holding other predictors constant. It helps identify nonlinearity or other issues in the relationship between the response and predictors.

Scatterplot matrix: A scatterplot matrix displays scatterplots between pairs of predictor variables. It can help detect issues like perfect multicollinearity, which occurs when two or more predictors are highly correlated, leading to problems in estimating the regression coefficients.

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Of the 180 students in a college course, of the 4 1 students earned an a for the course, of the students 3 earned a b for the course, and the rest of the students earned a c for the course. So, 136 students earned a C for the course.

To find the number of students who earned a C in the course, we'll follow these steps:

1. Determine the total number of students in the course.
2. Find out how many students earned an A and how many earned a B.
3. Subtract the number of A and B students from the total to find the number of C students.

We are given that there are 180 students in the course. It is also mentioned that 41 students earned an A and 3 students earned a B.

Now let's perform the calculations:

Step 1: We know that the total number of students is 180.

Step 2: We need to find the combined number of A and B students. We are given that 41 students earned an A, and 3 students earned a B. So, to find the total number of A and B students, we simply add these two numbers:

41 (A students) + 3 (B students) = 44 (A and B students)

Step 3: To find the number of C students, we subtract the total number of A and B students (44) from the total number of students (180):

180 (total students) - 44 (A and B students) = 136 (C students)

So, 136 students earned a C for the course.

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You slept for 9 hours in those three days, calculated by multiplying 12.5% of the total hours (72) by 72, which equals 9.

To calculate the number of hours slept in three days, we first need to determine how many hours there are in three days.

As given, 1 day has 24 hours. So, three days will have 3 x 24 = 72 hours.

Now, we are told that you slept for 12.5% of those 72 hours. To calculate this, we multiply the percentage by the total number of hours:

12.5% x 72 hours = (12.5/100) x 72 = 0.125 x 72 = 9 hours

Therefore, you slept for 9 hours in those three days.

Percentage is a way to express a proportion or ratio as a fraction of 100. The sign "%" is widely used to represent it. For example, if you had 20 apples and you ate 5 of them, you would have consumed 25% of the apples (5 out of 20).

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The number of cans required to paint an area of 2000 square units is equal to 5 cans.

As given in the question,

Total area to be painted is equal to 2000 square units.

Area covered by one can of paint is equal to 400 square units

400 square units = 1 can of paint

⇒ 1 square units = ( 1 / 400 ) cans of paint

⇒ 2000 square units =  ( 2000 / 400 ) cans of paint

⇒ 2000 square units = 5 cans of paint

Therefore, the number of cans required to paint an area of 2000 square units using given can is equal to 5 cans.

The above question is incomplete, the complete question is:

How many cans of paint are needed to cover an area of 2000 square units if one can of paint covers in area 400 square units?

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The perimeter of the polygon will be 30 units. Then the correct option is D.

All the sides of the regular polygon are congruent to each other. The perimeter of the regular polygon of n sides will be the product of the number of the side and the side length of the regular polygon.

P = (Side length) x n

The sides length of the polygon is 10 units, 5 units, 3 units, 2.5 units, 7 units, and 2.5 units.

Then the perimeter of the polygon is given as,

P = 10 + 5 + 3 + 2.5 + 7 + 2.5

P = 30 units

The perimeter of the polygon will be 30 units. Then the correct option is D.

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Answer:

A quadratic equation is a polynomial equation of degree 2 . The standard form of a quadratic equation is

0=ax2+bx+c

where a,b and c are all real numbers and a≠0 .

If we replace 0 with y , then we get a quadratic function

y=ax2+bx+c

whose graph will be a parabola .

The axis of symmetry of this parabola will be the line x=−b2a . The axis of symmetry passes through the vertex, and therefore the x -coordinate of the vertex is −b2a . Substitute x=−b2a in the equation to find the y -coordinate of the vertex. Substitute few more x -values in the equation to get the corresponding y -values and plot the points. Join them and extend the parabola.

Example 1:

Graph the parabola y=x2−7x+2 .

Compare the equation with y=ax2+bx+c to find the values of a , b , and c .

Here, a=1,b=−7 and c=2 .

Use the values of the coefficients to write the equation of axis of symmetry .

The graph of a quadratic equation in the form y=ax2+bx+c has as its axis of symmetry the line x=−b2a . So, the equation of the axis of symmetry of the given parabola is x=−(−7)2(1) or x=72 .

Substitute x=72 in the equation to find the y -coordinate of the vertex.

y=(72)2−7(72)+2    =494−492+2    =49 − 98 + 84     =−414

Answer:

$261,500

Step-by-step explanation:

What amount should Nash report as its December 31 inventory?

Item                                                             Amount

Goods on hand as per physical count    $208,000

(+) Goods purchased from Swifty             $30,000

Corporation FOB shipping point    

(+) Goods sold to Marigold Corp               $23,500

FOB destination (at cost value)

Ending inventory                                        $261,500

Notes:

1) In case of FOB shipping point, the ownership of goods is transferred to the buyer when the goods are shipped and hence in the case of purchases from Swifty corporation, the goods should be included in the inventory of Nash's Trading Post as the goods are shipped and are in transit.

2) In case of FOB destination, the ownership of goods is transferred to the buyer when the goods reaches to the buyer, hence in the case of sales made to Marigold Corp, the goods are still in transit and the ownership is not transferred to Marigold Corp, hence Nash's Trading Post should included that goods in its inventory.

Answer: 60°C

Step-by-step explanation:

Because you would find the absolute number of the negative so it would be 13 instead of -13 and then you add it to 47..... 13+47=60

Answer:

it has two zeros because it is touching x axis two times

Answer:

Hi,

Step-by-step explanation:

\(\begin{array}{|c|c|c|c|}x&3x^2+5&\Delta_1x&\Delta_2x\\--&--&--&--\\0&5&-&-\\1&8&3&-\\2&17&9&6\\3&32&15&6\\4&53&21&6\\--&--&--&--\\\end{array}\)

Answer: Hello

Step-by-step explanation: The answer is

1/3 (3/2 x -3) = -5/6x

Answer: x=3/4

Hope This Helps!

Answer:

x=3/4

Step-by-step explanation:

1/3 times 3/2 x is 1/2x

1/3 times -3 is -1

1/2x-1=-5/6x

1/2 is equal to 3/6

-1=-5/6x-3/6x

-1=-8/6x

x=6/8

x=3/4

Answer: The slope is 0

Step-by-step explanation:

The main difference between everyday logic and mathematical logic is that everyday logic is based on general observations and opinions, while mathematical logic is based on precise statements and facts.

Differences:
- Everyday logic is based on common sense and intuition, while mathematical logic is based on strict rules and formulas.
- Everyday logic is often used to make decisions or solve problems in daily life, while mathematical logic is used to solve complex mathematical problems.
- Everyday logic can be subjective and influenced by personal beliefs or experiences, while mathematical logic is objective and follows a set of universally accepted principles.

Similarities:
- Both everyday logic and mathematical logic use reasoning to draw conclusions.
- Both everyday logic and mathematical logic rely on evidence and facts to support their conclusions.
- Both everyday logic and mathematical logic can be used to solve problems and make decisions.

In conclusion, while everyday logic and mathematical logic have some similarities in terms of their use of reasoning and evidence, they differ in their approach and application. Everyday logic is based on common sense and intuition, while mathematical logic is based on strict rules and formulas.

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Answer:

2.39130435

Step-by-step explanation:

[(51+3)-32]÷9.2

[54-32]÷9.2.

22÷9.2

2.39130435

A rational equation is defined as the quotient of two polynomials, with the denominator not being zero. It is a type of algebraic expression that involves variables and rational functions with rational exponents.

The error in the given rational equation is that it's not allowed to cancel out the x-2 and X+2 terms, as they are in the denominators. It is because of the fact that it may make the denominator zero, which would result in undefined expressions. Therefore, we need to find the least common multiple (LCM) of the denominators and then convert the equation into equivalent forms with the same denominator.B):

Correction of the error1-2/x-2 = x+1/X+2Given rational equation can be re-written as:((1 - 2)/(x - 2)) = ((x + 1)/(X + 2))The LCM of x - 2 and X + 2 is (x - 2) (X + 2).Multiplying the numerator and denominator of the left side by (X + 2) and the numerator and denominator of the right side by (x - 2) we get,(1 - 2)(X + 2) = (x + 1) (x - 2)Now simplify the equation:2X - 3x = -3The given rational equation becomes 2X - 3x = -3 after correction.Note: You should always double-check if the obtained solution satisfies the initial equation.

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We can represent 0.614 using only 5 tenths as \(\mathbf{\dfrac{6.14}{10}}\)

A decimal is a number that is divided into two parts: a whole and a fraction. Between integers, decimal numbers are used to express the numerical value of complete and partially whole quantities.

The accepted method for representing both integer and non-integer numbers is the decimal number system.

From the given information, we are to represent 0.614 by using only 5 tenths.

Representing 0.614 in the same form, we have:

\(\mathbf{=\dfrac{0.614\times 1000}{1\times 1000}}\)

\(\mathbf{=\dfrac{614}{1000}}\)

\(\mathbf{=\dfrac{6.14}{10}}\)

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Answer: 6.14/10

Step-by-step explanation:

Answer:

They are parallel because they both have the same gradient of 5.

Step-by-step explanation:

For lines to be parallel they need to contain the same gradient.

1. therefore we rearrange the second equation to get y the subject so it's in the format of y=mx+c

2.       2y-10x+3=0

- we +10x and -3 on both sides to get y on its own

         2y=10x-3

- we divide each side by 2 as we want y not 2y

          y=5x-\(\frac{3}{2}\)

3. From this we can see that both the equation contains the same gradient (5)

therefore, they are parallel.

Answer:

\(\sqrt{x^2+y^2}-x\)

Step-by-step explanation:

\(\textsf{Mulitply by}\quad\dfrac{\sqrt{x^2+y^2}-x}{\sqrt{x^2+y^2}-x}:\)

\(\implies \dfrac{y^2}{\sqrt{x^2+y^2}+x} \times \dfrac{\sqrt{x^2+y^2}-x}{\sqrt{x^2+y^2}-x}\)

\(\implies \dfrac{y^2(\sqrt{x^2+y^2}-x)}{(\sqrt{x^2+y^2}+x)(\sqrt{x^2+y^2}-x)}\)

\(\implies \dfrac{y^2(\sqrt{x^2+y^2}-x)}{(\sqrt{x^2+y^2})^2-x^2}\)

\(\implies \dfrac{y^2(\sqrt{x^2+y^2}-x)}{x^2+y^2-x^2}\)

\(\implies \dfrac{y^2(\sqrt{x^2+y^2}-x)}{y^2}\)

\(\textsf{Cancel the common factor}\:y^2:\)

\(\implies \sqrt{x^2+y^2}-x\)

Rationalising the denominator of the given fraction means we need to multiply both the numerator and the denominator of the fraction by the conjugate of the expression in the denominator. For example:

\(\;\longrightarrow\dfrac{1}{a+b}\)

Here the conjugate of denominator of the expression is a - b. So we need to multiply both the numerator and denominator with the fraction.

\(\;\longrightarrow \dfrac{1}{a+b} \times \dfrac{a-b}{a-b}\)

Hence, this is what the rationalization means.

We have been given and equation and we have been asked to rationalise the equation.

The conjugate of the denominator of the given equation is √(x² + y²) - x. Therefore;

\(\implies \dfrac{y^2}{\sqrt{x^2+y^2}+x} \times \dfrac{\sqrt{x^2+y^2}-x}{\sqrt{x^2+y^2}-x}\)

\(\implies \dfrac{y^2(\sqrt{x^2+y^2}-x)}{(\sqrt{x^2+y^2}+x)(\sqrt{x^2+y^2}-x)}\)

\(\implies \dfrac{y^2(\sqrt{x^2+y^2}-x)}{(\sqrt{x^2+y^2})^2-x^2}\)

\(\implies \dfrac{y^2(\sqrt{x^2+y^2}-x)}{x^2+y^2-x^2}\)

\(\implies \dfrac{y^2(\sqrt{x^2+y^2}-x)}{y^2}\)

\(\implies \boxed{\sqrt{x^2+y^2}}\)

Hence, this is our required solution for this question.

Answer:

a) $1961

b) $710

c) $2671

Step-by-step explanation:

Bi-weekly mortgage & taxes: 718/2 weeks = 2 x 718 = $1436/month

Condo fees: $525/month

Electricity bill bi-monthly $320/2 weeks = 2 x 320 = $640/month

Water bill is quarterly, so 210/3 months. 210/3 = $70/month

a) housing expenses = mortgage, taxes, condo fees

1436 + 525 = $1961

b) utilities = electricity and water

640 + 70 = $710

c) all expenses listed

1961 + 710 = $2671

Answer:

The answer is A. 135 cm2.

Area of a parallelogram is base * height. In this case, the base is 24 cm and the height is 9 cm. Therefore, the area is 24 * 9 = 135 cm2.

Answer: the answer would be 360

Step-by-step explanation:

the equation for area of a parallelogram is base x height.

The base is 24 as it is at the top of the shape.

The height is 15 as well since a parallelogram is congruent.

multiply the two and it gives you 360

Using the linear approximating polynomial, e^(-0.7) is approximately 1.7, and using the quadratic approximating polynomial, e^(-0.7) is approximately 1.945.

To find the linear approximating polynomial, we need the first-degree Taylor polynomial centered at a = 0. The linear approximating polynomial is given by p_1(x) = f(a) + f'(a)(x - a), where f(x) = e^(-x).

First, we find f(a) and f'(a):

f(a) = f(0) = e^0 = 1

f'(a) = f'(0) = -e^0 = -1

Substituting these values into the linear approximating polynomial, we get:

p_1(x) = 1 - 1(x - 0) = 1 - x

b. To find the quadratic approximating polynomial, we need the second-degree Taylor polynomial centered at a = 0. The quadratic approximating polynomial is given by p_2(x) = f(a) + f'(a)(x - a) + (1/2)f''(a)(x - a)^2.

First, we find f''(a):

f''(a) = f''(0) = -f'(0) = -(-1) = 1

Substituting all the values into the quadratic approximating polynomial, we get:

p_2(x) = 1 - 1(x - 0) + (1/2)(1)(x - 0)^2

= 1 - x + (1/2)x^2

= 1 - x + (1/2)x^2

c. Using the linear approximating polynomial p_1(x) = 1 - x, we can approximate e^(-0.7) by substituting x = -0.7:

p_1(-0.7) = 1 - (-0.7) = 1 + 0.7 = 1.7

Using the quadratic approximating polynomial p_2(x) = 1 - x + (1/2)x^2, we can approximate e^(-0.7) by substituting x = -0.7:

p_2(-0.7) = 1 - (-0.7) + (1/2)(-0.7)^2 = 1 + 0.7 + (1/2)(0.49) = 1 + 0.7 + 0.245 = 1.945

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Answer:

240inch per min

Step-by-step explanation:

4inch per 1 sec

×60 for inch per min

240 inch per min.

The exponential function between (-1, 2/5) and (3, 250) is as follows:

\(f(x) = 2 * 5^x\)

By combining the fourth roots from both sides, we arrive at:

b = 5

When we use the expression we discovered for a and this value of b, we get:

a = (2/5) * 5 = 2

As a result, the exponential function between (-1, 2/5) and (3, 250) is as follows:

\(f(x) = 2 * 5^x\)

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input. A function is typically represented as y = f. (x).

In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.

from the question:

This is the shape of the exponential function:

f(x) = a *\(b^x\)

where a represents the starting point and b represents the exponential function's base.

We must solve the system of equations to determine the values of a and b that meet the requirements:

a * \(b^(-1)\) = 2/5 (equation 1) 

a *\(b^3\)= 250 (equation 2) 

We can solve for an in equation 1 by multiplying both sides by b:

a = (2/5) * b

Substituting this expression into equation 2, we get:

(2/5) * b *\(b^3\) = 250

Simplifying, we get:

\(b^4 = 3125\)

By combining the fourth roots from both sides, we arrive at:

b = 5

When we use the expression we discovered for a and this value of b, we get:

a = (2/5) * 5 = 2

As a result, the exponential function between (-1, 2/5) and (3, 250) is as follows:

\(f(x) = 2 * 5^x\)

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