If an object travels at 6 feet per second, how many feet does it travel in 4 hours?

It will take 4 hours for Ashley to clean the house alone.Answer: Ashley will take 4 hours to clean the house alone.

Given:Ashley and Rod cleaned the house in 4 hours. Rod can clean the house alone in 2 hours.To find:How long will it take for Ashley to clean the house alone?Solution:Let's suppose the time Ashley takes to clean the house alone is x hours.Then, Ashley and Rod can clean the house in 4 hours.Thus, using the concept of work, we have:\begin{aligned} \text { Work done by Ashley in 1 hour } + \text { Work done by Rod in 1 hour } &= \text { Work done by Ashley and Rod in 1 hour } \\ \Rightarrow \frac {1}{x} + \frac {1}{2} &= \frac {1}{4} \\ \Rightarrow \frac {2 + x}{2x} &= \frac {1}{4} \\ \Rightarrow 8 + 4x &= 2x \\ \Rightarrow 2x - 4x &= -8 \\ \Rightarrow x &= 4 \end{aligned}Therefore, it will take 4 hours for Ashley to clean the house alone.Answer: Ashley will take 4 hours to clean the house alone.

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The solution of expression is,

⇒ (6 + a⁴b) / a²b²

We have to given that,

An expression to solve is,

⇒ 6/a²b² + a²/b

Since, Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Now, WE can simplify the expression as,

⇒ 6/a²b² + a²/b

Take LCM;

⇒ (6 + a² × a²b)  / a²b²

⇒ (6 + a⁴b) / a²b²

Therefore, The solution of expression is,

⇒ (6 + a⁴b) / a²b²

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Answer:

n = x + 8

Step-by-step explanation:

Using the rules of exponents

\(a^{m}\) × \(a^{n}\) = \(a^{(m+n)}\)

\((a^m)^{n}\) = \(a^{mn}\)

Then

\(3^{x}\) × \(9^{4}\) = \(3^{n}\)

\(3^{x}\) ×\((3^2)^{4}\) = \(3^{n}\)

\(3^{x}\) × \(3^{8}\) = \(3^{n}\)

\(3^{x+8}\) = \(3^{n}\)

Since bases on both sides are equal, both 3, then equate exponents

n = x + 8

The maximum distance the mouse can jump is 30.0029 ft. This means that the mouse can jump 30.0029 feet horizontally.

Given that y=−0.2222x2+1.3333x represents how high (in feet) the mouse can jump for a relatively long hop modeled, where x represents how far (in feet) the mouse can jump.

To determine how high the mouse can jump, we are given the equation of the hop as; y = −0.2222x² + 1.3333x

We will use the given equation to find out the maximum height attained by the mouse. We are given that a relatively long hop can be modeled by y=−0.2222x²+1.3333x.

Using the quadratic formula, we can determine the maximum height by evaluating the value of x using the formula;

x = -b/2a

Where a = -0.2222 and b = 1.3333x = -1.3333 / 2(-0.2222) = 30.0029 ft

We can substitute this value into the equation to determine how high the mouse can jump.

y = −0.2222(30.0029)² + 1.3333(30.0029)≈ 5.00 ft.

Therefore, the maximum height the mouse can jump is 5.00 ft.

To determine how far the mouse can jump horizontally, we need to determine the value of x that maximizes y.

We can achieve this using the formula;

x = -b/2a

Where a = -0.2222 and b = 1.3333x = -1.3333 / 2(-0.2222) = 30.0029 ft.

Therefore, the maximum distance the mouse can jump is 30.0029 ft.

This means that the mouse can jump 30.0029 feet horizontally.

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The 3 cans of peas cost 39 = $27

The 5 bags of flour cost 515 = $75

The 7 packs of milk cost 7*12.50 = $87.50

The total cost of all the items is 27+75+87.50 = $189.50

To calculate the change she received, you subtract the total cost from the amount she had:

change = 200 - 189.50 = $10.50

So Alicia received $10.50 change.

I'm not sure if you mean ( \( \sqrt{x + 7} \) ) or ( \( \sqrt{x} + 7\) ) I solved it both ways .

\(f(x) = \sqrt{x + 7} \\ \\ f( \: g(x) \: ) = \sqrt{(8x - 11)+ 7} \\ = \sqrt{8x - 11 + 7} \\ = \sqrt{8x - 4} \\ = 2 \sqrt{2x - 1} \)

____o_____o______

\(f(x) = \sqrt{x} + 7 \\ \\ f( \: g(x) \: ) = \sqrt{(8x - 11)} + 7 \\ = \sqrt{8x - 11} + 7\\ \)

I hope I helped you^_^

An expression for cos(2θ) in terms of x is cos(2θ) = 1 - 2x²

To find an expression for cos(2θ) in terms of x, we can use the double angle identity for cosine:

cos(2θ) = 2cos²(θ) - 1

Since we know sin(θ) = x, we can use the Pythagorean identity for sine and cosine to find cos(θ):

cos²(θ) = 1 - sin²(θ) = 1 - x²

Now we can substitute this expression for cos²(θ) into the double angle identity:

cos(2θ) = 2(1 - x²) - 1 = 1 - 2x²

Therefore, an expression for cos(2θ) in terms of x is:

cos(2θ) = 1 - 2x²

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Answer:

- x+2y= - 4

2y= - x - 4

Y=x-4/2

Y=x-2

Now, 2nd equation

4x+3y=5

4x+3.x-2=5

4x+3x-2=5

7x-2=5

7x=5+2

x=5+2/7

x=7/7

x=1

Now, continue with 1st equation

y=x-2

y=1-2

y=1

Therefore x=1

And

y=1

Answer:

y <= 0

Step-by-step explanation:

it's shaded when the value of y is 0 or below 0 (the vertical axis)

Answer:

c)  36, 48, 60

Step-by-step explanation:

A Pythagorean Triple is a set of positive integers (a, b, c) that follows the rule:

\(\boxed{a^2+b^2=c^2}\)

where a < c and b < c.

It always consists of:

When a and b are both even, c is even.

When one of a and b is odd and the other is even, c is odd.

(5, 7, 9) cannot be a Pythagorean Triple since it consists of all odd numbers.

(17, 20, 23) is not a Pythagorean Triple since:

\(\implies 17^2+20^2=23^2\)

\(\implies 289+400=529\)

\(\implies 689 \neq 529\)

(36, 48, 60) is a Pythagorean Triple since:

\(\implies 36^2+48^2=60^2\)

\(\implies 1296+2304=3600\)

\(\implies 3600=3600\)

(19, 22, 25) is not a Pythagorean Triple since:

\(\implies 19^2+22^2=25^2\)

\(\implies 361+484=625\)

\(\implies 845\neq 625\)

To have a total mass of 100 kg, we should set k ≈ 1.85 kg/m^2.

The mass of a thin metal plate can be found by integrating its density over its surface area. In this case, the surface area is the rectangle [0, 3] × [0, 2]. So we have:

Total mass = ∬[0,3]×[0,2] ρ(x,y) dA

= ∫0^2 ∫0^3 2y kx^2 dxdy (switching the order of integration)

= k * ∫0^2 ∫0^3 2y x^2 dxdy

= k * ∫0^2 [y * x^3]0^3 dy

= k * ∫0^2 27y dy

= k * [13.5y^2]0^2

= 0

This means that the total mass is 0 unless we choose a value of k that makes the integral nonzero. Since we want the total mass to be 100 kg, we can set the integral equal to 100 and solve for k:

100 = k * ∫0^2 ∫0^3 2y x^2 dxdy

100 = k * ∫0^2 [y * x^3]0^3 dy

100 = k * ∫0^2 27y dy

100 = k * [13.5y^2]0^2

100 = k * 54

k = 100/54

k ≈ 1.85 kg/m^2

Therefore, we should set the value of k ≈ 1.85 kg/m^2.

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The expression for the difference of two linear functions is (f - g)(x) = 4x - 6.

A linear function is a type of function in mathematics that has the form f(x) = mx + b, where x is the independent variable, f(x) is the dependent variable, m is the slope of the line, and b is the y-intercept.

To find the expression for the difference of two linear functions, f(x) and g(x), denoted by (f - g)(x).

The expression for (f - g)(x) can be found by subtracting g(x) from f(x):

(f - g)(x) = f(x) - g(x)

Substituting the given functions f(x) = x - 2 and g(x) = -3x + 4, we get:

(f - g)(x) = f(x) - g(x)

= (x - 2) - (-3x + 4) [Substitute the given values of f(x) and g(x)]

= x - 2 + 3x - 4 [Distribute the negative sign in front of (-3x + 4)]

= 4x - 6 [Combine like terms]

Therefore, (f - g)(x) = 4x - 6.

Option D (-3x² - 2x - 8) is incorrect as it involves squaring a linear expression, which would result in a quadratic expression. Option A (which has no operation between 3 and 22) is not a valid expression. Option B (-3x - 8) and C (3x3x22 or 198) do not take into account the fact that each sundae can be made using one of 3 syrups and one of 3 candy toppings.

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We can gain a comprehensive understanding of the distribution and characteristics of a quantitative variable.

In mathematics, a variable is referred to as the alphanumeric symbol used to represent a number or numerical value. An unknown quantity is represented as a variable in algebraic equations. From a to z, these variables can be any alphabet.

The four key features used in describing a graphical display of a quantitative variable are:

1. Shape: The shape of the distribution refers to whether it is symmetric or skewed. A symmetric distribution has a similar shape on both sides of the center, while a skewed distribution is asymmetrical, with one tail longer or stretched out compared to the other. Additionally, the shape can also indicate whether there are multiple peaks or modes in the distribution.

2. Center: The center of the distribution represents the typical or average range of values. It is often described using measures such as the mean, median, or mode. These measures provide information about the central tendency of the data.

3. Spread: The spread, also known as variability or dispersion, describes how much the data points deviate from the center. It provides information about the range or extent of values in the dataset. Common measures of spread include the range, interquartile range (IQR), variance, and standard deviation.

4. Outliers/Unusual features: Outliers are data points that significantly deviate from the rest of the dataset. They can indicate extreme values or errors in measurement. Unusual features refer to any other noteworthy characteristics or patterns observed in the data, such as clusters, gaps, or unusual shapes that do not conform to a typical distribution.

By considering these four key features, we can gain a comprehensive understanding of the distribution and characteristics of a quantitative variable.

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The four key features used in describing a graphical display of a quantitative variable are the:

Shape: Is the distribution symmetric or skewed? Are there multiple 'peaks?'

Center: What seems to be a 'typical' range of values?

Spread: How variable is the data set?

Outliers/unusual features: Are there any other odd things to note?

Answer:

a. 19

b. Subtract by 13, then divide by 6.

Step-by-step explanation:

-2, _ , _

-2(6) = -12

-12+13=1.

-2, 1, _

1(6)=6

6+13=19

a. 19 is your third term

If the three terms of the sequence are reversed:

19, 1, -2

The new term-to-term rule would be:

b. Subtract by 13, then divide by 6.

19 - 13 = 6 / 6

= 1

1-13= -12 / 6 = -2.

Answer:

x = 1/3

Step-by-step explanation:

f(x) = -3x^2 + 2x-17

This is in the form

ax^2 +bx+c

a = -3  b = 2  c = -17

The axis of symmetry is at

x = -b/2a

x = -2/ (2*-3)

x = -2/-6

x = 1/3

Probability is a measure of the likelihood or chance of an event occurring. To find the probability that the sum of the two bills drawn is $20 or more, we need to consider the different combinations of bills that satisfy this condition.

Let's analyze the possibilities:

1. Drawing two $20 bills: There are two $20 bills in the envelope. The probability of drawing one $20 bill first is 2/8, and the probability of drawing the second $20 bill without replacement is 1/7. Therefore, the probability of this case is (2/8) * (1/7).

2. Drawing one $20 bill and one $10 bill: There are two $20 bills and two $10 bills in total. The probability of drawing one $20 bill first is 2/8, and the probability of drawing one $10 bill without replacement is 2/7.

However, we also need to consider the case where the $10 bill is drawn first, followed by a $20 bill. So the probability of this case is [(2/8) * (2/7)] + [(2/8) * (2/7)].

3. Drawing two $10 bills and no $20 bill: There are two $10 bills in total. The probability of drawing one $10 bill first is 2/8, and the probability of drawing the second $10 bill without replacement is 1/7.

Therefore, the probability of this case is (2/8) * (1/7).

Adding up the probabilities of these three cases will give us the total probability of drawing two bills with a sum of $20 or more:

(2/8) * (1/7) + [(2/8) * (2/7)] + (2/8) * (1/7) = 1/28 + 2/28 + 1/28 = 4/28Simplifying, we get:4/28 = 1/7

Therefore, the probability that the sum of the two bills drawn is $20 or more is 1/7 or approximately 0.142857.

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Answer:

hope i helped

Step-by-step explanation:

The x and y intercept of the given equation is required.

The x intercept is \(\left(\dfrac{2}{3},0\right)\)

The y intercept is \(\left(0,-\dfrac{1}{3}\right)\).

The given equation is

\(3x-6y=2\)

The x intercept is the point where \(y=0\)

\(3x-6\times 0=2\\\Rightarrow x=\dfrac{2}{3}\)

\(\left(\dfrac{2}{3},0\right)\)

The y intercept is the point where \(x=0\)

\(3\times 0-6y=2\\\Rightarrow y=\dfrac{-2}{6}=-\dfrac{1}{3}\)

\(\left(0,-\dfrac{1}{3}\right)\)

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Answer:

4

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

add the exponents

(7+(-6)

=7-6

=1

and let the same base =4^1 =4

Answer:

48 sq. inches

Step-by-step explanation:

8x12/2

4x12

48 sq. inches

Answer:

perimeter = 32 inches

area = 42inches

Step-by-step explanation:

area= b X h / 2

The p-value is .11 and the significance level is .05, then we fail to reject the null hypothesis.

The p-value represents the probability of obtaining the observed results, or results more extreme, assuming the null hypothesis is true. In this case, the p-value is greater than the significance level, which means that the observed results are not significant enough to reject the null hypothesis.
With a p-value of .11 and a significance level of .05, we can conclude that there is not enough evidence to reject the null hypothesis.
When comparing the p-value to the significance level (0.05), if the p-value is less than or equal to the significance level, you would reject the null hypothesis, indicating that there is a significant effect or difference.

If the p-value is greater than the significance level, you would fail to reject the null hypothesis, meaning that you cannot conclude that there is a significant effect or difference.

Hence, the p-value (0.11) is greater than the significance level (0.05), you fail to reject the null hypothesis, which means you cannot conclude that there is a significant effect or difference.

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The general solution of the given second-order linear ordinary differential equation is y = (c1 + c2x)e^(5x) + 22/25, where c1 and c2 are arbitrary constants.

The given differential equation is y'' - 10y' + 25y = 22. To find the general solution, we first need to find the complementary function by solving the associated homogeneous equation, which is y'' - 10y' + 25y = 0.

Assuming a solution of the form y = e^(rx), we substitute it into the homogeneous equation and obtain the characteristic equation r^2 - 10r + 25 = 0. Solving this quadratic equation, we find that r = 5 is a repeated root.

Therefore, the complementary function is of the form y_c = (c1 + c2x)e^(5x), where c1 and c2 are arbitrary constants.

Next, we find a particular solution for the non-homogeneous equation y'' - 10y' + 25y = 22. Since the right-hand side is a constant, we can assume a constant solution y_p = a.

Substituting y_p = a into the differential equation, we find that 25a = 22, which gives a = 22/25.

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The simplified form of the expression is \(2n^3 + 2n^2\) + 7n + lgn.

To simplify the given expression, let's break it down step by step:

nO\((n^2\)+5) = n * (\(n^2\) + 5) = \(n^3\) + 5n

\((n^2+2)O(n)\) = (\(n^2 + 2) * n = n^3 + 2n^2\)

Putting it together:\(nO(n^2+5) + (n^2+2)O(n) + 2n + lgn = (n^3 + 5n) + (n^3 + 2n^2) +\) 2n + lgn

Combining like terms, we get:

\(n^3 + n^3 + 2n^2 + 5n + 2n + lgn\\= 2n^3 + 2n^2 + 7n + lgn\)

The concept is to simplify an expression involving big-O notation by identifying the dominant term or growth rate. This allows us to focus on the most significant factor in the expression and understand the overall complexity or scalability of an algorithm or function as the input size increases.

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9514 1404 393

Answer:

  3π units

Step-by-step explanation:

The full circumference of a circle with radius 2 is ...

  C = 2πr

  C = 2π(2) = 4π

The arc shown is 3/4 of the full circle circumference so is ...

  3/4C = (3/4)(4π) = 3π . . . units

Answer:

.46 x 14 = 6.44

46 x 1.4 = 64.4

46 x 14 = 644

4.6 x 14 = 64.4

46 x .14 = 6.44

Step-by-step explanation:

Answer:

The answer is D

Step-by-step explanation:

Answer:

  D, E

Step-by-step explanation:

The applicable formula is ...

  s = rθ

so, for θ = 1.5, the arc length is 1.5 times the radius. The true statements are ...

  D) The length of the arc defined by the angle is 1.5 times longer than the radius.

  E) The ratio of arc length to radius is 1.5.

Answer:

5000 N

Step-by-step explanation:

Given,

Mass ( m ) = 20 kg

Acceleration ( a ) = 250 m/s^2

To find : Force ( F ) = ?

Formula : -

F = ma

F

= 20 x 250

= 5000 N

Answer:

The approximate area between the curves is -0.34956.

Step-by-step explanation:

To find the area between the curves x = -1, x = 2, y = 3e^(3x), and y = 2e^(3x) + 1, we need to integrate the difference of the curves over the given interval.

First, let's find the points of intersection between the curves by setting them equal to each other:

3e^(3x) = 2e^(3x) + 1

Subtracting 2e^(3x) from both sides gives:

e^(3x) = 1

Taking the natural logarithm of both sides:

3x = ln(1) = 0

x = 0

So, the curves intersect at x = 0.

Now we can calculate the area by integrating the difference between the curves:

Area = ∫(-1)^(2) [3e^(3x) - (2e^(3x) + 1)] dx

Simplifying, we have:

Area = ∫(-1)^(2) (e^(3x) - 1) dx

Using the power rule of integration, we integrate term by term:

Area = [1/3e^(3x) - x] | from -1 to 2

Substituting the limits of integration:

Area = [1/3e^(3(2)) - 2] - [1/3e^(3(-1)) - (-1)]

Simplifying further:

Area = [1/3e^6 - 2] - [1/3e^(-3) + 1]

Calculating the exponential terms:

Area = [1/3e^6 - 2] - [1/3e^(-3) + 1]

≈ 0.01832 - 0.36788 - 1/3 + 1

≈ -0.34956

Therefore, the approximate area between the curves is -0.34956.

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An expert system differs from conventional systems in that it incorporates knowledge and expertise in a specific domain to make intelligent decisions or provide recommendations.

Conventional systems are typically rule-based or algorithmic, where predefined rules or instructions are followed to process data or perform tasks. These systems are designed to handle specific functions but lack the ability to mimic human expertise or reasoning.

On the other hand, an expert system utilizes artificial intelligence (AI) techniques, such as knowledge representation, inference engines, and learning algorithms, to capture and apply human expertise in a particular domain. It relies on a knowledge base, which contains expert knowledge and rules, and an inference engine, which uses logical reasoning to draw conclusions or provide recommendations based on the given input.

The key distinction of an expert system lies in its ability to handle complex, knowledge-intensive tasks that would typically require human expertise. By emulating the decision-making processes of human experts, expert systems can analyze complex data, diagnose problems, offer solutions, and provide expert-level advice.

Expert systems have applications in various fields, including medicine, finance, engineering, and customer support. They enable organizations to leverage and preserve expert knowledge, enhance decision-making processes, and improve overall efficiency and accuracy.

In summary, expert systems differ from conventional systems by incorporating AI techniques to emulate human expertise, allowing them to handle complex tasks and provide intelligent recommendations. This makes expert systems particularly valuable in domains where expert knowledge is critical for decision-making and problem-solving.

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An expert system differs from conventional systems in terms of their knowledge base, reasoning and inference capabilities, adaptability, and domain-specificity.

An expert system is a computer program that mimics the decision-making ability of a human expert in a specific domain. It uses a knowledge base, which contains facts and rules, and an inference engine to provide intelligent solutions to complex problems. Expert systems are designed to handle complex and uncertain situations by using reasoning and inference techniques.

On the other hand, conventional systems are traditional computer programs that follow a predefined set of instructions to perform specific tasks. They do not possess the ability to learn or adapt like expert systems.

The main differences between expert systems and conventional systems are:

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