What is the missing rational expression in the following multiplication sentence (b³(a=7)/a^2)(?)=b(a-7)/14a​

The shell method, we integrate 2πrh*dx, where r is the distance from the axis of revolution to the shell,

The volume of the solid generated by revolving the region bounded by the line y = f(x), where f(x) is a function, using the shell method, we integrate 2πrh*dx, where r is the distance from the axis of revolution to the shell, h is the height of the shell, and dx represents an infinitesimally small change in x.

The limits of integration are determined by the intersection points of the line y = f(x) with the x-axis. We evaluate the integral from the lower limit to the upper limit to obtain the volume of the solid.

The shell method allows us to calculate the volume by considering infinitesimally thin cylindrical shells perpendicular to the axis of revolution.

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Answer:

answer is down below

Step-by-step explanation:

9 to 16

The fact that the median weight is equidistant from both the minimum and maximum weights indicates a symmetric distribution.

In a distribution, symmetry refers to the balance or equality between the left and right sides of the distribution. When the median, which represents the center of the distribution, is equidistant from both the minimum and maximum values, it suggests a symmetric distribution.

In this case, the median weight is equally distant from the minimum weight, which is around 90-ish pounds, as it is from the maximum weight, which is around 200-ish pounds. This suggests that there is an equal number of data points on both sides of the median, creating a balanced distribution.

A symmetric distribution is characterized by a bell-shaped curve, with the mean, median, and mode all located at the center. It indicates that the data is evenly spread around the central tendency, without any skewness or asymmetry. This information about the distribution can be useful for understanding the overall pattern and variability of the data.

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The selection depends on individual needs, preferences, and the intended use of the tiny house.

a) To find the amount of space inside each house, we need to calculate the volume for each design.

House on the left:

Volume = length x width x height = 2.5 m x 18 m x 2.8 m = 126 m³

Triangular house:

Volume of a triangular prism = (base area x height) / 2

Base area = (1/2) x base x height = (1/2) x 4 m x 10 m = 20 m²

Volume = (20 m² x 7 m) / 2 = 70 m³

b) When comparing the environmental impacts of each house, several factors need to be considered:

Positive impacts:

1. Material usage: Tiny houses use fewer materials, reducing resource consumption and waste generation.

2. Energy efficiency: Smaller living spaces require less energy for heating, cooling, and lighting, leading to lower energy consumption.

3. Land utilization: Tiny houses can be built on smaller plots of land, preserving green spaces and reducing urban sprawl.

Negative impacts:

1. Construction materials: Although tiny houses use less material overall, the environmental impact depends on the types of materials used. Sustainable and eco-friendly materials should be prioritized.

2. Water and waste management: Adequate provisions for water supply and waste disposal should be implemented to minimize environmental impacts.

3. Transportation: The transportation of tiny houses to their locations can contribute to carbon emissions if not done efficiently.

c) The choice of design for a tiny house depends on personal preferences and priorities. However, considering the provided information:

The house on the left offers a larger interior space of 126 m³, providing more room for living and storage. It may be suitable for individuals or couples who desire more space and functionality within their tiny house.

The triangular house has a smaller interior volume of 70 m³ but offers a unique design and aesthetic appeal. It may be preferred by individuals who prioritize a distinctive architectural style or who are looking for a minimalist and cozy living space.

Ultimately, the selection depends on individual needs, preferences, and the intended use of the tiny house. Factors such as lifestyle, desired amenities, and personal values regarding sustainability and resource conservation should be considered when making the final decision.

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Answer:

5/9

Step-by-step explanation:

we add all of the values and divide by the total number in this case 9, all of them add to make 5 so we do 5÷9 to get 5/9

Answer:

y=-x+5

Step-by-step explanation:

i plotted the points on a graph and found that the slope was -1 and went back and found the y intercept 5

The equation of the line in slope intercept form will be y = - x + 5.

Let the equation of the line pass through (x₁, y₁) and (x₂, y₂). Then the equation of the line is given as,

\(\rm (y - y_2) = \left (\dfrac{y_2 - y_1}{x_2 - x_1} \right ) (x - x_2)\)

The points are given below.

(1, 4) and (6, -1)

Then the equation of the line that passes through (1, 4) and (6, -1) will be given as,

(y + 1) = [(-1 - 4) / (6 - 1)] (x - 6)

Simplify the equation, then we have

y + 1 = - 1(x - 6)

y = -x + 6 - 1

y = - x + 5

The equation of the line in slope intercept form will be y = - x + 5.

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Answer:

x = 2

Step-by-step explanation:

First, you cross multiply then that will give you

9x - 3 = 5x + 5

collect like terms

9x - 5x = +5 + 3

= 4x = 8

Divide both sides by the coefficient of x that's 4

= 2

Answer:

27.5

Step-by-step explanation:

Well for me i would divide 110 by 4 because there are 4 sides and that will be your answer

The existing system with one service crew is cheaper.

Given: The crew of mechanics at the Highway Department garage repair vehicles that break down at an average of 12 vehicles per hour (approximately Poisson in nature). The mechanic crew can service an average of 3 vehicles every 10 minutes with a repair time distribution that approximates an exponential distribution.

The crew cost is approximately $50 per hour. The cost associated with lost productivity from the breakdown is estimated at $80 per vehicle per hour (or any fraction thereof).

We need to find which system is cheaper, the existing system with one service crew, or a revised system with two service crews.

Calculation of existing system cost:

Let's calculate the existing cost by servicing with one crew.

λ = 12/hourμ = 3/20 = 0.15/minute

ρ = λ/μ = 12/0.15 = 80 (since 0 < ρ < 1,

we can use Little's Law)Cost of 1 crew = $50/hour

Cost of lost productivity = $80/hour

We know that if λ is the rate at which the jobs arrive at the system, and μ is the rate at which jobs are serviced, the average number of jobs in the system is given by L, which is:

L = λ/μ L = 80

So, the average number of vehicles in the system is 80.

Therefore, the total cost per hour = cost of 1 crew + cost of lost productivity= $50 + 80 × 80 = $50 + $6400 = $6450

Calculation of revised system cost: Now, let's calculate the cost of servicing with two crews.

Each crew now serves at a rate of μ/2 = 0.15/2 = 0.075/minute.ρ = λ/μ = 12/0.075 = 160 (since 0 < ρ < 1, we can use Little's Law)

The average number of vehicles in the system is:L = λ/μ L = 160

So, the average number of vehicles in the system is 160.

Therefore, the total cost per hour = cost of 2 crews + cost of lost productivity= 2 × $50 + 160 × 80 = $100 + $12800 = $12900

Since the cost of the revised system is higher than the existing system, it's cheaper to continue with the existing system.

Therefore, the existing system with one service crew is cheaper.

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Answer:

-12.

Step-by-step explanation:

x=0

Answer:

∴ x = 1, y = -3

Step-by-step explanation:

x - y = 4 ------ equation (1)

2x + y = 5 ------ equation (2)

Add equations (1) and (2):
(2x + y) + (x - y) = 5 - 4

    2x + y - x - y = 1

                   ∴ x = 1

Substitute x = 1 into equation (1):

1 - y = 4

  -y = 3

∴ y = -3

The given statement "it is possible to have a distribution of scores where no individual has a score exactly equal to the mode" is true because the mode represents the most frequently occurring score, and it is possible for the scores to be spread out in a way that no score occurs more frequently than any other.

In a distribution of scores, the mode is the score that occurs most frequently. However, it is possible for the scores to be spread out in a way that no score occurs more frequently than any other, making it impossible for any one score to be the mode.

For example, if a group of students all score differently on a test, with no two students receiving the same score, there is no mode. In such a case, no individual would have a score exactly equal to the mode since there is no mode in the distribution. Therefore, the given statement is true.

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B) Waiting for a package can be so agonizing is the sentence which uses a gerund as the subject of a sentence.

A gerund is a verb form that functions as a noun, and in this sentence, "waiting" is the gerund acting as the subject of the sentence. The sentence is expressing the idea that the act of waiting for a package is a frustrating experience.

Option A) "I am waiting for the delivery man to come," uses the present participle "waiting" as a verb in the present continuous tense. Option C) "The patient woke up on the operating table," uses the noun "patient" as the subject of the sentence. Option D) "The economy has been booming since we sold our stock," uses the noun phrase "the economy" as the subject of the sentence.

Knowing how to identify gerunds and their role in a sentence can help improve one's writing skills and clarity of expression.

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Answer: 28 hours

Step-by-step explanation:

\(V=7(4)(1.2)\\\\v=33.6\ m^3\)

\(\displaystyle\\20\ l/min=\\\\\frac{20(60)}{1000} =\\\\\frac{1200}{1000}=\\\\1.2\ m^3/hour\)

\(\displaystyle\\v=\frac{V}{t} \\\)

Multiply both parts of the equation by t(t≠0):

\(vt=V\)

Divide both parts of the equation by v (v≠0):

\(\displaystyle\\t=\frac{V}{v} \\\\t=\frac{33.6}{1.2} \\\\t=28 \ hours\)

Answer:

We need to find the volume first.

We will use our famous volume of a rectangular solid formula:

V = l x w x h

So, V = 12 x 7 x 1.2 = 100.8 cubic meters.

Now, cost = 100.8 x 27.25 = 2746.8 PHP

Conclusion:The water will cost PHP 2,746.8.

Answer:

x = 11

z = 86

Step-by-step explanation:

8x + 6 and 10x-16 are vertical angles

Vertical angles are pairs of angles that are opposite each other and have the same vertex, or point of intersection. They are formed when two lines intersect at a point, and are always congruent, or of equal measure.

To solve this equation, we need to isolate the variable x on one side of the equation. To do this, we can start by subtracting 6 from both sides of the equation:

8x + 6 - 6 = 10x - 16 - 6

8x = 10x - 22

Now we can subtract 8x from both sides of the equation:

8x - 8x = 10x - 22 - 8x

0 = 2x - 22

To solve for x, we can add 22 to both sides of the equation:

0 + 22 = 2x - 22 + 22

22 = 2x

Finally, we can divide both sides of the equation by 2 to find the value of x: 22 / 2 = 2x / 2

x = 11

Therefore, the solution to the equation is x = 11.

Now that we have x, z is a supplementary angle to 8x + 6 (or you could do 10x - 16)

Supplementary angles are pairs of angles that add up to 180 degrees. They are formed when two lines intersect at a point, and the angles formed at the intersection are supplementary.

First plug in x, 8x + 6 = 8(11) + 6 = 88 + 6 = 94

180 - 94 = z

z = 86

The value of the given expression is \(\frac{1}{5}\). The solution has been obtained by using the arithmetic operations.

What are arithmetic operations?

The four basic operations, also referred to as "arithmetic operations," can be used to describe all the real numbers. The operations like division, multiplication, addition, and subtraction gives the results as quotient, product, sum, and difference respectively in mathematics.

We are given an expression as \(\frac{3}{5}\) - \(\frac{2}{5}\).

Since, both the terms have the same denominator which is 5 so, using the subtraction operation, we get the following value:

⇒  \(\frac{3}{5}\) - \(\frac{2}{5}\) =  \(\frac{1}{5}\)

Hence, the second option is the correct answer.

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The conclusion from this study is that while there may be a moderate effect of the new therapy on the amount of time participants could watch the snake video, the results are not statistically significant at the .05 level of significance, based on the small sample size of only 4 participants.

The results of the paired-samples t-test are as follows:

The mean difference between the before and after measurements is 5 minutes, with a standard deviation of 2 minutes.

The t-statistic is 2.5, with 3 degrees of freedom (df= n-1 = 4-1 = 3).

The p-value is 0.088.

Since the p-value is greater than the level of significance of 0.05, we fail to reject the null hypothesis. This means that we do not have sufficient evidence to conclude that the new therapy significantly changed the amount of time participants could watch the video without looking away.

The effect size measures (Cohen's d and Hedges' correction) suggest that there is a moderate effect of the therapy on the participants, but the confidence intervals suggest that the true effect size could range from small to large.

Therefore, the conclusion from this study is that while there may be a moderate effect of the new therapy on the amount of time participants could watch the snake video, the results are not statistically significant at the .05 level of significance, based on the small sample size of only 4 participants. Further research with a larger sample size is needed to confirm these findings.

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Answer:

x = q/(3 - b)

Step-by-step explanation:

Step 1: Write equation

3x = q + bx

Step 2: Solve for x

Statistical methods of forecasting labor supply and demand are most accurate when they are based on a comprehensive analysis of a variety of factors. This includes demographic changes, technological advancements, industry trends, government policies, and economic indicators.

The accuracy of the forecast also depends on the quality and reliability of the data used. Therefore, it is important to gather and analyze data from multiple sources, such as surveys, job postings, and employment statistics. Additionally, statistical methods should be regularly updated and refined to ensure that they reflect the most recent changes in the labor market. Ultimately, the accuracy of labor supply and demand forecasts can have a significant impact on business planning, workforce development, and economic growth, making it essential to use reliable statistical methods to produce the most accurate results.

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Answer: (below)

Step-by-step explanation:

1) n/6 + 6 = -3

2) 2n + 5 = 27

3) n/2 - 10 = 5

The probability that the next customer to enter the shop will order a cookie is given as follows:

31/60.

The parameters that are needed to calculate a probability are listed as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

The outcomes in which a cookie is ordered are given as follows:

Hence the probability is obtained as follows:

3/4 x 1/3 + 2/5 x 2/3 = 1/4 + 4/15 = 15/60 + 16/60 = 31/60.

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Therefore, The values of x are 1/2 + i√6/2 and 1/2 - i√6/2.

To use the quadratic formula, we need to rearrange the equation into the standard form: 2x^2 - 4x + 7 = 0. Then, using the formula x = (-b ± √(b^2 - 4ac)) / 2a, we plug in a=2, b=-4, and c=7 to get:
x = (4 ± √(-24)) / 4
Since the square root of a negative number is not a real number, the solutions are complex. We can simplify by factoring out the 2 from the numerator:
x = 2(1 ± i√6) / 4
Simplifying further by canceling the 2s, we get:
x = 1 ± i√6 / 2

Therefore, The values of x are 1/2 + i√6/2 and 1/2 - i√6/2.

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Answer:

The answer is C

Step-by-step explanation:

y = 4x + 12

y = 4(3) + 12

y = 12 + 12

y=24

y = 4x + 12

y = 4(5) + 12

y=20+12

y=32

y = 4x + 12

y = 4(8) + 12

y=32+12

y=44

the correct option for the given Equation at the different values of x will be C.

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.

Given y = 4x + 12, using the x-values, 3, 5, and 8.

To find the value of y, at x = 3, 5, and 8

Thus,

For x = 3

y = 4 * 3 + 12

y = 24

For x = 5,

y = 4 * 5 + 12

y = 32

for x = 8

y = 4 * 8 + 12

y = 44

therefore, the correct option for the given Equation at the different values of x will be C.

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Answer:

21³

it's the answer coz in division power is subtracted

mark me brainliest

Answer:

3

Step-by-step explanation:

I think iits 3........

Answer:

Step-by-step explanation:

From the figure attached,

Given: ∠P ≅ ∠S

          TQ ≅ RQ

To Prove : ΔQRS ≅ ΔQTP

        Statements                          Reasons

1).     ∠P ≅ ∠S, TQ ≅ RQ                  Given

2).    ∠RQS ≅ ∠TQP                  Reflexive property

3).     ΔQRS ≅ ΔQTP                           AAS

Assuming QF is the full employment equilibrium then in the Figure, if the level of spending is equal to AD1, the AD shortfall would be greater than XZ. The answer is B.

The respective figure as referred in the question is as attached.

Full employment equilibrium refers to the equilibrium where all resources in the economy are fully utilized (employed). Full employment is a situation in which all available labor resources are being used in the most economically efficient way, so there is no cyclical or deficient-demand unemployment.

When the natural rate of unemployment is equal to the unemployment rate, this means the cyclical rate of unemployment is zero. So, when this relationship happens, the economy is considered to be at full employment.

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