the altitude of a triangle is increasing at a rate of 2.5 2.5 centimeters/minute while the area of the triangle is increasing at a rate of 2.5 2.5 square centimeters/minute. at what rate is the base of the triangle changing when the altitude is 8 8 centimeters and the area is 81 81 square centimeters?

The equation of a line passing through the points (2,-2) and (0,2) is to be determined. The options are y = -3x, y = -2x + 2, y = -3x + 3, and y = -3x + 2.

The slope of the line can be found by using the formula:

slope = (y2 - y1) / (x2 - x1)

where (x1,y1) and (x2,y2) are the given points on the line.

slope = (2 - (-2)) / (0 - 2) = 4 / (-2) = -2

The y-intercept can be found by using the slope-intercept form of the equation of a line:

y = mx + b

where m is the slope and b is the y-intercept.

Substituting the values of m, x, and y from the given point (2,-2):

-2 = (-2) * 2 + b

b = 2

Therefore, the equation of the line passing through the given points is:

y = -2x + 2

Hence, option b is the correct answer.

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Answer:

18

Step-by-step explanation:

properties of a triangle: all the angles add up to 180 degrees

so

180 - 90 - 72 = 18

answer is 18 degrees

Answer:

43.3%

Step-by-step explanation:

35.3% + 21.4% = 56.7%

so 100-56.7 =43.3%

a) A department manager receiving an allocation of costs will care about management's methodology of overhead allocation because the overhead costs allocated to their department will have a direct impact on the department's profitability and cost efficiency.

b) The allocation base is the measure used to determine how much of the overhead costs should be allocated to a particular department or product, while the allocation rate is the amount of overhead costs allocated to each unit of the allocation base

c) Budgets are an important tool for cost planning, but their effectiveness depends on how well they are developed and implemented.

a) If the allocation method used by management is not accurate or fair, it could result in the department being burdened with more costs than they actually incur, which could affect their ability to meet their targets and objectives. It is, therefore, important for department managers to ensure that the allocation of costs is done fairly and accurately.

b) The allocation base and rate are important because they determine how the overhead costs are allocated to different departments or products.

Different allocation bases and rates can result in significantly different amounts of overhead costs being allocated to different departments or products, which can impact their profitability. While all of the overhead costs eventually make their way to the income statement, the allocation of these costs can have a significant impact on the accuracy of the income statement and the ability of the organization to make informed decisions.

c) Budgets can be helpful in providing a roadmap for achieving the organization's goals and objectives, but they need to be flexible enough to adapt to changing circumstances and priorities.

The budget(s) that are most important to the organization's success will depend on the nature of the organization and its objectives. However, typically the operating budget, capital budget, and cash budget are the most important budgets for most organizations.

The government's budget process is similar to the operating budgeting process described in the chapter in that it involves the development of a budget to allocate resources and achieve goals. However, the government's budget process is more complex and involves additional considerations such as political priorities and public opinion. Additionally, the government's budget process involves a more detailed review and approval process than the operating budgeting process.

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Answer:

2079

Step-by-step explanation:

is the correct answer 2079

Answer:

40 vanilla cookies

Step-by-step explanation:

Lets say that

N = No-bake cookies

V = Vanilla cookies

C = Cinnamon cookies

If the ratio is 2 : 2 : 2

And there are 40 no-bake cookies

It would be 40 vanilla cookies and 40 cinnamon cookies because the ratio is all the same

( N : V : C )

( 40 : 40 : 40 )

Hope this helps  (๑ > ᴗ <)وxx

( I am so sorry if this is wrong!!)

Answer:

2/5m - 1/5

Step-by-step explanation:

Given the equation :

2(1/5m - 2/5) + 3/5

First step:

Open the bracket by multiplying values in the bracket by 2

2/5m - 4/5 + 3/5

-4/5 + 3/5 = (-4 + 3) / 5 = - 1 / 5

Hence,

2/5m - 4/5 + 3/5 = 2/5m - 1/5

= 2/5m - 1/5

Answer:

The function is a direct variation function with a constant of variation of 1.5.

Step-by-step explanation:

I just took the test :/

Answer:

The function is a direct variation function with a constant of variation of 1.5.

Step-by-step explanation:

Answer:

5p + 2 = 4p - 1

p = -3

Step-by-step explanation:

The average period of the trials that were conducted with an amplitude of 10 degrees is 1.694 seconds.

What is amplitude ?

In mathematics, amplitude refers to the maximum displacement or distance from the equilibrium position of a periodic function, such as a sine or cosine wave. In other words, if a periodic function oscillates back and forth between two extreme values, the amplitude is the maximum distance from the average value or midpoint of the oscillation to one of the extreme values.

To calculate the average period of the trials that were conducted with an amplitude of 10 degrees, we simply add up all the periods and divide by the total number of trials.

10 degrees: 1.66 s, 1.700 s, 1.71 s, 1.68 s, 1.72 s

Average period = (1.66 + 1.700 + 1.71 + 1.68 + 1.72) / 5 = 1.694 seconds

Therefore, the average period of the trials that were conducted with an amplitude of 10 degrees is 1.694 seconds.

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Answer:

1. 25  2. 11  3. 9

Step-by-step explanation:

Answer:

16 meters

Step-by-step explanation:

1 3/5 x 10=10 30/5=16

Answer: To complete the square for the quadratic equation x^2 + 5x - 1 = 0, we need to add a constant term that will allow us to rewrite the left-hand side of the equation as a perfect square trinomial.

To determine this constant term, we take half of the coefficient of x, square it, and add it to both sides of the equation. The coefficient of x in this equation is 5, so we have:

(5/2)^2 = 6.25

Adding 6.25 to both sides of the equation, we get:

x^2 + 5x - 1 + 6.25 = 6.25

x^2 + 5x + 5.25 = 0

Now, we can factor this equation as:

(x + 2.5)^2 = 0.25

To solve for x, we take the square root of both sides and solve for x:

x + 2.5 = ±0.5

x = -2.5 ± 0.5

So, the number that had to be added to "complete the square" was 6.25.

Step-by-step explanation:

Answer:

divide them by what?

or fivide it with eachother?

Answer:

126 mm / 3 = 42 mm

The length of each side of this equilateral triangle is 42 mm.

Cases (iii) and (iv) are left as exercises, meaning the proof for those cases is not provided in the given information. To fully establish the Characterization Theorem, the proof for these remaining cases needs to be completed.

Theorem 2.5.1 (Characterization Theorem):

If S is a subset of R that contains at least two points and has the property that if x, y ES and x < y, then (x, y)C S, then S is an interval.Proof.

There are four cases to consider:

(i) S is bounded,

(ii) S is bounded above but not below,

(iii) S is bounded below but not above, and

(iv) S is neither bounded above nor below.

Case (i): Let a = inf S and b = sup S.

Then SC[a, b] and we will show that (a, b)C S. If a < z < b, then there exist x, y

ES such that x < z < y. Since x < y and S has property (1), we have (x, y)C S.

Since zEP(x, y), it follows that zES.

Thus (a, b)C S.

Now if a S and b S, then S =[a, b].

If a S and b S, then S=(a, b).

The other possibilities lead to either S = (a, b) or S = [a, b].

Case (ii): Let b = sup S.

Then SC (-[infinity]o, b] and we will show that (-oo, b)C S. For, if z < b, then there exists y

ES such that z < y < b.

Since b is the least upper bound of S and yES, it follows that y 6S. But then (z, y)C (-oo, b) and (z, y)C S.

Thus (-oo, b)C S. Now if S contains its smallest element a, then S = [a, b]. Otherwise, S=(a, b).

Cases (iii) and (iv) are left as exercises.

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Answer:

La temperatura a las diez de la mañana fue +2°

Step-by-step explanation:

Tasa de Cambio de Funciones

Algunas funciones modelan el estado de una variable respecto al tiempo. La variación de ese estado en cierto intervalo se llama tasa de cambio.

En nuestro problema, tenemos información de los cambios de la temperatura en la ciudad de Londres. Hagamos la secuencia según la historia nos la cuenta:

A las tres de la mañana, la temperatura era -4°. Una hora después la temperatura aumentó 3°, por lo tanto:

A las cuatro de la mañana, la temperatura era -4°+3°=-1°. Dos horas después la temperatura desciende 5° (se obvia el signo). Por lo tanto:

A las seis de la mañana, la temperatura era -1°-5°=-6°

Las cinco horas siguientes, la temperatura aumenta 2° por hora. Queremos saber la temperatura a las diez de la mañana, es decir, cuatro horas luego de la última calculada.

Si aumenta 2° por hora, en 4 horas aumentó 4*2°=8°. Finalmente, la temperatura a las diez de la mañana fue -6°+8° = +2°

The type of sampling that requires giving every part an equal chance of being selected for the sample is called "simple random sampling."

Simple random sampling is a method of selecting a sample from a population where each member has an equal probability of being chosen. In this type of sampling, every part or element of the population is assigned a number or label, and a random process, such as a lottery or a random number generator, is used to select the sample. The main characteristic of simple random sampling is that each member of the population has an equal and independent chance of being selected, without any bias or preference.

This sampling method ensures that every part of the population has an equal opportunity to be included in the sample, making it a fair representation of the entire population. By giving each part an equal chance of being selected, simple random sampling helps to minimize sampling errors and increase the generalizability of the findings to the larger population. It is often used in research studies and surveys when the goal is to obtain an unbiased and representative sample.

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The percent change for people living with the disease is 36.78% and with the number of deaths is 60%

In 2005 there were 29.9 million people worldwide living with a certain disease

By 2015, the number of people living with the disease had fallen to 28.8 million

Decrease in number of people living with a disease = 29.9 - 28.8 = 1.1

decrease in percentage of people living with a disease = (1.1/29.9)/100 = 36.78%

In 2005, 1.5 million deaths from the disease

In 2015,  2.6 million deaths were reported

change in number of deaths from the disease = 2.6 - 1.5 = 0.9

Change in percentage = (0.9/1.5) 100 = 60%

Therefore,  the percent change for people living with the disease is 36.78% and with the number of deaths is 60%

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Answer:

Every year, a pet food company sells its food to stores across the nation. ... In the first month of the new year, the Midwest region secured sales orders from ... Suppose the strategy of the pet food company is to increase the proportion of ... Do you think additional field training is necessary for all of the sales representatives?

Step-by-step explanation:

Answer:

StartFraction 1 Over 8 EndFraction

Step-by-step explanation:

Given statement solution is :- a) Power set for two sets A and B with any 2 elements:

Set A: {1, 2}, Set B: {3, 4}

Power set of A: {{}, {1}, {2}, {1, 2}}

Power set of B: {{}, {3}, {4}, {3, 4}}

b) Power set for two sets A and B with any 3 elements:

Set A: {1, 2, 3}, Set B: {4, 5, 6}

Power set of A: {{}, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}}

Power set of B: {{}, {4}, {5}, {6}, {4, 5}, {4, 6}, {5, 6}, {4, 5, 6}}

c) Power set for two sets A and B with any 4 elements:

Set A: {1, 2, 3, 4}, Set B: {5, 6, 7, 8}

Power set of A: {{}, {1}, {2}, {3}, {4}, {1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, {3, 4}, {1, 2, 3}, {1, 2, 4}, {1, 3, 4}, {2, 3, 4}, {1, 2, 3, 4}}

Power set of B: {{}, {5}, {6}, {7}, {8}, {5, 6}, {5, 7}, {5, 8}, {6, 7}, {6, 8}, {7, 8}, {5, 6, 7}, {5, 6, 8}, {5, 7, 8}, {6, 7, 8},

a) Power set for two sets A and B with any 2 elements:

Set A: {1, 2}, Set B: {3, 4}

Power set of A: {{}, {1}, {2}, {1, 2}}

Power set of B: {{}, {3}, {4}, {3, 4}}

Set A: {apple, banana}, Set B: {cat, dog}

Power set of A: {{}, {apple}, {banana}, {apple, banana}}

Power set of B: {{}, {cat}, {dog}, {cat, dog}}

Set A: {red, blue}, Set B: {circle, square}

Power set of A: {{}, {red}, {blue}, {red, blue}}

Power set of B: {{}, {circle}, {square}, {circle, square}}

b) Power set for two sets A and B with any 3 elements:

Set A: {1, 2, 3}, Set B: {4, 5, 6}

Power set of A: {{}, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}}

Power set of B: {{}, {4}, {5}, {6}, {4, 5}, {4, 6}, {5, 6}, {4, 5, 6}}

Set A: {apple, banana, orange}, Set B: {cat, dog, elephant}

Power set of A: {{}, {apple}, {banana}, {orange}, {apple, banana}, {apple, orange}, {banana, orange}, {apple, banana, orange}}

Power set of B: {{}, {cat}, {dog}, {elephant}, {cat, dog}, {cat, elephant}, {dog, elephant}, {cat, dog, elephant}}

Set A: {red, blue, green}, Set B: {circle, square, triangle}

Power set of A: {{}, {red}, {blue}, {green}, {red, blue}, {red, green}, {blue, green}, {red, blue, green}}

Power set of B: {{}, {circle}, {square}, {triangle}, {circle, square}, {circle, triangle}, {square, triangle}, {circle, square, triangle}}

c) Power set for two sets A and B with any 4 elements:

Set A: {1, 2, 3, 4}, Set B: {5, 6, 7, 8}

Power set of A: {{}, {1}, {2}, {3}, {4}, {1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, {3, 4}, {1, 2, 3}, {1, 2, 4}, {1, 3, 4}, {2, 3, 4}, {1, 2, 3, 4}}

Power set of B: {{}, {5}, {6}, {7}, {8}, {5, 6}, {5, 7}, {5, 8}, {6, 7}, {6, 8}, {7, 8}, {5, 6, 7}, {5, 6, 8}, {5, 7, 8}, {6, 7, 8},

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To prove that the given categorical syllogism invalid using the counterexample method, we first need to check whether the syllogism follows the standard form of categorical syllogisms. The standard form of categorical syllogism is:

Premise 1: All A are B. (Major Premise)

Premise 2: All C are A. (Minor Premise)

Conclusion: All C are B.

Let's represent the given syllogism in the standard form:

Premise 1: No undocumented individuals are people who are paid decent wages. (Major Premise)

Premise 2: Some undocumented individuals are not farm workers. (Minor Premise)

Conclusion: Some farm workers are not people who are paid decent wages.

Now, we will use the counterexample method to disprove the given syllogism. We will use real-world examples that will make the premises true but will make the conclusion false. Suppose Premise 1 is "No birds can swim." and Premise 2 is "Some penguins are not birds". Then, the Conclusion will be "Some penguins cannot swim." which is true. Here, we see that the premises are true, and the conclusion is also true.

Let's take another example. Suppose Premise 1 is "No reptiles can fly." and Premise 2 is "Some birds are reptiles." Then, the Conclusion will be "Some birds cannot fly." which is false. Here, we see that the premises are true, but the conclusion is false.

Hence, the syllogism is invalid. Using the same method, we can disprove the given syllogism. Some farm workers are not people who are paid decent wages, because no undocumented individuals are people who are paid decent wages, and some undocumented individuals are not farm workers.

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The measure of angle a is 15 degrees and this can be determined by using the properties of the isosceles triangle.

In geometry, interior angles are formed in two ways. One is inside a polygon, and the other is when parallel lines cut by a transversal. Angles are categorized into different types based on their measurements.

Given:

The following steps can be used in order to determine the measure of angle a:

Step 1 - According to the given data, it can be concluded that triangle PQR and triangle PSR are isosceles triangles.

Step 2 - Apply the sum of interior angle property on triangle PQR.

\(\angle\text{Q}+\angle\text{P}+\angle\text{R}=180\)

\(\angle\text{Q}+2\angle\text{R}=180\)

\(2\angle\text{R}=180-60\)

\(\angle\text{R}=60^\circ\)

Step 3 - Now, apply the sum of interior angle property on triangle PSR.

\(\angle\text{P}+\angle\text{S}+\angle\text{R}=180\)

\(\angle\text{S}+2\angle\text{R}=180\)

\(2\angle\text{R}=180-90\)

\(\angle\text{R}=45^\circ\)

Step 4 - Now, the measure of angle a is calculated as:

\(\angle\text{a}=60-45\)

\(\angle\text{a}=15\)

The measure of angle a is 15 degrees.

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