“Hunter tutors students in mathematics to earn
money. He earns between $50 and $60 each
week. About 20% of the time he tutors sixth
grade students. Which of the following is a
reasonable estimate of the amount of money
Hunter will earn during the next 3 weeks tutoring
sixth graders?”

The graph of the first five terms can be seen in the image at the end.

We know that we have an arithmetic sequence:

3, -10, -23, -36

The common difference is what we get when we subtract two consecutive terms, we will get:

d = -36 - (-23) = -3

Then the recursive relation is:

a(n) = a(n - 1) - 13

At the moment we know:

a(1) = 3

a(2) = -10

a(3) = -23

a(4) = -36

Then fifth term will be:

a(5) = a(4) - 13 = -36 - 13 = -49

Now to graph it, we use the "n-th" value as the input, then we need to graph the five points (1, 3), (2, -10), (3, -23), (4, -36), (5, -49).

The graph can be seen in the image below:

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The train will arrive at its final destination at 2:57 P.M. in the afternoon.

The total distance of the trip is 221 miles and the train travels at an average speed of 34 miles per hour. Using the formula:

time = distance / speed

We can calculate the total time it will take for the train to complete the journey without stopping at stations:

time = 221 / 34 = 6.5 hours

However, the train stops at each of ten stations for four minutes each, so the total time spent stopping is 10 x 4 = 40 minutes, or 0.67 hours. Therefore, the total time the journey will take, including the stops, is:

total time = 6.5 + 0.67 = 7.17 hours

The train departs at 7:30 A.M., so we can add 7.17 hours to this time to find the arrival time:

7:30 A.M. + 7.17 hours = 2:57 P.M.

Therefore, the train will arrive at its final destination at 2:57 P.M. in the afternoon.

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Answer:

-√2

Step-by-step explanation:

For the typing purpose I replaced θ with n in the calculation

\(\lim_{n \to \frac{\pi }{4}} \frac{cos n-sin n}{\frac{\pi }{4} } ...limits L'Hopital's Rule\\= \lim_{n \to \frac{\pi }{4}} \frac{-sin n-cos n}{1 } ... plug. in . \frac{\pi }{4} \\= - sin \frac{\pi }{4} - cos \frac{\pi }{4}\\= - \frac{\sqrt{2} }{2} - \frac{\sqrt{2} }{2}\\= \frac{- 2\sqrt{2}}{2} \\= - \sqrt{2}\)

Answer:

Step-by-step explanation:

1. 2x

2. m^2 - 2

3. x^2 + 3x - 2

4. m - 2n + 3

You can just simply cancel out the given answers to the given problem.

1. 4x^2 - 2x = ___ (2x + 1)

4/2 = 2

x^2 - x is just x^2-1 so x.

= 2x

To check the answer, 2x (2x + 1) = 4x^2 - 2x

#1

\(\\ \rm\star\leadsto \underbrace{2x}(2x+1)\)

\(\\ \rm\star\leadsto 4x^2+2x\)

#2

\(\\ \rm\star\leadsto n\underbrace{(m^2-2)}\)

\(\\ \rm\star\leadsto m^2n-2n\)

#3

\(\\ \rm\star\leadsto x\underbrace{(x^2+3x-2)}\)

\(\\ \rm\star\leadsto x^3+3x^2-2x\)

#4

\(\\ \rm\star\leadsto 2mn\underbrace{(m-2n+3)}\)

\(\\ \rm\star\leadsto 2m^2n-4mn^2+6mn\)

Answer:

B

Step-by-step explanation:

A=4 so its wrong cause the original one is 10-12=-2

Answer:

Question 1 = 4.90

Question 3 = 9.28

Question 7 = 35.00

Answer:

-0.5

Step-by-step explanation:

I just added it into my calculator

The area of the surface obtained by rotating the curve x = 20 cos(3θ), y = 20 sin(3θ), where 0 ≤ θ ≤ π/2, about the x-axis is calculated using the formulA for surface area of revolution

To find the area of the surface, we can use the formula for the surface area of revolution. Given a curve defined parametrically by x = f(θ) and y = g(θ), where α ≤ θ ≤ β, the surface area obtained by rotating the curve about the x-axis is given by:

A = ∫[α,β] 2πy √(1 + (f'(θ))²) dθ

In this case, we have x = 20 cos(3θ) and y = 20 sin(3θ), with 0 ≤ θ ≤ π/2. Taking the derivatives, we find f'(θ) = -60 sin(3θ) and g'(θ) = 60 cos(3θ).

Plugging these values into the surface area formula and simplifying, we get:

A = ∫[0,π/2] 2π(20 sin(3θ))(√(1 + (-60 sin(3θ))²)) dθ

Evaluating this integral will give us the exact value of the surface area of the rotated curve about the x-axis within the given range of θ.

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1 with a remainder of 1

Answer:

Step-by-step explanation:

this expression is equal to

18m+m=19 m

Answer:

B) 1/2 barrel/hour

Step-by-step explanation:

1/3 divided by 2/3 = 1/3 * 3/2 = (1*3)/(3*2) = 3/6 = 1/2, therefore the correct unit rate is B) 1/2 barrel/hour

Answer:

1/2

Step-by-step explanation:

1/3 x 3/2 = 1/2

To find the probability, we'll need to find the number of possibilities with an outcome that we want, as well as the total number of outcomes.

Multiples of 4: 4, 8, 12

---There are 3 possibilities

Total outcomes: 12

3 / 12 = 1/4 = 0.25 = 25%

Probability Amy rolls a multiple of 4 = 25%

Hope this helps!

Answer:

2

Step-by-step explanation:

(1/2) elevado -1

2/1

The only statements that is false is A. I only: 1. We use one-sample procedures when our samples are equal in size but aren't independent.

A one-sample procedure is used when we want to compare a sample mean to a known population mean or when we want to estimate a population mean using a sample mean. In a one-sample procedure, the sample is selected independently and is typically assumed to be random. So, independence of the sample is a requirement for one-sample procedure.

While statement II and III are true.

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Answer:

6 or -6

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

Step 2: Take square root of both sides.

Therefore, the answer is 6 or -6.

Answer:

It's in Quadrant IV.

..............

Yes , the integer k is divisible by 4 and statement (1) alone is sufficient to determine that k is divisible by 4.

Given data ,

Let the equation be represented as A

Now , the value of A is

a)

To determine if the integer k is divisible by 4, let's analyze the given statements:

Statement (1): 8k is divisible by 16.

This means that 8k is a multiple of 16. Since 16 is divisible by 4, we can conclude that k must be divisible by 4 as well. Therefore, statement (1) alone is sufficient to determine that k is divisible by 4.

8k = 16

k = 2

b)

This statement does not provide direct information about the divisibility of k by 4. While 12 is divisible by 4, the fact that 9k is divisible by 12 does not guarantee that k itself is divisible by 4.

9k = 12

k = 12/9

k = 4/3

So , it is not an integer

In conclusion, statement (1) alone is sufficient to determine that k is divisible by 4. Statement (2) is not sufficient on its own.

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Answer:

3/10

Step-by-step explanation:

12/40, divide by four on the top and bottom -> 3/10

Answer:

the ratio as a fraction in simplest form :12/40=3/10

Downsizing refers to the process of reducing the size and workforce of a company to cut costs, increase efficiency, or adapt to changing market conditions. It involves eliminating positions, reducing staff numbers, or even closing down certain business units or branches.

Downsizing can occur for various reasons, such as financial difficulties, mergers and acquisitions, technological advancements, or strategic reorganization. Companies often assess their operational costs and decide to downsize to improve their financial performance.

During the downsizing process, companies may calculate the potential cost savings by considering factors such as salaries, benefits, severance packages, and operational expenses. For example, if a company decides to eliminate 100 positions with an average salary of $50,000 per year, it could result in annual savings of $5 million.

While downsizing can help companies achieve short-term cost reductions, it often has significant implications for the affected employees, including layoffs, reduced morale, and increased workload for remaining staff. It is crucial for organizations to handle the downsizing process with sensitivity and transparency, providing support to affected employees and communicating the rationale behind the decisions.

It is important to note that downsizing should not be seen as a long-term solution, but rather as a strategic measure to address specific challenges. Companies should also explore alternatives to downsizing, such as retraining and redeploying employees, implementing productivity improvements, or seeking new business opportunities, to ensure sustainable growth and success in the long run.

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Answer:

6x-7=3x-29

6x-3x=-29+7

3x=-23

x=-23/3

6x-7=8y+17

6(-23/3)-7=8y+17

-46-7=8y+17

8y+17+53=0

y=70/8

Y=8.75

ANS!!

The closure property refers to the mathematical law that states that if we perform a certain operation (addition, multiplication) on any two numbers in a set, the result is still within that set.In the expression (2x3 x2 - 4x) - (9x3 - 3x2), we are simply subtracting one polynomial from the other.

To simplify it, we'll start by combining like terms. So, we'll add all the coefficients of x3, x2, and x, separately.The given expression becomes: (2x3 x2 - 4x) - (9x3 - 3x2) = 2x3 x2 - 4x - 9x3 + 3x2We will then combine like terms as follows:2x3 x2 - 4x - 9x3 + 3x2 = 2x3 x2 - 9x3 + 3x2 - 4x= -7x3 + 5x2 - 4x

Therefore, the correct simplification of the expression is -7x3 + 5x2 - 4x. The demonstration of the closure property is shown as follows:The subtraction of two polynomials (2x3 x2 - 4x) and (9x3 - 3x2) results in a polynomial -7x3 + 5x2 - 4x. This polynomial is still a polynomial of degree 3 and thus, still belongs to the set of polynomials. Thus, the closure property holds for the subtraction of the given polynomials.

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According to the given information the integral of the quantity g(x) - f(x) from 1 to 5 is -10.

Addition is a mathematical operation that involves combining two or more numbers or quantities to obtain a total or sum. In basic arithmetic, addition is represented by the plus sign (+), and is typically performed by adding the individual values together. For example, the sum of 2 and 3 is 5, which can be written as 2 + 3 = 5. Addition can also be performed with negative or decimal numbers, and can be extended to more complex mathematical structures such as matrices and vectors.

In calculus, the linearity property of integrals states that the integral of a sum or difference of functions is equal to the sum or difference of their integrals. That is, for any two functions f(x) and g(x) and constants a and b, we have:

∫[a,b] (f(x) ± g(x)) dx = ∫[a,b] f(x) dx ± ∫[a,b] g(x) dx

Using this property, we can rewrite the given integral as:

∫[1,5] (g(x) - f(x)) dx = ∫[1,5] g(x) dx - ∫[1,5] f(x) dx

We are given that ∫[1,5] f(x) dx = 6 and ∫[1,5] g(x) dx = -4. Substituting these values, we get:

∫[1,5] (g(x) - f(x)) dx = (-4) - 6 = -10

Therefore, according to the given information the integral of the quantity g(x) - f(x) from 1 to 5 is -10.

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Answer:

36 / 4 = 9 half-lives

2^9 = 512

Therefore after 36 hrs 512 / 512 = 1 mg remains

Answer:

1 mg

Step-by-step explanation:

The position of a typical star on the HR diagram changes during its main-sequence phase, with more massive stars shifting toward the upper left due to increasing luminosity and lower-mass stars moving toward the lower right due to decreasing temperature.

In the Hertzsprung-Russell (HR) diagram, the main sequence represents the phase of a star's evolution when it is actively fusing hydrogen in its core. During this phase, the position of a typical star on the main sequence can change, and option D provides an accurate explanation.

Massive stars, with a mass of around 4 solar masses or more, have a higher luminosity compared to lower-mass stars. As these massive stars evolve, their luminosity increases, causing them to move toward the upper left region of the HR diagram. This shift is because higher luminosity corresponds to a larger radius and a higher surface temperature for massive stars.

On the other hand, lower-mass stars, like our Sun, have lower luminosity. As they evolve, their luminosity decreases, leading them to move toward the lower right region of the HR diagram. This movement occurs as the star exhausts its hydrogen fuel, causing its core to contract and its surface temperature to decrease.

Therefore, the position of a typical star on the HR diagram changes during its main-sequence phase, with more massive stars shifting toward the upper left due to increasing luminosity and lower-mass stars moving toward the lower right due to decreasing temperature.

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Incomplete question:

In the Hertzsprung-Russell diagram, how does the position of a typical star change while it is at the main-sequence phase of its evolution?

A) A star's position on the main sequence is determined only by its mass, not its age, so stars do not move along the main sequence during evolution.

B) Stars move from upper right to lower left while they are on the main sequence.

C) Stars move from upper left to lower right while they are on the main sequence.

D) Massive stars (4 solar masses) move toward the upper left as their luminosity increases, while lower-mass stars move toward the lower right as their temperature decreases.

Answer:

Step-by-step explanation:-109.3=t-184.9

T=75.6

Answer: Hi!

4.89 * 2.2 = 10.758 (rounded is 10.76 or 10.8)

Tip: Line up the terms vertically and multiply.

Hope this helps!

The correct answers are:

vertical angle theorem

angle addition postulate

An angle is a mathematical term, which we can define, when two straight lines or rays meet at a common endpoint. The common point is called the vertex of an angle. The word angle comes from a Latin word named ‘angulus,’.

Interior angles:- The inner angle made by the intersection of two polygonal sides.

Exterior angles:- The outer angle made by the intersection of two polygonal sides.

The evidence in the proof that supports the statement that m/AOW = 45° is:

Statement 3: ZZOB ZXOA. This means that ZOB and ZOA are vertical angles, which means they are congruent.

Statement 4: m/XOA = 45°. This is the measure of ZOA, which is congruent to ZOB.

Statement 7: m/XOA + m/AOW = m/XOW. This is the angle addition postulate, which states that the sum of the measures of the angles in a triangle is 180°.

So, combining these pieces of evidence, we have:

m/XOA = 45° and m/XOA + m/AOW = m/XOW,

therefore m/AOW = m/XOW - m/XOA

                              = 90° - 45°

                              = 45°.

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Answer:7, 4, 6,

Step-by-step explanation: