Juan drove from his mother's house to his apartment at Arkansas Tech. After driving for 20 minutes, he was 62 miles away from his apartment. After driving for 32 minutes he was only 38 miles away. The time driving and the distance away from his apartment form a linear relationship. What is the independent and dependent variables

Answer:

16, 10

Step-by-step explanation:

There are 4 quarts in a gallon, so 4 gallons has 16 qt.

There are 2 pints in a quart, so 5 quarts has 10 pt.

a. The degree of the polynomial is 6.

b. Factoring the equation, we have:

x6 - 49x^4 = x^4(x^2 - 49) = x^4(x - 7)(x + 7)

a.The degree of the polynomial equation x^6 - 49x^4 = 0 is 6. This is determined by the highest exponent of x in the polynomial, which is 6.

b. The two roots of multiplicity 1 can be found by factoring the equation as x^4(x^2 - 49) = 0. Setting each factor equal to zero, we have x^4 = 0 and x^2 - 49 = 0.

From x^4 = 0, we find the root x = 0 with multiplicity 4.

From x^2 - 49 = 0, we get (x - 7)(x + 7) = 0. Therefore, the roots x = 7 and x = -7 each have multiplicity 1.

In summary, the equation x^6 - 49x^4 = 0 has a degree of 6, and the roots with multiplicity 1 are x = 0, x = 7, and x = -7.

So the roots of the equation are:

x = 0 (multiplicity 4)

x = 7 (multiplicity 1)

x = -7 (multiplicity 1)

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The population increases by 500 units between the 4th and the 6th years.

To calculate the increase in population between the 4th and the 6th years, we need to find the difference in population at these two time points.

The rate of increase in the population is given by the function 200 + 10t, where t is measured in years. We can find the population at a specific time by integrating this function with respect to t.

Integrating the function 200 + 10t, we get:

∫(200 + 10t) dt = 200t + 5t^2 + C

Now, let's calculate the population at the 4th and the 6th years:

Population at the 4th year: 200(4) + 5(4)^2 + C = 800 + 80 + C

= 880 + C

Population at the 6th year: 200(6) + 5(6)^2 + C = 1200 + 180 + C

= 1380 + C

The increase in population between the 4th and the 6th years is the difference between the population at these two time points:

1380 + C - (880 + C) = 1380 - 880

= 500

Therefore, the population increases by 500 units between the 4th and the 6th years.

The population increases by 500 units between the 4th and the 6th years.

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Answer:

If a table of values shows a constant rate of change, it is linear. ANSWER: Sample answer: A non-vertical graph that is a straight line is linear. An equation that can be written in the form y = mx + b is linear. If a table of values shows a constant rate of change, it is linear

Answer:

Hi,

The first one is the second one, the one on the top right. This is because you add two branches every step.

I'm not so sure about the second question. sorry ! hope it helps tho

Answer:

------------------

Use circumference formula:

Find the radius by rearranging the formula and substituting 32 for C:

Answer:

5.09 in

Step-by-step explanation:

We know that the formula to find the circumference of a circle is:

C = 2πr

Here,

C → Circumference → 32 in

r → radius

Let us find the radius of the circle by substituting the given values.

\(\sf C = 2\pi r\\\\\sf 32 = 2\pi r\\\\Divide\:both\:sides\:by\:2 \pi \:and\:make\:r\:the \:subject\\\\\dfrac{32}{2 \pi} =\dfrac{2 \pi r}{2 \pi} \\\\\red{5.09 \:in=r}\)

The n building exemplifies interactive design because it integrates into its façade interactive digital displays.

The n building showcases interactive design by seamlessly incorporating interactive digital displays into its façade. These displays allow for dynamic content, such as visuals, videos, and interactive elements, to be presented on the building's exterior.

By engaging with passersby and creating an interactive experience, the n building transforms a static architectural structure into a vibrant and participatory environment.

This integration of interactive digital displays into the building's façade not only enhances its visual appeal but also fosters a sense of connection and engagement with the surrounding community, blurring the boundaries between the physical and digital realms.

The n building exemplifies interactive design because it integrates into its façade elements that engage and interact with the users. This can include features such as interactive screens, touch-sensitive panels, or interactive lighting displays. These elements encourage user participation and create an immersive and engaging experience for those interacting with the building.

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Sanofi is utilizing Industry 4.0 technologies and blockchain technology in its supply chain to enhance efficiency, traceability, and transparency.

Sanofi, a pharmaceutical company, has embraced Industry 4.0 technologies to optimize its supply chain operations. These technologies include advanced analytics, Internet of Things (IoT) devices, automation, and robotics. By leveraging these technologies, Sanofi aims to improve operational efficiency, reduce costs, and enhance product quality.

For example, IoT devices can monitor temperature and humidity during transportation, ensuring the integrity of pharmaceutical products.

Additionally, Sanofi is leveraging blockchain technology in its supply chain management. Blockchain provides a decentralized and immutable ledger that enables secure and transparent tracking of products throughout the supply chain.

By implementing blockchain, Sanofi enhances traceability, reduces counterfeiting risks, and increases trust among stakeholders.

Pharmaceutical companies face various challenges, including stringent regulations, supply chain complexity, counterfeit drugs, and data security concerns. Technology can help address these challenges by improving supply chain visibility, enhancing product authentication, enabling data-driven decision-making, and ensuring regulatory compliance.

By leveraging Industry 4.0 technologies and blockchain, companies like Sanofi can overcome these challenges and drive innovation in the pharmaceutical industry.

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Answer:

Neither

Step-by-step explanation:

They need a 90°angle to be perpendicular.

And it has to not be touching to be parallel.

Answer:

10 students

Step-by-step explanation:

Hi there!

To find the answer, we first know that 9/11 students attend tutoring.

If 55 are assigned, that means that 45/55 students showed up.

This is because 11 * 5 = 55, which means this can be solved fairly easily now.

Since we multiplied the denominator, 11, by 5, we have to do the same thing to 9.

9 * 5 = 45

Now we have 45/55. We know that 45 students out of the 55 that were assigned showed up, but its asking for how many did not show up, so we just subtract 45 from 55 to get 10.

10 students did not show up for tutoring.

I hope this helped!

Answer:

The rule is add 4

The next number would be 772

Step-by-step explanation:

Hope this helps!!

Answer:

That will be 1/14 points

Step-by-step explanation:

==============================================

Work Shown:

1/4 = 0.25

1 & 1/4 = 1 + 1/4 = 1 + 0.25 = 1.25

The stock dropped by 1.25 points each day for 5 days

It dropped a total of 5*1.25 = 6.25 = 6 & 1/4 points.

------------

Alternative method:

5*(1 & 1/4) = 5*(1 + 1/4)

5*(1 & 1/4) = 5*1 + 5*(1/4)

5*(1 & 1/4) = 5 + 5/4

5*(1 & 1/4) = 5*(4/4) + 5/4

5*(1 & 1/4) = 20/4 + 5/4

5*(1 & 1/4) = (20+5)/4

5*(1 & 1/4) = 25/4

5*(1 & 1/4) = (24+1)/4

5*(1 & 1/4) = 24/4 + 1/4

5*(1 & 1/4) = 6 + 1/4

5*(1 & 1/4) = 6 & 1/4

We get the same answer as before.

Histograms are used to determine the empirical distribution of a variable. Therefore, option (e) is the correct one.

Histogram is used to summarize discrete or continuous data measured on an interval scale. It is often used to describe key features of the distribution of data in a practical way.

A histogram divides the range of possible values ​​in a data set into different classes or groups. For each group, a rectangle is created with a base length equal to the range of values ​​in that particular group and a length equal to the number of observations that fall into that group.

Histograms are similar to column charts, but there are no gaps between the bars. Histograms generally have equal width bars.

Thus, it can be concluded that histograms are used to determine the empirical distribution of a variable. Therefore, option (e) is the correct one.

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I believe target has the better deal.

Answer:

Ayudame a ayudarte, sube la foto que no esté borrosa

para ayudarte

Answer:

A is not a function because the x value is the same. Each x value can only have one y value for it to be a function.

Answer:

6

Step-by-step explanation:

Answer 3 kilometers

15 kilometers total minus 12 kilometers of the east bound car leaves only 3 kilometers for the northbound car to travel.

Answer: 1

Step-by-step explanation:

Pythagorean Theorem: a^2+b^2=c^2
2^2+b^2=(sqrt5)^2
4+b^2=5

b^2=5-4
b^2=1
b=1

the series Σ((-1)^(n+1)) / (n²+1) converges absolutely and conditionally.

To determine the convergence of the series Σ((-1)^(n+1)) / (n²+1), we can analyze its absolute convergence and conditional convergence separately.

Absolute Convergence:

To test for absolute convergence, we consider the series formed by taking the absolute value of each term: Σ|((-1)^(n+1)) / (n²+1)|.

Let's simplify the terms: \(|((-1)^{(n+1))} / (n^2+1)| = 1 / (n^2+1).\)

Now, we can use the comparison test. Comparing this series to the p-series 1/n², we can see that 1/(n²+1) ≤ 1/n² for all n > 1.

The p-series Σ(1/n²) converges since its exponent is greater than 1. Therefore, by the comparison test, the series Σ(1/(n²+1)) also converges absolutely.

Conditional Convergence:

To test for conditional convergence, we need to investigate whether the series Σ((-1)^(n+1)) / (n²+1) converges when the terms are considered with their signs intact.

By using the alternating series test, we check the conditions:

1. The terms (-1)^(n+1) / (n²+1) are alternately positive and negative for all n > 1.

2. The absolute values of the terms, 1/(n²+1), form a decreasing sequence.

Since both conditions are satisfied, the series Σ((-1)^(n+1)) / (n²+1) converges conditionally

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(a) The production function has constant returns to scale, as doubling the inputs results in a doubling of the output, and similarly for other scaling factors.

(b) The per-worker production function is obtained by dividing the production function by the labor input, denoted by L or workers.

(a) To determine if the production function exhibits constant returns to scale, we need to examine the behavior of the function when inputs are scaled proportionally. Let's assume the production function is given by \(y = f(x1, x2) = x1^2 \times x2^(2\pi ).\)

To test for constant returns to scale, we evaluate the production function when inputs are multiplied by a constant factor, say λ. Therefore, we have \(y' = f(\lambda x1, \lambda x2) = (\lambda x1)^2 \times (\lambda x2)^(2\pi) = \lambda ^2 \times (x1^2 \times x2^(2\pi)) = \lambda ^2 \times y.\)

Since \(\lambda ^2 \times y = \lambda \times \lambda \times y = \lambda \times y'\), we see that the output is proportional to the input scale factor λ. This indicates that the production function has constant returns to scale, as doubling the inputs results in a doubling of the output, and similarly for other scaling factors.

(b) Let's denote the per-worker production function as \(y/L = f(x1, x2)/L = (x1^2 \times x2^(2\pi))/L.\)

To find the steady-state levels of income per worker (y/L) and consumption per worker (C/L), we need to analyze the equilibrium conditions. However, the provided information is insufficient to derive the specific equations or parameters required for the analysis.

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Farmer Ed has 3,000 meters of fencing and wants to enclose a rectangular plot that borders on a river.The largest area that can be enclosed is 750,000 square meters.

To get the largest area that can be enclosed, we have to find the dimensions of the rectangular plot. Let's assume that the width of the rectangle is x meters.The length of the rectangle can be found by subtracting the width from the total length of fencing available:L = 3000 - x. The area of the rectangle can be found by multiplying the length and width:Area = L × W = (3000 - x) × x = 3000x - x²To find the maximum value of the area, we can differentiate the area equation with respect to x and set it equal to zero.

Then we can solve for x: dA/dx = 3000 - 2x = 0x = 1500. This means that the width of the rectangle is 1500 meters and the length is 3000 - 1500 = 1500 meters.The area of the rectangle is therefore: Area = L × W = (3000 - 1500) × 1500 = 750,000 square meters. So the largest area that can be enclosed is 750,000 square meters.

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Answer:

26.7

Hope this helped

Answer:

w

Step-by-step explanation:

Answer: I can see the page it say file is deleted

:(

Answer:

5.(x+7)(4x2+7)

6.(b−3x)(3x2−1)

Answer:

x= -b ±√b²- 4ac/2a

Step-by-step explanation:

ax2 + bx + c = 0

Dividing the quadratic equation by a gives

x2 + b/ax + c/a = 0

x2 + b/ax = - c/a

Applying the square formula

(x)^2 + 2(x) (b/2a) + (b/2a)^2= + (b/2a)^2- c/a

(x+b/2a)^2= b²/4a² - c/a

(x+b/2a)^2= b²/4a² - 4ac/4a²

(x+b/2a)^2= b²- 4ac/4a²

Taking square root of both sides gives

(x+b/2a)= ±√b²- 4ac/2a

x= -b/2a±√b²- 4ac/2a

x= -b ±√b²- 4ac/2a

This is called the quadratic formula and it can solve the value for x for the given value of a, b and c for the quadratic equation.

From this it is concluded that

Discriminant = b2 - 4ac > 0 means there will be two distinct real roots. Discriminant = b2 - 4ac = 0 means there will be only one real root. Discriminant = b2 - 4ac < 0 means there will be no real roots.

This is because a square root of a value greater than 0 is possible and gives two values for roots of x.

The square root of a value less than 0 gives a negative number and therefore the roots are an imaginary number.

The square root of a value greater equal to 0 gives a zero leaving behind only one real root.

To solve for angle A and angle B in the given triangle, we can use the Law of Sines. The Law of Sines states that the ratio of the length of a side to the sine of its opposite angle is constant for all sides and angles in a triangle.

In this case, we have side a with length 2 and side c with length 9. Let's denote angle A as angle opposite side a and angle B as angle opposite side b (which is unknown).

Using the Law of Sines, we have:

sin(A) / a = sin(B) / b

Plugging in the known values, we get:

sin(A) / 2 = sin(B) / 9

To find angle A, we can use the arcsine function:

A = arcsin((sin(B) / 9) * 2)

To find angle B, we can rearrange the equation:

sin(B) = (sin(A) / 2) * 9

B = arcsin((sin(A) / 2) * 9)

Now we can calculate the angles using a calculator:

A ≈ 19.5 degrees (rounded to one decimal place)

B ≈ 84.1 degrees (rounded to one decimal place)

Therefore, angle A is approximately 19.5 degrees and angle B is approximately 84.1 degrees.

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The amount of sales tax is $87.79.

Given a total purchase price of a sofa as $1,254.07 and state taxes of 7%.

We are required to calculate the amount of sales tax.

The amount of sales tax can be calculated by multiplying the purchase price by the sales tax rate.

Let's represent the sales tax rate by `r`.

Therefore, the sales tax formula is expressed as:

Sales tax = r * purchase price

In this case, the rate of the sales tax `r` is 7%.

Therefore, we have:r = 7% = 0.07

Now we substitute the values given into the formula:

Sales tax = 0.07 * $1,254.07= $87.79

Therefore, the amount of sales tax is $87.79.

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Answer:

just think(0,6) as A,(4,-2) as B and (6,0)as C then join ABC and you will get your's parabola

Answer:

\(y = \dfrac12x^2 - 4x + 6\)

Step-by-step explanation:

vertex form of parabola:  y = a(x - h)² + k

where (h, k) is the vertex

Given vertex = (4, -2) :

⇒ y = a(x - 4)² - 2

Given y-intercept = (0, 6) substitute values into equation and solve for a:

⇒ 6 = a(0 - 4)² - 2

⇒ 6 = 16a - 2

⇒ 16a = 8

⇒ a = 1/2

Therefore, equation of parabola:

⇒ y = 1/2(x - 4)² - 2

⇒ y = 1/2(x² - 8x + 16) - 2

⇒ y = (1/2)x² - 4x + 6

ABC reports the liability on the balance sheet as a $1 million current liability, and a $4 million long-term liability.

A current liability is a liability that is payable within 12 months or one year.

On the other hand, a long-term liability is a liability that is payable after 12 months or one year.

Since $1 million is payable in each of the next five years, this implies $1 million is payable within one year while $4 million is payable after one year.

Therefore, ABC reports the liability on the balance sheet as a $1 million current liability, and a $4 million long-term liability.

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