Is the ordered pair (2,1) a solution to the system below? 2.x + 3y = 7 8x – 3y = 13 yes Or no​

To accurately represent men's and women's shoe sizes separately, it is recommended to calculate and compare the average or median shoe size for each group separately.

The problem with the central measure, mean or median, in this case is that the data is not gender-specific and there is a possibility that male and female shoe size distributions are different. Therefore, calculating the average or median shoe size for all students may not accurately reflect the typical male and female shoe sizes, respectively.

For example, if the males in the sample have, on average, a larger shoe size than the females, then the average shoe size of all students might be biased towards the larger size, even if most of the students are female. On the other hand, if you have several boys with very large shoe sizes, the median shoe size of all students may be biased toward the larger size, even if most of the students are women with small shoe sizes.

To accurately represent men's and women's shoe sizes separately, it is recommended to calculate and compare the average or median shoe size for each group separately. Alternatively, a fashion report representing the most common shoe sizes in the data might be a better measure of the centroid.

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1. Power series representation of 1+1² and determination of interval of convergence: Given the function, 1 + 1². For f(2) = 1/24 + 1/16 = 5/48, g(x) = 0 + 0x + 0x^2 + ... and its interval of convergence is (-∞, +∞).

To determine the power series representation for this function, we can consider its derivative in order to calculate a general formula for its nth derivative.

This derivative of the given function can be calculated as: f′(x) = 0 + 2(1) x^(2 - 1) = 2x.

We can then find the nth derivative of this function, f^(n)(x) = n! × 2x^(n).

Thus, we can write the power series representation of the function f(x) = 1 + x^2 as:

f(x) = Σn = 0 ∞(1 + x^2)^n/n!

The interval of convergence for this power series can be determined using the ratio test:

lim(n→∞) |(1 + x^2)^(n + 1)/(n + 1)!| / |(1 + x^2)^n/n!|

= lim(n→∞) |(1 + x^2)/(n + 1)| = 0.

The above limit equals 0, which implies that the series converges for all values of x. Hence, the interval of convergence is (-∞, +∞).

a. Given the function, 1 + 1², its power series representation is:

f(x) = 1 + x^2Σn = 0 ∞(1 + x^2)^n/n!

For f(2) = 1/24 + 1/16

= 5/48,

the given value is in the interval of convergence, hence, it is valid.

b. Given the function, g(x) = 1 - 1² = 0, which is a constant function. Its power series representation is simply g(x) = 0 + 0x + 0x^2 + ... and its interval of convergence is (-∞, +∞).

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Answer:

The number in front of the x

Step-by-step explanation:

Once you have your formula set to y = , then whatever number is in front of the x is the slope. This is according to the formula y = mx + b, where m is the slope.

1. y = -x  slope: -1

2. y = x - 3   slope: 1

3. y = 3x    slope: 3

4. y = 1/2x    slope: 1/2

5. y = 2x     slope: 2

Answer:

Step-by-step explanation:

divide both sides by 3

3z>6

3z/3>6/3

z>2

Answer:

The answer is C.

Step-by-step explanation:

I would simplify the expression first.

Equation: (6m^-1)^-3

You can get rid of n^0 because that equals 1.

Any expression raised to the power of -1 equals its reciprocal.

Equation: (6/m)^-3

Equation: (m/6)^3

Final Equation: m^3/216

Now, plug in 3.

(3)^3/216.

27/216 = 1/8

Hope this helps!

Answer:

(1000-10/10)%

(990/10)%

99%

Answer:

A. (-2, 0)

I hope this helps you.

Answer:

x+a= b , where a,b are uncertain values. Although both can be solved similarly, the difference is that, in literal equations, the letters representing the amount of a numerical value do not always change; however, in a single-variable equation, the letters representing these can/may vary.

Step-by-step explanation:

x+a= b , where a,b are uncertain values. Although both can be solved similarly, the difference is that, in literal equations, the letters representing the amount of a numerical value do not always change; however, in a single-variable equation, the letters representing these can/may vary.

Answer:

I think acute angle

hope it will helpful to you

Answer:

As I think the correct answer must be Right angle as according to pythagoras theorem,✓24^2+7^2=25.So third option is correct.100%.

Answer:

brainliest?

Step-by-step explanation:

5.3 years

we know that    

The compound interest formula is equal to  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have  

substitute in the formula above  and solve for t

applying log both sides

Answer:

2\(\sqrt{3}\)

Step-by-step explanation:

Using the rule of radicals

\(\sqrt{a}\) × \(\sqrt{b}\) ⇔ \(\sqrt{ab}\) , then

\(\sqrt{12}\)

= \(\sqrt{4(3)}\)

= \(\sqrt{4}\) × \(\sqrt{3}\)

= 2\(\sqrt{3}\)

Yes, leading coefficient and degree of the polynomial functions can affect the behavior of its graph. Because of the positive leading coefficient, the graph ascends to the right. To ascertain the behavior, consider the function's degree and the sign of the leading coefficient.

The term with the greatest x power is the leading term in a polynomial function. The leading coefficient is the coefficient of the leading phrase.

Given,

Yes, leading coefficient and degree of the polynomial functions can affect the behavior of its graph.

The graph's final behavior is determined by a polynomial function's degree and leading coefficient. For very big or very small values, the leading coefficient is more important than the other function coefficients. The coefficient of the leading term is the leading coefficient in a polynomial. Because of the positive leading coefficient, the graph ascends to the right. To ascertain the behavior, consider the function's degree and the sign of the leading coefficient.

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The correct answer is:

The results of the ANOVA indicate that both Kia and Honda have significantly better gas mileage than Ford.

Given is an information about,
Least Squares Means

Adjustment for Multiple Comparisons: Tukey-Kramer

We need to identify the correct answer from the options given.

So, from the table we can conclude that "the results of the ANOVA indicate that both Kia and Honda have significantly better gas mileage than Ford."

This can be inferred from the comparison of LSMEAN numbers in the table.

The LSMEAN number for Ford is 1, for Honda it is 2, and for Kia it is 3. Comparing the values in the table, we can see that the Pr > t values for the comparisons between Ford and both Honda and Kia are less than the significance level (0.05).

This indicates that there are significant differences in gas mileage between Ford and both Honda and Kia, suggesting that both Honda and Kia have significantly better gas mileage than Ford.

Hence the correct option is 4th.

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Complete question is attached.

Answer:

To add integers having the same sign, keep the same sign and add the absolute value of each number.

Step-by-step explanation:

hope it help

The strongest argument in favor of homework is that it reinforces classroom learning. The strongest argument against homework is that it infringes upon students' personal time and can cause unnecessary stress. The topic is about Education and Pedagogy specifically focusing on the surrounding the effectiveness and implications of homework .

Homework has been a long-standing educational practice, with proponents and detractors on both sides of the debate. One of the strongest arguments in favor of homework is that it reinforces classroom learning. By completing homework assignments, students are able to practice and solidify the concepts they learned in class.

This can help them better retain the information and apply it to future tasks.

On the other hand, the strongest argument against homework is that it infringes upon students' personal time and can cause unnecessary stress. Students are often involved in extracurricular activities, sports, and other interests, leaving little time for homework.

This can cause stress and anxiety for students who are already struggling to balance their academic and personal lives. Additionally, some argue that homework assignments are often too difficult or time-consuming, leaving students feeling overwhelmed and frustrated.

In conclusion, while there are valid arguments on both sides of the homework debate, it is ultimately up to individual schools and teachers to determine the amount and type of homework that is appropriate for their students. It is important for educators to consider the potential benefits and drawbacks of homework assignments and make informed decisions that prioritize student learning and well-being.

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Answer:

D. 12

Step-by-step explanation:

Answer:

Always

Step-by-step explanation:

I know this question is 3 weeks old, but for people in the future who need the answer.

The first derivatives of the functions are

(a) ln(x¹⁰) = 10/x

(b) tan-¹(x²) = 2x/(x⁴ + 1)

(c) sin-¹(4x) = 4/√(1 - 16x²)

From the question, we have the following parameters that can be used in our computation:

(a) ln(x¹⁰)

(b) tan-¹(x²)

(c) sin-¹(4x)

The derivative of the functions can be calculated using the first principle which states that

if f(x) = axⁿ, then f'(x) = naxⁿ⁻¹

Using the above as a guide, we have the following:

(a) ln(x¹⁰) = 10/x

(b) tan-¹(x²) = 2x/(x⁴ + 1)

(c) sin-¹(4x) = 4/√(1 - 16x²)

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The value of y is 2/3

An algebraic expression is an expression made up of variables and constants, along with algebraic operations such as addition, subtraction, multiplication, division, etc

Given;

8y+4(5y-3)

With the knowledge of BODMAS,

Expand the bracket

8y + 20y - 12

Now, let's add like terms

18y - 12

Make into an equation

18y - 12 = 0

18y = 12

Make 'y' the subject of formula

y = 12/ 18

Find a common divisor

y = 2/ 3

Thus, the value of y is 2/3

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Solution

Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, translation, reflection and dilation.

Dilation is the enlargement or reduction in the size of an image. If a point A(x, y) is dilated by a factor k, the new point is A'(kx, ky).

A Dilation is defined as a transformation in which the Image (The figure obtained after the transformation) and the Pre-Image (The original figure, before the transformation) have the same shape, but their sizes are different.

In this case you know that the triangle ABC is dilated by a scale factor of 3 with a center of dilation at the origin.

Given triangle ABC has vertices at A(-1, 0), B(0, 1), C(3, 0).

If the triangle is dilated by a scale factor of 3, the new point is:

The new point is: A'(-1/3, 0), B'(0, 1/3), C'(1, 0). Hence the area of the triangle after dilation will be (one third) of the old points

Answer:

-40

Step-by-step explanation:

-7 x 7 + 9 x (-1) / (-1)

-49 + 9 x (-1) / (-1)

-49 - 9 / (-1)

-49 + 9

= -40

Here are the vectors **t**, **n**, and **b** at the given point:

* **t** = (-3 sin t, 3 cos t, 0)

* **n** = (-3 cos t, -3 sin t, 3 / cos^2 t)

* **b** = (3 cos^2 t, -3 sin^2 t, -3)

The vector **t** is the unit tangent vector, which points in the direction of the curve at the given point. The vector **n** is the unit normal vector, which points in the direction perpendicular to the curve at the given point. The vector **b** is the binormal vector, which points in the direction that is perpendicular to both **t** and **n**.

To find the vectors **t**, **n**, and **b**, we can use the following formulas:

```

t(t) = r'(t) / |r'(t)|

n(t) = (t(t) x r(t)) / |t(t) x r(t)|

b(t) = t(t) x n(t)

```

In this case, we have:

```

r(t) = (3 cos t, 3 sin t, 3 ln cos t)

r'(t) = (-3 sin t, 3 cos t, 3 / cos^2 t)

```

Substituting these into the formulas above, we can find the vectors **t**, **n**, and **b** as shown.

The vectors **t**, **n**, and **b** are all orthogonal to each other at the given point. This is because the curve is a smooth curve, and the vectors are defined in such a way that they are always orthogonal to each other.

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The binormal vector (b) is perpendicular to both the tangent and normal vectors and completes the orthogonal coordinate system.

To find the vectors t, n, and b at the given point, we need to calculate the first derivative, second derivative, and third derivative of the position vector r(t).
Given r(t) = (3 cos t, 3 sin t, 3 ln cos t), we can calculate the derivatives as follows:
First derivative:
r'(t) = (-3 sin t, 3 cos t, -3 sin t / cos t)
Second derivative:
r''(t) = (-3 cos t, -3 sin t, -3 cos t / cos^2 t + 3 sin^2 t / cos t)
       = (-3 cos t, -3 sin t, -3 cos t / cos^2 t + 3 tan^2 t)
Third derivative:
r'''(t) = (3 sin t, -3 cos t, 6 cos t / cos^3 t - 6 sin t / cos t)
        = (3 sin t, -3 cos t, 6 sec^3 t - 6 tan t sec t)
At the given point (3, 0, 0), substitute t = 0 into the derivatives to find the vectors:
r'(0) = (0, 3, 0)
r''(0) = (-3, 0, 3)
r'''(0) = (0, -3, 6)
Therefore, at the given point, the vectors t, n, and b are:
t = r'(0) = (0, 3, 0)
n = r''(0) = (-3, 0, 3)
b = r'''(0) = (0, -3, 6)
These vectors represent the tangent, normal, and binormal vectors, respectively, at the given point.
The tangent vector (t) represents the direction of motion of the curve at that point. The normal vector (n) is perpendicular to the tangent vector and points towards the center of curvature.

The binormal vector (b) is perpendicular to both the tangent and normal vectors and completes the orthogonal coordinate system.
Remember to check your calculations and units when applying this method to different functions.

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Answer:

Note that I slightly misread the question and in the steps below found the answer to the nearest thousandth.  To the nearest hundredth though, the rectangle has a length of 6.69cm, and a width of 1.35 cm.

Step-by-step explanation:

We are told that the rectangle has an area of nine square centimetres, and that it's length is 4 centimetres more than twice its width. We can express those as:

\(a = 9cm^2\)

and

\(l = 2w + 4\)

We also know that the area of a rectangle is its length times its width:

\(a = l \times w\)

We can take that last expression, and plug in the other two, to solve for w

\(a = l \times w\\9 = (2w + 4) \times w\\9 = w(2w + 4) \\9 = 2w^2 + 4w\\4.5 = w^2 + 2w\\5.5 = w^2 + 2w + 1\\5.5 = (w + 1)^2\\w + 1 = \sqrt{5.5}\\w = \sqrt{5.5} - 1\\w \approx 2.345 - 1\\w \approx 1.345\)

We can then plug that into expression "l = 2w + 4" to find the length:

\(l = 2w + 4\\l = 2(\sqrt{5.5} - 1) + 4\\l = 2 * \sqrt{5.5} - 2 + 4\\l = \sqrt{4} * \sqrt{5.5} + 2\\l = \sqrt{22} + 2\\l \approx 4.690 + 2\\l \approx 6.690\)

Now let's see if we have that right, we can multiply these and see if we get an area of 9:

\(1.345 \times 6.690 \approx 8.998\\\)

Which after accounting for rounding errors is matches the 9 square centimetres.

a) The forecast is approximately miles. b) the Mean Absolute Deviation (MAD) based on the forecast is approximately miles. c) The forecast for year 6 is approximately miles. d) the last forecast is 3,468 miles.

a) To calculate the forecast for year 6 using a 2-year moving average, we take the average of the mileage for years 5 and 4. This provides us with the forecasted value for year 6.

b) The Mean Absolute Deviation (MAD) for the 2-year moving average forecast is calculated by taking the absolute difference between the actual mileage for year 6 and the forecasted value and then finding the average of these differences.

c) When using a weighted 2-year moving average, we assign weights to the most recent and previous periods. The forecast for year 6 is calculated by multiplying the mileage for year 5 by 0.40 and the mileage for year 4 by 0.60, and summing these weighted values.

The MAD for the weighted 2-year moving average forecast is calculated in the same way as in part b, by taking the absolute difference between the actual mileage for year 6 and the weighted forecasted value and finding the average of these differences.

d) Exponential smoothing involves assigning a weight (α) to the most recent forecasted value and adjusting it with the previous actual value. The forecast for year 6 is calculated by adding α times the difference between the actual mileage for year 5 and the previous forecasted value, to the previous forecasted value.

In this case, with α=0.20 and a forecast of 3,100 miles for year 1, we perform this exponential smoothing calculation iteratively for each year until we reach year 6, resulting in the forecasted value of approximately 3,468 miles.

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To find only one fake coin from 8 coins can be done in two weighings.

Divide the coins into three groups, A, B, and C, each consisting of three coins.

A and B are first weighed against one another. If the balancing scale is straight, fake coins belong in group C; otherwise, they belong in A or B, depending on which side of the scale is up.

Finding the lighter fake coin requires a second weighing if the first weighing indicates that the fake coins are in group C. Weigh any two phony coins from the group if A/B. The third coin is phony if the scale is balanced; else, choose the coin that is lighter.

For 3 weighing, make pair of 4 and followed by pair of 2 for the lighter group. At last, compare the last 2 coins to find the lighter coins.

8 → 4 →2 →1

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Inference is referred to as all the data collected in a particular study.

Etymologically, the word "infer" means to "carry ahead." Inferences are stages in reasoning that connect premises to logical conclusions. The dichotomy between deduction and induction in inference theory, which dates at least to Aristotle in Europe, is a classic one (300s BCE). Deduction is inference that results in logical conclusions from premises that are known to be true or that are presumed to be true, while the logic of correct inference is investigated. A universal conclusion is inferred by induction from specific evidence. Contradistinguishing abduction from induction, Charles Sanders Peirce is credited with identifying a third sort of inference. Researchers in the domains of logic, argumentation studies, and cognitive psychology traditionally study human inference (i.e., how people draw conclusions); artificial intelligence researchers create automated inference systems to mimic human inference.

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Yes, the argument is valid. If the two premises (p1 and p2) are true, then the conclusion (c) must also be true.

The argument is valid because the conclusion is logically entailed by the two premises. If it is raining then the car will get wet, and if it is not raining then the car will not get wet. This follows from the logical law of noncontradiction, which states that for any statement, either it is true or its negation is true, but not both. Since the first premise states that it is raining, and the second premise states that it is not raining, the logical conclusion is that the car will not get wet.

The argument is based on a logical principle known as noncontradiction, which states that for any statement, either it is true or its negation is true, but not both. In this case, the two premises (p1 and p2) both concern the same statement: that it is raining. The first premise states that if it is raining then the car will get wet, and the second premise states that it is not raining. Therefore, the logical conclusion is that the car will not get wet. This conclusion follows logically from the two premises, so the argument is valid.

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Answer:

it's 1 of a 6 chance fir getting six

Answer: 30.5 %

explanation: When you roll two dice, you have a 30.5 % chance at least one 6 will appear. This figure can also be figured out mathematically, without the use of the graphic.