It is known that lim 20 sin(2.c) 2x - 1. What is lim tan(2x) X+0 6x sec(3x) ? A 0 B 1 6 C 1 3 D nonexistent

The set {(x, y): xy ≥ 1; x > 0; y > 0} is not convex because there exist line segments connecting two points within the set that extend outside the set.

To determine if the set is convex, we need to check if any two points within the set form a line segment that lies entirely within the set.

Consider two points A = (x1, y1) and B = (x2, y2) in the set, where xy ≥ 1, x > 0, and y > 0.

Let's assume A and B are distinct. Now, consider the midpoint M = ((x1 + x2)/2, (y1 + y2)/2) of the line segment AB.

To determine if M lies in the set, we need to check if (x1 + x2)/2 * (y1 + y2)/2 ≥ 1, x1 + x2 > 0, and y1 + y2 > 0.

However, it is possible to find points A and B in the set such that their midpoint M does not satisfy the above conditions. For example, if A = (1, 1) and B = (3, 1/3), the midpoint M = (2, 2/3) does not satisfy (x1 + x2)/2 * (y1 + y2)/2 ≥ 1.

Therefore, the set is not convex because there exist line segments connecting two points within the set that extend outside the set.

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Answer:

Step-by-step explanation:

∫41 xh''(x)dx=41[x∫h''(x)dx-∫{1∫h''(x)dx}dx]+c

The value of \(\int\limits^{4}_{1} {x\cdot h''(x)} \, dx\) is 8.5. The choice that represent the best approximation is A.

This integral can be approximated by the following Riemann sum:

\(A = \Sigma\limits_{i=0}^{2} \left\{(x_{i+1}-x_{i})\cdot x_{i}\cdot h''(x_{i})+\frac{1}{2}\cdot (x_{i+1}-x_{i})\cdot [x_{i+1}\cdot h''(x_{i+1})-x_{i}\cdot h''(x_{i})] \right\}\)

\(A = \frac{1}{2} \cdot \Sigma\limits_{i=0}^{2} \left\{(x_{i+1}-x_{i})\cdot [x_{i+1}\cdot h''(x_{i+1})+x_{i}\cdot h''(x_{i})] \right\}\)

Then, the approximate value of the integral is:

\(A = \frac{1}{2}\cdot \{(2-1)\cdot [(2)\cdot 2+(1)\cdot (-5)]+(3-2)\cdot [(3)\cdot 1+(2)\cdot 2]+(4-1)\cdot [(4)\cdot 2+(3)\cdot 1]\}\)

\(A = 8.5\)

The value of \(\int\limits^{4}_{1} {x\cdot h''(x)} \, dx\) is 8.5. The choice that represent the best approximation is A. \(\blacksquare\)

The statement is incomplete and poorly formatted and table is missing. Complete statement is:

Selected values of the twice-differentiable function and its first and second derivatives are:

\(h(1) = 3\), \(h(2) = 6\), \(h(3) = 2\), \(h(4) = 10\)

\(h'(1) = 4\), \(h'(2) = -4\), \(h'(3) = 3\), \(h'(4) = 5\)

\(h''(1) = -5\), \(h''(2) = 2\), \(h''(3) = 1\), \(h''(4) = 2\)

Selected values of the twice-differentiable function \(h\) and its first and second derivatives are given in the table above. What is the value of \(\int\limits^{4}_{1} {x\cdot h''(x)} \, dx\)?

A. 9, B. 13, C. 23, D. 38

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The values of the missing angles and sides after dilation are:

m∠C'B'D' = 95°,  CQ = 6 and  B'D' = 11.

m∠C'B'D = 180° - m∠B'C'D' - m∠B'D'C'

m∠B'C'D = m∠BCD, m∠B'D'C' = m∠BDC  (dilation)

m∠C'B'D = 180° - 34° - 51° = 95°

Thus, by way of scale factor we can say that:

BC/B'C' = BD/B'D' = 36/18 = 2

B'D' = ¹/₂BD = ¹/₂ * 22 = 11

ΔC'P'Q ∼ ΔCPQ

Thus:

C'Q'/CQ = C'D'/CD = D'Q'/DQ

CQ = 2C'Q' = 2 * 3 = 6

Therefore, m∠C'B'D' = 95°,  CQ = 6 and  B'D' = 11.

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The 90% confidence interval estimate of the difference between the means of the two populations is (4.228, 13.772).

To find a 90% confidence interval estimate of the difference between the means of the two populations, we can use the formula:

Confidence interval = (x₁ - x₂) ± Z * sqrt((σ₁² / n₁) + (σ₂² / n₂))

Where:

x₁ and x₂ are the sample means

σ₁ and σ₂ are the population standard deviations

n₁ and n₂ are the sample sizes

Z is the critical value corresponding to the desired confidence level

Given:

x₁ = 123

x₂ = 114

σ₁ = 25

σ₂ = 11

n₁ = 90

n₂ = 81

First, we need to find the critical value (Z) corresponding to a 90% confidence level. Since we want to find the two-sided confidence interval, we will use the standard normal distribution.

Using a standard normal distribution table or calculator, we find that the critical value for a 90% confidence level is approximately 1.645.

Now, we can calculate the confidence interval:

Confidence interval = (123 - 114) ± 1.645 * sqrt((25² / 90) + (11² / 81))

Confidence interval = 9 ± 1.645 * sqrt((625 / 90) + (121 / 81))

Confidence interval = 9 ± 1.645 * sqrt(6.944 + 1.493)

Confidence interval = 9 ± 1.645 * sqrt(8.437)

Confidence interval = 9 ± 1.645 * 2.902

Confidence interval = 9 ± 4.772

The 90% confidence interval estimate of the difference between the means of the two populations is (4.228, 13.772).

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(a) The greatest common divisor of \(x^3\) - 6x - 7 and \(x^4\) is 1.

(b) The greatest common divisor of \(x^2\)- 1 and 2\(x^7\) - 4x\(^5\) + 2 is 1.

(a) To find the greatest common divisor (GCD) of the polynomials, we can use polynomial long division.

Dividing \(x^3\) - 6x - 7 by \(x^4\), we get a remainder of \(x^3\) - 6x - 7.

Since the remainder is non-zero, the GCD of \(x^3\) - 6x - 7 and \(x^4\) is 1.

(b) To find the GCD of \(x^2\) - 1 and 2\(x^7\) - 4\(x^5\) + 2, we can again use polynomial long division.

Dividing 2\(x^7\) - 4\(x^5\) + 2 by \(x^2\) - 1, we get a remainder of 2\(x^5\) + 2.

Since the remainder is non-zero, the GCD of \(x^2\) - 1 and 2\(x^7\) - 4\(x^5\) + 2 is 1.

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Answer:

> -24.32 I hope that help so it is a on your screen

Step-by-step explanation:

1) = 4ab

2) 12a2b

3) 8ab2

4) 6ab2

5) 12abc

6) 6ab2c

7) 16a2bc

8) 27abc

Answer:

$4.16

Step-by-step explanation:

To find out how much 8 ounces of frozen yogurt costs if each ounce costs $0.52, we can use an equation that looks like this:

Therefore, for 8 ounces of yogurt is will cost $4.16.

The possible value of x is 17 and the degree measure of each angle is m∠P = 57°, m∠Q = 110°, and m∠R = 17°.

What are the degree measures of the three angles in triangle?

The angle sum of a triangle will always be equal to 180°. The angle sum of a quadrilateral is equal to 360°, and a triangle can be created by slicing a quadrilateral in half from corner to corner. Since a triangle is essentially half of a quadrilateral, its angle measures should be half as well. Half of 360° is 180°.

We have given,

The triangle PQR,

m∠P=(4x - 9), m∠Q=(6x+2), and m∠R=x. (a) Write an equation to find x.

a)

In a triangle, the sum of the degree measures of the three angles must be 180 degrees.

So for the triangle with angles P, Q, and R, we can use this rule to write the following equation:

m∠P + m∠Q + m∠R = 180

(4x - 9) + (6x + 2) + x = 180

11x - 7 = 180

11x = 187

x = 17

This equation shows that x = 17 is the only possible value of x that satisfies the triangle inequality rule for the given triangle.

b) To find the degree measure of each angle:

m∠P = 4x - 9 = 4(17) - 9 = 57°

m∠Q = 6x + 2 = 6(17) + 2 = 110°

m∠R = x = 17°

Hence, the possible value of x is 17 and the degree measure of each angle is m∠P = 57°, m∠Q = 110°, and m∠R = 17°.

.

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Step-by-step explanation:

the last one is the correct answer

\( \frac{1}{ {n}^{18} } \\ = {n}^{ - 18} \\ = {n}^{( - 3 \times 6)} \\ = ( {n}^{ - 3} ) ^{6} \)

\(( {n}^{ - 3} ) ^{6} \)

The point on the graph where the tangent plane is parallel is (52, 52, -5382).

What is the tangent plane?

The surface that contains all tangent lines of the curve at a point, $P$, that lies on the surface and passes through the point is represented by the tangent plane. We discovered earlier in our talks of derivatives and tangent lines that we can use tangent lines to mimic the behavior of a graph. We may employ tangent planes for a similar reason now that we're working with multivariable functions and three-dimensional coordinate systems.

Here, we have

Given: Let P be the tangent plane to the graph of g(x, y) = 26 – 13x² – 26y² at the point (4, 2, –286). Let f(x, y) = 26 – x² - y².

We have to find the point on the graph where the tangent plane is parallel.

Let P be the tangent plane to the graph z = g(x, y) = 26 – 13x² – 26y² at the point (4, 2, –286).

φ(x,y,z) = 13x² + 26y² + z - 26

Δφ = 26xi + 52yj + k

Δφ(4, 2, –286) = 104i + 104j + k

Then,

P: 104(x-4) + 104(y-2)+1(z+286) = 0

104x + 104y + z = 338...(1)

Now, Let

ψ(x,y,z) =  x² + y² + z - 26

Δψ = 2xi + 2yj + k

Let (x₀,y₀,z₀) be the point of the graph z = f(x,y) = 26 – x² - y² where the tangent plane in the plane is parallel to equation (1).

Δψ (x₀,y₀,z₀)  =  (2x₀,2y₀,1)

= 2x₀/104 = 2y₀/104 = 1/1

x₀ = 52 = y₀

Now, z₀ = 26 – x₀² - y₀² = 26 – 52² - 52²= -5382

Hence,  the point on the graph where the tangent plane is parallel is (52, 52, -5382).

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The derivative \(\( y' \)\) of the implicit function \(\( y^2 - xy = -2 \)\) is 0, indicating a constant slope with no change in relation to \(\( x \)\).

To find \(\( y' \)\)for the implicit function \(\( y^2 - xy = -2 \)\), we can differentiate both sides of the equation with respect to \(\( x \)\) using the chain rule. Let's go step by step:

Differentiating \(\( y^2 \)\) with respect to \(\( x \)\) using the chain rule:

\(\[\frac{d}{dx}(y^2) = 2y \cdot \frac{dy}{dx}\]\)

Differentiating \(\( xy \)\) with respect to \(\( x \)\) using the product rule:

\(\[\frac{d}{dx}(xy) = x \cdot \frac{dy}{dx} + y \cdot \frac{dx}{dx} = x \cdot \frac{dy}{dx} + y\]\)

Differentiating the constant term (-2) with respect to \(\( x \)\) gives us zero since it's a constant.

So, the differentiation of the entire equation is:

\(\[2y \cdot \frac{dy}{dx} - (x \cdot \frac{dy}{dx} + y) = 0\]\)

Now, let's rearrange the terms:

\(\[(2y - y) \cdot \frac{dy}{dx} - x \cdot \frac{dy}{dx} = 0\]\)

Simplifying further:

\(\[y \cdot \frac{dy}{dx}\) \(- x \cdot \frac{dy}{dx} = 0\]\)

Factoring out:

\(\[(\frac{dy}{dx})(y - x) = 0 \]\)

Finally, solving:

\(\[\frac{dy}{dx} = \frac{0}{y - x} = 0\]\)

Therefore, the derivative \(\( y' \)\) of the given implicit function is 0.

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Answer:

21606 ft

Step-by-step explanation:

get difference between elevations with subtraction

20320 - - 1286

20320 + 1286

21606 ft

Answer:

180

Step-by-step explanation:

100%-> 150

1%->1.5

120%-> 180

The statement "the expected value of an unbiased estimator is equal to the parameter whose value is being estimated" is true.

An estimator is a function of the sample data used to estimate the value of a population parameter. An estimator is said to be unbiased if its expected value is equal to the true value of the population parameter. In other words, if we were to repeatedly take samples from the population and calculate the estimator for each sample, the average value of the estimator over all the samples would be equal to the true value of the population parameter. The expected value of an unbiased estimator is a key property because it ensures that the estimator is not systematically overestimating or underestimating the population parameter. Instead, the estimator provides an unbiased estimate of the population parameter on average across all possible samples. It is important to note that not all estimators are unbiased. Biased estimators may systematically overestimate or underestimate the population parameter, leading to incorrect conclusions. Therefore, unbiasedness is a desirable property for an estimator to have.

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Answer:

f(-2) = -12

Step-by-step explanation:

f(x)= x² + 8x

We want to find f(-2)

f(-2) = (-2)² + 8(-2)

Apply exponent : (-2)² = 4

f(-2) = 4 + 8(-2)

multiply 8 and - 2 : 8 * -2 = -16

f(-2) = 4 - 16

subtract 16 from 4 : 4 - 16 = -12

f(-2) = -12

Step-by-step explanation:

f(-2) = (-2)² + 8(-2) = 4 - 16 = -12

Answer:

1.49216*10^8 km

Step-by-step explanation:

The first thing is to pass all the distances to the same unit system, since the distance from the earth to the sun is in kilometers and from the earth to the moon is in meters, therefore we will pass the distance of the moon in kilometers:

3.84 x 10 ^ 8m * 1 km / 1000 m = 3.84 x 10 ^ 5 km

To calculate the distance between the moon and the sun, it would be the difference between the distance they give us in the statement, because they have a point in common which is the earth, it would be:

1.496 x 10 ^ 8 km - 3.84 x 10 ^ 5 km = 149216000 = 1.49216 * 10 ^ 8 km

Therefore the distance between the moon and the sun is 1,49216 * 10 ^ 8 km

In these options, 0ption D that is, Multicollinearity, is not an assumption of the regression model.

The regression model is a statistical technique used to model the relationship between a dependent variable and one or more independent variables. There are several assumptions associated with the regression model, which should be satisfied for accurate and reliable results.

Option A, Linearity, assumes that there is a linear relationship between the independent variables and the dependent variable. It implies that the relationship can be represented by a straight line.

Option B, Independence, assumes that the observations or data points used in the regression model are independent of each other. This means that the value of one observation does not depend on or influence the value of another observation.

Option C, Homoscedasticity, assumes that the variance of the errors or residuals in the regression model is constant across all levels of the independent variables. It implies that the spread or dispersion of the residuals is consistent.

Option D, Multicollinearity, is not an assumption of the regression model. Multicollinearity refers to a high correlation between independent variables in the regression model, which can cause issues in estimating the individual effects of the independent variables.

Therefore, the correct answer is D) Multicollinearity, as it is not an assumption of the regression model.

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Answer:

y = 0.

Step-by-step explanation:

The line y = 4 is a horizontal line, parallel to the x-axis.

The point (4,0) is on the axis so the rquired equation is:

y = 0.

Infinity is not a variable or a constant; it is a concept representing an unbounded or limitless quantity.

Infinity is a mathematical concept that represents a value larger than any real number. It is not considered a variable because variables can take on different specific values within a given range.

Infinity does not have a specific value; it is a notion of limitless magnitude. Similarly, it is not a constant because constants in mathematics are fixed values that do not change.

Infinity is often used in mathematical equations, especially in calculus and set theory. It is used to describe the behavior of functions or sequences that approach or diverge towards an unbounded magnitude. For example, the limit of a function may be defined as approaching infinity when its values become arbitrarily large.

Infinity can be conceptualized in different forms, such as positive infinity (∞) and negative infinity (-∞). These symbols are used to represent the direction in which values increase or decrease without bound.

It is important to note that infinity is not a number in the conventional sense. It cannot be manipulated algebraically like real numbers, and certain mathematical operations involving infinity can lead to undefined or indeterminate results.

Therefore, infinity is better understood as a concept or a tool used in mathematics to describe unboundedness rather than a variable or a constant with a specific numerical value.

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The equation of a line in slope-intercept form that is parallel to the line y-2=3(x+7) and passes through the point (4,2) is y = 3x - 10.

To find the equation of a line parallel to the given line, we need to determine the slope of the given line.

The given line is in the form y - 2 = 3(x + 7), which can be rewritten as y = 3x + 23.

The slope-intercept form of a line is y = mx + b, where m represents the slope of the line.

Since we want the parallel line to have the same slope, the slope of the parallel line will also be 3.

Using the point-slope form of a line, which is y - y1 = m(x - x1), we can substitute the coordinates (4,2) and the slope m = 3 into the equation. This gives us y - 2 = 3(x - 4).

Simplifying further, we have y - 2 = 3x - 12.

By isolating y on one side of the equation, we get y = 3x - 10.

Therefore, the equation of the line parallel to y - 2 = 3(x + 7) and passing through the point (4,2) is y = 3x - 10.

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Answer:

-0.3999... = -⅖

-0.393939... = -13/33

Step-by-step explanation:

Only ones I could think of.

Answer:

-39/100

Step-by-step explanation:

The lateral surface area of the rectangular prism given in the picture is 36 cm ²

The lateral surface area of a rectangular prism can be found by the formula :

= 2 x height x ( Length + Breadth )

Height = 2 cm

Length = 3 cm

Breadth = 6 cm

The lateral surface area is therefore:

= 2 x 2  x ( 3 + 6 )

= 4 x 9

= 36 cm ²

In conclusion, the lateral surface area is 36 cm ².

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\( \large \mathfrak{Answer : }\)

The given series are :

6.) 7, 14, 28, 54 - Geometric series

7.) 1000, 200, 40, 8, 5 - Geometric series

8.) 7, 14, 21, 28 - Arithmetic series

Answer:

Step-by-step explanation:

To factor 25x^6 + 10x^3 + 12, we can first factor out the greatest common factor of the three terms which is 1, then use a substitution:

Let's substitute y = x^3. Then, the expression becomes:

25y^2 + 10y + 12

We can now try to factor this quadratic expression. However, since the discriminant (b^2 - 4ac) of this quadratic equation is negative (10^2 - 4*25*12 = -440), this expression cannot be factored using real numbers.

Therefore, the final answer for the factoring is:

25x^6 + 10x^3 + 12 = (unfactorable)

Answer: 12...12...12...57

When a figure is dilated with a scale factor of 1, there is no change in size or shape. The figure remains unchanged, with every point retaining its original position. This is because a scale factor of 1 indicates that there is no stretching or shrinking occurring.

When a figure is dilated with a scale factor of 1, it means that the size and shape of the figure remains unchanged. The word "dilate" means to stretch or expand, but in this case, a scale factor of 1 implies that there is no stretching or shrinking occurring.

To understand this concept better, let's consider an example. Imagine we have a square with side length 5 units. If we dilate this square with a scale factor of 1, the resulting figure will have the same side length of 5 units as the original square. The shape and proportions of the figure will be identical to the original square.

This happens because a scale factor of 1 means that every point in the figure remains in the same position. There is no change in size or shape. The figure is essentially a copy of the original, overlapping perfectly.

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