factor the expression x^2+4-12

The given limit is 0.

To solve the given limit, we can recognize the sum as a Riemann sum and convert it into an integral.

The given sum can be rewritten as:

\(\lim_{n \to \infty} \sum_{i=1}^{n} \frac{3}{n} \sqrt{1+\frac{3i}{n}}\)

Let's rewrite it in terms of integration:

\(\lim_{n \to \infty} \frac{3}{n} \sum_{i=1}^{n} \sqrt{1+\frac{3i}{n}}\)

Since we are taking the limit as n approaches infinity, we can approximate the sum as an integral.

The integral that corresponds to the given sum is:

\(\lim_{n \to \infty} \frac{3}{n} \sum_{i=1}^{n} \sqrt{1+\frac{3i}{n}} \approx \lim_{n \to \infty} \frac{3}{n} \int_{0}^{1} \sqrt{1+3x} ,dx\)

To solve this integral, we can use a change of variables.

Let u = 1 + 3x, then du = 3dx.

The integral becomes:

\(\lim_{n \to \infty} \frac{3}{n} \int_{0}^{1} \sqrt{1+3x} ,dx = \lim_{n \to \infty} \frac{1}{n} \int_{1}^{4} \sqrt{u} ,du\)

Integrating \(\sqrt{u}\), we get,

\(\lim_{n \to \infty} \frac{1}{n} \int_{1}^{4} \sqrt{u} ,du = \lim_{n \to \infty} \frac{1}{n} \left[\frac{2}{3} u^{3/2}\right]_{1}^{4}\)

Substituting the limits, we have:

\(\lim_{n \to \infty} \frac{1}{n} \left[\frac{2}{3} (4)^{3/2} - \frac{2}{3} (1)^{3/2}\right]\)

Simplifying further:

\(\lim_{n \to \infty} \frac{1}{n} \left[\frac{2}{3} (8 - 2)\right] = \lim_{n \to \infty} \frac{1}{n} \left[\frac{12}{3}\right] = \lim_{n \to \infty} \frac{4}{n} = 0\)

Therefore, the given limit is 0.

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Answer:

=\( \sqrt{85} \)

Step-by-step explanation:

let, (x1,y1) = (2,-5) & (x2,y2) = (-7,-7)

now, for distance between two points,

D = \(\sqrt[]{(x_{1}-x_{2} )^{2} +(y_{1}-y_{2} )^{2} }\)

=\(\sqrt[]{(2-(-7))^{2}+(-5-(-7))^2 }\)

\(=\sqrt{(2+7)^2+(-5+7)^2}\)

\(=\sqrt{9^2+2^2}\)

\(=\sqrt{81+4}\)

\(=\sqrt{85}\)

Answer:

\( \huge{ \boxed{ \sqrt{85} \: \text{or} \: 9.219 \: \text{units}}}\)

Step-by-step explanation:

The distance between two points say \( A(x_1,y_1) \) and B(x_2,y_2) can be found by using the formula;

\( \bold{d = \sqrt{{x_2-x_1}^{2}+{y_2-y_1}^{2}}} \)

From the question the points are (2, – 5) and ( – 7, – 7)

\( x_1=2 \\ y_1=-5 \\ x_2=-7 \\ y_2=-7 \)

Substituting the values into the formula that is;

\(d = \sqrt{ {( - 7 - 2)}^{2} + {( - 5 - - 7)}^{2} } \\ d = \sqrt{ {( - 9)}^{2} + {(2)}^{2} } \\ d = \sqrt{81 + 4} \\ d = \sqrt{85} = 9.219\)

We have the final answer as

Answer:

b . all of the other ones look the same and that one is the different one

Answer:

B

Step-by-step explanation:

A proportional relationship graph should be a straight line, no curves.

Answer:

please help!!!!!!!!!!

Answer:

3 formas

Step-by-step explanation:

Se nos pide que averigüemos cuántas formas puede utilizar para cruzar un río si tiene 1 bote y 2 barcos

Número total de barcos = 3 barcos.

Resolvemos esto usando la regla de combinación.

C (n, r) = nCr = n! / R! (n - r)!

n = Número de barcos = 3

r = Número de ríos = 1

3C1 = 3! / 1! (3 - 1)!

= 3! / 1! × 2!

= 3 × 2 × 1/1 × 2 × 1

= 3 formas.

Por lo tanto, el número de vías por las que puede cruzar un río utilizando 1 bote y 2 barcos es de 3 formas.

The equations for circles of a diameter of 12 units and centered on the y-axis are:

For a circle of radius R, centered at the point (a, b), the general equation is:

(x - a)^2 + (y - b)^2 = R^2

so if we want a circle centered on the y-axis, we need to have x = 0, then:

x^2 + (y - b)^2  = R^2

And we also know that the diamter is 12 units, then the radius is half of that:

R = 12/2 = 6 units

Then the circle equation is:

x^2 + (y - b)^2 = 6^2

x^2 + (y - b)^2 = 36

Of the given options the only ones that have this form is the first one:

x^2 + (y - 3)^2 = 36

And the last one:

x^2 + (y + 8)^2 = 36

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Answer:

hi

Step-by-step explanation:

jsjdbdgdydbdbdjsisjbdnsmsosjdbsb sorry for wasting your time

Answer:

Exposure to nicotine is the independent variable

Step-by-step explanation:

An independent variable is a factor that remains unchanged (by other factors in the experiment) throughout the course of an experiment. It can however be manipulated by the researcher. A dependent variable, on the other hand, is the factor being measured that relies on the independent variable. In the case above, exposure to 1 hr of nicotine intake forms the independent variable while the levels of hand steadiness, which will be measured, form the dependent variable.

Answer:

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

Initial value of the toy is €450.

After 10% increase the value is:

After further 10% decrease the value becomes:

The final value of the toy is €445.50.

The equation that shows the Pythagorean identity is true for 0 = pi/2 is

C. 0² + 1² = 1

The Pythagorean identity is given by sin^2 θ + cos^2 θ = 1 for all values of θ, including θ = 0 and θ = π/2.

When θ = 0, sin 0 = 0 and cos 0 = 1. Thus, plugging in these values into the Pythagorean identity, we get:

sin^2 0 + cos^2 0 = 0^2 + 1^2 = 1

Therefore, the equation that shows that the Pythagorean identity is true for θ = 0 is:

0^2 + 1^2 = 1

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Answer:

B. (0.87, 0.48)

Step-by-step explanation:

I calculated it logically

Based on the information given, there are a total of 118 solutions.

This is a problem of solving a Diophantine equation subject to some conditions. Let's introduce a new variable y4 = 20 - (x1 + x2 + x3 + x4). Then the problem can be restated as finding the number of solutions to:

x1 + x2 + x3 + y4 = 20

Subject to the following conditions:

0 ≤ x1 < 3

0 ≤ x2 < 4

0 ≤ x3 < 5

0 ≤ y4 < 6

We can solve this problem using the technique of generating functions. The generating function for each variable is:

(1 + x + x^2) for x1

(1 + x + x^2 + x^3) for x2

(1 + x + x^2 + x^3 + x^4) for x3

(1 + x + x^2 + x^3 + x^4 + x^5) for y4

The generating function for the equation is the product of the generating functions for each variable:

(1 + x + x^2)^3 (1 + x + x^2 + x^3 + x^4 + x^5)

We need to find the coefficient of x^20 in this generating function. We can use a computer algebra system or a spreadsheet program to expand the product and extract the coefficient. The result is: 1118

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Answer: This problem involves finding the number of non-negative integer solutions to the equation x₁ + x₂ + x3 + x₁ = 20 subject to the given constraints. We can use the stars and bars method to solve this problem.

Suppose we have 20 stars representing the sum x₁ + x₂ + x3 + x₁. To separate these stars into four groups corresponding to x₁, x₂, x₃, and x₄, we need to place three bars. For example, if we have 20 stars and 3 bars arranged as follows:

**|**||

then the corresponding values of x₁, x₂, x₃, and x₄ are 2, 4, 6, and 8, respectively. Notice that the position of the bars determines the values of x₁, x₂, x₃, and x₄.

In general, the number of ways to place k identical objects (stars) into n distinct groups (corresponding to x₁, x₂, ..., xₙ-₁) using n-1 separators (bars) is given by the binomial coefficient (k+n-1) choose (n-1), which is denoted by C(k+n-1, n-1).

Thus, the number of non-negative integer solutions to the equation x₁ + x₂ + x3 + x₁ = 20 subject to the given constraints is:

C(20+4-1, 4-1) = C(23, 3) = 1771

However, this count includes solutions that violate the upper bounds on x₁, x₂, x₃, and x₄. To eliminate these solutions, we need to use the principle of inclusion-exclusion.

Let Aᵢ be the set of non-negative integer solutions to the equation x₁ + x₂ + x3 + x₁ = 20 subject to the given constraints, where xᵢ ≥ mᵢ for some integer mᵢ. Then, we want to find the cardinality of the set:

A = A₀ ∩ A₁ ∩ A₂ ∩ A₃

where A₀ is the set of all non-negative integer solutions to the equation x₁ + x₂ + x3 + x₁ = 20, and Aᵢ is the set of solutions that violate the upper bound on xᵢ.

To find the cardinality of A₀, we use the formula above and obtain:

C(20+4-1, 4-1) = 1771

To find the cardinality of Aᵢ, we subtract the number of solutions that violate the upper bound on xᵢ from the total count. For example, to find the cardinality of A₁, we subtract the number of solutions where x₂ ≥ 4 from the total count. To count the number of solutions where x₂ ≥ 4, we fix x₂ = 4 and then count the number of solutions to the equation x₁ + 4 + x₃ + x₄ = 20 subject to the constraints 0 ≤ x₁ < 3, 0 ≤ x₃ < 5, and 0 ≤ x₄ < 6. This count is given by:

C(20-4+3-1, 3-1) = C(18, 2) = 153

Similarly, we can find the cardinalities of A₂ and A₃ by fixing x₃ = 5 and x₄ = 6, respectively. Using the principle of inclusion-exclusion, we obtain:

|A| = |A₀| - |A

Step-by-step explanation:

The ΔBAE is congruent to ΔDAE. ΔBAE and ΔDAE have three corresponding angles that are congruent, so they are congruent.

The Triangle Congruence Theorem states that if two triangles have three corresponding angles that are congruent, then the triangles are congruent.

This can be seen by looking at the angles BAE, BAE, and DAE. All three of these angles are equal, so they are congruent. Additionally, the side lengths of the triangles are the same, so the triangles are also congruent. The Triangle Congruence Theorem is an important tool for determining the congruence of two triangles.

It is used to compare the angles and side lengths of two triangles, and if the angles and side lengths are the same, then the triangles are congruent. When ΔBAE and ΔDAE have the same angles and side lengths, then it is clear that they are congruent.

According to question,

E is the midpoint of,

AC⊥ BD,

As given E is the midpoint of the line ,

So, BE = ED,

further, line AE = AE, because this is the common line between the two triangles.

Also, ∠BED =∠DEA =90°, as AC⊥ BD.

Therefore, the ΔBAE is congruent to ΔDAE.

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Answer:

See the picture.

Refer to the attachment

Answer:

Step-by-step explanation:

Using the vector formula \(u.v = |u||v|cos\theta\)

|u| = magnitude of vector u

|v| = magnitude of vector v

u.v is the dot product of vector u and v

Given |u| = 88, |v| = 99 and u.v = 77, to get \(\theta\) we will substitute the given values into the equation above;

\(77 = 88*99cos\theta\\cos\theta = \frac{77}{88*99} \\cos\theta = \frac{77}{8712} \\cos\theta = 0.008838\\\theta = cos^{-1} 0.008838\\\theta = 89.5^{0}\)

Answer:

2√2 units.

Step-by-step explanation:

To find the length of the line joining points A(3, 5) and B(1, 3), we can use the distance formula. The distance formula is given by:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Substituting the coordinates of points A and B into the formula, we have:

d = sqrt((1 - 3)^2 + (3 - 5)^2)

  = sqrt((-2)^2 + (-2)^2)

  = sqrt(4 + 4)

  = sqrt(8)

  = 2sqrt(2)

Therefore, the length of the line joining points A and B is 2√2 units.

Given the coordinate that represents the ordered pair of the function expressed as:

The set of the inverse of the function will be determined by simply switching the coordinates of the function. The inverse function rule is described as:

Applying this rule, the inverse of the set of ordered pairs will be given as:

This gives the relation of its inverse function.

Answer:

The top and the bottom numbers are not in scientific notation; the other two are in scientific notation.

Answer:

a. Possible outcomes for this chance experiment are:

(Here, D means a defective battery, and N means a nondefective battery.)

b. The number of outcomes in the sample space is infinite, as the experiment could potentially continue indefinitely. However, in practice, we can define a maximum number of batteries that could be examined before the experiment is stopped.

c. The event E, that the number of batteries examined is a number, would include outcomes where the experiment stopped at a particular number of batteries. For example, if the experiment stopped after examining three batteries (i.e., the fourth battery was nondefective), then the outcome would be DDDN, and it would be included in event E. However, outcomes where the experiment continued indefinitely (e.g., DDDDD...) would not be included in event E.

Answer:

C

Step-by-step explanation:

I believe the answer is C because both lines cross through point 1,1

Answer:

6/21

Step-by-step explanation:

Answer:

Step-by-step explanation:

Me toooo i need it really

Answer:

A. The area of parallelogram 1 is 4 square units greater than the area of parallelogram 2.

Step-by-step explanation:
I just took the test

Answer:

21.4

Step-by-step explanation:

Given that :

Mean number of days (m) = 30

Standard deviation (σ) = 2

Sample size (n) = 1000

First find the Zscore

Using the relation :

Zscore = (x - m) / σ

For x = 24

Zscore = (24 - 30) / 2

Zscore = - 6/ 2

Zscore = - 3

For x = 26

Zscore = (26 - 30) / 2

Zscore = - 4/ 2

Zscore = - 2

P(-3 < z < - 2)

P(z < - 3) = 0.0013499

P(Z < - 2) = 0.02275

0.02275 - 0.0013499 = 0.0214001

Hence,

n * 0.0214001

1000 * 0.0214001 = 21.4001

= 21.4

Answers for A:

0 | 1.5 | 3 | 4.5 | 6 | 7.5

Answer for B:

C = 1.5w

Answer for C:

C = 1.5(8) = 12

Answer:

y + 5 = -1 (x - 1)

Step-by-step explanation:

y = -1

y + 5 = -1 (x - 1)

As the triangles are similar to each other, using congruent theorem, we get the value of side JK = 63.8.

Comparable triangles are those that resemble one another but may not be precisely the same size. Comparable items are those that share the same shape but differ in size.

This shows that when shapes are amplified or demagnified, they superimpose one another. This feature of similar shapes is often known as "similarity".

As per the triangles,

Let JK be = x.

GF/GH = JI/JK

⇒ 11/18 = 36 /x

⇒ x = 36 × 18/11

⇒ x = 63.8.

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