N°1. (1+1)x1-1
N°2. (2+2)x 2-6​

Answer:

y = -7x -4

Step-by-step explanation:

Slope-intercept form: y = mx + b

given:

m = -7

b = -4

answer: y = -7x -4

hope this helps :)

The metric unit from pounds to tons is 250 pounds = 0.125 tons

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

250 pounds = how many tons

As a general rule, we have

1 pound = 0.0005 tons

Multiply both sides of the equation by 250

So, we have

250 * 1 pound = 0.0005 tons * 250

Evaluate the products

250 pounds = 0.125 tons

Hence, the conversion is 250 pounds = 0.125 tons

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Step 1

State an expression for the probability of an event.

Number of required events = 4

Total number of events = 7

Step 2

Find the probabilities of defective batteries with replacement and without replacement

Step 3

Find the probabilities that both are defective.

Hence the probability that 2 batteries selected at random without replacement are both defective is 2/7

Answer:

Option (4)

Step-by-step explanation:

Given expression is,

\(\text{log}(\frac{1000a^3}{b})\)

To solve this expression we will use the logarithmic properties.

\(\text{log}(\frac{1000a^3}{b})=\text{log}1000a^3-\text{log}(b)\) [Since, \(\text{log}\frac{p}{q}=\text{log}p-\text{log}q\)]

                 = log(1000) + log(a³) - log(b) [Since, log(pq) = log(p) + log(q)]

                 = 3 + 3log(a) - log(b)

                 = 3[1 + log(a)] - log(b)

Therefore, Option (4) will be the correct option.

Among the provided functions, the ones that approach positive infinity as x approaches negative infinity are:

- f(x) = 2x^5

- f(x) = 6x^8 + 9x^6 + 32

- f(x) = -x + 8x^4 + 248

To determine which functions approach positive infinity as x approaches negative infinity, we need to analyze the leading terms of the functions. The leading term dominates the behavior of the function as x becomes very large or very small.

Let's examine each function and identify their leading terms:

1. f(x) = 2x^5

The leading term is 2x^5, which has a positive coefficient and the highest power of x.

As x approaches negative infinity, this term becomes very large and positive, indicating that f(x) approaches positive infinity.

2. f(x) = 9x + 100

The leading term is 9x, which has a positive coefficient but a lower power of x compared to the constant term 100.

As x approaches negative infinity, the leading term becomes very large and negative, indicating that f(x) approaches negative infinity, not positive infinity.

3. f(x) = 6x^8 + 9x^6 + 32

The leading term is 6x^8, which has a positive coefficient and the highest power of x.

As x approaches negative infinity, this term becomes very large and positive, indicating that f(x) approaches positive infinity.

4. f(x) = -8x^3 + 11

The leading term is -8x^3, which has a negative coefficient and the highest power of x.

As x approaches negative infinity, this term becomes very large and negative, indicating that f(x) approaches negative infinity, not positive infinity.

5. f(x) = -10x + 5x + 26

Combining like terms, we have f(x) = -5x + 26.

The leading term is -5x, which has a negative coefficient but a lower power of x compared to the constant term 26.

As x approaches negative infinity, the leading term becomes very large and positive, indicating that f(x) approaches negative infinity, not positive infinity.

6. f(x) = -x + 8x^4 + 248

The leading term is 8x^4, which has a positive coefficient and the highest power of x.

As x approaches negative infinity, this term becomes very large and positive, indicating that f(x) approaches positive infinity.

Therefore, the correct choices are:

- f(x) = 2x^5

- f(x) = 6x^8 + 9x^6 + 32

- f(x) = -x + 8x^4 + 248

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The inverse Laplace transform of F(s) = 10(s²+1) / [s² (s + 2)] is f(t) = 5t - 5sin(2t) + \(10e^(^-^2^t^).\)

To find the inverse Laplace transform of F(s), we first express F(s) in partial fraction form. The denominator s² (s + 2) can be factored as s² (s + 2) = s² (s + 2). Using partial fraction decomposition, we can express F(s) as:

F(s) = A/s + B/s² + C/(s + 2),

where A, B, and C are constants to be determined.

Next, we multiply both sides of the equation by the common denominator s² (s + 2) to eliminate the denominators. This gives us:

10(s²+1) = A(s + 2) + Bs(s + 2) + Cs².

Expanding and collecting like terms, we have:

10s² + 10 = As + 2A + Bs² + 2Bs + Cs².

Comparing coefficients of s², s, and the constant term on both sides of the equation, we can determine the values of A, B, and C. Solving the resulting system of equations, we find A = 5, B = -10, and C = 0.

Now, we have the expression for F(s) in terms of partial fractions as:

F(s) = 5/s - 10/s² - 10/(s + 2).

To find the inverse Laplace transform of F(s), we use the inverse Laplace transform table to obtain the corresponding time-domain functions for each term. The inverse Laplace transform of 5/s is 5, the inverse Laplace transform of -10/s² is -10t, and the inverse Laplace transform of -10/(s + 2) is \(10e^(^-^2^t^).\)

Finally, we add the inverse Laplace transforms of each term to obtain the solution f(t) = 5t - 5sin(2t) + \(10e^(^-^2^t^)\).

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To find the coefficient C in a linear regression task using Matlab or by hand, you can follow a few steps. First, organize your data into matrices. In this case, you have the predictor variable X and the response variable Y.

Construct the design matrix X by including a column of ones followed by the values of X. Next, calculate C using the formula C = (X'X)^-1X'Y, where ' denotes the transpose operator. This equation involves matrix operations: X'X represents the matrix multiplication of the transpose of X with X, (X'X)^-1 is the inverse of X'X, X'Y is the matrix multiplication of X' with Y, and C is the resulting coefficient matrix. Using the formula C = (X'X)^-1X'Y, you can compute the coefficient matrix C. Here, X'X represents the matrix multiplication of the transpose of X with X, which captures the covariance between the predictor variables. Taking the inverse of X'X ensures the solvability of the system. The term X'Y represents the matrix multiplication of X' with Y, capturing the covariance between the predictor variable and the response variable.

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Answer:

\(\sf\:Negative = \boxed{\sf\:\theta =\pi n_{1}+\frac{5\pi }{6}\text{, }n_{1}\in \mathbb{Z}}\\\sf\: Positive = \boxed{\sf\:\theta =\pi n_{1}+\frac{\pi }{6}\text{, }n_{1}\in \mathbb{Z}}\)

Step-by-step explanation:

\(4 - 3 \sec ^ { 2 } \theta = 0\)

Let's solve this.

Isolate sec²θ.

\(4 -3 \sec ^ { 2 } \theta = 0\\- 3 \sec^{2}\theta = -4\\3 \sec^{2}\theta=0\\\sec^{2} \theta=\frac{4}{3}\)

Now, we now that, cos θ is the reciprocal of sec θ. Therefore,

\(\sec^{2}\theta = \frac{4}{3}\\\cos^{2}\theta = \frac{3}{4}\)

Bring the square root on both the sides of the equation to remove the square.

\(\sqrt{\cos^{2}\theta} = \sqrt{\frac{3}{4} }\\\cos^{2}\theta = (+/-) \frac{\sqrt{3} }{2}\)

If,

\(\cos\theta = + \frac{\sqrt{3}}{2}\\= cos \left( \frac{\pi}{6} \right)\\\Longrightarrow \boxed{\sf\:\theta =\pi n_{1}+\frac{\pi }{6}\text{, }n_{1}\in \mathbb{Z}}\)

Also if,

\(\cos\theta = -\frac{\sqrt{3}}{2}\\= \cos \left(\pi - \frac{\pi}{6}\right)\\= \cos \left({\frac{5\:\pi}{6}\right)\\\Longrightarrow \boxed{\sf\:\theta =\pi n_{1}+\frac{5\pi }{6}\text{, }n_{1}\in \mathbb{Z}}\)

\(\rule{150pt}{2pt}\)

0.0912   is the probability that the score will be 120 or higher .

What is probability explain with an example?

Zlower = X₁ - μ/σ  = 120 - 100/15  = 1.33

the probability is compared as

                    Pr ( X ≥ 120 ) = Pr(X - 100/15 ≥ 120 - 100/15)

                                         = Pr(Z ≥ 120 - 100/15

                                          = Pr( Z ≥ 1.33)

                                          = 0.0912

Since 0.0912 > 0.05 i.e. this IQ score is not unusual and hence I can believe the claim.

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The closest answer is 80 cupcakes per minute, so the correct option is .8. The closest answer is 165 minutes, so the correct option is 165.

The throughput capacity of the icing stage can be calculated by dividing the number of cupcakes in a batch (100) by the time required to process each cupcake (1.25 minutes).

Throughput capacity = Number of cupcakes in a batch / Time to process each cupcake

Throughput capacity = 100 cupcakes / 1.25 minutes

Throughput capacity = 80 cupcakes per minute

The closest answer is 80 cupcakes per minute, so the correct option is .8.

The throughput time for a batch of cupcakes is the time required to process the entire batch, including the setup time.

Throughput time = Time for setup + (Number of cupcakes in a batch * Time to process each cupcake)

Throughput time = 40 minutes + (100 cupcakes * 1.25 minutes per cupcake)

Throughput time = 40 minutes + 125 minutes

Throughput time = 165 minutes

The closest answer is 165 minutes, so the correct option is 165.

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A stem-and-leaf display is a statistical tool used for organizing and displaying data.

It is especially useful for analyzing small data sets and can be used for a variety of purposes. With stem-and-leaf displays, individual data points can be easily observed and analyzed, which is particularly useful for answering multiple-choice questions.

Additionally, stem-and-leaf displays can be used to analyze qualitative data by observing patterns and relationships between data points. By determining the central tendency and dispersion of the data, a stem-and-leaf display can help to provide a clearer understanding of the data set as a whole.

Furthermore, the shape of the data can be analyzed through the use of a stem-and-leaf display, which can be helpful in identifying outliers and skewness. In conclusion, stem-and-leaf displays are a useful tool for organizing and analyzing data and can provide valuable insights into data sets.

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Answer:

35.00?

Step-by-step explanation:

Answer:

x = -2

Step-by-step explanation:

Answer:

x=-2

Step-by-step explanation:

255. Using your expression from the preceding problem, (Hint: Examine the limiting behavior:The expression of velocity from the preceding problem is given as, V = 49(1 - e⁻⁰·²⁵t)Here, V is the velocity and t is the time taken. As time passes by, the exponential term e⁻⁰·²⁵t goes closer and closer to zero and eventually becomes zero.

Hence, at the terminal velocity, V = 49

(1 - 0) = 49

Therefore, the terminal velocity is 49.259. Solve the generic equation y' = 4x+ A. The given differential equation is

y' = 4x+ A. Here, A is a constant, which could be either positive or negative. Differentiating both sides with respect to x, we get

y'' = 4dy/dx = 4Therefore, y'' is a constant and independent of A. The second derivative of y is a constant which represents the rate of change of the slope of y.

Hence, varying A does not change the behavior.261. Solve

y-y=e^kt with the initial condition

y(0)= 0. As k approaches 1. Given,

y - y₀ = e^(kt)

where y₀ = y(0) = 0

Substituting y₀ in the above equation, we get

y - 0 = e^(kt) => y = e^(kt)As k

approaches 1, the formula remains the same, but y grows exponentially with respect to t. Hence, as k approaches 1, the solution of the differential equation y - y₀ = e^(kt) approaches infinity. 255. The expression of velocity from the preceding problem is given as,

V = 49(1 - e⁻⁰·²⁵t).

Here, V is the velocity and t is the time taken.As time passes by, the exponential term e⁻⁰·²⁵t goes closer and closer to zero and eventually becomes zero. Hence, at the terminal velocity,

V = 49(1 - 0) = 49.

Therefore, the terminal velocity is 49.259.

The given differential equation is

y' = 4x+ A.

Here, A is a constant, which could be either positive or negative.Differentiating both sides with respect to x, we get

y'' = 4dy/dx = 4

Therefore, y'' is a constant and independent of A.The second derivative of y is a constant which represents the rate of change of the slope of y. Hence, varying A does not change the behavior.261. Given,

y - y₀ = e^(kt)

where y₀ = y(0) = 0.

Substituting y₀ in the above equation,

we gety - 0 = e^(kt) => y = e^(kt).

As k approaches 1, the formula remains the same, but y grows exponentially with respect to t. Hence, as k approaches 1, the solution of the differential equation y - y₀ = e^(kt) approaches infinity.

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Answer:

84km

Step-by-step explanation:

\( \sf \: \: \: \: \: \: = 7 \times 4 \times 3 \\ \sf = \underline \green8 \underline \green 4 \: km\)

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===========

V = 7 × 4 × 3

V = 84 km

===========

-CallMeKi

Answer:

Step-by-step explanation:

Este es muy fácil, simplemente dibujas los nueve corrales y pones diez vacas en entre. ¿¿Como??

Por ejemplo, tú tienes algo como esto

D

I

E

Z

V

A

C

A

S

Donde, cada letra es la vacas tú tienes, y pones en el corral. Esta camina, tienes poner diez vacas en entre nueve corrales. Espero que me entiendas. Gracias

The simplest form of a fraction is when the numerator (top number) and denominator (bottom number) have no common factors.

A fraction is a mathematical expression that represents a part of a whole, where a numerator is divided by a denominator. To simplify a fraction, we must divide both the numerator and the denominator by the same number until we cannot divide any further. To simplify a fraction, you must divide both the numerator and denominator by their greatest common factor (GCF).

For example, let's simplify the fraction 24/36. The GCF of 24 and 36 is 12. So, dividing both numbers by 12 will give us the simplified fraction 2/3.

24 ÷ 12 = 2

36 ÷ 12 = 3

Therefore, the simplified fraction of 24/36 is 2/3.

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Answer:

in the first table, you have to list the tool that is used to measure the property, then you put the unit that it's measured in. example:

property.      tool.         unit

mass.           scale.       kg/ lbs

in the second part, all you have to do is describe the chemical properties of the reactions

Answer:

The answer is 20

Step-by-step explanation:

(h⁰g)(1) = 10, which corresponds to option (H).

To find (h⁰g)(1), we need to perform the function composition of h(x) and g(x), and then evaluate the resulting function at x = 1.

Given:

g(x) = x - 3

h(x) = x² + 6

To perform function composition, we substitute g(x) into h(x), replacing the variable x with g(x):

h(g(x)) = (g(x))² + 6

Replacing g(x) with its expression x - 3:

h(g(x)) = (x - 3)² + 6

Now, we evaluate this composite function at x = 1:

h(g(1)) = (1 - 3)² + 6

        = (-2)² + 6

        = 4 + 6

        = 10

Therefore, (h⁰g)(1) = 10, which corresponds to option (H).

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The solution for the given quadratic equation v² - 9v = -4 are v = [9 ± √65] / 2

To solve a quadratic equation in the form of ax² + bx + c = 0 using the quadratic formula, we can use the following formula:

x = [-b ± √(b² - 4ac)] / 2a

In this case, we have the equation v² - 9v = -4, which can be rearranged to the standard form of ax² + bx + c = 0 by adding 4 to both sides:

v² - 9v + 4 = 0

Now we can identify the values of a, b, and c:

a = 1, b = -9, c = 4

Substituting these values into the quadratic formula, we get:

v = [9 ± √(81 - 16)] / 2

Simplifying under the square root:

v = [9 ± √65] / 2

These are the two solutions for v, which can be expressed as decimals rounded to the nearest hundredth or as exact fractions.

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Using Binomial distribution, the probability that more than 2 fail-safe components will fail is 0.00154

For given question,

The pmf of a Binomial Distribution is given by,

\(f(x) =^nC_x(p)^x(q)^{n-x}\)

where n = number of trials

p = probability of success (success event being missile failing)

q = 1 - p i.e. probability of failure (failure event being missile succeeding)

x = number of successes required (number of failed missiles)

In the given case,

n = 5, p = 0.055,

⇒ q = 0.945

We need to find the probability that more than 2 will fail.

So, x = 3

Using Binomial distribution, the required probability is,

\(P(x > 2)\\\\= P(x=3) + P(x=4) + P(x=5)\\\\=^5C_3(0.055)^3(0.945)^2 +~^5C_4(0.055)^4(0.945)+~^5C_5(0.055)^5\\\\ =0.0015 + 0.00004 + 0.0000005\\\\ = 0.00154\)

Therefore, using Binomial distribution, the probability that more than 2 fail-safe components will fail is 0.00154

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Let f be a continuous function in c[a, b] such that f(a) = 200. Then for all real numbers c, the scalar multiple cf is also a continuous function in c[a, b]. Specifically, cf(a) = c(200) = 200c.

To demonstrate that c[a, b] is a subspace, the following facts must be proved:
1. If f and g are both continuous functions in c[a, b], then the sum f + g is also a continuous function in c[a, b].
2. If f is a continuous function in c[a, b], then the scalar multiple cf is also a continuous function in c[a, b], where c is a real number.
3. The zero vector of c[a, b] is the constant zero function.

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a.we get, `A = √(2α³/π)`.

b.`⟨H⟩ = (3/4)hω - (h²/4ma²)` where `a = α/√(mω/h)`.

c.we can say that the variational principle is valid in this case.

(a) Let's find the normalization constant A.

We know that the integral over all space of the absolute square of the wave function is equal to 1, which is the requirement for normalization.  `∫⟨ψ|ψ⟩dx= 1`

Hence, using the given trial wavefunction, we get, `∫⟨ψ|ψ⟩dx = ∫ |A/(x^2+α²)|²dx= A² ∫ dx / (x²+α²)²`

Using a substitution `x = α tan θ`, we get, `dx = α sec² θ dθ`

Substituting these in the above integral, we get, `A² ∫ dθ/α² sec^4 θ = A²/(α³) ∫ cos^4 θ dθ`

Using the identity, `cos² θ = (1 + cos2θ)/2`twice, we can write,

`A²/(α³) ∫ (1 + cos2θ)²/16 d(2θ) = A²/(α³) [θ/8 + sin 2θ/32 + (1/4)sin4θ/16]`

We need to evaluate this between `0` and `π/2`. Hence, `θ = 0` and `θ = π/2` limits.

Using these limits, we get,`⟨ψ|ψ⟩ = A²/(α³) [π/16 + (1/8)] = 1`

Therefore, we get, `A = √(2α³/π)`.

Hence, we can now write the wavefunction as `ψ(x) = √(2α³/π)/(x²+α²)`.  

(b) Using the wave function found in part (a), we can now determine the expectation value of energy using the time-independent Schrödinger equation, `Hψ = Eψ`. We can write, `H = (p²/2m) + (1/2)mω²x²`.

The first term represents the kinetic energy of the particle and the second term represents the potential energy.

We can write the first term in terms of the momentum operator `p`.We know that `p = -ih(∂/∂x)`Hence, we get, `p² = -h²(∂²/∂x²)`Using this, we can now write, `H = -(h²/2m) (∂²/∂x²) + (1/2)mω²x²`

The expectation value of energy can be obtained by taking the integral, `⟨H⟩ = ⟨ψ|H|ψ⟩ = ∫ψ* H ψ dx`Plugging in the expressions for `H` and `ψ`, we get, `⟨H⟩ = - (h²/2m) ∫ψ*(∂²/∂x²)ψ dx + (1/2)mω² ∫ ψ* x² ψ dx`Evaluating these two integrals, we get, `⟨H⟩ = (3/4)hω - (h²/4ma²)` where `a = α/√(mω/h)`.

(c) Since we have an approximate ground state wavefunction, we can expect that the expectation value of energy ⟨H⟩ should be greater than the true ground state energy.

Hence, the value obtained in part (b) should be greater than the true ground state energy obtained by solving the Schrödinger equation exactly.

Therefore, we can say that the variational principle is valid in this case.

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Answer:

16.33628179866692

Step-by-step explanation:

I dont know how far you wanted me to round so you will have to do that part

Answer:

Answer is 10% of 30 = 3

Answer 8.06 X 10-8 M*4

Step-by-step explanation: No Explanation Just Answer srry could think of a way to say it.