A box of book has a mass of 4.1 kilograms for every meter of its height . Convert your this ratio into pound per inch

Answer:

Step-by-step explanation:

A proportional relationship is one that starts at (0,0) and is usually a straight line relationship.

Of those choices offered, only a is correct by this definition.

Answer:

I think it would be -2 or h(x)=-2

Step-by-step explanation:

because if x=3 then that would be 5 x 3 and that would be 15 so 15-17=-2

hope this helps if not sorry!! :)

Therefore , the solution of the given problem of function comes out to be the duckweed to grow a mass triple the original size will be 45 hours.

The mathematics curriculum involves examining numbers, the equation the environment we live in, structures, and both actual and hypothetical locations. A function is a variable representation of the relationship between the quantities of intake and the corresponding outputs for each. Simply explained, a function is a collection of inputs that, when combined, provide unique outputs for each input.

Here,

Given :

mass of a population of duckweed is 500g

=>  function m(t)= 500x³^t/45

So,

=> t = 45 hours

Since it is given that the mass of the population of the duckweed triples every 45 hours

it is clear that the time taken for the duckweed to grow a mass triple the original size will be 45 hours .

Therefore , the solution of the given problem of function comes out to be the duckweed to grow a mass triple the original size will be 45 hours.

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Answer:

22

Step-by-step explanation:

a) the dimension of its column space is also 2. b) the rank of A is 2. c) the nullity of matrix A is 1. d) the dimension of the solution space of the homogeneous system \(A_x = 0\) is also 1.

(a) The dimension of the row space of a matrix is equal to the dimension of its column space. So, if the dimension of the row space of matrix A is 2, then the dimension of its column space is also 2.

(b) The rank of a matrix is defined as the maximum number of linearly independent rows or columns in the matrix. Since the dimension of the row space of matrix A is 2, the rank of A is also 2.

(c) The nullity of a matrix is defined as the dimension of the null space, which is the set of all solutions to the homogeneous equation Ax = 0. In this case, the matrix A is a 3 x 3 matrix, so the nullity can be calculated using the formula:

nullity = number of columns - rank

nullity = 3 - 2 = 1

Therefore, the nullity of matrix A is 1.

(d) The dimension of the solution space of the homogeneous system Ax = 0 is equal to the nullity of the matrix A. In this case, we have already determined that the nullity of matrix A is 1. Therefore, the dimension of the solution space of the homogeneous system \(A_x = 0\) is also 1.

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Answer: 4x+6/x^2

Step-by-step explanation:

The sample space of rolling a 6 sided number cube is the set of all possible outcomes of rolling the number cube. The sample space for a 6 sided number cube is the set of numbers 1,2,3,4,5, and 6.

When rolling a 6 sided number cube, the sample space is the set of all possible outcomes, which are the numbers from 1 to 6. This means that the sample space includes each of the six numbers, with no bias towards any particular number. Each of the six numbers has an equal chance of being obtained when rolling the number cube.

The sample space of a 6 sided number cube is also known as a discrete sample space, since all of the possible outcomes are predetermined and known. The sample space of a 6 sided number cube is finite and can be easily calculated by listing all the possible outcomes. Since there are 6 possible outcomes, the sample space consists of 6 elements.

The sample space of a 6 sided number cube can be easily visualized by imagining a six-sided die being rolled and each side being labeled with a number from 1 to 6. This demonstrates that the sample space of a 6 sided number cube is a discrete sample space, and each of the six numbers has an equal chance of being obtained.

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The most appropriate units to describe the cost of the sandbox would indeed be dollars.

When describing the cost of an item or service, it is essential to use the unit that represents the currency being used for the transaction. In this case, the total cost of the sand for the school's sandbox is given in dollars. To maintain consistency and clarity, it is best to express the cost in the same unit it was provided.

Using dollars as the unit for the cost allows for clear communication and understanding among individuals involved in the transaction or discussion. Dollars are widely recognized as the standard unit of currency in many countries, including the United States, where the dollar sign ($) is commonly used to denote monetary values.

Using meters, the unit for measuring the dimensions of the sandbox, to describe the cost would be inappropriate and could lead to confusion or misunderstandings. Mixing units can cause ambiguity and hinder effective communication.

Therefore, it is most appropriate to describe the cost of the sand in dollars, aligning with the unit of currency provided and commonly used in financial transactions. This ensures clarity and facilitates accurate comprehension of the cost associated with the sand purchase for the school's sandbox.

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Answer:

x = 74 degrees

Hope that helps

Answer:

74

Step-by-step explanation:

2x+32=180

2x=148

x=74

The factored form of the polynomial 7x³ + 14x² + 3x + 6​ is ( x + 2 )( 7x² + 3 ).

Given the polynomial in the question;

7x³ + 14x² + 3x + 6​

To completely factor, we factor out the greatest common factor from each group.

First, group the first two terms and the last two terms.

( 7x³ + 14x² ) + ( 3x + 6 ​)

Now, factor out the greatest common factor from each group.

( 7x³ + 14x² ) + ( 3x + 6 ​)

7x²( x + 2 ) + ( 3x + 6 )​

7x²( x + 2 ) + 3(x + 2 )

Hence, we have;

( x + 2 )( 7x² + 3 )

Therefore, the factored form is ( x + 2 )( 7x² + 3 ).

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Answer: B: b=1/2

Step-by-step explanation: 1/4+2/4=3/4

2/4=1/2 so B or b=1/2

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If these conditions are met, the sampling distribution of x will be approximately normally distributed. This is helpful in statistical analyses, as it allows us to make inferences about the population mean using the properties of the normal distribution.

The sampling distribution of x (the sample mean) will be approximately normally distributed if certain conditions are met. These conditions are based on the Central Limit Theorem (CLT), which states that:

1. The sample size (n) is large enough, typically n > 30. This ensures that the sampling distribution of x becomes more normally distributed as the sample size increases.
2. The population from which the sample is drawn is either normally distributed or the sample size is large enough to compensate for non-normality.

The sampling distribution of x overbarx (the sample mean) will be approximately normally distributed if certain conditions are met. These conditions include:
1. The population distribution must be normal or approximately normal.
2. The sample size should be large (typically n > 30).
3. The samples should be randomly selected from the population.

If these conditions are met, the sampling distribution of x will be approximately normally distributed. This is helpful in statistical analyses, as it allows us to make inferences about the population mean using the properties of the normal distribution.

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Answer:

4/8 or reduced 1/2

Step-by-step explanation:

It's 4/8 or reduced as 1/2 because there are 4 even numbers 2, 4, 6, 8

The condition that is one of the assumptions of a valid multiple linear regression model is: the relationship between the dependent and independent variables is linear.

Condition that is one of the assumptions of a valid multiple linear regression model is that the relationship between the dependent and independent variables is linear. This means that the change in the dependent variable is proportional to the change in each independent variable, and there is no curved or nonlinear relationship between them. The assumption of linear independence of the independent variables is also important, meaning that they are not highly correlated with each other.

The assumption of constant residuals means that the errors in the model are consistent across all values of the independent variables. The assumption of a quadratic relationship between the dependent and independent variables is not appropriate for a multiple linear regression model.

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This is the graph hope this helps friend :)

Answer:

y = \(\frac{4}{3}\) x + \(\frac{29}{3}\)

Step-by-step explanation:

assuming you require the equation of the perpendicular line.

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - \(\frac{3}{4}\) x - 3 ← is in slope- intercept form

with slope m = - \(\frac{3}{4}\)

given a line with slope m then the slope of a line perpendicular to it is

\(m_{perpendicular}\) = - \(\frac{1}{m}\) = - \(\frac{1}{-\frac{3}{4} }\) = \(\frac{4}{3}\) , then

y = \(\frac{4}{3}\) x + c ← is the partial equation

to find c substitute (- 2, 7 ) into the partial equation

7 = - \(\frac{8}{3}\) + c ⇒ c = 7 + \(\frac{8}{3}\) = \(\frac{21}{3}\) + \(\frac{8}{3}\) = \(\frac{29}{3}\)

y = \(\frac{4}{3}\) x + \(\frac{29}{3}\) ← equation of perpendicular line

The equation of the line is y = (4x +29)/3

The line y = -3/4x - 3 has a slope of -3/4.  A line perpendicular to -3/4 has a slope of 4/3. So the slope of our new line will be 4/3.

We are told that the line goes through the point (-2, 7).  That is x = -2 and y = 7.  Now that we know a point and a slope, we can use the formula:

y2 - y1 = m(x2 - x1)

where,

x1 = -2

y1 = 7

m = 4/3 [slope]

Substituting in the formula,

y2 - 7 = 4/3(x2 - (-2))

y2 - 7 = 4/3*x2 + 4/3*2

3(y2 - 7) = 4(x2) + 8    

3y2 - 21 = 4(x2) +8

3y2 = 4(x2) + 8 +21

3y2 = 4(x2) +29

y2 = (4(x2) +29)/3          

Therefore, the equation of the line is y = (4x +29)/3

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The completer question is

'Find the equation of the line that is perpendicular to y = -3/4x - 3 and passes through the points (-2,7).'

The solution to the given initial value problem using the Laplace transform is y(t) = 3e⁻²ᵗ - (19e⁻⁵ᵗ - 3e²ᵗ)u₋ₜ(t). The solution of the given differential equation using Laplace transforms is \(\[y(t)=3{{e}^{-2t}}-\left(19{{e}^{-5t}}-3{{e}^{2t}}\right){{u}_{-t}}\left( t \right)\]\).

First, we will apply Laplace transform to the given ODE. Laplace transform of the given ODE \(\[{y}''+{y} '-30y=0\] \[\Rightarrow \mathcal{L}\left\{ {y}'' \right\}+\mathcal{L}\left\{ {y} ' \right\}-30\mathcal{L}\left\{ y \right\}=0\] \[\Rightarrow s^2\mathcal{L}\left\{ y \right\}-s{y}\left( 0 \right)-{y} ' \left( 0 \right)+s\mathcal{L}\left\{ y \right\}-y\left( 0 \right)-30\mathcal{L}\left\{ y \right\}=0\]\). By putting the given values we get,  \(\[{s}^2Y\left( s \right)+1\times s-39+ sY\left( s \right)+1+30Y\left( s \right)=0\] \[\Rightarrow {s}^2Y\left( s \right)+sY\left( s \right)+31Y\left( s \right)=38\] \[\Rightarrow Y\left( s \right)=\frac{38}{s^2+s+31}\] The partial fraction of the above function \[\Rightarrow Y\left( s \right)=\frac{19}{s+5}-\frac{3}{s+(-2)}\]\).

We have to find the inverse Laplace of the given function. Using Laplace transform table:  \(\[\mathcal{L}\left\{ e^{at} \right\}=\frac{1}{s-a}\]  \[Y\left( s \right)=\frac{19}{s+5}-\frac{3}{s+(-2)}\] \[\Rightarrow Y\left( t \right)=\left(19{{e}^{-5t}}-3{{e}^{2t}}\right)u(t)\] \[\Rightarrow Y\left( t \right)=3{{e}^{-2t}}-\left(19{{e}^{-5t}}-3{{e}^{2t}}\right){{u}_{-t}}\left( t \right)\]\). Thus, the solution of the given differential equation using Laplace transforms is \(\[y(t)=3{{e}^{-2t}}-\left(19{{e}^{-5t}}-3{{e}^{2t}}\right){{u}_{-t}}\left( t \right)\]\).

The solution has been obtained by using the method of Laplace transform. We have given a differential equation of y″ + y′ − 30y = 0, and the initial conditions of the equation are y(0) = −1 and y′(0) = 39. We will solve the given equation using Laplace transform.

Applying Laplace transform to the given differential equation, s²Y(s) - s(y(0)) - y′(0) + sY(s) - y(0) - 30Y(s) = 0We will substitute the given values into the above equation. Therefore, we get s²Y(s) + sY(s) + 31Y(s) = 38Solving for Y(s), we have Y(s) = 38 / (s² + s + 31). To obtain the inverse Laplace of Y(s), we have to break the function into partial fractions. After breaking the function into partial fractions, we get Y(t) = 3e⁻²ᵗ - (19e⁻⁵ᵗ - 3e²ᵗ)u₋ₜ(t).

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Step-by-step explanation:

m1= 35

m2=65

m3=29

m4=115

m5=65

m6=36

m7=144

hope u got it......

Answer:

11√6

Step-by-step explanation:

5√6 +6√6 will equal to 11√6, because since √6 is the same, you just add the number on the outside

Answer:

Wouldn't the answer be C) Positive Integers?

Step-by-step explanation: Because the complement of a set include all of the elements not included in the indicated set. I hope I'm making some sense. :)

Answer:

T = 15 + 0.75c

T = $19.5

Step-by-step explanation:

Assume that T stands for total cost and c stands for number of single cookies purchased, the equation would be:

T = 15 + 0.75c

Therefore, a dozen cookies plus six single cookies would cost:

T = 15 + 0.75(6)

T = 15 + 4.5

T = $19.5

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:

for ponits

Step-by-step explanation:

Answer:

<C = 54 degrees

b = 123.6

a = 72.6

Step-by-step explanation:

<C = 180 - 90 - 36 = 54 degrees

b = 100/sin54 = 123.6

a = sqrt (123.6^2 - 100^2) = 72.6

Answer:

\(-6 < k < 2\)

Step-by-step explanation:

Given

\(y = x^2 - 2x\)

\(y =kx -4\)

Required

Possible values of k

The general quadratic equation is:

\(ax^2 + bx + c = 0\)

Subtract \(y = x^2 - 2x\) and \(y =kx -4\)

\(y - y = x^2 - 2x - kx +4\)

\(0 = x^2 - 2x - kx +4\)

Factorize:

\(0 = x^2 +x(-2 - k) +4\)

Rewrite as:

\(x^2 +x(-2 - k) +4=0\)

Compare the above equation to: \(ax^2 + bx + c = 0\)

\(a = 1\)

\(b= -2-k\)

\(c =4\)

For the equation to have two distinct solution, the following must be true:

\(b^2 - 4ac > 0\)

So, we have:

\((-2-k)^2 -4*1*4>0\)

\((-2-k)^2 -16>0\)

Expand

\(4 +4k+k^2-16>0\)

Rewrite as:

\(k^2 + 4k - 16 + 4 >0\)

\(k^2 + 4k - 12 >0\)

Expand

\(k^2 + 6k-2k - 12 >0\)

Factorize

\(k(k + 6)-2(k + 6) >0\)

Factor out k + 6

\((k -2)(k + 6) >0\)

Split:

\(k -2 > 0\) or \(k + 6> 0\)

So:

\(k > 2\) or k \(> -6\)

To make the above inequality true, we set:

\(k < 2\) or \(k >-6\)

So, the set of values of k is:

\(-6 < k < 2\)

Answer:

Quadrant IV

Step-by-step explanation:

You can easily find in which quadrant a point lies using this key :

We have the coordinate (4, -5)

Answer:

Quadrant IV

Step-by-step explanation:

The Cartesian plane is divided into 4 quadrants.

Quadrant I is the top right quadrant, where x and y are positive.

We then move in a counterclockwise direction for quadrants II, III and IV.

Therefore:

As point (4, -5) has a positive x-value and a negative y-value, it will lie in Quadrant IV

We can use either one tailed or two tailed as our interest.

The coefficient of determination (R-squared) measures the proportion of the variance in the dependent variable that can be explained by the independent variables in a regression model. It ranges from 0 to 1, where 0 indicates no relationship and 1 indicates a perfect fit.

When conducting a hypothesis test for the significance of the coefficient of determination, you typically assess whether R-squared is significantly different from zero. This is done using a one-tailed test, as the alternative hypothesis is usually stated as either "R-squared is greater than zero" or "R-squared is less than zero."

Thınking about testing the significance of the coefficient of determination, we set up the hypothesis test. This is data from the given question

We can use either one tailed test or two tailed test depending on our interest. We can use anything one tailed test or two tailed test

The   coefficient of determination is cannot be negative so we no need to test using the low tailed , so we no need to test the coefficient of determination it should be less than 0 , so we are using one tailed test or two tailed test

Therefore, We can use either one tailed or two tailed as our interest.

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

Degree of a polynomial is the highest exponential power in the expression.

i.e 9 here

so, degree of the given expression is 9

Answer: 0.26

Step-by-step explanation: 0.26 because it has a greater value, nothing much to solve unless im missing something.

if I am missing something please comment on my answer so I can help you further with your question.

3⁴ is 3 times larger than 3³, 5³ is 5 times larger than 5², 7¹⁰ is 49 times larger than 7⁸ and 17⁶ is 289 times larger than 17⁴.

3⁴ / 3³ = (3 × 3 × 3 × 3) / (3 × 3 × 3) = 3

This means that 3⁴ is 3 times larger than 3³.

5³ is 5 times larger than 5².

5³ / 5² = (5 × 5 × 5) / (5× 5) = 5

7¹⁰ is 49 times larger than 7⁸.

7¹⁰/ 7⁸ = 7² =49

17⁶ is 289 times larger than 17⁴.

17⁶ /17⁴ = 289

Hence, 3⁴ is 3 times larger than 3³, 5³ is 5 times larger than 5², 7¹⁰ is 49 times larger than 7⁸ and 17⁶ is 289 times larger than 17⁴.

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