Sarah is a healthy baby who was exclusively breast-fed for her first 12 months. Which of the following is most likely a description of her weights (at 3, 6, 9, and 12 months of age) as percentiles of the CDC growth chart reference population? 85th percentile at 3 months; 85th percentile at 6 months; 9oth percentile at 9 months; 95th percentile at 12 months 75th percentile at 3 months; 40th percentile at 6 months; 25th percentile at 9 months; 25th percentile at 12 months 30th percentile at 3 months; 50th percentile at 6 months; 70th percentile at 9 months; 80th percentile at 12 months 25th percentile at 3 months; 25th percentile at 6 months; 25th percentile at 9 months; 25th percentile at 12 months

Answer:

(6,-2)

Step-by-step explanation:

graph and see the point where they cross and that is the solution

Answer:

5-hour reunion at Picnic Place will cost $250.

5-hour reunion at Total Tent will cost $350.

15 hours for both choices to cost the same.

Explanation:

Let x represent the number of hours.

Let y represent the total cost.

For Picnic Place, our equation can be written as;

For a 5-hour reunion at Picnic Place, the charge will be;

For Total Tent, our equation can be written as;

For a 5-hour reunion, the cost will be;

To determine how many hours onwill need to reserve both shelters for both choices to cost the same, we just need to equate both equations and solve for x;

Answer:

280

Step-by-step explanation:

the vertical asymptοtes οf the functiοn are given by: x = 3 and x = -3.

Asymptοtes are lines that a curve apprοaches but dοes nοt intersect as it extends infinitely in οne οr mοre directiοns. They can be vertical, hοrizοntal, οr οblique.

Vertical asymptοtes οccur when the denοminatοr οf a ratiοnal functiοn is equal tο zerο and the numeratοr is nοt equal tο zerο. This creates a pοint οf discοntinuity in the functiοn, where the functiοn apprοaches infinity οr negative infinity as it apprοaches the vertical line.

The functiοn y = 5tan(0.1x) has vertical asymptοtes whenever the tangent functiοn is undefined, which οccurs at οdd multiples οf π/2.

the vertical asymptοtes οf y = 5tan(0.1x) are given by:

x = (2n+1)π/2*10, where n is an integer.

Fοr Explοratiοn 4.3.3, Questiοn 2, the given functiοn is:

\(y = (x^2 - 5x + 6)/(x^2 - 9)\)

Tο find the vertical asymptοtes οf this functiοn, we need tο determine where the denοminatοr becοmes zerο. This οccurs at x = 3 and x = -3.

Therefοre, the vertical asymptοtes οf the functiοn are given by: x = 3 and x = -3.

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Answer:

24 days

Step-by-step explanation:

8 divided by 1/3 is 24

Answer:

y+4=-5/6(x-8)

Step-by-step explanation:

y-y1=m(x-x1)

y-(-4)=-5/6(x-8)

y+4=-5/6(x-8)

Please mark me as Brainliest if you're satisfied with the answer.

Answer:

(4.5, 7)

Step-by-step explanation:

x = 1/2(x^1 + x^2)

x = 1/2(8 +1)

x = 1/2(9)

x = 4.5

y = 1/2(y^1 + y^2)

y = 1/2(10 + 4)

y = 1/2(14)

y = 7

(4.5, 7)

The tangent vector  → \(r(t)=〈4cos(2t),4sin(2t),5t〉\), normal vector at t=0 is given by →N(0) = 〈-1,0,0〉, and binormal vector at t=0 is given by →\(B(0) = 〈0, -0.441, -0.898〉\)

The tangent vector, normal vector, and binormal vector of the given curve are as follows:

Given curve:

→ \(r(t)=〈4cos(2t),4sin(2t),5t〉\) at the point t=0

To find: Tangent vector, the Normal vector, and the Binormal vector (→T, →N and →B) at the point t=0

Tangent vector: To find the tangent vector of the given curve

→\(r(t)=〈4cos(2t),4sin(2t),5t〉\) at the point t=0,

we need to differentiate the equation of the curve with respect to t.t = 0, we have:

→\(r(t) = 〈4cos(2t),4sin(2t),5t〉→r(0) = 〈4cos(0),4sin(0),5(0)〉= 〈4,0,0〉\)

Differentiating w.r.t t:→\(r(t) = 〈4cos(2t),4sin(2t),5t〉 → r'(t) = 〈-8sin(2t),8cos(2t),5〉t = 0\),

we have:

→\(r'(0) = 〈-8sin(0),8cos(0),5〉= 〈0,8,5〉\)

Therefore, the tangent vector at t = 0 is given by

→\(T(0) = r'(0) / |r'(0)|= 〈0,8,5〉 / sqrt(89)≈〈0.000,0.898,0.441〉\)

Normal vector:To find the normal vector of the given curve

→\(r(t)=〈4cos(2t),4sin(2t),5t〉\)

at the point t=0, we need to differentiate the equation of the tangent vector with respect to t.t = 0, we have:

→\(T(0) = 〈0.000,0.898,0.441〉\)

Differentiating w.r.t t:

→\(T'(t) = 〈-16cos(2t),-16sin(2t),0〉t = 0\),

we have:

→\(T'(0) = 〈-16cos(0),-16sin(0),0〉= 〈-16,0,0〉\)

Therefore, the normal vector at t = 0 is given by

→\(N(0) = T'(0) / |T'(0)|= 〈-16,0,0〉 / 16= 〈-1,0,0〉\)

Binormal vector: To find the binormal vector of the given curve

→\(r(t)=〈4cos(2t),4sin(2t),5t〉\)

at the point t=0, we need to cross-product the equation of the tangent vector and normal vector of the curve.t = 0, we have:

→\(T(0) = 〈0.000,0.898,0.441〉→N(0) = 〈-1,0,0〉\)

The cross product of two vectors:

→\(B(0) = →T(0) × →N(0)= 〈0.000,0.898,0.441〉 × 〈-1,0,0〉= 〈0, -0.441, -0.898〉\)

Therefore, the binormal vector at t = 0 is given by→B(0) = 〈0, -0.441, -0.898〉

Hence, the tangent vector, normal vector, and binormal vector of the given curve at t=0 are as follows:

→\(T(0) = 〈0.000,0.898,0.441〉→N(0) = 〈-1,0,0〉→B(0) = 〈0, -0.441, -0.898〉\)

The given curve is

→\(r(t)=〈4cos(2t),4sin(2t),5t〉 at the point t=0.\)

We are asked to find the tangent vector, the normal vector, and the binormal vector of the given curve at t=0.

the tangent vector at t=0. To find the tangent vector, we need to differentiate the equation of the curve with respect to t. Then, we can substitute t=0 to find the tangent vector at that point. the equation of the curve Is:

→\(r(t) = 〈4cos(2t),4sin(2t),5t〉\)

At t = 0, we have:

→\(r(0) = 〈4cos(0),4sin(0),5(0)〉= 〈4,0,0〉\)

We can differentiate this equation with respect to t to get the tangent vector as:

→\(r'(t) = 〈-8sin(2t),8cos(2t),5〉\)

At t=0, the tangent vector is:

→\(T(0) = r'(0) / |r'(0)|= 〈0,8,5〉 / sqrt(89)≈〈0.000,0.898,0.441〉\)

Next, we find the normal vector. To find the normal vector, we need to differentiate the equation of the tangent vector with respect to t. Then, we can substitute t=0 to find the normal vector at that point.

At t=0, the tangent vector is:

→\(T(0) = 〈0.000,0.898,0.441〉\)

Differentiating this equation with respect to t, we get the normal vector as:

→\(T'(t) = 〈-16cos(2t),-16sin(2t),0〉\)

At t=0, the normal vector is:

→\(N(0) = T'(0) / |T'(0)|= 〈-16,0,0〉 / 16= 〈-1,0,0〉\)

Finally, we find the binormal vector. To find the binormal vector, we need to cross-product the equation of the tangent vector and the normal vector of the curve.

At t=0, we can cross product →T(0) and →N(0) to find the binormal vector.

At t=0, the tangent vector is:

→\(T(0) = 〈0.000,0.898,0.441〉\)

The normal vector is:

→N(0) = 〈-1,0,0〉Cross product of two vectors →T(0) and →N(0) is given as:

→\(B(0) = →T(0) × →N(0)= 〈0.000,0.898,0.441〉 × 〈-1,0,0〉= 〈0, -0.441, -0.898〉\)

Therefore, the tangent vector, normal vector, and binormal vector of the given curve at t=0 are:

→\(T(0) = 〈0.000,0.898,0.441〉→N(0) = 〈-1,0,0〉→B(0) = 〈0, -0.441, -0.898〉\)

The tangent vector of the given curve

→\(r(t)=〈4cos(2t),4sin(2t),5t〉\)

at the point t=0 is given by →\(T(0) = 〈0.000,0.898,0.441〉.\)

The normal vector at t=0 is given by →N(0) = 〈-1,0,0〉.

The binormal vector at t=0 is given by →B(0) = 〈0, -0.441, -0.898〉.

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it is proven that there are no integers x, y, z such that x² + y² = 8z + 3.

What is Integers?

A whole number is a number that can be written without a fractional component. For example, 21, 4, 0, and −2048 are integers, while 9.75, 5+, and √2 are not. The set of integers consists of zero, positive natural numbers, also called integers or counting numbers, and their additive inverses.

To prove that there are no integers x, y, z such that x² + y² = 8z + 3, we can use the concept of modulo arithmetic.

First, let's consider the possible values of x² and y² modulo 8:

For any integer n, n² modulo 8 can only be 0, 1, or 4.

Now, let's examine the possible values of 8z + 3 modulo 8:

8z modulo 8 is always 0.

3 modulo 8 is equal to 3.

Therefore, the possible values of x² + y² modulo 8 can only be 0, 1, or 4, while 8z + 3 modulo 8 is equal to 3. Since 0, 1, and 4 are not equal to 3 modulo 8, there are no integers x, y, z that satisfy the equation x² + y² = 8z + 3.

Hence, it is proven that there are no integers x, y, z such that x² + y² = 8z + 3.

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As per the formula of surface area of cube, the length of the cube is 5.45 meters.

The general formula to calculate the surface area of the cube is calculated as,

=> SA = 6a²

here a represents the length of cube.

Here we know that  the side of a cube with a surface area of 180 square meters than a cube with the surface area of 120 square meters.

When we apply the value on the formula, then we get the expression like the following,

=> 180 = 6a²

where a refers the length of the cube.

=> a² = 30

=> a = 5.45

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Step-by-step explanation:

The given number is 7,594,000,000.

To convert it into scientific notation,

First move the decimal point places to the left to find a number that is greater than or equal to 1 and less than 10. Then multiply by 10 , using an exponent on 10 that equals the number of places you moved the decimal. The exponent is negative if the original no was <1 and the exponent is positive, if the original number was  > 1.

In 7,594,000,000, we move the decimal point places to the left before 5. It means we have moved 9 digits left.

Hence, \(7,594,000,000=7.59\times 10^9\) is the scientific notation.

Answer:

7.875

Step-by-step explanation:

Write the whole number as a fraction with a denominator of 1.

Multiply the numerators.

Multiply the denominators.

Simplify. , if needed. If your answer is greater than 1, you may want to write your answer as a mixed number.

Answer:

A) \(\theta=30^\circ+180n^\circ\)

Step-by-step explanation:

\(tan\theta=4tan\theta-\sqrt{3}\\\\-3tan\theta=-\sqrt{3}\\\\9tan^2\theta=3\\\\tan^2\theta=\frac{3}{9}\\ \\tan^2\theta=\frac{1}{3}\\ \\\frac{1-cos(2\theta)}{1+cos(2\theta)}=\frac{1}{3}\\ \\ 3-3cos(2\theta)=1+cos(2\theta)\\\\2-3cos(2\theta)=cos(2\theta)\\\\2=4cos(2\theta)\\\\\frac{2}{4}=cos(2\theta)\\ \\\frac{1}{2}=cos(2\theta)\\ \\2\theta=60^\circ+360n^\circ\\\\\theta=30^\circ+180n^\circ\)

Recall the identity \(tan^2(\theta)=\frac{1-cos(2\theta)}{1+cos(2\theta)}\)

Answer:divide 55 by 4

Step-by-step explanation:

Answer:

x = 7

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

Solve for

x

by simplifying both sides of the inequality, then isolating the variable.

Inequality Form:

x>7

Interval Notation:

7

Answer:

B

Step-by-step explanation:

-4y-3<9

-4y<12

y<-3

==> B

Answer:

We can rewrite the given expressions as:

(3x² - y² - 2yz - z²) and (y² - z² - 2zx - x²)

To find the H.C.F., we can use the Euclidean algorithm. We start by dividing the first expression by the second expression:

(3x² - y² - 2yz - z²) ÷ (y² - z² - 2zx - x²)

Using long division or synthetic division, we get:

(3x² - y² - 2yz - z²) = (3x + y + z)(x - y + z) + 2y(x - z)

Therefore, the remainder is 2y(x - z). We can now divide the second expression by this remainder:

(y² - z² - 2zx - x²) ÷ 2y(x - z)

Using long division or synthetic division, we get:

(y² - z² - 2zx - x²) = -x(x - y + z) + z(x - y + z)

Therefore, the remainder is z(x - y + z).

Since the second remainder is not zero, we need to continue with the algorithm. Now we divide the remainder 2y(x - z) by the remainder z(x - y + z):

2y(x - z) ÷ z(x - y + z)

Using long division or synthetic division, we get:

2y(x - z) = 2y(x - y + z) - 2y²

Therefore, the remainder is -2y². Now we divide the previous remainder z(x - y + z) by this new remainder:

z(x - y + z) ÷ (-2y²)

Using long division or synthetic division, we get:

z(x - y + z) = -1(-2y²) + z²

Therefore, the H.C.F. of the original expressions is the absolute value of the last remainder, which is |-2y²| = 2y².

Therefore, the H.C.F. of (3x² - y² - 2yz - z²) and (y² - z² - 2zx - x²) is 2y².

Answer:

Step-by-step explanation:

when you divide fraction, turn the division into × and flip the other fraction

72/7÷8/7= 72/7×7/8=72/8 = 9

21÷7/3 = 21×3/7 =63/7=9

12/7÷2/7 = 12/7 × 7/2 = 12/2 = 6

9÷9/2=9×2/9=18/9= 2

4 2/3 ÷7/9 = 14/3 ×9/7=126/21 = 6

4 1/2 ÷1/2 = 9/2 × 2=18/2=9

∫sin^−1(x)/4x^2 dx = -(sin^−1(x)/4x) + (1/4) arcsin(x) + C.

et u = sin^−1(x)/4 and dv = 1/x^2 dx. Then, du/dx = 1/(4√(1-x^2)) and v = -1/x.

Using integration by parts formula, we have:

∫sin^−1(x)/4x^2 dx = uv - ∫v du/dx dx

= -(sin^−1(x)/4x) + ∫1/(4x√(1-x^2)) dx

= -(sin^−1(x)/4x) + (1/4)∫(1-x^2)^(-1/2) d(1-x^2)

= -(sin^−1(x)/4x) + (1/4) arcsin(x) + C

Therefore, ∫sin^−1(x)/4x^2 dx = -(sin^−1(x)/4x) + (1/4) arcsin(x) + C.

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Answer:

The correct answer is, Student A, who is paid $255 for 20 hours of work.

Step-by-step explanation:

have a nice day.

Step-by-step explanation:

2x⁴ = 9x²

2x⁴ - 9x² = 0

x²(2x² - 9) = 0

Either x² = 0 or 2x² - 9 = 0.

When x² = 0, x = 0.

When 2x² - 9 = 0, x² = 9/2, x = ± 3/√2.

Hence the solutions are

x = 0, x = 3/√2 and x = -3/√2.

Equations −2x+5y=−2 and 4x−10y=4 have no solution.

An inconsistent system is a set of equations that cannot be solved. Although a system of linear equations typically has a single solution, it occasionally may have infinite or no solutions (parallel lines) (same line). The solution set refers to all possible answers to an equation or inequality. The no solution symbol,, is used to indicate that there is no solution to an equation or inequality. None Found: There are no solutions when the lines that make up a system are parallel because the two lines have no points in common.

Given,

Equations,

−2x+5y=−2 .. Equation 1

4x−10y=4 .. Equation 2

Multiplying equation 1 by 2

-4x + 10y = -4

4x - 10 y = 4

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

0

Equations −2x+5y=−2 and 4x−10y=4 have no solution.

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The general solution to the given nonhomogeneous system.

x(t) = (c₁\(e^{t\) - \(e^{-9t\) + C₁)(8  1) + (c₂\(e^{8t\) + 8\(e^{-9t\) + C₂)(1  1  1)

To solve the given nonhomogeneous system using the variation of parameters method, we will first find the general solution to the associated homogeneous system, and then we will find a particular solution to the nonhomogeneous system. Finally, the general solution to the nonhomogeneous system will be obtained by combining the solutions.

The given system is:

x' = (0 8 -1 9) x + (8\(e^{-9t\))

Step 1: Find the general solution to the associated homogeneous system.

To do this, we need to solve the equation:

x' = (0 8 -1 9) x

The characteristic equation of the coefficient matrix is:

|λ - 0 8 |

|-1 λ - 9| = λ^2 - 9λ - 8 = (λ - 1)(λ - 8)

So the eigenvalues are λ₁ = 1 and λ₂ = 8.

For λ₁ = 1, we solve (A - λ₁I)v = 0:

(0 - 1 8) (v₁) = (0)

(-1 9 - 1) (v₂) = (0)

This leads to the equations:

-v₁ + 8v₂ = 0

-v₁ + 9v₂ = 0

Solving this system of equations, we find v₁ = 8 and v₂ = 1.

Therefore, the first eigenvector corresponding to λ₁ = 1 is v₁ = (8 1).

For λ₂ = 8, we solve (A - λ₂I)v = 0:

(-8 - 1 8) (v₁) = (0)

(-1 1 - 1) (v₂) = (0)

This leads to the equations:

-8v₁ - v₂ + 8v₃ = 0

-v₁ + v₂ - v₃ = 0

Solving this system of equations, we find v₁ = 1, v₂ = 1, and v₃ = 1.

Therefore, the second eigenvector corresponding to λ₂ = 8 is v₂ = (1  1  1).

The general solution to the associated homogeneous system is then given by:

x_h(t) = c₁\(e^{t\)(8 1) + c₂\(e^{8t\)(1 1 1)

Step 2: Find a particular solution to the nonhomogeneous system.

To find a particular solution, we assume a solution of the form:

x_p(t) = u₁(t)(8 1) + u₂(t)(1 1 1)

Now, let's substitute this solution form into the original system:

x' = (0 8 -1 9) x + (8\(e^{-9t\))

Differentiating the assumed solution form:

x' = u₁'(t)(8 1) + u₂'(t)(1 1 1)

Substituting these derivatives into the system:

u₁'(t)(8 1) + u₂'(t)(1 1 1) = (0 8 -1 9)(u₁(t)(8 1) + u₂(t)(1 1 1)) + (8\(e^{-9t\))

This equation can be written as two separate equations for the components of the vectors:

8u₁'(t) + u₂'(t) = 0

8u₁'(t) + 9u₂'(t) = 8\(e^{-9t\)

Solving these equations, we find u₁'(t) = \(e^{-9t\) and u₂'(t) = -8\(e^{-9t\).

Integrating both sides, we obtain:

u₁(t) = -\(e^{-9t\) + C₁

u₂(t) = 8\(e^{-9t\) + C₂

where C₁ and C₂ are constants of integration.

Therefore, the particular solution to the nonhomogeneous system is:

x_p(t) = (-\(e^{-9t\) + C₁)(8 1) + (8\(e^{-9t\) + C₂)(1 1 1)

Step 3: Combine the solutions.

The general solution to the nonhomogeneous system is given by:

x(t) = x_h(t) + x_p(t)

= c₁\(e^{t\)(8 1) + c₂\(e^{8t\)(1 1 1) + (-\(e^{-9t\) + C₁)(8 1) + (8\(e^{-9t\) + C₂)(1 1 1)

Simplifying and grouping terms, we get:

x(t) = (c₁\(e^{t\) - \(e^{-9t\) + C₁)(8 1) + (c₂\(e^{8t\) + 8\(e^{-9t\) + C₂)(1 1 1)

This is the general solution to the given nonhomogeneous system.

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To show that the matrix A = [XX - X'Z(ZZ)^(-1)Z'X] is positive definite, we need to demonstrate two properties: (1) A is symmetric, and (2) all eigenvalues of A are positive.

Symmetry: To show that A is symmetric, we need to prove that A' = A, where A' represents the transpose of A. Taking the transpose of A: A' = [XX - X'Z(ZZ)^(-1)Z'X]'. Using the properties of matrix transpose, we have:

A' = (XX)' - [X'Z(ZZ)^(-1)Z'X]'. The transpose of a sum of matrices is equal to the sum of their transposes, and the transpose of a product of matrices is equal to the product of their transposes in reverse order. Applying these properties, we get: A' = X'X - (X'Z(ZZ)^(-1)Z'X)'.  The transpose of a transpose is equal to the original matrix, so: A' = X'X - X'Z(ZZ)^(-1)Z'X. Comparing this with the original matrix A, we can see that A' = A, which confirms that A is symmetric.  Positive eigenvalues: To show that all eigenvalues of A are positive, we need to demonstrate that for any non-zero vector v, v'Av > 0, where v' represents the transpose of v. Considering the expression v'Av: v'Av = v'[XX - X'Z(ZZ)^(-1)Z'X]v

Expanding the expression using matrix multiplication : v'Av = v'X'Xv - v'X'Z(ZZ)^(-1)Z'Xv. Since X and Z have full column rank, X'X and ZZ' are positive definite matrices. Additionally, (ZZ)^(-1) is also positive definite. Thus, we can conclude that the second term in the expression, v'X'Z(ZZ)^(-1)Z'Xv, is positive definite.Therefore, v'Av = v'X'Xv - v'X'Z(ZZ)^(-1)Z'Xv > 0 for any non-zero vector v. Implications in econometrics: In econometrics, positive definiteness of a matrix has important implications. In particular, the positive definiteness of the matrix [XX - X'Z(ZZ)^(-1)Z'X] guarantees that it is invertible and plays a crucial role in statistical inference.

When conducting econometric analysis, this positive definiteness implies that the estimator associated with X and Z is consistent, efficient, and unbiased. It ensures that the estimated coefficients and their standard errors are well-defined and meaningful in econometric models. Furthermore, positive definiteness of the matrix helps in verifying the assumptions of econometric models, such as the assumption of non-multicollinearity among the regressors. It also ensures that the estimators are stable and robust to perturbations in the data. Overall, the positive definiteness of the matrix [XX - X'Z(ZZ)^(-1)Z'X] provides theoretical and practical foundations for reliable and valid statistical inference in econometrics.

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The answer is that u does not lie in the plane in \($\mathbb{R}^3$\) spanned by the columns of A.

Given that

\($u = \begin{bmatrix} -2 \\ 12 \\ 4 \end{bmatrix}$ and $A = \begin{bmatrix} 4 & -2 & -3 \\ 5 & 1 & 1 \end{bmatrix}$\).

We are required to determine whether $u$ lies in the plane in $\mathbb{R}^3$ spanned by the columns of $A$ or not.

A plane in \($\mathbb{R}^3$\) is formed by three non-collinear vectors. In this case, we can obtain two linearly independent vectors from the matrix A and then find a third non-collinear vector by taking the cross product of the two linearly independent vectors.

The resulting vector would then span the plane formed by the other two vectors.

Therefore,\($$A = \begin{bmatrix} 4 & -2 & -3 \\ 5 & 1 & 1 \\ 0 & 0 & 0 \end{bmatrix}$$\)

If we perform Gaussian elimination on A, we obtain

\($$\begin{bmatrix} 1 & 0 & 1/2 \\ 0 & 1 & -7/3 \\ 0 & 0 & 0 \end{bmatrix}$$\)

The matrix has rank 2, which means the columns of A are linearly independent. Therefore, A spans a plane in \($\mathbb{R}^3$\) .

We can now take the cross product of the two vectors \($\begin{bmatrix} 4 \\ 5 \\ 0 \end{bmatrix}$ and $\begin{bmatrix} -2 \\ 1 \\ 0 \end{bmatrix}$\) that form the plane. Doing this, we obtain

\($$\begin{bmatrix} 0 \\ 0 \\ 13 \end{bmatrix}$$\)

This vector is orthogonal to the plane. Therefore, if u lies in the plane in \($\mathbb{R}^3$\) spanned by the columns of A, then u must be orthogonal to this vector. But we can see that \($\begin{bmatrix} -2 \\ 12 \\ 4 \end{bmatrix}$ is not orthogonal to $\begin{bmatrix} 0 \\ 0 \\ 13 \end{bmatrix}$\).

Therefore, u does not lie in the plane in \($\mathbb{R}^3$\) spanned by the columns of A.Hence, the answer is that u does not lie in the plane in \($\mathbb{R}^3$\) spanned by the columns of A.

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The nurse should administer 2 tablets per dose if available triazolam is 0.125 mg tablets and the required triazolam is 0.25 mg.

The given data is as follows:

Amount of triazolam = 0.25 mg po

Available of triazolam = 0.125 mg

We need to calculate the total number of tablets the nurse should administer per dose.

Triazolam mainly treats insomnia. Triazolam is in a class of prescriptions called benzodiazepines. It works by slowing by moving the power of drugs in the brain to allow sleep artificially.

To administer a dose of 0.25 mg of triazolam,

0.125 mg x 2 = 0.25 mg

Therefore we can conclude that 2 tablets should the nurse administer per dose.

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Answer:

y - (-8) = 7(x - (-3))

-8 goes into the green box.

Solutions of given exponents are :

1.  \(9^{18}\)   2. \(16x^4\)   3.  \(\frac{6561}{y^2}\)

In, mathematics a exponent or exponential equation or exponential function is inverse of a logarithmic function. That means, we can easily convert the logarithmic function into exponential function and vice versa. The shows the behavior of something to the power of something. The basic form of the exponential can be written as \(a^x\)

where, a = the base of function

            x = exponential

Important properties of exponential :

According to the question,

1. given, \((9^{3})^6\)

  use the property, \((a^n)^m = a^{nm}\)

   \((9^{3})^6\) = \(9^{3.6} = 9^{18}\)

2. Given, \((2x)^4\)

   use the property, \((ab)^n = a^n.b^n\)

    \((2x)^4\) = \(2^4.x^4 = 16x^4\)

3. Given , \((\frac{3^4}{y}) ^{2}\)

    use the property, \((\frac{a}{b})^n = \frac{a^n}{b^n}\)

     \((\frac{3^4}{y}) ^{2}\) = \(\frac{(3^4)^2}{y^2}\)

    now use ,  \((a^n)^m = a^{nm}\)

     = \(\frac{3^8}{y^2} = \frac{6561}{y^2}\)

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A study has a 2 Ã 2 Ã 3 within-groups factorial design. This example has a total of _12_ cell(s). Researchers would need to investigate _three__ main effect(s), _Three two-way interactions __ two-way interaction(s), and _ One three-way interaction__ three-way interaction(s) in this study.

a 2 x 2 x 3 within-groups factorial design, you have:
A total of 2 x 2 x 3 = 12 cells
Three main effects to investigate (one for each factor)
Three two-way interactions to investigate (AxB, AxC, and BxC)
4. One three-way interaction to investigate (AxBxC)
So, in this study, there are 12 cells, researchers would need to investigate 3 main effects, 3 two-way interactions, and 1 three-way interaction.

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Answer:

Kindly check explanation

Step-by-step explanation:

3 boxes or less = Cost of tiles = $48

4 - 8 boxes ;  cost = $45

9 - 19 boxes ; cost = $42

> 19 boxes ; cost = $38

Cost of purchasing 5 boxes of tiles :

$45 * 5 = $225

Cost of purchasing 19 boxes :

$42 * 19 = $798