What is the area, in square units, of the rectangle? L 2/9 W 3/7

The concept of simplifying a Boolean expression involves reducing the expression to its most concise form by applying logical rules and simplification techniques. This helps in reducing complexity, improving readability, and optimizing logic circuits by eliminating redundant terms and literals.

The simplified expression consists of two terms with a total of 5 literals.

To simplify the expression:

xyz + xyz' + x'yz' + x'y'z

We can apply Boolean algebra rules to simplify the terms:

Combine terms with common literals:

xyz + xyz' = xy(z + z') = xy

Combine terms with common literals:

x'yz' + x'y'z = x'z(y + y') = x'z

Now we have simplified the expression to:

xy + x'z

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A horizontal line is a line extending from left to right. When you look at the sunrise over the horizon you are seeing the sunrise over a horizontal line. The x-axis is an example of a horizontal line.

Now, According to the question:

What is a Horizontal Line?

Horizontal lines are also known as sleeping lines. In coordinate geometry, horizontal lines are those lines that are parallel to the x-axis. In geometry, we can find horizontal line segments in many shapes, such as quadrilaterals, 3d shapes, etc. In real life, we can find horizontal lines on the steps of the staircase, planks on the railway tracks, etc.

The x-axis is an example of a horizontal line.

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Step-by-step explanation:

the answer is 3.142

\(3.142 \times 20 \times 18 \\ 2 = 1131.2 \times 3.142 \times 10^{2} = 628.4 \\ \\ = 1759.52\)

The Values of (a+b)ab are undefined.

Given that, a = 3an and db = -2We need to find the values of (a+b)

Now, we have a = 3an... equation (1)Also, we have db = -2... equation (2)From equation (1), we get: n = 1/3... equation (3)Putting equation (3) in equation (1), we get: a = a/3a = 3... equation (4)Now, putting equation (4) in equation (1), we get: a = 3an... 3 = 3(1/3)n = 1

From equation (2), we have: db = -2=> d = -2/b... equation (5)Multiplying equation (1) and equation (2), we get: a*db = 3an * -2=> ab = -6n... equation (6)Putting values of n and a in equation (6), we get: ab = -6*1=> ab = -6... equation (7)Now, we need to find the value of (a+b).For this, we add equations (1) and (5),

we get a + d = 3an - 2/b=> a + (-2/b) = 3a(1) - 2/b=> a - 3a + 2/b = -2/b=> -2a + 2/b = -2/b=> -2a = 0=> a = 0From equation (1), we have a = 3an=> 0 = 3(1/3)n=> n = 0

Therefore, from equation (5), we have:d = -2/b=> 0 = -2/b=> b = ∞Now, we know that (a+b)ab = (0+∞)(0*∞) = undefined

Therefore, the values of (a+b)ab are undefined.

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The observed allele frequencies for the T102C locus are as follows: T allele frequency = 0.388 and C allele frequency = 0.612.


To calculate the observed allele frequencies, we divide the number of occurrences of each allele by the total number of alleles observed.

In this case, the T allele is observed in 108 TT genotypes and 194 TC genotypes, giving a total of 108 + 194 = 302 T alleles. Similarly, the C allele is observed in 194 TC genotypes and 48 CC genotypes, giving a total of 194 + 48 = 242 C alleles.

To calculate the T allele frequency, we divide the number of T alleles by the total number of alleles: 302 T alleles / (302 T alleles + 242 C alleles) = 0.388 (or approximately 0.39).

Similarly, the C allele frequency is calculated as: 242 C alleles / (302 T alleles + 242 C alleles) = 0.612 (or approximately 0.61).

Therefore, the observed allele frequencies for the T102C locus are T allele frequency = 0.388 and C allele frequency = 0.612.

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The  directed graph for the given values given by the relation {(a, a), (a, b), (b, c), (c, b), (c, d), (d, a), (d, b)} is expained.

The directed graph that represents the relation {(a, a), (a, b), (b, c), (c, b), (c, d), (d, a), (d, b)} is shown below:

We can clearly see from the directed graph that there are four vertices: a, b, c, and d.

For the given relation, there are three edges that start and end on vertex a, two edges that start and end on vertex b, one edge that starts from vertex c and ends on vertex b, one edge that starts from vertex c and ends on vertex d, and one edge that starts from vertex d and ends on vertex a.

The vertex a is connected to vertex a and b.

The vertex b is connected to vertices c and d.

The vertex c is connected to vertices b and d.

The vertex d is connected to vertices a and b.

A directed graph is a graphical representation of a binary relation in which vertices are connected by arrows.

Each directed edge shows the direction of the relation.

A directed graph is also called a digraph.

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Answer:

5.6

Step-by-step explanation:

11*7=77

11.8*7= 82.6

82.6-77=5.6

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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Considering that you have 55 degrees of freedom, your sample size must be of 56.

It is given by one less than the sample size.

In this problem, you have 55 degrees of freedom, hence:

n - 1 = 55

n = 56.

Your sample size must be of 56.

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Answer:  B 9:21

Step-by-step explanation:

9 reduces to three and 21 reduced to 7

a. The appropriate amount of safety stock is 92 kg. b. The item should be reordered when the inventory level reaches approximately 692 kg.

To determine the amount of safety stock and the reorder point (ROP), we need to consider the expected demand during the lead time, the standard deviation of demand during the lead time, and the acceptable stockout risk.

a. Amount of safety stock:

Safety stock is the additional inventory kept to mitigate the risk of stockouts. It acts as a buffer to account for unexpected fluctuations in demand. The formula to calculate safety stock is:

Safety stock = (Z * Standard deviation of demand during lead time)

Where Z is the z-score corresponding to the acceptable stockout risk. Since the acceptable stockout risk is 5 percent, we need to find the corresponding z-score.

Looking up the z-values table for a 5 percent risk (two-tailed test), the z-score is approximately 1.645.

Substituting the values into the formula:

Safety stock = (1.645 * 56)

≈ 92.12 kg

b. Reorder point (ROP):

The reorder point is the level of inventory at which an item should be reordered to ensure that it arrives before the stock runs out during the lead time. It can be calculated using the formula:

ROP = Expected demand during lead time + Safety stock

Substituting the given values:

ROP = 600 + 92

≈ 692 kg

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Answer:

Either the abscissa is positive and the ordinate is negative or the abscissa is positive and the ordinate is negative. So, a point could be either (+,-), which lie in quadrant IV, or it could be of the type (-,+), which lie in quadrant II.

V is at its maximum when \(a = b\ \pi x\),  \(V = \pi x2h\), and \(c = a x2 + b\ \pi xh\).

This question uses the principles of geometry, specifically the formulas for the area of a circle and the area of a curved surface. In addition, the concept of cost maximization is used to determine the cost of the tank when the volume is at its maximum.

Given,

\(c = a x2 + b\ \pi xh\)

This equation states that the cost of the tank is equal to the cost of the base plus the cost of the curved surface.

The cost of the base is equal to the area of the base multiplied by the cost per square metre, which is a.

The area of the base is equal to \(\pi x2\), where x is the radius of the base. The cost of the curved surface is equal to the area of the curved surface multiplied by the cost per square metre, which is b.

The area of the curved surface is equal to πxh, where h is the height of the tank.

Combining these two equations gives the equation for c.

\(V = \pi x2h\)

This equation states that the volume of the tank is equal to the area of the base multiplied by the height.

The area of the base is equal to \(\pi x2\), where x is the radius of the base. The height of the tank is h. Combining these two equations gives the equation for V.

V is at its maximum when \(a = b\pi x\)

This equation states that the volume of the tank is maximized when the cost of the base is equal to the cost of the curved surface.

The cost of the base is equal to the area of the base multiplied by the cost per square metre, which is a.

The area of the base is equal to \(\pi x2\), where x is the radius of the base. The cost of the curved surface is equal to the area of the curved surface multiplied by the cost per square metre, which is b.

The area of the curved surface is equal to πxh, where h is the height of the tank.

Setting a equal to bπx gives the equation for the maximum volume.

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There are 6 ways to have one ripe pear and five unripe pears in the bowl.

To determine the number of ways in which there can be one ripe pear and five unripe pears in a bowl containing six pears, we can approach the problem by analyzing the position of the ripe pear within the group of pears.

Since we know that one pear is ripe and five are unripe, there are six possible positions where the ripe pear can be placed within the group of six pears. We can denote these positions as follows:

Ripe Pear, Unripe Pear, Unripe Pear, Unripe Pear, Unripe Pear, Unripe Pear

Unripe Pear, Ripe Pear, Unripe Pear, Unripe Pear, Unripe Pear, Unripe Pear

Unripe Pear, Unripe Pear, Ripe Pear, Unripe Pear, Unripe Pear, Unripe Pear

Unripe Pear, Unripe Pear, Unripe Pear, Ripe Pear, Unripe Pear, Unripe Pear

Unripe Pear, Unripe Pear, Unripe Pear, Unripe Pear, Ripe Pear, Unripe Pear

Unripe Pear, Unripe Pear, Unripe Pear, Unripe Pear, Unripe Pear, Ripe Pear

As each position is distinct, we can see that there are six possible ways in which there can be one ripe pear and five unripe pears in the bowl.

C(n, k) = n! / (k! * (n - k)!)

where n is the total number of pears and k is the number of ripe pears we want to choose.

In this case, n = 6 (total pears) and k = 1 (ripe pear).

C(6, 1) = 6! / (1! * (6 - 1)!)

= 6! / (1! * 5!)

= (6 * 5 * 4 * 3 * 2 * 1) / (1 * (5 * 4 * 3 * 2 * 1))

= 6

Therefore, there are 6 ways to have one ripe pear and five unripe pears in the bowl.

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Based on the mathematical statement, the unit rate is 3/4 books per hour

The mathematical statement is given as

"rewrite 1/4 book 1/3hour as a unit rate"

The above means that

Book = 1/4

Time = 1/3 hour

The unit rate is then calculated as

Unit rate = Book/Time

Substitute the known values in the above equation

So, we have the following equation

Unit rate = (1/4)/(1/3)

Evaluate

Unit rate = 3/4

Hence, the solution is 3/4 books per hour

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\(\stackrel{\textit{not distributed yet}}{\cfrac{x+1}{(x-2)(x+1)}\stackrel{\downarrow }{\text{\LARGE -}}\cfrac{x-2}{(x-2)(x+1)}}\implies \stackrel{\textit{already distributed}}{\cfrac{x+1}{(x-2)(x+1)}\stackrel{\downarrow }{\text{\LARGE +}}\cfrac{-x+2}{(x-2)(x+1)}} \\\\\\ \cfrac{x+1-x+2}{(x-2)(x+1)}\implies \cfrac{3}{(x-2)(x+1)}\)

Answer:

The error is in the 3rd step.  The denominator should be 3, not -1.

Step-by-step explanation:

The third step has an error.  The second fraction is subtracted from the first.  The calculation should have been (x+1) - (x-2).  x+1-x+2 = 3.

See the attached worksheet.

Answer:

y=-7

Step-by-step explanation:

-2=y+5

-7=y

the 95% confidence interval for the population mean is approximately 73.74 to 74.26.

To construct a confidence interval for the population mean, use the following formula:

Confidence Interval = X ± Z * (σ/√n)

Where:

X is the sample mean

Z is the z-score corresponding to the desired confidence level

σ is the population standard deviation

n is the sample size

Given:

c = 0.95 (95% confidence level)

X = 74

σ = 0.5

n = 56

To find the z-score for a 95% confidence level, use a Z-table or a statistical calculator. The z-score for a 95% confidence level is approximately 1.96.

Now we can calculate the confidence interval:

Confidence Interval = X ± Z * (σ/√n)

Confidence Interval = 74 ± 1.96 * (0.5/√56)

To calculate the lower bound:

Lower bound = 74 - 1.96 * (0.5/√56)

To calculate the upper bound:

Upper bound = 74 + 1.96 * (0.5/√56)

Calculating these values:

Lower bound ≈ 73.74

Upper bound ≈ 74.26

Therefore, the 95% confidence interval for the population mean is approximately 73.74 to 74.26.

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Answer: X

Step-by-step explanation:

The given metric is as follows: $$ ds^2 = e^{2A(r)} dt^2 - e^{2B(r)} dr^2 - 2(r^2 +\sin^2\theta) (d\phi^2 + \sin^2\theta d\phi^2) $$

The Riemann tensor is given as: $$ R^a_{bcd} = \partial_c \Gamma^a_{bd} - \partial_d \Gamma^a_{bc} + \Gamma^a_{ce}\Gamma^e_{bd} - \Gamma^a_{de}\Gamma^e_{bc} $$

Here, $\Gamma^a_{bc}$ is the Christoffel symbol of the second kind defined as:

$$ \Gamma^a_{bc} = \frac{1}{2} g^{ad}(\partial_b g_{cd} + \partial_c g_{bd} - \partial_d g_{bc}) $$

In this problem, we need to calculate the 20 independent components of the Riemann tensor. First, let's calculate the Christoffel symbols of the second kind.

Here, $g_ {00} = e^{2A(r)}$, $g_ {11} = -e^{2B(r)} $, $g_ {22} = -(r^2 + \sin^2\theta) $, and $g_{33} = -(r^2 + \sin^2\theta) \sin^2\theta$.

Using these, we get:$$ \Gamma^0_{00} = A'(r)e^{2A(r)}$$$$ \Gamma^0_{11} = B'(r)e^{2B(r)}$$$$ \Gamma^1_{01} = A'(r)e^{2A(r)}$$$$ \Gamma^1_{11} = -B'(r)e^{2B(r)}$$$$ \Gamma^2_{22} = -r(r^2 + \sin^2\theta)^{-1}$$$$ \Gamma^3_{33} = -\sin^2\theta(r^2 + \sin^2\theta)^{-1}$$$$ \Gamma^2_{33} = \cos\theta\sin\theta(r^2 + \sin^2\theta)^{-1}$$$$ \Gamma^3_{32} = \Gamma^3_{23} = \cot\theta $$

Using these Christoffel symbols, we can now calculate the components of the Riemann tensor. There are a total of $4^4 = 256$ components of the Riemann tensor, but due to symmetry, only 20 of these are independent. Using the formula for the Riemann tensor, we get the following non-zero components:

$$ R^0_{101} = -A''(r)e^{2A(r)}$$$$ R^0_{202} = R^0_{303} = (r^2 + \sin^2\theta)(\sin^2\theta A'(r) + rA'(r))e^{2(A-B)}$$$$ R^1_{010} = -A''(r)e^{2A(r)}$$$$ R^1_{121} = -B''(r)e^{2B(r)}$$$$ R^2_{232} = r(r^2 + \sin^2\theta)^{-1}$$$$ R^3_{323} = \sin^2\theta(r^2 + \sin^2\theta)^{-1}$$$$ R^2_{323} = -\cos\theta\sin\theta(r^2 + \sin^2\theta)^{-1}$$$$ R^3_{322} = -\cos\theta\sin\theta(r^2 + \sin^2\theta)^{-1}$$$$ R^0_{121} = A'(r)B'(r)e^{2(A-B)}$$$$ R^1_{020} = A'(r)B'(r)e^{2(A-B)}$$$$ R^2_{303} = -\sin^2\theta A'(r)e^{2(A-B)}$$$$ R^3_{202} = -rA'(r)e^{2(A-B)}$$$$ R^0_{202} = (r^2 + \sin^2\theta)\sin^2\theta A'(r)e^{2(A-B)}$$$$ R^0_{303} = (r^2 + \sin^2\theta)A'(r)e^{2(A-B)}$$$$ R^1_{010} = A''(r)e^{2(A-B)}$$$$ R^1_{121} = B''(r)e^{2(A-B)}$$$$ R^2_{232} = r(r^2 + \sin^2\theta)^{-1}$$$$ R^3_{323} = \sin^2\theta(r^2 + \sin^2\theta)^{-1}$$

Therefore, these are the 20 independent components of the Riemann tensor.

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(a) To find the partial derivatives, we differentiate the function f(x, y) with respect to x and y while treating the other variable as a constant.

fx(x, y) = d/dx [ (4x^2 + 2xy + 4y^2) / (x^2 + y^2) ]

          = [(8x(x^2 + y^2) - (4x^2 + 2xy + 4y^2)(2x)) / (x^2 + y^2)^2]

          = [(8x^3 + 8xy^2 - 8x^3 - 4x^2y - 8xy^2) / (x^2 + y^2)^2]

          = [-4x^2y / (x^2 + y^2)^2]

fy(x, y) = d/dy [ (4x^2 + 2xy + 4y^2) / (x^2 + y^2) ]

          = [(8y(x^2 + y^2) - (4x^2 + 2xy + 4y^2)(2y)) / (x^2 + y^2)^2]

          = [(8xy^2 + 8y^3 - 8xy^2 - 4x^2y - 8y^3) / (x^2 + y^2)^2]

          = [-4x^2y / (x^2 + y^2)^2]

(b) To find fx(0, 0) and fy(0, 0), we substitute x = 0 and y = 0 into the partial derivative expressions:

fx(0, 0) = -4(0)^2(0) / ((0)^2 + (0)^2)^2 = 0

fy(0, 0) = -4(0)^2(0) / ((0)^2 + (0)^2)^2 = 0

(c) Both partial derivatives, fx(x, y) and fy(x, y), are continuous at every point in the set {(x, y): (x, y) ≠ (0, 0)}.

However, at the point (0, 0), the partial derivatives fx(0, 0) and fy(0, 0) are both 0, indicating that the partial derivatives are continuous at that point as well.

Therefore, the correct answer is (a) Yes, both the partial derivatives are continuous at every point in that set.

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Answer:

The number that belongs in the green P' = ([?], [ ]) with P' = (7, -8) box is;

7

Step-by-step explanation:

The coordinate of the given point 'P' is P = (3, -5)

The preimage of (x, y) after the translation, \(T_{(x, \ y)}\) = (x-coordinate + 4, y-coordinate - 3)

Therefore, the translation, \(T_{(x, \ y)}\) = T₍₄, ₋₃₎

Therefore, we have;

Preimage P(3, -5) under the translation T₍₄, ₋₃₎ gives the image P' as follows

P(3, -5) \(\overset{T_{\left ( 4, \, -3 \right )}}{\rightarrow}\)P'(3 + 4, -5 - 3) = P'(7, -8)

Therefore, the number that belongs in the green box is the x-coordinate value of the point P'(7, -8) which is seven.

Answer:

8-1

Step-by-step explanation:

Answer:

2 4 2 y-3

•

•

•

•

•

Yan po answer

The mixed fraction is express as :

The given expression is :

Simplify the mixed fraction into decimal form :

Substitute the value and then subtarct :

Answer : 14 3/4 - 4 1/8​ = 10.625

Answer:

5/8

Step-by-step explanation:

3/4 can be multiplied by 2 to get 6/8 and now you have common denominators so you do 4 6/8 - 4 1/8

4-4= 0

6/8 - 1/8 = 5/8 so 5/8 is the answer

Answer:

k = 24·√2

Step-by-step explanation:

Given that the angles of the triangle are 45° by 45 by 90°, we have;

The given right triangle = An isosceles right triangle by two angles being equal

The given angle of the right triangle = 90°

The given leg of the right triangle = 24

For an isosceles right triangle, both legs are equal, therefore;

The length of the other leg of the right triangle = 24

By Pythagoras theorem, the measure of the side opposite the 90° side, 'k', is given as follows;

k² = (One leg length)² + (The other leg length)²

∴ k² = 24² + 24² = 1152

k = √1152 = 24·√2 ≈ 33.94.

Answer:

Step-by-step explanation:

The dimension of the basis is {[1 0 0 2], [-1 1 0 0]}.

To find a basis for the subspace S = span {[1 -1 0 2], [3 -5 4 8], [0 1 -2 -1]}, we can use the same method as in the example. First, we put the vectors in a matrix and row-reduce it:

[1 -1 0 2]
[3 -5 4 8]
[0 1 -2 -1]

R2 - 3R1 -> R2
R3 -> R3 + 2R1

[1 -1 0 2]
[0 -2 4 2]
[0 1 -2 -1]

-1/2R2 -> R2

[1 -1 0 2]
[0 1 -2 -1]
[0 1 -2 -1]

R3 - R2 -> R3

[1 -1 0 2]
[0 1 -2 -1]
[0 0 0 0]

We can see that the last row is all zeros, so we have only two pivots and one free variable. This means that the dimension of the subspace S is 2. To find a basis, we can write the pivots as linear combinations of the original vectors:

[1 -1 0 2] = [1 0 0 2] + [-1 1 0 0]
[0 1 -2 -1] = [0 1 -2 -1]

Therefore, a basis for S is {[1 0 0 2], [-1 1 0 0]}.

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To determine how much of a 35% ammonia solution is needed to produce 5 liters of a 10% ammonia solution, we can set up a proportion based on the concentrations and volumes. By solving the proportion, we can find the volume of the 35% ammonia solution required.

Let's assume that x represents the volume of the 35% ammonia solution needed.

To set up the proportion, we can compare the concentrations of ammonia in the two solutions:

(35 g ammonia / 100 mL solution) = (10 g ammonia / 1000 mL solution)

Since the desired final volume is 5 liters (5000 mL), we can rewrite the proportion as:

(35 g ammonia / 100 mL solution) = (10 g ammonia / 5000 mL solution)

By cross-multiplying and solving for x, we find:

35 g ammonia * 5000 mL solution = 10 g ammonia * 100 mL solution

175000 g·mL = 1000 g·mL * x

175 x = 1000

x = 1000 / 175

x ≈ 5.71 mL

Therefore, you would need approximately 5.71 mL of the 35% ammonia solution to produce 5 liters of a 10% ammonia solution.

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