Solve for x in the triangle. Round your answer to the nearest tenth

The critical path is the path with the longest duration, which in this case is A -> B -> D -> E with a duration of 11 days.

To determine the critical path of the project, we need to find the longest path of activities that must be completed in order to finish the project on time. This is done by calculating the earliest start time (ES) and earliest finish time (EF) for each activity.

Starting with activity A, ES = 0 and EF = 4. Activity B can start immediately after A is complete, so ES = 4 and EF = 7. Activity C can start after A is complete, so ES = 4 and EF = 6. Activity D can start after B is complete, so ES = 7 and EF = 9. Finally, activity E can start after C and D are complete, so ES = 9 and EF = 11.

The variance for each activity is also given, which allows us to calculate the standard deviation and determine the probability of completing the project on time. The critical path is the path with the longest duration, which in this case is A -> B -> D -> E with a duration of 11 days.

Using the expected durations and variances, we can calculate the standard deviation of the critical path. This information can be used to determine the probability of completing the project on time.

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Answer:

so pascal is 13 and serge is 10

Step-by-step explanation:

i really hope this helps!

Answer:

Step-by-step explanation:

Let Pascal's age be x

Then Serge is x - 3

Sum of their ages is 23

Pascal is 13 and Serge is 10

The total number of boxes that can be loaded onto the trailer is 27.

Here we have to determine the maximum number of boxes.

That can be stored in a locker by the volume of one box.

From the given information volume of the box is Vb and the volume f the locker is Vl.

\(Volume=Length\times width\times height\)

Therefore we get,

\(V_b=4\times3\times2\\V_b=24ft^3\)

The volume of the locker is

\(V_L=12\times6\times 9\\V_L=684ft^3\)

Therefore the number of the maximum boxes are

\(\frac{VL}{V_b} =\frac{648}{24} \\=27\)

Therefore, The total number of boxes can be loaded onto the trailer are 27.

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Answer:

A.) DGF

Step-by-step explanation:

To determine the number of tons of metal per year needed for Machine A to be favored over Machine B, we compare their costs. Machine A costs $323,000 with an annual operating cost of $2.40/ton, while Machine B costs $178,000 with an annual operating cost of $8.00/ton. The machines have useful lives of 10 years and 6 years, respectively, and the minimum attractive rate of return (MARR) is 18% per year.

By calculating the equivalent annual costs (EAC) for each machine using the given formula and comparing them, we can determine the point at which Machine A becomes more favorable. However, specific values for the discounting factors and the tons per year needed are missing, making it impossible to provide an exact answer.

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Answer:

A. $500

C. 7 percent

Step-by-step explanation:

Your problem follows the format of the Simple Interest Formula.

The formula is described as follows: A = P(1 + r*t)

Where P = initial value

r = interest rate as a decimal

t = amount of time.

In your equation of A = 500 ( 1 + 0.07 t )

we can see that 500 represents the P value which is the initial value of the investment.

We can also see that the rate is 0.07. Then converted from a decimal to a percent would be 7 percent.

Answer:

25 ÷ 20

Step-by-step explanation:

The fraction is for divided (÷)

Answer:

C

Step-by-step explanation:

is the correct information

Answer:

\(32x^4\)

Step-by-step explanation:

Given:

\(\dfrac{(4x)^2 \times 2x^3}{x}\)

\(\textsf{Apply exponent rule} \quad (ab)^c=a^cb^c:\)

\(\implies \dfrac{4^2x^2 \times 2x^3}{x}\)

Simplify 4²:

\(\implies \dfrac{16x^2 \times 2x^3}{x}\)

Multiply the numbers:

\(\implies \dfrac{32x^2x^3}{x}\)

\(\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}:\)

\(\implies \dfrac{32x^{(2+3)}}{x}\)

\(\implies \dfrac{32x^5}{x}\)

\(\textsf{Apply exponent rule} \quad \dfrac{a^b}{a^c}=a^{b-c}:\)

\(\implies 32x^{(5-1)}\)

\(\implies 32x^4\)

Let's try to understand how we can solve this equation

Given equation,4f+2=6f-12

Now we will take the terms on one side and constants on the other.

=> 2+12=6f-4f

=> 14=2f

=>7=f

So, the value of f would be 7. Remember that while bringing value to another side, the sign of that value changes. If it is a positive sign then it is going to be transformed into a negative one and vice versa.

In the worst-case scenario, the company should use the following values: price = $799 per unit, variable cost = $289 per unit, fixed costs = $2.89 million, and quantity = 60,950 units.

In the best-case scenario analysis for Automatic Transmissions, Inc.'s new gear assembly project, the company assumes the upper limit of the ±15 percent range for its estimates. For the price per unit, they take a 15 percent increase, resulting in a value of $1081. Similarly, the variable cost per unit is increased by 15 percent to $391. The fixed costs are also adjusted upwards by 15 percent, reaching $3.91 million. Finally, the quantity is decreased by 15 percent, leading to a value of 45,050 units.

On the other hand, in the worst-case scenario analysis, the company assumes the lower limit of the ±15 percent range for its estimates. The price per unit is decreased by 15 percent, resulting in $799. The variable cost per unit is decreased to $289. The fixed costs are adjusted downwards to $2.89 million. Lastly, the quantity is increased by 15 percent to 60,950 units.

Therefore, in the worst-case scenario, the company should use the following values: price = $799 per unit, variable cost = $289 per unit, fixed costs = $2.89 million, and quantity = 60,950 units

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(1) The length of side BC is 9 cm.

(2) The length of side PQ is 5.385 m.

(3) The length of side UW is 6.71 mm.

(4) The length of side XZ is 14.32 mm.

(5) The length of side EF is  6 cm.

The missing lengths of the right triangle is calculated by applying the Pythagoras theorem formula.

(1) The length of side BC is calculated as;

BC = √ (15² - 12² )

BC = 9 cm

(2) The length of side PQ is calculated as;

PQ = √ (5² + 2² )

PQ = 5.385 m

(3) The length of side UW is calculated as;

UW = √ (9² - 6² )

UW = 6.71 mm

(4) The length of side XZ is calculated as;

XZ = √ (14² + 3² )

XZ = 14.32 mm

(5) The length of side EF is calculated as;

EF = √ (10² - 8² )

EF = 6 cm

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The rank of matrix A can be determined based on the given information in the question is as follows.

The rank of a matrix refers to the maximum number of linearly independent columns (or rows) in the matrix. From the given information:

a. Since A has linearly independent columns, the rank is equal to n, where n is the number of columns.

b. If Null(A)={0}, it means that the only solution to the homogeneous equation Ax=0 is the trivial solution (where x=0). This implies that the columns of A are linearly independent. Since A is a 6-by-4 matrix, the rank is equal to the number of columns, which is 4.

c. The dimension of the null space (denoted as dim(Null(A))) is equal to the number of linearly independent solutions to the homogeneous equation Ax=0. In this case, dim(Null(A))=3, which means that there are 3 linearly independent solutions. Since A is a 5-by-6 matrix, the rank can be found by subtracting the dimension of the null space from the number of columns: rank(A) = 6 - dim(Null(A)) = 6 - 3 = 3.

d. The determinant of a square matrix measures its invertibility. If det(A) is non-zero, it means that A is invertible, and an invertible matrix has full rank. Therefore, the rank of A is equal to the number of columns, which is 3.

e. The dimension of the row space (denoted as dim(Row(A))) represents the number of linearly independent rows in A. Since dim(Row(A))=3, it means that there are 3 linearly independent rows. Thus, the rank of A is 3.

f. An invertible matrix is non-singular and has full rank. Therefore, if A is a 4-by-4 invertible matrix, its rank is equal to the number of columns, which is 4.

g. If the system Ax=b has either a unique solution or no solution, it means that the column space of A has dimension 3. Hence, the rank of A is 3.

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The area of the largest rectangle is 46.47 square root.

Consider a semi-circle with a rectangle ABCD inscribed in it.

Let, O = centre of the semi-circle

A and B lies on the base of the semi-circle

OA = OB = x

D and C lie on the semi-circle

BC = AD = y

AB = CD = 2x

By Pythagorean theorem,

CB² + OB² = OC²

⇒ y² + x² = (6)²

⇒ y² = 36 - x²

⇒ y = √(36 - x²)

Now, area of rectangle in terms of x,

Area, A = 2x × y

= 2x × √(36 - x²)

Differentiating,

A' = 2 × √(36 - x²) - 2x²/(36 - x²)

When x = 0, y = 6 and when x = 6, y = 0, area = 0.

It implies that area is maximum when the value of x lies between 0 and 6.

This will occur where A’ = 0.

⇒ 2 × √(36 - x²) - 2x²/(36 - x²) = 0

⇒ 2 × √(36 - x²) = 2x²/(36 - x²)

On simplification, we get,

⇒ 2 × (36 - x²) = 2x²

⇒ 36 - x² = x²

⇒ 2x² = 36

⇒ x² = 36/2

⇒ x = √36/2

Now, y = √(36 - x²) becomes

⇒ y = √(36 - (√36/2)²)

⇒ y = √(36 - 36/2)

⇒ y = √(96 - 36)/2

⇒ y = √60/2

Maximum area = 2xy

= 2(√36/2)(√60/2)

= 46.47

Therefore, the area of the largest rectangle = 46.47 square units.

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Answer:

61

Step-by-step explanation:

Answer:

3(6m) + m

first you multiply (you MUST do parentheses first) so 3*6 is 18 and you add the m in there is its 18m so then its:

18m + m

now you just add 18m + m which is 19m

answer: 19m

In the collection, there are 11 nickels and 23 dimes. If each nickel is replaced with a quarter, the value of the collection becomes $5.05. So, C is correct. By writing them in the system of equations, we get the required value.

The given units are nickels, dimes, and quarters. Their conversion into dollars is as follows:

1 nickel = $0.05

1 dime = $0.10

1 quarter = $0.25

Given a collection of nickels and dimes is worth $2.85.

And there are 34 coins in the collection.

So, consider the number of nickel coins = n and the number of dime coins = d.

Then, the equation for the given collection is

n + d = 34...(1)

0.05n + 0.10d = 2.85...(2)

On simplifying (2), we get

5n + 10d = 2.85 × 100

⇒ 5n + 10d = 285

From (1), n = 34 - d, we get

5(34 - d) + 10d = 285

⇒ 170 - 5d + 10d = 285

⇒ 5d = 285 - 170 = 115

∴ d = 115/5 = 23

Thus, the number of dime coins is 23.

So, from (1), we get n + 23 = 34 ⇒ n = 34 - 23 = 11

∴ n = 11

Thus, the number of nickel coins is 11.

If each nickel coin in the collection is replaced with a quarter, then the value of the collection is

q + d = 34 and 0.25q + 0.10d = Y

Here q = 11; d = 23

So, we get

0.25(11) + 0.10(23) = Y

⇒ 2.75 + 2.3 = Y

⇒ 5.05 = Y

∴ Y = $5.05

The value of the new collection becomes $5.05.

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The constraints are xy = 1 and y² + z² = 25.

To find the extreme values of f subject to the given constraints, we will use the method of Lagrange multipliers. This method allows us to optimize a function subject to constraints by introducing additional variables called Lagrange multipliers.

We start by defining the Lagrange function L, which combines the original function f with the constraints. The Lagrange function is given by:

L(x, y, z, λ, μ) = f(x, y, z) - λ(xy - 1) - μ(y² + z² - 25)

Here, λ and μ are the Lagrange multipliers associated with the two constraints. The first term f(x, y, z) is the original function, and the subsequent terms are the constraints multiplied by their respective multipliers.

Next, we need to find the partial derivatives of the Lagrange function with respect to all the variables: x, y, z, λ, and μ.

∂L/∂x = 0 (Partial derivative of L with respect to x)

∂L/∂y = 0 (Partial derivative of L with respect to y)

∂L/∂z = 0 (Partial derivative of L with respect to z)

∂L/∂λ = 0 (Partial derivative of L with respect to λ)

∂L/∂μ = 0 (Partial derivative of L with respect to μ)

We solve the system of partial derivative equations obtained in step 2 to find the values of x, y, z, λ, and μ that satisfy the equations.

Once we obtain the solutions, we need to analyze the critical points. We evaluate the original function f at these points to determine whether they correspond to maximum or minimum values.

After analyzing the critical points, we compare the values of f at these points to determine the maximum and minimum values that satisfy the given constraints.

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Answer:

0.4

Step-by-step explanation:

−2 4/5÷(−7)=0.4

Answer:

0.4

THERE YOUR ANWSER SIR

Sorry cap lock

Answer:

The equation for the width is:

1056 = (2w+4) * w

And the solution is:

Width: 22 inches

Length: 48 inches

Step-by-step explanation:

Area of a rectangle = length * width

1056 = h * w   Eq. 1

h = 2w + 4         Eq. 2

h = length

w = width

Replacing Eq. 2 in Eq. 1:

1056 = (2w+4) * w

1056 = 2w*w + 4*w

1056 = 2w² + 4w

2w² + 4w - 1056 = 0

w = {-4±√((4²)-(4*2*-1056))} / (2*2)

w = {-4±√(16 + 8448)} / 4

w = {-4±√8464} / 4

w = {-4±92} / 4

Is a geometric figure, therefore, only the positive value will be obtained

w = {-4+92}/4

w = {88} / 4

w = 22

From Eq. 2:

h = 2w+4

h = 2*22+4

h = 44+4

h = 48

Check:

From Eq. 2

1056 = h * w

1056 = 48 * 22

Answer:

diameter is 28

Step-by-step explanation:

615.75216/3.14=196.099

\(\sqrt{196}\)=14

14*2=28

a)  The equation for the exponential distribution of waiting times is given by \(f(x) = \lambda e^{-\lambda x}\)

b) The probability of waiting less than 2 minutes to check out is 0.427

c) The probability of waiting between 4 and 6 minutes is 0.242

d) The probability of waiting more than 5 minutes to check out is 0.082

a. The equation for the exponential distribution of waiting times is given by:

\(f(x) = \lambda e^{-\lambda x}\)

where λ is the rate parameter of the distribution, and e is the natural logarithmic constant (approximately equal to 2.71828). The graph of the exponential distribution is a decreasing curve that starts at λ and approaches zero as x approaches infinity. The mean waiting time, denoted by E(X), is equal to 1/λ.

b. To find the probability that a customer waits less than 2 minutes to check out, we need to calculate the area under the exponential distribution curve between zero and 2 minutes. This can be expressed mathematically as:

P(X < 2) = \(\int_0^2 \lambda e^{-\lambda x} dx\)

Solving this integral yields:

P(X < 2) = 1 - \(e^{(-2\lambda)}\)

Substituting the given average waiting time of 2.5 minutes into the formula for the mean waiting time, we can calculate λ as:

E(X) = 1/λ

2.5 = 1/λ

λ = 0.4

Therefore, the probability of waiting less than 2 minutes to check out is:

P(X < 2) = 1 - \(e^{-2*0.4}\)

P(X < 2) ≈ 0.427

c. To find the probability of waiting between 2 and 4 minutes, we need to calculate the area under the exponential distribution curve between 2 and 4 minutes. This can be expressed mathematically as:

P(2 < X < 4) =\(\int_2^4 \lambda e^{(-\lambda x)} dx\)

Solving this integral yields:

P(2 < X < 4) = \(e^{(-2\lambda)} - e^{(-4\lambda)}\)

Substituting the value of λ obtained in part (b), we get:

P(2 < X < 4) = \(e^{(-20.4)} - e^{(-40.4)}\)

P(2 < X < 4) ≈ 0.242

d. To find the probability of waiting more than 5 minutes to check out, we need to calculate the area under the exponential distribution curve to the right of 5 minutes. This can be expressed mathematically as:

P(X > 5) = \(\int_5^{ \infty} \lambda e^{(-\lambda x)} dx\)

Solving this integral yields:

P(X > 5) = \(e^{(-5\lambda)}\)

Substituting the value of λ obtained in part (b), we get:

P(X > 5) = \(e^{(-5*0.4)}\)

P(X > 5) ≈ 0.082

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Answer:

C)9,5,1,3

a1=9

a2=a(2-1)-4= a1-4= 9-4=5

a3=a(3-1)-4= a2-4= 5-4=1

Hope this will help :-)

Answer:

3/8 might me ans

Step-by-step explanation:

12/33

6/16

3/8

1000 cubic centimeters would need to be placed in a tub of water to displace 1 Lter of water

Conversion of units simply refers to the method used in determining the equivalent of one unit in relation to another.

From the information given, we have that;

Number of cubic centimeters that would be placed in a tub of water to displace 1 L of water

So, we have that there is 1 liter of water in the tub

In order to displace, you need to put something in that is the same amount

Now, let's convert the units

1 liter = 1000 cubic cm

Hence, you need 1000 cubic cm to displace 1 liter

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Answer:

27

Step-by-step explanation:

substitute the given value of x: 2(4) + 3 + (4)^2

simplify: 8 + 3 + 16

add: 8 + 3 + 16 = 27

If Rick used 4 2/3 yards of fabric to sew 3 1/2 shirts. The unit rate of cloth he used in terms of yards per shirt will be 4/3.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.

It is given that, Rick used 4 2/3 yards of fabric to sew 3 1/2 shirts.

We'll apply division by Splitting into equal halves or groups, the division may be used to decide how to distribute a dish of cookies evenly among a group.

The unit rate of cloth he used in terms of yards per shirt is found by dividing the  3 1/2 shirts by 4 2/3 yards,

\(= 4 \dfrac{2}{3} / 3 \dfrac{1}{2} \\\\ = \dfrac{14}{3} / \dfrac{7}{2} \\\\ = \dfrac{14}{3} \times \dfrac{2}{7} \\\\ = \dfrac{4}{3}\)

Thus, if Rick used 4 2/3 yards of fabric to sew 3 1/2 shirts. The unit rate of cloth he used in terms of yards per shirt will be 4/3.

The question is incomplete

The complete question is"Rick used 4 2/3 yards of fabric to sew 3 1/2 shirts. What is the unit rate of cloth he used in terms of yards per shirt?"

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Therefore, the compound interest of the annuity due of BD 400 paid each 4 months for 6.2 years at a nominal rate of 3% per annum is BD 40,652.17.

Compound interest of an annuity due can be calculated using the formula:A = R * [(1 + i)ⁿ - 1] / i * (1 + i)

whereA = future value of the annuity dueR = regular paymenti = interest raten = number of payments First, we need to calculate the effective rate of interest per period since the nominal rate is given per annum. The effective rate of interest per period is calculated as

:(1 + i/n)^n - 1 = 3/1003/100 = (1 + i/4)^4 - 1

(1 + i/4)^4 = 1.0075i/4 = (1.0075)^(1/4) - 1i = 0.0303So,

the effective rate of interest per 4 months is 3.03%.Next, we can substitute the given values in the formula:

A = BD 400 * [(1 + 0.0303)^(6.2 * 3) - 1] / 0.0303 * (1 + 0.0303)A = BD 400 * [4.227 - 1] / 0.0303 * 1.0303A = BD 400 * 101.63A = BD 40,652.17

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The curve is concave upward for t values greater than zero, according to the assertion made.

Curve, An abstract phrase used to characterize the trajectory of a series of movements particle in mathematics (see continuity). Usually, an equation will create such a route. The term may also be used to describe a linear model or a collection of connected line segments. The IS curve displays combinations of borrowing costs and production levels where anticipated expenditure and income are equal. The many interest and income configurations along which is something the goods market is still in equilibrium are represented by the IS Curve.

dx/dt = e^t

dy/dt = -te^-t + e^-t

so dy/dt X dt/dx = dy/dx= -te^-t + e^-t /e^t = -t e^(-2t) + e^(-2t)

d2y/dx2 = -dt/dx e^(-2t) +2 t e^(-2t) dt/dx -2e^(-2t) dt/dx

= -e^(-3t) +2te^(-3t) -2e^(-3t)

-t e(-2t) + e(-2t) >0 for curved dy/dx >0

=> t<0 the curve is concave.

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