What is equivalent to (3-2x) (4x - 7)?
A. 26x
B. -8x-21
C. -8x²+26x – 21
D. 12x² - 2x +21

The form of the partial fraction decomposition of the given functions are: Partial fraction decomposition

x² + x + 12(ax + b) / (x² + x + 12)x⁴ + 1 / ((25 + 623³)) [Ax + B]/ (x² + 1) + [Cx + D] / (x² - 1)(x² – 9)² [A / (x - 9)] + [B / (x - 9)²] + [C / (x + 9)] + [D / (x + 9)²]

Given function is x² + x + 12, we are to write out the form of the partial fraction decomposition of the function and not to determine the numerical values of the coefficients.

Partial fraction decomposition of the given function x² + x + 12 is:  

x² + x + 12 = (ax + b) / (x² + x + 12)

Where a and b are constants.

We are also given another function which is:

(a) X⁴ +1 25 + 623 3

To write out the form of the partial fraction decomposition of the function, it is important to factorize the denominator of the function in order to determine the form of the partial fraction decomposition.

The factors of x⁴ + 1 can be obtained as: (x² + 1)(x² - 1) = (x² + 1)(x + 1)(x - 1)

Therefore, the partial fraction decomposition of x⁴ + 1 / ((25 + 623³) is given as:

(x⁴ + 1) / ((25 + 623³)) = [Ax + B]/ (x² + 1) + [Cx + D] / (x² - 1)(b) (x² – 9)²

To write out the form of the partial fraction decomposition of the function, we will consider the factors of the denominator.

The factors of (x² - 9)² can be obtained as:

(x - 9)² (x + 9)²

Therefore, the partial fraction decomposition of (x² – 9)² is given as:

(x² – 9)² = [A / (x - 9)] + [B / (x - 9)²] + [C / (x + 9)] + [D / (x + 9)²]

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The  answer is:

\((x² – 9)² = (A / x + 3) + (B / (x + 3)²) + (C / x – 3) + (D / (x – 3)²)\)

(a) x² + x + 12

Partial fraction decomposition is the process of expressing a fraction that contains a polynomial of the numerator and a polynomial of the denominator as the sum of two or more fractions with simpler denominators. By using partial fraction decomposition, it is possible to integrate many rational functions.To write out the form of the partial fraction decomposition of the function x² + x + 12, first, we need to factorize the denominator. In this case, we cannot factorize x² + x + 12 into linear factors with real coefficients. Therefore, the partial fraction decomposition does not exist, and the answer is DNE.(b) (x² – 9)²We can factorize the denominator of (x² – 9)² to obtain\((x² – 9)² = (x + 3)²(x – 3)²\)Now, we can express the function as(x² – 9)² = (A / x + 3) + (B / (x + 3)²) + (C / x – 3) + (D / (x – 3)²)By solving for the constants A, B, C, and D, we can obtain the numerical values of the coefficients.

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Answer:

12

Step-by-step explanation:

Create a ratio

AB : DE

5 : 4

BC : EF

15: x

5/4 = 15/x

5x = 15*4

5x = 60

x = 12

EF = 12

The probability that a student who has a brother also has a sister is 2/7 or approximately 0.2857.

To find the probability that a student who has a brother also has a sister, we need to use the concept of conditional probability.

Let's first find the probability of a student having both a brother and a sister. According to the problem, there are 2 students who have both a brother and a sister. Therefore, the probability of a student having both a brother and a sister is:

P(Brother and Sister) = 2/23

Now, let's find the probability of a student having a brother:

P(Brother) = 7/23

Using the formula for conditional probability, we can find the probability that a student who has a brother also has a sister:

P(Sister|Brother) = P(Brother and Sister) / P(Brother)

Substituting the values we found, we get:

P(Sister|Brother) = (2/23) / (7/23) = 2/7

This means that if we randomly select a student who has a brother, the probability that they also have a sister is about 0.2857.

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Answer:

45

Step-by-step explanation:

Because there are no outliers in the data set, the mean is the best indicator of the centre in this particular situation.

An outlier in statistics is an incident that deviates greatly from the predicted range of values for a given dataset. There are several different reasons why outliers can happen, including measurement errors, data entry issues, or genuinely odd numbers in the population getting measured. If they are not handled properly, outliers can significantly affect statistical analysis and skew results. For instance, outliers have a big impact on measurements of variability like the standard deviation as well as central tendency indicators like the mean. Consequently, before conducting statistical analysis on a dataset, it is crucial to find and assess any outliers.

given

There are no extreme outlier numbers in this instance, and the data seems to be rather symmetrical around the core value. As a result, the mean would be a suitable gauge of the centre.

The mean would be impacted by any values that were significantly out of the ordinary, such as a book that cost $100, and might not accurately reflect the data's mean if there were one or more of these values.

Since it is unaffected by extreme values, the median would be a better indicator of the centre in these situations.

Because there are no outliers in the data set, the mean is the best indicator of the centre in this particular situation.

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Answer: C: A=18

Step-by-step explanation: If your are adding 5 every time the x value goes up by one, then you would add 5 to13, henceforth getting 18.

The value of a that completes the table is 18

The rate of change of a function is expressed in term of the slope.

In order to determine the value of a, we will use the expression below;

Slope = a - 13/4-3 = 23-13/5-3
a-13 = 10/2

a - 13 = 5

Add 13 to both sides

a =5 + 13

a = 18

Hence the value of a that completes the table is 18

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Given function is Z(A, B, C) = A² B³ + 6BC + A and we need to find dzdc | (1,3,-2) where z is the partial derivative of the function Z with respect to the variable C and dzdc denotes the notation for the partial derivative of Z with respect to C.

Applying partial differentiation with respect to the variable C, we get;`∂Z/∂C = 6B,

Now, we need to find dzdc at point (1,3,-2);  Z(A, B, C) = A² B³ + 6BC + A``dZ/dC = ∂Z/∂C * dc/dx = 6B * (0) = 0

Therefore, dzdc | (1,3,-2) = 0. Hence, the solution is 0.

Given that Z(A, B, C) = A²B³ + 6BC + A.Z(A, B, C) = A²B³ + 6BC + AZ(A, B, C) = A²B³ + 6BC + A

To find dzdc | (1,3,-2), we need to differentiate the given function with respect to

c. dzdc = ∂Z/∂cdzdc = ∂/∂c (A²B³ + 6BC + A)

Let's differentiate each term of the function with respect to c. ∂/∂c(A²B³) = 0  (since there is no c in the term)

∂/∂c(6BC) = 6B (since the derivative of c is 1), ∂/∂c(A) = 0 (since there is no c in the term)

Therefore, dzdc = ∂Z/∂c = 6B Now, we need to evaluate dzdc at (1, 3, -2).

When A = 1, B = 3, and C = -2, we have dzdc | (1, 3, -2) = 6B = 6(3) = 18. Hence, the value of dzdc | (1, 3, -2) is 18.

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As the project progresses, the actual finish times (AFs) of completed activities play a crucial role in determining various aspects of the project schedule.

The AFs are used to calculate the earliest start and earliest finish times for the remaining activities in the network diagram. These calculations are based on the dependencies between activities and the actual durations of completed activities.

By considering the AFs, the project team can determine the earliest possible start and finish times for the remaining activities, taking into account the sequence of activities and any imposed constraints. This information helps in managing the project schedule and identifying any potential delays or critical paths.

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Answer:

m < 1 OR m > 7

Step-by-step explanation:

3m + 2 < 5

3m < 3

m < 1

(m + 1) / 2 > 4

m + 1 > 8

m > 7

C gets $1000, B gets $2000, and A gets $4000.

Let's solve the problem step by step:

Let's assume that C's share is represented by x dollars.

According to the given information:

B's share is twice that of C's share, so B's share is 2x dollars.

A's share is twice that of B's share, so A's share is 2 * 2x = 4x dollars.

The sum of their shares should equal $7000:

C's share + B's share + A's share = x + 2x + 4x = 7x

Now, we can set up an equation:

7x = 7000

To find the value of x, we can divide both sides of the equation by 7:

x = 7000 / 7

x = 1000

Now, we can find the individual shares:

C's share = x = $1000

B's share = 2x = $2000

A's share = 4x = $4000

Therefore, C gets $1000, B gets $2000, and A gets $4000.

Each person's share is as follows:

C: $1000

B: $2000

A: $4000

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The number of kilowatt-hours consumed in a week by the 850-Watt window air conditioner that is left on all day is approximately 14.28 kW-hrs.

To calculate the number of kilowatt-hours (kW-hrs) consumed by the air conditioner in a week, we need to consider the power rating of the air conditioner (850 Watts) and the duration it is left on each day.

Power of the air conditioner = 850 Watts

Duration of usage per day = 24 hours (left on all day)

Number of days in a week = 7 days

To calculate the energy consumption, we can use the formula:

Energy (kW-hrs) = Power (kW) * Time (hours)

First, let's convert the power from Watts to kilowatts by dividing it by 1000:

Power (kW) = 850 Watts / 1000 = 0.85 kW

Now we can calculate the energy consumption in a week:

Energy (kW-hrs) = Power (kW) * Time (hours)

Energy (kW-hrs) = 0.85 kW * 24 hours/day * 7 days

Energy (kW-hrs) = 14.28 kW-hrs

Therefore, the number of kilowatt-hours consumed in a week by the 850-Watt window air conditioner that is left on all day is approximately 14.28 kW-hrs.

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the answer will be 5,427 because we need to round the six and since 8 is greater that 5, we aproximate 6 to 7

Answer:

x=(2,-5.3)

Step-by-step explanation:

Hope this helps

It is not necessary to tabulate Φ(z) for z negative because the standard normal distribution is symmetric about the mean, which is 0. That is, Φ(z) = Φ(–z) for all z. Therefore, if we know Φ(z) for z ≥ 0, we can compute Φ(–z) by subtracting Φ(z) from 1.

If Appendix Table A.3 contained Φ(z) only for z ≥ 0, we could still compute probabilities of the form P(a ≤ Z ≤ b) for any real numbers a and b as follows:

a. P(–1.72 ≤ Z ≤ –0.55) = P(Z ≤ –0.55) – P(Z ≤ –1.72) = Φ(–0.55) – Φ(–1.72)

b. P(–1.72 ≤ Z ≤ 0.55) = Φ(0.55) – Φ(–1.72)

It is not necessary to tabulate Φ(z) for z negative because the standard normal distribution is symmetric about the mean, which is 0. That is, Φ(z) = Φ(–z) for all z. Therefore, if we know Φ(z) for z ≥ 0, we can compute Φ(–z) by subtracting Φ(z) from 1.

In part (a) above, we used the fact that P(a ≤ Z ≤ b) = P(Z ≤ b) – P(Z ≤ a), which follows from the cumulative distribution function of the standard normal distribution. We then computed Φ(–0.55) and Φ(–1.72) using the symmetry property of the standard normal distribution.

In part (b) above, we used the same property of the standard normal distribution to compute Φ(0.55) and Φ(–1.72) directly from the table.
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Step-by-step explanation:  To begin, negative exponents denote reciprocal. To remove the negative exponent, you "flip it" to 1/x. The first part (q 1 r 1 s 6) would be replaced by ((1/q) * (1/r) * (1/s 6)). Simplifying, we get (1 / (qrs 6)). In the same way as the second parth (r 3 sq 5): ((1/r3) * s * (1/q 5)).

Answer: 17/28

Step-by-step explanation:

Since there is a total profit of 6/7 million dollars and the spinning department gave a profit of 1/4 million, then the profit gotten from other departments will be the fraction of profit from the spinning department subtracted from the total profit. This will be:

= 6/7 - 1/4

= 24/28 - 7/28

= 17/28

The fraction of profit from other department is 17/28.

Circular Motion

When a body has a uniform circular motion, its distance to a fixed point is always the same and it travels at equal angles in equal amounts of time.

We are given the equation of a circle as:

Where x is the horizontal distance and y is the vertical distance. The parametric equations for this motion are:

x = r cos θ

y = r sin θ

Differentiating with respect to time:

x' = -r sin θ θ'

y' = r cos θ θ'

Where θ' is the angular speed. The linear speed is defined as:

Substituting:

The angular speed is the number of radians traveled per unit of time.

The moon travels 29.8 days of 22 hours each per revolution, that is,

29.8*22 = 655.6 hours per revolution. The angular speed is:

Finally, the linear speed is:

Answer:

x = -9

Step-by-step explanation:

Standard equation of direct variation:

y = kx

We need to find k.

We use the given point.

When x = 3, y = 9.

9 = k * 3

k = 3

Our equation is

y = 3x

Now we find x when y = -27.

y = 3x

-27 = 3x

x = -9

Answer:

3.52

Step-by-step explanation:

subtract the price of milk chocolate and caramels

Answer:

the answer is y = 4x - 19. hope this helps!

(a) False. The set {x∈R^n | Ax=b} is not necessarily convex. It depends on the matrix A and the vector b. For example, if A is a non-convex matrix, then the set of solutions {x∈R^n | Ax=b} will also be non-convex.

(b) True. The set {(x₁,x₂) | x₂ ≤ 3x₁²} is convex. The inequality defines a downward parabolic region, and any line segment connecting two points within this region will lie entirely within the region. (c) False. Not all polygons on the R² plane are convex. For example, a polygon with a concave portion, such as a crescent shape, would not be convex.

(d) True. If S⊆R² is convex, then it must enclose a region of finite area. Convex sets do not have "holes" or disjoint parts, so they form a connected and bounded region. (e) False. If S₁⊆R² and S₂⊆R², and S₁∩S₂=ϕ (empty set), then S₁∪S₂ can be convex. If S₁ and S₂ are both convex sets that do not overlap, their union can still be a convex set. (f) True. If S₁⊆R² and S₂⊆R² are both closed sets, then their union S₁∪S₂ must also be closed. However, it may or may not be convex. The convexity of the union depends on the specific sets S₁ and S₂.

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Answer:

10x + 10

Step-by-step explanation:

Thank me later

Answer:

No. It is not possible to construct a triangle with lengths of its sides 4cm, 5cm and 9cm because the sum of two sides is not greater than the third side:

5 + 4 is not greater than 9.

Step-by-step explanation:

May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I only need 10 more brainliest to become a genius! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!

\(\sqrt{m^4 n^7}\\ \\\\=\left( m^4 n^7 \right)^{\tfrac 12}~~~~~~~~~~~~~~~~~~;\left[\sqrt a = a^{\tfrac 12}\right]\\\\\\=\left(m^4 \right)^{\tfrac 12} \cdot \left(n^7 \right)^{\tfrac 12} \\\\\\=m^{\tfrac 42} \cdot n^{\tfrac 72}\\\\\\=m^2 n^{\tfrac 72}\)

Answer:

For example, the solution to the equations 2x + 3y = 15 and x - y = -10 is x = -3 ... Equation 2: 4x + 2y = 20

Answer:

x=0, y=0 this is so easy

To balance the line by choosing the assignable task with the longest task time first, you need to follow these steps. Determine the task times for each assignable task in the line.

Identify the assignable task with the longest task time. Assign that task to the first station in the line. Calculate the remaining cycle time by subtracting the task time of the assigned task from the total cycle time.
Repeat steps 2-4 for the remaining assignable tasks, considering the updated cycle time after each assignment.

Task A has the longest task time, so it is assigned to the first station. After each assignment, the cycle time is updated by subtracting the task time of the assigned task.  Task B is assigned to the second station, and Task C is assigned to the third station. Since Task C has a task time of 1.2 minutes, the remaining cycle time becomes 0. After that, Task D and Task E are not assigned any task time because the remaining cycle time is already 0. The specific values will depend on the actual task times and cycle time in your scenario.

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By following these steps, you will be able to balance the line by choosing the assignable task with the longest task time first. The final answer will be the completed table with all the relevant information.

To balance the line by choosing the assignable task with the longest task time first, we need to follow certain steps and fill in the table accordingly.

Step 1: Determine the cycle time.

Given that the cycle time is 2.3 minutes, we will use this value as a reference for balancing the line.

Step 2: List the tasks and their task times.

Create a table with columns for tasks and task times. List all the tasks that need to be performed on the line and their respective task times.

Step 3: Sort the tasks in descending order.

Sort the tasks in descending order based on their task times, with the longest task time at the top and the shortest at the bottom.

Step 4: Calculate the number of operators required for each task.

Starting from the top of the table, divide the task time by the cycle time. Round up the result to the nearest whole number to determine the number of operators needed for each task.

Step 5: Calculate the balance delay.

For each task, calculate the difference between the number of operators required and the number of operators available. This represents the balance delay for each task.

Step 6: Fill in the table.

Fill in the table with the tasks, task times, number of operators required, and balance delay for each task.

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Answer:

The zeros are x = -2, x = 0, x = 4.

Step-by-step explanation:

The zeros describe where the function crosses the x-axis, or where the y-value is zero. In this case, the zeros are x = -2, x = 0, x = 4.

Step-by-step explanation:

First you subtract five on both sides. Now we're left with C=6