Factor of this expression 3X + 21 IS

Answers

Answer 1

Answer: The answer is: 3 (x + 7)

Explanation:

3 can go into 3x one time.
3 can go into 21 seven times.

Therefore when factorized it is written as:

3 (x + 7)

Answer 2

Answer:

Answer:

3 (x + 7)

Step-by-step explanation:

3 can go into 3x one time.

3 can go into 21 seven times.

Therefore when factorized it is written as:

3 (x + 7)

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Answers

Based on the given information, we can determine the characteristics of the polygon MNOP.

1. MN || OP and NO || PM:

- This means that the opposite sides MN and OP are parallel, and the opposite sides NO and PM are also parallel.

2. m/M = 93°, m/N = 87°, m/O = 93°, m/P = 87°:

- These angle measurements indicate that the opposite angles M and O are congruent, as well as the opposite angles N and P.

Based on these characteristics, we can conclude that the polygon MNOP is a parallelogram. A parallelogram is a quadrilateral with opposite sides that are parallel. In addition, opposite angles of a parallelogram are congruent.

However, we cannot determine from the given information whether the polygon MNOP is specifically a rectangle, rhombus, square, or trapezoid. These classifications require additional information, such as side lengths or angle measures, to be determined.

Therefore, the correct answers are:

- Parallelogram

- Quadrilateral

Please note that rectangle, rhombus, square, and trapezoid cannot be confirmed based on the given information.

EBookPrint ItemQuestion Content Area
FIFO Method, Valuation of Goods Transferred Out and Ending Work in Process

K-Briggs Company uses the FIFO method to account for the costs of production. For Crushing, the first processing department, the following equivalent units schedule has been prepared:

Direct Materials Conversion Costs
Units started and completed 28,000 28,000
Units, beginning work in process:
10,000 × 0% — —
10,000 × 40% — 4,000
Units, ending work in process:
6,000 × 100% 6,000 —
6,000 × 75% — 4,500
Equivalent units of output 34,000 36,500
The cost per equivalent unit for the period was as follows:

Direct materials $2.00
Conversion costs 6.00
Total $8.00
The cost of beginning work in process was direct materials, $40,000; conversion costs, $30,000.

Answers

Therefore , the solution of the given problem of unitary comes out to be price of terminating the work-in-progress inventory is $12,000 + $27,000 = $39,000.

An unitary method is what?

Applying what was learned, using this variable approach, and combining all relevant data from two individuals who used a particular tactic will enable completion of the task. The entity indicated in the formula will either also be recognized, or both crucial processes integers will honestly disregard the colour, if the preferred assertion outcome materialises. A refundable fee of Rupees ($1.21) may be necessary for fifty pencils.

Here,

The cost of goods transferred out of Crushing would be determined using the FIFO method in the manner shown below:

Units started and completed plus equivalent units in the ending work-in-process inventory equal equivalent units of output completed.

=> Completed equivalent units = 28,000 + 6,000 100%

34,000 completed units of output are equivalent.

Cost of goods shipped out equals Cost per equivalent unit minus the number of completed equivalent units of output.

=> ($2.00 + $6.00) * 34,000 equals the cost of the goods transferred out.

Transfer of Goods Cost:

=> $8.00 x 34,000

$272,000 is the cost of transferring the products.

We must multiply the equivalent units in the ending work in process inventory by the cost per equivalent unit in order to determine

the expense of ending work in process inventory:

=>Direct materials: 6,000 units x 100% of 6,000

Direct material costs for ending work-in-progress inventory are $2.00 multiplied by 6,000 to equal $12,000

=> Costs of conversion: 6,000 x 75% = 4,500 units.

Cost of conversion costs in ending work in progress inventory = $6.00 divided by 4,500 equals $27,000.

The price of terminating the work-in-progress inventory is therefore $12,000 + $27,000 = $39,000.

To know more about unitary method visit:

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One seventh of an unknown value

Answers

one seventh of x = (1/7)x
where x is the unknown value

A reservation service employs six information operators who receive requests for information independently of one another, each according to a Poisson process with rate ???? = 2 per minute. a. What is the probability that during a given 1 min period, the first operator receives no requests? (Round your answer to three decimal places.) b. What is the probability that during a given 1 min period, exactly three of the six operators receive no requests? (Round your answer to five decimal places.)

Answers

Answer:

a) 0.135 = 13.5% probability that during a given 1 min period, the first operator receives no requests.

b) 0.03185 = 3.185% probability that during a given 1 min period, exactly three of the six operators receive no requests

Step-by-step explanation:

To solve this question, we need to understand the Poisson distribution and the binomial distribution.

Poisson distribution:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

$P(X = x) = (e^(-\mu)*\mu^(x))/((x)!)$

In which

x is the number of sucesses

e = 2.71828 is the Euler number

$\mu$ is the mean in the given time interval.

Binomial distribution:

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_(n,x).p^(x).(1-p)^(n-x)$

In which $C_(n,x)$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_(n,x) = (n!)/(x!(n-x)!)$

And p is the probability of X happening.

Poisson process with rate 2 per minute

This means that $\mu = 2$

a. What is the probability that during a given 1 min period, the first operator receives no requests?

Single operator, so we use the Poisson distribution.

This is P(X = 0).

$P(X = x) = (e^(-\mu)*\mu^(x))/((x)!)$

$P(X = 0) = (e^(-2)*2^(0))/((0)!) = 0.135$

0.135 = 13.5% probability that during a given 1 min period, the first operator receives no requests.

b. What is the probability that during a given 1 min period, exactly three of the six operators receive no requests?

6 operators, so we use the binomial distribution with $n = 6$

Each operator has a 13.5% probability of receiving no requests during a minute, so $p = 0.135$

This is P(X = 3).

$P(X = x) = C_(n,x).p^(x).(1-p)^(n-x)$

$P(X = 3) = C_(6,3).(0.135)^(3).(0.865)^(3) = 0.03185$

0.03185 = 3.185% probability that during a given 1 min period, exactly three of the six operators receive no requests

the width of a rectangle is fixed at 8ft. what lengths will make the perimeter at least 200 ft at most 200

Answers

it will be 2(1+8)<=200

Evaluate the given integral by making an appropriate change of variables, where R is the region in the first quadrant bounded by the ellipse 64x2 + 81y2 = 1. $ L=\iint_{R} {\color{red}9} \sin ({\color{red}384} x^{2} + {\color{red}486} y^{2})\,dA $.

Answers

$\displaystyle\iint_R\sin(384x^2+486y^2)\,\mathrm dA$

Notice that Given that $R$ is an ellipse, consider a conversion to polar coordinates:

$\begin{cases}x(r,\theta)=\frac r8\cos\theta\ny(r,\theta)=\frac r9\sin\theta\end{cases}$

The Jacobian for this transformation is

$J=\begin{bmatrix}\frac18\cos\theta&-\frac r8\sin\theta\n\frac19\sin\theta&\frac r9\cos t\end{bmatrix}$

with determinant $\det J=\frac r{72}$

Then the integral in polar coordinates is

$\displaystyle\frac1{72}\int_0^(\pi/2)\int_0^1\sin(6r^2\cos^2t+6r^2\sin^2t)r\,\mathrm dr\,\mathrm d\theta=\int_0^(\pi/2)\int_0^1r\sin(6r^2)\,\mathrm dr\,\mathrm d\theta=\boxed{(\pi\sin^23)/(864)}$

where you can evaluate the remaining integral by substituting $s=6r^2$ and $\mathrm ds=12r\,\mathrm dr$ .

Final answer:

To evaluate the integral, we make a change of variables using the transformation x=u/8 and y=v/9 to transform the region into a unit circle. Then we convert the integral to polar coordinates and evaluate it.

Explanation:

To evaluate the given integral, we can make the appropriate change of variables by using the transformation x = u/8 and y = v/9. This will transform the region R into a unit circle. The determinant of the Jacobian of the transformation is 1/72, which we will use to change the differential area element from dA to du dv. Substituting the new variables and limits of integration, the integral becomes:

L = \iint_{R} 9 \sin (612 u^{2} + 768 v^{2}) \cdot (1/72) \,du \,dv

Next, we can convert the integral from Cartesian coordinates(u, v) to polar coordinates (r, \theta). The integral can be rewritten as:

L = \int_{0}^{2\pi} \int_{0}^{1} 9 \sin (612 r^{2} \cos^{2}(\theta) + 768 r^{2} \sin^{2}(\theta)) \cdot (1/72) \cdot r \,dr \,d\theta

We can then evaluate this integral to find the value of L.