Solve the following quadratic equation. *
x^2+12x-45=0

The Economic Order Quantity (EOQ) formula is used to compute the optimal quantity of an inventory to order at any given time. It is calculated by minimizing the cost of ordering and carrying inventory, and it is an important element of supply chain management.

According to the problem given, the following information is given:Demand = 100 bags / weekOrder cost = $55 / orderAnnual holding cost = 25% of costDesired cycle-service level = 92%Lead time = 4 week(s) (20 working days)Standard deviation of weekly demand = 13 bagsCurrent on-hand inventory is 350 bags, with no open orders or backorders.a. To calculate the Economic Order Quantity (EOQ), we need to use the formula:EOQ = √[(2DS)/H],whereD = Demand per periodS = Cost per orderH = Holding cost per unit per period. Substitute the given values,D = 100 bags/weekS = $55/orderH = 25% of cost = 0.25Total cost of inventory = S*D + Q/2*H*DIgnoring Q, the above expression is the annual ordering cost. Since we know the annual cost, we can divide the cost by the number of orders per year to obtain the average cost per order.Substituting the given values in the above formula,

EOQ = √[(2DS)/H] = √[(2*100*55)/0.25] = 420 bags

Sam's optimal order quantity is 420 bags. Hence, the answer to this part is 420.b. To calculate the reorder point (R), we use the formula:R = dL + SS,whereL = Lead timed = Demand per dayS = Standard deviation of demandSubstituting the given values,d = 100 bags/weekL = 4 weeksS = 13 bags/week

R = dL + SS = (100*4) + (1.75*13) = 425 bags

Therefore, the reorder point is 425 bags.c. If the inventory withdrawal of 10 bags has been made, we can calculate the new on-hand inventory using the formula:On-hand inventory = Previous on-hand inventory + Received inventory – Issued inventoryIf there are no open orders,Received inventory = 0Hence,On-hand inventory = 350 + 0 – 10 = 340Since the current on-hand inventory is more than the reorder point, it is not time to reorder. Therefore, the answer to this part is "It is not time to reorder."d. Annual holding cost of the current policy is the product of the holding cost per unit per period and the number of units being held.Annual holding cost =

(350/2) * 0.25 * 55 = $481.25

The annual holding cost is $481.25.Annual ordering cost = Total ordering cost / Number of orders per yearIf we assume 52 weeks in a year,Number of orders per year = 52/4 = 13Total ordering cost = 13 * $55 = $715Annual ordering cost = $715/13 = $55Therefore, the annual ordering cost is $55.

The Economic Order Quantity (EOQ) formula is used to compute the optimal quantity of an inventory to order at any given time. Sam's optimal order quantity is 420 bags. The reorder point is 425 bags. If there is an inventory withdrawal of 10 bags, then it is not time to reorder. The annual holding cost is $481.25. The annual ordering cost is $55. The average time between orders is 4.46 weeks.

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he indefinite integral of (x - 1)/(x² + 2x)² dx is (1/8) ln|x + 2| - (1/8) ln|x| - 1/(4(x + 1)²) + C, where C is the constant of integration.

To evaluate the indefinite integral ∫(x - 1)/(x² + 2x² + 2x)² dx, we can proceed with a substitution. Let u = x² + 2x. Then, du = (2x + 2) dx.

Now, let's rewrite the integral in terms of u:

∫(x - 1)/(x² + 2x² + 2x)² dx = ∫(x - 1)/(u²)² * (1/(2x + 2)) du

= ∫(x - 1)/(4u²) * (1/(2x + 2)) du

= ∫(x - 1)/(8u²) * (1/(x + 1)) du

We can simplify the expression further

∫(x - 1)/(8u²) * (1/(x + 1)) du = ∫(x - 1)/(8(x² + 2x)²) du

Now, we can split the integrand into partial fractions

(x - 1)/(8(x² + 2x)²) = A/(x² + 2x) + B/(x² + 2x)²

To find the values of A and B, let's find the common denominator:

A(x² + 2x)² + B(x² + 2x) = x - 1

Expanding and combining like terms:

(A + B) x³ + (4A + 2B) x² + (4A) x + (4A) = x - 1

Matching coefficients, we have the following equations

A + B = 0 (coefficient of x³ terms)

4A + 2B = 0 (coefficient of x² terms)

4A = 1 (coefficient of x terms)

4A = -1 (constant terms)

From the first equation, B = -A.

Substituting this into the second equation: 4A + 2(-A) = 0, we get A = 0.

From the fourth equation: 4A = -1, we find A = -1/4.

Therefore, A = -1/4 and B = 1/4.

Now, we can rewrite the integral with the partial fractions:

∫(x - 1)/(8(x² + 2x)²) du = ∫(-1/4)/(x² + 2x) dx + ∫(1/4)/(x² + 2x)² dx

Let's evaluate each integral separately

∫(-1/4)/(x² + 2x) dx = (-1/4) ∫1/(x(x + 2)) dx

We can apply the method of partial fractions again for this integral. Let's find the values of C and D such that:

1/(x(x + 2)) = C/x + D/(x + 2)

Multiplying both sides by x(x + 2), we get:

1 = C(x + 2) + Dx

Expanding and combining like terms:

1 = (C + D) x + 2C

Matching coefficients, we have:

C + D = 0 (coefficient of x terms)

2C = 1 (constant terms)

From the first equation, D = -C.

Substituting this into the second equation: C - C = 0, we get C = 1/2.

Therefore, C = 1/2 and D = -1/2.

Now, let's rewrite the integral:

∫(-1/4)/(x² + 2x) dx = (-1/4) ∫(1/2x - 1/2(x + 2)) dx

= (-1/8) ln|x| - (-1/8) ln|x + 2| + K1

= (1/8) ln|x + 2| - (1/8) ln|x| + K1

Next, let's evaluate the second integral

∫(1/4)/(x² + 2x)² dx = (1/4) ∫1/(x² + 2x)² dx

We can apply a u-substitution here. Let u = x² + 2x + 1. Then, du = (2x + 2) dx.

Rewriting the integral in terms of u:

(1/4) ∫1/(x² + 2x)² dx = (1/4) ∫1/u² du

= (1/4) (-1/u) + K₂

= -1/(4u) + K₂

Substituting back u = x₂ + 2x + 1:

-1/(4u) + K₂ = -1/(4(x² + 2x + 1)) + K₂

= -1/(4(x + 1)²) + K2

Finally, we can combine the results of both integrals

∫(x - 1)/(8(x² + 2x)²) dx = (1/8) ln|x + 2| - (1/8) ln|x| - 1/(4(x + 1)²) + C

So, the indefinite integral of the given expression is (1/8) ln|x + 2| - (1/8) ln|x| - 1/(4(x + 1)²) + C, where C is the constant of integration.

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--The given question is incomplete, the complete question is given below " Evaluate the indefinite integral. (Use C for the constant of

integration.) ∫(x - 1)/(x² + 2x² + 2x)²dx "--

Answer:

m∠EON = 48°

m∠ONP = 48°

m∠PSE = 90°

Answer:

y = 3x + -8

Step-by-step explanation:

The exact value of the expression is (x-1)/√(1² - (x-1)²).

What is Pythagoras Theorem?

Pythagoras' theorem is a fundamental principle in geometry that states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

In a reference triangle for sin⁻¹(x-1), the opposite side is x-1, the hypotenuse is 1, and the adjacent side can be found using the Pythagorean theorem:

a² + b² = c²

b² = c² - a²

b = √(c² - a²)

In this case, a = x - 1 and c = 1, so:

b = √(1² - (x-1)²)

Now, we can use the tangent function:

tan(sin⁻¹(x-1)) = tan(θ) = opposite/adjacent = (x-1)/√(1² - (x-1)²)

Therefore, the exact value of the expression is:

(x-1)/√(1² - (x-1)²).

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No, the F-test statistic cannot be less than 1 when it represents the larger of two sample variances.

The F-distribution is always a positive distribution with a range of values greater than zero. The F-test value is always greater than or equal to 0, but it is not always less than or equal to 1.

The numerator, representing the bigger sample variance, is always greater than or equal to the denominator, representing the smaller sample variance. Consequently, the F-ratio, which is the ratio of the larger to the smaller variance, is always greater than or equal to 1. Thus, an F-test statistic that is less than 1 is mathematically incorrect.

Therefore, an F-test statistic is always a positive number that is greater than or equal to zero and greater than or equal to 1. This is because the numerator of an F-distribution is always greater than or equal to the denominator.

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Answer:
21 tables

Step-by-step explanation:

First, let’s simplify the ratio by dividing both sides by 11.

Once we’ve done that, we're left with a ratio of 3 tables for every 7 chairs.

Because 49 is divisible by 7, we will divide seven and get a quotient of 7.

All that’s left is to multiply 7 by 3, and get our final answer of 21 tables sold.

To find the numerical value of the algebraic expression B²(c+d)-a²(m+n)+2x, we need to substitute the given values of the variables into the expression and then simplify.

Here is the step-by-step explanation:

1. Substitute the given values of the variables into the expression:
(2)²(3+4)-(1)²(1/2+2/3)+2(0)

2. Simplify the expression by following the order of operations:
(4)(7)-(1)(7/6)+0

3. Simplify further:
28-7/6

4. Find a common denominator and combine the terms:
168/6-7/6

5. Simplify the expression to get the final numerical value:
161/6

Therefore, the numerical value of the algebraic expression B²(c+d)-a²(m+n)+2x is 161/6.

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The numerical value of the algebraic expression B²(c+d)-a²(m+n)+2x is 161/6.

To find the numerical value of the algebraic expression B²(c+d)-a²(m+n)+2x, we need to substitute the given values of the variables into the expression and then simplify.

Here are the steps to do this:

1. Substitute the given values of the variables into the expression:
(2)²(3+4)-(1)²(1/2+2/3)+2(0)

2. Simplify the expression inside the parentheses:
(2)²(7)-(1)²(7/6)+0

3. Simplify the exponents:
4(7)-1(7/6)+0

4. Multiply the numbers:
28-7/6+0

5. Simplify the expression by finding a common denominator and combining the terms:
28-7/6 = 168/6-7/6 = 161/6

So the numerical value of the algebraic expression B²(c+d)-a²(m+n)+2x is 161/6.

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(a) The chance that the sum of the draws will be more than 1,500

(b) The chance that there will be fewer than 90 occurrences of the number 3.

(a) To estimate the chance that the sum of the draws will be more than 1,500, we need to consider the possible combinations and their probabilities. Since there are four numbers in the box, each with an equal chance of being drawn, we can calculate the mean and standard deviation of the draws. With this information, we can use statistical methods such as the normal distribution to estimate the probability of the sum exceeding 1,500.

(b) To estimate the chance that there will be fewer than 90 occurrences of the number 3, we need to calculate the probability of drawing a 3 in each individual draw and then consider the distribution of the number of 3's over the 400 draws. Using statistical techniques such as the binomial distribution, we can estimate the probability of having fewer than 90 occurrences of 3 in the 400 draws.

Both estimations involve applying statistical methods to analyze the probabilities of specific events occurring in the random drawing process. The precise calculations and estimations would require detailed information about the probabilities of drawing each number and the distribution of these numbers in the box.

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The basic function equivalent to the piecewise-defined function f(x) = x if x ≥ 0 and -x if x < 0 is f(x) = |x|, which represents the absolute value of x.

The given piecewise-defined function f(x) has different expressions for different intervals. For x greater than or equal to zero, f(x) takes the value of x. For x less than zero, f(x) is equal to -x. We need to find a basic function that captures this behavior.

Among the options provided, f(x) = |x| is equivalent to the given piecewise function. The absolute value function, denoted by |x|, returns the positive value of x regardless of its sign. When x is non-negative, |x| equals x, and when x is negative, |x| is equal to -x, mirroring the conditions of the piecewise-defined function.

The function f(x) = |x| represents the absolute value of x and matches the behavior of the given piecewise-defined function, making it the equivalent basic function.

In summary, the basic function equivalent to the piecewise-defined function f(x) = x if x ≥ 0 and -x if x < 0 is f(x) = |x|, which represents the absolute value of x.

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The pairing is not a function, as the input 2 is mapped to two different outputs.

A relation represents a function if each value of the input is mapped to only one value of the output, that is, one input cannot be mapped to multiple outputs.

From the table, the mappings are given as follows:

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Answer:

D

Step-by-step explanation:

add them together

Answer:

Step-by-step explanation:

Answer: 70ᴼ

Step-by-step explanation:

The triangles are vertical so their angle measures are congruent.

The angles of a triangle add to equal 180ᴼ.

55 + 55 = 110

180 - 110 = 70

6900 hours, make a list of multiples until lcm is found

Answer:

50 degs

140 degs

145 degs

Step-by-step explanation:

Complementary angles are two degree angles that add up to 90 degrees.

You can take what's given of 40 degs and do 90 - 40 to get the missing angle.

Supplementary angles add to 180 degs so 180 - 40 = 14.

l

l

--> They also are straight lines pretty much since a linear/straight line is 180 degrees.

So 180 - 35 = 145

Answer:

y=-1/2x+7

Step-by-step explanation:

the y intercept is where the line crosses on the y intercept and thats 7. the slope is how much each dot rises and runs to the next which for this problem its -1/2

Among the 769 team members, 706 of them are assigned to operates in 2 shifts schedule. The proportion of team members not assigned to one of the stations is 63 / 769

Proportion means a share from total set being discussed.

Data from the given case:

- The assembly has 769 team members.

- The assembly has 353 stations

- At each station, there are 2 shifts operations.

Assuming that 1 person is assigned to 1 shift operation, then there will:

353 x 2 = 706 person assigned.

The remaining team members that not assigned is:

769 - 706 = 63 person.

Therefore, the share or the proportion of unassigned team members is:

63/769

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Answer:

No

Step-by-step explanation:

the line has to be straight for it to be a proportional relationship..

Answer: No.

Step-by-step explanation: It has to start from the Origin  (which is the two arrows crossing on the bottom left corner, 0,0) and it needs to be in a straight line in order to be proportinal.

Proof of The median from the vertex angle of an isosceles triangle divides the triangle into two congruent triangles is stated below.

Triangles are said to be congruent if, under a correspondence, two of a triangle's sides and the angle that connects them are equal to two of another triangle's sides and the angle that connects them.

The base angles theorem converse states if two angles in a triangle are congruent, then the sides opposite those angles are also congruent.

The Isosceles Triangle Theorem states that the perpendicular bisector of the base of an isosceles triangle is also the angle bisector of the vertex angle.

Thus, The median from the vertex angle of an isosceles triangle divides the triangle into two congruent triangles.

For the second one:

Triangle RAS is isosceles, AM is a median.

Definition of an isosceles triangle.

2. AR = AS

Reflexive

3. AM = AM

Definition of median

4. MR = MS

From the sss theorem of congruency, we can state that RAM is congruent to the SAM.

5. Triangle RAM congruent to Triangle SAM.

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Answer: Parallel

Step-by-step explanation:

if two secanys of a circle are made them they cut off congruent arcs

Answer:

sinT = \(\frac{15}{17}\)

Step-by-step explanation:

We require to calculate RT before obtaining sinT

Using Pythagoras' identity in the right triangle

RT² = 30² + 16² = 900 + 256 = 1156 ( take the square root of both sides )

RT  = \(\sqrt{1156}\) = 34 , then

sinT = \(\frac{opposite}{hypotenuse}\) = \(\frac{RS}{RT}\) = \(\frac{30}{34}\) = \(\frac{15}{17}\)

The main answer for the first argument is that we cannot prove that the band could play rock music based on the given premises and rules of inference.

1. Let's assign the following propositions:

  - P: The band could play rock music.

  - Q: The refreshments were delivered on time.

  - R: The New Year's party was canceled.

  - S: Alicia was angry.

  - T: Refunds were made.

2. The given premises can be expressed as:

  (¬P ∨ ¬Q) → (R ∧ S)

  R → T

3. To prove that the band could play rock music (P), we need to derive it using valid rules of inference.

4. Using the premises, we can apply the rule of modus tollens to the second premise:

  R → T        (Premise)

  Therefore, ¬R.

5. Next, we can use disjunctive syllogism on the first premise:

  (¬P ∨ ¬Q) → (R ∧ S)     (Premise)

  ¬R                    (From step 4)

  Therefore, ¬(¬P ∨ ¬Q).

6. Applying De Morgan's law to step 5, we get:

  ¬(¬P ∨ ¬Q)  ≡  (P ∧ Q)

7. Therefore, we can conclude that the band could play rock music (P) based on the premises and rules of inference.

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The cost of 3 pens will be 27P and the cost of 2 rulers will be 30p.

The mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also be used to denote the logical syntax's operation order and other properties.

Given that the cost of 5 pens and 3 rulers is 90p the cost of 2 pens and 1 ruler is 33p. the cost of 3 pens and 2 rulers will be calculated as below:-

From the equations and solve:-

5p + 3r = 90p

2p + r = 33p

5p + 3r = 90p

-6p - 3r = -99p

Cost of one pen P = 9

The cost of the 1 ruler:-

2p + r = 33p

2 x 9 + r = 33

18 + r = 33

r = 33 - 18

r = 15

Cost of 3 pens = 3 x 9 = 27

Cost of 2 rulers = 2 x 15 = 30

Therefore, the cost of 3 pens will be 27P and the cost of 2 rulers will be 30p.

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Answer:

it vertical so it an undefinded slope.

Step-by-step explanation:

hope that helps

Answer:

\(slop = \frac{y2 - y1}{x2 - x1} = \frac{y2 - y1}{0} = indefinded \: \: \: or \: \: \infty \)

The expressions that gives x in terms of y from the given expression 7 y = 2 x − 5 is x = (7y +5)/2.

The concept that will be used in this question is solving of linear equation, because the equation is linear, then we perform the simplification.

The given expression is  is 7 y = 2 x − 5

Then from the expression we can make 2x the subject of the formula by rearranging it as 2x = 7y +5

Then this can be further expressed by dividing the both sides by the factor of 2, which can be expressed as ;

x = (7y +5)/2

Therefore, option A is correct because it is the expression that gives the x in terms of y.

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Check the missing options:

A. x = (7y +5)/2

B. y = (7x +5)/2

C. x=(7y +5)/3

Answer:

Explanation:

A number is said to be in standard form when it is written as a product of a number between 1 and 10 and a power of 10.

The given length is:

This number is already in standard form.

los lados faltantes del triángulo rectángulo son de 5.1 y 11.83.

Para resolver este problema, necesitamos recordar las propiedades de un triángulo rectángulo. Primero, sabemos que uno de los ángulos es de 90 grados. Además, el lado opuesto al ángulo recto se llama hipotenusa y los otros dos lados se llaman catetos.

En este caso, sabemos que uno de los ángulos es de 25 grados, por lo que el otro ángulo es de 90 - 25 = 65 grados. Ahora podemos usar la ley de senos para encontrar la longitud del otro cateto.

La ley de senos establece que la longitud de un lado dividida por el seno del ángulo opuesto es igual a la longitud de otro lado dividido por el seno del ángulo opuesto. Entonces, podemos escribir:

12 / sen(90) = x / sen(25)
x = 12 * sen(25) / sen(90) = 5.1

Por lo tanto, el lado faltante tiene una longitud de 5.1. Para encontrar la longitud del otro cateto, podemos usar el teorema de Pitágoras, que establece que la suma de los cuadrados de los catetos es igual al cuadrado de la hipotenusa. Entonces, podemos escribir:

a^2 + b^2 = 12^2 - 5.1^2 = 130.19
a^2 + b^2 = 130.19
b = sqrt(130.19 - a^2)

Donde "a" es la longitud del cateto que conocemos y "b" es la longitud del cateto que queremos encontrar. Podemos usar la ecuación anterior para encontrar la longitud de "b" para diferentes valores de "a". Por ejemplo, si "a" fuera de 4, tendríamos:

b = sqrt(130.19 - 4^2) = 11.83

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Answer:

ex:Speed (S) is the ratio of the distance (D) covered to the time (t) taken.

That is, S = D/t

Suppose Andrew ran a distance D1 in 1 hour (3600 seconds) at a Speed, say S1, we have

S1 = D1/t

We can then say he ran a distance

D1 = t × S1

= 3600S1

Similarly, let's say Karleigh ran a distance

D2 = t × S2

= 3600S2

Let us compare these two, you will notice that the bigger number between S1 and S2 is going to determine the bigger number between D1 and D2.

Let's choose random numbers for S1 and S2 for clarity, say S1 = 5, S2 = 10

D1 = 3600 × 5

= 18000

D2 = 3600 × 10

= 36000

This makes D2 bigger than D1. this is an example i found on the internet.

Step-by-

hope this helps, good luck

The ratio of the change in distance to the corresponding change in time

gives the speed of a runner.

Reasons:

The tables are;

Andrew

\(\begin{tabular}{|cc|c|}Time in Minutes&&Distance in miles\\18&&1.5\\24&&2\end{array}\right]\)

Karleigh

\(\begin{tabular}{|cc|c|}Time in Minutes&&Distance in miles\\30&&3\\40&&4\end{array}\right]\)

The duration each on the treadmills is 1 hour = 60 minutes

\(\displaystyle Speed = \mathbf{\frac{Change \ in \ distance}{Change \ in \ time}}\)

Therefore;

\(\displaystyle Andrew's \ speed = \frac{2 \, miles - 1.5 \, miles}{24 \, minutes - 18\, minutes} = \mathbf{\frac{1}{12} \ mile/minute}\)

\(\displaystyle The \ distance \ Andrew \ ran = \frac{1}{12} \ miles/min \times 60 \ min = \mathbf{5 \ miles}\)

\(\displaystyle Karleigh's \ speed = \frac{4 \, miles - 3 \, miles}{40 \, minutes - 30 \, minutes} = \mathbf{\frac{1}{10} \, mile/minute}\)

\(\displaystyle The \ distance \ Karleigh \ ran = \frac{1}{10} \, miles/min \times 60 \ min = \mathbf{6 \ miles}\)

Therefore;

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