Two wives and their husbands have tickets for a play. they have the first four seats on the left side of the center aisle. they will be arriving seperately from their jobs. so they agreee to take their seats from the inside to the aisle in whatever order they arrive. there is a propability of 2/3 that they will all have arrived by curtain time.

The Economic Order Quantity (EOQ) is calculated to be 547.72 units. The number of orders placed per year is 5.84, and the reorder point (ROP) is 32.01.

The total holding cost of lawnmowers is R1369.30, and the total ordering cost of lawnmowers is R876.00. These calculations provide valuable insights for efficient inventory management.

The Economic Order Quantity (EOQ) can be calculated by using the formula: EOQ = √2DS / H,

where D = Total Demand = 3200 units,

S = Ordering cost per order = R150,

and H = Annual holding cost per unit = R5.

Therefore, EOQ = √ (2 x 3200 x 150) / 5 = 547.72 units.

4.2 Number of orders placed per year: No of orders per year = D / Q,

where D = Total Demand = 3200 units and Q = EOQ = 547.72 units.

Therefore, No of orders per year = D / Q = 3200 / 547.72 = 5.84 orders.

4.4 Total holding cost of lawnmowers:

Total holding cost of lawnmowers = (Average inventory level) x (Annual holding cost per unit),

where (Average inventory level) = EOQ / 2 = 547.72 / 2 = 273.86 units and Annual holding cost per unit = R5.

Thus, the Total holding cost of lawnmowers = 273.86 x R5 = R1369.30.

4.1 Reorder Point (ROP): ROP can be calculated by using the formula:

ROP = dL, where d = Daily demand = D / Number of working days

= 3200 / 300 = 10.67 and L = Lead time = 3 days.

Hence, ROP = dL = 10.67 x 3 = 32.01.

4.5 Total ordering cost of lawnmowers:

Total ordering cost of lawnmowers = (Number of orders placed per year) x (Ordering cost per order),

where (Number of orders placed per year) = 5.84 orders and Ordering cost per order = R150.

Therefore, the Total ordering cost of lawnmowers = 5.84 x R150 = R876.00.

The Economic Order Quantity (EOQ) is calculated to be 547.72 units.

The number of orders placed per year is 5.84, and the reorder point (ROP) is 32.01.

The total holding cost of lawnmowers is R1369.30, and the total ordering cost of lawnmowers is R876.00.

These calculations provide valuable insights for efficient inventory management.

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The actual numerical differences or intervals between the categories may not be equal or well-defined. Therefore, the measurement level is ordinal.

The level of measurement for the given age categories (0-16, 17-19, 20-24, 25-29, 30-34, 35-39, 40+) is ordinal.

In an ordinal scale of measurement, the values assigned to variables have a meaningful order or ranking. In this case, the age categories are arranged in a specific order, from the youngest (0-16) to the oldest (40+). This order represents a meaningful progression of age groups. However, the actual numerical differences or intervals between the categories may not be equal or well-defined. Therefore, the measurement level is ordinal.

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Answer:

A. 55h + 275 = 440; h=3

Step-by-step explanation:

Since all answer choices have a different H= , finding how many hours you have left to drive will give you the right answer.

You've already driven 275 miles in your 440 mile trio so you can subtract the 275 to find out how much you will still need to drive.

440 - 275 = 165

You already know that you are driving at 55 mph so divide 165 by 55 and the answer is three.

Option A was the only answer choice which listed h=3 so that is the correct answer.

Options b, d, and e are the true statements about the substitution method.

b. It is useful to solve the integral ∫2x sin x^2 dx.

d. It utilizes the formula ∫ f(u(x))u'(x) dx = ∫ f(u) du.

e. It is based on the chain rule for derivatives.

The true statements about the substitution method are:

b. It is useful to solve the integral ∫2x sin x^2 dx.

The substitution method is commonly used to simplify integrals and make them easier to evaluate. It can be applied to various types of integrals, including the given example.

d. It utilizes the formula ∫ f(u(x))u'(x) dx = ∫ f(u) du.

The substitution method involves making a substitution in the integral by introducing a new variable. This formula represents the fundamental principle of substitution, where the derivative of the substituted function appears in the integral.

e. It is based on the chain rule for derivatives.

The substitution method is based on the chain rule of derivatives. By making an appropriate substitution, the integral can be transformed into a new form that corresponds to a derivative of a simpler function.

Therefore, options b, d, and e are the true statements about the substitution method.

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By solving simultaneous linear equation, it can be calculated that

Speed of the current is 5 miles/hour

What is simultaneous linear equation?

At first it is important to know about linear equation

Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.

A one degree equation is known as linear equation.

Two or more linear equations, which can be solved together to obtain common solution are known as simultaneous linear equation.

Here a simultaneous linear equation needs to be solved

Let the speed of boat in still water be x miles/hour and speed of stream be y miles/hour

Speed of the boat downstream = (x  + y) miles/hour

Speed of the boat upstream = (x - y) miles/hour

A boat travels 80 miles downstream in 4 hours

x + y = \(\frac{80}{4}\)

x + y = 20 .... (1)

A boat travels 80 miles upstream in 8 hours

x - y = \(\frac{80}{8}\)

x - y = 10 .... (2)

Subtracting (2) from (1)

2y = 10

y = \(\frac{10}{2}\)

y = 5 miles/hour

Speed of the current is 5 miles/hour

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1.  The average rate of change for P between 1992 and 2000 is  -1.025.

2.  For values of t = 1996 and t = 1992, the function has a negative average rate of change, and value of rate of change will be -2.4.

3.   For values of t = 2000 and t = 1996, the function has a positive average rate of change, and value of rate of change will be 0.35.

Rate is a mathematical term which we use, When two quantities are compared and expressed as a ratio and both have different units.

1.   we need to calculate the average rate of change in 1992 & 2000

    percentage of voters in 2000 = 34.5

    percentage of voters in  1996 =  33.1

    percentage of voters in 1992  = 42.7

it is known that,

Rate of change = change in percentage/change in years

Rate of change in between 1992 &1996 is,

R₁=   (33.1 - 42.7)/(1996-1992)

R₁=    -2.4  

Rate of change in between 1996 & 2000 is,

R₂=   (34.5-33.1)/(2000-1996)

R₂=    0.35

Average rate of change = (R₁ + R₂)/2

Average rate of change = (-2.4 + 0.35)/2

Average rate of change =  -1.025

2. One of the pair of values of t  for which rate of change will be negative are 1996 & 1992,

R=   (33.1 - 42.7)/(1996-1992)

R=   -2.4  

3. One of the pair of values of t  for which rate of change will be positive are 1996 & 2000,

R=   (34.5-33.1)/(2000-1996)

R=   0.35

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Answer: 20

Step-by-step explanation:

4 x 2 = 8

4 x 2 = 8

+

---------

16 round to twenty

The probability of getting all three multiple-choice questions right in this scenario is therefore:0.25 x 0.25 x 0.25 = 0.015 or 1.5%So, the probability of getting all three questions correct by guessing is 1.5%.

The probability of getting all three multiple-choice questions right in a test that includes several such questions, each with four choices, given that one doesn't know the answer to any of them and guesses on each,

can be determined as follows:

Step 1: Determine the probability of getting one multiple-choice question right, given that there are four choices for each question. The probability is 1/4 or 0.25, because there is one correct answer and three incorrect ones.

Step 2: Multiply the probability of getting the first question right by the probability of getting the second question right, which is also 0.25.

Step 3: Multiply the probability of getting the first two questions right by the probability of getting the third question right, which is again 0.25.

Step 4: Multiply the resulting probability by 100 to convert it to a percentage.

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Answer:

6(3t + 5)

Step-by-step explanation:

6 is their least common factor

The fencing needed to keep our rabbits is approximately 44 meters

Given that a circle garden has an area of 25π and the radius is increased by 2 meters and fencing is sold only in one meter section. We need to find how much fencing is needed to keep our rabbits.

Step 1: Area of a circle is given by:

A = πr²

where

r is the radius of the circle garden.

So, the area of circle garden with radius r is given by:

25π = πr²

Dividing both sides by π,

we get:

r² = 25r = ± 5

The radius cannot be negative.

So, r = 5 m

Step 2: When the radius is increased by 2 m, the new radius is:

r + 2 = 5 + 2

= 7 m

Step 3: The length of fencing required will be equal to the circumference of the new circle with radius 7 m.

Circumference of the new circle with radius 7 m is given by:

C = 2πr

= 2π(7)

≈ 43.98 m

Therefore, the fencing needed to keep our rabbits is approximately 44 meters.

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Answer:

as written

\(\frac{6}{x} -3\)  zero would not be allowed....

BUT !!! I think that your question

is ......

\(\frac{6}{x-3}\)    then the answer is "3"

Step-by-step explanation:

Answer:

58.6 miles per hour

Step-by-step explanation:

205.1 miles /3.5 hours= 58.6 mph

The total income is represented by: 5r - 2c - 3p

The rent is $500 (r = 500)

The cable bill is $80 (c = 80)

The phone bill is $40 (p = 40)

Replacing these data into the equation, we get:

Income = 5(500) - 2(80) - 3(40)

Income = 2500 - 160 - 120

Income = $2220

Answer:

Look at attachment

Step-by-step explanation:

Calculating \(P(x > 4) = 1 - CDF(4)\) using a calculator or software, we find that \(P(x > 4)\) is approximately 0.5646 (rounded to 4 decimal places).

To find the probability that x is more than 4 in a Poisson distribution with mean 4.5.

We can use the cumulative distribution function (CDF).

The CDF of a Poisson distribution is given by the formula:
\(CDF(x) = e^(-λ) * (λ^0/0! + λ^1/1! + λ^2/2! + ... + λ^x/x!)\)

In this case, λ (the mean) is 4.5 and we want to find P(x > 4), which is equal to \(1 - P(x ≤ 4).\)

To calculate P(x ≤ 4), we substitute x = 4 in the CDF formula:
\(CDF(4) = e^(-4.5) * (4.5^0/0! + 4.5^1/1! + 4.5^2/2! + 4.5^3/3! + 4.5^4/4!)\)

To find P(x > 4), we subtract P(x ≤ 4) from 1:
\(P(x > 4) = 1 - CDF(4)\)

Calculating this using a calculator or software, we find that P(x > 4) is approximately 0.5646 (rounded to 4 decimal places).

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The probability that x is more than 4 is approximately 0.8304.

The probability that a Poisson random variable x is more than 4 can be calculated using the Poisson probability formula. In this case, the mean of the Poisson distribution is given as 4.5.

To find p(x > 4), we need to calculate the cumulative probability from 5 to infinity, since we want x to be more than 4.

Step 1: Calculate the probability of x = 4 using the Poisson probability formula:
P(x = 4) = (e^(-4.5) * 4.5^4) / 4! ≈ 0.1696

Step 2: Calculate the cumulative probability from 0 to 4:
P(x ≤ 4) = P(x = 0) + P(x = 1) + P(x = 2) + P(x = 3) + P(x = 4)

Step 3: Calculate the probability of x > 4:
P(x > 4) = 1 - P(x ≤ 4)

Step 4: Substitute the values into the formula:
P(x > 4) = 1 - (P(x = 0) + P(x = 1) + P(x = 2) + P(x = 3) + P(x = 4))

Step 5: Calculate the final answer:
P(x > 4) ≈ 1 - 0.1696 ≈ 0.8304

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Answer:

y=-4

Step-by-step explanation:

The answer is going to be -4 as when y=-16 x=8.

The newly transformed function, known as g(x), is g(x) = 2x - 7. This transformation shifted the original function f(x) = 2x + 3 five units to the right along the x-axis. The resulting graph will have the same shape as the original function, but it will be shifted horizontally by five units to the right.

To horizontally translate the function f(x) = 2x + 3 five units to the right, we need to subtract 5 from the variable x in the original function. This will shift the entire graph to the right by five units.

Let's denote the transformed function as g(x). To find g(x), we subtract 5 from x in the original function f(x):

g(x) = f(x - 5)

Substituting f(x) = 2x + 3 into the equation, we have:

g(x) = 2(x - 5) + 3

Simplifying further:

g(x) = 2x - 10 + 3

g(x) = 2x - 7

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The ratio of dividends to the average number of common shares outstanding is known as the dividend yield. It is a measure of the return on an investment in the form of dividends received relative to the number of shares held.

To calculate the dividend yield, you need to divide the annual dividends per share by the average number of common shares outstanding during a specific period. The annual dividends per share can be obtained by dividing the total dividends paid by the number of outstanding shares. The average number of common shares outstanding can be calculated by adding the beginning and ending shares outstanding and dividing by 2.

For example, let's say a company paid total dividends of $10,000 and had 1,000 common shares outstanding at the beginning of the year and 1,500 shares at the end. The average number of common shares outstanding would be (1,000 + 1,500) / 2 = 1,250. If the annual dividends per share is $2, the dividend yield would be $2 / 1,250 = 0.0016 or 0.16%.

In summary, the ratio of dividends to the average number of common shares outstanding is the dividend yield, which measures the return on an investment in terms of dividends received per share held.

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The equation for the given sequence representing the diameter of the circle is

f(n) = f(n-1) + 0.6, where f(1) = 2.5

Given, a sequence of diameters of a circle used to create an art project

2.5 , 3.1 , 3.7 , 4.3

We have to find a sequence that represents the diameter of the given circle,

Let f(n) be representing the diameter of the circle,

Now, for n = 1

f(n) = 2.5

for n = 2

f(n) = 3.1

for n = 3

f(n) = 3.7

for n = 4

f(n) = 4.3

As, f(2) = f(1) + 0.6 and so,

So, f(n) = f(n-1) + 0.6

Hence, the equation for the given sequence representing the diameter of the circle is

f(n) = f(n-1) + 0.6, where f(1) = 2.5

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The value of a + c in the equation is -5

From the question, we have the following parameters that can be used in our computation:

y = ax² + 5x + c

x- intercepts at 1 and 3

This means that

When x = 1 and 3, the value of y is 0

So, we have

When x = 1:

a(1)² + 5(1) + c = 0

a + 5 + c = 0

a + c = -5

When x = 3:

a(3)² + 5(3) + c = 0

9a + 15 + c = 0

9a + c = -15

So, we have

a + c = -5

9a + c = -15

Hence, the value of a + c is -5

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The property that is not true for the normal distribution among the given options is: "The mean, median, and mode are all equal."

The normal distribution is characterized by several key properties. It has a bell shape, meaning it is symmetric around its mean. The tails of the distribution asymptotically approach the horizontal axis, which means they gradually decrease in height as they extend toward positive and negative infinity. The area underneath the curve and to the right of the mean is equal to 0.5, not 1. This is because the total area under the curve represents the probability of all possible outcomes and must sum up to 1. Lastly, the mean, median, and mode of the normal distribution are all equal to each other, making them measures of central tendency that coincide.

Therefore, the property that does not hold for the normal distribution is that the area underneath the curve and to the right of the mean is 1, as it is actually 0.5.

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Answer:

1. Jerome and Jewel Jones are looking to buy their family home for their burgeoning brood. They are looking for a five-bedroom house. The average price of a five- bedroom house is GH¢450,000 in their locality. A bank offers the couple a 15- year mortgage facility at an interest rate of 24.5%. The bank also requires that the instalment payments do not exceed 30% of the couple’s monthly income. What should be the couple’s combined monthly income if they wish to take the facility?

2. You are willing to pay GH¢15,625 now to purchase a perpetuity that will pay you and your heirs GH¢1,250 each year, forever, starting at the end of this year. If your required rate of return does not change, how much would you be willing to pay if this were a 20-year, annual payment, annuity instead of a perpetuity?

3. Desmodus Limited, a toy maker, prepares its accounts to 31 December each year. For the 2017 financial year the company paid a dividend of GH¢0.55 per share. Dividends paid are paid at the end of year but the 2017 were 80% lower than that of the previous year due to a difficult financial year. Members of the com- pany at its annual general meeting agreed not to pay dividends over the next two years and instead pay down the company’s bonds. Dividend payment will resume thereafter at the level of the 2017 dividends for three years. Management be- lieves that the company can afford to increase dividends at a rate of 4% thereafter for the foreseeable future. What is the intrinsic value of the company’s shares at the start of 2019 financial year if firms in the toy industry deliver returns of 13.5% on average?

4. YouhavejustjoinedtheMaaretsGroup,andyourbossasksyoutoreviewarecent analysis that was done to compare three alternative proposals to enhance the firm’s manufacturing facility. You find that the prior analysis ranked the proposals according to their IRR, and recommended the highest IRR option, Proposal A. You are concerned and decide to redo the analysis using NPV to determine whether this recommendation was appropriate. But while you are confident the IRRs were computed correctly, it seems that some of the underlying data regarding the cash flows that were estimated for each proposal was not included in the report. Here is the information you have, all amounts in millions of GH¢ o.:

PROPOSAL IRR YEAR 1 YEAR 2 YEAR 3 YEAR 4

A 60% -100 30 153 88

B 55% ? 0 206 95

C 50% -100 37 0 204+?

(a) Which projects would recommend based on the NPV of each proposal if the appropriate cost of capital is 10%?

(b) Would your recommendations be valid if the company has capital limitation of GH¢285 million? Explain your with appropriate detail.

Step-by-step explanation:

The complex-expression "(-1/2)i³(√(-9) - 4) - 3i²" in simplest-form of "a + bi" can be written as  (3/2) - 2i.

In order to express the expression "(-1/2)i³(√(-9) - 4) - 3i²" in simplest form , we first simplify the exponents:

i³ = i² × i = (-1) × i = -i

i² = -1

Substituting these values in the expression,

We get,

= (-1/2)(-i)(√(-9) - 4) - 3(-1)

= (1/2)i(3i - 4) + 3      ...because √(-9) = 3i,

= (1/2)(3i² - 4i) + 3

= (1/2)(-3 - 4i) + 3

= (-3/2) - 2i + 3

= (3/2) - 2i

Therefore, the expression in the simplest "a + bi" form is (3/2) - 2i.

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The given question is incomplete, the complete question is

Write "(-1/2)i³(√(-9) - 4) - 3i²" in simplest "a + bi" form.

Answer:

D. Because even if you put the negative sign where the line separating the numerator and denominator the numerator is negative.

Answer:Perimeter, 50ft

Step-by-step explanation:since it is around the answer is 50 ft

Answer:

7 rentals in a month is $19.

Step-by-step explanation:

Let y be Lee's total cost of renting movies for a month, and x the number of movies he rents that month.

We can write an equation for this:

1.  y = $5   [he pays a base fee of $5]

2.  y = $5 + $2x  [rent movies at $2 each]

Use this equation to calculate a month's rent for each of the scenarios isted in the question.  If the equation correctly predicts the month's rent for the know cases, use it to calculate the month with 7 rentals.  

See the attached worksheet.  The month with 7 rentals is $19.