Juan has a profitable web business of selling T-shirts priced at $25 each. His demand is pretty steady throughout the year (his website is up and running 365 days a year), approximately normally distributed with a mean of 30 T-shirts/day and a standard deviation of 10 T-shirts/day. He has a supplier in China that charges him $5 per T-shirt T and a flat rate of $150 every time he places an order. Orders take exactly 50 days to arrive by container ship. His calculates his annual per unit holding costs at 20% of the wholesale cost of T-shirts. a) What type of inventory management problem is this? Explain your answer. i) Newsvendor (single period) model ii) EOQ model with continuous demand distribution 111) EOQ model with discrete demand distribution b) Calculate how many T-shirts he should order from his China supplier at a time. c) Calculate the level at which he should reorder T-shirts from China to experience at most a 10% chance of a stocking out. a T-shirts, Juan should place an order for d) Fill in: When inventory drops to more T-shirts.

No the octopus can not differentiate between circles and rectangle and the probability of picking circle is 0.295.

In the give question we have to find the octopus can tell the difference between circles and rectangles or not.

From the question;

Circles: 13

Rectangles: 31

Null hypothesis: proportion of circles found = 0.5

Alternate hypothesis: Proportion of circles found > 0.5

Total number of trials is 31+13=44

Since 13 times circle is choosen.

So the probability that octopus chooses circle is

P(C) = Total number of circle/Total number of trials

P(C)=13/44

P(C)=0.295

As probability is 0.295<0.50

So, no the octopus can not differentiate between circles and rectangle and the probability of picking circle is 0.295.

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The system of equations are solved and have infinitely many solutions

Given data ,

Let the system of equations be represented as A and B

Now , the value of A and B are

5x - 8y = 40   be equation (1)

-1.25x + 2y = -10   be equation (2)

On simplifying , we get

Multiply equation (2) by 4 , we get

-5x + 8y = -40   be equation (3)

On simplifying , we get

5x - 8y = 40

Therefore , the equations are same and have infinite solutions

Hence , the solution to the equations are infinitely many solutions

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The point- slope form of the line is y-5 = -0.25(x+6).

What is line?

A line is an one-dimensional figure. It has length but no width. A line can be made of a set of points which is extended in opposite directions to infinity. There are straight line, horizontal, vertical lines or may be parallel lines perpendicular lines etc.

A line with a slope of –1/4 passes through the point (–6,5)

Any line in point - slope form can be written as

y - y₁= m(x -x₁) -------(1)

where,

y= y coordinate of second point

y₁ = y coordinate of first point

m= slope of the line

x= x coordinate of second point

x₁ = x coordinate of first point

In the given problem (x₁ , y₁) = (-6,5) and m= -1/4

Putting all these values in equation (1) we get,

y-5= (-1/4) (x- (-6))

⇒ y-5 = -0.25(x+6)

Hence, the point- slope form of the line is y-5 = -0.25(x+6).

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The Gibbs-Duhem equation relates the activity coefficients of the individual components in a mixture. It states that the activity coefficients are not independent of each other but are related by a differential equation.

In the case of a binary mixture (chemical A and chemical B), the Gibbs-Duhem relation can be written as:

x1 * (∂x1/∂lnγ1)T,P = x2 * (∂x2/∂lnγ2)T,P

Here, x1 and x2 represent the mole fractions of chemical A and chemical B, respectively. The activity coefficients for chemical A and chemical B are denoted as γ1 and γ2, respectively.

The equation shows that the change in mole fraction of one component (x1) with respect to the change in the logarithm of its activity coefficient (lnγ1) is proportional to the change in mole fraction of the other component (x2) with respect to the change in the logarithm of its activity coefficient (lnγ2).

This relationship helps us understand how changes in the activity coefficients of the components affect each other in a binary mixture. By studying this relationship, we can gain insights into the behavior of the mixture and make predictions about its properties.

For example, let's consider a mixture of ethanol (chemical A) and water (chemical B). If the activity coefficient of ethanol (γ1) decreases, the Gibbs-Duhem equation tells us that the mole fraction of ethanol (x1) will also decrease. Similarly, if the activity coefficient of water (γ2) increases, the mole fraction of water (x2) will increase.

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Answer:

Step-by-step explanation:

the first tick mark

Answer:

2nd Division

Step-by-step explanation:

Given :-

And we need to tell where does 42% lies on the number line . So , since there are 4 equal divisions , therefore each division has ,

\(:\implies\) Each division = 100% ÷ 4

\(:\implies\) Each division = 25%

So after two divisions the marking will be 50%. Therefore , 42% lies in the second division .

Answer:

x = - \(\frac{2}{3}\) , x = \(\frac{34}{3}\)

Step-by-step explanation:

The absolute value function always gives a positive value, however, the expression inside can be positive or negative, that is

- 3x + 16 = 18 or -(- 3x + 16) = 18

Solving

- 3x + 16 = 18 ( subtract 16 from both sides )

- 3x = 2 ( divide both sides by - 3 )

x = - \(\frac{2}{3}\)

or

-(- 3x + 16) = 18

3x - 16 = 18 ( add 16 to both sides )

3x = 34 ( divide both sides by 3 )

x = \(\frac{34}{4}\)

As a check

Substitute these values into the left side of the equation and if equal to the right side then they are the solutions.

| - 3(- \(\frac{2}{3}\) ) + 16 | = | 2 + 16 | = | 18 | = 18 ← True

| - 3(\(\frac{34}{3}\) ) + 16 | = | - 34 + 16 | = | - 18 | = 18 ← True

Thus x = - \(\frac{2}{3}\) and x = \(\frac{34}{3}\) are the solutions

Given:-

g(x)=18

To find:-

x

Solution:-

g(x)=(-3x+16)

18=-3x+16

18-16=-3x

2=-3x

x=2/-3

hope it helps you!

The child passes through 18π radians in the course of the carousel ride.

To determine the number of radians the child passes during the 6-minute ride on the carousel, we need to know the distance traveled in terms of radians.

Since there are 20 horses spaced evenly around the carousel, each horse is separated by an angle of 360/20 = 18 degrees or π/10 radians.

Therefore, during one rotation of the carousel, the child passes through 20π/10 = 2π radians. And since the carousel completes one rotation every 40 seconds, the angular velocity is 2π/40 = π/20 radians per second.

To find the total distance traveled in radians during a 6-minute ride, we need to multiply the angular velocity by the time elapsed.

6 minutes is equal to 360 seconds,

so the child passes through π/20 x 360 = 18π radians during the ride.

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To find x, the number of books the library had last year, we can use the equation:

x + 50 = 2,402

This equation takes into account that the library acquired 50 books over the summer and now has a total of 2,402 books. By subtracting 50 from 2,402, we can determine that the library had x books last year.

Therefore, the equation simplifies to:

x = 2,402 - 50

x = 2,352

So, last year the school library had a total of 2,352 books. To find the number of books the library had last year (x), we can set up an equation using the information provided.

Last year, the library had x books. Over the summer, the library acquired 50 more books. Now, the library has a total of 2,402 books.

So, the equation to find x would be:

x + 50 = 2,402

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a. To represent the garden's width, w, in terms of its length, I, we can use the equation: w = 300 - 2I

b. g(l) = l * (300 - 2l) this function gives the area of the rose garden (g) as a function of its length (l)

a. To represent the garden's width, w, in terms of its length, I, we can use the equation:

w = 300 - 2I

The width is equal to the remaining fence length (300 feet) after subtracting twice the length (2I) because the rectangular planter has two equal sides and two equal ends.

b. To define a function g that represents the rose garden's area in terms of its length, l, we can use the equation:

g(l) = l * w

Substituting the expression for the width from part (a), the function becomes:

g(l) = l * (300 - 2l)

This function gives the area of the rose garden (g) as a function of its length (l), taking into account the relationship between length and width.

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complete question is below

A gardener is designing a rectangular planter for a rose garden in front of the administration building on a university campus. The gardener has enough material to build a 300-foot fence to enclose the garden. He also has enough roses to fill a 5,200 square foot planter.

a. Define an expression to represent the garden's width, w, in terms of it length, I.

b. Define a function g to represent the rose garden's area in terms of its length, l.

The price per unit is equal to R2.29 per unit.

Generally speaking, a unit price is sometimes referred to as price per unit or unit rate and it can be defined as the price that is being charged by a seller for the sale of a single unit of product.

In this scenario, we would determine the unit price for number of unit of electricity by using the following mathematical expression;

Unit price = Cost of electricity/Number of units

Substituting the given parameters into the unit price formula, we have the following;

Unit price = R350/152.84

Unit price = R2.29 per unit.

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Therefore, there are 4 vertices in this graph.

Let V be the number of vertices in the graph. The sum of the degrees of all vertices in an undirected graph is twice the number of edges, so in this case, the sum of degrees is 2 * 10 = 20.

We know that two vertices have degree 4, so the degrees of the remaining vertices must add up to 20 - 2 * 4 = 12.

If there are v vertices of degree 3, then the total degree contributed by those vertices is 3v, so we have:

3v + 2 * 4 = 20

3v = 12

v = 4

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Answer:

w ≤ 19

Step-by-step explanation:

4w−16≤60

Add 16 to both sides.

4w−16+16≤60+16

4w≤76

Divide both sides by 4.

4w/4 ≤ 76/4

w≤19

Answer:

w<=19

Step-by-step explanation:

4w<=60+16

w<=76/4

The process capability index, Cpk, is the minimum of the two ratios. In this case, Cpk = 0.44.

The process capability index (Cpk) is a statistical measure that indicates the ability of a manufacturing process to produce output within specified limits,

in this case, the diameter of holes drilled in wood. To calculate the Cpk, we need to determine the minimum of two ratios: (USL - μ) / (3σ) and (μ - LSL) / (3σ), where USL is the upper specification limit (0.5 inches), LSL is the lower specification limit (0.4 inches), μ is the process mean (0.46 inches), and σ is the standard deviation (0.03 inches).

First, calculate the upper ratio:
(USL - μ) / (3σ) = (0.5 - 0.46) / (3 * 0.03) = 0.04 / 0.09 ≈ 0.44

Next, calculate the lower ratio:
(μ - LSL) / (3σ) = (0.46 - 0.4) / (3 * 0.03) = 0.06 / 0.09 ≈ 0.67

This value indicates how well the drilling process is able to maintain the required diameter specifications. A higher Cpk value (greater than 1) signifies that the process is more capable of producing within the specified limits, whereas a lower Cpk value (less than 1) suggests that the process may not consistently meet the diameter requirements.

In this instance, the Cpk of 0.44 indicates that there may be room for improvement in the drilling process to achieve greater consistency in meeting the specified diameter limits.

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Answer:

y= (x - 12)^3

y= (x - 4)^3

Step-by-step explanation:

Shift to the right is a horizontal shift so it needs to be with x in the parenthesis. And negative because it is to the right.

y= (x - 12)^3

y= (x - 4)^3

are the two that fit those criteria

Answer:

y = (x - 12)^3

y = (x - 4)^3

Step-by-step explanation:

If you look in the picture, red line is y = x^3 (the original parent equation), green line is y = (x - 4)^3, and blue line is y = (x - 12)^3

Answer:

The Formula for Percent Proportion is Parts /whole = percent/100. This formula can be used to find the percent of a given ratio and to find the missing value of a part or a whole.

Answer:

a = 9

Step-by-step explanation:

\(\frac{4}{12}\) = \(\frac{a}{27}\) ( cross- multiply )

12a = 108 ( divide both sides by 12 )

a = 9

The perimeter of the polygon is 202 ft

The perimeter of a polygon is the sum of its sides.

Given the polygon below, we desire its perimeter. We proceed as follows.

The sum of all its sides is P = 62 ft + (15 ft + 12 ft) + 20 ft + 12 ft + (62 ft - (20 ft + 20 ft)) + 12 ft + 20 ft + (15 ft + 12 ft)

=  62 ft + 27 ft + 20 ft + 12 ft + (62 ft - 40 ft) + 12 ft + 20 ft + 27 ft

= 62 ft + 27 ft + 20 ft + 12 ft + 22 ft + 12 ft + 20 ft + 27 ft

= 89 ft + 32 ft + 34 ft + 47 ft

= 121 ft + 34 ft + 47 ft

= 155 ft + 47 ft

= 202 ft

So, the perimeter is 202 ft

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Answer

The answer in scientific = 6×10^2

Explanation

We are asked to simplify the expression.

48×10^5 / 8×10^3

We need to break this down to simplify it

6×10^2 = 600.

Hope this Helps!!!

Answer:

A. One solution

Step-by-step explanation:

6 + x/5 = x/5 - 5 - 3x/10

Cancel equal terms on both sides.

6=-5-3x/10

Multiply both sides of the equation by 10.

60=-50-3x

Move the variable to the left-hand side and change the sign.

60+3x=-50

Move the constant to the right-hand side and change the sign.

3x=-50-60

Calculate the difference.

3x=-110

Divide both sides by 3.

x=-110/3

=-36 2/3

Meaning one solution.

Hope this helps :)

Answer:

The answer you are looking for is A

Let me fill in the statement reasoning for you:

Statement         |           Reasoning

∆ABC ~ ∆RST               Given

∆DEF ~ ∆RST                

∠A = ∠R, ∠D = ∠R         Definition of ~ ∆

∠C = ∠T, ∠F = ∠T          

∠A = ∠D,∠C = ∠F          Transitivity

∆ABC ~ ∆DEF                AA

Answer:

Step-by-step explanation:

SOLVING

================================================================

6=-2(7-c)

Use distribution to multiply -2 by parenthesis

6=-14+2c

Add to both sides 14

20=2c

Divide 2 into both sides

10=c

5(h-4)=8

Use distribution to multiply 5 by the parenthesis

5h-20=8

Add to both sides 20

5h=28

Divide 5 into both sides

\(h=\frac{28}{5}\)

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==============================================================

Answer:   \(\bold{log_5\bigg(\dfrac{x^5}{(8-x)^{\frac{1}{4}}}\bigg)}\)

Step-by-step explanation:

Notes: Coefficients condense to exponents.

           Subtraction condenses to division

\(5\log_5(x)-\dfrac{1}{4}\log_5(8-x)\\\\\\=\log_5(x)^5-\log_5(8-x)^\frac{1}{4}\\\\\\=\large\boxed{\log_5\bigg(\dfrac{x^5}{(8-x)^\frac{1}{4}}\bigg)}\)

To find the probability that x is greater than or equal to 62.48, we can use the standard normal distribution. First, we need to standardize the value of 62.48 using the z-score formula:

z = (x - μ) / σ

Where x is the value, μ is the mean, and σ is the standard deviation.

In this case, we have:

x = 62.48

μ = 20

σ = 18

z = (62.48 - 20) / 18

z = 2.36

Now, we can find the probability using a standard normal distribution table or a calculator. The probability of x being greater than or equal to 62.48 is the same as the probability of z being greater than or equal to 2.36.

Using a standard normal distribution table or calculator, we find that the probability is approximately 0.0091 or 0.91%.

Therefore, p(x ≥ 62.48) is approximately 0.0091 or 0.91%.

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Answer:  

0.125 inches  

Step-by-step explanation:  

we know that  

The volume of a cylinder is equal to  

we have  

----> the radius is half the diameter

substitute

solve for h

Divide the height by the number of saw blade to determine the thickness of 1 blade

Answer: f(x) = -1/2(x+3)

Example: g(x) = -1/2(-x-3)

This function is a dilation and a reflection of the parent function f(x) because when graphed, the two functions have the same shape but are reflected over the y-axis and are half the size of the original.

Answer: 1/9

Step-by-step explanation: hope this help if im wrong correct me

Answer:

the answer is 1

Step-by-step explanation:

The number of players the team can bring to the tournament = 19 .

Given : amount raised by team = $1775.50

            rent of bus = $901.50

            budget for meal per player = $46

To find : the number of players the team can bring to the tournament

Equation :

taking bus charge as y - intercept ( since it does not depend on the no . of members riding on it )

taking meal amount as slope ( since it depends on the no . of members a team can bring to the tournament )

Let x be the no . of players a team can bring to the tournament .

Therefore , the equation is :

1775.50 = 46 x + 901.50

874 = 46 x

x = 19

Hence , the number of players the team can bring to the tournament = 19 .

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Answer:

350

Step-by-step explanation:

154/0.44 = 350

Answer: 350

Check: 44% of 350 = 0.44 × 350 = 154

The solution is 350

The maximum score for the examination is given by the equation A = 350

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

The score of the examination = 154

The percentage of the score 154 = 44 %

So , the equation will be

score of the examination = 44 % of the maximum score A

Substituting the values in the equation , we get

154 = ( 44 / 100 ) x A

On simplifying the equation , we get

A ( 0.44 ) = 154

Divide by 0.44 on both sides of the equation , we get

A = 154 / 0.44

A = 350

Therefore , the value of A is 350

Hence , the maximum score is 350

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Answer:

8-10 feet

Step-by-step explanation:

If the length of the carpet is two more than the width, the width can be expressed as x and the length can be expressed as x+2. This means that the area(x^2+2x) must be greater than 48 but no less than 80.

Now we can solve for both the maximum and minimum cases:

x^2+2x=48, x^2+2x-48=0, now we can factor, (x+8)(x-6)=0, and now we can use the Zero Product Property to find x=-8;x=6. Since we cant have negative width, x at least has to be equal to 6.

x^2+2x=80,x^2+2x-80=0, now we can factor, (x+10)(x-8), and now using the Zero Product Property to find x=-10;x=8, and since it must be positive, at most x can equal 8.

Now since the length is two more than the width, x, you add two to both of these values and get a range of 8-10 feet.

To determine the y-intercept of a slope intercept form, we must follow the two requirements: (1) The y-variable must be completely isolated. (2) If case 1 is followed, then the y-intercept is the numerical value in the equation.

Given equation: y = 6x + 2

Explanation: We can see that the "y" variable is completely isolated. Therefore, this equation follows the first requirement. So, the y-intercept is the numerical value in the equation. Clearly, the only numerical value of the provided equation is 2. Therefore, the y-intercept is (0, 2).

Given equation: 10x + 5y = 30

Explanation: We can see that the y-variable is not completely isolated. Therefore, we have to isolate the y-variable using the four operations. To consider the y-variable as isolated, it must not have anything being divided, multiplied, subtracted, or added. In this equation, we can see the y-variable being multiplied to 5. We can also see that 5y is being added to 10x. Therefore, we must subtract 10x on both sides of the equation.

To remove the coefficient, we must divide both sides by 5.

Now, since the y-variable is isolated completely, this equation satisfies the first requirement. Clearly, the only numerical value of the equation is 6.

Therefore, the y-intercept is (0, 6).

Given equation: y - 6 = 2(3x - 4)

Explanation: This equation requires some simplifying. Let us first apply the distributive property to simplify the right-hand-side of the equation.

We do see two numerical values, but there can only be one y-intercept in any equation when graphed on a coordinate plane. So, let us add 6 on both sides of the equation to cancel out the -6 and thus, get one numerical value.

Since 2 is being subtracted from 6x, the y-intercept is (0, -2).