May you please go over step by step of how to do this

a) To find out how much L is needed to produce 400 toys per hour when K is equal to 20, we can use the production function formula provided, which is Q = 4K + 5L.

To solve for L, we can rearrange the formula as follows: Q - 4K = 5L 400 - 4(20) = 5L 320 = 5L L = 64

Therefore, to produce 400 toys per hour with K = 20, the manufacturer would need 64 units of labor input per hour.

b) Similarly, to find out how much K is needed to produce 500 toys per hour when L is equal to 40, we can use the production function formula: Q = 4K + 5L

Substituting the given values, we get: 500 = 4K + 5(40) 500 = 4K + 200 4K = 300 K = 75

Therefore, to produce 500 toys per hour with L = 40, the manufacturer would need 75 units of capital input per hour.

In conclusion, the production function formula provides a useful tool for toy manufacturers to produce a desired level of output. By manipulating the formula, the manufacturer can also calculate the maximum output possible given a certain combination of inputs.

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If in a rectangular-prism, the length is doubled, width is tripled and height is same, then the volume of new rectangular prism will be 6 times the original-prism.

The "Volume" of a 3-D object is defined as the amount of space that object occupies in three-dimensional space. It is a measure of the total capacity or size of the object

Volume of a rectangular prism is ⇒ Volume = Length × Width × Height,

If the length of the rectangular prism is doubled, the new length would be 2 times the original length.

If the width is tripled, the new width would be 3 times the original width, and

If the height remains the same, it would be the same as the original height.

Let the original length be = "L",  width be = "W", and height be = "H",

So, New Length = 2L , New Width = 3W, New Height = H (remains unchanged),

So, volume of new rectangular prism is :

⇒ New Volume = (New Length)×(New Width)×(New Height),

⇒ (2L) × (3W) × H

⇒ 6LWH

Therefore, volume of "new-rectangular prism' is 6 times volume of  original rectangular prism.

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Answer:

50/100 or 1/2 or 50%

Step-by-step explanation:

total =  30 + 20 + 50 = 100

the probability of choosing a marble that is not blue is equal to the total minus all marbles that are blue therefore 100-30-20=50 therefore the probability is 50/100 or 1/2 or 50%

When the top of the ladder is 16 feet above the ground, the foot of the ladder is moving away from the wall at a speed of approximately 3.86 feet per second.

This is a related rates problem involving a ladder leaning against a wall. Let's denote the distance of the foot of the ladder from the wall as x, and the height that the top of the ladder reaches as y. We are given that dy/dt = -2 ft/s (since the top is slipping down the wall) and we want to find dx/dt (the speed at which the foot of the ladder is moving away from the wall) when y = 16 ft.

Using the Pythagorean theorem, we have:

[tex]x^2 + y^2 = 17^2[/tex]

Differentiating implicitly with respect to time, we get:

[tex]2x(dx/dt) + 2y(dy/dt) = 0[/tex]

Substituting the given values, we get:

[tex]2x(dx/dt) + 2(16)(-2) = 0[/tex]

Simplifying, we get:

[tex]2x(dx/dt) = 64[/tex]

Dividing both sides by 2x, we get:

dx/dt = 64/(2x)

We know that y = 16, so we can use the Pythagorean theorem to solve for x:

[tex]x^2 + 16^2 = 17^2x^2 = 17^2 - 16^2x^2 = 33[/tex]

Taking the square root, we get:

[tex]x = sqrt(33)[/tex]

Substituting this into our expression for dx/dt, we get:

[tex]dx/dt = 64/(2*sqrt(33)) ≈ 3.86 ft/s[/tex]

Therefore, when the top of the ladder is 16 feet above the ground, the foot of the ladder is moving away from the wall at a speed of approximately 3.86 feet per second.

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Step-by-step explanation:

for the perimeter you have to say two brackets live plus height plus with plastic

The correct statements for the triangles are given as follows:

The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

The theorem is expressed as follows:

c² = a² + b².

In which:

The Pythagorean Theorem holds true for triangle XYZ, hence:

For triangle STU, the symbol shows that it a right triangle, hence the hypotenuse length is obtained as follows:

a² + b².

Which is equals to the hypotenuse length of XYZ.

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The standard deviation of the height distribution is approximately 6 inches (since 6 is half of 12), which corresponds to option (C).

The distribution of the heights of students in a large class is roughly Normal, with an average height of 68 inches, and approximately 95% of the heights are between 62 and 74 inches.

The height distribution is approximately Normal, we can use the empirical rule, which states that approximately 95% of the data falls within 2 standard deviations of the mean, to estimate the standard deviation.

The range of heights within which approximately 95% of the students fall is from 62 to 74 inches.

This range is 12 inches wide, and it corresponds to 2 standard deviations from the mean.

Thus, we have:

2 standard deviations = range of 95% of the data = 74 - 62 = 12 inches

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The statement that correctly describes the scatter plot is

A scatter plot is a type of data visualization that displays the relationship between two numerical variables.

It is a graph that uses dots or points to represent the values of each variable, with one variable plotted on the x-axis and the other on the y-axis.

The position of each dot on the graph represents the values of the two variables for a single observation or data point.

Scatter plots are commonly used to identify patterns or relationships between variables, such as correlation or causation.

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The probability that a randomly selected gas station customer on that day did not purchase gasoline is 10/27.

We know that, the probability of any event is the ratio of the number of favorable case to that event to the total number of cases.

The total number of customers in that Gas Station on that day = 135

According to the data table,

Number of customers did not purchase gas but purchased beverage = 35

Number of customers neither purchase gas nor beverage = 15

So total number of customers did not purchase gas = 35 + 15 = 50

Here number of favorable cases = 50

So the probability that a randomly selected gas station customer on that day did not purchase gasoline = 50/135 = 10/27.

Hence the required probability is 10/27.

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The given question is incomplete. The complete question is -

"On Tuesday, a local gas station had 135 customers. The table above summarizes whether or not the customers on Tuesday purchased gasoline, a beverage, both, or neither. Based on the data in the table, what is the probability that a gas station customer selected at random on that day did not purchase gasoline?

Customer Purchases at a Gas Station"

Answer: There is an approximate 10.7% probability that it will snow on Sunday, making it the day with the lowest likelihood of snow.

Step-by-step explanation: Snow is highly likely on Friday with an 80% probability. The likelihood of no snowfall occurring on Friday is 20%, which can be calculated by subtracting 0.8 (or 80%) from 1.

There is a high probability of snowfall on Saturday with a 7 in 9 likelihood. In simpler terms, the probability can be reduced to 7 out of 9 or around 0.78. The likelihood of snowfall on Saturday is 78%, therefore the chance of no snow on that day is 22% which is equivalent to 1 minus 0.78.

There is a high likelihood of snow on Sunday with a probability of 75 out of 100 or 14 out of 19. It is possible to reduce this to a likelihood of 0.7514, or about 0.107. The likelihood of Sunday not having snow is equivalent to subtracting 0.107 from 1, resulting in a 0.893 or 89.3% probability.

Answer:

Aquí respondemos a la pregunta: "¿Qué dos números se multiplican por 4 y suman 5?"

La respuesta a tu pregunta es:

1 y 4

A continuación ilustramos y demostramos que 1 y 4 se multiplican por 4 y suman 5:

1 × 4 = 4

1 + 4 = 5

¿Estás preguntando porque estás tratando de averiguar cómo factorizar la siguiente ecuación cuadrática?

x2 + 5x + 4 = 0

Si es así, la solución para factorizar la ecuación cuadrática anterior es:

(x+1) (x+4)

Para resumir, dado que 1 y 4 se multiplican por 4 y suman 5, sabes que lo siguiente es cierto:

x2 + 5x + 4 = (x + 1 ) (x + 4)

Step-by-step explanation:

Answer:

B and then A

Step-by-step explanation:

volume is × so the . means times

so it's the only option

and then the second area is

6×3×4= 72cm³

The number of kilometres that are equivalent to 28.5 cm² is 2.85 × 10⁹ km². Hence, after careful consideration concerning every option, the required answer for the given question is Option A.

Here, we have to depend on the principles of conversation of units and using this principles derive a formula.

To convert 28.5 cm² to km², we have to implement the formula

Total number of square centimeters x 1.0 x [tex]E^{-10}[/tex] = Total number of square kilometers .

The number of kilometres that are equivalent to 28.5 cm² is 2.85 × 10⁹ km². Hence, after careful consideration concerning every option, the required answer for the given question is Option A.

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To rewrite the equation of the circle in graphing form, we need to complete the square for both the x and y terms.

x² + 6x + y² - 4y = -9

Step 1: Move the constant term to the right side of the equation.

x² + 6x + y² - 4y + 9 = 0

Step 2: Group the x terms and the y terms separately.

(x² + 6x) + (y² - 4y) + 9 = 0

Step 3: Complete the square for the x terms. To do this, take half of the coefficient of x (which is 6), square it, and add and subtract it inside the parentheses.

(x² + 6x + 9 - 9) + (y² - 4y) + 9 = 0

(x + 3)² - 9 + (y² - 4y) + 9 = 0

(x + 3)² + (y² - 4y) = 0

Step 4: Complete the square for the y terms. To do this, take half of the coefficient of y (which is -4), square it, and add and subtract it inside the parentheses.

(x + 3)² + (y² - 4y + 4 - 4) = 0

(x + 3)² + (y - 2)² - 4 = 0

Step 5: Move the constant term to the right side of the equation.

(x + 3)² + (y - 2)² = 4

The equation is now in graphing form, which is:

(x - h)² + (y - k)² = r²

where (h, k) is the center of the circle and r is the radius.

Comparing the equation to the graphing form, we see that the center of the circle is (-3, 2) and the radius is 2. Thus, the graph of the circle is centered at (-3, 2) with a radius of 2.

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Answer:

The answer for x is 11

Step-by-step explanation:

x²=144-1

Square root of both sides

√x²=√144-1

x=12-1

x=11

Answer:

if no initial high im guessing 4.8 weeks

Step-by-step explanation:

4.8 divied by .8 = 6

Answer:

7 week 3 days and 12 hour

Step-by-step explanation:

x is the required week and to calculat it

1st for 1 week= o.8 inch

x = 6 inch

2nd u solve it after u solve it u get 7.5 but week dosen't said by decimals so u will multiply 0.5 by days of the week which is 7 .

3rd u will get 3.5 as we said before for days we can't use decimals so yo will multiply 0.5 by hour which 24 then u will get 12 . so the answer is 7 week 3 days and 12 hour .

The correct function that defines the area of the rectangle is:

A(z) = 2[tex]x^{2}[/tex]+ 9x + 4 (option A).

The area of a rectangle is given by the product of its length and width. So, the function that defines the area of the rectangle would be:

A(x) = l(x) * w(x)

where l(x) is the length of the rectangle given by the function 1(x) = 2x + 1, and w(x) is the width of the rectangle given by the function w(x) = x + 4.

Substituting the given functions for length and width, we get:

A(x) = (2x + 1) * (x + 4)

Now, we can expand and simplify the expression:

A(x) = [tex]2x^2 + 8x + x + 4[/tex]

A(x) = [tex]2x^2 + 9x + 4[/tex]

So, the correct function that defines the area of the rectangle is:

A(z) =[tex]2x^2 + 9x + 4 ([/tex]option A).

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As x approaches 2 from both sides, the values of f(x) do not approach a single value, and f(x) does not have a limit. The answer is option (d).

The calculus concept known as the limit of a function describes how a function behaves when the input variable approaches a particular value.

The phrase "lim f(x) as x approaches a" (or "limit of a function f(x) as x approaches a") describes what occurs to the output of the function when x approaches a value without actually reaching a.

The limit can be expressed in terms of two-sided, left-sided, or right-sided limits, depending on whether x approaches a from both sides, the left, or the right.

We must look at the values of f(x) as x approaches 2 in order to determine lim f(x) as x approaches 2.

Looking at the table, we can see that the values of f(x) rise from 3.99 to 4 as x approaches 2 from the left (that is, as x approaches 2 while remaining smaller than 2). The values of f(x) decline from -5 to -5.01 as x moves towards 2 from the right (that is, as x approaches 2 but staysgreater than 2).

The limit of f(x) as x approaches 2 does not exist because the values of f(x) do not approach a single integer as x approaches 2 from both sides.

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To find D(15), we simply substitute t = 15 into the function:

D(15) = 2,280 - 60(15)

D(15) = 2,280 - 900

D(15) = 1,380

Therefore, when the Chang family has been driving for 15 hours, they are 1,380 miles away from home.

Interpreting this result in the context of the problem, we can say that the family has made good progress on their trip and has covered a distance of 1,380 miles from home.

Therefore , the solution of the given problem of ratio comes out to be the Udderly Delicious Cheese Factory needs 550 gallons of milk in total.

A group comprising values both variable "a" and "" that seem to be equal is found using the straightforward formula "a / b," whenever "b" might be a greater number than zero. A ratio is created by combining two ratios. The ratio , fraction could have been 1:1 if there were just one guy and three women. There are 1/4 men and 3/4 women in the group.

Here,

For cheddar cheese, multiply the quantity of blocks by 200 and the amount of milk consumed by each block by 5.

200 blocks of cheddar cheese divided by 5 quarts per block equals a total of 1000 quarts.

For Swiss cheese, the formula is as follows: 200 blocks of Swiss cheese, or 6 quarts of milk per block.

200 blocks of Swiss cheese divided by 6 quarts per block equals 1200 quarts of milk in total.

Total milk used equals the sum of the milk required to make cheddar cheese and the milk used to make Swiss cheese, or 1000 quarts plus 1200 quarts, or 2200 quarts.

We can convert quarts to gallons by dividing by 4 because there are 4 quarts in a gallon.

= 1000 quarts + 1200 quarts

= 2200 quarts

We can convert quarts to gallons by dividing by 4 because there are 4 quarts in a gallon.

=> Total gallons of milk used = 2200 quarts / 4 quarts/gallon = 550 gallons

Thus, to make 200 blocks of cheddar cheese and 200 blocks of Swiss cheese each day,

the Udderly Delicious Cheese Factory needs 550 gallons of milk in total.

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Answer:

In a triangle, the sum of the interior angles is 180 degrees. So, we can set up the following equation:

72° + (x+4)° + A = 180°

where A is the measure of the third angle in the triangle.

Simplifying the equation, we get:

(x+4)° + 72° + A = 180°

x + 76° + A = 180°

Subtracting 76° from both sides, we get:

x + A = 104°

Therefore, an equation that can be used to find the value of x is x + A = 104°, where A is the measure of the third angle in the triangle. Note that we do not have enough information to solve for x or A individually, but we can use this equation to relate the two angles in the triangle.

If the noon class has a symmetric distribution, the median would be 15.

From the given table,

a) Evening class has the highest average age, that is 22 years.

b) Morning class has age that are the most spread out, that is 2.4.

c) If the noon class has a symmetric distribution, the median would be 15 (which is equal to the mean).

Therefore, if the noon class has a symmetric distribution, the median would be 15.

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The length of XZ in circle C is equal to the √34. This can be found using the Pythagorean theorem and the fact that XZ is a radius of the circle.

As WZ and XR are diameters, they intersect at the center of the circle, which we'll call point O.

Since WX is a chord of the circle, we can use the perpendicular bisector of WX, which passes through O, to find the length of XZ.

Let's call the midpoint of WX point M. Then OM is perpendicular to WX and bisects it.

So we have two right triangles, OXM and MXZ. We know that OM = 5 and XM = 3 (half of WX).

Using the Pythagorean theorem, we can find the length of OX:

OX² = OM² + MX²

OX² = 5² + 3²

OX² = 34

OX = √(34)

Since XZ is also a radius of the circle, we have XZ = OX = √(34).

Therefore, the measure of XZ in circle C is √(34).

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1. The radius (r) of the space swept is 1.5 m; 2. The angle measure is 75°.

3. The formula to use is Area = ∅/360 * πr²; 4. Area of the space is approximately 1.47 m².

The formula to use to find the area of a sector is given as:

Area = ∅/360 * πr², where:

r is the radius; and ∅ is the angle measure.

From the image given, we will solve the problem as follows:

1. The radius (r) = 1.5 m

2. The angle measure (∅) = 75°

3. The formula is:

Area = ∅/360 * πr²

4. Plug in the values:

Area = 75/360 * π * 1.5²

Area ≈ 1.47 m²

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There are 36 different combinations possible when spinning the two spinners in the game, obtained by multiplying the number of outcomes on each spinner (6 × 6 = 36).

A combination is a way of selecting a group of items from a larger set without regard to the order, often represented as unordered arrangements of objects, used in mathematics, statistics, and various fields of science.

According to the given information:

To determine the total number of different combinations possible in the game, we need to multiply the number of outcomes on each spinner. The first spinner has six equally likely outcomes (1, 2, 3, 4, 5, or 6), and the second spinner also has six equally likely outcomes (A, B, C, D, E, or F). Therefore, the total number of different combinations possible is:

6 (number of outcomes on the first spinner) × 6 (number of outcomes on the second spinner) = 36

So, there are 36 different possible combinations that can be obtained from spinning the two spinners. These combinations can be used to match with the combinations on the players' game cards and determine the winner of the game.

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The amount of interest that Baron Blakk would receive in total after eight years would be 6, 118. 03 krona

To find the interest that Baron Blakk received in eight years of savings, we first need to find the future value of the savings. We can do this with the Future value of annuity due formula as this is an annuity and it is an Annuity due as it is paid at the beginning of the year.

The total value after eight years is:

= Amount saved x ( Future value of annuity, interest, number of years)

= 7, 000 x 8. 87

= 62, 118.03 Krona

The interest earned is:

= Total value - ( Amount saved )

=  62, 118.03 - ( 7, 000 x  8 )

= 6, 118. 03 krona

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Answer:

66.25

technically 67 glasses

Step-by-step explanation:

Answer:

It is trapizium so the area can be calculated as

[tex] \frac{1}{2} (6ft + 8ft) \times 5ft \\ = {35ft}^{2} [/tex]

u can solve area of trapizium by

1/2(a+b)h

and when you solve it u get the answer 35ft^2

The minimum number of cuts John needs to make to cut a 5-inch piece of paper using scissors with blades that are 4 and 3/8 inches long is either one or two

To determine the minimum number of cuts John needs to make to cut a 5-inch piece of paper using scissors with blades that are 4 and 3/8 inches long:

Subtract the length of the blades from the desired length of the paper:

5 - 4 3/8 = 1/8 inch

Therefore, the minimum number of cuts John needs to make are 4 and 3/8 inches long is either one or two, depending on whether he chooses to fold the paper or not.

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--The complete Question is, John needs to cut a piece of paper using a pair of scissors. He measures the scissors to the nearest 1/8 inch and finds that the length of the blades is 4 and 3/8 inches. If John wants to cut a piece of paper that is exactly 5 inches long, what is the minimum number of cuts he needs to make? --