Minimize a firms total costs, C = 45X^2+90XY=90Y^2 When the firm has to meet a production quota equal to 2X+3Y=60 by
A. Finding the critical values

This statement essentially establishes a relationship between the sets X, Y, and z, stating that there exists a subset Y for each element x in X such that the elements in Y are present in some subset z of X.

The given statement is a symbolic representation of a logical proposition involving quantifiers and logical connectives. Let's break down its meaning:

∀ X ∃ Y ∀u(u ∈ Y ↔ ∃z(z ∈ X ∧ u ∈ z))

The symbol ∀ (universal quantifier) indicates that the statement applies to all elements in the set X.

The symbol ∃ (existential quantifier) indicates that there exists at least one element in the set Y.

The statement can be interpreted as follows:

"For all elements x in the set X, there exists a set Y such that for every element u in Y, u is an element of Y if and only if there exists a set z in X such that u is an element of z."

In simpler terms, the statement asserts that for every element x in the set X, there is a set Y that contains elements u if and only if there exists a set z in X that also contains u.

It is important to note that the precise meaning and implications of this statement may depend on the context and interpretation of the sets X, Y, and their elements.

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The length of x is 3.42cm

To determine the value, we have to know the different trigonometric identities.

These identities are listed thus;

From the information shown in the diagram, we have that;

Opposite side = x

The hypotenuse side = 10

The angle = 20 degrees

Now, using the sine identity, we get;

sin 20 = x/10

cross multiply the values, we get;

x = 10(0.3420

Multiply the values, we have;

x = 3.42cm

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Kendra | | | |

Madison | | | | | | | | | | | | | | | | | | | | | | | |

Madison drew 24 dolphins.

To solve this problem, we need to use the information given in the problem and represent it in a bar model. Let's use the following bar model:

Kendra: 4 dolphins

Madison: 6 times as many dolphins as Kendra

Kendra | | | |

Madison | | | | | | | | | | |

From the model, we can see that Kendra drew 4 dolphins and we don't know how many dolphins Madison drew, which is represented by "d". The problem tells us that Madison drew 6 times as many dolphins as Kendra, so we can multiply Kendra's number of dolphins by 6:

Kendra: 4 dolphins

Madison: 6 x 4 = 24 dolphins

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Answer:

3

Step-by-step explanation:

tan(A) = y-coordinate / x-coordinate

tan(A) = -3 / -1

tan(A) = 3/1

tan(A) = 3

Therefore, the value of tan(A) is 3.

Both angle K and angle L must be acute angles, measuring less than 90 degrees, in order to satisfy the conditions of the given triangle.

In triangle JKL, if angle J is less than 90 degrees, then angle K and angle L are both acute angles.

An acute angle is defined as an angle that measures less than 90 degrees. Since angle J is given to be less than 90 degrees, it is an acute angle.

In a triangle, the sum of the interior angles is always 180 degrees. Therefore, if angle J is less than 90 degrees, the sum of angles K and L must be greater than 90 degrees in order to satisfy the condition that the angles of a triangle add up to 180 degrees.

Hence, both angle K and angle L must be acute angles, measuring less than 90 degrees, in order to satisfy the conditions of the given triangle.

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Answer:Yes

Step-by-step explanation:

By the communitive property, they are equal to each other.

The amount of money he will have after eight years of savings would be = 15,600.

To calculate the total amount of money the skateboarder will have after the number of giveyears, the formula that should be used would be given below as follows:

Simple interest = Principal×time ×rate /100

Where:

principal = 10,000

Time = 8 years

Rate = 7%

Simple interest = 10,000×8×7/100

= 560000/100

= 5600

The total amount of money the skateboarder will have will be = 10,000+5600 = 15,600

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The volume of the composite figure in this problem is given as follows:

76 ft³.

The volume of a rectangular prism, with dimensions defined as length, width and height, is given by the multiplication of these three defined dimensions, according to the equation presented as follows:

Volume = length x width x height.

The figure in this problem is composed by two prisms, with dimensions given as follows:

Hence the volume is given as follows:

2 x 6 x 3 + 2 x 4 x 5 = 76 ft³.

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The horizontal distance needed for the ramp is 518.4 cm to ensure a slope of 5/32 and reach the entrance of the school, which is 81 cm above the ground.

To find the horizontal distance needed for the ramp, we can use the formula:

Horizontal distance = Vertical distance / Slope

Given that the slope must be 5/32 and the entrance to the school is 81 cm above the ground, we can substitute these values into the formula:

Horizontal distance = 81 cm / (5/32)

To divide by a fraction, we can multiply by its reciprocal:

Horizontal distance = 81 cm * (32/5)

Simplifying:

Horizontal distance = (81 cm * 32) / 5

Horizontal distance = 2592 cm / 5

Horizontal distance = 518.4 cm

Therefore, the horizontal distance needed for the ramp is 518.4 cm to ensure a slope of 5/32 and reach the entrance of the school, which is 81 cm above the ground.

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627 x 26 equals 16,302 when solved using the standard algorithm.

The steps below can be used to solve the multiplication issue 627 x 26 using the conventional algorithm:

627 and 26 should be written one above the other, with the larger number appearing above and the smaller number beneath.

Start by adding each digit of the top number to the ones digit of the bottom number (six). Write the answers below the line after multiplying 6 by 7 and then by 2.

1254 -- a 6 x 7 partial product

1254 -- a half 6 x 2 product

Repeat the process by moving the bottom number one position to the left after that. Multiply 2 by 7 and then by 2, and then write the results one space to the left of the line below the line.

1254 x 627

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Answer:

$61.29 per day.

Step-by-step explanation:

Checking account balance on February 1st: $443

Checking account balance on February 7th: $872

Difference in balances: $872 - $443 = $429

Number of days between February 1st and February 7th: 7 days

Rate of change = Difference in balances / Number of days

Rate of change = $429 / 7 days

To find the rate of change per day, divide the difference in balances by the number of days:

Rate of change = $429 / 7 days ≈ $61.29 per day

Therefore, the rate of change in your checking account balance during that period was approximately $61.29 per day.

De acuerdo con la información, podemos inferir que un ejemplo de experimento aleatorio con orden y reemplazo: Lanzar un dado y registrar el resultado en cada lanzamiento.

Los experimentos aleatorios tienen diferentes formas de aplicación según su tipo, a continuación explicamos algunos:

De acuerdo con lo anterior, UN ejemplo de experimento aleatorio con orden y reemplazo: Lanzar un dado y registrar el resultado en cada lanzamiento.

Question in English

Give examples of randomized experiments with order, replacement, and no repetition.

Answer in English

Based on the information, we can infer that an example of a random experiment with order and replacement: Throw a die and record the result on each throw.

Random experiments have different forms of application depending on their type, some of which are explained below:

Order involve recording the results in sequence, while experiments. Orderless do not take into account the order in which the results occur. With replacement, items can be repeated in each selection, while in experiments. Without replacement, the selected items they are no longer available for subsequent selections.

Based on the above, ONE example of a random experiment with order and replacement: Roll a die and record the result on each roll.

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The system of equations that represents this is:

x + y = 144

x*23 + y*90 = 10347

Solving it, we conclude that they sold 39 of the Basic ones and 105 of the Super ones.

To do this, first we need to define the variables we will be using. Let's define:

x = number of basic graphers sold.

y = number of SuperGraphers sold.

They sold a total of 144 items, so x + y = 144

And they earned a total of $10347, then we can write:

x*23 + y*90 = 10347

Then the system of equations that represents this is:

x + y = 144

x*23 + y*90 = 10347

The graph of this system is on the image below, there we can see that the solution is (39, 105).

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Answer: -16

Step-by-step explanation:

The distance away from zero is 16 and -16 is negative + do u do rsm

The equation of the midline of the graph is y = -2

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

The graph

Where we have

Max = 1

Min = -5

Using the above as a guide, we have the following:

Midline, y = (Max + MIn)/2

substitute the known values in the above equation, so, we have the following representation

y = (1 - 5)/2

Evaluate

y = -2

Hence, the equation of the midline of the graph is y = -2

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when the scale factor is 1, we have:

(side length of side opposite ∠A) / (length of hypotenuse) = sin A

When the scale factor is 1, the ratio of the side length of the side opposite ∠A to the length of the hypotenuse remains the same as in the original triangle. In a right triangle, the side opposite ∠A is referred to as the "opposite" side, and the hypotenuse is the longest side.

The ratio of the side length of the side opposite ∠A to the length of the hypotenuse is commonly known as the sine of angle A (sin A). So, when the scale factor is 1, the ratio of the side length of the side opposite ∠A to the length of the hypotenuse is equal to sin A.

In mathematical terms, when the scale factor is 1, we have:

(side length of side opposite ∠A) / (length of hypotenuse) = sin A

It's important to note that this ratio holds true for any right triangle, regardless of its size or dimensions, as long as the angle A remains the same.

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Jasmine has 8 glasses of lemonade remaining in the pitcher.

Jasmine made a pitcher of lemonade, which contains 12 glasses of lemonade. She served 4 glasses of lemonade, and we need to determine how many more glasses she has left.

To solve this problem, we can subtract the number of glasses served from the total number of glasses in the pitcher:

12 (total glasses) - 4 (glasses served) = 8 (glasses remaining)

Therefore, Jasmine has 8 glasses of lemonade left in the pitcher after serving 4 glasses.

In terms of the equation, we have:

Total number of glasses - Number of glasses served = Number of glasses remaining

Or:

12 - 4 = 8

So, the correct equation and solution are:

12 - 4 = 8

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Answer:

$393,120

Step-by-step explanation:

To find the decrease in the house's value in dollars, we need to calculate 9% of the initial value:

Decrease in value = (Initial value) * (Percentage decrease) = $432,000 * 9%

Converting the percentage to a decimal:

Decrease in value = $432,000 * 0.09 = $38,880

The house's value decreased by $38,880.

Now, to find the current value of the house, we need to subtract the decrease in value from the initial value:

Current value = Initial value - Decrease in value = $432,000 - $38,880 = $393,120

The current value of the house is $393,120.

Hope this helps!

The surface integral in terms of ρ and θ ∫∫S.((6y - 5)e^(x^2))

To evaluate ∬s.curl F•nds using Stokes' Theorem, we first need to find the curl of the vector field F and then compute the surface integral over the given surface S.

Given vector field F = (6yz)i + (5x)j + (yz(e^(x^2)))k, let's find its curl:

∇ × F = ∂/∂x (yz(e^(x^2))) - ∂/∂y (5x) + ∂/∂z (6yz)

Taking the partial derivatives, we get:

∇ × F = (0 - 0) i + (0 - 0) j + (6y - 5)e^(x^2)

Now, let's parametrize the surface S, which is the portion of the paraboloid z = (1/4)x^2 + y^2 for 0 ≤ z ≤ 4. We can use cylindrical coordinates for this parametrization:

r(θ, ρ) = ρcos(θ)i + ρsin(θ)j + ((1/4)(ρcos(θ))^2 + (ρsin(θ))^2)k

where 0 ≤ θ ≤ 2π and 0 ≤ ρ ≤ 2.

Next, we need to find the normal vector n to the surface S. Since S is oriented upward, the normal vector points in the positive z-direction. We can normalize this vector to have unit length:

n = (∂r/∂θ) × (∂r/∂ρ)

Calculating the partial derivatives and taking the cross product, we have:

∂r/∂θ = -ρsin(θ)i + ρcos(θ)j

∂r/∂ρ = cos(θ)i + sin(θ)j + (1/2)(ρcos(θ))k

∂r/∂θ × ∂r/∂ρ = (-ρsin(θ)i + ρcos(θ)j) × (cos(θ)i + sin(θ)j + (1/2)(ρcos(θ))k)

Expanding the cross product, we get:

∂r/∂θ × ∂r/∂ρ = (ρcos(θ)(1/2)(ρcos(θ)) - (1/2)(ρcos(θ))(-ρsin(θ)))i

+ ((1/2)(ρcos(θ))sin(θ) - ρsin(θ)(1/2)(ρcos(θ)))j

+ (-ρsin(θ)cos(θ) + ρsin(θ)cos(θ))k

Simplifying further:

∂r/∂θ × ∂r/∂ρ = ρ^2cos(θ)i + ρ^2sin(θ)j

Now, we can calculate the surface integral using Stokes' Theorem:

∬s.curl F•nds = ∮c.F•dr

= ∫∫S.((∇ × F)•n) dS

Substituting the values we obtained earlier:

∫∫S.((∇ × F)•n) dS = ∫∫S.((6y - 5)e^(x^2))•(ρ^2cos(θ)i + ρ^2sin(θ)j) dS

We can now rewrite the surface integral in terms of ρ and θ:

∫∫S.((6y - 5)e^(x^2))

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Step-by-step explanation:

I'm pretty sure you just use the law of cosines in this case.

c= sqrt(a^2+b^2﹣2ab (cos γ))
where a is a Side, b is a Side, γ is Gamma or the angle. Sqrt means square root

In your case, a is 20, b is 13, and  γ is 93. Just plug it into the formula now :). I got 24.41751 ish.

Calculating the area of a road involves considering the road's shape and cross-sectional profile. There are two common methods for calculating the area:

Cross-Sectional Area Method: This method involves measuring the width of the road at regular intervals along its length and taking elevation measurements. By dividing the road into sections and multiplying the width by the corresponding elevation difference, you can calculate the area of each section and sum them up to obtain the total road area.

Digital Terrain Model (DTM) Method: This method uses advanced surveying techniques to obtain a digital terrain model of the road surface. By applying surface area algorithms to the DTM, you can calculate the surface area of the road, considering the elevation data and interpolating the area between points.

The chosen method depends on available data, accuracy requirements, and project needs. It is essential to refer to engineering standards and guidelines specific to your region or project for accurate and appropriate road area calculations.

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Answer:

The percent of change in Anna's working hours is 22%, indicating an increase.

Step-by-step explanation:

Step 1: Calculate the difference:

Difference = 36 hours - 28 hours

Difference = 8 hours

Step 2: Calculate the percent change:

Percent Change = (Difference / Original Value) * 100

Percent Change = (8 hours / 36 hours) * 100

Percent Change ≈ 22.22%

Therefore, the percent change in Anna's working hours is approximately 22.22%, representing an increase.

Answer:

Step-by-step explanation:

The measures of central tendency of the dataset, and the measurements in the dataset indicates;

(a) Mode

(b) Mean

(c) Mean, Median

(d) Roughly symmetrical

Measures of central tendency are descriptive statistical values that represent the typical value or centerpoint of a data set.

(a) The mean of a data set always has only one value. The mode of the dataset are 11 and 14. Therefore, the measure of central tendency that takes more than one value is the mode. The correct option is therefore;

Mode

(b) The mode will remain the same. The middle value or median will remain the same. The mean, which i the average value will increase. The correct option for measure of central tendency that will be affected by the change is therefore the mean.

Mean

(c) The smallest measurement which is 1, if removed, the mean will change and the median will change from 11 to (10 + 11)/2 = 10.5. The correct options for the measures of central tendency that will change are therefore;

Mean

Median

(d) The distribution of the original dataset can be presented as shown in the histogram, which is symmetrical about the class with one of the modes, indicating that the original data is roughly symmetrical about the class with the mode 11. The correct option is therefore;

Roughly symmetrical

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Rounding to the nearest liter, the volume of the liquid in the pipe is approximately 0.01 liters. Therefore, none of the options A, B, C, or D provided is the correct answer.

To calculate the volume of the liquid in the cylindrical steel pipe, we need to find the difference in volume between the solid cylinder (hollow part) and the hollow cylinder.

Given:

Length of the cylindrical steel pipe (hollow part) = 21 cm

Radius of the solid cylinder = 0.4 cm

Radius of the hollow cylinder = 0.1 cm

First, let's calculate the volume of the solid cylinder (hollow part):

V1 = π × [tex]r1^2[/tex] × h

V1 = π × [tex](0.4 cm)^2[/tex] × 21 cm

Next, let's calculate the volume of the hollow cylinder:

V2 = π × [tex]r2^2[/tex] × h

V2 = π × [tex](0.1 cm)^2[/tex] × 21 cm

Now, we can find the volume of the liquid in the pipe by subtracting V2 from V1:

Volume of liquid = V1 - V2

Let's calculate these values:

V1 = π ×[tex](0.4 cm)^2[/tex] × 21 cm ≈ 10.572 cm³

V2 = π × [tex](0.1 cm)^2[/tex] × 21 cm ≈ 0.693 cm³

Volume of liquid = V1 - V2 ≈ 10.572 cm³ - 0.693 cm³ ≈ 9.879 cm³

To convert the volume from cubic centimeters (cm³) to liters (L), we divide by 1000:

Volume of liquid in liters ≈ 9.879 cm³ / 1000 ≈ 0.009879 L

Rounding to the nearest liter, the volume of the liquid in the pipe is approximately 0.01 liters.

Therefore, none of the options A, B, C, or D provided is the correct answer.

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In the class, Lucy's score is 6.

In statistics, the median is the middle value in a sorted, ascending or descending list of numbers. Thus, it represents the midpoint of the data.

The median is often compared with other descriptive statistics such as the mean (average), mode, and standard deviation.

Since Lucy is one of the 29 students in the class and her score was the same as the median score for her class.

Thus, the median score will be 15th score (i.e. the midpoint of 29). Using the frequency in of each score from the figure, let's keep adding the frequency until we reach 15 and we will then check the corresponding score at the 15th position:

2 + 2 + 4 + 7 = 15

Thus, the the corresponding score at the 15th position is 6.

Therefore, the median score is 6 and consequently Lucy's score is 6.

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The larger number is 35.Let's assume the two numbers are represented by the variables "x" and "y," where "x" is the smaller number.

Equation 1: x + y = 59 (The sum of the two numbers is 59)

Equation 2: x - y = 11 (The difference between the two numbers is 11, with the smaller number being y)

According to the given information, the sum of the two numbers is 59, which can be expressed as:

x + y = 59

The difference between the two numbers is 11, with "x" being the smaller number. This can be expressed as:

y - x = 11

We can now solve these two equations simultaneously to find the values of "x" and "y."

Rearranging the first equation to solve for "y" gives us:

y = 59 - x

Substituting this value of "y" into the second equation:

(59 - x) - x = 11

Simplifying the equation:

59 - 2x = 11

Subtracting 59 from both sides:

-2x = 11 - 59

-2x = -48

Dividing both sides by -2:

x = -48 / -2

x = 24

Therefore, the smaller number is 24. To find the larger number, we substitute the value of "x" into the first equation:

24 + y = 59

y = 59 - 24

y = 35.

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