Question 7 of 25 Step 1 of 1 Use the method of Lagrange multipliers to find the maximum and minimum values of f(x, y) = 6xy subject to 4x2 + y2 = 200. Write the exact answer. Do not round. Answer 2 Po

The solution of the inequality is (x > - 8 and x < 2) or (x > 6 and x < 16).

Herein we find an inequality that involves two absolute values. Absolute values are defined by the following piecewise functions:

Now we proceed to solve the inequality given:

||x - 4| - 7| < 5

- 5 < |x - 4| - 7 < 5

0 < |x - 4| - 2 < 10

|x - 4| - 2 > 0 and |x - 4| - 2 < 10

Case 1: |x - 4| - 2 > 0

|x - 4| > 2

x - 4 > 2 and x - 4 < - 2

x > 6 and x < 2

Case 2: |x - 4| - 2 < 10

|x - 4| < 12

x - 4 < 12 and x - 4 > - 12

x < 16 and x > - 8

The solution of the inequality is (x > - 8 and x < 2) or (x > 6 and x < 16).

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Answer:

\(1:5\) is the answer

Step-by-step explanation:

→\(4:20\\\\\frac{4}{20}\\\\\frac{1}{5} \\\\1:5\)

Answer:

1/5

Step-by-step explanation:

Answer:

The answer to your problem is, D. $13,564.80

Step-by-step explanation:

We know it took her 4 years to pay this amount. Let's solve for the total amount she paid including the interest.

12,560 x 0.02 = 251.2 per year

251.2 x 4 = 1004.8 dollars for 4 years.

1004.8 + 12,560 = 13,564.8 dollars.

Thus the answer to your problem is, D. $13,564.80

The function rule for this scenario can be written in slope-intercept form as: y = 6x + 30.

A function rule can be written in slope-intercept form using the unit rate or slope (m), and the starting value/initial value or y-intercept (b). The values of m and b, when determined, are simply plugged into the equation, y = mx + b.

We are given that the design fee that is charged by the cloth designer is a fixed fee of $30. This means that the starting value or y-intercept (m) is 30.

From the problem, we are also given that the additional charge per shirt printed is $6, this also implies that the slope or unit rate (m) of the function is 6.

To write a function rule in slope-intercept form, substitute m = 6 and b = 30 into y = mx + b:

y = 6x + 30.

The function rule for the cost of t-shirt produced based on the number of shirts is expressed as: y = 6x + 30.

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We are given the following function:

The graph of this equation is a parabola for values of x < 2 and a line for values of 2<= x <= 6. The graph is the following:

Answer: x=6 y=3

Step-by-step explanation:

12/2 = 6

1 pizza is 6 dollars

6/2=3

1 soda is 3 dollars

3*4=12

6*3=18

18+12=30

Answer:

6 miles

Step-by-step explanation:

because the common denominator is 12 so the man will walk 12 miles in 4 hours and the woman will walk 12 miles in 2 hours so they will meet in the middle

If point A and point B are 15 miles apart, they will meet H) 10 miles from point B.

The answer to the question is H: 10 miles.

To solve this problem, we can use the concept of relative velocity. Relative velocity is the velocity of one object as seen by another object. In this case, the man and the woman are moving towards each other, so their relative velocity is the sum of their individual velocities.

The man's velocity is 3 miles per hour and the woman's velocity is 6 miles per hour, so their relative velocity is 3 + 6 = 9 miles per hour.

We know that point A and point B are 15 miles apart, so they will meet when the distance between them is 0. The time it takes them to meet is 15 / 9 = 5/3 hours.

In 5/3 hours, the man will travel 3 * 5/3 = 5 miles and the woman will travel 6 * 5/3 = 10 miles. Therefore, they will meet 10 miles from point B.

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The correct statement is: d.  "The impact on the volume if the dimensions are multiplied by 14  the new volume will be 14 times the original volume.      

To determine the impact on the volume when the dimensions of the cone are multiplied by 14, we need to calculate the new volume and compare it to the original volume. Let's denote the original radius as r and the original height as h.

Given:

Original radius (r) = 12 ft

Original height (h) = 24 ft

New radius = 14 * r

New height = 14 * h

The formula for the volume of a cone is V = (1/3) * π * r^2 * h.

Original Volume (V_original) = (1/3) * π * (r^2) * h

= (1/3) * π * (12^2) * 24

≈ 10845.12 cubic feet

New Volume (V_new) = (1/3) * π * ((14 * r)^2) * (14 * h)

= (1/3) * π * (196 * r^2) * (14 * h)

= (1/3) * π * (196 * (12^2)) * (14 * 24)

= (1/3) * π * 196 * 144 * 336

≈ 1086615.36 cubic feet

Comparing the new volume to the original volume:

a. The volume will decrease by 116.

False. The new volume is significantly larger than the original volume, so it does not decrease by 116.

b. The original volume will be divided by 43.

False. Dividing the original volume by 43 does not yield the new volume.

c. The original volume is decreased by approximately 2111.15 units^3.

False. The difference between the new volume and the original volume is much larger than 2111.15 units^3.

d. The new volume will be 14 times the original volume.

True. The new volume is approximately 14 times the original volume.

e. The original volume will be multiplied by 164.

False. Multiplying the original volume by 164 does not yield the new volume.

Therefore, the correct statement is:

d. The new volume will be 14 times the original volume.

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Answer:

-10n - 60

Step-by-step explanation:

Use the distributive property to simplify [ a(b + c) = ab + ac ]

-10(n + 6)

(-10 * n) + (-10 * 6)

-10n + -60

-10n - 60

Best of Luck!

The corporation should make 1000 of a certain sort of car in order to reduce production cost using minimal cost function and derivatives.

Finding the value of x that minimizes the cost function will help us determine the optimal number of automobiles to construct. \(C(x) = 25000 - 40x + 0.02x^2\).

The derivative of C(x) with respect to x can be taken, set to zero, and then the value of x can be determined.

\(C'(x) = -40 + 0.04x = 0 0.04x = 40 \sx = 1000\)

Hence, when 1000 cars are created, the least cost is incurred. We can check the second derivative of C(x) at x = 1000 to make sure this is a minimum.

\(C''(x) = 0.04 > 0\)

The fact that the second derivative is positive demonstrates that the minimum of C(x) occurs at x = 1000.

As a result, the corporation should make 1000 of a certain sort of car in order to reduce production costs. Cost is reduced to $21000 at this manufacturing level.

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Answer:

$20.64

Step-by-step explanation:

0.20x25.80=5.16

25.80-5.16=20.64

The original price to get entry to a museum is $20.64 .

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

Let call 'a' be the original price.

if it rose of 20 % , it's mean that it will multiplicate by 0.20

0.20 x 25.80=5.16

a = 25.80 - 5.16=20.64

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Answer:

35

Step-by-step explanation:

The measure of an inscribed angle whose endpoints are points S and T will be 35°.

It is the close curve of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.

The central angle is double the angle at the periphery that was subtended by the same chords.

The central angle of arc ST is 70°.

The measure of an inscribed angle whose endpoints are points S and T is given by the half of the central angle of arc ST. Then we have

Inscribed angle = 70° / 2

Inscribed angle = 35°

The measure of an inscribed angle whose endpoints are points S and T will be 35°.

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The profit function for the company is Profit = (19x - 7x) - 105,000. When the company produces and sells 7500 book covers, the profit earned is $99,000. When the company produces and sells 8750 book covers, the profit earned is $152,500.

A. Profit = (19x - 7x) - 105,000

B. Profit = (19(7500) - 7(7500)) - 105,000 = $99,000

C. Profit = (19(8750) - 7(8750)) - 105,000 = $152,500

D. Profit = (19(11835) - 7(11835)) - 105,000 = $229,495

A. The profit for the company for a single book cover is the difference between the selling price and the production cost. The selling price is $19 and the production cost is $7. The difference is $12. The company's fixed cost is $105,000, so the profit function is Profit = (19x - 7x) - 105,000.

B. To find the profit earned by the company when it produces and sells 7500 book covers, substitute 7500 for x in the profit function. Profit = (19(7500) - 7(7500)) - 105,000 = $99,000.

C. To find the profit earned by the company when it produces and sells 8750 book covers, substitute 8750 for x in the profit function. Profit = (19(8750) - 7(8750)) - 105,000 = $152,500.

D. To find the profit earned by the company when it produces and sells 11,835 book covers, substitute 11,835 for x in the profit function. Profit = (19(11835) - 7(11835)) - 105,000 = $229,495.

The profit function for the company is Profit = (19x - 7x) - 105,000. When the company produces and sells 7500 book covers, the profit earned is $99,000. When the company produces and sells 8750 book covers, the profit earned is $152,500. When the company produces and sells 11,835 book covers, the profit earned is $229,495.

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Answer:

just know so please give me a good rating

Answer:

1:3

Step-by-step explanation:

The total animals is 45 and the cats is 15.

The ratio is 15:45

Simplified, it would be 1:3 because you can divide each side my 15.

Hope this helped!! :)

Brainliest?!?!

Have a safe and wonderful day/night/afternoon!!!

Answer:

60 ft

Step-by-step explanation:

120 = x + 2x + 3x

120 = 6x

x = 20

Answer:

55 degrees

Step-by-step explanation:

sum of all angles of a triangle equal 180

to find x we add them all and set them equal to 180

(57+x)+(72+x)+55=180

129+2x+55=180

184+2x=180

-184.    -184

2x= -4

/2.  /2

x=-2

now to find angle A

57+(-2)

55

hopes this helps

Theorem 1: For a random sample from a normal population, the sample standard deviation follows the chi distribution with n - 1 degrees of freedom. Mathematically, the distribution of the random variable (n - 1)S²/σ² follows the chi-square distribution with n - 1 degrees of freedom (denoted by χ²(n - 1)).

For this particular problem, we will require the following theorem:

Theorem 1: For a random sample from a normal population, the sample standard deviation follows the chi distribution with n - 1 degrees of freedom. Mathematically, the distribution of the random variable (n - 1)S²/σ² follows the chi-square distribution with n - 1 degrees of freedom (denoted by χ²(n - 1)).

Using Theorem 1, we can find the expectation of the sample standard deviation (denoted by S) as follows:

We know that the expected value of χ²(n - 1) is (n - 1) and the expected value of σ² is equal to 62, by definition. Therefore, we can write:

E[(n - 1)S²/σ²] = E[χ²(n - 1)]

Multiplying both sides by σ²/(n - 1), we get:

E[S²] = σ²E[χ²(n - 1)]/(n - 1)

Substituting the expected value of χ²(n - 1), we get:

E[S²] = σ²(n - 1)/(n - 1) = σ²

Taking the square root on both sides, we get:

E[S] = σ

Therefore, the expectation of the sample standard deviation is equal to the population standard deviation. Now, coming back to the original problem:

Given that X1, X2, ..., Xn is a random sample from N(C1, 62), we need to find the MLE and the MVUE of the constant b such that P

(X < b) = p.

For this, we need to find the distribution of the random variable (X - C1)/σ, where σ is the population standard deviation.

We know that (X - C1)/σ follows the standard normal distribution (denoted by Z) under the null hypothesis.

Therefore, we can write:

P(X < b) = p ⇔ P((X - C1)/σ < (b - C1)/σ) = p ⇔ P(Z < (b - C1)/σ) = p

We can find the value of (b - C1)/σ such that

P(Z < (b - C1)/σ) = p

using the standard normal distribution table.

Let this value be denoted by zp, i.e.,

P(Z < zp) = p.

Then, we can write:

(b - C1)/σ = zp ⇔ b = C1 + σzp

Since we do not know the value of σ, we cannot find the exact value of b. However, we can find the MLE and the MVUE of b as follows:

MLE of b: Let X1, X2, ..., Xn be a random sample from N(C1, 62).

Then, the likelihood function is given by:

L(b | x) = f(x | b) = (1/√(2π62))^n exp(-∑(xi - b)²/(2*62))

The log-likelihood function is given by:

l(b | x) = ln L(b | x) = -n/2 ln(2π) - n/2 ln(62) - ∑(xi - b)²/(2*62)

The derivative of the log-likelihood function with respect to b is given by:

l'(b | x) = (1/62) ∑(xi - b)

Setting this derivative equal to zero, we get:

(1/62) ∑(xi - b) = 0 ⇔ b = (∑xi)/n

Therefore, the MLE of b is the sample mean, which is an unbiased estimator of C1.

MVUE of b: Let X1, X2, ..., Xn be a random sample from N(C1, 62).

Then, we know that (X - C1)/σ follows the standard normal distribution (denoted by Z) under the null hypothesis.

Therefore, the distribution of (X - b)/S is the t-distribution with n - 1 degrees of freedom (denoted by t(n - 1)).

We know that the statistic

T = (n - 1)S²/σ² follows the chi-square distribution with n - 1 degrees of freedom (denoted by χ²(n - 1)).

Also, we know that T/σ² follows the gamma distribution with shape parameter (n - 1)/2 and scale parameter 2.

Therefore, the distribution of the random variable Z = [(X - b)/S] √n follows the t-distribution with n - 1 degrees of freedom (denoted by t(n - 1)).

We can use the pivotal quantity Z = [(X - b)/S] √n to construct the confidence interval for (b - C1)/σ.

Specifically, we know that P(-t(n - 1, α/2) < Z < t(n - 1, α/2)) = 1 - α,

where t(n - 1, α/2) is the (1 - α/2)th quantile of the t-distribution with n - 1 degrees of freedom.

We can use this confidence interval to construct the confidence interval for b.

Specifically, we can write: P(-t(n - 1, α/2) < [(X - b)/S] √n < t(n - 1, α/2)) = 1 - α ⇔ P(X - t(n - 1, α/2) S/√n < b < X + t(n - 1, α/2) S/√n) = 1 - α

Therefore, the MVUE of b is the midpoint of this confidence interval, which is an unbiased estimator of C1.

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The mean is calculated by summing up all the values in the distribution and dividing it by the total number of values, while the median is the middle value when the data is arranged in ascending or descending order.

Another difference is that the mean is affected by outliers, meaning that extreme values can greatly influence its value. On the other hand, the median is not affected by outliers, as it only depends on the position of the middle value.

Therefore, to summarize, the mean is influenced by all values in the distribution and is affected by outliers, while the median is only influenced by the middle value and is not affected by outliers.

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Answer:

A. Line r intersects line p

Step-by-step explanation:

to find the second graph multiply the slope of line p by -10

slope is 1/5 or 0.2

So,

0.2 * -10 = -2

slope of second line is -2

Graph shown

Altered line shown in blue

Line p shown in green

As you can see, they intersect and meet no other answers

Given statement is True.

A system of equations can be represented in different forms, such as point form (showing the x and y values that make the equations true) or equation form (showing the equations in standard form, with variables on one side and constants on the other). A solve by substitution calculator can be used to find the solution to a system of two or three equations in both point form and equation form of the answer.

The process of solving a system of equations by substitution involves isolating a variable in one equation and then substituting it into the other equation(s) to find the values of the other variable(s). The calculator can display the solution in point form by showing the values of x and y (or x, y, and z for a system of three equations) that make the equations true. It can also display the solution in equation form by showing the equations with the variable(s) replaced by the values found in the solution.

In conclusion, solve by substitution calculator can find the solution to a system of two or three equations in both point form and equation form of the answer, it can be a helpful tool for solving systems of equations.

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Answer:

5,040

Step-by-step explanation:

There are a total of 5,040 interesting numbers, which can be calculated using basic combinatorics. To calculate this, the first step is to count the total number of 10-digit numbers with distinct digits. Since there are 10 distinct digits (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9), there are 10! (10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1) possible numbers with distinct digits. The next step is to count the number of 10-digit numbers divisible by 11,111. To do this, we need to find the number of 10-digit numbers divisible by 11. Since 11 is a prime number, there are 11 possible combinations of 10-digit numbers divisible by 11. For example, 0XXXXXXXXX, 1XXXXXXXXX, 2XXXXXXXXX, etc. So, there are 11 x 10! (110,000) possible 10-digit numbers divisible by 11. Finally, to find the number of interesting numbers, we need to subtract the number of 10-digit numbers divisible by 11,111 from the total number of 10-digit numbers with distinct digits. This gives us 10! - 11 x 10! = 5,040. Therefore, there are a total of 5,040 interesting numbers.

Answer:

To find the number of interesting numbers, we need to find the number of 10-digit numbers that are divisible by 11,111 and have distinct digits.

A number is divisible by 11,111 if and only if the alternating sum of its digits is divisible by 11. For example, 27,183,642 is divisible by 11,111 because 2 - 7 + 1 - 8 + 3 - 6 + 4 - 2 = -3, which is divisible by 11.

Since we want the number to have distinct digits, we can choose any 5 digits from the set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} and arrange them in any order. There are 10 choices for the first digit, 9 choices for the second digit (since we can't repeat the first digit), 8 choices for the third digit, and so on, giving us a total of 10 x 9 x 8 x 7 x 6 = 30,240 possible 5-digit numbers with distinct digits.

To form a 10-digit number, we can repeat the 5 digits in any order. There are 5! = 120 ways to arrange the 5 digits, so there are 120 different 10-digit numbers that can be formed from each 5-digit number.

Therefore, the total number of interesting numbers is:

30,240 x 120 = 3,628,800

So there are 3,628,800 interesting numbers that are 10-digit numbers divisible by 11,111 with distinct digits.

The category in the Excel Options dialog box that contains the option to change the user name is "General".

In the Excel Options dialog box, the category that contains the option to change the user name is the General category.

Excel graphing methods, Go to Insert > Line after selecting the data. The type of line chart you want may be chosen from a dropdown menu that appears when you click the icon.

We'll use the fourth 2-D line graph (Line with Markers) for this illustration. Your line graph for the chosen data series will be added by Excel.

What are the primary three graphs?

How to Use Graphs in Science

Bar, circle, and line graphs are the three most often utilized graph kinds. Each form of graph may be used to display a certain kind of data.

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1. The total of birds(y) in terms of bird feeder(x) is y = 5+3x

2. The number of bird feeder(x) in terms of bird(y) is x = (y - 5)/3

A word problem in math is a math question written as one sentence or more . These statements are interpreted into mathematical equation or expression.

Represent the number of bird feeder by x

for a bird feeder , 3 birds appear

number of birds that come for feeder = 3x

Total number of birds (y)

y = 5+3x

re arranging it to make x subject

3x = y -5

x = (y-5)/3

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The figure is cut by a plane containing its altitude and perpendicular to its base, the cross-section formed is (A) Triangle.

When a triangular pyramid is cut by a plane containing its altitude and perpendicular to its base, the resulting cross-section will be a triangle.

To understand why, let's visualize the pyramid. A triangular pyramid has a base that is a triangle and three triangular faces that converge at a single point called the apex.

The altitude of the pyramid is a line segment that connects the apex to the base, perpendicular to the base.

When we cut the pyramid with a plane containing its altitude and perpendicular to its base, the plane will intersect the pyramid along its height.

This means that the resulting cross-section will be a slice that is perpendicular to the base and parallel to the other two triangular faces.

Since the base of the pyramid is a triangle, and the plane cuts through it perpendicularly, the resulting cross-section will also be a triangle.

The shape of the cross-section will be similar to the base triangle of the pyramid, with the same number of sides and angles.

Therefore, the correct answer is a. Triangle.

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Answer:

From what I found, the answer is parallel

Step-by-step explanation:

not much of an explanation haha

The graph of the system of equations, 2x + y = 6  and 6x + 3y = 12 is:  C. Intersecting lines

Note:

Given that 2x + y = 6  and 6x + 3y = 12 is a system of equations, when both equations are graphed, it will give us two intersecting lines.

The coordinate of the point of intersection is the solution to the system of equations.

Therefore, the graph of the system of equations, 2x + y = 6  and 6x + 3y = 12 is:  C. Intersecting lines

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