the difference between two numbers is six and there sum is ten. find the two numbers​

The value after minimizing f(x, y) = x2 + y2 with respect to constraint - x + 2y − 10 = 0, using Lagrange multipliers, is 50.

To solve this problem using Lagrange multipliers, we first write the function to be minimized as:

f(x,y) = x² + y²

And the constraint equation as:

g(x,y) = x + 2y - 10 = 0

We then form the Lagrangian function L(x,y,λ) as follows:

L(x,y,λ) = f(x,y) - λg(x,y)

Substituting in our expressions for f(x,y) and g(x,y), we get:

L(x,y,λ) = x² + y² - λ(x + 2y - 10)

Now, we take partial derivatives of L with respect to x, y and λ and set them equal to zero:

∂L/∂x = 2x - λ = 0 ∂L/∂y = 2y - 2λ = 0 ∂L/∂λ = x + 2y - 10 = 0

Solving these equations simultaneously gives us:

x = λ y = λ/2 x + 2y - 10 = 0

Substituting these values back into our original function f(x,y), we get:

f(5,5) = (5)² + (5)² = 50

Therefore, the minimum value of f(x,y) subject to the given constraint is 50.

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The population of interest is the group of students who submitted an application to the college in 2017.

A sample is a subset of a population that is selected and studied in order to make inferences or conclusions about the population. The sample is usually selected to be representative of the population in some way, so that the conclusions drawn from the sample can be generalized to the population as a whole.

The correct answer is C.

The purpose of the study is to determine why students who are interested in the college decide to enroll or not. Therefore, the population of interest is the group of students who submitted an application to the college in 2017.

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a) The drawing of all data points on a 2D plane is illustrated below.

b) The angle in between the five other points is 27

c) The matrix outer product for X is R = XXT.

d) The matrix outer product can also be calculated via R is (2,27)

The data matrix X is a 2-by-7 matrix, where each column represents a data point with two components. We can visualize each data point as a vector in a two-dimensional plane, where the horizontal axis represents the first component and the vertical axis represents the second component.

To draw all data points on a 2D plane, we can plot each column of X as a vector starting from the origin. Proper labeling of the two axes and providing important tick values will facilitate a precise graphical description of the data.

Next, we can use the inner product formula to calculate the angle between the first data point (2, 27) and the other five data points, respectively.

The inner product, also known as the dot product, is a way to measure the similarity between two vectors by multiplying their corresponding components and summing the products.

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Answer:

Based on the given information, we know that:

g(n) = 80 - 4g(n-1)

Also, we have the initial condition:

g(1) = g(n) = g(n-1)

Putting everything together, we can write the recursive formula for g(n) as follows:

g(1) = g(n) = g(n-1) (initial condition)

g(n) = 80 - 4g(n-1) (recursive formula)

where n > 1.

(please mark my answer as brainliest)

Using matrices, we can find that the products of EH and FG are defined, the rest does not satisfy.

A matrix is a rectangular array of values that are defined for mathematical operations including addition, subtraction, and multiplication.

The quantity of rows and columns in a matrix—also referred to as the order of the matrix—determines its size. A 6 4 symbol and 6 by 4 reading are used to symbolise and denote the order of a matrix having 6 rows and 4 columns.

Here in the question,

When the matrices, E and H are multiplied, the resulting matrix is a defined matrix.

Similarly, we can see when F and G are multiplied, the resulting matrix is a defined matrix.

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The inventory turnover ratio can be calculated by dividing the cost of goods sold by the average inventory value. In this case, the inventory turnover ratio is 0.5, and the correct answer is (D) 0.5.

The inventory turnover ratio measures the number of times a company sells and replaces its inventory during a period. It can be calculated by dividing the cost of goods sold by the average inventory value.

The inventory turnover ratio = Cost of goods sold / Average inventory value

In this case, the cost of goods sold is $600,000 and the average inventory value is $1,200,000.

Inventory turnover ratio = $600,000 / $1,200,000 = 0.5

Therefore, the inventory turnover ratio is 0.5, and the correct answer is (D) 0.5.

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Complete question:

If the average aggregate inventory value is $1,200,000 and the cost of goods sold is $600,000, which of the following is inventory turnover?

A)60

B)10.4

C)2

D)0.5

E)None of these

Answer:

D 20

Step-by-step explanation:

Let's call the integer we're looking for "x". We know that 18% of x is greater than 3.5, so we can write the inequality:

0.18x > 3.5

To solve for x, we can divide both sides by 0.18:

x > 3.5 ÷ 0.18

x > 19.44

We want the smallest possible integer that satisfies this inequality, which is 20. So the answer is D) 20.

Answer:

slope = 5

slope = (y2 - y1) / (x2 - x1)

Using this formula, calculate the slope between pairs of points in the given set of data. For example, the slope between the first two points (-2, -12) and (-1, -7) is:

slope = (-7 - (-12)) / (-1 - (-2)) = 5 / 1 = 5

Calculate the slope between each pair of points as follows:

Between (-2,-12) and (-1,-7): slope = 5

Between (-1,-7) and (0,-2): slope = 5

Between (0,-2) and (1,3): slope = 5

Between (1,3) and (2,8): slope = 5

Answer:

Example of a function that satisfies the following conditions:

a. Domain and range are both all real numbers except 5:

f(x) =

{

x if x ≠ 5

0 if x = 5

}

b. Domain is all positive numbers greater than 1, including 1:

f(x) =

{

(x-1)^2 / (x-1) if x > 1

0 if x = 1 or x = 5

}

c. Domain is all positive numbers greater than 1, but not including 1:

f(x) =

{

(x-1)^2 / (x-1) if x > 1 and x ≠ 1

0 if x = 1 or x = 5

}

The set of ordered pairs does not represent a function is the one in the third option.

{(-1,9), (-8, 5), (-1, 3), (-9, 1)}

A relation maps elements from one set, the domain, into elements of other set, the range.

Such that these mappings are of the form (x,y).

A function is a relation where each input is mapped into a single one output, then if you see a relation that has two points with the same value of x and different values of y, then that relation is not a function.

Particularly, if you look at the third option:

{(-1,9), (-8, 5), (-1, 3), (-9, 1)}

You can see that the first and second points have the same input and different outputs, then this is not a function, and that is the correct answer.

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Answer:

if u want total price then,

=Rs.35×80=Rs.2800

Answer:

The smallest possible average of five distinct positive even integers will occur if we choose the five smallest even integers. Since we want the integers to be distinct, we start with 2 and add the next four even integers:

2, 4, 6, 8, 10

The average of these five integers is:

(2 + 4 + 6 + 8 + 10) / 5 = 30 / 5 = 6

Therefore, the smallest possible average of five distinct positive even integers is 6, which is answer choice C.

By answering the presented questiοn, we may cοnclude that 0.4 οf an expressiοns hοur is 0.4 x 60 = 24 minutes in this situatiοn. As a result, 3.4 hοurs equals 3 hοurs and 24 minutes.

An expressive in mathematics is a collection of numbers, variables, and complicated mathematical operations (such as addition, subtraction, multiplication, division, multiplicands, and others) that convey a quantity's value. Expressions can be as straightforward as "3 + 4" or as complex as "(3x2 - 2) / (x + 1)". They could also include functions like "sin(x)" or "lg(y)".

The real way to evaluate an expression is to insert the variables with their values and carry out the arithmetic operations in the order specified. For instance, the phrase "3x + 5" means 3(2) + 5 = 11 if x = 2. In mathematics, expressions are typically used to describe actual situations, build equations, and decompose challenging mathematical diagrams.

3 hοurs and 24 minutes is cοmparable tο 3.4 hοurs.

Yοu may separate the full number (which represents the hοurs) frοm the decimal tο cοnvert decimal hοurs tο hοurs and minutes (which represents the fractiοn οf an hοur in minutes).

0.4 οf an hοur is 0.4 x 60 = 24 minutes in th

is situation. As a result, 3.4 hours equals 3 hours and 24 minutes.

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Answer: D

Step-by-step explanation:

i think so

Step-by-step explanation:

2x + ay + 2 = 0

the gradient or slope of the line is the factor m of x in the form

y = mx + b

so let's transform the given equation into that form :

ay = -2x - 2

y = (-2/a)x - 2/a

we know that m = 1.

so,

-2/a = 1

-2 = a

TRUE. Combinations and permutations are used in probability calculations to determine the number of possible outcomes in a sample space.

When order is important, permutations are utilized, and when order is not important, combinations are used. The formula P(n,r) = n!/(n-r)!, where n! signifies the factorial of n, and the expression C(n,r) = n!/r!(n-r)!, give the number of permutations of n items taken r at a time and the number of combinations of n objects taken r at a time, respectively.

It is possible to count the number of ways that a subset of items can be chosen from a larger set using both permutations and combinations. These ideas are crucial for estimating probabilities because they let us know how many different outcomes could satisfy a certain condition.

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The probability that a randomly selected bottle is correctly placed AND is a Plastic #4 bottle is 0.25 or 25%

What is Conditional probability?

Conditional probability is the probability of an event occurring given that another event has occurred or is known to have occurred. It is denoted by P(A|B), which reads as "the probability of A given B."

The formula for conditional probability is:

P(A|B) = P(A and B) / P(B)

where P(A and B) is the probability of both events A and B occurring, and P(B) is the probability of event B occurring.

The total number of Plastic #2 bottles is 8 (correctly placed) + 5 (incorrectly placed) = 13.

The total number of Plastic #4 bottles is 5 (correctly placed) + 2 (incorrectly placed) = 7.

The probability that a randomly selected bottle is correctly placed AND is a Plastic #4 bottle is given by:

(number of Plastic #4 bottles correctly placed) / (total number of bottles)

So the probability is:

5/20 = 1/4 = 0.25

Therefore, the probability that a randomly selected bottle is correctly placed AND is a Plastic #4 bottle is 0.25 or 25%.

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The piecewise function will be continuous in its domain if k = 49/48

Here we have a piecewise function and we want to find the value of k suc that the function is continuous on the domain.

To get that, both piecese of the function must ahve the same value in the jump, then we will get:

f(7) = f(7)

Replacing the functions we will get:

k·7²  = 7·7 + k

Let's solve that equation for k.

49k = 49 + k

49k - k = 49

48k = 49

k = 49/48

That must be the value of k such that the function is continuous in all its domain.

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Answer:

24 different lunches

Step-by-step explanation:

There are three choices for the beverage, two choices for the appetizer (soup or salad), and four choices for the sandwich. Therefore, using the multiplication principle of counting, the number of different lunches possible is:

3 choices for beverage x 2 choices for appetizer x 4 choices for sandwich = 24 different lunches.

The 1,262 students who received a merit scholarship, the amount they received varied per student and totaled an average of $3,458 ($454). That amount is 78.2% of the full tuition cost of $4,400.

Merit is a term used to describe the quality of something or someone that makes them worthy of recognition or respect. It is an indicator of worthiness and is usually based on a person's ability, effort, or accomplishments. Merit is often used when evaluating an individual or a group for a promotion, hiring, or award. Merit is subjective, as different people have different standards for what merits recognition.

Therefore, 21.8% of the students who received a merit scholarship did not receive enough to cover full tuition. Therefore, the percentage of students who received a merit scholarship and did not receive enough to cover full tuition is 21%.

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The measurement of angle PCD in equilateral triangle  is 67.38°.

Let $s$ be the side length of the square $abcd$, and let $O$ be the center of the square. Then $OP = s/\sqrt{2}$.

Since triangle $ABP$ is equilateral, we have $\angle ABP = 60^\circ$ and $AP=BP=s$. Let $E$ be the foot of the perpendicular from $P$ to $AB$. Then $AE=BE=s/2$ and $EP=s\sqrt{3}/2$.

Since $EP$ is perpendicular to $AB$ and $AB$ is parallel to $CD$, we have $\angle PCD = \angle ACE$.

Since $OP$ is perpendicular to $AB$, we have $\angle OEP = \angle AEP = 30^\circ$. Also, $OE=OP/\sqrt{2}=s/2$.

Using the Pythagorean theorem in triangle $OCE$, we have

CE= [tex]\sqrt{(OE)^{2} + (OC)^{2}} = \sqrt{(s/2)^{2} + s^{2}} = s\sqrt{5}/2[/tex]

Therefore, $\sin \angle ACE = CE/CP = \sqrt{5}/2$. Thus,

∠PCD = ∠ACE = arcsin(√5/2) ≈ 67.38°

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The correct option b) [tex]\rm y = \sqrt{x+ 3} + 3[/tex] is a function of the given graph.

The graph οf a relatiοn is said tο reflect a functiοn if a vertical line drawn anywhere οn the graph οnly intersects the graph οnce. In the event when a vertical line can graph is nοt a representatiοn οf a functiοn if there are mοre than twο pοints οn it.

The graphs coordinate is at (-3, 3)

Lets put the value in all the given function to find the correct function

a. [tex]\rm y = \sqrt{x - 3} + 3[/tex]

Using (-3, 3) as x and y

[tex]\rm 3 = \sqrt{(-3) - 3} + 3[/tex]

[tex]\rm 3 = \sqrt{9} + 3[/tex]

[tex]\rm 3 \neq 3 + 3[/tex]

[tex]\rm y = \sqrt{x - 3} + 3[/tex] is not a function of graph.

b. [tex]\rm y = \sqrt{x+ 3} + 3[/tex]

Using (-3, 3) as x and y

[tex]\rm 3 = \sqrt{-3+ 3} + 3[/tex]

[tex]\rm 3 = \sqrt{0} + 3[/tex]

[tex]\rm 3 = 0 + 3[/tex]

[tex]\rm 3 = 3[/tex]

[tex]\rm y = \sqrt{x+ 3} + 3[/tex] is a function of the given graph.

The other two options are no the functions as cube root is used and the value of x wont satisfy there.

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V is not a vector space, since at least one of the vector space axioms fails. Specifically, the axiom of closure under addition fails, since for any positive real numbers x and y, their sum xy may not be positive.

V is not a vector space, since some of the vector space axioms fail with the given operations.

Closure under addition fails For example, taking x=2 and y=3, we have xy = 6, but xy is not a positive real number, so xy is not in V.

Distributivity of scalar multiplication over vector addition fails For example, taking x=2, y=3, and c=-1, we have c(x+y) = cxy = -6, but cx + cy = -2 -3 = -5, which is not in V.

Other vector space axioms, such as associativity of addition, existence of additive identity and inverse, and compatibility of scalar multiplication with field multiplication, are still satisfied with the given operations.

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_____The given question is incomplete, the complete question is given below:

Let V be the set of all positive real numbers. Determine whether V is a vector space with the following operations. x + y = xy Addition cx = x Scalar multiplication If it is, then verify each vector space axiom; if it is not, then state all vector space axioms that fail. STEP 1: Check each of the 10 axioms. (1) U + v is in V. This axiom holds. This axiom fails. (2) U + V = V + u This axiom holds. This axiom fails. (3) U+ (v + w) = (u + v) + w This axiom holds. This axiom fails. STEP 2: Use your results from Step 1 to decide whether V is a vector space. O V is a vector space. O Vis not a vector space.

The people who are included in the survey conducted by Bureau of Labor Statistics are (a) certain unpaid workers, (b) part-time workers and (c) workers on vacation, the correct option is (d).

The Bureau of Labor Statistics (BLS) is a unit of the US Department of Labor that is responsible for collecting, analyzing, and publishing data on labor market activity, working conditions, and price changes in the economy.

The Bureau of Labor Statistics (BLS) considers individuals to be employed if they meet any of the given criteria:

(i) Worked at least one hour as paid employees

(ii) Worked at least 15 hours as unpaid workers in a family-owned enterprise

(iii) Were temporarily absent from their regular jobs due to illness, vacation, strike, etc.

⇒ This means that certain unpaid workers, such as family members working in a family-owned business, would be considered employed by the BLS.

⇒ Part-time workers, who work less than 35 hours per week but are paid for their work, are also included in the employed category.

⇒ The Workers on vacation are considered employed by the BLS because they are temporarily absent from their job.

Therefore, all the options are correct , which is Option(d).

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The given question is incomplete, the complete question is

Who of the following are included in the Bureau of Labor Statistics "employed" category?

(a) certain unpaid workers

(b) part-time workers

(c) workers on vacation

(d) All of the above are correct.

Answer:

D

Step-by-step explanation:

Sallys= 2(Jims) -5

Sally's + Jim's = 25

Answer:

Step-by-step explanation:

You want the system of equations that models, "Sally mows 5 less than twice the number of lawns Jim mows, and together they mow 25 lawns."

The letters 's' and 'j' represent the number of lawns that Sally and Jim mow, respectively.

Then "twice the number of lawns Jim mows" is represented be 2j. And 5 less than that is represented by 2j-5. Since this is the number of lawns Sally mows, the equation is ...

  s = 2j -5 . . . . . . . matches only one answer choice (D)

The equation for "together they mow 25 lawns" is ...

  s +j = 25

In response to the stated question, we may state that As a result, the overall probability of an accurately picked drive-thru order across all chains is roughly 0.929, or 92.9%.

Probability theory is an area of mathematics that calculates the likelihood of an occurrence or a proposition being true. A risk is a number in the range of 0 and 1, whereas 1 implies certainty and a probability of roughly 0 indicates how likely an event seems to be to occur. Probability is a mathematical expression of the chance or chances that a given event will occur. Probabilities can alternatively be stated as integers between 0 and 1 or as % from 0% to 100%. the ratio of occurrences among equally likely choices that result in a certain event in comparison to all other outcomes.

Using the data in the table, we can compute the likelihood of a correct drive-thru order for each fast food chain, as well as the overall chance of an accurate order across all chains.

Divide the number of accurate orders by the total number of orders to find the chance of a randomly picked order being accurate at each chain:

P(accurate order) = 1246 / 1300 = 0.958 for McDonald's

P(accurate order) = 1020 / 1100 = 0.927 Taco Bell

P(accurate order) = 708 / 800 = 0.885 for Burger King

P(accurate order) = 940 / 1000 = 0.94 for Wendy's

P(adequate overall order) = 0.3 * 0.958 + 0.25 * 0.927 + 0.2 * 0.885 + 0.25 * 0.94 = 0.929

As a result, the overall likelihood of an accurately picked drive-thru order across all chains is roughly 0.929, or 92.9%.

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answer: 175

Step-by-step explanation:

Answer:

71.9 degrees

Step-by-step explanation:

The find the value of x on the given diagram, we must first find the included angle between the two line segments labelled 94 mi and 119 mi in the triangle. To do this, we can use the Law of Cosines.

[tex]\boxed{\begin{minipage}{6 cm}\underline{Law of Cosines} \\\\$c^2=a^2+b^2-2ab \cos C$\\\\where:\\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides.\\ \phantom{ww}$\bullet$ $C$ is the angle opposite side $c$. \\\end{minipage}}[/tex]

The values to substitute into the formula are:

Solving for the angle C:

[tex]\begin{aligned}173^2&=119^2+94^2-2(119)(94)\cos C\\\\29929&=14161+8836-22372\cos C\\\\29929&=22997-22372\cos C\\\\6932&=-22372\cos C\\\\-\dfrac{6932}{22372}&=\cos C\\\\C&=\cos^{-1}\left(-\dfrac{6932}{22372}\right)\\\\C&=108.0502874...^{\circ}\end{aligned}[/tex]

As angles on a straight line sum to 180°, the value of x can be calculated by subtracting the found value of C from 180°:

[tex]x=180^{\circ}-108.0502874...^{\circ}[/tex]

[tex]x=71.9497125...^{\circ}[/tex]

[tex]x=71.9^{\circ}\; \sf (nearest\;tenth)[/tex]

Therefore, the ship turned 71.9 degrees north of west when it changed direction.

Answer:

a+b>0, a>0, b>0, a-b<0

Step-by-step explanation:

well, a>0 and b>0 since they're both positive

Answer:

sample answer

Step-by-step explanation:

The number further left on a number line is the smaller number. For positive numbers, the number closest to zero is smaller. For negative numbers, the number closest to zero is larger. If a is less than b, and they are both positive, then a is closer to 0 than b. The opposite of a is also closer to zero than the opposite of b, so the opposite of a must be larger than the opposite of b.

To construct a confidence interval for sigma the population from which the sample was drawn must be normally distributed. -

It is not necessary to make the normalcy assumption in order to build a confidence interval for sigma. To employ the central limit theorem, however, the sample size must be adequate which ideally enables the use of the normal distribution to approximate the sampling distribution of the sample variance. Alternative techniques, like t-distribution, can be employed if total sample size is limited.

It's also important to remember that, regardless of sample size, the distribution of sample variance will be normal if population is known and recognizable to have a normally distributed population. As long as the sample size is appropriate, the sample variance may still be utilized to create a confidence range for sigma even if the population is not normally distributed.

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