Find the limit, if it exists, or show that the limit does not exist.
Lim(x,y,z) → (0,0,0) xy+yz+xz / x^2+y^2+z^2

The factors of 180 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90 and 180.

A number or algebraic expression that divides another number or expression evenly—i.e., with no remainder. For example, 3 and 6 are factors of 12 because 12 ÷ 3 = 4 exactly and 12 ÷ 6 = 2 exactly. The other factors of 12 are 1, 2, 4, and 12.

The factors of 180 are integers that divide 180 without leaving any remainder, or in other words, the factors of 180 are divisors of 180.

For example, 90 is a factor of 180 because when we divide 180 by 90, it gives us 2 as the quotient and 0 as the remainder. The quotient 2 is also a factor of 180.

So, to check if any number is a factor of 180, divide 180 by that number and check if the remainder is zero or not.

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Answer:

after working for at least 10 1/4 years

Step-by-step explanation:

After working for at least  10 1/4 years  a project manager would be eligible for a $20,000 monthly salary.

A quadratic equation, \(ax^{2} +bx+c=0\) is solved by

\(x=\frac{-b \pm \sqrt{b^2-4ac} }{2}\)

Given function \(f(x)=x^4-10x^2+10000\)

Function that has monthly salary $20,000 will be \(x^4-10x^2+10000=20000\)

\(x^4-10x^2+10000-20000=0\)

\(x^4-10x^2-10000=0\)

Now using the formula \(x=\frac{-b \pm \sqrt{b^2-4ac} }{2}\)

\(x^2=\frac{10 \pm \sqrt{10^2+40000} }{2}\)

\(x^2=\frac{10 \pm \sqrt{40100} }{2}\)

\(x^2=\frac{10 \pm 200.2}{2}\)

\(x^2=5 \pm 100.1\)

\(x^2=105.1\)

\(x=\sqrt{105.1}\)

\(x=10.25\)

Hence, after working for at least  10 1/4 years  a project manager would be eligible for a $20,000 monthly salary.

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The area of the region enclosed by the curves 10x=2y²+12y+19 and x=-4y-10 is 174/3 units².

To find the area of the region enclosed by the curves 10x=2y²+12y+19 and x=-4y-10, we need to solve this problem in the following way:

Since the curves are already in the form of x = f(y), we need to use vertical strips to find the area.

So, the integral for the area of the region is given by:

A = ∫a b [x₂(y) - x₁(y)] dy

Here, x₂(y) = 10 - 2y² - 12y - 19/5 = - 2y² - 12y + 1/2 and x₁(y) = -4y - 10

So,

A = ∫(-3)⁻²[(-2y² - 12y + 1/2) - (-4y - 10)] dy + ∫(-2)⁻²[(-2y² - 12y + 1/2) - (-4y - 10)] dy

=> A = ∫(-3)⁻²[2y² + 8y - 19/2] dy + ∫(-2)⁻²[2y² + 8y - 19/2] dy

=> A = [(2/3)y³ + 4y² - (19/2)y]₋³ - [(2/3)y³ + 4y² - (19/2)y]₋² | from y = -3 to -2

=> A = [(2/3)(-2)³ + 4(-2)² - (19/2)(-2)] - [(2/3)(-3)³ + 4(-3)² - (19/2)(-3)]

=> A = 174/3

Hence, the area of the region enclosed by the curves is 174/3 units².

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Answer:

  36.4%

Step-by-step explanation:

You want the percentage change from $22 to $30.

The percentage change is given by the formula ...

  percent change = ((new value)/(old value) -1) × 100%

  = (30/22 -1)(100%) ≈ 36.4%

The stock increased in value by about 36.4%.

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Answer:

A

Step-by-step explanation:

4x + 104 = 180

4x = 180 - 104

4x = 76

x = 76/4

x = 19°

Step-by-step explanation:

\( \sqrt{(x + 6) ^{2} } = \sqrt{18} \\ x + 6 = + - \sqrt{18} \\ x + 6 = + - \sqrt[3]{2} \)

Answer:

To three decimal places, The process capability index is 0.167

Step-by-step explanation:

We have to find the process capability index,

Upper specification = 16.5 ounces,

Lowe specification = 15.5 ounces

Mean = 16.0 ounces

Standard Deviation = S = 1 ounce

process capability index = (upper specification - lower specification)/6S

process capability index = (16.5 - 15.5)/6(1)

= 1/6

Process capability index = 1/6 = 0.16666667

To 3 decimal places, we get,

Process capability index = 0.167

A positive correlation is a relationship between two variables such that their values increase or decrease together.

This is TRUE statement.

If the decreases in the X variable it means accompanied to the decrement of Y variable. Hence, the correlation between the X and Y ia always negative. Now, for positive correlation, if the X variable is decrease then the accompanied by decreases in the Y variable.

The Pearson correlation measures the degree to which the X and Y data points fit on a straight line.

A positive correlation relationship between X and Y: as X increases, Y increases.

A negative correlation  relationship between X and Y: as X increases, Y decreases. It is opposite to X and Y in the case of negative. If correlation of zero it means no linear relationship between X and Y.

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The area of a rectangle is given by the product of its dimensions.

If this rectangle has a length of 2x + 7 and a width of x + 4, its area is:

The perimeter is the sum of all side lengths, so we have:

Answer:

B. -8

Step-by-step explanation:

Company: Amazon, 8 Steps in the Business Model: Define the value proposition. What value does Amazon offer its customers? Amazon offers a convenient and affordable way to shop for a wide variety of products.

Identify the target market. Who are Amazon's customers? Amazon's target market is people who want to buy products online.

Determine the revenue streams. How does Amazon make money? Amazon makes money through product sales, advertising, and subscription fees.

Assess the cost structure. What are Amazon's costs? Amazon's costs include salaries, rent, and marketing.

Develop a marketing plan. How will Amazon reach its target market? Amazon's marketing plan includes online advertising, search engine optimization, and social media marketing.

Create a sales strategy. How will Amazon sell its products? Amazon's sales strategy includes a focus on customer service and convenience.

Build a team. What skills and experience does Amazon need to build a successful business? Amazon needs a team with a variety of skills, including product development, marketing, and sales.

Continuously improve. How will Amazon ensure that its business model is successful? Amazon will continuously improve its business model by listening to customer feedback and adapting to changes in the market.

The 8 steps in the business model are essential for any company that wants to be successful. By following these steps, companies can ensure that they are offering a valuable product or service to the right customers, and that they are able to make money.

In the case of Amazon, the company has clearly defined its value proposition, target market, and revenue streams.

Amazon's marketing plan is also effective, and the company has built a team with the skills and experience necessary to be successful. Finally, Amazon is committed to continuous improvement, which is why the company has been so successful over the years.

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The expected value of M is described as C: "it is the mean of the distribution of sample means.

In probability theory, the expected value of M is a generalization of the weighted average. In informal words, the expected value refers to the arithmetic mean of a large sample of independently chosen outcomes of a random variable.

Thus, the mean of the distribution of sample means is referred to as the 'expected value' of M. And it is always equal to the mean μ of the population. So the correct answer pertaining to this question is held in option 'C'.

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The probability that the number of people who show up will exceed the capacity of the plane is 0.002607722

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

The probability that x people show up follows a binomial distribution,

\(P(x)=\frac{n!}{x!(n-x)!}*p^{x}*(1-p)^{n-x}\)

Here, n represents the number of booked people and p represents the probability that a person shows up.

Then, the probability that x people show up is:

\(P(x)=\frac{78!}{x!(78-x)!}*0.90^{x}*(1-0.90)^{78-x}\)

So, the probability that the number of people who show up will exceed the capacity of the plane is:

P(x>76) = P(77) + P(78)

Where P(77) and P(78) are calculated as follows:

\(P(77)=\frac{78!}{77!(78-77)!}* 0.90^{77}* (1-0.90)^{78-77} \\ =78*0.00029969*0.10\\ =0.0023375\)

\(P(78)=\frac{78!}{78!(78-78)!}* 0.90^{78}* (1-0.90)^{78-78} \\ =1*0.00026972*1\\ =0.00026972\)

Finally, P(x>76) is:

\(P(x > 76) = 0.0023375 + 0.00026972\\=0.002607722\)

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Answer:

235 cm²

Step-by-step explanation:

Area can be split into top and bottom rectangles.

Area = 11 x (14 - 9) + 9 x 20

= 11 x 5 + 180

= 55 + 180

= 235 cm²

To find the limit of the given function, we need to approach the point (0, 0) along different paths and check if the limit exists and if it is the same along all the paths. Let's consider the limit along the x-axis first, i.e., when y = 0. In this case, the function reduces to lim (x, 0)→(0, 0) 0 = 0.

Now, let's consider the limit along the y-axis, i.e., when x = 0. In this case, the function reduces to lim (0, y)→(0, 0) 0 = 0. So far, it seems like the limit exists and is equal to 0. However, let's now consider the limit along the curve y = x. In this case, the function reduces to lim (x, x)→(0, 0) x^3 cos(x) / (6x^4) = cos(0)/6 = 1/6. Since the limit is different along this path, we can conclude that the limit does not exist. Therefore, the answer is "dne."

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Answer:

5) 4а²+8ас=4а(а+2с)

6) 3m²-6mn=3m(m-2n)

7) ab-ac+yb-yc=a(b-c)+y(b-c)=(a+y)(b-c)

8) ab+ac+xb+c=b(a+x)+c(a+1)

Answer:

B. 5k + 11l

Step-by-step explanation:

Add similar terms:

3k + 2k = 5k

5l + 6l = 11l

Therefore:

3k + 5l+ 6l + 2k = 5k + 11l

The least number of main courses that the restaurant should offer is 8.

The mathematical expression with unequal sides is known as an inequality in mathematics. Inequality is referred to in mathematics when a relationship results in a non-equal comparison between two expressions or two numbers. In this instance, any of the inequality symbols, such as greater than symbol (>), less than symbol (), greater than or equal to symbol (), less than or equal to symbol (), or not equal to symbol (), is used in place of the equal sign "=" in the expression. Polynomial inequality, rational inequality, and absolute value inequality are the various types of inequalities that can exist in mathematics.

let m be  the number of main courses restaurant serves

so, 2m is the number of appetizers  

then the number of dinner combination is =  2m x m x 3 = 6m^2

since the customer wants to eat a different dinner in all 365 days of 2003,

we must have ,

\(6m^{2}\) ≥  365

\(m^{2}\)  ≥ 60.83.....

also the 2003 is not a leap year

because 2003 / 4 is not equal to an integer

the smallest integer value satisfies this is 8 .

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Answer:

It will take them 7.89 days

Answer:

C (-2,0)

D (-5,3)

A (0, 5)

B (1, 3)

Step-by-step explanation:

All your points (x,y) become (-x,-y) when you rotate 180 degrees about the origin.

The solution to the system of equations is x = 5 and y = -1.

Simultaneous equations, a system of equations Two or more equations in algebra must be solved jointly (i.e., the solution must satisfy all the equations in the system). The number of equations must match the number of unknowns for a system to have a singular solution.

There are four methods for solving systems of equations: graphing, substitution, elimination, and matrices.

Given a system of equation 2x - 6y = 16 and x + y = 4

Let's start with the second equation:

x + y = 4

We can solve for one of the variables, say y, by subtracting x from both sides:

y = 4 - x

Now we can substitute this expression for y into the first equation:

2x - 6y = 16

2x - 6(4 - x) = 16

Expanding and simplifying, we get:

2x - 24 + 6x = 16

Combining like terms, we get:

8x - 24 = 16

Adding 24 to both sides, we get:

8x = 40

Dividing both sides by 8, we get:

x = 5

Now we can substitute this value of x into either of the original equations to find y. Let's use the second equation:

x + y = 4

5 + y = 4

Subtracting 5 from both sides, we get:

y = -1

Therefore, The solution to the system of equations is x = 5 and y = -1.

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Answer:

The third one, I think.

Step-by-step explanation:

Hopes this helps. <3

Answer:

40 points

Step-by-step explanations

divide 50 by 5 to get the number of answers

you get 10 answers so then you subtract 2 and get 8

times that by 5 and you get the answer 40

Based on the given conditions, formulate: 

34÷1 1/3

Find common denominator and write the numerators above common denominator:

34/3/3+1/3

Write the numerators over common denominator:

34/3+1/3

Calculate the sum or difference:

34/4/3

Divide a fraction by multiplying its reciprocal:34×3/4

Cross out the common factor:

17×3/2

Calculate the product or quotient:

51/2

get the result:

25.5 or 25 1/2

=25.5 or 25 1/2

Answer:Solution for 0.3(y-2)+0.4y=0.3y-0.6 equation:

0.3(y-2)+0.4y=0.3y-0.6

We move all terms to the left:

0.3(y-2)+0.4y-(0.3y-0.6)=0

We add all the numbers together, and all the variables

0.4y+0.3(y-2)-(0.3y-0.6)=0

We multiply parentheses

0.4y+0.3y-(0.3y-0.6)-0.6=0

We get rid of parentheses

0.4y+0.3y-0.3y+0.6-0.6=0

We add all the numbers together, and all the variables

0.4y=0

y=0/0.4

y=0

The given numbers are:(10 1010 1010)2 and (1 1111 0001)2To find the sum of two binary numbers, we can add them using binary addition.

Similarly, to find the product of two binary numbers, we can multiply them using binary multiplication.Therefore, using binary addition:1 1 1 1 1 0 0 0 1 0(10 1010 1010)2+ (1 1111 0001)2-------------------1 0 0 1 0 1 1 0 1 1(11 1010 1011)2Therefore, the sum of the given binary numbers is (1 0 0 1 0 1 1 0 1 1)2To find the product of two binary numbers,

we use binary multiplication.(10 1010 1010)2 × (1 1111 0001)2---------------------------(10 1010 1010)2(×) (1) (1 0101 0101 0)2(×) (1 1111 0001)2--------------------------(10 1011 0001 1 0 1 0)2Therefore, the product of the given binary numbers is (10 1011 0001 1 0 1 0)2.Note: To represent the binary number, (10 1011 0001 1 0 1 0)2, it is better to split it into groups of 4 starting from the right side. Therefore, it can be written as (1 0101 1000 1110 1010)2.

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