Given the function f(x,y)=In (5x² + y²), answer the following questions
a. Find the function's domain
b. Find the function's range
c. Describe the function's level curves
d. Find the boundary of the function's domain.
e. Determine if the domain is an open region, a closed region, both, or neither
f. Decide if the domain is bounded or unbounded

a. Choose the correct domain of the function f(x,y)= In (5x² + y²)

O A. All values of x and y except when f(x,y)=y-5x generate real numbers
O B. All points in the xy-plane except the origini
O C. All points in the first quadrant
O D. All points in the xy-plane

Answer:

The answer would be $12. You would need to change the 30% to 0.3 then multiply by $20. Then take the -$6 and subtract it by $20.

The rate of increase of the y-coordinate as it approaches the point (1, 5) is 4 cm/s.At that instant, the x-coordinate of the point is not changing; it is staying at 1.

When a point reaches a certain coordinate, it means that the point is not changing anymore. In this case, the point has reached the coordinate (1, 5), which means that the x-coordinate (1) is not changing, while the y-coordinate (5) is increasing at a rate of 4 cm/s. Therefore, the x-coordinate of the point is not changing at that instant.

x = 1

Rate of Change (x-coordinate) = 0 cm/s

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The minimum sterilization time required to achieve a 99.9% confidence level in successfully sterilizing 50 L of medium containing 10^6 contaminating organisms is approximately 1.95 minutes.

To calculate the minimum sterilization time required to yield 99.9% confidence of successfully sterilizing 50 L of medium containing 10^6 contaminating organisms, we need to use the concept of decimal reduction time (D-value) and the number of organisms.

The D-value represents the time required to reduce the population of microorganisms by one log or 90%. In this case, the given D-value is 0.65 minutes.

To achieve a 99.9% confidence level, we need to reduce the population of microorganisms by three logs or 99.9%, which corresponds to a 10^-3 reduction.

To calculate the minimum sterilization time, we can use the following formula:

Minimum Sterilization Time = D-value × log10(N0/Nf)

Where:

D-value is the decimal reduction time (0.65 minutes).

N0 is the initial number of organisms (10^6).

Nf is the final number of organisms (10^6 × 10^-3).

Let's calculate it step by step:

Nf = N0 × 10^-3

= 10^6 × 10^-3

= 10^3

Minimum Sterilization Time = D-value × log10(N0/Nf)

= 0.65 minutes × log10(10^6/10^3)

= 0.65 minutes × log10(10^3)

= 0.65 minutes × 3

= 1.95 minutes

Therefore, the minimum sterilization time required to yield 99.9% confidence of successfully sterilizing 50 L of medium containing 10^6 contaminating organisms using this procedure is approximately 1.95 minutes

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A zero vertical asymptote removable discontinuity means that there is a zero of the function at the input value where the vertical asymptote would occur,

A zero of a function occurs when the value of the function is zero. A vertical asymptote of a function occurs when the value of the function becomes unbounded (either positive or negative) as the input approaches a certain value.

A removable discontinuity of a function occurs when there is a hole in the graph of the function at a certain input value, but the function can be made continuous at that point by defining its value at that input.

In the case of a zero vertical asymptote removable discontinuity, this means that there is a zero of the function at the input value where the vertical asymptote would occur, and the function can be made continuous at that input value by defining its value to be the value of the function at that input.

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Answer: 38/9

Step-by-step explanation: Because the fractions presented already have common denominators, the only thing you need to do in order to solve the problem is add the numerators. 36+2= 38, and you keep your denominator the same when adding fractions (when they are the same).

Answer:

Step-by-step explanation:

Step one

Given data

We are told that the rate of leakage is

60 barrels per minute

time = 1 hours= 60 minute

Required

The quantity of the oil that leaked after time = 1 hour= 60 minutes

Step two:

From

Rate=Quantity/time

Quantity= rate*time

Quantity= 60*60

Quantity= 3600 barrels

The length of the missing side is 8.9

We need to take note of the Pythagorean theorem

The Pythagorean theorem is a theorem that states that the square of the longest side of a triangle is equal to the sum of the squares of the other two sides of the triangle.

This theorem is represented as;

a² = b² + c²

Such that;

From the information given, we have that;

4² +8²= c²

find the squares

16 + 64 = c²

add the values

c = √80

Find the square root

c = 8. 9

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In order to calculate the time it will take for Andrew to settle the loan, we can use the formula for compound interest. So, it will take Andrew approximately 5.22 years to settle the loan.

The formula is given as A = P(1 + r/n)^(nt), Where: A = the final amount, P = the principal (initial amount borrowed), R = the annual interest rate, N = the number of times the interest is compounded in a year, T = the time in years.

We know that Andrew borrowed R200 000 from a bank at an annual interest rate of 5.25% compounded quarterly and that he will make repayments of R6 000 at the end of every 3 months.

Since the first repayment will be made 3 months from now, we can consider that the initial loan repayment is made at time t = 0. This means that we need to calculate the value of t when the total amount repaid is equal to the initial amount borrowed.

Using the formula for compound interest: A = P(1 + r/n)^(nt), We can calculate the quarterly interest rate:r = (5.25/100)/4 = 0.013125We also know that the quarterly repayment amount is R6 000, so the amount borrowed minus the first repayment is the present value of the loan: P = R200 000 - R6 000 = R194 000

We can now substitute these values into the formula and solve for t: R194 000(1 + 0.013125/4)^(4t) = R200 000(1 + 0.013125/4)^(4t-1) + R6 000(1 + 0.013125/4)^(4t-2) + R6 000(1 + 0.013125/4)^(4t-3) + R6 000(1 + 0.013125/4)^(4t)

Rearranging the terms gives us: R194 000(1 + 0.013125/4)^(4t) - R6 000(1 + 0.013125/4)^(4t-1) - R6 000(1 + 0.013125/4)^(4t-2) - R6 000(1 + 0.013125/4)^(4t-3) - R200 000(1 + 0.013125/4)^(4t) = 0

Using trial and error, we can solve this equation to find that t = 5.22 years (rounded to 2 decimal places). Therefore, it will take Andrew approximately 5.22 years to settle the loan.

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1 When four more than ten times a number is twenty-four. The number is 2.

2. When four less than eight times a number is twenty. The number is 3.

3. When the difference between ten times a number and two is twenty-eight. The number is 3.

4. When five more than the quotient of a number and six is fifteen. The number is 60.

5. When four less than four times a number and six is twenty-eight. The number is 6.5.

1. Let the number be x

Four more than ten times a number is twenty-four.

10x + 4 = 24

10x = 24 - 4

10x = 20

Divide

x = 20/10

x = 2

The number is 2.

2. Four less than eight times a number is twenty. Let the number be x.

8x - 4 = 20

8x = 20 + 4

8x = 24

Divide

x = 24 / 8

x = 3

The number is 3.

3. The difference between ten times a number and two is twenty-eight. Let the number be x.

(10 × x) - 2 = 28

10x - 2 = 28

Collect the like terms

10x = 28 + 2

10x = 30

Divide

x = 30 / 10

x = 3

4. Five more than the quotient of a number and six is fifteen. Let the number be n.

n/6 + 5 = 15

n/6 = 15 - 5

n/6 = 10

Cross multiply

n = 6 × 10

n = 60

5. Four less than four times a number and six is twenty-eight. Let the number be n.

(4n + 6) - 4 = 28

4n + 2 = 28

Collect the like terms

4n = 28 - 2

4n = 26.

Divide

n = 26 / 4

n = 6.5

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If the original quantity is 8 and the new quantity is 2, then the correct answer is 75%.

For this question we need to subtract and multiply the numbers. We know that 2 = 25% of 8 so:

\(\boxed{8-2=6}\\\boxed{6/2=3}\)

We are going to take that 25% and multiply it with 3 to get are final answer.

\(\boxed{25*3=75}\\\boxed{So,2=75}\)

Therefore, If the original quantity is 8 and the new quantity is 2, then the correct answer is 75%.

Answer:

You can just flip a coin five times either with a real one (heads being a face or a picture and tails being the other side) or online, then put a tick on either heads or tails depending on what you got on that toss. Then just put how many times you got heads in the first question.

Hope this helps I guess.

Answer:

197 pounds of cans

Step-by-step explanation:

Find how many pounds of cans they have collected by subtracting 8 from both of their barrel weights:

115 - 8

= 107

98 - 8

= 90

Add these two weights together:

107 + 90

= 197

So, they collected 197 pounds of cans

After 3 years, the balance in the account would be approximately $2,708.

To find the balance after 3 years for an account that pays 2.5% annual interest compounded monthly, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A is the final balance

P is the principal amount (initial deposit)

r is the annual interest rate (as a decimal)

n is the number of times the interest is compounded per year

t is the number of years

In this case:

P = $2500

r = 2.5% = 0.025 (as a decimal)

n = 12 (monthly compounding)

t = 3 years

Plugging in these values into the formula, we get:

A = $2500(1 + 0.025/12)^(12*3)

A = $2500(1.00208333333)^(36)

Using a calculator, we can evaluate the expression inside the parentheses and calculate the final balance:

A ≈ $2500(1.083282498) ≈ $2708.21

Therefore, after 3 years, the balance in the account would be approximately $2,708.

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The travel time x is 41.162 min such that 17.36% of the 60 days have a travel time that is at least x.

We have to determine the travel time such that 17.36% of the 60 days have a travel time that is at least.

Total work days to work = 60 days

The travel mean time = 35.6

Standard deviation = 10.3

For normal distribution,

P(X < A) = P(Z < (A - mean)/standard deviation)

P(X > x) = 0.2946

P(X < x) = 1 - 0.2946 = 0.7054

P(Z < (x - 35.6)/10.3) = 0.7054

Take the z value that corresponds to 0.7054 in the table of the standard normal distribution.

(x - 35.6)/10.3 = 0.54

x = 41.162 min

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Answer:

Step-by-step explanation:

90-28=62

62 is the answer

Answer:

60m^3

Step-by-step explanation:

In order to find the volume of this shape, you must solve the volume of the 2 different portions separately. You can do this by considering both of them to be rectangular prisms.

The smaller portion has a length of 1, a height of 2, and a depth(? im not sure if its called depth) of 3, you can get the 3 from the depth(?) of the larger one.

Since the volume of a rectangular prism is length x width x depth(?), the smaller figure has an volume of 6 m cubed, or 6m^3

The larger figure has a length of 6, a height of 3, and a depth(?) of 3, meaning you can multiply 3 x 3 x 6, which gives 54, which means the larger figure's volume is 54m^3

Now, you add the volumes of both figures, which gives a volume of 60m^3.

Answer:

Step-by-step explanation:

In a case whereby Adam traveled out of town for a regional basketball tournament. He drove at a steady speed of 72.4 miles per hour for 4.62 hours. The exact distance Adam traveled was miles Adam traveled a distance of about 335 miles.

The distance traveled in a unit of time is called speed. It refers to a thing's rate of movement. The scalar quantity known as speed is the velocity vector's magnitude. It has no clear direction.

Speed = Distance/ time

speed =72.4 miles

time=4.62 hours

Distance =speed * time

= 72.4 *4.62

Distance = 334.488 miles

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complete question;

Adam traveled out of town for a regional basketball tournament. He drove at a steady speed of 72.4 miles per hour for 4.62 hours. The exact distance Adam traveled was miles. Rounding decimals to the nearest whole number, Adam traveled a distance of about miles.

The volume of the gas approximately directly proportional to its number of moles of gas when both temperature and pressure are constant.

V∝ n at constant P and T

V = constant × (n)

Vn = constant

This can be mathematically stated as follows: As before, we can anticipate what will change to the volume of the a sample of gas as we adjust the number of moles using Avogadro's law.

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Angles theorem and Reflexive property of congurence

The solution is

Each diagonal of a parallelogram separates it into two congruent triangles

So , ΔABC ≅ ΔCDA

Opposite angles are congruent

So , ∠B ≅ ∠D

What is a Parallelogram?

A parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure

The four types are parallelograms, squares, rectangles, and rhombuses

Properties of Parallelogram

Opposite sides are parallel

Opposite sides are congruent

Opposite angles are congruent.

Same-Side interior angles (consecutive angles) are supplementary

Each diagonal of a parallelogram separates it into two congruent triangles

The diagonals of a parallelogram bisect each other

Given data ,

Let the parallelogram be ABCD

Now , AC is a diagonal of the parallelogram

According to the postulates of parallelogram

Opposite sides are parallel

Opposite sides are congruent

Opposite angles are congruent

Same-Side interior angles (consecutive angles) are supplementary

Each diagonal of a parallelogram separates it into two congruent triangles

The diagonals of a parallelogram bisect each other

And ,

From the figure , we can deduct that ΔABC ≅ ΔCDA by

Angle A is congruent to angle C, and angle D is congruent to angle B

So , from congruent triangle theorem ΔABC ≅ ΔCDA

And ,

∠B ≅ ∠D

Because Opposite angles are congruent of a parallelogram

Hence , Each diagonal of a parallelogram separates it into two congruent triangles

So , ΔABC ≅ ΔCDA

Opposite angles are congruent

So , ∠B ≅ ∠D

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Answer:

2.38 Kg were eaten

Step-by-step explanation:

first we should divide 34 by 100

the result will be 0.34

then we multiply 0.34 x 7 Kg = 2.38 Kg

If a random variable "z" follows a standard normal distribution and the probability of "z" being greater than "k" is 0.39, then the value of "k" such that satisfies the equation [p(z > k) = 0.39] will be 0.28

As per the question statement, a random variable "z" follows a standard normal distribution.

We are required to determine the value of "k" such that the equation   [p(z > k) = 0.39] is satisfied.

To solve this question, first we will have to calculate the probability of "z" being greater than "k" and then from the Z-table, we will determine the z-score corresponding the above calculated probability value. This z-score will be our desired answer, i.e.,

Given, P(Z > k)  = 0.39

Or, P(Z < k) = (1 - 0.39)

Or, P(Z < k) = 0.61

Now, from the Z table, we get the z-score corresponding to probability value of 0.61 is 0.28

Hence, (k = 0.28)

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It would be 768 because you just keep multiplying by 2.

Answer:768

Step-by-step explanation:

Multiply by 2

For example:

6 at the start(6 × 2 ) 12 then 12 × 2 and so on

Answer:

Rate of boat in still water = 56 km per hour

Rate of the current = 8 km per hour

Step-by-step explanation:

This question is incomplete; to understand how to solve these questions let the question is,

A motorboat takes 4 hours to travel 192 km going upstream. The return trip takes 3 hours going downstream. What is the rate of the boat in still water and what is the rate of current.

Let the rate of current = u km per hour

And the rate of boat in still water = v km per hour

Then going upstream, rate of the boat = Rate of the boat in still water - Rate of current

= (v - u) km per hour

Similarly, going downstream, rate of the boat = Rate of boat in still water + Rate of current

= (v + u) km per hour

Since, the boat takes 4 hours upstream,

By using the formula,

Rate = \(\frac{\text{Distance}}{\text{Time}}\)

Distance traveled = Rate × Time

For upstream,

192 = 4(v - u)

v - u = 48 ------(1)

For downstream,

192 = 3(v + u)

v + u = 64 ------(2)

By adding equation (1) and (2),

(v - u) + (v + u) = 48 + 64

2v = 112

v = 56 km per hour

From equation (1),

56 - u = 48

u = 56 - 48

u = 8 km per hour

Rate of boat in still water = 56 km per hour

Rate of the current = 8 km per hour

Answer:

y = -1/2 = -0.500

Step-by-step explanation:

your welcome have a good day :)

stay safe

stay hydrated

wear a mask

┐(^▂ ^ ；)┌

Answer:

x=32

Step-by-step explanation:

Multiply both sides by 4.

(x/4)*(4) = (8)*(4)

The weighted average cost of capital (WACC) for company C is 6.63%.

The weighted average cost of capital (WACC) is a financial metric that represents the average rate of return a company must earn on its investments to satisfy its shareholders and creditors. It takes into account the proportion of debt and equity in a company's capital structure and the respective costs associated with each.

To calculate WACC, we need to consider the cost of debt and the cost of equity. The cost of debt is the interest rate a company pays on its debt, adjusted for taxes. In this case, the pre-tax cost of debt is 2% and the tax rate is 24%. Therefore, the after-tax cost of debt is calculated as (1 - Tax Rate) multiplied by the pre-tax cost of debt, resulting in 1.52%.

The cost of equity represents the return required by equity investors to compensate for the risk associated with owning the company's stock. Here, the cost of equity for company C is 6%.

The debt represents 10% of the total capital, while the equity represents the remaining 90%. To calculate the weighted average cost of capital (WACC), we multiply the cost of debt by the proportion of debt in the capital structure and add it to the cost of equity multiplied by the proportion of equity.

WACC = (Proportion of Debt * Cost of Debt) + (Proportion of Equity * Cost of Equity)

In this case, the calculation is as follows:

WACC = (0.10 * 1.52%) + (0.90 * 6%) = 0.152% + 5.4% = 6.552%

Therefore, the weighted average cost of capital (WACC) for company C is approximately 6.63%.

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"Financial" as it is not an effectiveness MIS metric.

To determine which one is not an effectiveness MIS metric, we need to understand the purpose of these metrics. Effectiveness MIS metrics measure how well a system is achieving its intended goals and objectives.

Customer satisfaction is a common metric used to assess the effectiveness of a system. It measures how satisfied customers are with the product or service provided.

Conversion rates refer to the percentage of website visitors who complete a desired action, such as making a purchase. This metric is often used to assess the effectiveness of marketing efforts.

Financial metrics, such as revenue and profit, are crucial indicators of a system's effectiveness in generating financial returns.

Response time measures the speed at which a system responds to user requests, which is an important metric for evaluating system performance.

Therefore, based on the given options, "Financial" is not a type of effectiveness MIS metric. It is a separate category of metrics that focuses on financial performance rather than the overall effectiveness of a system.

In summary, the answer is "Financial" as it is not an effectiveness MIS metric.

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Proportional relationship are used to represent direct variations.

The equation that represents the proportional relationship is \(y = \frac{28}{17}x\)

From the question,

When x = 34, y = 56

So, the proportionality constant (k) is calculated as:

\(k = \frac yx\)

This gives

\(k = \frac {56}{34}\)

Reduce the fraction

\(k = \frac {28}{17}\)

The proportional relationship is then calculated as:

\(y = kx\)

This gives

\(y = \frac{28}{17}x\)

Hence, the equation that represents the proportional relationship is \(y = \frac{28}{17}x\)

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Answer: 1 1/9x

Step-by-step explanation: