Divide negative 3 and one-sixth ÷ negative 8 and two-fifths.


252 over 95

95 over 252

51 over 30

30 over 51

A revenue function is a mathematical formula that represents the total income earned by a business or organization at different levels of output or sales. It is typically used in economics and finance.

(a) To find the revenue function, R(x), you need to multiply the number of memory sticks sold (x) by the price per unit (p). Using the given price function, p = 80000/x + 6. So,

R(x) = x * (80000/x + 6)

(b) To determine the cost function, C(x), use the financial department's estimates. The weekly fixed cost is 1500 dollars, and the additional cost per unit is 21 dollars. Therefore,

C(x) = 1500 + 21x

(c) To find the profit function, P(x), subtract the cost function from the revenue function:

P(x) = R(x) - C(x) = (x * (80000/x + 6)) - (1500 + 21x)

(d) To find the marginal profit when 20 memory sticks are produced and sold each week, you need to first find the derivative of the profit function with respect to x (P'(x)), and then evaluate it at x=20:

P'(x) = d/dx[(x * (80000/x + 6)) - (1500 + 21x)]

After calculating the derivative, evaluate P'(20) to find the marginal profit at 20 memory sticks produced and sold per week.

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Answer:

r=140

Step-by-step explanation:

Answer:

140

Step-by-step explanation:

The amount of money in Iris's checking account can be modeled by a linear function of the form:

y = mt + b

where y is the amount of money in the account, t is the time (measured in years), m is the rate of interest, and b is the initial amount in the account.

In this case, we have m = 0.04 (since the interest rate is 4% per year) and b = 180 (since that's the initial amount in the account). Therefore, the linear function that models the amount of money in Iris's checking account at any time t is:

y = 0.04t + 180

For example, if t = 5 (years), then the amount of money in Iris's checking account is 0.04 * 5 + 180 = 198 dollars.

The slope of the given equation of the line is -0.8 and the y-intercept = 0.4.

Given: y = -0.8x + 0.4

As we know that the slop-intercept form of the equation of a line is given by: y = mx + c, where

On comparing the given equation of line with the above form of equation of line, we get: m = -0.8 and c = 0.4.

Hence, The slope of the given equation of the line is -0.8 and the y-intercept = 0.4.

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Best guess for the function is

\(\displaystyle f(x) = \sum_{n=1}^\infty \frac{x^n}{n^2}\)

By the ratio test, the series converges for

\(\displaystyle \lim_{n\to\infty} \left|\frac{x^{n+1}}{(n+1)^2} \cdot \frac{n^2}{x^n}\right| = |x| \lim_{n\to\infty} \frac{n^2}{(n+1)^2} = |x| < 1\)

When \(x=1\), \(f(x)\) is a convergent \(p\)-series.

When \(x=-1\), \(f(x)\) is a convergent alternating series.

So, the interval of convergence for \(f(x)\) is the closed interval \(\boxed{-1 \le x \le 1}\).

The derivative of \(f\) is the series

\(\displaystyle f'(x) = \sum_{n=1}^\infty \frac{nx^{n-1}}{n^2} = \frac1x \sum_{n=1}^\infty \frac{x^n}n\)

which also converges for \(|x|<1\) by the ratio test:

\(\displaystyle \lim_{n\to\infty} \left|\frac{x^{n+1}}{n+1} \cdot \frac n{x^n}\right| = |x| \lim_{n\to\infty} \frac{n}{n+1} = |x| < 1\)

When \(x=1\), \(f'(x)\) becomes the divergent harmonic series.

When \(x=-1\), \(f'(x)\) is a convergent alternating series.

The interval of convergence for \(f'(x)\) is then the closed-open interval \(\boxed{-1 \le x < 1}\).

Differentiating \(f\) once more gives the series

\(\displaystyle f''(x) = \sum_{n=1}^\infty \frac{n(n-1)x^{n-2}}{n^2} = \frac1{x^2} \sum_{n=1}^\infty \frac{(n-1)x^n}{n} = \frac1{x^2} \left(\sum_{n=1}^\infty x^n - \sum_{n=1}^\infty \frac{x^n}n\right)\)

The first series is geometric and converges for \(|x|<1\), endpoints not included.

The second series is \(f'(x)\), which we know converges for \(-1\le x<1\).

Putting these intervals together, we see that \(f''(x)\) converges only on the open interval \(\boxed{-1 < x < 1}\).

Answer:

\(x^{2} -36 = 5x\)

\(x^{2} -5x -36 =0\)

(x-9)(x+4) = 0

x = 9 or x= -4    

Step-by-step explanation:

To determine if a function crosses the horizontal asymptote, analyse the behavior of the function as it approaches the asymptote and on either side of it.

1. Identify the horizontal asymptote of the function. The horizontal asymptote is a horizontal line that the function approaches as the independent variable (usually denoted as x) goes to positive or negative infinity. It is often denoted by a horizontal line y = a, where "a" is a constant.

2. Examine the behavior of the function as x approaches positive infinity. Evaluate the limit of the function as x goes to positive infinity. If the limit is equal to the value of the horizontal asymptote, then the function does not cross the asymptote. However, if the limit does not equal the asymptote, move to the next step.

3. Examine the behavior of the function as x approaches negative infinity. Evaluate the limit of the function as x goes to negative infinity. If the limit is equal to the value of the horizontal asymptote, then the function does not cross the asymptote. If the limit does not equal the asymptote, proceed to the next step.

4. Investigate the behavior of the function around critical points or points where the function changes its behavior. These points may include the x-intercepts or vertical asymptotes. Determine if the function crosses the asymptote around these points by analyzing the behavior of the function in their vicinity.

If, at any point in this process, the function crosses the horizontal asymptote, then it does not have a true horizontal asymptote. However, if the function approaches the asymptote and does not cross it at any point, then it has a horizontal asymptote.

It's important to note that some functions may have multiple horizontal asymptotes or no horizontal asymptote at all. The steps outlined above are a general guideline, but the specific behavior of the function needs to be analyzed to make a conclusive determination.

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Answer:

100

Step-by-step explanation:

85 +80+100+85+x(the unknown),/the number of numbers ie 5

350+x/5=90

350+x=90 * 5

350+x=450

x=450-350

x=100

The score on the last test in order to have a test average of 90 is 100.

Given that, Rob's first four test scores are 80, 85, 100 and 85.

We need to find the score on the last test in order to have a test average of 90.

By definition, an average is the arithmetic mean of the sum of all the values divided by the total number of values in a given set. An average is calculated for those sets of values which are more or less the same. The term average describes the numeric value that represents a large amount of data. An average can be derived by calculating the ratio of the sum of all the values to the number of units or values.

Let the score on the last test be x.

Now, average=(80+85+100+85+x)/5 =90

⇒350+x=450

⇒x=100

Therefore, the score on the last test in order to have a test average of 90 is 100.

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The simplified expression is y^5/3 * x^8/9. To simplify the expression (y^(5/2) * x^(4/3))^2, we need to apply the exponent rules. When raising a power to a power, we multiply the exponents. Therefore, we have:

(y^(5/2) * x^(4/3))^2 = y^((5/2)*2) * x^((4/3)*2) = y^5 * x^(8/3)

To write the answer with positive exponents, we can convert the fractional exponents to radicals. For y^5, the exponent 5 represents the fifth power, and for x^(8/3), the exponent 8/3 represents the cube root raised to the eighth power. Rewriting the expression with positive exponents, we have:

y^5 * x^(8/3) = y^5 * (x^(1/3))^8

Here, y^5 indicates the fifth power of y, and (x^(1/3))^8 indicates the eighth power of the cube root of x. The expression is now simplified and written with positive exponents.

It's important to note that the simplified expression assumes all variables represent positive numbers. If any of the variables are negative, additional considerations or transformations may be required to accurately simplify the expression.

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Answer:

2/3

Step-by-step explanation:

Answer:

you need to do the math then divide numerator by dumerstor then x 100

6.4 cm is the needed circumference of the gasket following dilatation with a scale factor of 2.

What does circumference mean?

The boundary length of any circular shape is known as the

circumference.

What is scale factor?

A scale factor is a quantity multiplier (also known as a scale). The scaling factor for x, for instance, is represented by the letter "C" in the equation y = Cx. The factor would be 5 if y = 5x were the equation.

According to the given data:

After scale factor 2 is applied, 6.4 cm must be the gasket's needed circumference.

It includes a rubber gasket with a 3.2 cm circumference. The circumference of the gasket has must be calculated after scaling up by factor 2.

Here,

3.2 cm is the gasket's circumference.

The circumference changed upon scale factor 2 dilatation.

Dilated gasket circumference: 2 * 3.2 = 6.4 cm

As a result, 6.4 cm is the needed circumference of the gasket following dilatation with a scale factor of 2.

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Answer:

C. 6.4 cm

Hope this helps!

Step-by-step explanation:

Answer:

194444.4

Step-by-step explanation:

The number of fish catch in 9 years were 48,477.37.

Exponential decay is a scalar multiple of the exponential distribution i.e. the individual lifetime of each object is exponentially distributed, which has a well-known expected value.

Given that the company's operations it managed to catch 70,000 fish.

The number of fish the company was able to catch decreased by 4% each year.

We need to find the number of fish catch in 9 years,

So, the exponential decay is to be used her, so,

Exponential decay = P(1-r)ⁿ

= 70,000(1-0.04)⁹

= 70,000 × 0.96⁹

= 48,477.37

Hence the number of fish catch in 9 years were 48,477.37.

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Answer:

-579

Step-by-step explanation:

The equation that describes the greatest horizontal length, H, in terms of the greatest vertical length, V, is \(H = \sqrt{ (V^2 + D^2)}\)

To create an equation that describes the greatest horizontal length, H, in terms of the greatest vertical length, V, we can use basic geometry principles.

Let's consider a right-angled triangle where V represents the vertical length and H represents the horizontal length. The hypotenuse of the triangle will be the greatest diagonal length.

According to the Pythagorean theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, the hypotenuse represents the greatest diagonal length.

Using the Pythagorean theorem, we can write the equation as:

\(H^2 = V^2 + D^2\)

Where H is the greatest horizontal length, V is the greatest vertical length, and D is the diagonal length (hypotenuse).

Since we are interested in expressing H in terms of V, we need to isolate H in the equation. Taking the square root of both sides gives us:

\(H = \sqrt{(V^2 + D^2)}\)

Therefore, the equation that describes the greatest horizontal length, H, in terms of the greatest vertical length, V, is:

\(H = \sqrt{ (V^2 + D^2)}\)

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The probability that at least 15 in the sample are among this group is given as follows:

0.9441 = 94.41%.

The z-score of a measure X of a variable that has mean symbolized by \(\mu\) and standard deviation symbolized by \(\sigma\) is obtained by the rule presented as follows:

\(Z = \frac{X - \mu}{\sigma}\)

The binomial distribution is the probability of x successes on n trials, with p probability of a success on each trial. It can be approximated to the normal distribution with \(\mu = np, \sigma = \sqrt{np(1-p)}\).

The parameters for the binomial distribution are given as follows:

n = 50, p = 0.4.

Hence the mean and the standard deviation for the approximation are of:

Using continuity correction, the probability that at least 15 in the sample are among this group is one subtracted by the p-value of Z when X = 14.5, hence:

\(Z = \frac{X - \mu}{\sigma}\)

Z = (14.5 - 20)/3.46

Z = -1.59

Z = -1.59 has a p-value of 0.0559.

1 - 0.0559 = 0.9441 = 94.41%.

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The value of gravitational force between two masses is,

⇒ Gravitational force (F) = 3

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Two masses are,

m₁ = 6

m₂ = 8

d = 4

Now, We know that;

Gravitational force (F) = m₁ m₂ / d²

Substitute all the values we get;

Gravitational force (F) = m₁ m₂ / d²

Gravitational force (F) = 6 × 8 / 4²

Gravitational force (F) = 48/16

Gravitational force (F) = 3

Thus, The value of gravitational force between two masses is,

⇒ Gravitational force (F) = 3

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Answer:

0.875

Step-by-step explanation:

Answer:

(\(\frac{5}{2}\)), \(-\frac{1}{2}\)

Step-by-step explanation:

Formula:

Add both "x" coordinates, divide by 2

Add both "y" coordinates, divide by 2

~I hope I helped you! :)~

Answer:

31.99, 34.23

Step-by-step explanation:

39.99 x .20=8 discount

39.99-8=31.99 tot price after discount

31.99x 1.07 (sales tax added)=34.23 total price with tax included.

Answer:

d = \(\frac{2}{5}\)

Step-by-step explanation:

\(\frac{3}{2}\) = 5d - \(\frac{1}{2}\)

multiply through by 2 to clear the fractions

3 = 10d - 1 ( add 1 to both sides )

4 = 10d ( divide both sides by 10 )

\(\frac{4}{10}\) = d , then

d = \(\frac{2}{5}\)

Answer:

  107 meters

Step-by-step explanation:

You want Nikko's distance from a 50 m high building if the angle of elevation to the top is 25°.

The tangent relation tells you the acute angle in a right triangle is related to the sides by ...

  Tan = Opposite/Adjacent

In this problem, the relation means ...

  tan(25°) = building height / distance to building

Solving for the distance to the building, we get ...

  distance to building = (building height)/tan(25°) = (50 m)/tan(25°)

  distance to building ≈ 107.225 m

Nikko is about 107 meters from the building.

Answer:

Step-by-step explanation:

You have a square with sides labeled (y-4), (3x-8), (2y-12), and you want to know the values of the variables as well as the side length.

All sides of the square are the same length. Equating two different y-expressions, we get ...

  y -4 = 2y -12

We can use the solution to that to find x:

  y -4 = 3x -8

Adding 12-y to the first of these equations gives us ...

  8 = y

Using this value in the second equation, we have ...

  8 -4 = 3x -8

  12 = 3x . . . . . . add 8

  4 = x . . . . . . . . divide by 3

The side length is ...

  y -4 = 8 -4 = 4

The values of the variables are x = 4, y = 8, and the side length of the square is 4.

Based on the AA Similarity Theorem, triangles PQR and TSR are proven to be similar to each other because they have two pairs of corresponding angles that are congruent to each other.

The AA (Angle-Angle) Similarity Theorem states that if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. This means that the corresponding sides of the triangles are in proportion to each other.

With the information given, the proof that shows that the two triangles are similar as as follows:

Statements                                         Reasons                                        

1. ∠QPR ≅ ∠STR                                1. Given

2. QR ⊥ PT                                         2. Given

3. ∠QRP ≅ ∠SRT                               3. def. of perpendicular

4. ΔPQR ~ ΔTSR                                4. AA Similarity Theorem

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Determining the 3PL with the most distribution space requires specific data on the size and capacity of each company's facilities.

The 3PL identified as having the most distribution (warehousing) space in square feet cannot be determined without specific information or data.

There are many asset-based 3PLs in the logistics industry, and their distribution space can vary significantly based on factors such as company size, industry focus, geographic coverage, and investments in facilities.

Without specific data on the distribution space of each asset-based 3PL, it is not possible to determine which one has the most square footage.

Asset-based 3PLs are companies that own and operate their own assets, such as warehouses, trucks, and equipment, to provide logistics and supply chain services.

These companies often make significant investments in their facilities to ensure efficient storage and distribution of goods for their clients.

Some large 3PL providers may have extensive warehousing networks and substantial distribution space, while smaller or specialized providers may have more focused or limited warehouse capacities.

Therefore, determining the 3PL with the most distribution space requires specific data on the size and capacity of each company's facilities.

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Answer:

5x – 30 = 176

Step-by-step explanation:

Answer:

Cost of shoes = $37.4925

Cost of jacket = $92.4533

Tax = $9.81

Total paid = $144.2458

Step-by-step explanation:

Normal price of shoes = $49.99

Discount = 25%

Discounted price:

\(\$49.99 - \$49.99\times \dfrac{25}{100} = \$37.4925\)

Normal price of jacket = $137.99

Discount = 33%

Discounted price:

\(\$137.99 - \$137.99\times \dfrac{33}{100} = \$92.4533\)

Price of pack of cookies = $4.49

No discount on cookies as per question statement.

Total amount without tax = $37.4925 + $92.4533 + $4.49 = $134.4358

Sales Tax = 7.3% of total amount without tax = 7.3% \(\times\) $134.4358 = $9.81

Total paid = $134.4358 + $9.81 = $144.2458

Answer:

13meters far from the supermarket

The distance between Supermarket A and Supermarket B is 35 units.

The distance formula which is used to find the distance between two points in a two-dimensional plane is also known as the Euclidean distance formula. On 2D plane the distance between two points (x₁, y₁) and (x₂, y₂) is Distance = √[(x₂-x₁)²+(y₂-y₁)²].

From the given coordinate plane, Supermarket A is at (12, 9), House is at (0, 0) and Supermarket B at (-16, -12).

1) Distance between Supermarket A and your house is

Substitute (x₁, y₁)=(12, 9) and (x₂, y₂)=(0, 0) in distance formula, we get

Distance = √[(0-12)²+(0-9)²]

= √144+81

= √225=15 units

2) Distance between Supermarket B and your house is

Substitute (x₁, y₁)=(-16, -12) and (x₂, y₂)=(0, 0) in distance formula, we get

Distance = √[(0+16)²+(0+12)²]

= √256+144

= √400=20 units

3) Distance between Supermarket A and Supermarket B is

Substitute (x₁, y₁)=(-16, -12) and (x₂, y₂)=(12, 9) in distance formula, we get

Distance = √[(12+16)²+(9+12)²]

= √28²+21²

= √1225=35 units

Therefore, the distance between Supermarket A and Supermarket B is 35 units.

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Answer:

y = 1

Step-by-step explanation:

horizontal asymptote

This is the value that the graph approaches but never reaches

It approaches 1 but never reaches 1

y = 1