The total revenue for Jane’s Vacation rental is given as the function R(x) = 100x-0.2x squared where x is the number of rooMs filled. What number of rooms filled produced the maximum revenue

Answer:

c.  1/3

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

Find points from graph.

Point (0, -1)

Point (3, 0)

Step 2: Find slope m

Simply plug in the 2 coordinates into the slope formula to find slope m

The correct standard deviation here is 24.25

You can adjust the standard deviation accurately, using a VERY useful algebraic identity.

Given that we don’t have all the xi or the xi - mean, but here’s a nice identity:

sum( (xi - mean )2) = sum(xi2) - (1/n)( sum(xi) )2

in other words,

(sum of the squares) minus (1/n)*(square of the sum)

We will start with the original numbers before the error was detected:

STD = 10

Sum(xi) = 4000

using the new identity,

std = \(\sqrt\)(sum(xi2) - (1/n)( sum(xi) ))2

From this, we can solve for sum(xi2)

std2= sum(xi2) - (1/n)(( sum(xi) )2)

sum(xi2) = std2 + (1/n)( (sum(xi))2  )

100 + 40002/100 = 160100

Now we can change those numbers to make the new standard deviation

The new sum(xi ) is the old sum minus the erroneous scores (30 and 70) plus the correct values (3 and 27) =

4000 -30 -70 + 3 + 27 = 3930

The new sum(xi2) Is the old sum minus the squares of the erroneous scores (900 and 4900) plus the squares of the correct scores (9 and 729) = 160100 -5800 + 738 = 154300+738 = 155038

Now the new standard deviation is

std = \(\sqrt(sum(xi2)\) - (1/n)( (sum(xi))2)

= \(\sqrt( 155038 - 39302/100)\\= \sqrt( 155038 - 15444900/100)\\= \sqrt( 155038 - 154449)\\= \sqrt( 589 )\)

= 24.25

Therefore, the correct standard deviation is 24.25

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9514 1404 393

Answer:

  A.  (f-g)(x) = -5^x +3x -2

Step-by-step explanation:

The only terms that can be combined are the constants.

  (f -g)(x) = f(x) -g(x)

  (f -g)(x) = (-5^x -4) -(-3x -2) = -5^x -4 +3x +2

  (f -g)(x) = -5x^4 +3x -2 . . . . . matches A

The eigenvalues of the matrix are -1,1,3 and the corresponding eigenvectors are [-1,2,2], [1,-1,-1], [1,1,1] respectively.

The matrix is given as

2 1 -1

3 2 -3

3 1 -2

To find the eigenvalues and eigenvectors of a matrix A, we need to solve the following equation:

Av = λv

where v is the eigenvector and λ is the eigenvalue.

So, we have

(2 1 -1) (x) = λ (x)

(3 2 -3) (y) (y)

(3 1 -2) (z) (z)

We can find the eigenvalues by solving the characteristic equation which is det(A-λI) = 0.

The characteristic equation for the above matrix is

(2-λ)((-λ-2)(-λ+1) - 2) - 3(1)(-λ+1) + 3(1)(-λ-2) = 0

Solving the above equation we get λ = -1,1,3

Now we can find the eigenvectors for each eigenvalue.

For λ = -1

(2 1 -1) (x) = -1 (x)

(3 2 -3) (y) (y)

(3 1 -2) (z) (z)

Solving the above equation we get x = -1, y = 2 and z = 2. So the eigenvector is [-1,2,2].

For λ = 1

(2 1 -1) (x) = 1 (x)

(3 2 -3) (y) (y)

(3 1 -2) (z) (z)

Solving the above equation we get x = 1, y = -1 and z = -1. So the eigenvector is [1,-1,-1].

For λ = 3

(2 1 -1) (x) = 3 (x)

(3 2 -3) (y) (y)

(3 1 -2) (z) (z)

Solving the above equation we get x = 1, y = 1 and z = 1. So the eigenvector is [1,1,1].

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Based on the limited information provided, it is not possible to definitively determine the type of economy in Country A. More specific details and factors would be necessary to make a conclusive determination.

Answer:

43-(+13)

43-13

=30

-× + would give you -

+×- would give you -

+×+ would give you -

-×-would give you +.

The length of segment CD is approximately 28.84.

To calculate the length of segment CD, we need to use the properties of a tangent line and the given information.

In a circle, when a line is tangent to the circle, it forms a right angle with the radius drawn to the point of tangency. This means that triangle AEC is a right triangle.

Given that AE = 12 and EC = 8, we can use the Pythagorean theorem to find the length of AC, which is the hypotenuse of triangle AEC.

AC^2 = AE^2 + EC^2

AC^2 = 12^2 + 8^2

AC^2 = 144 + 64

AC^2 = 208

Taking the square root of both sides:

AC = √208

AC ≈ 14.42

Now, segment CD is a part of the diameter of the circle and passes through the center of the circle. Therefore, it is twice the length of the radius.

CD = 2 * AC

CD = 2 * 14.42

CD ≈ 28.84

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The general form representation of the polynomial which is as described in the task content is; f(x) = 4x³ + 38x² + 24x - 360.

It follows from the task content that the Polynomial in discuss has;

Therefore, the factored form of a polynomial can be written as follows;

P(x) = a (x - p) (x - q) (x - r) where p, q and r are the roots of the polynomial and a is the leading coefficient.

Since the factors of the polynomial f(x) are; (x + 6), (x + 6) and (x - 5/2).

Hence, the polynomial f(x) in discuss can be written as follows;

f(x) = 4 (x + 6) (x + 6) (x - 5/2)

f(x) = (x + 6) (x + 6) (4x - 10)

f(x) = 4x³ + 38x² + 24x - 360

Therefore, the required polynomial in standard form is; f(x) = 4x³ + 38x² + 24x - 360.

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Answer: 3,650 days

Step-by-step explanation:

In the Gregorian Calendar, a common year has 365 days. We are going to assume that a common year always has 365 days for the purposes of this problem.

If one day is 20 minutes, then let us multiply that by 365 days, giving us 7,300 minutes in 1 year. Let us then multiply 7,300 minutes by 10 years. That gives us 73,000 minutes. We know that (based on this problem) there are 20 minutes in 1 day, so we divide 73,000 minutes by 20 minutes. The final answer is 3,650 days.

Answer:

(2x - 9)(x + 6) .

Step-by-step explanation:

2x^2 + 3x - 54

Use the 'ac' method to do this.

First multiply the first number by the last:

2 * -54 = -108.

Now we want 2 numbers whose product is -108 and whose sum is + 3,

- these are +12 and -9, so we write:

2x^2 + 12x - 9x - 54        Now factor by grouping:

= 2x(x + 6) - 9(x + 6)        x +6 is common, so:

= (2x - 9)(x + 6) .

If If LaMagna Corporation's common stock has 50,000,000 shares authorized, 45,000,000 shares issued,. The number of  shares that are considered "outstanding is: C. 46,750,000 shares.

Using this formula to find the number of outstanding shares

Number of outstanding shares = Outstanding shares + Treasury stock

Let plug in the formula

Number of outstanding shares = 45,000,000 shares + 1,750,000 shares

Number of outstanding shares = 46,750,000 shares

Therefore the correct option is C.

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Answer:

CD, JS, and CT.

Step-by-step explanation:

Hope it helps.

All the value of chords are, CD and CT.

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

Given that;

The circle is shown in image.

Now, We know that;

The chord of a circle is defined as the line segment joining any two points on the circumference of the circle.

Hence, By figure;

The chords are,

⇒ CD and CT

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To achieve a comparable rate of return, Hank would need to earn an interest rate of approximately 0.86% per month, compounded monthly on his ordinary annuity.

To find the interest rate, compounded monthly, that Hank would need to earn on an ordinary annuity for a comparable rate of return, we can use the present value formula for an ordinary annuity.

First, let's calculate the present value of Hank's payments. He made payments of $219 per month for 30 years, so the total payments amount to $219 * 12 * 30 = $78840.

Now, we need to find the interest rate that would make this present value equal to the selling price of the property, which is $195,258.

Using the formula for the present value of an ordinary annuity, we have:

PV = P * (1 - (1+r)\(^{(-n)})\)/r,
where PV is the present value, P is the payment per period, r is the interest rate per period, and n is the number of periods.

Plugging in the values we have, we get:
$78840 = $219 * (1 - (1+r)\({(-360)}\))/r.

Solving this equation for r, we find that Hank would need to earn an interest rate of approximately 0.86% per month, compounded monthly, in order to have a comparable rate of return.

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Answer: x= 13/2 or 6 1/2

Step-by-step explanation:

2(x+4)-3(2x-5)=-3

Simplify the equation,

2x+8-6x+15 = -3

-4x+23= -3

-4x = -26

Cancel the minus sign, now we get

2x = 13

i.e., x= 13/2

11, - 6, -1, 4, 9, 14, 19, ... are mapped onto 4. ... A;-l = (-ltQn (mod N),. (A5.34) ... 131 2, 14, 34, 38, 42, 78, 90, 178, 778, 974(1000).

Step-by-step explanation:

the nearest .1/2 incp, we say the 'unit 131/2 incl. 1.4 a measUrement is-stated tp- be 546 inch, this UM= the

A personal example of a measurement I use routinely is converting weight from U.S. customary units to metric units. Let's convert pounds to kilograms.

To convert pounds to kilograms, we use the conversion factor of 1 pound = 0.453592 kilograms.

For example, if I have a weight of 150 pounds, I can calculate the equivalent weight in kilograms as follows:

150 pounds * 0.453592 kilograms/pound = 68.0388 kilograms

Therefore, 150 pounds is approximately equal to 68.0388 kilograms.

In this conversion, we multiply the weight in pounds by the conversion factor to obtain the weight in kilograms. By using the appropriate conversion factor, we can accurately convert weights from U.S. customary units to metric units.

It's important to note that conversion factors may vary slightly depending on the rounding used and the exact value of the conversion factor.

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The water cooler tank has to be filled 18 times to quench the thirst of 1200 students.

We have

Number of students= 1200

Water consumption per student= 750 ml

So, Total water consumption

= Number of students × Water consumption per student

= 1200 × 750 ml

= 900000 ml

= 900 Liter

Now, the time cooler tank has to be filled to quench the thirst

= 900 / 50

= 18 times

Thus, the water cooler tank has to be filled 18 times to quench the thirst of 1200 students.

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The rate of change of the simple index over one day is approximately 12.78%.

To calculate the rate of change of the simple index over one day, we need to determine the percent change in the total value of the index between Monday's opening and Tuesday's opening.

On Monday, Stock A has 5000 shares at $2.75 per share, so its total value is:

Total value of Stock A on Monday = 5000 * $2.75 = $13,750

Similarly, on Monday, Stock B has 3000 shares at $4.30 per share, so its total value is:

Total value of Stock B on Monday = 3000 * $4.30 = $12,900

The total value of the index on Monday is the sum of the values of Stock A and Stock B:

Total value of the index on Monday = $13,750 + $12,900 = $26,650

On Tuesday, Stock A opens at $3.10 per share, and Stock B opens at $4.85 per share. Both stocks still have the same number of shares as on Monday.

The total value of Stock A on Tuesday is:

Total value of Stock A on Tuesday = 5000 * $3.10 = $15,500

The total value of Stock B on Tuesday is:

Total value of Stock B on Tuesday = 3000 * $4.85 = $14,550

The total value of the index on Tuesday is the sum of the values of Stock A and Stock B:

Total value of the index on Tuesday = $15,500 + $14,550 = $30,050

To calculate the percent change in the index, we use the formula:

Percent Change = ((New Value - Old Value) / Old Value) * 100

Percent Change = (($30,050 - $26,650) / $26,650) * 100 ≈ 12.78%

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Answer:

Step-by-step explanation:

Answer: B. Blind experiment

Step-by-step explanation: While conducting an experiment, experimenters may aim to eliminate factors which are very likely to cause bias and hence affect the veracity of the study. In the scenario above, the participants of the study (coworkers) were only provided with samples of the two coffee types without any of them knowing if it was the coffee they drank now or the new coffee brand. Hence, withholding such information from the participant is a technique in experimenting called blinding. Because, the information could affect the outcome and hence objective of the study as the participants were already partial towards the present coffee being consumed.

Answer: B

Step-by-step explanation:

As regards if there is evidence that the true mean of number of posts is less than 27, A. No. There is not evidence for the population mean to be less than 27, because 27 is within the 95% confidence interval.

The 95% confidence interval is given as 19.7 to 27.3 posts, which means that if we were to repeat the sampling process many times and construct 95% confidence intervals using each sample, approximately 95% of those intervals would contain the true population mean u.

Since the value of 27 is within the confidence interval, there is not enough evidence to suggest that the true population mean is less than 27. In other words, we cannot reject the null hypothesis that the population mean is greater than or equal to 27 based on this confidence interval.

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Answer:

\(x=2$\pm$\sqrt{42}\)

Step-by-step explanation:

The given equation is:

\(x^{2} -4x-9=29\\\Rightarrow x^{2} -4x-9-29=0\\\Rightarrow x^{2} -4x-38=0\)

Formula:

A quadratic equation \(ax^{2} +bx+c=0\) has the following roots:

\(x=\dfrac{-b+\sqrt D}{2a}\ and\\x=\dfrac{-b-\sqrt D}{2a}\)

Where \(D= b^{2} -4ac\)

Comparing the equation with \(ax^{2} +bx+c=0\)

a = 1

b = -4

c= -38

Calculating D,

\(D= (-4)^{2} -4(1)(-38)\\\Rightarrow D = 16+152 = 168\)

Now, finding the roots:

\(x=\dfrac{-(-4)+\sqrt {168}}{2\times 1}\\\Rightarrow x=\dfrac{4+2\sqrt {42}}{2}\\\Rightarrow x=2+\sqrt {42}\\and\\x=\dfrac{-(-4)-\sqrt {168}}{2\times 1}\\\Rightarrow x=\dfrac{4-2\sqrt {42}}{2}\\\Rightarrow x=2-\sqrt {42}\)

So, the solution is:

\(x=2$\pm$\sqrt{42}\)

Answer is A or the first one

Answer:

17.89 miles long.

Step-by-step explanation:

The pedestrian route that runs diagonally across the rectangular park is the hypotenuse of a right triangle whose legs are the length and width of the park. We can use the Pythagorean theorem to find the length of this diagonal route.

According to the Pythagorean theorem, the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of its legs. In this case, one leg of the right triangle is 16 miles long and the other leg is 8 miles long. So, we have:

d² = 16² + 8²

d² = 256 + 64

d² = 320

d = √320

d ≈ 17.89

So, the pedestrian route that runs diagonally across the park is approximately 17.89 miles long.

Answer:

the percentage increase in the USD/Euro exchange rate from 01/02/16 to 01/01/17 is 3.26%.

Step-by-step explanation:

To calculate the percentage increase in the USD/Euro exchange rate from 01/02/16 to 01/01/17, we need to use the following formula:

Percentage increase = (New value - Old value) / Old value x 100%

First, let's identify the old and new values:

Old value (01/02/16): 0.92055 USD/Euro

New value (01/01/17): 0.95058 USD/Euro

Now, let's plug these values into the formula:

Percentage increase = (0.95058 - 0.92055) / 0.92055 x 100%

Percentage increase = 0.03003 / 0.92055 x 100%

Percentage increase = 3.26%

Therefore, the percentage increase in the USD/Euro exchange rate from 01/02/16 to 01/01/17 is 3.26%.

Answer:

charged with providing of three types of clients

Answer:

x = 2 , y = 1 , z = 2

Step-by-step explanation:

\(\overrightarrow{a} \perp \overrightarrow{c} \Longrightarrow \left( \begin{gathered}1\\ 0\\ -1\end{gathered} \right) \cdot \left( \begin{gathered}x\\ y\\ z\end{gathered} \right) =0 \Longleftrightarrow x - z=0 \Longleftrightarrow x = z\)

\(\overrightarrow{b} \perp \overrightarrow{c} \Longrightarrow \left( \begin{gathered}-2\\ 2\\ 1\end{gathered} \right) \cdot \left( \begin{gathered}x\\ y\\ z\end{gathered} \right) =0 \Longleftrightarrow -2x +2y +z=0\)

Now ,we have to solve the system:

\(\begin{cases}x=z&\\ -2x+2y+z=0&\end{cases}\)

\(\Longleftrightarrow \begin{cases}x=z&\\ -x+2y=0&\end{cases}\)

\(\Longleftrightarrow \begin{cases}x=z&\\ x=2y&\end{cases}\)

then x = 2y = z

\(\Longrightarrow \overrightarrow{c} \left( \begin{gathered}2y\\ y\\ 2y\end{gathered} \right)\)

|C| = 3 ⇒ (2y)² + y² + (2y)² = 9 ⇒ 9y² = 9 ⇒ y² = 1 ⇒ y = ±1 ⇒ y = 1

(x>0  ⇒ y>0)

\(\Longrightarrow \overrightarrow{c} \left( \begin{gathered}2\\ 1\\ 2\end{gathered} \right)\)

The angles of the triangle are 125 degrees, 20 degrees, and 35 degrees.

A triangle is a closed geometric shape with three sides, three angles, and three line segments. Three non-collinear points are joined by line segments to create the simplest polygon, which has three non-collinear points.

Triangles can be categorized according to the size of their sides and angles. Triangles can be categorized as equilateral (all sides are equal in length), isosceles (both sides are equal in length), or scalene based on their sides (all sides are different in length). Triangles can be categorized as acute (all angles are less than 90 degrees), obtuse (one angle is greater than 90 degrees), or right (one angle is greater than 90 degrees) (one angle is exactly 90 degrees).

In any triangle, the sum of the three interior angles is always 180 degrees. Therefore, we can write:

a + b + c = 180

Substituting the given values, we get:

(6x-1) + 20 + (x+14) = 180

Simplifying and solving for x, we get:

7x + 33 = 180

7x = 147

x = 21

Now that we have the value of x, we can substitute it back into the expressions for the angles to find their values:

angle a = (6x-1) = (6*21-1) = 125 degrees

angle b = 20 degrees

angle c = (x+14) = (21+14) = 35 degrees

Therefore, the angles of the triangle are 125 degrees, 20 degrees, and 35 degrees.

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