which project will you choose if you apply the npv decision rule

The rational root of the function is x = -1/2, and the complex roots are x = 21/4 and x = 1.

To find the rational root of the function f(x) = 4x³ - 17x² - 39x - 18, we can apply the Rational Root Theorem. According to the theorem, any rational root of the function must be of the form p/q, where p is a factor of the constant term (in this case, -18) and q is a factor of the leading coefficient (in this case, 4).

Let's list the factors of -18: ±1, ±2, ±3, ±6, ±9, ±18.

And now the factors of 4: ±1, ±2, ±4.

Possible rational roots are formed by dividing a factor of the constant term by a factor of the leading coefficient. So the possible rational roots are:

±1/1, ±1/2, ±1/4, ±2/1, ±2/2, ±2/4, ±3/1, ±3/2, ±3/4, ±6/1, ±6/2, ±6/4, ±9/1, ±9/2, ±9/4, ±18/1, ±18/2, ±18/4.

Now, test each of these possible roots by substituting them into the function f(x) and see if any of them result in f(x) = 0.

By evaluating the function for each of these possible roots, the rational root is x = -1/2.

Now let's proceed to find the complex roots of the function. To do this, use polynomial division or synthetic division to divide f(x) by (x - (-1/2)).

Performing the synthetic division, we have:

4 | 4 -17 -39 -18

| -8 60 -105

| ___________________

| 4 -25 21 -123

The result of the synthetic division is 4x² - 25x + 21 with a remainder of -123. Now we have a quadratic equation. To solve it, we can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

For our quadratic equation 4x² - 25x + 21, the coefficients are:

a = 4

b = -25

c = 21

Applying the quadratic formula, we get:

x = (-(-25) ± √((-25)² - 4 x 4 x 21)) / (2 x 4)

= (25 ± √(625 - 336)) / 8

= (25 ± √289) / 8

= (25 ± 17) / 8

So the two complex roots are:

x = (25 + 17) / 8 = 42 / 8 = 21 / 4

x = (25 - 17) / 8 = 8 / 8 = 1

Therefore, the rational root of the function is x = -1/2, and the complex roots are x = 21/4 and x = 1.

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Answer:

B. "R is 85% of the original cost."

Step-by-step explanation:

The given equation is P - 0.15P = R, where P is the original cost of the shirt and R is the discounted price that Brandon paid.

Simplifying the equation, we get:

0.85P = R

Dividing both sides by P, we get:

0.85 = R/P

Therefore, the discounted price R is 85% of the original cost P.

So, the answer is (B) "R is 85% of the original cost."

Answer:

I'm sorry for not answering but have you got the answer to this question

Answer:

27 hours

Step-by-step explanation:

Take the amount of dirt and divide by the amount per hour

18 tons ÷ 2/3 ton per hour

Copy dot flip

18 * 3/2

Rewriting

18/2 * 3/1

9*3 = 27

27 hours

Answer:

141.6 cm cubed

Step-by-step explanation:

The equation in point-slope form is y - 5 = (5/3)(x + 5). The general form of the equation is 5x - 3y + 40 = 0.

To find the equation of a line parallel to the given line and passing through the point (-5,5), we can use the point-slope form of a linear equation. The point-slope form is y - y₁ = m(x - x₁), where (x₁, y₁) is a point on the line and m is the slope of the line. First, we need to find the slope of the given line, and then we can substitute the values into the point-slope form to obtain the equation. Additionally, we can convert the equation to the general form, which is Ax + By + C = 0, by rearranging the terms.

The given line has the equation 5x - 3y - 2 = 0. To find the slope of this line, we can rearrange the equation in slope-intercept form (y = mx + b), where m represents the slope. Rearranging the equation gives us:

-3y = -5x + 2

y = (5/3)x - 2/3

From the equation, we can see that the slope of the given line is 5/3. Since the line we want to find is parallel to this line, it will have the same slope.

Now, using the point-slope form with the point (-5,5) and the slope 5/3, we can write the equation:

y - 5 = (5/3)(x - (-5))

y - 5 = (5/3)(x + 5)

This is the equation of the line in point-slope form.

To convert it to general form, we can multiply through by 3 to eliminate the fraction:

3y - 15 = 5x + 25

5x - 3y + 40 = 0

This is the equation of the line in general form.

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edward makes $20.01 back from each pair of shoes he makes

Step-by-step explanation:

$35-$14.99=$20.01

Answer:

21.17 to 2d.p.

Step-by-step explanation:

Using Pythagoras rearrage to find b c^2-a^2 = b^2

c= hypothenuse

32^2 = 1024 and 24^2 = 576

1024 -576 = 448

\(\sqrt{448}\) = 21.1660105

21.17 to 2d.p.

Answer:

8 degrees Celsius

-4 -7 = -11

-11+3 = 8

Step-by-step explanation:

Answer:

200%

Step-by-step explanation:

if you substitute in numbers you'll find this as the answer.

as an example:

suppose the sides of the rectangle was 1 unit long.

area before change: 1 * 1 = 1

then, the length gets increase by 50% making it 1.5 ( 50% of 1 is 0.5, then you add it onto 1, 1 + 0.5 = 1.5 )

the width gets increased by 100% making it 2 ( 1 + 1 = 2 )

new area: 1.5 * 2 = 3

1 increased by 200% is 3, therefore the answer is 200%

Answer:

sorry dont know

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

5-2

=3

................

The feasibility area is empty. The solution of the LP-problem is not possible (does not exists).

With the constraint that x and y are both non-negative, the second constraint has only one point in common with each of the first and third constraints; and those two points are different.

The feasibility region is empty; so nothing can be optimized.

Plots x + 2y = 30 (red),  2x + 2y = 30 (green)  and  2x+y = 30 (blue)

The feasibility area, according to the condition, is the area of the first quadrant

   - above the red line,

   - below the green line,

   - above the blue line.

It can be seen from the plot that this set is empty.

Therefore, the feasibility area is empty. The solution of the LP-problem is not possible (does not exists).

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Disclaimer

The question given by you is incomplete, so the above solution is of a similar question, and the question is

Solve the LP problem. If no optimal solution exists, indicate whether the feasible region is empty or the objective function is unbounded. HINT

Maximize p = x + y subject to

x + 2y ≥ 30

2x + 2y ≤ 30

2x + y ≥ 30

x ≥ 0, y ≥ 0.

p=

(x, y)=

Answer:

they don't have any but her

Step-by-step explanation:

.

Answer: 4.)

Step-by-step explanation: An undefined slope is a vertical line.

Answer:

6.025 as a mixed number is 6 1/40

Answer:

6 1/40

Step-by-step explanation:

Since 0.25 = 1/4, 0.025 = 1/40.

sorry this is late!!

#1 - A circular grid like this one can be helpful for performing dilations

#2 - To perform a dilation, we need a (In order to perform a dilation, students will need to know the center of dilation (which can be communicated using the coordinate grid), the coordinates of the polygon that they are dilating (also communicated using the coordinate grid), and the scale factor.)

Lets try to figuring out the definition of it.

1. Planning for the distribution of one's estate after death is Estate planning.

2. Trust: an estate, or other property or money, given to a person or institution to manage.

3. Compound interest: figured on the amount of money in the savings account plus the amount of interest already earned.

4. Dividend: a share of money earned as profits by a company and distributed to its stockholders.

5. Checking account: account allows you to write an instruction to the bank, as a check, to make a payment from that account.

6. Will a legal document that describes how your estate should be distributed upon.

8. Purchasing a bond is like loaning money to the company for interest.

9. Club accounts: accounts are set up to save for specific purchases.

11. Mutual fund: instrument in which you purchase a part of a collection of investments.

12. A debit card can be used like a credit card, but money is deducted directly from bank account.

13. Automatic Teller Machine: permits the customer to make transactions by using a special computer terminal.

14. Adjusted balance: balance after adding the outstanding deposits and subtracts the outstanding checks to the balance on the statement.

15. Certificate of deposit (CD) is a sum on deposit usually for a given period of time at a fixed interest rate.

18. A trust created while a person is still alive is called a Living Trust.

19. Intestate: without a will.

20. Interest is the fee a bank pays you to keep your money.

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Answer:

1. Planning for the distribution of one's estate after death is Estate planning.

2. Trust: an estate, or other property or money, given to a person or institution to manage.

3. Compound interest: figured on the amount of money in the savings account plus the amount of interest already earned.

4. Dividend: a share of money earned as profits by a company and distributed to its stockholders.

5. Checking account: account allows you to write an instruction to the bank, as a check, to make a payment from that account.

6. Will a legal document that describes how your estate should be distributed upon.

8. Purchasing a bond is like loaning money to the company for interest.

9. Club accounts: accounts are set up to save for specific purchases.

11. Mutual fund: instrument in which you purchase a part of a collection of investments.

12. A debit card can be used like a credit card, but money is deducted directly from bank account.

13. Automatic Teller Machine: permits the customer to make transactions by using a special computer terminal.

14. Adjusted balance: balance after adding the outstanding deposits and subtracts the outstanding checks to the balance on the statement.

15. Certificate of deposit (CD) is a sum on deposit usually for a given period of time at a fixed interest rate.

18. A trust created while a person is still alive is called a Living Trust.

19. Intestate: without a will.

20. Interest is the fee a bank pays you to keep your money.

Step-by-step explanation:

(a) To guarantee that at least 2 people have a birthday on the same day of the week, at least 8 people must be selected.

(b) To guarantee that at least 6 people have a birthday on the same day of the week, at least 43 people must be selected.

(a) To find the minimum number of people needed to guarantee that at least 2 of them have a birthday on the same day of the week, we can apply the Pigeonhole Principle.

There are 7 days of the week, so each person can have their birthday on one of these 7 days. If we select 8 people, then there are 8 pigeons (people) and 7 pigeonholes (days of the week). Since we have more pigeons than pigeonholes, by the Pigeonhole Principle, at least 2 people must have their birthday on the same day of the week.

(b) Similarly, to find the minimum number of people needed to guarantee that at least 6 of them have a birthday on the same day of the week, we apply the Pigeonhole Principle. Again, there are 7 days of the week, and each person can have their birthday on one of these 7 days.

If we select 43 people, then we have 43 pigeons (people) and 7 pigeonholes (days of the week). Since we have more pigeons than pigeonholes, by the Pigeonhole Principle, at least 6 people must have their birthday on the same day of the week.

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Circle Y has a greater area than Circle X by approximately \($159.25\pi cm^2.\)

To determine which circle has a greater area and by how much, we will be using the formula which is given as, \($A = \pi r^2, where A\) is the area and \($r$\) is the radius.

As the first step we will calculate the radius of each circle:

For Circle X, the diameter is given as 18 cm. The radius, \($r_X$\), is half the diameter, so \($r_X = \frac{18}{2} = 9 cm.\)

For Circle Y, the diameter is given as 31 cm and the radius, \($r_Y$\), is half the diameter, so \($r_Y = \frac{31}{2} = 15.5 cm.\)

Now, for the next step, we can calculate the area of each circle:

The area of Circle X, \($A_X$\), is given by \($A_X = \pi (r_X)^2 = \pi (9)^2 = 81\pi cm^2.\)

The area of Circle Y, \($A_Y$\), is given by \($A_Y = \pi (r_Y)^2 = \pi (15.5)^2 = 240.25\pi cm^2\)

Comparing the two areas, we can see that \($A_Y > A_X$\). The difference in their areas is \($A_Y - A_X = 240.25\pi - 81\pi = 159.25\pi cm^2$\). Therefore, Circle Y has a greater area than Circle X by approximately \($159.25\pi cm^2$\).

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This polynomial has two complex roots, 2+3i and 2-3i, and two real roots, 4+2i and 4-2i. Therefore, our matrix satisfies the conditions of having exactly two complex eigenvalues and no real eigenvalues.

A complex eigenvalue is a solution to the characteristic equation of a matrix that has the form λ = a + bi, where a and b are real numbers and i is the imaginary unit (√-1). For a matrix to have a complex eigenvalue, it must also have a complex eigenvector, which is a vector with complex entries that satisfies the equation Ax = λx, where A is the matrix, λ is the eigenvalue, and x is the eigenvector.

Now, to find a 4×4 matrix with exactly two complex eigenvalues and no real eigenvalues, we need to construct a matrix that has a characteristic equation with two complex roots and no real roots. One way to do this is to use a diagonal matrix with two complex conjugate pairs of entries on the diagonal.
For example, consider the following matrix:
| 2+3i    0     0    0 |
|  0     2-3i   0    0 |
|  0      0    4+2i  0 |
|  0      0     0   4-2i|
This matrix has two complex conjugate pairs of eigenvalues: 2+3i and 2-3i, and 4+2i and 4-2i. To see this, we can compute the characteristic polynomial of the matrix:
| λ - 2-3i    0         0          0      |
|    0     λ - 2+3i     0          0      |
|    0         0     λ - 4-2i      0      |
|    0         0         0      λ - 4+2i |

Expanding this determinant gives us:
(λ - 2-3i)(λ - 2+3i)(λ - 4-2i)(λ - 4+2i) = (λ^2 - 4λ + 13)(λ^2 - 16)
This polynomial has two complex roots, 2+3i and 2-3i, and two real roots, 4+2i and 4-2i. Therefore, our matrix satisfies the conditions of having exactly two complex eigenvalues and no real eigenvalues.

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let $p$ and $q$ be the two distinct solutions to the equation$$\frac{4x-12}{x^2 2x-15}=x 2.$$if $p > q$. The value of $p - q$ is 4.

To find the value of $p - q$, we first need to solve the given equation and determine the values of $p$ and $q$.

The equation is:

$$\frac{4x-12}{x^2 - 2x - 15} = x^2.$$

Step 1: Factorize the denominator:

The denominator can be factored as $(x - 5)(x + 3)$.

Step 2: Simplify the equation:

$$\frac{4x-12}{(x - 5)(x + 3)} = x^2.$$

Step 3: Multiply both sides of the equation by $(x - 5)(x + 3)$ to eliminate the denominator:

$$(4x - 12) = x^2(x - 5)(x + 3).$$

Step 4: Expand and rearrange the equation:

$$4x - 12 = x^4 - 2x^3 - 15x^2 + 25x.$$

Step 5: Rearrange the equation and combine like terms:

$$x^4 - 2x^3 - 15x^2 + 21x - 12 = 0.$$

Step 6: Factorize the equation:

$$(x - 3)(x + 1)(x - 2)(x + 2) = 0.$$

From this, we get four possible solutions: $x = 3$, $x = -1$, $x = 2$, and $x = -2$.

However, we are interested in the two distinct solutions $p$ and $q$, where $p > q$. Therefore, the values of $p$ and $q$ are $p = 3$ and $q = -1$.

Finally, we can find the value of $p - q$:

$$p - q = 3 - (-1) = 3 + 1 = 4.$$

Hence, the value of $p - q$ is 4.

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Answer:

y=-3x+4

Step-by-step explanation:

im assuming that you need the equation of the table

to find slope, y2-y1/x2-x1    10-4/-2-0

6/-2=-3   slope=-3  

y=mx+b   just sub in the numbers from a point in the table

10=-3(-2)+b

10=6+b

b=4

y=-3x+b

Answer: x=2

Step-by-step explanation: f(x) = x + 8

f(x) = 10

10 = x + 8

minus 8 from the both sides

10 - 8 = x

2 = x

x = 2

Given data:

The length of the wire is l= 50 foot.

The given base length is b= 35 feet.

The expression for the height of the antena is,

Substitute the given values in the above expression.

Thus, the height of the antena is 36 ft.

In this study, a receptor binding measure, specifically adjusted distribution volume, was assessed for a sample of 13 healthy individuals. The observed values were: 23, 38, 39, 40, 44, 47, 50, 59, 63, 65, 67, 69, and 71. These data points can be used to analyze the receptor binding measure in this group of participants.

Based on the given observations of a receptor binding measure for 13 healthy individuals, we can see that the values range from 23 to 71. Without any additional information, it is difficult to draw any specific conclusions about the distribution or the significance of these values. However, we can say that this sample includes a range of values that may be useful for further analysis or comparison to other studies. It is important to note that more information about the study design and methodology would be necessary to fully interpret these results.

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The set of all possible solutions to a linear equation with two variables is called the solution set. Specifically, the collection of all ordered pairs that are equivalent to the equation.

A region always appears on the graph of the solution to a linear inequality. However, that set might not always include the boundary. The "or equal to" part of the inclusive inequality made the line a part of the solution set in the previous example.

Any value of a variable that makes the equation true is a solution. The set of all variables that makes the equation true is called a solution set. Because 2(4) + 6 = 14, the solution set for 2y + 6 = 14 is 4.

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The empirical rule can be used to estimate the percentage of vehicles that are traveling between certain speeds on a highway. This rule is a statistical method for determining the proportion of data that lies within a certain number of standard deviations from the mean.

For normally distributed data, the empirical rule states that approximately 68% of the data falls within one standard deviation of the mean, approximately 95% falls within two standard deviations, and approximately 99.7% falls within three standard deviations.
In this case, the mean speed of the sample of vehicles along the highway is miles per hour with a standard deviation of miles per hour. To estimate the percentage of vehicles whose speeds are between miles per hour and miles per hour, we need to determine how many standard deviations from the mean these speeds are.
First, we need to calculate the z-scores for the speeds of miles per hour and miles per hour.

The z-score for miles per hour is:
\(z = (x - μ) / σ = (55 - 60) / 5 = -1\)
The z-score for miles per hour is:

\(z = (x - μ) / σ = (65 - 60) / 5 = 1\)
These z-scores tell us how many standard deviations from the mean these speeds are. A z-score of -1 means that the speed of miles per hour is one standard deviation below the mean, while a z-score of 1 means that the speed of miles per hour is one standard deviation above the mean.
Since the data is bell-shaped and we are looking at speeds that are within two standard deviations from the mean, we can use the empirical rule to estimate the percentage of vehicles that are traveling between miles per hour and miles per hour.

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Answer:

that graph will feature an area delimited by a line of slope m passing through the origin (0,0). Since m>0 the slope is positive, meaning the line goes up. Since the equation is y > mx, the inequality sign being >, that means the area represented will be ABOVE the line drawn.

the minimum score needed to be in the top 7% is 85.48, which can be rounded to 85.4. To determine the minimum score needed to be in the top 7%, we need to use the properties of the normal distribution and the corresponding z-score.

First, we need to find the z-score that corresponds to the top 7%. This can be done by using the standard normal distribution table or a calculator with a normal distribution function. The z-score that corresponds to the top 7% is approximately 1.48.

Next, we can use the formula for transforming a z-score to a raw score:

raw score = z-score * standard deviation + mean    

Substituting the values given in the problem, we get:

raw score = 1.48 * 6.1 + 76.4

raw score = 85.48

Therefore, the minimum score needed to be in the top 7% is 85.48, which can be rounded to 85.4.

In conclusion, the minimum score needed to be in the top 7% is 85.4. This calculation was performed by finding the z-score that corresponds to the top 7%, and then transforming the z-score to a raw score using the mean and standard deviation of the distribution.

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