Let A = {−5, −4, −3, −2, −1, 0, 1, 2, 3} and define a relation R on A as follows: For all (m, n) is in A, m R n ⇔ 5|(m2 − n2). It is a fact that R is an equivalence relation on A. Use set-roster notation to list the distinct equivalence classes of R. (Enter your answer as a comma-separated list of sets.)

The conventional B/C ratio using the expected EUAC (Equivalent Uniform Annual Cost) can be computed as 1 / EUAC

To calculate the conventional B/C ratio using the expected EUAC, we need to determine the present value of costs and benefits over the project's life and then compare them.

Cost Data:

Year 1: $10,000

Year 2: $8,000

Year 3: $6,000

Benefit Data:

Year 1: $15,000

Year 2: $12,000

Year 3: $9,000

Life Probability Distribution:

Year 1: 0.2

Year 2: 0.5

Year 3: 0.3

To calculate the present value of costs and benefits, we multiply each cash flow by the respective probability and discount it to present value. Assuming a discount rate of r%, the present value (PV) can be calculated using the formula:

PV = Cash Flow / (1 + r)^n

where n is the year of the cash flow.

Calculating the present value of costs:

PV(Costs) = ($10,000 / (1 + r)^1) + ($8,000 / (1 + r)^2) + ($6,000 / (1 + r)^3)

Calculating the present value of benefits:

PV(Benefits) = ($15,000 / (1 + r)^1) + ($12,000 / (1 + r)^2) + ($9,000 / (1 + r)^3)

The expected EUAC can be calculated as the sum of PV(Costs) divided by the sum of PV(Benefits), considering the probabilities:

EUAC = (PV(Costs) * 0.2 + PV(Costs) * 0.5 + PV(Costs) * 0.3) / (PV(Benefits) * 0.2 + PV(Benefits) * 0.5 + PV(Benefits) * 0.3)

Finally, the conventional B/C ratio is obtained by taking the inverse of the EUAC:

B/C ratio = 1 / EUAC

The conventional B/C ratio using the expected EUAC for the given cost, benefit data, and life probability distribution can be computed using the provided calculations. This ratio allows for a comparison between the present value of costs and benefits over the project's life, considering the probability distribution.

To know more about ratio , visit;

https://brainly.com/question/13419413

#SPJ11

Answer:

The door was opened by whom?

Answer:

Yes.

Step-by-step explanation:

Yes.

You can prove it using SAS and CPCTC.

Start with an  isosceles triangle with a horizontal base and the vertex angle above.

Draw the angle bisector at the vertex angle and extend it down until it intersects the base of the isosceles triangle.

Now you have two smaller triangles, right and left sides of the original triangle.

We now prove the two smaller triangles are congruent. The two congruent sides of the main triangle are congruent corresponding sides of the two smaller triangles. The bisected angle becomes two congruent angles in the two smaller triangles. Finally, the angle bisector is congruent to itself and is a side of both smaller triangles. By SAS, the two smaller triangles are congruent. Then, the two segments in the base of the isosceles triangle are congruent by CPCTC. That makes the point of intersection of the angle bisector and the base of the isosceles triangle the midpoint of the base.

Answer:

P(A' ∩ B) = 0.12

Step-by-step explanation:

Given:

P(A) = 0.41, P(B) = 0.32 and P(B' ∩ A) = 0.21

To Find:

P(A' ∩ B)

Solution:

Since, P(B' ∩ A) = P(A) - P(A ∩ B)

By substituting the values given,

0.21 = 0.41 - P(A ∩ B)

P(A ∩ B) = 0.41 - 0.21

              = 0.20

Since, P(A' ∩ B) = P(B) - P(A ∩ B)

P(A' ∩ B) = 0.32 - 0.20

               = 0.12

Therefore, P(A' ∩ B) = 0.12 is the answer.

Answer:

1,3,9

Step-by-step explanation:

Answer:

1,3,9

Step-by-step explanation:

Three, one and nine are the only factors of nine.

Answer:c

Step-by-step explanation:

Answer:

6 aduts and 5 kids

Step-by-step explanation:

$20 for the kids in total and $54 for the adults

Answer:

The height is 3

Step-by-step explanation:

The formula to find the volume is pi r^2 h/3

So we change the formula: 400pi is 1256.64 rounded

Divide 1256.64 by pi 20^2 and you get 3

The answer is A

I put D bc someone said it was D and i got it wrong and it showed the answer was A so yeah ;-;

To proceed with this analysis, we assume that the individuals in the sample were randomly selected and that the samples are independent.

Additionally, the sample sizes are large enough to apply the normal approximation to the sampling distribution of the difference in proportions.Using these assumptions, we can calculate the confidence in is 37/77 ≈ 0.481. The proportion of men who follow a regular exercise program is 44/85 ≈ 0.518. The difference between these proportions is 0.518 - 0.481 ≈ 0.037.

The 95% confidence interval for the difference in proportions can be calculated using the formula: difference ± (critical value) * sqrt[(p1 * (1 - p1) / n1) + (p2 * (1 - p2) / n2)] where p1 and p2 are the proportions of women and men, n1 and n2 are the respective sample sizes, and the critical value corresponds to a 95% confidence level. Performing the calculations, the 95% confidence interval for the difference in proportions is approximately 0.037 ± 0.129, which gives us a range from -0.092 to 0.166.

Interpreting this interval, we can say that with 95% confidence, the true difference between the proportions of women and men who follow a regular exercise program lies within the range of -0.092 to 0.166. This means that there is insufficient evidence to conclude that there is a significant difference in the proportions of women and men who follow a regular exercise program. The interval includes zero, indicating that the difference could be negligible or non-existent.

To learn more about interval click here:

brainly.com/question/17212516

#SPJ11

Answer:

30

Step-by-step explanation:

21 + 9 = 30

The probability that the number drawn is a multiple of 2 or 3 is 8/15 or 0.53.

This can be easily found by finding the number of multiples of 2 and 3 between 1 and 15 and adding them together. The multiples of three go from 3 to 15 and therefore there are 5 such numbers. The multiples of two go from 2 to 14 and hence there are 7 such numbers. Therefore, when we add these two numbers together, we get 12.

This is the total number of multiples of 2 or 3 between 1 and 15. We divide this by the total number of elements in the box, which is 15, to get the probability that the number drawn is a multiple of 2 or 3. This comes out to be 8/15 or 0.53.

know more about probability here

https://brainly.com/question/31828911#

#SPJ11

9514 1404 393

Answer:

  x = 10

Step-by-step explanation:

The exterior angle is equal to the sum of the remote interior angles.

  (12x +12)° = 79° +(5x+3)°

  7x = 70 . . . . . . . . divide by °; subtract 12+5x; collect terms

  x = 10 . . . . . . . . divide by 7

The following is true about the study: e. It has one factor (medication) blocked by age.

In statistics, when a factor (independent variable) is blocked by another factor, it means that the effect of the first factor is controlled or eliminated by the second factor.

In this case, the factor that is blocked is the medication, which means that the effect of medication on the outcome variable is controlled by age.

Blocking a factor is often done in experimental design to remove the effects of extraneous variables or to control the influence of certain factors on the outcome variable.

In this case, age is considered a blocking variable because it is not of interest in the study, but it may have an effect on the outcome variable. By blocking the effect of medication by age, the study can better isolate the effect of medication on the outcome variable.

In summary, the statement e. "It has one factor (medication) blocked by age" is correct which means that the study controlled for the effect of age on the outcome variable by blocking the effect of medication by age.

To learn more outcome, refer below:

https://brainly.com/question/27292589

#SPJ11

The amount of Miranda's total monthly expense is  $970.

Basically, an expense refers to any cost of operations that a company incurs to generate revenue. It also means the cost that one is required to spend on obtaining something.

In a typical firm, the common expenses include a payment to suppliers, employee wages, factory leases, equipment depreciation etc.

in the question context, the expenses are:

Total monthly expenses = $60 + $85 + $195 + $55 + $575

Total monthly expenses = $970.

Read more about expense

brainly.com/question/25169847

#SPJ1

9514 1404 393

Answer:

  A. Given; B. multiplication; C. distributive; D. collect terms; E. addition; F. division

Step-by-step explanation:

You are expected to compare each line to the previous line and identify the changes. Apart from combining like terms (collecting terms), there are generally only three properties of interest: distributive property, addition property, multiplication property. Of course, subtraction and division are just addition and multiplication using the appropriate (additive, multiplicative) inverse.

The distributive property involves adding or deleting parentheses, so it is easy to identify.

If terms disappear, it can be due to terms being combined, or due to addition/subtraction. If coefficients disappear, it will generally be due to multiplication/division.

__

-2.5(-2-3x)+2.5(-4x-1) = -2x -4x . . . . Given

-5(-2 -3x) +5(-4x -1) = -4x -8x . . . . multiplication by 2 (fractions eliminated)

10 +15x -20x -5 = -4x -8x . . . . distributive property (eliminate parentheses)

-5x +5 = -12x . . . . collect terms

5 = -7x . . . . addition of 5x (-5x term disappeared)

-5/7 = x . . . . division by -7 (x coefficient of -7 disappeared)

The equation of the straight line which makes intercepts 3 and "-4" on the axes is 4x - 3y =12 and the point (1, 2) not lie on the line.

When you know the slope of the line to be investigated and the provided point is also the y intercept, you may utilize the slope intercept formula, y = mx + b. (0, b). The intercept form of a line's equation is written as \(\frac{x}{a} +\frac{y}{b} = 1\), where a is the x- intercept and b is the y-intercepts, respectively. The x-intercept is the point on the x-axis that is closest to the origin where the line crosses the x-axis, and the y-intercept is the point on the y-axis that is closest to the origin where the line crosses the y-axis.

Now, finding the equation of line by putting the value of intercepts,

\(\frac{x}{a} +\frac{y}{b} = 1\\\frac{x}{3} +\frac{y}{-4} = 1\\-4x+3y=-12\\4x-3y=12\)

so, the equation is 4x-3y=12.

Now, putting x=1 and y=2 to find whether (1,2) lie on the line or not,

4(1)-3(2)=12

4-6=12

-2≠12

So, the point (1, 2) not lie on the line.

Therefore, the equation of the straight line which makes intercepts 3 and "-4" on the axes is 4x - 3y =12 and the point (1, 2) not lie on the line.

To learn more about the Intercept form of line visit here:

https://brainly.com/question/25722412

#SPJ9

Based on the questions, 13 guests are attending her best friend’s baby shower.

Firstly, we need to write down the numbers that are already stated in the question.

43 + 9 × х = 160

Secondly, move the x to continue counting.

9x = 160 – 43

Thirdly, calculate the numbers above.

9x = 117

Then, move the X to get the answer.

X = \(\frac{117}{9}\)

Lastly, try to finish the division.

X = 13

In conclusion, the result shows that 13 guests attend Mrs. Wright’s best friend's baby shower.

The above question is about the algebraic word problem.

A word problem is a math question written in a short story scenario. Usually, it is a simple short story that is easy to understand.

Learn more about Algebra word problem:

https://brainly.com/question/21405634

#SPJ4

The initial size of the bacteria culture was approximately 202.02.

To solve this problem, we can use the formula for exponential growth:

N(t) = N0 * e^(kt)

where N(t) is the size of the culture at time t, N0 is the initial size of the culture, k is the growth rate, and e is the natural logarithmic base.

We can use the given information to set up two equations:

300 = N0 * e^(k10)

1400 = N0 * e^(k40)

Dividing the second equation by the first equation gives:

1400/300 = e^(k40) / e^(k10)

Simplifying:

4.67 = e^(k*30)

Taking the natural logarithm of both sides:

ln(4.67) = k*30

Solving for k:

k = ln(4.67) / 30

Substituting back into the first equation:

300 = N0 * e^(ln(4.67)/3)

300 = N0 * 1.484

Solving for N0:

N0 = 300 / 1.484

N0 ≈ 202.02

Therefore, the initial size of the bacteria culture was approximately 202.02.

You can learn more about exponential growth at

https://brainly.com/question/13223520

#SPJ11

Answer:

y= x +4

Step-by-step explanation:

The equation of a line can be written in the slope-intercept form, y= mx +c, where m is the slope and c is the y-intercept.

Overview of steps:

The slope can be found using the gradient formula below:

\(\boxed{\text{Gradient} = \frac{y_1 - y_2}{x_1 - x_2} }\)

Given: (5, 9) and (0, 4)

Start by finding the slope, m:

m

\( = \frac{9 - 4}{5 - 0} \)

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

= 1

Substitute m= 1 into y= mx +c:

y= x +c

In this case, the y-intercept is given by the point (0, 4). This is because y-intercepts occur at x= 0. This also means that c takes the value of 4.

Substitute c= 4:

y= x +4

Thus, the equation of the line is y= x +4.

To learn more about writing the equation of lines, check out: https://brainly.com/question/14536958

Answer:THe answer is 98.78x

Step-by-step explanation:

2r34 means 567

Answer:70/100 or 7/10

Step-by-step explanation:

one hour is 60 mins

1/5 of an hour is 12 mins

1/2 of an hour is 30

30 + 12 = 42

42/60 simplified is 7/10

A statement which best explains if the graph correctly represents the proportional relationship y = −2x include the following: D. Yes, the points shown on the line would be part of y = −2x.

In Mathematics, a proportional relationship can be defined as a type of relationship that generates equivalent ratios, a straight line, and it can be modeled or represented by the following mathematical expression:

y = kx

Where:

Generally speaking, the graph of any proportional relationship such as the linear equation (y = -2x) is characterized by a straight line as shown in the image attached below, with the following ordered pairs (0, 0), (1, -2),(2, -4), and (-1, 2).

Read more on proportional relationship here: brainly.com/question/20167968

#SPJ1

The length of the altitude to line segment $\overline{em}$ in triangle $gem$ is 16 units.

Let's denote the length of the altitude to line segment $\overline{em}$ in triangle $gem$ as $h$.

The area of a triangle is given by the formula:

Area = (base * height) / 2

The area common to triangle $gem$ and square $aime$ is 80 square units. Since the base of triangle $gem$ is $\overline{em}$, we have:

80 = (10 * h) / 2

160 = 10h

Solving for $h$, we have:

h = 160 / 10

h = 16

Therefore, the length of the altitude to line segment $\overline{em}$ in triangle $gem$ is 16 units.

Learn more about  length from

https://brainly.com/question/2217700

#SPJ11

Answer: she bought 12  

The points where the tangent line is vertical are (13/16, -5/16) and (-13/16, 5/16) and The slope of the tangent line is positive on the intervals t < -1 and t > 1, and negative on the interval -1 < t < 1.

(a) To find where the tangent line is horizontal, we need to find values of t where the derivative of y with respect to x (dy/dx) is equal to 0.

We have:

dy/dx = (dy/dt)/(dx/dt) = (5t^4 - 5)/(12t^2 - 3)

Setting dy/dx = 0, we get:

5t^4 - 5 = 0

t^4 = 1

t = ±1 or t = ±i

Substituting t = 1 into the parametric equations gives us the point (1,-4). Substituting t = -1 gives us the point (-1,4). Substituting t = i or t = -i gives us points on the imaginary axis, which are not part of the real plane.

Therefore, the points where the tangent line is horizontal are (1,-4) and (-1,4).

To find where the tangent line is vertical, we need to find values of t where dx/dt is equal to 0.

We have:

dx/dt = 12t^2 - 3

Setting dx/dt = 0, we get:

t^2 = 1/4

t = ±1/2

Substituting t = 1/2 into the parametric equations gives us the point (13/16, -5/16). Substituting t = -1/2 gives us the point (-13/16, 5/16).

Therefore, the points where the tangent line is vertical are (13/16, -5/16) and (-13/16, 5/16).

(b) To determine the intervals where the slope of the tangent line is positive or negative, we need to examine the sign of the derivative dy/dx.

From part (a), we know that dy/dx is equal to:

dy/dx = (5t^4 - 5)/(12t^2 - 3)

The denominator is always positive, so the sign of dy/dx is determined by the numerator.

For t < -1, we have 5t^4 - 5 > 0, so dy/dx > 0.

For -1 < t < 1, we have 5t^4 - 5 < 0, so dy/dx < 0.

For t > 1, we have 5t^4 - 5 > 0, so dy/dx > 0.

Therefore, the slope of the tangent line is positive on the intervals t < -1 and t > 1, and negative on the interval -1 < t < 1.

(c) To determine the intervals where the curve is concave upward or downward, we need to examine the sign of the second derivative d^2y/dx^2.

We have:

d^2y/dx^2 = ((d^2y/dt^2)(dx/dt) - (dy/dt)(d^2x/dt^2)) / (dx/dt)^3

Calculating the second derivatives, we get:

d^2y/dt^2 = 20t^3

d^2x/dt^2 = 24t

Substituting these into the expression for d^2y/dx^2, we get:

d^2y/dx^2 = (20t^3)(12t^2 - 3) - (5t^4 - 5)(24t) / (12t^2 - 3)^3

Simplifying this expression, we get:

d^2

Learn more about analyzing the properties of a parametric curve

brainly.com/question/15585522

#SPJ11

Poor road conditions, a slippery surface, or the undertow of the ocean are examples of the following type of factors that may cause injury are  human behavior, awareness, and response

Let's consider poor road conditions as an example. When roads are in a state of disrepair, they may contain potholes, loose gravel, or uneven surfaces. To evaluate the risk of injury, we can assign a probability value to the occurrence of an injury given the presence of poor road conditions. This probability could be denoted as P(injury|poor road conditions).

Similarly, a slippery surface, such as a wet floor or icy pavement, can also increase the chances of injury. By assigning a probability value to the event of injury given a slippery surface, we can express it as P(injury|slippery surface).

Lastly, the undertow of the ocean refers to a strong current beneath the water's surface that can pull swimmers away from the shore. To analyze the risk of injury in this scenario, we can again assign a probability value to the event of injury given the presence of an undertow, represented as P(injury|undertow).

To further understand the overall risk, we can consider the joint probability of multiple factors occurring simultaneously. For example, if both poor road conditions and a slippery surface are present, we can calculate the joint probability of injury as P(injury| poor road conditions and slippery surface).

This joint probability provides insight into the combined impact of these factors on the likelihood of injury.

To know more about injury here

https://brainly.com/question/29648597

#SPJ4