56. kenji and mary are members of a school committee
that will be meeting this afternoon. the 6 members of
the committee will be seated randomly around a
circular table. what is the probability that kenji and
mary will not sit next to each other at the meeting?

y = -1/3x + 1

y = -2x - 3

We can compare the equations to the graphs and see which graph represents the intersection point of the two equations.

The first equation, y = -1/3x + 1, has a negative slope (-1/3) and a y-intercept of 1.

The second equation, y = -2x - 3, also has a negative slope (-2) and a y-intercept of -3.

Based on the slopes and y-intercepts, we can identify the correct graph by finding the point where the two lines intersect.

Unfortunately, since the graphs are not provided, I am unable to determine which specific graph shows the solution to the system of linear equations. I recommend referring to the graph representation of the equations and identifying the intersection point to determine the correct graph.

Answer:

2) Yes, because every input (x) has an individual output (y)

6) No, because there is an input that has 2 outputs

8) No, because there is an input that has 2 outputs

11) (I am unsure, but I think it is) No, there is no inputs

12) No, because there is an input that has 2 outputs

Step-by-step explanation:

For functions, every input needs to have only one output

It should take approximately 1.98 hours, or around 1 hour and 59 minutes, to cook a 5.17 pound beef rib roast based on the recommended guideline of 23 minutes per pound at a 325°F oven setting.

To calculate the cooking time for a 5.17 pound roast, we can use the recommended guideline of 23 minutes per pound. First, we need to convert the weight from pounds to minutes, and then convert minutes to hours.

Cooking time in minutes = 5.17 pounds * 23 minutes/pound

Cooking time in minutes = 118.91 minutes

To convert minutes to hours, we divide the total minutes by 60:

Cooking time in hours = 118.91 minutes / 60

Cooking time in hours ≈ 1.98 hours

Therefore, it should take approximately 1.98 hours to cook a 5.17 pound beef rib roast based on the recommended guideline of 23 minutes per pound at a 325°F oven setting.

To know more about recommended guideline refer here:

https://brainly.com/question/28617982#

#SPJ11

Answer:

32

Step-by-step explanation:

This is the step by step explanation

32×3=96

96÷4=24

Answer:

It is false, the sine function represents the y-coordinate while the cosine function represents the x-coordinate

Answer: 1. s*h  2. 20.4 hours

Step-by-step explanation:  1. s*h

2. 20.4 hours  hope this helps.

The logistic equation that models the population of panthers in the preserve is:

\(P(t) = \frac{150}{ (1 + 135/150 * e^{(-0.02*t)})}\)

What is the constant of proportionality?

The constant of proportionality is the ratio between two directly proportional quantities. It can represent a number of things such as; an increase or decrease in a set of numbers, a(x,y) point on a graph, or it can just be shown in a table to show rate change.

The logistic equation models population growth when there is a carrying capacity. The equation is given by:

\(P(t) = \frac{K}{ (1 + A * e^{(-r*t)})}\)

where P(t) is the population size at time t, K is the carrying capacity, r is the growth rate, and A is a constant that determines the initial population size.

In this case, we can use the given information to determine some of these parameters. Let P(0) be the initial population size when the conservation organization releases 15 panthers into the preserve. Then we have:

P(0) = A

P(3) = 60

K = 150

To determine r, we can use the fact that the growth rate is proportional to the size of the population relative to the carrying capacity. That is:

r = k * (1 - P(t) / K)

where k is a constant of proportionality.

To find k, we can use the fact that the growth rate is the derivative of the logistic function:

r = dP/dt = k * P(t) * (1 - P(t) / K)

Plugging in P(0) = A and solving for k, we get:

k = r * A * (1 - A/K)

Now we can substitute these values into the logistic equation:

\(P(t) = K / (1 + A/K * e^{(-r*t)})\)

P(0) = A

P(3) = 60

K = 150

k = r * A * (1 - A/K)

Solving for A and k, we get:

A = P(0) = 15

k = r * A * (1 - A/K) = 0.231

To find r, we can use the formula we derived earlier:

r = k * (1 - P(t) / K)

Plugging in P(0) = 15 and k = 0.231, we get:

r = 0.231 * (1 - 15/150) = 0.02

Therefore, the logistic equation that models the population of panthers in the preserve is:

\(P(t) = \frac{150}{ (1 + 135/150 * e^{(-0.02*t)})}\)

where t is the time in years. Rounded to four decimal places, k = 0.231.

Hence, the logistic equation that models the population of panthers in the preserve is:

\(P(t) = \frac{150}{ (1 + 135/150 * e^{(-0.02*t)})}\)

To learn more about the constant of proportionality visit:

https://brainly.com/question/29161376

#SPJ1

Answer: it looks great but are all sides like that

Step-by-step explanation:

As someone who has turned in many of these projects in the last 4 years, I'd say it looks awsome but what made you think to make this design, If you coppied it off of an oragmi book or an ikea lamp change it to be more original

Angle ∠ABC and angle ∠CDE are supplementary angles. Then the value of the variable x will be 18°.

The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.

Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.

From the figure, the angle ∠ABC and angle ∠CDE are supplementary angles. Then we have

∠ABC + ∠CDE = 180°

2x + 8x = 180°

10x = 180°

x = 180° / 10

x = 18°

Then the value of the variable x will be 18°.

More about the angled link is given below.

https://brainly.com/question/15767203

#SPJ1

Answer:

y = 1.5x + 1.5

Step-by-step explanation:

Since it says it is growing at a constant rate, it means that is linear.

The linear formula follows this form: y = mx + c, where m is the gradient and c is the y-intercept

To find the gradient, you sub the values into the gradient formula.

That would be 4.5 - 3.0 divided by 2-1

That would be 1.5/1 = 1

Hence the gradient is 1.5

y = 1.5x + c

To find c, you sub in one point into the equation

I'm going to go with (3, 6.0)

6 = 1.5*(3) + c

6 - 4.5 = c

c = 1.5

Hence the formula is: y = 1.5x + 1.5

Answer:

3/4

Step-by-step explanation:

12kg/16kg= 6/8= 3/4

Hope this helps!

Pls mark brainliest if correct:)

If the sales tax in Brian’s area is 8.51%, then Brian pay in total is option (d) $507.96

Brian's credit card has an interest rate of 9.4% compounded monthly, which means that the interest is calculated based on the balance of the credit card at the end of each month. Therefore, the interest will accumulate over time, and Brian will have to pay more than the base price of $435.

Additionally, the sales tax in Brian's area is 8.51%, which means that he needs to pay this percentage of the total cost of his purchase as well.

To calculate how much Brian paid in total, we need to take into account the base price, the interest rate, and the sales tax.

First, let's calculate the total cost of the air conditioning unit including sales tax. The sales tax is 8.51% of the base price, which is:

8.51% x $435 = $37.02

So, the total cost of the air conditioning unit including sales tax is:

$435 + $37.02 = $462.04

Now, let's calculate how much Brian paid in interest. Since the interest rate is compounded monthly, we need to divide the annual rate by 12 to get the monthly rate. Therefore, the monthly interest rate is:

9.4% / 12 = 0.78333% (rounded to five decimal places)

Over a year and a half (or 18 months), the interest accumulated on Brian's credit card balance can be calculated using the following formula:

\(A = P(1 + r/n)^{nt} - P\)

where A is the total amount paid, P is the principal amount (which is the same as the base price of the air conditioning unit), r is the interest rate in decimal form, n is the number of times the interest is compounded per year (which is 12 in this case since the interest is compounded monthly), and t is the time in years (which is 1.5 in this case since Brian made monthly payments for a year and a half).

Substituting the values we have:

A = $435\((1 + 0.0078333)^{12\times1.5}\) - $435 = $45.92

Therefore, the total amount of interest paid by Brian is $45.92.

Finally, to calculate the total amount that Brian paid, we need to add the total cost of the air conditioning unit including sales tax and the total amount of interest paid:

$462.04 + $45.92 = $507.96

So, the correct answer is (d) $507.96, rounded to the nearest cent.

To know more about interest here.

https://brainly.com/question/29335425

#SPJ4

Answer:

Step-by-step explanation: You want to figure out how much it costs per ounce. You’ll divide $4.50/18 ounces to get $0.25 per ounce for the 18 ounce bag and $8.80/40 ounces to get $0.22 per ounce for the 40 ounce bag. The 40 ounce bag is cheaper per ounce.

Answer:

3.Events A and B are not independent because P(A|B) ≠ P(A).

Step-by-step explanation:

Given this information, which statement is true?

1.Events A and B are independent because P(A|B) = P(A).

2.Events A and B are independent because P(A|B) ≠ P(A).

3.Events A and B are not independent because P(A|B) ≠ P(A).

4.Events A and B are not independent because P(A|B) = P(A).

Solution:

Two events A and B are independent if A occurring does not change the probability of B. For independent events:

P(A ∩ B) = P(A) * P(B)

Hence: P(A/B) = P(A ∩ B) / P(B) = P(A) * P(B) / P(B) = P(A)

Let event A represent the probability that roger wins a tennis tournament and event B represent the probability that Stephan wins a tennis tournament.

Therefore:

P(A) = 0.45, P(B) = 0.4

The probability of Roger winning the tournament, given that Stephan wins, is 0. Hence, P(A/B) = 0

P(A/B) = P(A∩B) / P(B)

0 = P(A∩B) / 0.4

P(A∩B) = 0

The probability of Stephan winning the tournament given that Roger wins, is 0. Hence P(B/A) = 0

P(B/A) = P(B∩A) / P(A)

0 = P(B∩A) / 0.4

P(B∩A) = 0

Therefore since P(A∩B) = P(B∩A) =0, this means that event A and event B are mutually exclusive. That is both events cannot occur at the same time.

Events A and B are not independent because P(A|B) ≠ P(A).

The answer is (f) None of the above.

We can use the inclusion-exclusion principle to find the cardinality of the set A ∪ (B ∩ C). The formula is:

n(A ∪ (B ∩ C)) = n(A) + n(B) + n(C) - n(B ∪ C) - n(A ∩ B ∩ C)

We are given the values of n(A), n(B), n(C), n(A ∩ B), n(B ∩ C), and n(C ∩ A) from the Venn diagram. We can use these values to find n(B ∪ C) and n(A ∩ B ∩ C) as follows:

n(B ∪ C) = n(B) + n(C) - n(B ∩ C)

n(A ∩ B ∩ C) = n(A) + n(B) + n(C) - n(A ∪ B) - n(B ∪ C) - n(C ∪ A) + n(A ∩ B ∩ C)

Substituting the values from the Venn diagram, we get:

n(B ∪ C) = 50 + 28 - 16 = 62

n(A ∩ B ∩ C) = 18 + 16 + 28 - 50 - 62 - 20 + 10 = 0

Therefore,

n(A ∪ (B ∩ C)) = n(A) + n(B) + n(C) - n(B ∪ C) - n(A ∩ B ∩ C) = 32 + 50 + 20 - 62 - 0 = 40

So the answer is (f) None of the above.

Learn more about Venn

brainly.com/question/20795347

#SPJ11

Answer:

43cm

Step-by-step explanation:

Given

Length of Log = 291cm

First Piece = 67cm

Second Piece = 181cm

Required

Determine the length of the third piece

Given that the log was cut into three;

this implies that;

Length of Log = First Piece + Second Piece + Third Piece

Substitute values for first piece, second piece and length of log;

\(291 = 67 + 181 + Third\ Piece\)

\(291 = 248 + Third\ Piece\)

Subtract both sides by 248

\(291 - 248 = 248 - 248 + Third\ Piece\)

\(43 = Third\ Piece\)

\(Third\ Piece = 43\)

Hence, the length of the third piece is 43cm

$45 - 15% = $38.25

$53 - 20% = $42.04

So the Forever 21 dress would cost less.

Hope this helped.

Answer:

H

Step-by-step explanation:

As you can see the more shirt's that were bought the lower the price becomes per shirt.

You need to prove that ΔAEC ≅ ΔBED

You know that point E is the midpoint of AB and CD

The midpoint divides a line segment into two congruent lines. This means that E divides AB into two congruent segments AE and EB, and it also divides CD into two congruent segments CE and ED, then we can conclude that:

1. AE=EB → Reason Midpoint Theorem

2. CE=ED → Reason Midpoint theorem

Both lines AB and CD intersect at point E, forming an X shape. The ingles formed inside the X are vertically opposite angles, this means that

3. ∠AEC= ∠BED → Reason Vertically opposite angles

Since E is the midpoint where both "diagonals of the parallelogram" AB and CD intersect, then sides AC and DB are parallel. If AB || CD, then ∠ACE and ∠BDE are alternate interiors angles as well as ∠CAE and ∠DBE. Alternate interior angles are congruent, so that:

4. ∠ACE=∠BDE → Reason alternate interior angles, AB || CD

5. ∠CAE=∠DBE → Reason alternate interior angles, AB || CD

Then → ΔAEC ≅ ΔBED by SAS and AAA

Answer: $270

Step-by-step explanation:

I = prt

I = 0.18 x 750 x 2

I = 135 X 2

I = 270

Step-by-step explanation:

hope u understand from this picture

Answer:

292 and 2092

Step-by-step explanation:

Surface area:

Wall 1: 40 x 3 = 120m^2

Wall2: 40 x 3 = 120m^2

Wall 3: 15 x 3 = 45m^2

Wall 4: 15 x 3 = 45m^2

Ceiling: 15 x 40 = 600m^2

Total : 240 + 600 + 90 = 730

So, cost of painting = 730/25 x 10 = 29.2 x 10 = 292

Total: 292 + 1800 = 2092

The total cost of paint would be 2092 dollars.

The area of the cuboid is the sum of product of the length, breadth of the given prism.

Surface area:

Wall 1: 40 x 3 = 120m^2

Wall2: 40 x 3 = 120m^2

Wall 3: 15 x 3 = 45m^2

Wall 4: 15 x 3 = 45m^2

Ceiling: 15 x 40 = 600m^2

The Total area: 240 + 600 + 90 = 730

So, The cost of painting = 730/25 x 10

= 29.2 x 10

= 292

Total: 292 + 1800 = 2092

Learn more about cuboid;

https://brainly.com/question/15843335

#SPJ2

Answer:

the slope is 3

Step-by-step explanation:

The factored trinomial expression is (5p + 2)(2p - 1)

From the question, we have the following parameters that can be used in our computation:

10p^2-p-2

To factor the trinomial 10p^2 - p - 2, we can use the method of finding two numbers that multiply to -20p^2 and add to -p.

We can use these numbers to write the trinomial as a product of two binomials:

So, we have

10p^2 - p - 2 = 10p^2 - 5p + 4p - 2

Factorize

10p^2 - p - 2 = 5p(2p - 1) + 2(2p - 1)

This gives

10p^2 - p - 2 = (5p + 2)(2p - 1)

Read more about trinomial expression at

https://brainly.com/question/10799926

#SPJ1

Answer:

Pencils: 7 boxes

Erasers: 5 boxes

Step-by-step explanation:

She should buy 70 pencils and 70 erasers.

There are 7 pencil boxes for 70 pencils.

There are 5 eraser boxes for 70 erasers.

These are the smallest number of boxes she can buy without getting a fraction of a box.

Answer:

A line graph would best display the data for a student's average grade in math class for each month in a school year. A line graph would show the trend of the student's grades over time and help to identify any patterns or changes in the grades throughout the year.

Answer:

28 cm

Step-by-step explanation:

side opposite of 30° = x = shorter leg / opposite.

side opposite of 60° = x√3 = adjacent.

side opposite of 90° = 2x = hypotenuse.

Answer: Campbell to Hillsboro to Richmond to Winchester

(Note: Not taking the Washington route)

Step-by-step explanation:

Form Campbell all the way to Richmond have no other choices, From Richmond to Winchester has two choices, 12.2 mi +5.2 mi or 15.7 mi

12.2+5.2=17.4 mi while the other choice is only 15.7 mi

So taking the 15.7 mi option is faster

bro kjbvbbbbbbbbjnbbbjjjkkkkmnmkkknñ