Aubrey's dinner cost $85. She tips the waitstaff 30%% for excellent service How much does Aubrey tip the waitstaff? ​

Answer:

  1

Step-by-step explanation:

Use the form for the factoring of the sum of cubes.

To make this easier to write, we'll use the substitutions ...

  a = sin(θ), b = cos(θ)

It looks like you may want to simplify ...

  (a³ +b³)/(a +b) +ab

  = ((a +b)(a² -ab +b²))/(a +b) +ab

The factors of (a+b) cancel. In this case, we know that a² +b² = 1, so this becomes ...

  = (1 -ab) +ab

  = 1

  \(\boxed{\dfrac{\sin^3{\theta}+\cos^3{\theta}}{\sin{\theta}+\cos{\theta}}+\sin{\theta}\cos{\theta}=1}\)

The number one advantage of an experiment over an observational study is that an experiment allows for the manipulation of variables and the establishment of cause-and-effect relationships between variables.

In an experiment, researchers can control and manipulate the independent variable (the variable being tested) and observe the effects on the dependent variable (the variable being measured).

This level of control allows researchers to establish causal relationships between variables, which cannot be done in observational studies, where the researcher merely observes and measures the variables without intervening or manipulating them.

In other words, experiments allow researchers to determine whether a change in the independent variable causes a change in the dependent variable, which is crucial for making informed decisions in fields such as medicine, psychology, and social sciences.

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The equivalent of the expression \(\frac{(-7m^{4}+15m^{3}-12m^{2} )+(3m^{5}-12m^{4}-7m^{3} )}{m-6}\) is 3m⁴ - 19m³ + 8m² - 12m

Two expressions are said to be equivalent if they have the same value irrespective of the value of the variable(s) in them.

Equivalent algebraic expressions are those expressions which on simplification give the same resulting expression. Therefore, let's simplify the expression to get the equivalent.

Therefore,

\(\frac{(-7m^{4}+15m^{3}-12m^{2} )+(3m^{5}-12m^{4}-7m^{3} )}{m-6}\)

\(\frac{3m^{5} -7m^{4}-12m^{4}+15m^{3}-7m^{3}-12m^{2} }{m-6}\)

Hence,

\(\frac{3m^{5} -19m^{4}+8m^{3}-12m^{2} }{m-6}\)

Therefore,

3m⁴ - 19m³ + 8m² - 12m

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(a) There are 2²⁸ = 268,435,456 ways to place testing dummies into the rollercoaster

(b) There are 15 × 2²⁴ = 402,653,184 ways to place dummies into the rollercoaster if the front car must have 3 or fewer testing dummies.

(c) There is only 1 × 2²⁴ = 16,777,216 way to place dummies into the rollercoaster if the back car must be empty.

(d) There are 15 × 2²⁰ = 15,728,640 ways to place dummies into the rollercoaster if neither the front nor the back car can be full.

a) There are 7 cars and each car has 4 seats, there are a total of 7 × 4 = 28 seats. Each seat can either be occupied by a testing dummy or left empty.

For each seat, there are two possibilities (dummy or empty). Since each seat can be treated independently, the total number of ways to place the testing dummies is 2²⁸.

2²⁸ = 268,435,456

b) If the front car must have 3 or fewer testing dummies,

The front car can have 0, 1, 2, or 3 testing dummies.

There are C(4, 0) + C(4, 1) + C(4, 2) + C(4, 3) = 1 + 4 + 6 + 4 = 15 ways to select the number of dummies for the front car.

The remaining 6 cars can have any number of dummies between 0 and 4. Each car has 4 seats, and each seat can be occupied by a dummy or left empty. So, there are 2⁴ possibilities for each of the 6 remaining cars.

Total number of ways = 15 × (2⁴)⁶ = 15 × 2²⁴.

15 × 2²⁴ = 402,653,184

c) If the back car must be empty, we can calculate the number of arrangements by considering the possibilities for the back car and then multiplying it by the remaining possibilities for the other cars.

The back car can have 0 dummies. There is only 1 possibility for the back car.

The remaining 6 cars can have any number of dummies between 0 and 4. Each car has 4 seats, and each seat can be occupied by a dummy or left empty. So, there are 2^4 possibilities for each of the 6 remaining cars.

Total number of ways = 1 × (2⁴)⁶ = 1 × 224.

1 × 2²⁴ = 16,777,216

d) If neither the front nor back car can be full, we can calculate the number of arrangements by considering the possibilities for both the front and back cars and then multiplying it by the remaining possibilities for the other cars.

The front car can have 0, 1, 2, or 3 testing dummies. There are C(4, 0) + C(4, 1) + C(4, 2) + C(4, 3) = 1 + 4 + 6 + 4 = 15 ways to select the number of dummies for the front car.

The back car can have 0 dummies. There is only 1 possibility for the back car.

The remaining 5 cars (excluding the front and back cars) can have any number of dummies between 0 and 4. Each car has 4 seats, and each seat can be occupied by a dummy or left empty. So, there are 2^4 possibilities for each of the 5 remaining cars.

Total number of ways = 15 × 1 × (2⁴)⁵ = 15 × 2²⁰.

15 × 2²⁰ = 15,728,640

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The question is incomplete the complete question is :

an amusement park is testing a roller coaster ride for safety. the roller coaster has 7 distinguishable cars, each of which contains 4 distinguishable seats. each seat can either be occupied by a testing dummy or left empty. the dummies are indistinguishable from one another, and there are enough to fill every car. for all sub-problems below, you are allowed to leave the entire ride empty, fill every seat in the ride, or anything in between. (update 2/17/23: the cars cannot be rearranged. they are fixed in one order.) a.) how many ways are there to place testing dummies into the rollercoaster? b.) how many ways are there to place dummies into the roller coaster if the front car must have 3 or fewer testing dummies in it? c.) how many ways are there to place dummies into the roller coaster if the back car must be empty? d.) how many ways are there to place dummies into the roller coaster if the neither the front or back car can be full?

Points a,b and c satisfied the Pythagoras theorem. Thus, the triangle abc is a right angled triangle.

Every triangle has inner angles that add up to 180 degrees. A right angle and a right triangle are both formed when one of their internal angles is 90 degrees.

Given coordinates :

a(5,2) , b(2,-3) and c(-8,3).

Find the distance between the points using the distance formula:

d = √[(x2 - x1)² + (y2 - y1)²]

ab = √[(2 - 5)² + (- 3 - 2)²]

ab = √[(-3)² + (- 5)²]

ab = √[9 + 25]

ab = √34

ab² = 34

bc = √[(2 + 8)² + (- 3 - 3)²]

bc  = √[(10)² + (- 6)²]

bc  = √[100 + 36]

bc  = √136

bc²  = 136

ac = √[(-8 - 5)² + (3 - 2)²]

ac = √[(-13)² + (1)²]

ac = √[169 + 1]

ac = √170

ac² = 170

Now,

(ac)² = (bc)² + (ab)²

170 = 136 + 24

170 = 170

This, points a,b and c satisfied the Pythagoras theorem. Thus, the triangle abc is a right angled triangle.

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Answer:

x=72

Step-by-step explanation:

The values less than 4 or greater than 14 cannot be the length of the third side

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

Side lengths of 9 and 5.

Represent the third length of the triangle with x

So, we have the following representation (using the triangle inequality theorem)

a + b ≥ c.

Substitute the known values in the above equation, so, we have the following representation

9 + 5 ≥ x

9 + x ≥ 5

5 + x ≥ 9

Evaluate the sum

14 ≥ x

x ≥ -4

x ≥ 4

So, we have

14 ≥ x

x ≥ 4

Combine

4 ≤ x ≤ 14

This means that values less than 4 or greater than 14 cannot be the length of the third side

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The measure that  cannot be the length of the third side is 14. Option

An important rule to remember about triangles is called the third side rule:

Third side rule of triangles states that;

The length of the third side of a triangle is less than the sum of the lengths of the other two sides and greater than the (positive) difference of the lengths of the other two sides.

For this triangle, the length of the third side must be greater than

9- 5= 4

Also, the length of the third side must be less than

9 + 5 = 14

Hence,  all the answers are possible except for answer D, which is equal to 14 but not less than 14.

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The Complete question is added as:

A triangle has side lengths of 9 and 5. Which of the following cannot be the length of the third side? *

a. 4

b. 5

c. 11

d. 14

Answer:

congruent angles : are all corresponding angles, exterior and interior alternative angles

congruent to ABE :angles  GBC, BCF,HCD

angles FCD and HCD are supplementary angles=180

FCD+HCD=180

Answer:

y = 4x +17

Step-by-step explanation:

we can find the equation of line when given two points or a point and the gradient/slope.

In the above line we have two points (0,10) and (10,50),

The slope of the line is therefore 4

 Parallel lines have equal slopes or gradient, therefore the slope of the other line is still 4. And the line pases through a point (2,25), hence

Equation will be, (y-25)/(x-2) = 4

                          = y-25 = 4x-8

                          = y =4x +17

Thus the appropriate equation is y = 4x +17

Answer:

Y = 4 x + 17

Step-by-step explanation:

Confirmed. Just took it

(a) In the case where A is the set of all words of English and R is defined by the alphabetical order, R is a partial order on A. This is because R meets the criteria for a partial order: reflexivity, antisymmetry, and transitivity.

However, R is not a total order, as some words may not be directly comparable, such as words starting with the same letter.

(b) When A is the set of all words of English and R is defined by the first letter's alphabetical order, R is again a partial order on A.

It meets the same criteria as mentioned before: reflexivity, antisymmetry, and transitivity. But it is not a total order, as words with the same first letter cannot be compared based on this relation.

(c) For A being the set of all countries and R defined by population, R is a partial order on A. The criteria for reflexivity, antisymmetry, and transitivity are met as well.

However, R is not a total order since countries with the same population size cannot be compared.

In summary, all three cases exhibit partial orders on A, but none of them represent total orders.

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The coefficient of determination for the model is 0.8675

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

anova

                      df      ss                   ms                f                significance f

regression     11   21.2410567  1.93100515 23.20340372 9.2023e-14

residual          39 3.245610081 0.08322077

total               50  24.48666678

The coefficient of determination for the model is calculated as

r² = 1 - RSS/TSS

From the table, we have

RSS = 3.245610081

TSS = 24.48666678

Substitute the known values in the above equation, so, we have the following representation

r² = 1 - 3.245610081/24.48666678

Evaluate

r² = 0.8675

Hence, the value of r² is 0.8675

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Answer:

\(\frac{95}{5} \frac{km}{hour}= 19.2 km/hour\)

Step-by-step explanation:

Average speed = distance/time

Average speed = \(\frac{9.6}{30} \frac{km}{min}\) ; multiply by 60min/1hour

Average speed = \(\frac{95}{5} \frac{km}{hour}= 19.2 km/hour\)

Answer:

5

Step-by-step explanation:

5+5(0)

Answer:

g(x) = 3x - 3

Step-by-step explanation:

Slope-Intercept Form: y = mx + b

If a line is parallel to another, they have the same slope.

Step 1: Define variables

m = 3

Random pt (2, 3)

y = 3x + b

Step 2: Find b

3 = 3(2) + b

3 = 6 + b

b = -3

Step 3: Write parallel linear equation

y = 3x - 3

Answer:

1.False

2. True

3.) True

4. False

5.) False

6.) True

Step-by-step explanation:

1.)

Range = maximum - minimum

New year's eve :

Maximum = 22 ; minimum = 3

Range = 22 - 3 = 19

2.)

Median for Thanksgiving = 17

50% up to 17 ;hence the remaining 50% is also 17 and above

4.)

IQR for Thanksgiving

Q3 - Q1

23 - 12 = 11

5.)

The median number of people at new year's eve for dinner was 7 (line in between the box)

6.)

3/4th of new year eve's dinner = Q3 = 15

1/4 = Q1 ; have up to 5 people

Therefore ; the remaining (1 - 1/4) = 3/4 have 5 and above

Answer:

1.False

2. True

3.) True

4. False

5.) False

6.) True

Step-by-step explanation:

Answer:

I hope this helps:)

Step-by-step explanation:

Answer:

True.

Step-by-step explanation:

To find out if the statement is true, just plug in 8 each time you see x.

3(8)+ 4 = 28

5(8) - 12 = 28

This proves the statement is true, x = 8.

I hope this helps. If you have any more questions, please feel free to post them and someone will be able to help you, whether it's myself or others. Please leave a like, rating, and if possible, Brainliest. Have a great day!    

Answer: False

Step-by-step explanation:

3x + 4 =5x - 12

step1: get x by it self

you would get; 4 = 2x - 12

step2; make zero-pairs

you would get;   2x - 8

lastly; 8÷2=4x

The largest area possible is when the length and width of the chicken pen are both 100 feet. In that case, the area of the chicken pen would be 10,000 square feet.

We are given that the farmer has 200 feet of fencing to build a rectangular chicken pen along the side of a barn. We need to find the largest possible area the chicken pen can have.

To do this, we need to find the length and width of the chicken pen such that the total amount of fencing used is 200 feet.

Since the total amount of fencing needed is 200 feet, the length and width of the chicken pen must both be 100 feet. In this case, the area of the chicken pen would be 10,000 square feet.

Therefore, the largest area possible is 10,000 square feet when the length and width of the chicken pen are both 100 feet.

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To duplicate angle ABC, draw a line segment, position the compass on point A, and then draw an arc that intersects the line segment. Next, position the compass on point B, and then draw a second arc that intersects the first arc at a point on the line segment. Finally, position the compass on the point where the two arcs intersect, but without changing the width, and draw a third arc that intersects the line segment.

When two straight lines or rays intersect at a single endpoint, an angle is created. The vertex of an angle is the location where two points come together. The Latin word "angulus," which means "corner," is where the term "angle" originates.

Common instruments used to measure angles are:

1. Protractor

2.Compass

3.Digital Angle finder

4.Angle finder

5.Clinometer

6. Inclinometer

You can take the following actions to copy angle ABC:

Create a line segment that will serve as the foundation for the new angle you're going to create.

Draw an arc that crosses the line segment you produced in step 1 by positioning the compass on point A.

Draw a second arc that crosses the previous arc at a point on the line segment by setting the compass on point B.

Place the compass on the intersection of the two arcs without adjusting the compass's width, then create another arc that crosses the line segment.

Point D is where the second arc crosses the line segment. To finish the new angle, join points D and C.

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Answer: (a). M=7x180+39+700. (B) $731

Step-by-step explanation:

Equation to represent the given situation is 7(19.70 + 1.97 + m X 0.05) = 180.39; additional minutes, on average, you use each month is 82

A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept.

Given that;

Total cost for 7 month =$180.39

Let m be the average number of minutes  that exceeds 700 minutes every month

Equation formed;

7(19.70 + 1.97 + m X 0.05) = 180.39,

or,  7(19.70 + 1.97 + m X 0.05) = 180.39,

or, 21.67 + 0.05m = 180.39/ 7,

or, 0.05m = 25.77 – 21.67,

0.05m = 4.1

m= 82

Therefore,  equation for (a) : 7(19.70 + 1.97 + m X 0.05) = 180.39 and 82 will be the answer of (b)

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Answer:

(x+7)(x+6)

Step-by-step explanation:

x²+13x+42

x²+6x+7x+42

x(x+6)+7(x+6)

(x+6)(x+7)

Answer:

a) (x+7) (x+6)

Step-by-step explanation:

That is the correct answer because you get it when you factor the current equation.

Hope it helps

Answer:

[see below]

Step-by-step explanation:

I used a graphing program to graph the given system. I also graphed the points given.

Options B's choice lies in the double shaded area, so it would be a solution to the system.

See the graph attached!

Hope this helps you!  

Answer:

24 minutes

The answer is 24 I've had that question before

The probability that the next piece of track Carly picks will be straight is 8/24 or 1/3

From the given information, Carly has picked 8 straight, 7 curved, 4 cross, and 5 switch tracks.

The total number of pieces of the track she has picked is 8 + 7 + 4 + 5 = 24

The probability that the next piece of track Carly picks will be straight is calculated as follows:

Probability = Number of straight tracks/Total number of tracks= 8/24= 1/3T

Therefore, the probability that the next piece of track Carly picks will be straight is 1/3.

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Answer: 1/3

Step-by-step explanation: i did this question and got it right

Answer:

Step-by-step explanation:

3/4

Answer:

Aren't sufficiently brief!

The phrase add VERBAL IRONY to the paragraph would be that they "are too precise."

Irony means expressing by words, actions or events something opposite of what really is meant or desired.

Therefore, Verbal irony refers use of words to say something opposite of what one actually means or wants to say.

Examples:

The teacher finds her student that has hand-writing illegible and tells him that h deserves a prize for such a nice hand-writing.

We can conclude that phrase add VERBAL IRONY to the paragraph ;

they "are too precise."

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Answer: x= -30763/27

Step-by-step explanation:

The point \(2\sqrt{46},19,19\) is not on the unit circle. The point \(178,19,19\) is on the unit circle.

A point lies on the unit circle if and only if its distance from the origin is equal to one. Therefore, to determine whether the point lies on the unit circle or not, we will find its distance from the origin. Using the Pythagorean theorem, we get:

[\begin{aligned} &\sqrt{(2\sqrt{46})^2+(-178)^2+(19)^2+(19)^2}

&=\sqrt{184+31684+361+361}\\

&=\sqrt{32590}\\

&=\sqrt{50^2\cdot13}\\

&=50\sqrt{13}.

\end{aligned}\].

Since the distance from the origin is not equal to one, the point \((2\sqrt{46},

-178,19,19)\)

is not on the unit circle.

The point \(O(178,19,19)\) is on the unit circle because its distance from the origin is equal to one:

\[\sqrt{(178)^2+(19)^2+(19)^2}

=\sqrt{33436}

=2\sqrt{836}

=2\cdot2\sqrt{209]

=4\sqrt{209}.

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The perimeter of the rectangle is  4y + 6 (cm).

All four side lengths must be added up in order to get the perimeter, or the distance around the rectangle. Since there are two of each side length, it is simple to multiply the total of the length and the breadth by two in order to do this task effectively. The formula for perimeter is perimeter=(length Plus width)2.

The diagram shows a rectangle. All measurements are in centimetres  an expression in terms of y, for the perimeter of the rectangle.

The perimeter of the rectangle is

2(y+3)+24

=2y + 6 + 2y = 4y + 6 (cm)

{ the perimeter:

2 *  width + 2 * Length}

The perimeter of the rectangle is  4y + 6 (cm).

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