help meeeeeeeeeeeeee pleaseeeeeeeeee!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Help Meeeeeeeeeeeeee Pleaseeeeeeeeee!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

Answer 1

Answer:

0.64 feet

Step-by-step explanation:

make h the subject of this expression

[tex]t = \sqrt{ \frac{h}{16} } [/tex]

[tex] {t}^{2} = \frac{h}{16} [/tex]

[tex]h = 16 {t}^{2} [/tex]

then substitute in the value of t=0.2 into the equation of h:

h = 16 × (0.2)² = 0.64 feet(answer)


Related Questions

Can anyone write the equation of the graph?

Answers

Answer:

f(x) = |x-3| + 5

please help asap will give brainliest

Answers

1. The angles measures are larger than the original angle measures is a false statement.

2. If two sides parallel in the original figure, then those sides are parallel in the final figure is true statement.

3. The final angle measure are the same as the original angle measure is false statement.

4. The original figure and the final figure may not be congruent is true statement.

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 word "angle" originates.When two lines meet at a point, an angle is created. An "angle" is the measurement of the "opening" between these two rays. It is symbolised by the character. The circularity or rotation of an angle is often measured in degrees and radians. Angles are a common occurrence in daily life. Angles are used by engineers and architects to create highways, structures, and sports venues.When two rays are linked at their ends, they create an angle in geometry. The sides or arms of the angle are what are known as these rays. 

To know more about angles check the below link:

https://brainly.com/question/25716982

#SPJ1

The dimensions of a rectangular garden are 15 yards by 20 yards. A sidewalk, one yard wide, is to be built around the outside of the garden. What will be the area of the sidewalk?​

Answers

Answer:

74 square yards

Step-by-step explanation:

Area of two-dimensional shapes:

Area of rectangular garden:

                 l = 20 yds

                 w = 15 yds

     Area of the rectangular garden = l *w

                                                          = 20 * 15

                                                          = 300 square yards.

Area of the outer rectangle (rectangular garden and the sidewalk):

             length = 20 + 1 + 1 = 22 yds

            width   = 15 + 1 + 1  = 17 yds

       Area of outer rectangle = 22 * 17

                                               = 374 square yards

To find the area of the sidewalk, subtract the area of rectangular garden from the outer rectangle.

Area of the sidewalk = area of outer rectangle - area of sidewalk

                                  = 374 - 300

                                  = 74 square yards

Kenneth has entered a check payment of $350.25 in his checkbook. If the old balance was $545.95, what is his latest balance?
A.
$896.25
B.
$195.70
C.
$195

Answers

Answer: $195.70

Step-by-step explanation:

Beverly is making peanut butter-banana bread. She always doubles the amount of nuts and peanut butter chips. The total amount of chips and nuts after doubling is 412 cups.
Write and solve an equation to find the original amount of nuts, x, in the recipe.

Answers

The original amount of nuts, x, in the recipe is 103

The equation for the original amount is 2x + 2x = 412

What is an algebraic expression?

An algebraic expression can be defined as an expression made up of terms, factors, constants, coefficients, and variables.

These expressions are also known to be made up of mathematical operations such as;

SubtractionAdditionMultiplicationDivisionBracketParentheses

From the information given, we have that;

Beverly doubles the amount of nuts and peanut butter chips

Total number = 412

This is represented as;

2x + 2x = 412

collect like terms

4x = 412

Make 'x' the subject of formula

x = 412/ 4

x = 103

Hence, the value is 103

Learn more about algebraic expressions here:

https://brainly.com/question/4344214

#SPJ1

PLEASE HELP ME WITH GEOMERY

Answers

The blanks in this two-column proof should be completed (filled) as follows:

Statements                                             Reasons_______________

m∠RST = 5x° and m∠UVW = 7x°                Given

∠RST and ∠UVW are supplementary

m∠RST = 5x° + m∠UVW = 180           definition of supplementary angles

5x + 7x = 180                                       substitution property of equality

12x = 180                                              addition property of equality

x = 15                                                    division property of equality

What is a supplementary angle?

In Mathematics, a supplementary angle simply refers to two (2) angles or arc whose sum is equal to 180 degrees.

Additionally, the sum of all of the angles on a straight line is always equal to 180 degrees. In this context, we can logically deduce that the sum of angles RST and UVW are supplementary angles:

Read more on supplementary angle here: brainly.com/question/13250148

#SPJ1

What’s the answer 60 points plus brainliest also explanation needs to be included

Answers

Answer:

both a and b

Step-by-step explanation:

It is because in the elimination method it does not matter whether you eliminate x or y so if you use option a which multiplies -2 by 1st equation so it will become:

-4x+6y=40

4x+6y=8

so the -4x and 4x cancels and a is a valid option.

If you use the b which multiplies the second with 3 it becomes:

2x-3y=-10

4x+3y=24

so -3y and 3y cancel which also makes this a valid option.

Answer: both a and b

Determine the sum of the factors of 100​

Answers

The factors of the number 100 are: 1, 2, 4, 5, 10, 20, 25, 50, 100. If you add them up, you will get the total of 217

Solve the following system of equations. Show your work.

y=−3x+5

5x−4y=−3

Solution:

Answers

Y=-3x+5
5x-4y=-3

5x-4(-3x+5)=-3
5x+12x-20=-3
17x-20=-3
17x=17

X=1

Identify the kind of sequence shown: 2,-1,-4, -7, -10, ... *
O Arithmetic
O Geometric
ONeither

Answers

Arithmetic. Any Arithmetic sequence is constant


Consider the line y=-8/5x+6.

Find the equation of the line that is parallel to this line and passes through the point (5, 3).
Find the equation of the line that is perpendicular to this line and passes through the point (5, 3).
Note that the ALEKS graphing calculator may be helpful in checking your answer.
Equation of parallel line:
Equation of perpendicular line:

Answers

Step-by-step explanation:

the equation

y = -8/5 x + 6

tells us 2 things :

-8/5 is the slope of the line, 6 is the y-intercept (the y value when x = 0).

a parallel line has the same slope (just a different y-intercept) : -8/5

a perpendicular line (intercepts at 90°) turns the original slope upside-down and flips the sign : 5/8

we the use the given point as x and y values and calculate the y-intercepts.

parallel :

3 = -8/5 × 5 + y-intercept = -8 + y-intercept

11 = y-intercept

y = -8/5 x + 11

perpendicular :

3 = 5/8 × 5 + y-intercept = 25/8 + y-intercept

(3×8)/8 = 24/8 = 25/8 + y-intercept

-1/8 = y-interceot

y = 5/8 x - 1/8 = 1/8 × (5x - 1)

3
6
Find the value of x.
x
x = [?]

Answers

For the given triangle, the value of x would be 12.

What is the geometric mean theorem of a triangle?

According to the geometric mean theorem, the length of an altitude drawn from a triangle's right angle to its hypotenuse is equal to the geometric mean of the lengths of the segments formed on the hypotenuse.

For the given triangle, we can apply the geometric mean theorem,

                      By the geometric mean theorem, we can write

                                      6² = 3 * x

                                      36 =  3 * x

                                  ⇒ x = 36/3

                                  ⇒ x = 12.

Hence, for the given triangle, the value of x would be 12.

To learn more about the geometric mean theorem of a triangle, visit:

https://brainly.com/question/26257841

#SPJ1

i need help please!!! i dont know​

Answers

The locations of the destinations given by the angles formed between parallel lines and their common transversal in the question are;

1) US Capitol

2) CIA Building

3) US Capitol

4) US Treasury

5) Walmart

What are the relationships between the angles formed by parallel lines that have a common transversal?

The relationship between the angles formed are;

Corresponding angles are congruentSame side interior angles are supplementaryAlternate interior angles are congruentAlternate exterior angles are congruentVertical angles are congruent

1) The location that is at a corresponding angle to the White House is the Supreme Court

The location at the vertical angle to the Supreme Court is the Smithsonian Institute

The location that is at the angle right adjacent to the Smithsonian Institute is the US Capitol

The destination location is the US Capitol

2) The location that is vertical angles to the FBI Building is the National Zoo

The same side interior angle to the National Zoo is the National Coffee shop

The location at the alternate interior angle to the National Coffee Shop is the CIA Building

The location is the CIA Building

3) The location at the alternate exterior angles to Lincoln Memorial is Walmart

The adjacent location that is a right angle to Walmart is the White House Gardens

The location that is at the corresponding angle to the White House Gardens is the US Capitol

The location is the US Capitol

4) The location that is at the corresponding angle location to the Smithsonian Institute is the National Zoo Gift Shop

The location that is at the same side interior angle to the national gift shop is the US Capitol

The location that is at the vertical angle location to the US Capitol is the US Treasury

The current location is the US Treasury

5) The location that is at alternate interior angle location to the Ford's theater is the US Capitol.

The location that is supplementary with the Vietnam War Memorial and the National Zoo is the National Coffee Shop

The location at the angle that is vertical from the National Coffee Shop is the Lincoln  Memorial

The location that is at alternate exterior angle with the Lincoln Memorial is Walmart

The location is Walmart

Learn more about angles formed by parallel lines that have a common transversal here:

https://brainly.com/question/7134800

#SPJ1

Steven hit the ball 12 times out of 26 at bats in the first half of the season and 6 times out of 14 at bats in the second half of the season. What is his batting average for the whole season, written as a decimal?

Answers

Answer:123

Step-by-step explanation:

7328x3424

Steven battling average for the whole season he played was 0.45

How to solve an equation?

An equation is an expression showing the relationship between two or more numbers and variables.

Steven hit the ball 12 times out of 26 at bats in the first half of the season and 6 times out of 14 at bats in the second half of the season.

Hence:

Batting average = (total number of time he hit the ball in both season half) / (total number of balls thrown)

Therefore:

Battling average = (12 + 6)/ (26 + 14) = 18 / 40 = 0.45

Steven battling average was 0.45

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

(b)
Simplify
45e6f8
5ef²

Answers

Answer:
45e^7 f^87
Step-by-step explanation:

A cat’s heart beats approximately 45 times in 15 seconds. At this rate how many times does the cat′s heart beat per second?

Answers

Correct Answer:
3 beats per second.

Explanation:
45 beats = 15 seconds
45/15 beats = 15/15 second
3 beats = 1 second

a man has extra digits (six fingers on each hand and six toes on each foot). his wife and their daughter have a normal number of digits. having extra digits is a dominant trait. the couple's second child has extra digits. what is the probability that their next (third) child will have extra digits?

Answers

The likelihood of their next third child having additional digits of (six fingers on each hand and six toes on each foot) is 1/2.

Define the term dominant traits?A trait is a distinguishing characteristic that a person possesses. Dominant traits are defined as having only one copy of a gene on a chromosome which expresses a specific trait.Individuals exhibit the dominant traits most prominently. Polydactyly is the dominant condition in this case.

For the given condition,

The father has six fingers plus six toes, while the mother is still in normal condition. In this particular case, polydactyly is a dominant characteristic. Twelve percent of the couple's children are projected to have additional digits.

Because the father has the dominant feature as well as the mother is now in normal condition, there is a 50% chance that this deformity will be passed down to children.

Thus, the likelihood of their next (third) child having additional digits is 1/2.

To know more about the dominant traits, here

https://brainly.com/question/14675750

#SPJ4

BRAINLIEST!! A helicopter descends until it reaches the ground. The equation y=-300x+ 1200 gives the height. Y, in feet, x minutes after the pilot begins the descent

Answers

Graph for the equation ( y = -300x +  1200 ) below

y-intercept = ( 0, 1200 )

x-intercept = ( 4, 0 )

Hope this helps! :)

The y-intercept is ( 0, 1200 ) and the x-intercept is ( 4, 0 ).

What is Graph?

The graph is simply a structured representation of the data. It aids in our comprehension of the data. The numerical information gathered through observation is referred to as data.

In a line graph, the information or data is represented as a series of markers, or dots, and is then connected to one another by a straight line.

Given:

y=-300x+ 1200

Now, for y- intercept put x=0

y= 1200

and, for x- intercept put y= 0

0 = -300x +1200

x= 4

Hence, the y-intercept is ( 0, 1200 ) and the x-intercept is ( 4, 0 ).

Learn more about Graph here:

https://brainly.com/question/17267403

#SPJ2

Question 1 of 10
Which of the following is the solution to | x1-2 ≤-3?
O A. All values are solutions
OB. xs-1 and x 25
OC. xs-1
OD. No solution

Answers

x = -1 is the solution to the given inequality |x| - 2 ≤ -3.

The five steps to resolving inequalities are as follows?

When addressing an inequality, we can:

Equal numbers are added to both sides.Take the same amount away from both sides.Add the same positive number to both sides.Subtract the same positive value from both sides.Reverse the sign and multiply both sides by the same negative value.

Isolate the variable on one side of the inequality and place all other constants on the other. To achieve this, alter the inequality by performing opposing procedures. First, multiply each side by two to isolate the x. Any action you take toward one side must also be taken toward the other.

C) If x = -1,

|x| - 2 ≤ -3

|-1| - 2 ≤ -3.

1 - 2 ≤ -3.

-1 ≤ -3 which is true.

Hence, x = -1 is the solution to the given inequality |x| - 2 ≤ -3.

To know more about inequalities check the below link:

https://brainly.com/question/24372553

#SPJ1

The following graph shows a proportional relationship.

What is the constant of proportionality between y and x in the graph?​

Answers

Answer:

Step-by-step explanation:

parameters are group of answer choices numerical characteristics of a sample. numerical characteristics of a population. the averages taken from a sample. numerical characteristics of either a sample or a population.

Answers

The correct answer is Option B. Parameters are defined as a group of numerical characteristics of a population.

Parameters are generally the numbers or values that represent the whole population's numerical characteristics. There is a difference between Statistics and Parameters.

Statistics is generally defined as the numerical characteristics of a sample. For example, a sample of standard mean or a sample of standard deviation is an example of statistics.

Parameters are the numerical representation of the characteristics of a population. For example, Population mean or Population standard deviation are examples of Parameters. These represent the data or the characteristics of the population in numerical.

Hence, the correct answer is Option B.

To know more about Parameters, Click here:
https://brainly.com/question/14019949

#SPJ4

The correct answer is Parameters are described as a group of numerical characteristics of a population.

In general, Parameters are the numerical values that represent the entire population's numerical characteristics. There is a variation between Statistics and Parameters. Statistics are defined as the numerical characteristics of a sample. A sample of standard mean deviation or a sample of standard deviation are examples of statistics.

               Parameters are the numerical portrayal of the characteristics of a population.  Population mean deviation or Population standard deviation are examples of Parameters. These depict the information or the characteristics of the population in a numerical way.

Hence, the correct answer is Parameters are described as a group of numerical characteristics of a population.

To learn more about Parameters:

brainly.com/question/13794992

#SPJ4

help plss!!!

Based on the tables showing the price of buying different amounts of two brands of sugar. Suman determined that Sweet Sugar was the better buy based on price alone. How much money per pound will Suman save if he buys the Sweet Sugar brand?​

Answers

Answer: b

Step-by-step explanation:

Answer:

He will save 1 cent per pound if he buys the Sweet Sugar brand

Select the correct answer. Given that a function, g, has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45 and that g(0) = -2 and g(-9) = 6, select the statement that could be true for g. A. g(-13) = 20 B. g(7) = -1 C. g(0) = 2 D. g(-4) = -11

Answers

The statement which could be true for the function, g as required in the task content is; Choice C; g(0) = 2.

Which of the statements could be true for the function g?

It follows from the task content that the statement which could be true about the function g is to be identified.

Since the given function instances are; g(0) = -2 and g(-9) = 6.

Since the function, g, has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45.

Hence, the statement which could be true about the function, g is; Choice C; g(0) = 2.

This is so because, 0 is in the domain of the function and 2 is in the range of the function.

Read more on domain and range;

https://brainly.com/question/2264373

#SPJ1

You-Pick Blueberry Farm sells 6 pounds of blueberries for $16.50.

How much would 9 pounds of blueberries cost?
How much would 5 pounds of blueberries cost?

I will give brainly! worth 23 points! please hurry!

Answers

The value of 9 pounds of blueberries is $24.75.

The value of 5 pounds of blueberries is $13.75.

How to calculate the cost?

The fact that the Blueberry Farm sells 6 pounds of blueberries for $16.50 implies that the cost per pound will be:

= $16.50 / 6

= $2.75

Therefore, 9 pounds of blueberries cost:

= Cost per pound × 9

= $2.75 × 9

= $24.75

5 pounds of blueberries will cost:

= 5 × $2.75

= $13.75

Learn more about cost on:

brainly.com/question/25109150

#SPJ1

Delta Airlines' flights from Denver to Dallas are on time 80 % of the time. Suppose 7 flights are randomly selected, and the number on-time flights is recorded.

Round answers to 3 significant figures.


The probability that exactly 4 flights are on time is =



The probability that at most 3 flights are on time is =



The probability that at least 6 flights are on time is =

Answers

1) Probability that exactly 4 flights are selected is; P(X = 4) = 0.11469

2) The probability that at most 3 flights are on time is; P(X ≤ 3) = 0.99533

3) The probability that at least 6 flights are on time is; P(X ≥ 6) = 0.57672

How to solve Binomial Probability Distribution?

The formula for binomial probability distribution is;

P(r) = nCr * p^(r) * (1 − p)^(n − r)

Where;

n = Number of events

r = Number of successful events in the trials

p = Probability of success in the single trial of the events

We are given;

p = 80% = 0.8

n = 7

1) Probability that exactly 4 flights are selected is;

P(X = 4) = ⁷C₄ * 0.8⁴ * (1 − 0.8)^(7 − 4)

P(X = 4) = ⁷C₄ * 0.8⁴ * 0.2³

P(X = 4) = 0.11469

2) The probability that at most 3 flights are on time is;

P(X ≤ 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)

Solving using online binomial calculator gives;

P(X ≤ 3) = 0.99533

3) The probability that at least 6 flights are on time is;

P(X ≥ 6) = P(X = 6) + P(X = 7)

P(X ≥ 6) = 0.57672

Read more about Binomial Probability Distribution at; https://brainly.com/question/15278907

#SPJ1

Which equation represents a line which is perpendicular to the line y=-4x-5?
A. x+4y=-32
B.4x+y=3
C.4x−y=−4
D.4y−x=4

Answers

Answer:

D.4y−x=4

Step-by-step explanation:

Perpendicual lines have a slope that is the negative inverse of the referenced line.  The reference here is:

       y = -4x-5

The slope is -4

The negative inverse of -4 would be +(1/4).  Any line that has a slope of +(1/4) will be perpendicular to y=-4x+5.

The equations in the answer options are not arranged according to the standard format of y=mx+b, where m is the slope and b the y-intercept.

We could graph all the equations and look for the one(s) that are perpendicualr, but it might be safer, and faster, to rearrange them in the standard format, and then note the slope:

                                  Slope     =+(1/4)?

A. x+4y=-32  

    4y= -x-32

     y = -(1/4)x-8        -(1/4)           NO

B.4x+y=3

     y = -4x + 3            -4                NO

C.4x−y=−4

     y = 4x + 4             4                 NO

D.4y−x=4              

     4y=x+4               +(1/4)      <==YES

      y=(1/4)x+1    [Option D has a slope of +(1/4).  It will be perpendicular]

See the attached graph.

rocio is covering the curved surface of a cylindrical podium in wallpaper. the podium is 1.2 meters tall and has a diameter of 0.26 meters. about how much wallpaper does rocio need? a. b. c. d.

Answers

The area of wallpaper required is 0.98 [tex]m^{2}[/tex]

What is mensuration ?

Mensuration is a division of mathematics that studies geometric figure calculation and its parameters such as area, length, volume, lateral surface area, surface area, etc. It outlines the principles of calculation and discusses all the essential equations and properties of various geometric shapes and figures. 

Mensuration is a subject of geometry. Mensuration deals with the size, region, and density of different forms both 2D and 3D. Now, in the introduction to Mensuration, let’s think about 2D and 3D forms and the distinction between them.

Calculation

d = 0.26m

h = 1.2m

s = pi * d * h

 = 0.98 square meter

the area of wallpaper required is 0.98 [tex]m^{2}[/tex]

learn more about mensuration here :

brainly.com/question/14312097

#SPJ4

Answer:

0.98 m²

Step-by-step explanation:

I got it right hope this helps.

Find measure vzw pls helppppp

Answers

VZW=64

Step-by-step explanation:

Since the lines are straight the angles are equal. 2x+32=3x+16

Solve this for x.

32=x+16

16=x

Put the value for x (16) in to one of the angle equations

2(16) + 32 = 32 + 32 = 64

3x+16=2x+32 so -1x=16 16/-1 = -16 so x=-16

how many degrees in a right angle​

Answers

Answer:

90 degrees is the amount of degrees in a right angle

What is the relationship between Za and Zb?
Choose 1 answer:
A
B
a
Vertical angles
b
Complementary angles

Answers

Answer:

A

Step-by-step explanation:

∠ A and ∠ B are vertically opposite angles and are congruent. that is

∠ A and ∠ B are vertical angles

Other Questions
Listed in the Item Bank are some important labels for sections of the image below. Match each label to the corresponding area it identifies in the image.Silicon, Arsenic and AntimonyCan exchange electrons with each other to form ionic compoundsMay have no lusterTin, Calcium and PotassiumHydrogen, Oxygen and ChlorineCan be electrical conductorsComprised of atoms as compared to people living in other nations, people living in the united states are likely to be diagnosed with bipolar disorder. Summerize the story of Hiroshima the measure of the middle ordinate of a yaw mark is 6 ft. the radius of the arc is 70 ft. what was the length of the chord used in this situation? round the answer to the nearest tenth of a foot. Write An Argumentative Essay About "The Giver" Book by "Lois Lowry"Prompt:The giver tells Jonas, "Life here is so orderly so predictable - so painless." Jonas says, "We really have to protect people from wrong choices." The (parenthesis) is the question you are answering for the essay.(Do you think this is true? Do we need to take away some freedoms and/or choices in order to keep safe?)I NEED HELP WITH THIS, I NEED THIS IN 2 WEEKS!This school is from Colorado btw. This is a High School. fetuses who do not survive anemia in utero are usually stillborn, with gross edema of the entire body, a condition called: Rewrite using double object pronouns Urgent!! Question on photoA. X = 10, y = 6, z = 8B. X = 4, y = 2, z = 3C. X = 9, y = 5, z = 7D. X = 7, y = 3, z = 4 y= 3cos 4 0(theta) -1 change into Indirect speech.1) she said to me, " kindly close the window."2) He said, " He rang me up at twelve midnight.please answer this question The radius of a circle is 15 inches. What isthe circumference of the circle? Writeyour answer using T. How will this surfboards streamlined shape affect its speed? Do the tissues lining the gastrovascular cavity in Cnidarians differ at any point in the cavity? I eat alot into past perfect parents who feed their children when they are anxious and comfort them when they are tired, rather than giving them a nap, run the risk of producing children who: hich action showed that president andrew johnson did not support greater rights for africans americans in the south? a 76-year-old resident of an assisted living facility who has a history of heart failure has presented to her primary care provider for a scheduled appointment. which of the woman's statements suggests that her heart failure is worsening? Without the circulatory and respiratory systems, human bodies would not survive. Both systems play major roles in providing our bodies with what they need. They work individually as well as together to keep us alive and healthy,Which four statements describe functions of the circulatory system?ResponsesA Part of this system filters air as it enters the body.Part of this system filters air as it enters the body.B This system's organs passes oxygen into the bloodstream.This system's organs passes oxygen into the bloodstream.C This system plays a major role in fighting infections.This system plays a major role in fighting infections.D Oxygen is delivered to cells throughout the body by this system.Oxygen is delivered to cells throughout the body by this system.E Carbon dioxide exits the body through this system.Carbon dioxide exits the body through this system.F This system takes in oxygen from air outside the body.This system takes in oxygen from air outside the body.G This system removes carbon dioxide from organs and delivers it the lungs.This system removes carbon dioxide from organs and delivers it the lungs.H Nutrients are delivered to organs through this system. In 1924, edwin hubble proved that the andromeda galaxy lay far beyond the bounds of the milky way, thereby putting to rest the idea that it might have been a cloud within our own galaxy. What key observation enabled him to prove this?. derek receives a promotion at his law firm after winning an important case. this is an example of a: