Where r is the radius of the cylinder and h is the height of the cylinder.
Find the surface area when r is 7 inches and h is 9 inches.




Sa of cylinder= 2(pi)rh + 2(pi)r squared

Answers

Answer 1

Answer:

703.7 in²

Step-by-step explanation:

SA = 2πrh+2πr²

= 2×π×7×9+2×π×7²

= 224π

= 703.7 in² (rounded to the nearest tenth)

Answer 2

Answer:

224π

in²

Step-by-step explanation:


Related Questions

n a history class there are 88 history majors and 88 non-history majors. 44 students are randomly selected to present a topic. What is the probability that at least 22 of the 44 students selected are non-history majors

Answers

Answer:

0.5675 = 56.75% probability that at least 22 of the 44 students selected are non-history majors.

Step-by-step explanation:

The students are chosen without replacement from the sample, which means that the hypergeometric distribution is used to solve this question. We are working also with a sample with more than 10 history majors and 10 non-history majors, which mean that the normal approximation can be used to solve this question.

Hypergeometric distribution:

The probability of x successes is given by the following formula:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

In which:

x is the number of successes.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Approximation:

We have to use the mean and the standard deviation of the hypergeometric distribution, that is:

[tex]\mu = \frac{nk}{N}[/tex]

[tex]\sigma = \sqrt{\frac{nk(N-k)(N-n)}{N^2(N-1)}}[/tex]

In this question:

88 + 88 = 176 students, which means that [tex]N = 176[/tex]

88 non-history majors, which means that [tex]k = 88[/tex]

44 students are selected, which means that [tex]n = 44[/tex]

Mean and standard deviation:

[tex]\mu = \frac{44*88}{176} = 22[/tex]

[tex]\sigma = \sqrt{\frac{44*88*(176-88)*(176-44)}{176^2(175-1)}} = 2.88[/tex]

What is the probability that at least 22 of the 44 students selected are non-history majors?

Using continuity correction, as the hypergeometric distribution is discrete and the normal is continuous, this is [tex]P(X \geq 22 - 0.5) = P(X \geq 21.5)[/tex], which is 1 subtracted by the p-value of Z when X = 21.5. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{21.5 - 22}{2.88}[/tex]

[tex]Z = -0.17[/tex]

[tex]Z = -0.17[/tex] has a p-value of 0.4325

1 - 0.4325 = 0.5675

0.5675 = 56.75% probability that at least 22 of the 44 students selected are non-history majors.

create a graph of 4.95 + 3.99

Answers

Answer:

????

Step-by-step explanation:

as in y = 4.95 + 3.99 or points? if so just draw a horizontal line at 8.94

Find the final amount of money in an account if $7, 200 is deposited at 2.5 % interest compounded
quarterly (every 3 months) and the money is left for 9 years.
The final amount is $
Round answer to 2 decimal places

Answers

The final amount is $7,615.27

A = P(1 + r/n)^t

Where,

A = Final amount

P = principal = $7, 200

r = interest rate = 2.5% = 0.025

n = number of periods = 4

t = time = 9 years

A = P(1 + r/n)^t

= 7,200(1 + 0.025/4)^9

= 7,200(1 + 0.00625)^9

= 7,200(1.00625)^9

= 7,200(1.0576769512798)

= 7,615.2740492152

Approximately,

A = $7,615.27

https://brainly.com/question/14003110

Fill in the blanks.
(3b^3)^2 = _b^_

Answers

We can seperate (3b³) into two different parts, the constant and the variable.

The constant (3) and the variable (b) can both be squared and multiplied to get the correct answer, so:

3² = 9

(b³)² = [tex]b^{6}[/tex]

So, [tex](3b^{3})^{2} = 9b^{6}[/tex]

Which is a perfect square?
6’1
6’2
6’3
6’5

Answers

Answer:

6'2

Step-by-step explanation:

6’3 is the answer I believe



The 4th of an AP is 15 and the 9th term is 35. find the 15th term​

Answers

Consecutive terms in this sequence are separated by a constant c, so if the 4th term is 15, then the next terms would be

5th: 15 + c

6th: (15 + c) + c = 15 + 2c

7th: (15 + 2c) + c = 15 + 3c

and so on. More generally, since any given number in the sequence depends on the number that came before it, we can write the n-th term in terms of the 4th term,

n-th: 15 + (n - 4) c

Then the 9th term in the sequence is

15 + (9 - 4) c = 35

and solving for c gives

15 + 5c = 35   ==>   5c = 20   ==>   c = 4

Then the 15th term would be

15 + (15 - 4)×4 = 15 + 11×4 = 15 + 44 = 59

Train X traveled 216.6 kilometers in 38 minutes. How many miles per hour was it traveling?

Answers

Answer:

210 miles in 1 hour

Step-by-step explanation:

steps are in picture

You can run at a speed of 4 mph and swim at a speed of 2 mph and are located on the shore, 6 miles east of an island that is 1 mile north of the shoreline. How far (in mi) should you run west to minimize the time needed to reach the island

Answers

9514 1404 393

Answer:

  5.423 miles

Step-by-step explanation:

Let x represent the distance to run. Then the remaining distance to the point that is closest to the island is (6-x) miles. The straight-line distance (d) to the point x from the island is given by the Pythagorean theorem:

  d² = 1² +(6 -x)² = x² -12x +37

  d = √(x² -12x +37)

The total travel time is the sum of times running and swimming. Each time is found from ...

  time = distance/speed

  total time = x/4 + d/2 = x/4 +(1/2)√(x² -12x +37)

__

The total time will be minimized when its derivative with respect to x is zero.

  t' = 1/4 +(1/4)(2x -12)/√(x² -12x +37) = 0

Multiplying by 4 and combining fractions, we can see the numerator will be ...

  √(x² -12x +37) +2x -12 = 0

Subtracting the radical term and squaring both sides, we get ...

  4x² -48x +144 = x² -12x +37

  3x² -36x +107 = 0

The quadratic formula tells us the smaller of the two roots is ...

  x = (36 -√(36² -4(3)(107)))/(2(3)) = (36 -√12)/6 ≈ 5.423 . . . mi

You should run 5.423 miles west to minimize the time needed to reach the island.

__

A graphing calculator solves this nicely. The attached graph shows the time is a minimum when you run 5.423 miles.

One book is 4cm thick, find out how many such books can be placed in a space of 53cm.

Answers

You would divide the thickness of one book (4cm) by the area you want them to fit in (53 cm).

Then getting the answer 13.25. Since we can’t have (.25 cm) of a book we can fit 13 whole books

a game is played with a fishpond containing 100 fish; 90 white, 9 red, and 1 blue. a contestant randomly catches a fish and receives payments as follows: $0.30 for white, $1.00 for red, and $10.00 for blue. If it cists $0.60 to play this game, how much (on average) does a contestant win on each play

Answers

Answer:

loses  14 cents

- $0.14

Step-by-step explanation:

90%  $0.30   $(0.30)  $(0.27)

9%  $1.00   $0.40   $0.04  

1%  $10.00   $9.40   $0.09  

   

   $(0.14)

Given: 3x+11=y, solve for x if y = 29

Answers

answer is 6

Step-by-step explanation:

3x+11=y

y=29

3x+11=29

3x=29-11

3x=18

x=18÷3

x=6

Answer:6

Step-by-step explanation:

3x+11=29

3x=29-11

3x=18

X=18/3

X=6

find the LCM of 210, 280, 360 by prime factorisation​

Answers

Answer:

Step-by-step explanation:

210=2x3x5x7

280=2x2x2x5x7

360=2x2x2x3x3x5

Answer:

210= 2×3×5×7

280=2×2×2×5×7

360=2×2×2×3×3×5

common factors=2×2×2×3×5×7=840

uncommon factors=3

L.C.M=Common factors× uncommon factors

L.C.M=840×3

L.C.M=2520

Step-by-step explanation:

i hope it will be helpful

plzz mark as brainliest

HELP ASAP PLEASE I WILL MARK BRAINLEST


Show all work to identify the asymptotes and zero of the function f of x equals 6 x over quantity x squared minus 36.

Answers

Answer:

vertical asymptotes

x=6, x=-6

horizontal asymptotes

y=0

zeros (0,0)

Step-by-step explanation:

f(x) = 6x / ( x^2 - 36)

First factor

f(x) = 6x / ( x-6)(x+6)

Since nothing cancels

The vertical asymptotes are when the denominator goes to zero

x-6 = 0   x+6=0

x=6          x= -6

Since the numerator has a smaller power than the denominator (1 < 2), there is an asymptote at y = 0

To find the zeros, we find where the numerator = 0

6x=0

x=0

[tex]\\ \rm\Rrightarrow y=\dfrac{6x}{x^2-36}[/tex]

The h orizontal asymptote

As x has less degree than x²

y=0 is a asymptote

Vertical asymptote

x²-36=0x²=36x=±6

Let h(x)=20e^kx where k ɛ R (Picture attached. Thank you so much!)

Answers

Answer:

A)

[tex]k=0[/tex]

B)

[tex]\displaystyle \begin{aligned} 2k + 1& = 2\ln 20 + 1 \\ &\approx 2.3863\end{aligned}[/tex]

C)

[tex]\displaystyle \begin{aligned} k - 3&= \ln \frac{1}{2} - 3 \\ &\approx-3.6931 \end{aligned}[/tex]

Step-by-step explanation:

We are given the function:

[tex]\displaystyle h(x) = 20e^{kx} \text{ where } k \in \mathbb{R}[/tex]

A)

Given that h(1) = 20, we want to find k.

h(1) = 20 means that h(x) = 20 when x = 1. Substitute:

[tex]\displaystyle (20) = 20e^{k(1)}[/tex]

Simplify:

[tex]1= e^k[/tex]

Anything raised to zero (except for zero) is one. Therefore:

[tex]k=0[/tex]

B)

Given that h(1) = 40, we want to find 2k + 1.

Likewise, this means that h(x) = 40 when x = 1. Substitute:

[tex]\displaystyle (40) = 20e^{k(1)}[/tex]

Simplify:

[tex]\displaystyle 2 = e^{k}[/tex]

We can take the natural log of both sides:

[tex]\displaystyle \ln 2 = \underbrace{k\ln e}_{\ln a^b = b\ln a}[/tex]

By definition, ln(e) = 1. Hence:

[tex]\displaystyle k = \ln 2[/tex]

Therefore:

[tex]2k+1 = 2\ln 2+ 1 \approx 2.3863[/tex]

C)

Given that h(1) = 10, we want to find k - 3.

Again, this meas that h(x) = 10 when x = 1. Substitute:

[tex]\displaystyle (10) = 20e^{k(1)}[/tex]

Simplfy:

[tex]\displaystyle \frac{1}{2} = e^k[/tex]

Take the natural log of both sides:

[tex]\displaystyle \ln \frac{1}{2} = k\ln e[/tex]

Therefore:

[tex]\displaystyle k = \ln \frac{1}{2}[/tex]

Therefore:

[tex]\displaystyle k - 3 = \ln\frac{1}{2} - 3\approx-3.6931[/tex]

Solve each system by graphing.

Answers

Answer:

(2,-1)

Step-by-step explanation:

Solved using math.

Answer:

The solution is (2, -1) to show this by graphing do y = -1 by making a straight horizontal line at (0,-1) . And then for the other equation make a line where it starts at (0,4) and passes point (2,-1). Just plot those two points and connect them and you'll have made the line.

Step-by-step explanation:

Anna earned $9 an hour babysitting. She wants
to buy a 16 GB iPod that is $120. Anna has
saved $45 so far. How many more hours of
babysitting does she need to do to earn the rest
to purchase the iPod

Answers

Answer:

8.33 hours

Step-by-step explanation:

120-45 = 75

75 ÷ 9 = 8.33

5765865876+5737555586=

Answers

Answer:

5765865876+5737555586=11503421462

Devaughn is 6 years older than Sydney. The sum of their ages is 56 . What is Sydney's age?

Answers

Answer:

Devaughn = 31, Sydney = 25

Step-by-step explanation:

(56-6)÷2= 25

So they would both be 25 if they were the same age but Devaughn is 6 years older so 25+6=31

Age of Sydney=xAge of Devaghn=x+6

ATQ

[tex]\\ \sf\longmapsto x+x+6=56[/tex]

[tex]\\ \sf\longmapsto 2x+6=56[/tex]

[tex]\\ \sf\longmapsto 2x=56-6[/tex]

[tex]\\ \sf\longmapsto 2x=50[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{50}{2}[/tex]

[tex]\\ \sf\longmapsto x=25[/tex]

A manufacturer claims that its drug test will detect steroid use (that is, show positive for an athlete who uses steroids) 95% of the time. Further, 15% of all steroid-free individuals also test positive. 10% of the rugby team members use steroids. Your friend on the rugby team has just tested positive. The correct probability tree looks like

Answers

Answer:

The probability tree is;

                            0.95        [tex](+)[/tex]

                   [tex](S)[/tex]

          0.1              0.05        [tex](-)[/tex]

[  P  ]

          0.9             0.15          [tex](+)[/tex]                                                        

                  [tex](S_{no})[/tex]    

                             0.85         [tex](-)[/tex]        

Step-by-step explanation:

Given the data in the question;

10% of the rugby team members use steroids

so Probability of using steroid; P( use steroid ) = 10% = 0.10

Probability of not using steroid; P( no steroid use ) = 1 - 0.10 = 0.90

Since the test show positive for an athlete who uses steroids, 95% of the time.

Probability of using steroids and testing positive = 95% = 0.95

Probability of using steroids and testing Negative = 1 - 0.95 = 0.05

Also from the test, 15% of all steroid-free individuals also test positive.

so

Probability of not using steroids and testing positive = 15% = 0.15

Probability of not using steroids and testing negative = 1 - 0.15 = 0.85

To set up the probability tree, Let;

[tex](S)[/tex] represent steroid use

[tex](S_{no})[/tex] represent no steroid use

[tex](+)[/tex] represent test positive

[tex](-)[/tex] represent test negative

so we have;

                            0.95        [tex](+)[/tex]

                   [tex](S)[/tex]

          0.1              0.05        [tex](-)[/tex]

[  P  ]

          0.9             0.15          [tex](+)[/tex]                                                        

                  [tex](S_{no})[/tex]    

                             0.85         [tex](-)[/tex]        

what equation shows a slope of 2/3 and a white intercept of 0, -2

Answers

y = 2/3 x - 2

Or

y + 2 = 2/3 ( x )

Answer:

y= 2/3x - 2

hope this helps :)

Instructions: Find the measure of the indicated angle to the nearest degree.

Answers

Answer:

? = 13.6

Step-by-step explanation:

Let the unknown angle be y

so

tan y= p/b

tan y =8/33

y = tan‐¹(8/33)

y = 13.62699486

y = 13.6

13 is subtracted from the product of 4 and a certain number. The result is equal to the sum of 5 and the original number. Find the number.​

Answers

Answer:

The number is 6.

Step-by-step explanation:

[tex]4x-13=x+5\\3x-13=5\\3x=18\\x=6[/tex]

What is the slope-intercept equation of the line below?



10 minutes left

Answers

Answer:

y=-3x+4

Step-by-step explanation:

The y intercept is 4 because the line crosses the y axis at the 4 tic mark

The slope will be -3 because the y decreases by 3 every time the x incerases by 1

y=mx+b

y=-3x+4

Abigail buys two cartons of strawberries. One carton has 191919 berries and the other carton has 262626 berries. She wants to divide the berries into bags so there are exactly 666 berries in each bag.
How many bags will have 666 berries?

Answers

Abigail will have 682 bags full with 666 berries.

Answer:

682

Step-by-step explanation:

191,919 + 262,626

454545 ÷ 666 = 682.5

Thus meaning 682 bags will have 666 berries and one bag will have 333 berries.

What is the slope, m, and the y-intercept of the line that is graphed below?

On a coordinate plane, a line goes through points (negative 3, 0) and (0, 3).

Answers

Answer:

Slope: 1

Y-intercept: (0,3)

Step-by-step explanation:

The y intercept is when the slope reaches the y-axis line. In this case, it is given to us. Anything that is formed like this: (0, y) is the y-intercept.

Y intercept: (0, 3)

For slope, you can use the formula rise over run. [tex]\frac{Rise}{Run}[/tex]

From the picture, I have drawn the rise over run, which is [tex]\frac{3}{3}[/tex], which is also 1.

Slope: 1

Hope this helped.

Answer: 1

Step-by-step explanation: got it right on edge

Graphs of the following equations are straight lines except :
A. 3x+2y=8
B. y=x/2-5
C. x=4y
D. y=x^2+3

Answers

Answer:

D.

Step-by-step explanation:

D. This contains an x^2 and is called a parabola ( curved line like a U).

Answer:D

Step-by-step explanation: d is the correct answer

Please answer! These r my last questions

Answers

Answer:

8. -2a+14

9. w=3/2

Step-by-step explanation:

8.

The distributive property states that we can multiply each component in the parenthesis separately by the number on the outside, and then add that up to get our final answer.

For -2(a-7), this means that we can multiply -2 by a and then -2 by -7 (as 2 is the number on the outside, and a and -7 are the components in the parenthesis), add them up, and get our answer. This can be expressed as

-2 * a + (-2) * (-7) = final answer

= -2 * a + 14

We know that -2 * -7 = 14 because 2 * 7 = 14, and the two negatives in multiplication cancel each other out

9.

Using the subtraction property of equality, we can isolate the variable (w) and its coefficient (-2/3) by subtracting 5, resulting in

(-2/3)w = 4-5 = -1

Next, we can use the multiplication property of equality to isolate the w. To isolate the w, we can multiply its coefficient by its reciprocal. The reciprocal is the fraction flipped over. For (-2/3), its reciprocal is (-3/2), flipping the 2 and 3. We can multiply both sides by (-3/2) to get

w = (-3/2)

To check this, we can plug (-3/2) for w in our original equation, so

(-2/3) * (-3/2) + 5 = 4

-1 + 5 = 4

4 = 4

This works!

A triangle is rotated 90° about the origin. Which rule describes the transformation?
(x, y) (-x, -y)
O(x,y) (-y, x)
(x, y) (-), -x)
(x,y) →ly, -x)

Answers

Answer:

(x,y) -> (-y,x), second option.

Step-by-step explanation:

Rotation of 90 degrees about the origin:

The rule for a rotation of a point (x,y) 90 degrees about the origin is given by:

(x,y) -> (-y,x)

This is that the question asks, and so, this is the answer, which is the second option.

What is the volume of a cone with a height of 6m and a diameter of 12m? Nearest meter.

Answers

Answer:

0.0005m^3

Step-by-step explanation:

V=1/3hπr²

h=6m

d=12m

r=12÷2=6m

V=1/3×6×(3.14)×36

V=1/2034.72

V=0.0005m^3

A sequence is defined by the recursive function f(n + 1) = f(n) – 2.

If f(1) = 10, what is f(3)?

1
6
8
30

Answers

Answer:

f(3) = 6

Step-by-step explanation:

If f(1)=10, then f(1+1)=f(1)-2

f (2) = 10 - 2 = 8

Therefore f(3) = f(2) - 2 = 8 - 2 = 6

Other Questions
Convert 56 radians to degrees. Question 1 options: A) 25 B) 150 C) 150 D) 1080 Which of these is the main cause of habitat fragmentation? O A. Reduction in genetic diversity O B. Migration of mammal species O C. Demand for land use O D. Extinction of bird species The fluid inside the hydraulic jack has a pressure of 30,000 Pa. If the surface ofthe piston that is used to lift an object is 0.1 min area, how much weight canthe jack lift? Why is the unit of velocity called derived unit? What is one of the causes of mechanical weathering?A. acid rainB. oxidationC. animal actionsD. carbon dioxide Pls Answer it for 50 points pls What is arsenic??? One of the principles stated in the Declaration of Independence is that government shouldO have unlimited power to rule the peoplebe based upon the consent of the governedO guarantee economic equality among citizensbe led by educated citizens B Page view A Read aloud Grammar Practice A' Did you go to the cinema last night (go) B No. 1 at home (stay) you ever to Mexico? (go) B Yes, I have last year. (go) A you any Latin American novels? (read) B Yes, 1 Spanish when i was at university (study) A What? you for dinner last night? (have) B Nothing 1 hungry (not be . Read the sentences carefully, Identify whether it is the simple past or the present perfect form. Change the words in the brackets into the correct forms of the simple past OR the present perfect tense. Write your answers in the following slide. Question no 1 is done for you. you ever to a famous actor? (speak) a famous person. (meet) 10 B No, 1 never AN you at the end of Titonic? (cry) very sad. (be) B Yes, it2 A 13 the new James Bond film? (see) you B No. Is it good? AH you your homework last night? (do) ING Rob cuts a circular hole out of a rectangular piece of paper. The paper measures 20 centimeters by 30 centimeters. The hole is 10 centimeters in diameter. How much of the piece of paper, in square centimeters, is left over after the hole is cut out? please answer this question!! Write 55% as a fraction in simplest form --Gwendolyn BrooksWhy does Gwendolyn Brooks use diction such as "we/ real cool" and "we/ strikestraight" In her poem "We Real Cool'?O A.to convey the teenagers' rebellion against their parents and teachers B.to convey the teenagers* insecurity and their desire to be at school C.to convey the teenagers' wish to play pool rather than focus on academics D.to convey the teenagers' attitude and show of toughness find the greatest number than divides 45 60 75 without leaving remainder Find the values of x and y if (-x + 5, 1) = (-y, 2x - 5y). Determine the measure of the interior angle at vertex E.A. 135B. 45C. 225D. 75 3. True or False: A warm-up can include minimal stretching at the end. Another of Bhaskara's problems results in a quadratic equation Parthava was enraged and seized a certain number of arrows to slay Karna. He expended one-half of them in defending himself. Four times the square root of the number of arrows were discharged against the horses. With six more, he transfixed Shalya, the charioteer. With three more, he rent the parasol, the standard, and the bow; and with the last one he pierced the head of Karna. How many arrows did Parthava have? Find the bases for Col A and Nul A, and then state the dimension of these subspaces for the matrix A and an echelon form of A below.A= 1 3 8 2 7 1 3 8 2 7 2 7 20 6 20 --- 0 1 4 2 6 -3 -12 -36 -7 -19 0 0 0 1 4 3 13 40 9 25 0 0 0 0 0Start 4 By 5 Table 1st Row 1st Column 1 2nd Column 3 3rd Column 8 4st Column 2 5st Column 7 2nd Row 1st Column 2 2nd Column 7 3rd Column 20 4st Column 6 5st Column 20 3rd Row 1st Column negative 3 2nd Column negative 12 3rd Column negative 36 4st Column negative 7 5st Column negative 19 4st Row 1st Column 3 2nd Column 13 3rd Column 40 4st Column 9 5st Column 25 EndTabletildeStart 4 By 5 Table 1st Row 1st Column 1 2nd Column 3 3rd Column 8 4st Column 2 5st Column 7 2nd Row 1st Column 0 2nd Column 1 3rd Column 4 4st Column 2 5st Column 6 3rd Row 1st Column 0 2nd Column 0 3rd Column 0 4st Column 1 5st Column 4 4st Row 1st Column 0 2nd Column 0 3rd Column 0 4st Column 0 5st Column 0 EndTableA basis for Col A is given byStartSet nothing EndSet(Use a comma to separate vectors as needed.)The dimension of Col A is3.A basis for Nul A is given byStartSet nothing EndSet(Use a comma to separate vectors as needed.)The dimension of Nul A . A force of 15N acts on an area of 60m.What is the pressure? * An elderly man who has always had a difficult temperament lives in a different state from either his daughter or son. He has a room in the home of a middle-age couple, who attend to his needs. His daughter checks in regularly by telephone and thinks well of the couple. After the elderly man's death, the daughter discovers that the couple has systematically taken all of the man's money. This is a case of ________.