A recursive rule for a geometric sequence:
[tex]a_1\\\\a_n=r\cdot a_{n-1}[/tex]
---------------------------------------------------
[tex]a_1=3\\\\a_n=\dfrac{1}{2}a_{n-1}\to \boxed{r=\dfrac{1}{2}}[/tex]
--------------------------------------------------
Exciplit rule:
[tex]a_n=a_1r^{n-1}[/tex]
Substitute:
[tex]a_n=3\left(\dfrac{1}{2}\right)^{n-1}=3\cdot\left(\dfrac{1}{2}\right)^n\cdot\left(\dfrac{1}{2}\right)^{-1}=3\cdot\left(\dfrac{1}{2}\right)^n\cdot2\\\\\boxed{a_n=6\cdot\left(\dfrac{1}{2}\right)^n}[/tex]
Answer:
The answer is: a_n = 6*(1/2)^n
A store makes shirts and jackets to sell each shirt costs $4 to make and each jacket costs $25 to make
Marco books a room at a hotel. He spends $600 in total for a 3-night stay. Fill in each statement. For every 1 night that Marco stays at the hotel, he spends . If he stays at the hotel for 5 nights, he would spend .
RESPOND QUICK
Solve the first proportion for x. Use that value to solve the second proportion for
y. ,
x/24 = 9/72,
x/9 = y/12
A. x = 3, y = 4
B. x = 4, y = 3
C. x = 27, y = 36
D. x = 3, y = 6
Answer:
A
Step-by-step explanation:
3/24=9/72 3*3=9 24*3=72 x=3
3/9=y/12 9/3=3 12/3=4 y=4
X=3 y=4
Line segment AB has a length of 15 and angle a=35degrees . A segment with a length of 12 will form the third side of the triangle. What are the possible measures of the angle opposite side AB? Please explain the process.
Answer:
C = 45.8 or C = 117.69
Step-by-step explanation:
Remark
Only SSA gives the possibility of 2 answers. This one does not give that opportunity. There is one unique answer. We'll discuss 2 and zero after finding 1 answer. On looking at it again, the question might be ambiguous. We'll check that out as well.
Given
AB = 15
<A = 35
point C opposite line AB such that CB = 12 These givens give a unique answer.
Solution
Sin(35) / 12 = Sin(C) / 15 Multiply both sides by 15
15*Sin(35) / 12 = Sin(C) Find 15/12
1.25*sin(35) = Sin(C) Write Sin(35)
1.25*0.5736 = Sin(C) Multiply the left
0.71697 = Sin(C) Take the inverse Sin
C = 45.805 degrees This is the angle opposite AB
Angle B = 180 - 35 - 45.805 = 99.2
Ambiguous Case
If AC = 12 we have another answer entirely. This is SAS which will give just 1 set of answers for the triangle. The reason the case is ambiguous is because we don't exactly know where that 12 unit line is. It could be AC or BC.
I will set up the Sin law for you, and let you solve it
Sin(B) / 12 = Sin(35)/15
When you solve for Sin(B) as done above you, get 0.45886 from which B = 27.31 degrees
C = 180 - 35 - 27.31 = 117.69
So that's two values that C could have. I think that's all given these conditions.
Two Cases or None
<A = 35 degrees
AC = 15
CB = 12
This should give you two possible cases or none. You can check which by finding the height of the triangle from C down to AB (which has no distinct length. The h is 15 * Sin35 = 8.6. If CB < 8.6, there are no solutions. If CB < AC then if CB > that 8.6, there are 2 solutions.
Please answer this question!! 20 points and brainliest!
Answer:
A
Step-by-step explanation:
We can find the surface area of the object by adding the surface areas of each part. We have many rectangle faces to count and two triangular faces. Each has a formula for the area. We will find the area of each and then add them all together.
Triangle - 0.5 *b*h
Rectangle - b*h
Triangles
There are two triangles on either side. The height is 1.5. The base is 1.8.
0.5(1.5)(1.8)=1.35 meters squared
Since there are two, we will add 1.35+1.35 in our final calculation.
Rectangles
We will start by calculating the largest rectangle on the side. It has height of 4 and a base of 2.5 (shown above left).
4(2.5)=10
Since there are two (one we can see and one we can't), we will add 10+10 in our final calculation.
Next we calculate the top and bottom. The height is 3 and the base is 2.5 on top. But the bottom sticks out more and adds 1.8 to its base.
Top - 3(2.5)=7.5
Bottom-3(2.5+1.8)=12.9
Finally, we will calculate the front side and back(not visible) as well as the slant up front. The back side has height 4 and base 3. The front side has base 3 and height 4-1.5=2.5. The slant has base 2.3 and height 3.
Back - 4(3)=12
Front- 3(2.5)=7.5
Slant - 3(2.3)=6.9
We add all together for the total surface area: 1.35+1.35+10+10+7.5+12.9+12+7.5+6.9=69.5 meters squared.
What is the midpoint of a segment whose endpoints are (9, −9) and (−3, 7)?
Answer:
The midpoint is (3,-1)
Step-by-step explanation:
The midpoint of a segment is found by adding the ends together and dividing by 2
midpoint = (x1+x2)/2 , (y1+y2)/2
=(9+-3)/2 , (-9+7)/2
= 6/2, -2/2
=3,-1
he data set represents the number of miles Mary jogged each day for the past nine days.
6, 7, 5, 0, 6, 12, 8, 6, 9
The outlier of the data set is
Answer:
zero is your answer.
Step-by-step explanation:
Your answer for this question is 0
A rectangle has side lengths of a and b, which are non-zero integers. Determine possible values of a and b, which will make the diagonal of the rectangle a rational number.
A) a=1, b=1
B) a=4, b=5
C) a=3, b=4
D) a=1, b=2
Look at the picture.
Use the Pythagorean theorem:
[tex]a^2+b^2=d^2[/tex]
A) a = 1, b = 1
[tex]d^2=1^2+1^2\\\\d^2=1+1\\\\d^2=2\to d=\sqrt2\ \text{it's not rational number}[/tex]
B) a = 4, b = 5
[tex]d^2=4^2+5^2\\\\d^2=16+25\\\\d^2=41\to d=\sqrt{41}\ \text{it's not rational number}[/tex]
C) a = 3, b = 4
[tex]d^2=3^2+4^2\\\\d^2=9+16\\\\d^2=25\to d=\sqrt{25}\to d=5\ \boxed{:)}[/tex]
D) a = 1, b = 2
[tex]d^2=1^2+2^2\\\\d^2=1+4\\\\d^2=5\to d=\sqrt5\ \text{it's not rational number}}[/tex]
Answer: C) a = 3, b = 4.Options A, B, and D do not yield a perfect square, while option C does, with a=3 and b=4 resulting in a rational diagonal length of 5.
The diagonal of a rectangle can be found using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). Mathematically, this is represented as [tex]c^2 = a^2 + b^2,[/tex] where a and b are the sides of the rectangle and c is the diagonal.
Looking at the given options:
A) a=1, b=1: Here, [tex]a^2 + b^2 = 1^2 + 1^2 = 2,[/tex] it is not a perfect square, so the diagonal will not be rational.B) a=4, b=5: Here, [tex]a^2 + b^2 = 4^2 + 5^2 = 16 + 25 = 41,[/tex] it is not a perfect square, so the diagonal will not be rational.C) a=3, b=4: Here, [tex]a^2 + b^2 = 3^2 + 4^2 = 9 + 16 = 25[/tex], it is a perfect square (5^2), so the diagonal is rational.D) a=1, b=2: Here, [tex]a^2 + b^2 = 1^2 + 2^2 = 1 + 4 = 5,[/tex] it is not a perfect square, so the diagonal will not be rational.Therefore, the possible values of a and b which will make the diagonal of the rectangle a rational number are given in option C: a=3 and b=4.
Which best describes this triangle?
A.
All sides are the same length; each angle measures 90°.
B.
Two sides are the same length; one angle measures 90°.
C.
Two sides are the same length; one angle is obtuse.
D.
All sides are the same length; each angle is acute.
During The Month Of October, Sophie Raised $25 for a charity. During November, she raised 5 times as much money for charity. How much money did sophie raise in November
Simplify the expression
Answer:
729
Step-by-step explanation:
[(-1)^3]^2 /[(-3)^-3]^2
= 1 * [(-3)^3]^2
= 1 * 729
= 729
Answer:
729
To solve this, we need to start on the inside and work out; solving one part at a time.
[{(-1)^3 / (-3)^-3}]^2
1. (-1)^3 = -1
2. (-3)^-3 = - 1/27
3. (-1) / (- 1/27) = 27
4. 27^2 = 729
Delany can run 1 1/2 of a mile at a rate 16 minutes and 30 seconds. At this rate how many minutes will it take him to run one mile?
Answer:
11 minutes
Step-by-step explanation:
Do 16 mins. 30 secs. divided by 1.5, since that is what you divide the miles by to get the base amount. The answer is 11 minutes.
An angle measures 50° more than the measure of a supplementary angle. What is the measure of each angle?
Answer:
65° and 115°
Step-by-step explanation:
let one angle be x then the other is x + 50
The sum of 2 supplementary angles = 180°, hence
x + x + 50 = 180
2x + 50 = 180 ( subtract 50 from both sides )
2x = 130 ( divide both sides by 2 )
x = 65
Thus the 2 angles are x = 65° and x + 50 = 65 + 50 = 115°
Wally purchased a desk that was on sale do 2/3 of the original price. If the original price was $450, what was the price that Wally Paid?
Answer:
2/3 of 450 is 300 :)
suppose a normal distribution has a mean of 38 and a standard deviation of 2. What is the probability that a data value is between 36 and 43? Round your answer to the nearest 10th of a percent.
Answer:
83.5 %
Step-by-step explanation:
The mean is 38 and the standard deviation is 2
38 -2 is 36
36 is one standard deviation below the mean.
43 - 38 is 5
5/2 is 2 1/2 times the standard deviation above the mean
-1< z< 2.5
P ( Z<2.5 )−P (Z<−1 )
P ( Z<−1)=1−P ( Z<1 )
P ( Z<2.5 )-1+P ( Z<1 )
Using the standard normal table
0.9938 - 1 +0.8413
0.8351
83.51%
Rounding to the nearest tenth
83.5%
Yep the answer's 83.5%
godspeed in your adventures in cheating >:)
given f(x)=2^x, g(x) is found by translating f(x) three units right and two units down. Which function below shows g(x)?
[tex]\bf ~\hspace{10em}\textit{function transformations} \\\\\\ \begin{array}{llll} f(x)= A( Bx+ C)^2+ D \\\\ f(x)= A\sqrt{ Bx+ C}+ D \\\\ f(x)= A(\mathbb{R})^{ Bx+ C}+ D \end{array}\qquad \qquad \begin{array}{llll} f(x)=\cfrac{1}{A(Bx+C)}+D \\\\\\ f(x)= A sin\left( B x+ C \right)+ D \end{array} \\\\[-0.35em] ~\dotfill\\\\ \bullet \textit{ stretches or shrinks horizontally by } A\cdot B\\\\ \bullet \textit{ flips it upside-down if } A\textit{ is negative}\\ ~~~~~~\textit{reflection over the x-axis}[/tex]
[tex]\bf \bullet \textit{ flips it sideways if } B\textit{ is negative}\\ ~~~~~~\textit{reflection over the y-axis} \\\\ \bullet \textit{ horizontal shift by }\frac{ C}{ B}\\ ~~~~~~if\ \frac{ C}{ B}\textit{ is negative, to the right}\\\\ ~~~~~~if\ \frac{ C}{ B}\textit{ is positive, to the left}\\\\ \bullet \textit{ vertical shift by } D\\ ~~~~~~if\ D\textit{ is negative, downwards}\\\\ ~~~~~~if\ D\textit{ is positive, upwards}\\\\ \bullet \textit{ period of }\frac{2\pi }{ B}[/tex]
with that template in mind, let's check
C = -3, three units to the right
D = -2, two units down.
[tex]\bf f(x)=2^x~\hspace{10em}\stackrel{\stackrel{C=-3\qquad D=-2}{\cfrac{}{}}}{g(x)=2^{x-3}-2}[/tex]
Answer:
g(x) = 2^(x - 3) - 2.
Step-by-step explanation:
Translating 2^x 3 units to the right . This is done by changing it to 2^(x - 3). Then 2 units down is given by 2^(x -3) - 2.
Answer is 2^(x - 3) - 2.
Marcus estimates that 230 people will attend the choir contrary there was an actual total of 300 people who attended the choir concert What is the answer to this?
Answer:
23% error since 70 more people attended then Marcus counted
Step-by-step explanation:
To calculate the percent error:
We find the difference between the predicted and the actual.We divide the absolute value of the difference by the actual recorded value.Convert to a percent by multiplying by 100 and adding a % sign.Marcus counted 230 and 300 actually came.
1. 230-300=-70 but the absolute value is 70
2. 70/300=0.23
3. 0.23(100)=23%
Marcus' estimated had a 23% error.
Mario is setting up a new tent during a camping trip. The tent came with 7 feet of rope. The instructions were to use 34.5 inches of the rope to tie a tarp on top of the tent. Then, the remaining rope should be cut into 8 1/4 inch sections to tie the tent to stakes in the ground. Mario will use al the rope as instructed. Write and solve an equation to determine the number of 8 1/4 inch sections of rope Mario can cut from the rope.
Answer:
[tex] The\ number\ of\ 8 \frac{1}{4}\ inches\ of\ section\ of\ rope\ be\ 6. [/tex]
Step-by-step explanation:
As given
Mario is setting up a new tent during a camping trip.
The tent came with 7 feet of rope.
As 1 foot = 12 inches
Now convert 7 feet into inches.
7 feet = 7 × 12 inches
= 84 inches
As given
The instructions were to use 34.5 inches of the rope to tie a tarp on top of the tent.
Than
Rope left after tie a tarp on top of the tent = 84 - 34.5
= 49.5 inches
As given
[tex]The\ remaining\ rope\ should\ be\ cut\ into\ 8 \frac{1}{4}\ inch\ sections\ to\ tie\ the\ tent\ to\ stakes\ in\ the\ ground.[/tex]
i.e
[tex]The\ remaining\ rope\ should\ be\ cut\ into\ \frac{33}{4}\ inch\ sections\ to\ tie\ the\ tent\ to\ stakes\ in\ the\ ground.[/tex]
[tex]Let\ us\ assume\ the\ number\ of\ \frac{33}{4}\ inches\ section\ of\ rope\ be\ x.[/tex]
Than the equation becomes
[tex]\frac{33\times x}{4} = 49.5[/tex]
[tex]x = \frac{49.5\times 4}{33}[/tex]
[tex]x = \frac{198}{33}[/tex]
x = 6
Answer:
6
Step-by-step explanation:
Converting 7 ft to inches:
[tex]7*12=84[/tex] inches
34.5 inches is used, and remaining is used for [tex]8\frac{1}{4}[/tex] in. sections. Let [tex]x[/tex] be the number of [tex]8\frac{1}{4}[/tex] in. sections. ([tex]8\frac{1}{4}[/tex] can be written as 8.25 inches)We set up the equation as:
[tex]34.5+8.25x=84[/tex]
Now solving for [tex]x[/tex] would give us the number of 8.25 inch sections:
[tex]8.25x=84-34.5\\8.25x=49.5\\x=\frac{49.5}{8.25}=6[/tex]
Hence, Mario can cut 6 (8.25 inch) sections from the rope
Each year the soccer team, Peterson United, plays 25 games at their stadium. The owner of Peterson United claimed that last year the mean attendance per game at their home stadium was 24500.
Based on the owner´s claim, calculate the total attendance for the game at Peterson United´s home stadium last year.
High school question
3 parts
Answer:
Total attendance for the game at stadium last year was 612500.
Step-by-step explanation:
Each year the soccer team, Peterson United, plays 25 games at their stadium.
The owner of Peterson United claimed that last year the mean attendance per game was = 24500
Since mean of any set of data = [tex]\frac{sum of data}{Total number of data}[/tex]
When we apply this rule in this question formula becomes as
24500 = [tex]\frac{x}{25}[/tex]
x = 25 × 24500
x = 612500
The length of the poster is 16 inches. What is the length of this poster in centimeters. (1 inch = 2.54 centimeters)
Answer:
90
Step-by-step explanation:
The price of a cantaloupe at a fruit stand goes up 4 cents each month. The first month the stand was open, a cantaloupe cost $1.25.
What will the cost of a cantaloupe be in the 40th month?
A. $157.25
B. $16.85
C. $3.35
D. $2.81
Answer:
D. $2.81
Step-by-step explanation:
The statement says that the price of a cantaloupe goes up 4 cents each month and that the cost of the cantaloupe was $1.25 on the first month. Tto determine the cost in the 40th month, you have to multiply 4 cents for 39 months as the price for the first month was given and then you have to add this with the price for the first month:
0,04*39= 1.56
1.56+1.25= $2.81
The price in the 40th month is $2.81.
Mrs. Johnson is 3 times as old as her son. Ten years ago she was 5 times as old as her son was then. Find each of their ages
Answer:
her son is 20, Mrs. Johnson is 60
Step-by-step explanation:
if her son is x, Mrs. Johnson is 3x,
Ten years ago,
her son is x-10, Mrs. Johnson is 3x-10,
so:
3x-10=5(x-10)
x=20
How many 3 over 8 pound bags of trail mix can be made from 6 and 3 over 8 pounds of trail mix ? Write a division expression
Answer:
[tex]\frac{\frac{51}{8}} {\frac{3}{8}}[/tex]
17 bags.
Step-by-step explanation:
We are asked to find the number of bags with weight 3/8 pound can be made from [tex]6\frac{3}{8}[/tex].
To find the number of
[tex]\text{Number of bags that can be made from available mix trail}=6\frac{3}{8}\div \frac{3}{8}[/tex]
Convert mixed fraction into improper fraction.
[tex]\text{Number of bags that can be made from available mix trail}=\frac{51}{8}\div \frac{3}{8}[/tex]
Since we know that dividing a fraction with another fraction is same as multiplying the 1st fraction with the reciprocal of 2nd fraction.
[tex]\text{Number of bags that can be made from available mix trail}=\frac{51}{8}\times \frac{8}{3}[/tex]
After cancelling out 8 from numerator and denominator we will get,
[tex]\text{Number of bags that can be made from available mix trail}=\frac{51}{3}[/tex]
[tex]\text{Number of bags that can be made from available mix trail}=17[/tex]
Therefore, 17 bags each of weight 3/8 pounds can be made from [tex]6\frac{3}{8}[/tex] pounds of mix trail.
100 points!
Only 29 and 31
Rewrite each expression eliminating fractions. Simplified answers may be left in terms of any of the six trigonometric functions.
Answer:
29. sec w csc w - sec^2 w
31. - tan ^2 k (sin k +1)
Step-by-step explanation:
29. (cot w -1)/ (1- sin^2 w)
We know that cot w = cos w/ sin w
and 1 - sin^2 w = cos ^2 w
Replace these identities into the expression
(cos w/ sin w -1)
-----------------------
cos ^ 2 w
Get a common denominator on top of sin w
(cos w/ sin w -sin w/sin w)
-----------------------
cos ^ 2 w
(cos w - sinw)/ sin w
-----------------------
cos ^ 2 w
(cos w - sinw)
-----------------------
cos ^ 2 w sin w
Split into 2 terms
cos w sin w
----------------------- - ---------------------------------
cos ^ 2 w sin w cos ^2 w sin w
Cancel cos w in the first term and sin w in the second term
1 1
----------------------- - ---------------------------------
cos w sin w cos ^2 w
We know that 1/cos = sec and 1/ sin = csc
sec w csc w - sec^2 w
31. sin k/ (1 - csc k)
We know that csc k is 1/ sin k
sin k
---------------
1 - 1/ sin k
Get a common denominator for the bottom
sin k
---------------
sin k/ sin k - 1/ sin k
sin k
---------------
(sin k-1)/ sin k
Multiply by sin k/sin k
sin k * sin k
---------------
(sin k-1)/ sin k * sin k
sin k * sin k
---------------
(sin k-1)
sin^2 k
---------------
(sin k-1)
Multiply by (sin k +1)/ (sin k +1) so we can get rid of the denominator
sin^2 k (sin k +1)
-------------------------
(sin k-1) (sin k +1)
Foiling out the denominator, we get (sin^2 k-1)
sin^2 k (sin k +1)
-------------------------
(sin^2 k-1)
Factoring out a -1 from the denominator
sin^2 k (sin k +1)
-------------------------
-1 (1 - sin^2 k)
1 - sin ^2 k = cos ^ k
sin^2 k (sin k +1)
-------------------------
-1 (cos ^2 k)
sin ^2k/ cos ^2 k = tan ^2 k
- tan ^2 k (sin k +1)
Camp Oakes gets 32 juice boxes of orange juice and 56 boxes of apple juice each shelf in the cup board can hold eight boxes of juice what is the least number of cells needed for all the juice box
What is 2.45 x 10^4
A: 2450
B: 24,500
C: 245
D: 245,000
Answer:
I got B. 24,500 as my answer.
Step-by-step explanation:
2.45 x (10^4) = 24,500
Lynn has 4 more books than Jose. If Lynn gives Jose 6 of her books, how many more will Jose have than Lynn?
Jonas is conducting an experiment using a 10-sided die. He determines that the theoretical probability of rolling a 3 is 1/10. He rolls the die 20 times. Four of those rolls result in a 3. Which adjustment can Jonas make to his experiment so the theoretical and experimental probabilities are likely to be closer?
A.) He can decrease the sample space.
B.) He can increase the sample space.
C.) He can decrease the number of trials.
D.) He can increase the number of trials.
Answer:
D. He can increase the number of trials.
Step-by-step explanation:
Jonas is conducting an experiment using a 10-sided die. So the theoretical probability of rolling a 3 in a single trial is, [tex]\dfrac{1}{10}[/tex]
So the theoretical expected outcome of 3 in 20 roll would be,
[tex]=\dfrac{1}{10}\times 20=2[/tex]
But when he rolled the die 20 times, where four of those rolls resulted 3.
Which is 2 times more than the theoretical expectation.
Increasing the number of trials from 20, the expected outcome will increase.
As the number of trials is multiplied with [tex]\dfrac{1}{10}[/tex], so bigger the number is from 20, bigger the value.
As we know,
[tex]E(x)=n\cdot P(x)[/tex]
If we want to increase the expected value, we have to increase the number of trials.
Answer with explanation:
Number of faces of this unique Die = 10
Theoretical probability of rolling a 3 [tex]=\frac{1}{10}[/tex]
Now, the die is rolled 20, times.
Number of times, the rolls results in 3= 4
Probability of rolling '3' [tex]=\frac{4}{20}=\frac{1}{5}[/tex]
but, if you roll the die twenty times, Probability of rolling '3' should be [tex]=\frac{2}{20}=\frac{1}{10}[/tex]
When we want, theoretical probability and experimental probability,match each other, the number of trials should be large enough to get closer and better results.
The adjustment can Jonas make to his experiment so the theoretical and experimental probabilities are likely to be closer:
D: He can increase the number of trials.
Which expression is equal to (In picture)
[tex]3x^2+12x-15=3(x^2+4x-5)=3(x^2+5x-x-5)\\\\=3[x(x+5)-1(x+5)]=3(x+5)(x-1)\\----------------------\\4x^2+4x-8=4(x^2+x-2)=4(x^2+2x-x-2)\\\\=4[x(x+2)-1(x+2)]=4(x+2)(x-1)\\----------------------\\2x^2-8=2(x^2-4)=2(x^2-2^2)=2(x-2)(x+2)\\----------------------\\x^2-5x=x(x-5)\\----------------------\\\\\dfrac{3x^2+12x-15}{4x^2+4x-8}\cdot\dfrac{2x^2-8}{x^2-5x}\\\\=\dfrac{3(x+5)(x-1)}{4\!\!\!\!\diagup_2(x+2)(x-1)}\cdot\dfrac{2\!\!\!\!\diagup^1(x-2)(x+2)}{x(x-5)}\\\\\text{Canceled:}\ (x-1)\ \text{and}\ (x+2)[/tex]
[tex]=\boxed{\dfrac{3(x-2)(x+5)}{2x(x-5)}}[/tex]
The money used in Saudi Arabia is the Riyal.The exchange rate is 4 Riyals to 1 dollar. How many Riyals would you receive if you exchange 5 dollars?
Answer:
20 Riyals you receive if you exchange 5 dollars .
Step-by-step explanation:
As given
The money used in Saudi Arabia is the Riyal.
The exchange rate is 4 Riyals to 1 dollar.
i.e
4 Riyals = 1 dollar.
Now calculate for 5 dollars.
5 × 4 Riyals = 5 × 1 dollars
20 Riyals = 5 dollars
Therefore 20 Riyals you receive if you exchange 5 dollars .