Answer:
The trip consists of two parts. The rowing part is the hypotenuse of right angled triangle
whose sides are the distance from P to the island, which is 5, and the distance between P and
the landing point of the rowboat on the shore, which is x
so this part of trip is sqrt(25+ x^2)
The 2nd part is the walking part, which is (8-x)
Distance = rate times time (D = rt), so to get the time you have t = D/r. We must divide each
of the trip by the appropriate rate to get the time.
a) T(x) = sqrt(25+x^2)/3 + (8-x)/4
To find minimum time required take derivative of the T(x) function and find it's zeros
T'(x) = x/(3(sqrt(25+x^2)) - 1/4 = 0
x/(3(sqrt(25+x^2)) = 1/4
4x = 3sqrt(25+x^2
16x^2 = 9(25+x^2) = 225 + 9x^2
7x^2 = 225
x^2 = 225/7
x = sqrt(225/7) = 5.669467 miles
T(x) = 3.602386382 hours
Step-by-step explanation:
The point where the boat should be landed can be found by expressing
the distance travelled on the boat and walking as a function of time.
The point where the boat should be landed is the point 3.4 miles from the
point P towards the town.
Reasons:
x represent the distance from point P to the boat landing point.
Therefore, distance of rowing the boat = √((12 - x)² + 3²)
The total time, t, is therefore;
[tex]t = \dfrac{12-x}{4} +\dfrac{\sqrt{x^2 + 3^2} }{3}[/tex]
When the time is minimum, we get;
[tex]\dfrac{dt}{dx} = \dfrac{d}{dx} \left( \dfrac{12-x}{4} +\dfrac{\sqrt{x^2 + 3^2} }{3} \right) = \dfrac{12\cdot \left(-3 + 4 \cdot\dfrac{2 \cdot x }{2\cdot \sqrt{x^2 + 9} } \right)}{144}[/tex]
[tex]\dfrac{12\cdot \left(-3 + 4 \cdot\dfrac{2 \cdot x }{2\cdot \sqrt{x^2 + 9} } \right)}{144} = -\dfrac{1}{4} +\dfrac{x }{3 \cdot \sqrt{x^2 +9} }[/tex]
[tex]\dfrac{x }{3 \cdot \sqrt{x^2 +9} } = \dfrac{1}{4}[/tex]
4·x = 3·√(x² + 9)
16·x² = 9·(x² + 9)
7·x² = 81
[tex]x = \dfrac{9 \cdot \sqrt{7} }{7}[/tex]
x ≈ 3.4 miles.
The point where the boat should be landed is the point approximately 3.4
miles from the point P in the direction of the town.
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An elementary school is offering 2 language classes: one in Spanish (S) and one in French (F). Given that P(S) = 50%, P(F) = 40%, P(S ∪ F) = 70%, find the probability that a randomly selected student (a) is taking Spanish given that he or she is taking French; (b) is not taking French given that he or she is not taking Spanish. 2. A pair of fair dice is rolled until a sum of either 5 or 7 appears.
Answer:
(a) Probability that a randomly selected student is taking Spanish given that he or she is taking French = 0.5 .
(b) Probability that a randomly selected student is not taking French given that he or she is not taking Spanish = 0.6 .
Step-by-step explanation:
We are given that an elementary school is offering 2 language classes ;
Spanish Language is denoted by S and French language is denoted by F.
Also we are given, P(S) = 0.5 {Probability of students taking Spanish language}
P(F) = 0.4 {Probability of students taking French language}
[tex]P(S\bigcup F)[/tex] = 0.7 {Probability of students taking Spanish or French Language}
We know that, [tex]P(A\bigcup B)[/tex] = [tex]P(A) + P(B) -[/tex] [tex]P(A\bigcap B)[/tex]
So, [tex]P(S\bigcap F)[/tex] = [tex]P(S) + P(F) - P(S\bigcup F)[/tex] = 0.5 + 0.4 - 0.7 = 0.2
[tex]P(S\bigcap F)[/tex] means Probability of students taking both Spanish and French Language.
Also, P(S)' = 1 - P(S) = 1 - 0.5 = 0.5
P(F)' = 1 - P(F) = 1 - 0.4 = 0.6
[tex]P(S'\bigcap F')[/tex] = 1 - [tex]P(S\bigcup F)[/tex] = 1 - 0.7 = 0.3
(a) Probability that a randomly selected student is taking Spanish given that he or she is taking French is given by P(S/F);
P(S/F) = [tex]\frac{P(S\bigcap F)}{P(F)}[/tex] = [tex]\frac{0.2}{0.4}[/tex] = 0.5
(b) Probability that a randomly selected student is not taking French given that he or she is not taking Spanish is given by P(F'/S');
P(F'/S') = [tex]\frac{P(S'\bigcap F')}{P(S')}[/tex] = [tex]\frac{1- P(S\bigcup F)}{1-P(S)}[/tex] = [tex]\frac{0.3}{0.5}[/tex] = 0.6 .
Note: 2. A pair of fair dice is rolled until a sum of either 5 or 7 appears ; This question is incomplete please provide with complete detail.
A financial talk show host claims to have a 55.3 % success rate in his investment recommendations. You collect some data over the next few weeks, and find that out 10 recommendations, he was correct 3 times. If the claim is correct and the performance of recommendations is independent, what is the probability that you would have observed 4 or fewer successfu
Answer:
There is a 25.52% probability of observating 4 our fewer succesful recommendations.
Step-by-step explanation:
For each recommendation, there are only two possible outcomes. Either it was a success, or it was a failure. So we use the binomial probability distribution to solve this problem.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [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]
And p is the probability of X happening.
In this problem we have that:
[tex]p = 0.553, n = 10[/tex]
If the claim is correct and the performance of recommendations is independent, what is the probability that you would have observed 4 or fewer successful:
This is
[tex]P(X \leq 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{10,0}.(0.553)^{0}.(0.447)^{10} = 0.0003[/tex]
[tex]P(X = 1) = C_{10,1}.(0.553)^{1}.(0.447)^{9} = 0.0039[/tex]
[tex]P(X = 2) = C_{10,2}.(0.553)^{2}.(0.447)^{8} = 0.0219[/tex]
[tex]P(X = 3) = C_{10,3}.(0.553)^{3}.(0.447)^{7} = 0.0724[/tex]
[tex]P(X = 4) = C_{10,4}.(0.553)^{4}.(0.447)^{6} = 0.1567[/tex]
[tex]P(X \leq 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 0.0003 + 0.0039 + 0.0219 + 0.0724 + 0.1567 = 0.2552[/tex]
There is a 25.52% probability of observating 4 our fewer succesful recommendations.
Keeping water supplies clean requires regular measurement of levels of pollutants. The measurements are indirect—a typical analysis involves forming a dye by a chemical reaction with the dissolved pollutant, then passing light through the solution and measuring its "absorbence." To calibrate such measurements, the laboratory measures known standard solutions and uses regression to relate absorbence and pollutant concentration. This is usually done every day. Here is one series of data on the absorbence for different levels of nitrates. Nitrates are measured in milligrams per liter of water.
Nitrates 50 50 100 200 400 800 1200 1600 2000 2000
Absorbence 7.0 7.6 12.7 24.0 47.0 93.0 138.0 183.0 231.0 226.0
The calibration process sets nitrate level and measures absorbence. The linear relationship that results is used to estimate the nitrate level in water from a measurement of absorbence.
a. What is the equation of the line used to estimate nitrate level?
b. What does the slope of this line say about the relationship between nitrate level and absorbence?
c. What is the estimated nitrate level in a water specimen with absorbence 40?
Answer:
a) Equation is
[tex]y = 0.1135x+1.590[/tex]
b) Slope = 0.1135 represents the change in y for a unit change in x
i.e. When nitrate content is increasedby 1, absorbence is increased by 0.1135
Step-by-step explanation:
Nitrates Absorbence
x y
50 7
50 7.6
100 12.7
200 24
400 47
800 93
1200 138
1600 183
2000 231
2000 226
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.999911043
R Square 0.999822094
Adjusted R Square 0.999799856
Standard Error 1.2890282
Observations 10
Coefficients
Intercept 1.589782721
x 0.113500259
we get regression line as
y = 0.1135x+1.590
a) Equation is
[tex]y = 0.1135x+1.590[/tex]
b) Slope = 0.1135 represents the change in y for a unit change in x
i.e. When nitrate content is increasedby 1, absorbence is increased by 0.1135
Suppose that you play the game with three different friends separately with the following results: Friend A chose scissors 100 times out of 400 games, Friend B chose scissors 20 times out of 120 games, and Friend C chose scissors 65 times out of 300 games. Suppose that for each friend you want to test whether the long-run proportion that the friend will pick scissors is less than 1/3.
1) Select the appropriate standardized statistics for each friend from the null distribution produced by applet.
-3.47 (100 out of 400; 25%), -4.17 (20 out of 120; 16.7%), -3.80 (65 out of 300; 21.7%)
-3.80 (100 out of 400; 25%), -3.47 (20 out of 120; 16.7%), -4.17 (65 out of 300; 21.7%)
-3.47 (100 out of 400; 25%), -3.80 (20 out of 120; 16.7%), -4.17 (65 out of 300; 21.7%)
-4.17 (100 out of 400; 25%), -3.80 (20 out of 120; 16.7%), -3.47 (65 out of 300; 21.7%)
Answer:
Friend A
[tex]\hat p_A= \frac{100}{400}=0.25[/tex]
[tex]z=\frac{0.25 -0.333}{\sqrt{\frac{0.333(1-0.333)}{400}}}\approx -3.47[/tex]
Friend B
[tex]\hat p_B= \frac{20}{120}=0.167[/tex]
[tex]z=\frac{0.167 -0.333}{\sqrt{\frac{0.333(1-0.333)}{120}}}\approx -3.80[/tex]
Friend C
[tex]\hat p_C= \frac{65}{300}=0.217[/tex]
[tex]z=\frac{0.217-0.333}{\sqrt{\frac{0.333(1-0.333)}{300}}}\approx -4.17[/tex]
So then the best solution for this case would be:
-3.47 (100 out of 400; 25%), -3.80 (20 out of 120; 16.7%), -4.17 (65 out of 300; 21.7%)
Step-by-step explanation:
Data given and notation
n represent the random sample taken
X represent the number of scissors selected for each friend
[tex]\hat p=\frac{X}{n}[/tex] estimated proportion of scissors selected for each friend
[tex]p_o=\frac{1}{3}=0.333[/tex] is the value that we want to test
[tex]\alpha[/tex] represent the significance level
z would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the p value (variable of interest)
Concepts and formulas to use
We need to conduct a hypothesis in order to test the claim that the proportion that the friend will pick scissors is less than 1/3 or 0.333, the system of hypothesis would be:
Null hypothesis:[tex]p\geq 0.333[/tex]
Alternative hypothesis:[tex]p < 0.333[/tex]
When we conduct a proportion test we need to use the z statistic, and the is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
The One-Sample Proportion Test is used to assess whether a population proportion [tex]\hat p[/tex] is significantly different from a hypothesized value [tex]p_o[/tex].
Calculate the statistic
Since we have all the info requires we can replace in formula (1) like this:
Friend A
[tex]\hat p_A= \frac{100}{400}=0.25[/tex]
[tex]z=\frac{0.25 -0.333}{\sqrt{\frac{0.333(1-0.333)}{400}}}\approx -3.47[/tex]
Friend B
[tex]\hat p_B= \frac{20}{120}=0.167[/tex]
[tex]z=\frac{0.167 -0.333}{\sqrt{\frac{0.333(1-0.333)}{120}}}\approx -3.80[/tex]
Friend C
[tex]\hat p_C= \frac{65}{300}=0.217[/tex]
[tex]z=\frac{0.217-0.333}{\sqrt{\frac{0.333(1-0.333)}{300}}}\approx -4.17[/tex]
So then the best solution for this case would be:
-3.47 (100 out of 400; 25%), -3.80 (20 out of 120; 16.7%), -4.17 (65 out of 300; 21.7%)
********Please show work*********
Kenen loves trains, especially those that run on narrow-gauge tracks. (The gauge
of a track measures how far apart the rails are.) He has decided to build a model
train of the Rio Grande, a popular narrow-gauge train.
Use the following information to help him know how big his model should be:
* The real track has a gauge of 3 feet (36 inches).
* His model railroad track has a gauge of 3/4 inches.
*The Rio Grande train he wants to model has driving wheels that measure 44 inches high.
Your Task: With your team, discuss what you know about the model train Kenen will build.
1) What scale factor should he use?
2) What will be the height of the driving wheels of his model?
Since the real track has a gauge of 3 feet but the model railroad track has a gauge of 3/4 inches, the scale factor must be 1/4, because you must follow the rule
"true measurement * scale factor = model measurement"
In fact, we have
[tex]3\cdot\dfrac{1}{4}=\dfrac{3}{4}[/tex]
This implies that the original driving wheels height, 44 inches, must be scaled down to
[tex]44\cdot\dfrac{1}{4}=11[/tex]
inches.
The article "Chances are you know someone with a tattoo, and he's not a sailor" included results from a survey of adults aged 18 to 50. The accompanying data are consistent with the summary values given in the article. Assuming these data are representative of adult Americans and that an adult American is selected at random, use the given information to estimate the following probabilities.
(A) P(tattoo)
(B) P(tattoo | age 18-29)
(C) P(tattoo | age 30-50)
(D) P(age 18-29 | tattoo)
At Least One Tattoo No Tattoo
Age 18-29 126 324
Age 30-50 54 396
Answer:
a) 0.2
b) 0.28
c) 0.12
d) 0.7
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
We have the following table:
At Least One Tattoo No Tattoo
Age 18-29 126 324
Age 30-50 54 396
So in total, there are
126 + 324 + 54 + 396 = 900 people
(A) P(tattoo)
This is the probability that a randomly selected person has a tattoo.
Desired outcomes:
126 + 54 = 180
180 people have at least one tattoo
Total outcomes:
There are 900 people.
P(tattoo) = 180/900 = 0.2
(B) P(tattoo | age 18-29)
This the probability that a person aged 18-29 has a tattoo
Desired outcomes:
126 people aged 18-29 have tattoos
Total outcomes:
126 + 324 = 450 people aged 18-29
P(tattoo | age 18-29) = 126/450 = 0.28
(C) P(tattoo | age 30-50)
This the probability that a person aged 30-50 has a tattoo
Desired outcomes:
54 people aged 18-29 have tattoos
Total outcomes:
54 + 396 = 450 people aged 30-50
P(tattoo | age 18-29) = 54/450 = 0.12
(D) P(age 18-29 | tattoo)
The probability that a tattoed person is 18-29.
Desired outcomes:
126 tattoed people are 18-29
Total outcomes
126 + 54 = 180 tattoed people
P(age 18-29 | tattoo) = 126/180 = 0.7
The product of Donnie's height and
8
is
128
.
Answer:
128
Step-by-step explanation:
There are 39 members on the Central High School student government council. When a vote took place on a certain proposal, all of the seniors and none of the freshmen voted for it. Some of the juniors and some of the sophomores voted for the proposal and some voted against it.If a simple majority of the votes cast is required for the proposal to be adopted, which of the following statements, if true, would enable you to determine whether the proposal was adopted?a. There are more seniors than freshmen on the council.b. A majority of the freshmen and a majority of the sophomores voted for the proposal. c. There are 18 seniors on the council.d. There are the same number of seniors and freshmen combined as there are sophomores and juniors combined.e. There are more juniors than sophomores and freshmen combined, and more than 90% of the juniors voted against the proposal.
Answer:
Option b.
Step-by-step explanation:
Statement b would be true in this case.
Let's gather data from the question:
student council = seniors + juniors
Now, some few things to note:
1. Senior students are in their 12th grade. This is the senior year in high school.
2. The sophomore is the 10th year in school. These are not senior year students.
Isolating the students, the sophomore + junior students are likely to be the majority here.
Some junior and sophomore students voted for the proposal so it means that the combined number will be: all senior students + some juniors + some sophomores.
Therefore, the majority of the freshmen and a majority of the sophomores voted for the proposal.
If s is an increasing function, and t is a decreasing function, find Cs(X),t(Y ) in terms of CX,Y .
Answer:
C(X,Y)(a,b)=1−C(s(X),t(Y))(a,1−b).
Step-by-step explanation:
Let's introduce the cumulative distribution of (X,Y), X and Y :
F(X,Y)(x,y)=P(X≤x,Y≤y)
FX(x)=P(X≤x) FY(y)=P(Y≤y).Likewise for (s(X),t(Y)), s(X) and t(Y) :
F(s(X),t(Y))(u,v)=P(s(X)≤u
t(Y)≤v)Fs(X)(u)=P(s(X)≤u) Ft(Y)(v)=P(t(Y)≤v).Now, First establish the relationship between F(X,Y) and F(s(X),t(Y)) :
F(X,Y)(x,y)=P(X≤x,Y≤y)=P(s(X)≤s(x),t(Y)≥t(y))
The last step is obtained by applying the functions s and t since s preserves order and t reverses it.
This can be further transformed into
F(X,Y)(x,y)=1−P(s(X)≤s(x),t(Y)≤t(y))=1−F(s(X),t(Y))(s(x),t(y))
Since our random variables are continuous, we assume that the difference between t(Y)≤t(y) and t(Y)<t(y)) is just a set of zero measure.
Now, to transform this into a statement about copulas, note that
C(X,Y)(a,b)=F(X,Y)(F−1X(a), F−1Y(b))
Thus, plugging x=F−1X(a) and y=F−1Y(b) into our previous formula,
we get
F(X,Y)(F−1X(a),F−1Y(b))=1−F(s(X),t(Y))(s(F−1X(a)),t(F−1Y(b)))
The left hand side is the copula C(X,Y), the right hand side still needs some work.
Note that
Fs(X)(s(F−1X(a)))=P(s(X)≤s(F−1X(a)))=P(X≤F−1X(a))=FX(F−1X(a))=a
and likewise
Ft(Y)(s(F−1Y(b)))=P(t(Y)≤t(F−1Y(b)))=P(Y≥F−1Y(b))=1−FY(F−1Y(b))=1−b
Combining all results we obtain for the relationship between the copulas
C(X,Y)(a,b)=1−C(s(X),t(Y))(a,1−b).
Two solids are described in the list below.
One solid is a sphere and has a radius of 6 inches.
The other solid is a cylinder with a radius of 6 inches and a height of 6 inches.
what is the difference betwen the volumes in cubic inches of the solids in terms of pi
A.72pi
B.144pi
C.216pi
D.288pi
The difference between the volumes in cubic inches is option A) 72pi
Step-by-step explanation:
Volume of the sphere = 4/3 πr³radius r = 6 inchesVolume = 4/3 π(6)³
⇒ 4/3(216)π
⇒ 4[tex]\times[/tex]72π
⇒ 288π cubic inches
Volume of a cylinder = π r²hradius r = 6 inchesheight h = 6 inchesVolume = π(6)²(6)
⇒ 6³π
⇒ 216π cubic inches
Difference between the volumes = 288π - 216π = 72π
The difference in volume between the two solids is 226.08in^3
Data;
radius of sphere = 6inradius of cylinder = 6inheight of cylinder = 6inVolume of SphereThe volume of a sphere is given as
[tex]v = \frac{4}{3} \pi r^3\\[/tex]
Let's substitute the values and find the volume
[tex]v = \frac{4}{3}*3.14*6^3\\v = 904.32in^3[/tex]
Volume of CylinderThe formula of volume of a cylinder is given as
[tex]v = \pi r^2 h\\[/tex]
Let's substitute the values into the equation and solve
[tex]v = 3.14 * 6^2 * 6\\v = 678.24in^3[/tex]
The difference in volume between the two solids is
[tex]volume of sphere - volume of cylinder = 904.32 - 678.24 = 226.08in^3[/tex]
The difference in volume between the two solids is 226.08in^3
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The tip of a fisherman’s rod is 8 feet above the surface of the water when he catches a fish. If he reels in a fish at a rate of 1 foot per second, and never moves the position of the rod, at what rate is the fish approaching the base of the dock when 10 feet of fishing line is out?
Answer:
-1.28 ft/s
Step-by-step explanation:
We are given that
The height of tip of fisherman's rod from the water surface=y=8 ft
[tex]\frac{dz}{dt}=-1ft/sec[/tex]
We have to find the rate at which the fish is approaching the base of the dock when x=10 ft
[tex]z=\sqrt{x^2+y^2}[/tex]
By Pythagoras theorem
[tex]Hypotenuse=\sqrt{base^2+(perpendicular\;side)^2}[/tex]
Substitute x=10 and y=8
[tex]z=\sqrt{(10)^2+8^2}=\sqrt{164}=2\sqrt{41}ft[/tex]
[tex]x^2+y^2=z^2[/tex]
Differentiate w.r.t t
[tex]2x\frac{dx}{dt}+2y\frac{dy}{dt}=2z\frac{dz}{dt}[/tex]
[tex]x\frac{dx}{dt}+y\frac{dy}{dt}=z\frac{dz}{dt}[/tex]
Substitute the values
[tex]10\frac{dx}{dt}+8(0)=2\sqrt{41}\times (-1)[/tex]
[tex]\frac{dy}{dt}=0[/tex]
Because he never moves the rod.
[tex]\frac{dx}{dt}=\frac{-2\sqrt{41}}{10}=-1.28 ft/s[/tex]
Hence, the fish is approaching the base of the dock at the rate of 1.28 ft/s
Consider the following vector-valued function:~h(t) =〈2 sin(3t),3 cos(3t),√5 sin(3t)〉0≤t≤2π3This defines a smooth parameterized curve.(a) Find the unit tangent vector~T(t) for 0≤t≤2π3.(b) Find all of the values oftin the interval 0≤t≤2π3where~h(t) and~T(t) areorthogonal.(c) Show that the curve~h(t) lies on a sphere. What is the radius of the sphere?
Answer:
a) h'(t)= (6cos3t,-9sin3t,3[tex]\sqrt[]{5}[/tex]cos3t)
b) t=0.93994736+πn/3
c) Magnitude of h(t) is 3 which is a constant, so h(t) lies on a sphere
Step-by-step explanation:
A 22 KHz baseband channel is used by a digital transmission system. Suppose ideal pulses are sent at the Nyquist rate, and the pulses can take 1024 levels. There is no noise in the system. What is the bit rate of this system
Answer:
Bit rate = 440 kBits/sec
Step-by-step explanation:
Band width = W= 22 kHz
Number of levels = L = 1024 levels
Bit per sample:
[tex]m=log_2 L\\\\m =log_2(1024)\\\\m=10 bits/sample[/tex]
Ideal pulses are sent at the Nyquist rate then bit rate = 2 x W x m
[tex]bit\,\,rate= 2\times 22\times 10^3\times 10\\\\bit\,\,rate= 440\times 10^3 bits\,sec^{-1}[/tex]
bit rate = 440 kBits/sec
The information for 2008 in millions in the table below was reported by the World Bank. On the basis of this information, which list below contains the correct ordering of real GDP per person from highest to lowest? Country GDP (Constant USS) GDP(Current USS) Population Germany 2,091 573 3,649,493 82.11 Japan 5,166,281 4910,839 127.70 U.S 11,513,872 14,093.309 304.06 A. Japan, Germany, United States B. Japan, United States, Germany C. Germany, United States, Japan D. Unied States, Japan. Germany
Answer:
Option D
Step-by-step explanation:
The current GDP is a true reflective of the actual GDP per person.
The average GDP per person is given as follows:
average GDP = [tex]\frac{Current GDP}{total population}[/tex]
For example, take Germany:
Amount in millions ( current GDP) = 3,649,493
Total population = 82 110 000
GDP per person = [tex]\frac{3649493}{82110000}[/tex]
= 0.044
The list in the descending order will be:
U.S
Japan
Germany
The correct ordering of real GDP per person is Japan, Germany, United States.
Explanation:The correct ordering of real GDP per person from highest to lowest based on the given information is Japan, Germany, United States (option B).
GDP per person is calculated by dividing the GDP (Constant USS) by the population. In this case, for 2008, the GDP per person for Japan is 5,166,281 / 127.70 = 40,442.37, for Germany is 2,091,573 / 82.11 = 25,467.29, and for the United States is 11,513,872 / 304.06 = 37,868.49.
Therefore, option A) Japan has the highest real GDP per person, followed by the United States, and then Germany.
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Explain the meaning of each of the following. (a) lim x → −3 f(x) = [infinity] The values of f(x) can be made arbitrarily close to 0 by taking x sufficiently close to (but not equal to) −3. The values of f(x) can be made arbitrarily large by taking x sufficiently close to (but not equal to) −3.
Answer:
The right answer is option 3.
lim x → −3 f(x) = [infinity] means the values of f(x) can be made arbitrarily large by taking x sufficiently close to (but not equal to) −3.
Step-by-step explanation:
The limit of a function is a fundamental concept concerning the behavior of that function near a particular input.
A function f assigns an output f(x) to every input x. We say the function has a limit L at an input a: this means f(x) gets closer and closer to L as x moves closer and closer to a. More specifically, when f is applied to any input sufficiently close to a, the output value is forced arbitrarily close to L.
That is,
lim x → a f(x) = L
Hope this helps!
The limit lim x → −3 f(x) = [infinity] means that as x values get closer to -3 (without becoming -3), the value of the function f(x) goes towards infinity i.e., it grows without bound. This is akin to certain function behaviors near a value at which an asymptote is present. However, the second part about f(x) values getting close to 0 seems contradiction to the first statement.
Explanation:The statement lim x → −3 f(x) = [infinity] is related to a concept in Calculus known as a limit. When we say that the limit of f(x) as x approaches -3 is infinity, we mean that as we make x values closer and closer to -3 (without letting x actually be -3), the value of the function f(x) becomes larger and larger without bound, i.e., approaches infinity.
This is similar to some function behaviors near an asymptote. For example, the function y = 1/x has a vertical asymptote at x = 0, where y approaches infinity as x approaches zero from either direction. Here, as x gets arbitrarily close to 0, the value of y = 1/x gets arbitrarily large, or 'approaches infinity'.
On the other hand, when the question states, 'The values of f(x) can be made arbitrarily close to 0 by taking x sufficiently close to (but not equal to) -3', it signifies the tendency of the function values to get closer and closer to 0 as x gets closer to -3. This indicates a certain limit behavior, but it seems to be contradictory with the first part where the limit was stated to be infinity. It is important to scrutinize the function's properties and behavior around x = -3 carefully.
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The time taken for a computer to boot up, X, follows a normal distribution with mean 30 seconds and standard deviation 5 seconds. What is the probability that a computer will take more than 42 seconds to boot up?
Answer:
0.008 is the probability that a computer will take more than 42 seconds to boot up.
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = 30 seconds
Standard Deviation, σ = 5 second
We are given that the distribution of time taken for a computer to boot up is a bell shaped distribution that is a normal distribution.
Formula:
[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]
a) P(computer will take more than 42 seconds to boot up)
P(x > 42)
[tex]P( x > 42) = P( z > \displaystyle\frac{42 - 30}{5}) = P(z > 2.4)[/tex]
[tex]= 1 - P(z \leq 2.4)[/tex]
Calculation the value from standard normal z table, we have,
[tex]P(x > 42) = 1 - 0.992 = 0.008[/tex]
0.008 is the probability that a computer will take more than 42 seconds to boot up.
Consider a railroad bridge over a highway. A train passing over the bridge dislodges a loose bolt from the bridge, which proceeds to fall straight down and ends up breaking the windshield of a car passing under the bridge. The car was 25 m away from the point of impact when the bolt began to fall down; unfortunately, the driver did not notice it and proceeded at constant speed of 21 m/s. How high is the bridge
Answer:
the bridge has a height y₀ = 6.94 m
Step-by-step explanation:
The position y of the loose bolt is given by (0,y) where
y = y₀ - 1/2*g*t²
where
y₀ = initial position of the bolt (height of the bridge) , g= gravity , t=time
and the position x of the car is given by (x,0) where
x= x₀ + v*t
where
x₀= initial position of the car
v= car's velocity
then in order for the bolt to hit the windshield they should be at x=0 and y=0 at the same time , then
0= x₀ + v*t
t= -x₀/v
replacing in the equation for y
0 = y₀ - 1/2*g*t²
0 = y₀ - 1/2*g*(-x₀/v)²
0 = y₀ - 1/2*g*x₀²/v²
y₀ = 1/2*g*x₀²/v²
replacing values
y₀ = 1/2*g*x₀²/v² = 1/2* 9.8m/s² * (-25 m)²/(21 m/s)² = 6.94 m
then the bridge has a height y₀ =6.94 m
We have assumed that
- The bolt has no horizontal velocity ( only vertical velocity) , starts from rest and neglected air friction
- Neglecting the height of the car , position of the windshield and size of the loose bolt
Find the equation for the plane through the points Po(3,-2,5), Qo(-3,-1,-5), and Ro(0,-4,4) The equation of the plane is Type an equation.)
Answer:
- 21 x + 24 y + 15 z =120
Step-by-step explanation:
Given that
Po(3,-2,5), Qo (-3,-1,-5), and Ro (0,-4,4) ,These are the point in the space.
We know that equation of a plane is given as
[tex]\begin{vmatrix}x-x_1 & y-y_1 &z-z_1 \\ x_2-x_1 & y_2-y_1 &z_2-z_1 \\ x_3-x_1 &y_3-y_1 & z_3-z_1\end{vmatrix}=0\\[/tex]
[tex]\begin{vmatrix}x-0 & y+4 &z-4 \\ 3-0 & -2+4 &5-4 \\ -3-0 &-1+4 & -5-4\end{vmatrix}=0.[/tex]
[tex]\begin{vmatrix}x & y+4 &z-4 \\ 3 & 2 &1 \\ -3 &3 & -9\end{vmatrix}=0.[/tex]
Now by solving above determinate we get
x( -18 -3 ) -(y+4 ) ( -27 +3 ) + ( z- 4) (9+6) = 0
-21 x +24 y -24 x 4 + 15 z - 24 = 0
- 21 x + 24 y + 15 z -120 = 0
- 21 x + 24 y + 15 z =120
Therefore the equation of the plane will be
- 21 x + 24 y + 15 z =120
Find M. Write your answer in simplest radical
Answer:
(√6/√2)ft
Step-by-step explanation:
cos 45 = m / √6 ft
m = cos 45 x √6 ft
m = (1 / √2) x √6 ft = (√6/√2)ft
The U.S. Bureau of Labor Statistics reports that 11.3% of U.S. workers belong to unions (BLS website, January 2014). Suppose a sample of 400 U.S. workers is collected in 2014 to determine whether union efforts to organize have increased union membership. a. Formulate the hypotheses that can be used to determine whether union membership increased in 2014. H0: p Ha: p b. If the sample results show that 52 of the workers belonged to unions, what is the p-value for your hypothesis test (to 4 decimals)? c. At α = .05, what is your conclusion?
Answer:
a) Null hypothesis: [tex] p \leq 0.113[/tex]
Alternative hypothesis: [tex] p >0.113[/tex]
b) [tex]p_v =P(z>1.07)=0.1423[/tex]
c) So the p value obtained was a high low value and using the significance level given [tex]\alpha=0.05[/tex] we have [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to FAIL reject the null hypothesis, and we can said that at 5% of significance the proportion of workers belonged to unions is not significantly higher than 0.113.
Step-by-step explanation:
Part a
For this case we want to check the following system of hypothesis:
Null hypothesis: [tex] p \leq 0.113[/tex]
Alternative hypothesis: [tex] p >0.113[/tex]
Part b
Data given and notation
n=400 represent the random sample taken
X=52 represent the workers belonged to unions
[tex]\hat p=\frac{52}{400}=0.13[/tex] estimated proportion of workers belonged to unions
[tex]p_o=0.113[/tex] is the value that we want to test
[tex]\alpha=0.05[/tex] represent the significance level
Confidence=95% or 0.95
z would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the p value (variable of interest)
Concepts and formulas to use
When we conduct a proportion test we need to use the z statistic, and the is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
The One-Sample Proportion Test is used to assess whether a population proportion [tex]\hat p[/tex] is significantly different from a hypothesized value [tex]p_o[/tex].
Calculate the statistic
Since we have all the info requires we can replace in formula (1) like this:
[tex]z=\frac{0.13 -0.113}{\sqrt{\frac{0.113(1-0.113)}{400}}}=1.07[/tex]
Statistical decision
It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.
The significance level provided [tex]\alpha=0.05[/tex]. The next step would be calculate the p value for this test.
Since is a right tailed test the p value would be:
[tex]p_v =P(z>1.07)=0.1423[/tex]
Part c
So the p value obtained was a high low value and using the significance level given [tex]\alpha=0.05[/tex] we have [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to FAIL reject the null hypothesis, and we can said that at 5% of significance the proportion of workers belonged to unions is not significantly higher than 0.113.
A sports manufacturer produces two products: footballs and baseballs. These products can be produced either during the morning shift or the evening shift. The cost of manufacturing the football and the baseball in the morning shift is $20 each, and the cost of manufacturing the football and the baseball in the evening shift is $25 each. The amounts of labor, leather, inner plastic lining, and demand requirements are given as follows: Resource Football Baseball Labor (hours/unit) 0.75 2 Leather (pounds/unit) 7 15 Inner plastic lining (pounds/unit) 0.5 2 Total demand (units) 1500 1200 Based on the information about the company, we know that the maximum labor hours available in the morning shift and evening shift are 5,000 hours and 2,000 hours, respectively, per month. The maximum amount of leather available for the morning shift is 15,000 pounds per month and 14,000 pounds per month for the evening shift. The maximum amount of inner plastic lining available for the morning shift is 2,000 pounds per month and 1,500 pounds per month for the evening shift.
Step-by-step explanation:
From the above illlustration,
Let x, be the number of footballs produced in the morning shift,
y, the number of baseball in the morning shift,
z, the number of football in the evening shift,
t, the number of baseball in the evening shift.
Minimizing the objective function,
min {20(x+y) + 25(z + t)}
Therefore, since the number of labor hours is for both shifts(morning and evening shifts), we add the following constraints:
0.75x + 2y ≤ 5000
0.75z + 2t ≤ 2000
Remember, the amount of leather available in the shifts is also limited. The following constraints are got:
7x + 15y ≤ 15000
7z + 15t ≤1 4000
Also, adding the constraints for the use of inner plastic lining, we have:
0.5x + 2y ≤ 2000
0.5z + 2t ≤ 1500
Modelling their demands through the following constraints:
x + z ≥ 1500
y + t ≥ 1200
Also, we are producing whole number of baseballs or footballs but we only, so
x, y, z, t ∈Z.
Finally,
min20(x + y) + 25(z + t)
0.75x + 2y ≤ 5000
0.75z + 2t ≤ 2000
7x + 15y ≤ 15000
7z + 15t ≤ 14000
0.5x + 2y ≤ 2000
0.5z + 2t ≤ 1500
x + z ≥ 1500
y + t ≥ 1200
y, x, t, z ∈ Z.
The deck for a card game is made up of 108 cards. Twenty-five each are red, yellow, blue, and green, and eight are wild cards. Each player is randomly dealt a seven-card hand.
(a) What is the probability that a hand will contain exactly two wild cards?
(b) What is the probability that a hand will contain two wild cards, two red cards, and three blue cards?
(a) The probability that a hand will contain exactly two wild cards is 0.076.
(b) The probability that a hand will contain two wild cards, two red cards, and three blue cards is 0.0007.
Let's solve these problems using the concept of combinations in probability.
Remember, [tex]C(n, k)[/tex] denotes the number of ways to choose k items from a set of n items, and is calculated as
[tex]C(n,k)=\frac{n!}{k!(n-k)!}[/tex]
where "!" denotes factorial. For example, [tex]5! = 5 \times 4 \times 3 \times 2 \times 1[/tex]
(a) The probability that a hand will contain exactly two wild cards:
The total number of ways to choose 7 cards out of 108 is [tex]C(108, 7)[/tex].
The number of ways to choose 2 wild cards out of 8 is [tex]C(8, 2)[/tex].
The number of ways to choose the remaining 5 cards out of the 100 non-wild cards is [tex]C(100, 5)[/tex].
So, the probability is [tex]\frac{C(8, 2) \times C(100, 5)}{C(108, 7)} \approx 0.076[/tex]
(b) The probability that a hand will contain two wild cards, two red cards, and three blue cards:
The number of ways to choose 2 wild cards out of 8 is [tex]C(8, 2)[/tex].
The number of ways to choose 2 red cards out of 25 is [tex]C(25, 2)[/tex].
The number of ways to choose 3 blue cards out of 25 is [tex]C(25, 3)[/tex].
So, the probability is [tex]\frac{C(8, 2) \times C(25, 2) \times C(25, 3)}{C(108, 7)} \approx 0.0007[/tex]
Determine whether the given description corresponds to an experiment or an observational study. A stock analyst selects a stock from a group of twenty for investment by choosing the stock with the greatest earnings per share reported for the last quarter.A) Experiment B) Observational study
The description corresponds to an observational study as the analyst is merely observing and analyzing the existing data (earnings per share) to make an investment decision, there's no control or manipulation of the variables involved.
Explanation:The given description corresponds to an observational study. This is because the stock analyst is merely observing and analyzing the existing earnings per share of the stocks from a group of twenty and then making an investment decision based on this data. There is no manipulation or control of variables, which are defining characteristics of an experiment.
In an experiment, the researchers would have actively influenced the earnings per share (the variable) in some way to gauge the effect of that influence. However, in this case, the analyst is simply observing the earnings per share as they are to select a stock for investment.
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A sample of 100 cars driving on a freeway during a morning commute was drawn, and the number of occupants in each car was recorded. The results were as follows: NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. Occupants 1 2 3 4 5 Number of Cars 74 10 11 3 2 Find the sample standard deviation of the number of occupants. The sample standard deviation is 37.60 37.60 Incorrect . (Round the final answer to two decimal places.)
Answer:
[tex]E(X)=1*0.74 +2*0.1 +3*0.11+ 4*0.03 +5*0.02=1.49[/tex]
[tex]Var(X)=E(X^2)-[E(X)]^2 =3.11-(1.49)^2 =0.8899[/tex]
[tex]Sd(X)=\sqrt{Var(X)}=\sqrt{0.8899}=0.943[/tex]
Step-by-step explanation:
For this case we have the following data given:
X 1 2 3 4 5
F 74 10 11 3 2
The total number of values are 100, so then we can find the empirical probability dividing the frequency by 100 and we got the followin distribution:
X 1 2 3 4 5
P(X) 0.74 0.10 0.11 0.03 0.02
Previous concepts
In statistics and probability analysis, the expected value "is calculated by multiplying each of the possible outcomes by the likelihood each outcome will occur and then summing all of those values".
The variance of a random variable Var(X) is the expected value of the squared deviation from the mean of X, E(X).
And the standard deviation of a random variable X is just the square root of the variance.
Solution to the problem
In order to calculate the expected value we can use the following formula:
[tex]E(X)=\sum_{i=1}^n X_i P(X_i)[/tex]
And if we use the values obtained we got:
[tex]E(X)=1*0.74 +2*0.1 +3*0.11+ 4*0.03 +5*0.02=1.49[/tex]
In order to find the standard deviation we need to find first the second moment, given by :
[tex]E(X^2)=\sum_{i=1}^n X^2_i P(X_i)[/tex]
And using the formula we got:
[tex]E(X^2)=1^2 *0.74 +2^2 *0.1 +3^2 *0.11 +4^2 0.03 +5^2 *0.02=3.11[/tex]
Then we can find the variance with the following formula:
[tex]Var(X)=E(X^2)-[E(X)]^2 =3.11-(1.49)^2 =0.8899[/tex]
And then the standard deviation would be given by:
[tex]Sd(X)=\sqrt{Var(X)}=\sqrt{0.8899}=0.943[/tex]
An urn contains 13 red balls and 7 blue balls. Suppose that three balls are taken from the urn, one at a time and without replacement. What is the probability that at least one of the three taken balls is blue?
Answer:
0.749
Step-by-step explanation:
The probability that at least one of the three taken balls is blue is the inverse of the probability that none of the three taken balls is blue, aka all 3 of the taken balls are red. The probability of this to happen is
In the first pick: 13/20 chance of this happens
In the 2nd pick: 12/19 chance of this happens
In the 3rd pick: 11/18 chance of this happens
So the probability of picking up all 3 red balls is
[tex]\frac{13*12*11}{20*19*18} = \frac{1716}{6840} = 0.251[/tex]
So the probability of picking up at least 1 blue ball is
1 - 0.251 = 0.749
A circle's radius that has an initial radius of 0 cm is increasing at a constant rate of 5 cm per second. a. Write a formula to expresses the radius of the circle, r (in cm), in terms of the number of seconds, t since the circle started growing. Preview b. Write a formula to express the area of the circle, A (in square cm), in terms of the circle's radius, r (in cm). A = Preview c. Write a formula to expresses the circle's area, A (in square cm), in terms of the number of seconds, t, since the circle started growing. A = Preview d. Write your answer to part (c) in expanded form - so that your answer does not contain parentheses.
Answer:
a. r = 5t
b. [tex]A = \pi r^2[/tex]
c. [tex]A = \pi (5t)^2[/tex]
d. [tex]A = 25\pi t^2[/tex]
Step-by-step explanation:
a. Since the radius is increasing at a constant rate of 5 cm per second.
r = 5t
where r is the radius at time t (seconds)
b. Area of circle [tex]A = \pi r^2[/tex]
c. We can substitute r = 5t into the area formula to have
[tex]A = \pi r^2 = \pi (5t)^2[/tex]
d. In expand form
[tex]A = \pi (5t)^2 = 25\pi t^2[/tex]
a. The expression is R = 5t
b. The area of the circle in terms of R is A = πR²
c. The area of the circle in terms of t is A = π(5t)²
d. The area of the circle in terms of t in the expanded form is A = 25π×t²
Linear systemIt is a system of an equation in which the highest power of the variable is always 1. A one-dimension figure that has no width. It is a combination of infinite points side by side.
CircleIt is a locus of a point drawn at an equidistant from the center. The distance from the center to the circumference is called the radius of the circle.
Given
R = 5t where R is the radius, and t be the time.
Thus, the answer will be
a. The expression will be
R = 5t
b. The area of the circle in terms of R will be
Area = πR²
c. The area of the circle in terms of t will be
Area = πR²
Area = π(5t)²
d. The area of the circle in terms of t in the expanded form will be
Area = πR²
Area = π(5t)²
Area = 25π×t²
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Be my Valentine: The following frequency distribution presents the amounts, in dollars, spent for Valentine's Day gifts in a survey of 120 U.S. adults in a recent year. Approximate the mean amount spent on Valentine's Day gifts to two decimal places.Amount Frequency0-19.99 16 20.00-39.99 1340.00-59.99 21 60.00-79.99 19 80.00-99.99 12 100.00-119.99 10 120.00-139.99 7140.00-159.99 8160.00-179.99 7180,00-199.99 1200.00-219.99 3220.00-239.99 2240.00-259.99 1
Answer:
the mean is 82.75
Step-by-step explanation:
Amount Frequency Mid Point fx
0-19.99 16 9.995 159.92
20.00-39.99 13 29.995 389.935
40.00-59.99 21 49.995 1049.895
60.00-79.99 19 69.995 1329.905
80.00-99.99 12 89.995 1079.94
100.00-119.99 10 109.995 1099.95
120.00-139.99 7 129.995 909.965
140.00-159.99 8 149.995 1199.96
160.00-179.99 7 169.995 1189.965
180,00-199.99 1 189.995 189.995
200.00-219.99 3 209.995 629. 985
220.00-239.99 2 229.995 459.99
240.00-259.99 1 249.995 240.995
∑ 120 9930.4
Mean = ∑fx/∑x
Mean = 9930.4/120=82.7533 = 82.75
Answer: The mean amount spent on Valentine's day is;
$82.83
Step-by-step explanation: To find the mean amount we first arrange the numbers in a frequency table, then solve.
STEP1:
AMOUNT FREQUENCY
0-19.99 16
20.00-39.99 13
40.00-59.99 21
60.00-79.99 19
80.00-99.99 12
100.00-119.99 10
120.00-139.99 7
140.00-159.99 8
160.00-179.99 7
180,00-199.99 1
200.00-219.99 3
220.00-239.99 2
240.00-259.99 1
STEP 2: Find the center of each amount, to do this we have to find the average value of the amounts.
For the first amount is;
(0+19.99)/2 = 9.995
For the second amount is;
(20+39.99)/2 =29.995
Solving this for all the amount. Therefore the table comes
AMOUNT FREQUENCY
9.995 16
29.995 13
49.995 21
69.995 19
89.995 12
109.995 10
129.995 7
149.995 8
169.995 7
189.995 1
209.995 3
229.995 2
249.995 1
STEP 3: multiple each amount in step 2 with the frequency.
For the first amount;
9.995×16 = 159.92
For the second amount;
29.995×13= 389.935
For the third amount;
49.995×21= 1049.895
For the fourth amount;
69.99×19= 1329.81
For the fifth amount;
89.995×12=1079.94
For the six amount;
109.995×10= 1099.95
For the sixth amount;
129.995×7= 909.965
For the seventh amount;
149.995×8= 1199.96
For the eight amount;
169.995×7= 1189.965
For the ninth amount;
189.995×1= 189.995
For the tenth amount;
209.995×3= 629.985
For the eleventh amount;
229.995×2=459.99
For the twelveth amount;
249.995×1= 249.995
STEP 4: Sum up all the answers from the multiplication in step 3
Therefore;
159.92+389.935+1049.895+1329.81+1079.94+1099.95+909.965+1199.96+1189.965+189.995+629.985+459.99+629.985+459.99+249.995 = 9939.995
STEP 5: divide the sum of the value seen in step 4 with the total number of frequency to get the mean value.
The total number of frequency is 120
Therefore;
9939.305÷120=82.827541
Take the value to two decimal place, it becomes;
$82.83 this is the mean value of money spent on Valentine's day.
Please help! I dont know how to figure this out.
Answer: the third option is the correct answer.
Step-by-step explanation:
Looking at the line plot,
There are 3 bags of oranges that weigh 3 7/8 pounds each. Converting 3 7/8 to improper fraction, it becomes 31/8 pounds. Therefore, the weight of the three bags would be
3 × 31/8 = 93/8 pounds
There are 2 bags of oranges that weigh 4 pounds each. Therefore, the weight of the four bags would be
2 × 4 = 8 pounds
There are 3 bags of oranges that weigh 4 1/8 pounds each. Converting 4 1/8 to improper fraction, it becomes 33/8 pounds. Therefore, the weight of the three bags would be
3 × 33/8 = 99/8 pounds
There are 2 bags of oranges that weigh 4 2/8 pounds each. Converting 4 2/8 to improper fraction, it becomes 34/8 pounds. Therefore, the weight of the three bags would be
2 × 34/8 = 68/8
Therefore, the total number of oranges would be
93/8 + 33/8 + 4 + 102/8 = (93 + 64 + 99 + 68)/8 = 324/8 = 40 1/2 pounds
Which coordinate plane shows the graph of 3x + y > 9?
Answer:
'3'. x = 3 + 0.3333333333y Simplifying x = 3 + 0.3333333333y
Step-by-step explanation:
The admission price was $1.00 in 1909. How much would the Speedway have had to charge in 1999 to match the purchasing power of $1 in 1909? In other words, how much was that in 1999? (Don't use a $ sign, use 2 decimal places.)
Answer: 13.04
Here are some consumer price indexes from the past 100+ years:
Year CPI
1909 9.1
1919 17.3
1929 17.1
1939 13.9
1949 23.8
1959 29.1
1969 36.7
1979 72.6
1989 118.3
1999 166.6
2009 214.5
2015 238.5
The admission price was $1.00 in 1909. How much would the Speedway have had to charge in 1989 to match the purchasing power of $1 in 1909? In other words, how much was that in 1989?