Consider a game in which player 1 moves first. the set of actions available to player 1 is a1={a,b,c}. after observing the choice of player 1, player 2 moves. the set of actions available to player 2 is a2={a,b,c,d}. at how many information sets does player 2 move?
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Related Questions
A ball is launched from 8 feet off the ground at an initial vertical speed of 64 feet per second. It is aimed across a field at a target also 8 feet off the ground. The height of the ball at time, t, in seconds, is given by the function, h = –16t 2 + 64t + 8.
Answers
vertex = time at maximum height = -b/2a = -64 / 2(-16) = 2 seconds
The maximum height can be calculated by substituting the time we obtained to the function.
h = –16t 2 + 64t + 8
h = –16(2)^2 + 64(2) + 8 = 72 feet
On two investments totaling $11,500, Peter lost 3% on one and earned 4% on the other. If his net annual receipts were $201, how much was each investment?
Answers
X +Y = $11500. ----------(1)
Total yearly interest for thetwo a/c is - $201
-0.03X + 0.04Y = $201
Form (1)
X = 11500 - Y
Substitute for X
-0.03(11500 - Y) + 0.04 Y = $201
-345 + 0.03Y + 0.04Y =201
0.07Y = 546
Y = 7800 at 4 %
Calculate X
X = 11500 - Y
= 11500 - 7800
=3700 at - 3%
Check
-0.03×3700 + 0.04 × 7800 = $201
-111 + 312 = $201
$201 = $201
Final answer:
Peter invested $3,700 at a 3% loss and $7,800 at a 4% gain. By setting up a system of equations and solving them, we determined the amount invested in each.
Explanation:
To solve the problem of how much was invested by Peter in each investment, we need to set up a system of equations. Let's call the amount invested at 3% loss x, and the amount invested at 4% gain y. The total amount invested is $11,500, so we have x + y = $11,500.
Peter's net annual receipts were $201, which comes from a loss of 3% on investment x and a gain of 4% on investment y. The equation for this would be -0.03x + 0.04y = $201.
Now we have a system of two equations:
-0.03x + 0.04y = $201
Adding (1) and (2) gives us:
0.03y + 0.04y = $546
Combining like terms, we get:
0.07y = $546
Dividing both sides by 0.07, we find that:
y = $7,800
Substituting y back into the first equation, we get:
x = $11,500 - $7,800 = $3,700
So, Peter invested $3,700 in the investment with a 3% loss and $7,800 in the investment with a 4% gain.
Gambler is deciding whether or not to take a bet. she must pay $40 to take the bet, but if she wins, she willprofit$225.theprobability that she wins the bet is ¼. what is the player’s expected value in this situation
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the sum of the products of value of outcome and its probability,
less the amount paid to place the bet.
Outcomes value probability
win 225 1/4
lose 0 3/4
cost of bet = 40
So expected value of bet
E[X]=225*(1/4)+0*(3/4)-40
=56.25-40
=16.25
This means that in the long run, gambler will win, since the expected value is positive. (does NOT mean she will win in the next bet!)
Find the value of the variable that makes the statement true:
cube root of 3375= m.
what is m please asap.
Answers
Answer:
m=15
Step-by-step explanation:
cube root of 3375 =m
We need to solve the equation for m
[tex]\sqrt[3]{3375} = m[/tex]
In order to solve for m we need to find the cube root of 3375
3375 can be written as 3 times 3 times 3 times 5 times 5 times 5
[tex]\sqrt[3]{3375} = m[/tex]
[tex]\sqrt[3]{3 \cdot 3 \cdot 3 \cdot 5 \cdot 5 \cdot 5} = m[/tex]
For same three factors inside the cube root we pull out one factor outside the cube root
[tex]\sqrt[3]{3 \cdot 3 \cdot 3} = 3[/tex]
[tex]\sqrt[3]{3 \cdot 3 \cdot 3 \cdot 5 \cdot 5 \cdot 5} = m[/tex]
[tex]3 \cdot 5 = m[/tex]
m= 15
The value of the variable that makes the statement true is
m = 15
Cube Root FunctionsThe given equation is:
[tex]\sqrt[3]{3375} = m[/tex]
We are looking for a number that we can multiply by itself 3 times to get 3375
Note that the given equation can be re-written as:
[tex]m =3375^{\frac{1}{3}[/tex]
This can be further simplified as:
[tex]m=15^{3(\frac{1}{3} )}\\\\m=15[/tex]
Therefore, the value of the variable that makes the statement true is m = 15
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How do you rename 805 tens
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_____________________________________________________________
"80.5 tens" ; or "eighty point 5 tens" ; or "eighty and one-half tens".
______________________________________________________________
What compound inequality represents the phrase? Graph the solutions.
all real numbers that are greater than –8 and less than 8
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-8<x<8 (x=(-8,8) in interval notation)
**NEEDS TO BE ANSWERED ASAP**
Find the indicated probability. Express your answer as a simplified fraction unless otherwise noted.
The following table contains data from a study of two airlines which fly to Small Town, USA.
If one of the 87 flights is randomly selected, find the probability that the flight selected is an Upstate Airlines flight which was on time.
a. 43/87
b. 43/76
c. 43/48
d. 11/76
Answers
Answer: a. [tex]\dfrac{43}{87}[/tex]
Step-by-step explanation:
From the given table , it can be seen that the total number of flights are given : 43+33+6+5=87
Also, the the number of Upstate Airlines flights on time = 43
Now if one of the 87 flights is randomly selected, the probability that the flight selected is an Upstate Airlines flight which was on time will be :-
[tex]\dfrac{\text{Number of Upstate Airlines flight on time}}{\text{Total flight}}\\\\=\dfrac{43}{87}[/tex]
Hence, the probability that the flight selected is an Upstate Airlines flight which was on time [tex]=\dfrac{43}{87}[/tex]
The value of y is inversely proportional to the value of x. When y=24, x=4. What is the value of y when x=6?
Answers
When y=24, x=4
y= kx
24 = 4k
k = 24/4
k = 6
when x=6
y = kx
y = 6 (6)
y = 36
answer
y = 36 when x = 6
The value of [tex]\( y \)[/tex] when x = 6 is 16.
Given that [tex]\( y \)[/tex] is inversely proportional to [tex]\( x \)[/tex], we can write the relationship as:
[tex]\[ y = \frac{k}{x} \][/tex]
where [tex]\( k \)[/tex] is the constant of proportionality.
First, we need to determine the value of [tex]\( k \)[/tex]. We are given that [tex]\( y = 24 \)[/tex] when [tex]\( x = 4 \)[/tex].
[tex]\[ 24 = \frac{k}{4} \][/tex]
Solving for k:
[tex]\[ k = 24 \times 4 = 96 \][/tex]
Now that we have the value of [tex]\( k \)[/tex], we can find the value of [tex]\( y \)[/tex] when [tex]\( x = 6 \)[/tex]:
[tex]\[ y = \frac{96}{6} \][/tex]
[tex]\[ y = 16 \][/tex]
if ax +3=7-bx what is x expressed in terms of a and b
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ax + bx + 3 = 7 ...subtract 3 from each side
ax + bx = 7 - 3
ax + bx = 4 ....factor out x
x(a + b) = 4 ...divide both sides by (a + b)
x = 4 / (a + b) <==
18.666667 rounded to nearest hundredth
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30% of the 70 buttons had holes how many did not have holes
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70 - 21 = 59.
Answer: 59 buttons
The equation y = 0.75x + 10 describes the cost, y, of placing an ad with x words in the classified section of a newspaper. How many words are in an ad that costs $25?
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y = cost = $25
25 = 0.75 +10
subtract 10 from each side
15=0.75x
x = 15/0.75 = 20
there were 20 words in the ad
Raul received a score of 72 on a history test for which the class mean was 70 with a standard deviation of 9. he received a score of 71 on a biology test for which the class mean was 70 with standard deviation 7. on which test did he do better relative to the rest of the class?
Answers
Final answer:
Raul did better on the history test relative to his classmates, as indicated by a higher z-score of approximately 0.22, compared to 0.14 for the biology test.
Explanation:
To determine on which test Raul did better relative to the rest of the class, we need to calculate the z-scores for Raul's history and biology test results. A z-score is a statistical measurement that describes a value's relationship to the mean of a group of values, measured in terms of standard deviations from the mean. The formula for calculating a z-score is:
z = (X - μ) / σ
where X is the score, μ is the mean, and σ is the standard deviation. Let's apply this to Raul's scores:
For the history test:
z = (72 - 70) / 9 = 2 / 9 ≈ 0.22
For the biology test:
z = (71 - 70) / 7 = 1 / 7 ≈ 0.14
Comparing the two z-scores, we can see that Raul's z-score for history is higher than his z-score for biology. Hence, Raul did better on the history test relative to the rest of the class.
The area of a rectangle is 52ft ^2 and the length of the rectangle is 5ft less than twice the width. Find the dimensions of the rectangle.
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L= (2w-5)
(2w-5) * w= 52
2w^2-5w= 52
2w^2-5w-52=0
(2w-13)(w+4)=0
2w=13
W= 13/2
W= 6.5 ft
L=2w-5
2(6.5)-5
13-5
L= 8 ft.
Hope this helps.
The solution set of 3x+4y<0 lies in which quadrant?
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[tex]y \ \textless \ -\frac{3}{4} x[/tex]
Next graph the line....down 3, over 4...
The line should go through the 2nd and 4th quadrant.
The inequality is 'less than', so the solution is everything below the line.
Therefore the solution set lies in part of quadrant 2, all of quadrant 3, and part of quadrant 4.
Subtract 8-4 1/2. A. 3 B. 4 C. 4 1/2 D. 3 1/2
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An expression of the form [tex]a \frac{b}{c}[/tex] is called a "compound fraction"
Compound fractions can be written as simple fractions by multiplying c to a, and then adding the product to c as follows:
[tex]a \frac{b}{c}= \frac{c.a+b}{c}[/tex]
for example,
[tex]4\frac{1}{2}[/tex] can be written as:
[tex]4\frac{1}{2}= \frac{2.4+1}{2}=\frac{9}{2}[/tex]
2.
when we subtract or add a fraction [tex] \frac{m}{n} [/tex] from an integer k,
we first write k as a fraction with denominator n. We can do this as follows:
[tex]k=k. \frac{n}{n}= \frac{kn}{n} [/tex]
for example, if we want to subtract [tex] \frac{9}{2} [/tex] from 8,
we first write 8 as a fraction with denominator 2:
[tex]8=8. \frac{2}{2}= \frac{8.2}{2}= \frac{16}{2} [/tex]
3.
Thus,
[tex]8-4 \frac{1}{2}= \frac{16}{2}- \frac{9}{2}= \frac{16-9}{2}= \frac{7}{2} [/tex]
4.
The simple fraction 7/2 is not an option, so we write it as a compound fraction as follows:
[tex] \frac{7}{2}= \frac{6+1}{2}= \frac{6}{2}+ \frac{1}{2}=3+ \frac{1}{2}=3\frac{1}{2} [/tex]
(So write 7 as the sum of the largest multiple of 2, smaller than 7 + what is left. In our case these numbers are 6 and 1, then proceed as shown)
5. Answer: D
Subtraction of 8-4 1/2 is 3 1/2.
The correct option is D.
To subtract 8 - 4 1/2, we need to convert the mixed number 4 1/2 into an improper fraction.
To do this, we multiply the whole number (4) by the denominator (2), which gives us 8. Then we add the numerator (1) to get 9. So, 4 1/2 is equivalent to the improper fraction 9/2.
Now, we can subtract 8 from 9/2. To subtract fractions, the denominators must be the same. We can rewrite 8 as 8/1 to have a common denominator with 9/2.
Subtracting 8/1 from 9/2 gives us (8 - 9/2).
To subtract fractions, we need a common denominator, which is 2 in this case.
Converting 8/1 to have a denominator of 2, we get 16/2.
Now we can subtract the fractions: (16- 9)/2 = 7/2.
Therefore, the answer is 7/2, which can also be expressed as 3 1/2.
So the correct answer is D. 3 1/2.
To learn more about subtraction;
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The volume of a pyramid varies jointly with the base area of the pyramid and its height. The volume of one pyramid is 24 cubic inches when its base area is 24 square inches and its height is 3 inches. What is the volume of a pyramid with a base area of 10 square inches and a height of 9 inches?
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The volume of a pyramid with a base area of 10 square inches and a height of 9 inches will be 30 cubic inches.
What is the volume of the pyramid?Suppose the base of the pyramid has length = L units and width = W units, slant height = K units, and the height of the pyramid is of H units.
Then the volume of the pyramid will be
V = (L × B × H) / 3
V = (Base area x H) / 3
The volume of a pyramid varies jointly with the base area of the pyramid and its height.
The volume of one pyramid is 24 cubic inches when its base area is 24 square inches and its height is 3 inches.
Then the volume of a pyramid with a base area of 10 square inches and a height of 9 inches will be
V = (10 x 9) / 3
V = 30 cubic inches
More about the volume of the pyramid link is given below.
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The volume of a pyramid is obtained from the joint variation relationship with its base area and height. Given a certain pyramid's dimensions, we can determine the volume of another pyramid if we know its base area and height. The volume of the second pyramid is 30 cubic inches.
Explanation:The student's question pertains to joint variation, a concept in mathematics, specifically applied here to understand how the volume of a pyramid relates to its base area and height. For a pyramid, this relationship can be expressed as V = k * A * H, where V is volume, A is base area, H is height, and k is the constant of variation.
First, we find the value of 'k' using the given pyramid's measurements; so 24 = k * 24 * 3 gives us k = 1/3.
Then, we use this constant to find the volume of the other pyramid whose base area is 10 square inches and height is 9 inches. Therefore, V = 1/3 * 10 * 9, which simplifies to V = 30 cubic inches.
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solve for w.
-3w+2=-10w+30
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-3w+2=-10w+30
add 3 w to each side
2=-7w+30
subtract 30 from each side
-28 = -7w
divide both sides by -7
w = 4
double check
-3(4) +2 = -10
-10(4) +30 = -10
so w = 4
HELP PLZ!!!! A courtyard in the shape of a right triangle is set in the middle of three square office buildings, with one office building along each side. Which statement is true about the three office buildings?
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Melissa bought a new dishwasher for $1200 the manufacturers offering a 15% rebate how much will the dishwasher cost after the rebate
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1200*0.15 = 180
1200-180 = $1020
$1020 after the rebate
0.85(1200) = 1020 <==
A university found that 10% of its students withdraw without completing the introductory statistics course. assume that 20 students registered for the course.
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Write four hundred seven trillion six million one hundred five thousand twenty eight in standard form
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The standard form of four hundred seven trillion six million one hundred five thousand twenty-eight is 407,000,006,105,028.
As we know that,
In trillion, there are 12 zeros.In billion, there are 9 zeros.In million, there are 6 zeros, In thousand, there are 3 zeros.In hundred there are 2 zeros.In tens, there is 1 zero. In ones, there is no zero.So, it should be presented below.
Trillion Billion Million Thousand Hundred Tens Ones
407 , 000 , 006 , 105 , 0 2 8
Therefore we can conclude that the standard form of four hundred seven trillion six million one hundred five thousand twenty-eight is 407,000,006,105,028.
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how do i solve this question
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Write the standard form of the line that passes through the given points.
4, 7) and (0, 7)
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notice how ur points have the same y values....this means this is a horizontal line with a slope of 0.
equation is : y = 7...or y = 0x + 7...but we need it in standard form...
0x + y = 7 <== standard form
The equation of the line would be y = 7 which passes through the points (4, 7) and (0, 7).
What is the slope of the line?The slope of a line is defined as the gradient of the line. It is denoted by m
Slope m = (y₂ - y₁)/(x₂ -x₁ )
Given that line passes through points (4, 7) and (0, 7)
Let the required line would be y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]
x₁ = 4, y₁ = 7
x₂ = 0, y₂ = 7
⇒ y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]
Substitute values in the equation, we get
⇒ y - 7 = (7 - 7)/(0- 4)[x -4]
⇒ y - 7 = (0)/(-10 )[x -4]
⇒ y - 7 = 0(x -4)
⇒ y - 7 = 0
⇒ y = 7
Therefore, the equation of the line would be y = 7 which passes through the points (4, 7) and (0, 7).
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what is the meaning os slpoe in math and please give an example for
y=2x-1;(-2,2)
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Slope in math is the difference in y-values divided by x-values.
The slope helps determine the steepness of a line. Y-intercept is the y-value when x=0. The formula for slope, denoted as m, is (y2-y1)/(x2-x1).
Example: For the equation y = 2x - 1, if we have the point (-2, 2), we can calculate the slope by substituting the values into the formula: m = (2-(-1))/(-2-0) = 3/-2 = -1.5.
Y-intercept is the y-value when x=0, or where the graph crosses the y-axis.
what is 10 times as much as 700
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700*10=7000
Final answer: 7,000
You are driving 70 miles per hour, starting at mile marker 255. How many hours will it take you to reach mile marker 115?
Answers
255-115 = 140 miles
140/70 = 2 hours
The present value of an ordinary annuity of $350 each year for five years, assuming an opportunity cost of 4 percent, is ________.
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PVOA means present value of an ordinary annuity.
PMT = $350
PMT means recurring payment.
time = 5 years and interest rate is 4%
So n = 5 and i = 4%
So we can calculate PVOA as
PVOA = PMT times (PVOA factor for n = 5 and i = 4%)
[tex]= 350 * (4.452)[/tex] (PVOA factor PVOA table)
[tex]= 1558.2[/tex]
So present value is $1558.2
The present value of an ordinary annuity of $350 each year for five years with a 4 percent opportunity cost is $1,551.88, calculated using the present value formula for annuities.
To find the present value of an ordinary annuity, you can use the formula for the present value of an annuity:
[tex]\[ PV = Pmt \times \frac{{1 - (1 + r)^{-n}}}{{r}} \][/tex]
Where:
- PV is the present value of the annuity,
- Pmt is the annual payment (in this case, $350),
- r is the interest rate per period (in decimal form),
- n is the number of periods (in this case, 5 years).
Given that the opportunity cost (interest rate) is 4%, or 0.04 in decimal form, and there are 5 years of payments, we can plug these values into the formula:
[tex]\[ PV = 350 \times \frac{{1 - (1 + 0.04)^{-5}}}{{0.04}} \][/tex]
Let's calculate:
[tex]\[ PV = 350 \times \frac{{1 - (1.04)^{-5}}}{{0.04}} \][/tex]
[tex]\[ PV = 350 \times \frac{{1 - (0.8227)}}{{0.04}} \][/tex]
[tex]\[ PV = 350 \times \frac{{0.1773}}{{0.04}} \][/tex]
[tex]\[ PV \approx 350 \times 4.4325 \][/tex]
PV = $1551.88 (Approximately)
So, the present value of the annuity, assuming an opportunity cost of 4%, is approximately $1551.88.
a House sits on a 5/8 acre lot and 1/2 of the lot is lawn. 2/3 of lawn was mowed. how much was mowed?
Answers
5/8 x 1/2 = 5/16 acre is lawn
5/16 x 2/3 = 10/48 reduces to 5/24 of the lawn was mowed
Find the area. ABCD∼EFGHABCD∼EFGH The area of rectangle ABCD is 72 inches2 and a diagonal is 12 inches. The diagonal of rectangle EFGH is 22 inches. Find the area of rectangle EFGH. Round to the nearest inch2 if necessary.
Answers
d₁ / d₂ = 12 inches / 22 inches
The ratio of their areas should be the square of this ratio.
If we let x be the area of the larger rectangle, we have the equation,
A₁ / A₂ = (d₁/d₂)² = (72 inches² / x inches²)
Substituting the known values,
(12 /22)² = (72 inches² / x inches²)
The value of x is equal to 242 inches². Thus, the area of the larger rectangle is 242 inches².