Answer:
In the long run, ou expect to lose $4 per game
Step-by-step explanation:
Suppose we play the following game based on tosses of a fair coin. You pay me $10, and I agree to pay you $n^2 if heads comes up first on the nth toss.
Assuming X be the toss on which the first head appears.
then the geometric distribution of X is:
X [tex]\sim[/tex] geom(p = 1/2)
the probability function P can be computed as:
[tex]P (X = n) = p(1-p)^{n-1}[/tex]
where
n = 1,2,3 ...
If I agree to pay you $n^2 if heads comes up first on the nth toss.
this implies that , you need to be paid [tex]\sum \limits ^{n}_{i=1} n^2 P(X=n)[/tex]
[tex]\sum \limits ^{n}_{i=1} n^2 P(X=n) = E(X^2)[/tex]
[tex]\sum \limits ^{n}_{i=1} n^2 P(X=n) =Var (X) + [E(X)]^2[/tex]
[tex]\sum \limits ^{n}_{i=1} n^2 P(X=n) = \dfrac{1-p}{p^2}+(\dfrac{1}{p})^2[/tex] ∵ X [tex]\sim[/tex] geom(p = 1/2)
[tex]\sum \limits ^{n}_{i=1} n^2 P(X=n) = \dfrac{1-p}{p^2}+\dfrac{1}{p^2}[/tex]
[tex]\sum \limits ^{n}_{i=1} n^2 P(X=n) = \dfrac{1-p+1}{p^2}[/tex]
[tex]\sum \limits ^{n}_{i=1} n^2 P(X=n) = \dfrac{2-p}{p^2}[/tex]
[tex]\sum \limits ^{n}_{i=1} n^2 P(X=n) = \dfrac{2-\dfrac{1}{2}}{(\dfrac{1}{2})^2}[/tex]
[tex]\sum \limits ^{n}_{i=1} n^2 P(X=n) =\dfrac{ \dfrac{4-1}{2} }{{\dfrac{1}{4}}}[/tex]
[tex]\sum \limits ^{n}_{i=1} n^2 P(X=n) =\dfrac{ \dfrac{3}{2} }{{\dfrac{1}{4}}}[/tex]
[tex]\sum \limits ^{n}_{i=1} n^2 P(X=n) =\dfrac{ 1.5}{{0.25}}[/tex]
[tex]\sum \limits ^{n}_{i=1} n^2 P(X=n) =6[/tex]
Given that during the game play, You pay me $10 , the calculated expected loss = $10 - $6
= $4
∴
In the long run, you expect to lose $4 per game
Find the sum.
19+(-19)
19+(-19)=0
Step-by-step explanation:
So first lets simplify this. We can use the method keep,change, change to do this. Keep the value of positive 19. Then change the + sign to - and the - sign to plus which gets us
19-(+19).
We can remove the +since we know its positive leaving 19-19 which is 0
The total cost after tax to repair Deborah's computer is represented by0.08(50h)+50H, where h is the number of hours it takes to repair Deborah's computer. What part of the expression represents the amount of tax she has to pay? Explain
Answer:
.08(50h) Because if the tax rate is 8%, then that is 1.08% of 50h.
Step-by-step explanation:
Rachel tells Jonah that she can turn a square, but he won’t be able to tell that it was turned after she is finished turning it.
Please help with this question
-7 times -8? -40 divided by 10?
Suppose $x$ and $y$ are integers such that $xy+5x+4y=-5$. Find the greatest possible value of $y$.
Answer:
10
Step-by-step explanation:
xy + 5x + 4y = -5
(x + 4) y + 5x = -5
(x + 4) y = -5x − 5
y = -5 (x + 1) / (x + 4)
For y to be large as possible, (x + 1) / (x + 4) must be negative. That means -4 < x < -1. So x is either -2 or -3.
The possible values of y are:
y = -5 (-2 + 1) / (-2 + 4) = 5/2 (not an integer).
y = -5 (-3 + 1) / (-3 + 4) = 10.
Ashley works in accountant’s office and makes $45 per hour. She must pay $40 for daycare each day. If she wants to make more than $300 a day, at
Answer:
The answer is "8 hours"
Step-by-step explanation:
by the given value we create the equation that is:
[tex]\to 45x-40=300\\\\\to 45x=300+40\\\\\to 45x=340\\\\\to x=\frac{340}{45}\\\\\to x= 7.55\ \ hours \ or \ \ \ 8 \ hours[/tex]
Find the missing angle
Answer:
47 degrees
Step-by-step explanation:
shown by the square this angel is 90 degrees. 90 - 43 = 47
Answer:
47
Step-by-step explanation:
Therefore
90-43=41
SI units are the modern form of the:
a- geological system of measurement
b-metric system of measurement
c-US customary system of measurement
d-imperial units of measurement
Answer:
Step-by-step explanation:
SI units are the modern form of the metric system of measurement
The SI units are metric system of measurement
What is International System of Units?The International System of Units comprises a coherent system of units of measurement starting with seven base units. The units and their physical quantities are the second for time, the meter (sometimes spelled meter) for length or distance, the kilogram for mass, the ampere for electric current, the kelvin for thermodynamic temperature, the mole for amount of substance, and the candela for luminous intensity. It is represented as SI
Given data ,
Let the units of measurements be represented as A
Now , the value of A is
Seven base units - the second (symbol s, the unit of time), the metre (m, the unit of length), the kilogramme (kg, the unit of mass), the ampere (A, the unit of electric current), the kelvin (K, the unit of thermodynamic temperature), the mole (mol, the unit of substance amount), and the candela make up the SI's coherent system of units of measurement (cd, luminous intensity)
Therefore , the SI units are metric system of measurement
Hence , the SI units are solved
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how are T minus 4 and T plus 4 related?
Answer:
T will equal 4
Step-by-step explanation:
T-4=T-4
T+4=T+4
How many square feet is 75,480 square centimeters? (Round to the nearest tenth) *
Answer:
70123214.6cm^2
Step-by-step explanation:
Can someone please help??
Answer:
let the number of cows = x
let the number of chickens = y
since there are 42 heads:
x + y = 42
and since a cow has 4 legs, and a chicken has 2
4x + 2y = 144
from first equation:
x + y = 42
x = 42 - y (now, we will substitute this in the second equation)
4(42 - y) + 2y = 144
168 - 4y + 2y = 144
2y = 168 - 144
2y = 24
y = 12
now, we know the number of chickens. we will replace y with 12 in the first equation since it is more simpler
x + 12 = 42
x = 30
So, there are 30 cows and 12 chickens
Brainly it if you find the answer helpful
Let A and B be n-by-n matrices in R^n, and let c be a real number. Which of the following statements about trace is not necessarily true? a. tr(A+B) = tr(A) + tr(B) b. tr(AB) = tr(BA) c. tr(AB) = tr(A)tr(B) d. tr(CA) = ctr(A)
Answer:
c. tr(AB) = tr(A)tr(B)
Step-by-step explanation:
The trace of a matrix is only valid for a square matrix, that is a n by n matrix. The trace of a matrix is the sum of all its diagonal elements. The following properties of trace holds for a matrix A and B with size n by n and a real number c.
i) The trace sum of two matrix is equal to the sum of their individual traces. That is:
tr(A + B) = tr(A) + tr(B)
ii) The trace of the product of a scalar and a matrix is the same as the product of the scalar and the trace of the product, that is:
tr(cA) = ctr(A)
iii) The trace of a transpose of a matrix is equal to the trace of the matrix, that is:
[tex]tr(A^T)=tr(A)[/tex]
iv) The trace of a product of matrix is given as:
tr(AB) = tr(BA)
Answer:
c. tr(AB) = tr(A)tr(B)
WILL MARK BRAINLIST please help! Im stuck
Answer:
width = 5k²
length = 3k² + 7k + 4
Step-by-step explanation:
(see attached)
Solve the inequality.
The solution is....
Answer:
Step-by-step explanation:
-x - 6 > 21 - 28x
27x - 6 > 21
27x > 27
x > 1
equation
Be sure that your last entry is the solution to the equation
and in simplest form.
You do not need to use all rows of the table.
10x + 8 = 4x + (-4)
Enter equivalent equations below
Answer:
10x+8=4x+(-4).
10×+8=4x-4.
collect like terms.
10x-4x=-4-8.
6x=-12.
x=-12/6.
x=-2.
Simplify the expression: 2(5 + 7c) need help
Answer:
10+14c
Step-by-step explanation:
You multiply every number inside the parenthesis by 2.
Answer:
10+14c
Step-by-step explanation:
Multiply two times what is in parentheses.
10+14c
Some populations, such as bacteria, can be expected under the right conditions to show exponential growth. If 5500 bacteria of a certain type are incubated under ideal conditions, then after t hours
we expect to find 5500 x 1.07^t bacteria present. How many bacteria would we expect to find after 14 hours? (Round your answer to the nearest whole number.)
How many after 3 days?
Answer:
608945 is the answer.
Step-by-step explanation:
Because..
After 14 hours the population of bacteria is 14190.
What is Exponential Decay?A quantity is subject to exponential decay if it decreases at a rate proportional to its current value.
Given that Some populations, such as bacteria, can be expected under the right conditions to show exponential growth
If 5500 bacteria of a certain type are incubated under ideal conditions, then after t hours we expect to find [tex]5500(1.07)^{t}[/tex] bacteria present.
We need to find how many bacteria would we expect to find after 14 hours
To find this we have to replace t by 14
5500×(1.07)¹⁴
5500×2.58
14190
Hence, after 14 hours the population of bacteria is 14190.
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what set has a fixed number of elements
Answer:
Finite Set
Step-by-step explanation:
A finite set is a set that contains a fixed number of elements, that is, the elements are countable. However, the opposite of a finite set is an infinite set which does not have a fixed number of elements and is uncountable.
Examples of a finite set are
The set of all past American PresidentsThe set of all persons in ChinaThe set of birds in Australiaa
A pianist plans to play 7 pieces at a recital. In how many ways can she arrange these pieces in the program?
Answer:
5040
Step-by-step explanation:
7 x 6 x 5 x 4 x 3 x 2 = 5040 different ways. Look at it this way: The first place can be taken by any of the 7 objects, which leaves any of 6 objects available for second place, which leaves any of 5 objects that then leaves 4 then 3 then 2 then 1
HOPE THIS HELPS
B. You are given nine stones which look and feel identical. One of them contains a valuable gem worth $250,000 and is actually slightly heavier than the other eight (but not enough to detect by lifting by hand). If you identify the gemstone it is yours to keep. You have a balance scale, (see diagram) which you can use exactly two times. Once you have used the scale twice you never get another opportunity. How can you be certain to find the stone contains the gem. (If you guess at any point you lose your chance to win the gem stone.)
Answer:
Separate the stones into 3 groups of 3.
Let's call each the three groups A, B, and C.
1) Place group A and group B on the two plates of the scale. There are two possible outcomes i) and ii) below:
i) The groups have different weights. A is heavier than B or B is heavier than A. Take the heavier group. Place two stones from this group on the scale. If one is heavier than the other, this is it. If they are equal, the stone not on the scale is it.
ii) Groups A and B have equal weights. The heavier stone in in group C. Using group C, place two stones from this group on the scale. If one is heavier than the other, this is it. If they are equal, the stone not on the scale is it.
5. Topic 1 Independent Practice
Use the following set to answer the question.
{ (-2,1), (-1,0), (0,1), (1,2)}
True or false, this set is a function?
O True
O False
Plisss
Answer:
True
Step-by-step explanation:
This set is a function because every input value only has one output value.
What is the value of f(2)?
Question:
What is the equation?
1
Solve: -1/2x+2=-x+7
Answer:
x=10
Step-by-step explanation:
Step 1: Add x to both sides
Step 2: Subtract 2 from both sides.
Step 3: Multiply both sides by 2.
7. Compare the value of the 5 in 85,327 and 435.
Answer:
5 in the 85327= five thousand units
5 in the 435= five units
Step-by-step explanation:
85,327= eighty five thousand, three hundred and twenty seven
Value of five or the position if five in the above number is the thousand position
5 in the above = five thousand unit
435= four hundred and thirty five
The position of five in the above number is the unit position
Five in the above= five unit
If after two hours 4 Inches off snow has fallen how many inches would have fallen after 6.6 hours
Select expression that is mathematically equivalent to xy−z+ (a - b) X c. y - 2 O
a) x/y – z + (a - b)
b) Xc O x/(y – z) + (a - b)
c) Xc O x/y - 2 + a - b c O
d) x/(y – z) + a – b xc
Question:
Select expression that is mathematically equivalent to
[tex]\frac{x}{y-z} + (a-b)*c[/tex]
a) [tex]x/y - z + (a - b) * c[/tex]
b) [tex]x/(y - z) + (a - b) * c[/tex]
c) [tex]x/y - z + a - b * c[/tex]
d) [tex]x/(y - z) + a - b * c[/tex]
Answer:
[tex]x/(y - z) + (a - b) * c[/tex]
Step-by-step explanation:
Given
[tex]\frac{x}{y-z} + (a-b)*c[/tex]
Required
Determine its equivalent
Start by writing y - z in bracket;
[tex]\frac{x}{y-z} + (a-b)*c[/tex]
becomes
[tex]\frac{x}{(y-z)} + (a-b)*c[/tex]
When - is used as divide, it is equivalent to /
The given expression can then be rewritten as
[tex]x/(y - z) + (a - b) * c[/tex]
Hence;
[tex]\frac{x}{y-z} + (a-b)*c[/tex] is equivalent to [tex]x/(y - z) + (a - b) * c[/tex]
Write an expression that represents the volume of a rectangular-shaped box with a length 3 inches less than its height and a width 4 inches greater than its height
Answer: h(h-3)(h+4)
Step-by-step explanation:
To find the volume of rectangular-shaped box we will have to multiply the length by the width by the height.
Given the statements we can determine the length with the equation
L = h -3 where l is the length and h is the height.
the width can also be represent by the equation
w = h + 4
The height is is h and the length is h- 3 and the width is also h+4 so the expression will be h(h-3)(h+4)
Please, I need help! a positive integer is subtracted from its square. The sum is 56. Write and solve a quadratic equation to find the number. Thank you!
Answer:
8
Step-by-step explanation:
x² − x = 56
x² − x − 56 = 0
(x − 8) (x + 7) = 0
x = -7 or 8
x is positive, so x = 8.
4.
1
Solve for m in the following equation: 7m +
2 = 24.
Solve for m in the following equation 4/7m + 1/4n =24
1. m=22/7
2. m=672/23
7m+2=24
7m=24-2
7m=22
m=22/7
37 points! Need this asap
Answer:
a. Point E
b Line AB
Step-by-step explanation:
The lines AB and CD will intersect at a point
The Point is Point E
Planes will intersect at a line
Planes X and Plane Y intersect at line AB
Answer:
a. point E
b. points A and B ( which is line AB )
Step-by-step explanation:
a. the intersection of AB and CD = point E
b. the intersection of plane X and Y = points A and B ( which is line AB )