The conditional expectation of αX given Y=y is (αλy / β + αλ)^α * e^(-(β+αλ)/βy) and the Law of Iterated Expectation gives E[αX] = (αλ / β + αλ)^α * (β / (β+αλ))^α * (Γ(α) / β).
Let X be a Poisson random variable with parameter λ and Y be a Gamma random variable with parameters α and β. We want to find the conditional expectation of αX given Y=y and then apply the Law of Iterated Expectation to find E[αX].
The conditional probability density function of αX given Y=y is:
fX|Y(x|y) = P(X=x|Y=y) = P(X=x,Y=y) / P(Y=y)
Since X and Y are independent, we have:
P(X=x,Y=y) = P(X=x)P(Y=y)
Therefore, the conditional probability density function of αX given Y=y is:
fX|Y(x|y) = (λ^x/x!) * (β^α / Γ(α)) * y^(α-1) * e^(-βy) / (λ^y * e^(-λ) * β^α / Γ(α))
fX|Y(x|y) = (λ^x / x!) * (y^α * e^(-βy)) / (Γ(α) * λ^y * β^α)
Now we can calculate the conditional expectation of αX given Y=y:
E[αX|Y=y] = ∑ x=0^∞ αx * fX|Y(x|y)
E[αX|Y=y] = ∑ x=0^∞ αx * (λ^x / x!) * (y^α * e^(-βy)) / (Γ(α) * λ^y * β^α)
E[αX|Y=y] = (αλy / β + αλ)^α * e^(-(β+αλ)/βy)
Now we can apply the Law of Iterated Expectation to find E[αX]:
E[αX] = E[E[αX|Y]]
E[αX] = E[(αλY / β + αλ)^α * e^(-(β+αλ)/βY)]
Since Y is a continuous random variable, we need to integrate over all possible values of Y:
E[αX] = ∫ 0^∞ (αλy / β + αλ)^α * e^(-(β+αλ)/βy) * (β^α / Γ(α)) * y^(α-1) * e^(-βy) dy
E[αX] = (αλ / β + αλ)^α * (β / (β+αλ))^α * (Γ(α) / β)
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In ΔFCE, the ratio of ∠F to ∠C is 2:5. The measure of ∠E is one hundred ten degrees more than the sum of the measures of ∠F and ∠C. What is the measure of each angle in ΔFCE?
Answer:70
Step-by-step explanation:
Given: <f and <c ratio 2:5
To find: <f and <c
Solution: 2x+5n=180' minus 110'
7n=70'
x=10'
<f= 2x10=20'
<e= 5x10=50'
The sum of <F and <E
= 20'+50'=70'
Write down the first two terms (and the error term) in the Taylor series expansion of f(h) = ln(3 - 2h) around h = 0, The error term should involve a mysterious unknown constant xi. There's no way to determine xi from the information given here: in practice, if you were to evaluate your Taylor expansion at, say, h =, you would know that xi elementof (0, 4) and you could get bounds on the error by bounding the derivatives of f(h) on this interval.
The Taylor series expansion of f(h) = ln(3 - 2h) around h = 0 is given by:
f(h) = f(0) + f'(0)h + R(h)
where f(0) = ln(3), f'(0) = -2/3, and R(h) is the remainder term.
To find the remainder term, we need to take the higher-order derivatives of f(h) and evaluate them at h = 0. We have:
f''(h) = 4/(3(3 - 2h))^2, f'''(h) = -32/(3(3 - 2h))^3, and so on.
Evaluating these at h = 0, we get f''(0) = 4/9 and f'''(0) = -32/27.
Thus, the remainder term can be expressed as:
R(h) = (1/2)f''(xi)h^2 = (1/2)(4/9)(xi)^2h^2 = (2/9)(xi)^2h^2
where xi is some unknown constant between 0 and 4.
Therefore, the first two terms in the Taylor series expansion of f(h) are:
ln(3) - (2/3)h
and the remainder term involves the unknown constant xi, given by R(h) = (2/9)(xi)^2h^2.
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The ration of female to male shoppers at a department store has been found to be 10 to 9. If 1,188 male shoppers were at the store one Saturday, how many shoppers were there in all that day?
Answer:
2,508 shoppers
Step-by-step explanation:
Ratio of female to male : 10:9
Let F be the number of female shoppers and M be the number of male shoppers
That can be expressed as
[tex]\dfrac{F}{M}= \dfrac{10}{9}[/tex]
Given M = 1188
[tex]\dfrac{F}{1188}= \dfrac{10}{9}[/tex]
Multiply both sides by 1188
[tex]\dfrac{F}{1188} \times 1188= \dfrac{10}{9} \times 1188\\\\F = 1,320[/tex]
Total number of shoppers = M + F
= 1188 + 1320
= 2,508 shoppers
How would a scale factor of 0.25 be used to determine the lengths of the original figure?
A) The scale factor is added to the scale figure’s lengths.
B)The scale factor is subtracted from the scale figure’s lengths.
C) The scale factor is multiplied by the scale figure’s lengths.
D) The scale factor is divided into the scale figure’s lengths.
Answer:
The correct answer is C) The scale factor is multiplied by the scale figure's lengths.
When using a scale factor, you are typically working with a "scale figure," which is a smaller or larger version of the original figure. To determine the lengths of the original figure using a scale factor of 0.25, you would multiply each length of the scale figure by 0.25.
For example, if the scale figure has a length of 8 units, you would multiply 8 by 0.25 to get 2, which would be the corresponding length of the original figure. So if the original figure was four times larger than the scale figure, it would have a length of 32 units (4 times 8).
Therefore, when using a scale factor to determine the lengths of an original figure, you need to multiply each length of the scale figure by the scale factor to get the corresponding length of the original figure.
Step-by-step explanation:
) Reemplazar una obligación de $4.000.000 que vence en el mes 7, por tres pagos iguales, uno hoy, otro en el mes 10 y el final en el mes 15, considerando un interés del 10% Efectivo Semestral.
Three equal payments of $1,468834.26 made today, in month 10, and in month 15, with 5% semiannual interest, will be sufficient to cover the debt of $4,000,000 that matures in month 7.
What is the semiannual interest rateTo replace the obligation of $4,000,000 that matures in month 7, we need to calculate the size of three equal payments that can be made today, in month 10, and in month 15, that will cover the debt with interest.
First, we need to determine the semiannual interest rate. The annual interest rate is 10%, so the semiannual interest rate is 5% (10%/2).
Next, we can use the present value formula to calculate the size of the equal payments:
PV = PMT * [(1 - (1 + r)^-n) / r]
where PV is the present value of the debt, PMT is the size of the equal payments, r is the semiannual interest rate, and n is the number of semiannual periods.
Since the debt matures in month 7, which is the end of the sixth month, and the payments will be made today (month 0), in month 10 (the end of the ninth month), and in month 15 (the end of the fourteenth month), we have three semiannual periods to consider.
Using the values we have, we can substitute them into the formula:
PV = $4,000,000
r = 5%
n = 3
$4,000,000 = PMT * [(1 - (1 + 5%)^-3) / 5%]
Solving for PMT, we get:PMT = $1,468834.26
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Translation:
Replace an obligation of $4,000,000 that matures in month 7, by three equal payments, one today, another in month 10 and the final one in month 15, considering an interest of 10% Cash Semiannual.
Noah is making mini berry pies. For the filling, he mixes 1 pound each of raspberries, blueberries, and blackberries. Then, he scoops 6 ounces of the filling into each mini pie tin. If he wants to use up all of his filling, how many mini pies can he make?
Farid is able to produce 8 small pies.
What is addition?Addition is a way of combining things and counting them together as one large group. ... Addition in math is a process of combining two or more numbers.
here, we have,
Given: For the filling, Farid blends 1 pound of each blackberries, blueberries, and raspberries. Following that, he spoons 6 ounces of the filling into each tiny pie pan.
We need to find How many tiny pies can be made if he wants to use all of the filling.
Raspberries, blueberries, and blackberries, each weighing 1 pound, are combined by Faris for the filling.
3 pounds of filler total from 1+1+1= 3*16 ounces.
1 pound equals 16 ounces. = 48 ounces
Each little pie tin is filled with 6 ounces of filling by Faris.
48 ounces divided by 6 ounces equals 8 mini pies.
Hence, the Farid made 8 mini pies with 6 ounces.
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Decide if each is a measurement of length, area, volume, or weight (or mass).
How many centimeters across a handprint
How many square inches of paper needed to wrap a box
How many gallons of water in a fish tank
How many pounds in a bag of potatoes
How many feet across a swimming pool
How many ounces in a bag of grapes
How many liters in a punch bowl
How many square feet of grass in a lawn
Answer:
Step-by-step explanation:
1. measurement of length
2. measurement of area
3. measurement of volume
4. measurement of weight
5. measurement of length
6. measurement of weight
7.measurement of volume
8. measurement of area
HELP FAST WILL GIVE BRAINLYEST AND 100 PTS
The correct answers are: a reflection across the x-axis and a translation 1, unit right, a rotation of 180° about the origin and a translation of 1 unit left.
How to check for congruence?To check for congruence, we need to verify that the two triangles have the same shape and size, which means that one triangle can be mapped onto the other using a sequence of transformations.
For the first sequence of transformations (a reflection across the x-axis and a translation 1 unit right), we can reflect triangle ABC across the x-axis, which will map (-6, 2) to (-6, -2), (-4, 6) to (-4, -6), and (-2, 2) to (-2, -2). We can then translate the reflected triangle 1 unit to the right, which will map (-6, -2) to (-5, -2), (-4, -6) to (-3, -6), and (-2, -2) to (-1, -2). This mapped triangle is triangle ADEF, and since it was obtained by a sequence of transformations, we can conclude that ABC is congruent to ADEF.
For the second sequence of transformations (a rotation of 180° about the origin and a translation of 1 unit left), we can rotate triangle ABC 180° about the origin, which will map (-6, 2) to (6, -2), (-4, 6) to (4, -6), and (-2, 2) to (2, -2). We can then translate the rotated triangle 1 unit to the left, which will map (6, -2) to (5, -2), (4, -6) to (3, -6), and (2, -2) to (1, -2). This mapped triangle is also ADEF, and since it was obtained by a sequence of transformations, we can conclude that ABC is congruent to ADEF.
Therefore, the correct answers are:
a reflection across the x-axis and a translation 1 unit right
a rotation of 180° about the origin and a translation of 1 unit left.
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Let A be an mxn matrix, and let u and v be vectors in Rn with the property that Au = 0 and Av 0. Explain why A(u + v) must be the zero vector. Then explain why A(cu + dv) -0 for each pair of scalars c and d.
Suppose that, Au=0 and Av=0. Then, we already have A(u+v)=Au+Av. Now, A(u + v) = Au + Av = 0 + 0 = 0.
Now, let c and d be scalars. Using both parts of Theorem 5, A(cu + dv) = A(cu) + A(dv) = cAu + dAv = c0 + d0 = 0.
A matrix, also known as matrices, is a rectangular array or table with numbers, symbols, or expressions that are arranged in rows and columns to represent a mathematical object or a property of that object. Matrix types are not all associated with linear algebra. In particular, this applies to incidence matrices and adjacency matrices in graph theory.
Unless otherwise stated, all matrices in this article, which focuses on matrices related to linear algebra, represent linear maps or can be viewed as such. The majority of mathematical and scientific disciplines use matrices, either directly or indirectly through the use of geometry and numerical analysis.
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An airplane fies 3,780 miles in 7.5 hours. What is the speed of the airplane in miles per hour? Use the equation d=rt, where d is distance, r is rate, and t is time.
The airplane's speed ismiles per hour.
Answer:
504
Step-by-step explanation:
3780÷7.5=504
504 mph because 504 x 7.5 = 3780
Please give good review. :)
Which letter
A
B
C
D
Answer:
Step-by-step explanation:
a
Answer:
ITS A
Step-by-step explanation:
The reason why is because that dude up there said the same thing so yeah..
A redwood tree casts a shadow that is 8 meters long. A carpool lane sign near the redwood
tree casts a shadow that is 4 meters long. If the redwood tree is 6 meters tall, how tall is the
carpool lane sign?
Answer:
Hey bro, solving this would be relatively simple. If the Redwood tree is 6 meters tall, then the height of the carpool lane sign can be easily calculated using similar triangles. Using the lengths of their respective shadows, the carpool lane sign should be 3 meters tall, because the ratio between the height of the Redwood tree and the carpool lane sign, is the same ratio as between their respective shadows (8 to 4). The based way to solve this problem would be to measure the length of the shadows, and then use the ratio to calculate the height of the carpool lane sign.
Answer:
You need to set up the problem to solve for X. X = how tall is the tree? Set up your problem in this fashion. Set up the formula then arrange to solve for X. X/9 (shadow of the tree) = 15 (how tall the building is)/6 (shadow of building) X= 15/6 * 9 To get X alone, you need to move 9 to the other side of the equation. multiply by 9 on each side. For X side, this nullifies 9 and gets 9 to the other side. X= 2.5*9 You have divided 15 by 6, now multiply by 9 to get final answer for X X=22.5 meters The tree is 22.5 meters tall.
Step-by-step explanation:
If this is not.. right ill do another answer!!
Name the line of reflection that maps each pre-image to its image.
Answer: X axis , Y axis , y=-2
Step-by-step explanation:
2 rectangular pyramids are connected at their bases. The total height of the 2 figures if 10 units. The base edge lengths are 9 units and 1.5 units. The height of each pyramid is 5 units.
Which statements about the composite figure are true? Check all that apply.
The composite figure consists of two rectangular pyramids.
The composite figure can be broken down into rectangular prisms.
The volume of the composite figure is
1.5(9)(5) + 1.5(9)(5).
The total volume is 45 units3.
The total volume is 90 units3.
The composite figure consists of two rectangular pyramids, volume is 45 unit³.
What is rectangular pyramid?Pyramids are three-dimensional structures having triangle faces and have an encompassing polygon shape at its base. If the base of a pyramid is rectangular, then it is called a rectangular pyramid.
Given,
Total height of two rectangular pyramids = 10 units
height of each pyramid is 5 unit.
Base lengths are 9units and 1.5 units.
Both are connected at their bases.
Dimensions are same of both pyramids
Composite figure consists of two rectangular pyramids.
Volume of the composite figure
= 2(length × width × height)/3
= 2(9×1.5×5)/3
= 2(13.5×5)/3
= 2(67.5)/3
= 135/3
= 45 unit³
Hence, 45 unit³ is volume of composite figure, that consists of two rectangular pyramids.
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Answer:A D
Step-by-step explanation:
Lemon disinfectant is mixed 4 oz to one gallon. How many lemon disinfectant needs to be added to 6 gallons of water?
Answer:
If the ratio of lemon disinfectant to water is 4 oz to one gallon, then we can say that for each gallon of water, we need 4 oz of lemon disinfectant. To find how much lemon disinfectant is needed for 6 gallons of water, we can multiply the amount needed for one gallon by the number of gallons:
4 oz/gallon * 6 gallons = 24 oz
Therefore, we need 24 oz of lemon disinfectant to be added to 6 gallons of water.
Step-by-step explanation:
Answer:
Given: x * 4 oz = 6 gallons.
First, multiply 4 oz and x:
4x = 6 gallons.
Then convert 6 gallons to oz:
4x = 768 oz.
Then divide both sides by 4:
x = 192.
√6/√3 I’m struggling on this question this symbol / means divide
Answer:
√2
Step-by-step explanation:
√3 x√2/√3 =√2
Answer:
[tex]\sqrt{2}[/tex]
explanation:
[tex]\frac{\sqrt{6} }{\sqrt{3} }[/tex]
= [tex]\sqrt{2}[/tex]
(Decimal: 1.414214)
there are 36 boys and 45 girls in the track meet.the coach wants an equal number of boys and girls on each team.what is the greatest number of boys and girls the coach can have on one team.how many teams will he have
the coach can form 4 teams of 9 boys and 9 girls each, and there will be 9 players left over who cannot form a complete team.
What is greatest common divisor?The GCD (Greatest Common Divisor), also known as the HCF (Highest Common Factor), is the largest positive integer that divides two or more integers without leaving a remainder.
For example, the GCD of 12 and 18 is 6, because 6 is the largest positive integer that divides both 12 and 18 without leaving a remainder.
Given by the question.
To form teams with an equal number of boys and girls, we need to find the greatest common divisor (GCD) of 36 and 45.
The prime factorization of 36 is 2^2 x 3^2, and the prime factorization of 45 is 3^2 x 5.
The common factors are 3^2 = 9. Therefore, the GCD of 36 and 45 is 9.
This means that the coach can form teams of 9 boys and 9 girls each.
To find out how many teams he can form, we need to divide the total number of boys and girls by the number of players on each team:
Number of teams = Total amount of players / Number of players per team
Number of teams = (36 + 45) / 18
Number of teams = 81 / 18
Number of teams = 4 with a remainder of 9
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YZ = 9, LM = 3, MN = 2, and the measure of angle Z = 100 degrees. What additional information is needed to prove the triangles are similar by SAS?
The additional piece of information needed to prove that ΔLKN ~ ΔKNM by the SAS similarity theorem is; MN/LK||MN.
What is SAS (Side-Angle-Side) similarity theorem?The SAS (Side-Angle-Side) similarity theorem states that if two triangles have two pairs of corresponding sides that are in proportion, and the included angles are congruent, then the triangles are similar.
In this case, we are given that ΔLKN and ΔKNM share the angle at vertex K, and we know that LN/MN and LK/KN are in proportion.
However, we need to establish that MN/LK||MN, that means MN is parallel to LK and forms a transversal with LN.
This information is necessary to establish that the included corresponding sides are congruent, which is required for the triangles to be similar.
Therefore, the additional piece of information needed to prove that ΔLKN ~ ΔKNM by the SAS similarity theorem.
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What is (f- g)(x)?
f(x)= x¹ - x² +9
g(x) = x³ + 3x² + 12
Enter your answer in standard form in the box.
(f-g)(x) =
The value of the function (f-g)(x)=[tex]x-4x^{2} -x^{3} -3[/tex].
What is a function?
A function is defined as the relationship between input and output, where each input has exactly one output. The inputs are the elements in the domain and the outputs are elements in the co-domain.
f(x)= x¹ - x² +9
g(x) = x³ + 3x² + 12
To find (f-g)(x):
The operations on functions are as easy as the operations on numbers or polynomials.
We have to subtract the functions to find the above mentioned operation.
(f-g) (x)= f(x)-g(x)
= (x¹ - x² +9)-(x³ + 3x² + 12)
The minus will change the signs of function g.
= [tex]x-x^{2} +9-x^{3}-3x^{2} -12[/tex]
=[tex]x-4x^{2} -x^{3} -3[/tex]
Hence, the value of the function (f-g)(x)=[tex]x-4x^{2} -x^{3} -3[/tex]
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Evaluate y (x ÷2) if x = 20 and y = 10
Answer:
100
Step-by-step explanation:
1.) Plug in the values of x and y into the equation
10(20/2)
2.) Divide 20 by 2
10(10)
3.) Multiply 10 by 10
100
Avery had $25.83 in her wallet. If she bought lunch with 7 3/4 dollars from her wallet, how much money did she have in her wallet after lunch?
Answer: $ 18.08
Step-by-step explanation:
Given: Money in wallet = $25.83
Given: Money spent = $7.75
To find: Money left in the wallet after lunch = money in the wallet - money spent
= $(25.83-7.75)
= $ 18.08
What is the correct sequence of steps for calculating 96 on a scientific calculator?
First press button 9, then press the button on which the (^) sign is mentioned. Then button press 6. Then the value you get is 531,441.
What is the value of the expression?At the point when the important parts and fundamental cycles of a mathematical technique are given qualities, the articulation's outcome is the consequence of the calculation it portrays.
The meaning of straightforwardness is simplifying something to accomplish or get a handle on while likewise making it somewhat less troublesome.
The expression is given below.
⇒ 9⁶
First press button 9, then press the button on which the (^) sign is mentioned. Then button press 6.
The value of the exponent numerical expression 9⁶ will be 531,441.
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The correct question is given below.
What is the correct sequence of steps for calculating 9⁶ on a scientific calculator?
Find the probability of randomly selecting a number between 1 and 1000 (including both ends) which is divisible by:
a. 3.
b. 3 and 5.
c. 3 or 5.
The probability of randomly selecting a number between 1 and 1000 (including both ends) which is divisible by 3, 3 and 5, and 3 or 5 is 33.3%, 6.6%, and 46.7%, respectively.
To find the probability of randomly selecting a number between 1 and 1000 (including both ends), we can count the number of the desired outcomes and divide it by the total number of possible outcomes.
a. To find the probability of randomly selecting a number between 1 and 1000 (including both ends) which is divisible by 3, we can count the number of multiples of 3 between 1 and 1000, and divide by the total number of possible outcomes.
The first multiple of 3 is 3, and the last multiple of 3 that is less than or equal to 1000 is 999.
999/3 = 333
So there are 333 multiples of 3 between 1 and 1000.
probability = 333/1000 = 0.333 = 33.3%
b. To find the probability of randomly selecting a number between 1 and 1000 (including both ends) which is divisible by 3 and 5, we can count the number of multiples of 15 (the least common multiple of 3 and 5) between 1 and 1000, and divide by the total number of possible outcomes.
The first multiple of 15 is 15, and the last multiple of 15 that is less than or equal to 1000 is 990.
990/15 = 66
So there are 66 multiples of 15 between 1 and 1000.
probability = 66/1000 = 0.066 = 6.6%
c. To find the probability of randomly selecting a number between 1 and 1000 (including both ends) which is divisible by 3 or 5, we can count the number of multiples of 3 or 5 (or both) between 1 and 1000, and divide by the total number of possible outcomes.
To count the number of multiples of 3 or 5, we can add the number of multiples of 3 and the number of multiples of 5, and then subtract the number of multiples of 15 (to avoid double-counting).
The number of multiples of 3 between 1 and 1000 is 333, the number of multiples of 5 is 200, and the number of multiples of 15 is 66.
probability = (200 + 333 - 66)/1000 = 0.467 = 46.7%
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I need help please this question makes no sence to me and I keep getting it wrong
In a parallelogram, the consecutive angles are supplementary (add up to 180 degrees). x can represent the first angle, and 4x can represent the second angle. With this information you can create the equation x + 4x = 180 and solve.
5x = 180
x = 36
So the measure of the first angle is 36 degrees, and the one that is 4 times larger is 144 degrees.
What values of x
and y
satisfy the system {y=−2x+3
{y=5x−4?
If there is no solution, enter "no"; if there are infinitely many solutions, enter "inf."
The required solutions of the given system of equation are x = 1 and y = 1.
What is equation?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
According to question:To find the values of x and y that satisfy the system, we need to solve the equations simultaneously:
y = -2x + 3 ... (1)
y = 5x - 4 ... (2)
Setting the right-hand sides of (1) and (2) equal to each other, we get:
-2x + 3 = 5x - 4
Simplifying this equation, we get:
7x = 7
Dividing both sides by 7, we get:
x = 1
Substituting x = 1 into either equation (1) or (2), we get:
y = -2(1) + 3 = 1
Therefore, the only solution that satisfies both equations is x = 1 and y = 1.
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If $16,000 is invested at 10% for 20 years, find the future value if the interest is compounded daily.
The critical points of a rational inequality are –1, 3, and 4. Which set of points can be tested to find a complete solution to the inequality? x = 1 and x = 3.5 x = –1, x = 3, and x = 4 x = –2, x = 2, and x = 5 x = –3, x = 1, x = 3.5, and x = 5
The possible set of inequalities are;
x = -3,
x = -1,
x = 1,
x = 3,
x = 5.
What are inequalities?Inequalities are the comparison of mathematical expressions, whether one quantity is greater or smaller in comparison to another quantity.
We use these symbols to represent inequalities, '>' , '<', '≥', '≤'
The critical points of a rational inequality are the x-values at which the inequality changes direction (from "<" to ">" or vice versa). In this case, the critical points are -1, 3, and 4.
To find the complete solution to the inequality, we need to test points on either side of the critical points. For example, if we test a value less than -1, such as -2, and find that it satisfies the inequality, then all values less than -1 also satisfy the inequality. On the other hand, if a value less than -1 does not satisfy the inequality, then no values less than -1 satisfy the inequality.
Therefore, a complete solution to the inequality can be found by testing values around each critical point. A common set of points to test for this purpose is the critical points themselves, and values just less than and just greater than each critical point.
So, a possible set of points to test to find the complete solution to the inequality is:
x = -3,
x = -1,
x = 1,
x = 3,
x = 5.
These points bracket the critical values and allow us to determine which intervals of values satisfy the inequality.
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statistics is the science of average - elucidate this statement
Answer:
The average of all the data is calculated in statistics.
However, statistics is a field that goes beyond average and is not a complete science of it.
There are other additional statistical tools.
which explains how statistics is an extension of mathematics.
Dave Drinks a 12-ounce cup of coffee each morning on his way to work. This cup of coffee contains 136 mg of caffeine.
The caffeine in his system decreases about 40% every hour.
Function to calculate amount of coffee in Dave's system after x hours
= y = 135(0.6)ˣ
What is exponential expression?An exponential function is a Mathematical function in the form f (x) = aˣ, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0. The most commonly used exponential function base is the transcendental number e, which is approximately equal to.
Given,
Dave drinks 12-ounce cup of coffee each morning
One cup has 136 mg of caffeine
caffeine in his system decreases about 40% every hour
In x hours,
Amount of caffeine in his system
y = a(1 - 40/100)ˣ
or
y = 136(1-0.4)ˣ
y = 135(0.6)ˣ
Hence, y = 135(0.6)ˣ is the function to calculate amount of caffeine in system of Dave after x hours.
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2. Assume a firm operating in a purely competitive market has a constant selling price of
GH 60, a fixed cost of GH¢450 and a variable cost of GH¢35 an item. Derive;
a)
b)
c)
The total revenue function.
The total cost function.
The profit function.
The total revenue function is 60x.
The total cost function is 35x + 450.
The profit function is 25x - 450.
How derive the total revenue function, the total cost function and thee profit function?Since we have a constant selling price of GH 60, a fixed cost of GH¢450 and a variable cost of GH¢35 an item.
Let x be the number of items
Total revenue function = constant selling price * x
Total revenue function = 60x
Total Cost Function = Variable cost + Fixed cost
Total Cost Function = 35x + 450
Profit function = Total revenue function - Cost function
Profit function = 60x - (35x + 450)
Profit function = 60x - 35x - 450
Profit function = 25x - 450
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