The joint PMF of X and Y is [tex]P(X = x, Y = y) = \frac{e^{-10} \cdot 10^x}{x!} \cdot \frac{x!}{y!(x-y)!} \cdot \left(\frac{3}{4}\right)^y \left(\frac{1}{4}\right)^{x-y}, \quad \text{for } y = 0, 1, \ldots, x \text{ and } x = 0, 1, 2, \ldots[/tex]
Distributions of X and Y
X is the total number of customers visiting the store in an hour, which follows a Poisson distribution with mean [tex]\lambda = 10[/tex]
[tex]P(X = x) = \frac{e^{-10} \cdot 10^x}{x!}, \quad x = 0, 1, 2, \ldots[/tex]
Given X = x the number of female customers Y follows a binomial distribution because each customer is independently female with probability [tex]p = \frac{3}{4}[/tex]
[tex]P(Y = y \mid X = x) = \binom{x}{y} \left(\frac{3}{4}\right)^y \left(\frac{1}{4}\right)^{x-y}, \quad y = 0, 1, \ldots, x[/tex]
Joint PMF of X and Y
To find the joint PMF P(X = x, Y = y, we use the law of total probability:
[tex]P(X = x, Y = y) = P(Y = y \mid X = x) \cdot P(X = x)[/tex]
Substitute the expressions for [tex]P(Y = y \mid X = x)[/tex] and P(X = x)
[tex]P(X = x, Y = y) = \left( \binom{x}{y} \left(\frac{3}{4}\right)^y \left(\frac{1}{4}\right)^{x-y} \right) \cdot \left( \frac{e^{-10} \cdot 10^x}{x!} \right)[/tex]
Simplify the expression:
[tex]P(X = x, Y = y) = \frac{e^{-10} \cdot 10^x}{x!} \binom{x}{y} \left(\frac{3}{4}\right)^y \left(\frac{1}{4}\right)^{x-y}.[/tex]
A firm advertises for workers to address envelopes. Priscilla says she will work 100 hours. Herb will work for 80 hours. If each can address 10,000 envelopes in the time they work, how long would it take them to address 10,000 envelopes if they work together?
Priscilla and Herb would take approximately 44.44 hours to address 10,000 envelopes together, as Priscilla can address 100 envelopes per hour and Herb can address 125 envelopes per hour.
The question asks about the combined work rate of Priscilla and Herb in addressing 10,000 envelopes. To solve this, we calculate each of their rates of work and then combine them to find the total rate. Priscilla completes 10,000 envelopes in 100 hours, so her rate is 100 envelopes per hour. Herb completes 10,000 envelopes in 80 hours, so his rate is 125 envelopes per hour. Working together, their combined rate is 100 + 125 = 225 envelopes per hour. To address 10,000 envelopes at this rate, we divide 10,000 by 225, which equals approximately 44.44 hours.
Solve using the multiplication principle. Don't forget to perform a check.
48=6x
The solution is x=
Does Cos (x+y)=cosx+cosy? Or not?
When a decimal is written in word form, what indicates that the equivalent form is a mixed number and not a fraction?
Look at all the measurements in model 4. when a number in scientific notation is changed to expanded notation, are any of the added zeros significant
The added zeros when changing a number from scientific notation to expanded notation are usually not considered significant. They primarily serve as placeholders and do not indicate precision of measurements.
Explanation:In the field of Mathematics, specifically when working with numbers in scientific notation and expanded notation, the concept of significant zeros comes into play. When you convert a number from scientific notation to expanded notation, zeros that are included in this process are not considered to be significant. Rather, the concept of significant zeros mostly applies to measurements and the precision of those measurements. For example, in the measurement 300.0, the zero at the end is significant because it shows the measurement was precise to the tenth's place. However, in changing a number from scientific to expanded notation, any added zeros primarily serve as placeholders and are typically not considered significant.
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How to find the inverse of f(x) = -(3/-x-3) - 2
The inverse is f⁻¹(x) = -3(x + 1)/(x + 2).
To find the inverse of the given function f(x), follow these steps:
Replace f(x) with y: y = -(3/(-x-3)) - 2Swap x and y to start finding the inverse: x = -(3/(-y - 3)) - 2Isolate the term with y: x + 2 = -(3/(-y - 3))Multiply both sides by (-y - 3) to get: (x + 2)(-y - 3) = -3Distribute x + 2: -xy - 3x - 2y - 6 = -3Collect y terms on one side: -xy - 2y = 3x + 3Factor out y: y(-x - 2) = 3(x + 1)Solve for y: y = -3(x + 1)/(x + 2)Thus, the inverse function is f⁻¹(x) = -3(x + 1)/(x + 2).
62.4 percent of what number is 17.16
If f(x)=square root of 2-x and g(x)=x-1, then find the domain of h(x)=f(x)/g(x)
Answer:
Domain of h(x) : [2,∞)
Step-by-step explanation:
Given: Two functions
[tex]f(x)=\sqrt{2-x}[/tex]
[tex]g(x)=x-1[/tex]
Composite function, [tex]h(x)=\dfrac{f(x)}{g(x)}[/tex]
[tex]f(x)=\sqrt{2-x}[/tex], It is square root function. As we know square root function is always greater than 0.
2-x ≥ 0
2 ≥ x
Domain of f(x) : [2,∞)
[tex]g(x)=x-1[/tex], It is straight line equation (Linear function) As we know domain of linear function is all real number.
Domain of g(x) : (-∞,∞)
[tex]h(x)=\dfrac{f(x)}{g(x)}[/tex]
[tex]h(x)=\dfrac{\sqrt{2-x}}{x-1}[/tex] , It is rational function. Denominator can't be zero.
So, x-1 ≠ 0
x ≠ 1
Now, we will see domain of h(x) common all three domain.
Domain of h(x): [2,∞)
Hence, The domain of h(x) is [2,∞)
Drag each equation to show if it could be a correct first step to solving the equation
2 (x + 7) = 36.
_____________________________________
| (2 · x) + (2 · 7) = 36 | 2x + 7 = 36 |
| x + 7 = 18 | 2(x + 7) = 72 |
| 2x + 14 = 36 | x + 14 = 36
Yes No Not Enough Info
Answer:
Yes
(2 · x) + (2 · 7) = 36x + 7 = 182x + 14 = 36No
2x + 7 = 362(x + 7) = 72x + 14 = 36Step-by-step explanation:
It is appropriate to eliminate parentheses as a first step. This can be done using the distributive property, resulting in either of ...
2x +2·7 = 362x +14 = 36 . . . . . 2·7 evaluated mentallyor by dividing the equation by the factor outside parentheses, resulting in ...
x + 7 = 18___
Any of the equations other than these represent violations of the equal sign. Something has been done to one side of the equation without the same thing being done to the other side.
Write 2.64 as a percent. Please help me thank you do much.
How many feet are in 84 inches
Luis can drive 3 times as fast as rico can ride his bike. If it takes rico 4 hours longer than Luis to travel 72 miles, how fast can ricoride his bike
Suppose that block m = .050kg, sometime after reaching the base of the incline, undergoes a completely inelastic collision with the stationary block m = .075kg. use the principle of conservation of linear momentum to determine the common speed of the blocks just after the collision. (carry the answer to one decimal place)
The common speed of the blocks just after the collision is 0.4 times the initial velocity of the first block (v₁).
To determine the common speed of the blocks just after the completely inelastic collision, we can use the principle of conservation of linear momentum.
According to this principle, the total momentum before the collision is equal to the total momentum after the collision.
Let's denote the velocity of the first block (m = 0.050 kg) before the collision as v₁ and the velocity of the second block (m = 0.075 kg) before the collision as v₂. Since the second block is stationary, its initial velocity, v₂, is 0.
1. Before the collision, the total momentum is given by:
Initial momentum = m₁v₁ + m₂v₂
where m₁ and m₂ are the masses of the first and second blocks, respectively.
Plugging in the values, we have:
Initial momentum = (0.050 kg) v₁ + (0.075 kg) 0
Initial momentum = (0.050 kg)v₁
2. After the collision, the two blocks stick together and move as a single unit with a common velocity, denoted as vf.
The final momentum is given by:
Final momentum = (m₁ + m₂) vf
where (m₁ + m₂) is the total mass of the system.
Plugging in the values, we have:
Final momentum = (0.050 kg + 0.075 kg) × vf
Final momentum = 0.125 kg × vf
According to the principle of conservation of linear momentum, the total momentum before the collision is equal to the total momentum after the collision:
0.050 kg × v₁ = 0.125 kg × vf
To determine the common speed of the blocks just after the collision, we need to solve for vf:
vf = (0.050 kg × v₁) / (0.125 kg)
Calculating the numerical value, vf = 0.4 × v1
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Marcella divided 40.8 gallons of paint among 8 containers. How much paint is in each container?
Mrs. Goldstein pours 3 juice boxes into a bowl to make fruit punch. Each juice box holds 236 millimeters. How much juice does Mrs. Goldstein pour into the bowl ?
708 millimeters of juice Mrs. Goldstein pour into the bowl.
Given that, Mrs. Goldstein pours 3 juice boxes into a bowl to make fruit punch. Each juice box holds 236 millimeters.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Let the quantity of juice Mrs. Goldstein pour into the bowl be x millimeters.
Now, x=236 × 3
⇒ x = 708 millimeters
Therefore, 708 millimeters of juice Mrs. Goldstein pour into the bowl.
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Find the distributive property of 24+40
This is a question I don't quite understand, will someone please help me?
find real numbers a and b such that the equation a+bi=13+9i is true.
Final answer:
The real numbers a and b that make the equation a+bi=13+9i true are a = 13 and b = 9. We match real and imaginary parts of the complex numbers to find a and b.
Explanation:
To find the real numbers a and b such that the equation a+bi=13+9i is true, we simply match the real parts and the imaginary parts of the complex numbers on both sides of the equation. The real part of a+bi is a, and the real part of 13+9i is 13. Therefore, a = 13. Similarly, the imaginary part of a+bi is bi and the imaginary part of 13+9i is 9i. Thus, b = 9. Hence, the values we are looking for are a = 13 and b = 9.
Elissa and eight friends have lunch at a restaurant. The bill is $56.61. Can the friends split the bill nine equal shares? Use the divisibility rule for 9 to explain your answer.
Which formula gives the area of rectangle EFHG? area = d × j area = (e + h) × (f + i) area = (e + h) × j area = (e + h) × (f + c) NextReset
∠1 and ∠2 are supplementary and m∠1 = m∠3. Which one of these statements will always be true?
Given: Angle 1 and angle 2 are supplementary.
Angle 3 and angle 4 are supplementary.
Angle 1 is congruent to angle 3.
Prove: Angle 2 is congruent to angle 4.
What is the value of 3(2p + 4R) when P = 0.8 and R = 1.5
Find the solution of the differential equation (6−8xy2)dy/dx=y3 such that x=2 when y=4 by regarding y as the independent variable rather than x.
To solve for the differential equation where y is the independent variable, one must interchange x and y, do some algebraic manipulations to separate the variables, and then integrate. Additional steps may be necessary to solve for individual constants in the equation, using given points such as x=2 when y=4. Given the absence of a starting function, a definite solution cannot be provided.
Explanation:To find the solution of the differential equation (6−8xy2)dy/dx=y3 where y is the independent variable, we must first formulate the differential equation such that y is the independent variable. We do this by interchanging x and y, leading to (6-8x/y^2)dx/dy= x^3. By separating the variables and integrating, we will get the function y=f(x).
However, often with differential equations, a specific solution is also required. In this case, we know that x=2 when y=4. Plugging these into the function y=f(x) we can solve for the individual constant. Since no function f(x) is given in the question as a basis, it's impossible to come up with a definite solution, but I hope this general approach helps clarify how to solve such problems.
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I NEED THIS ASAP! 3(p+2)−7p=18
Can someone help me with this problem
Jose bought a bag of 6 oranges for $2.82. He also bought 5 pineapples. He gave the cashier $20 and received $1.43 change. How much did each pineapple cost?
Jose bought a bag of [tex]6[/tex] oranges for [tex]\$2.82[/tex] and Jose also bought [tex]5[/tex] pineapples each cost [tex]\$3.15[/tex].
Explanation:
Given: Jose bought a bag of [tex]6[/tex] oranges for [tex]\$2.82[/tex]. He also bought [tex]5[/tex] pineapples. He gave the cashier [tex]\$20[/tex] and received [tex]\$1.43[/tex] change.
Let cost of a pineapple be [tex]x[/tex].
According to the question:
Cost of pineapple is calculated as [tex]20-(2.82+5x)=1.43[/tex]
[tex]20-2.82-5x=1.43\\[/tex]
[tex]5x=17.18-1.43\\[/tex]
[tex]x=\frac{15.75}{5} \\x=3.15[/tex]
Therefore, cost of each pineapple is [tex]\$3.15[/tex].
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0.0013 in scientific notation
The scientific notation of the decimal number 0.0013 is [tex]0.0013 \times 10^{-3}[/tex].
Scientific notation is a way to express numbers in a concise form, particularly useful for very large or very small numbers.
It consists of two parts: a coefficient and an exponent of 10.
In the case of 0.0013, we can convert it to scientific notation as follows:
[tex]0.0013 \times 10^{-3}[/tex].
Hence, the scientific notation of 0.0013 is [tex]0.0013 \times 10^{-3}[/tex].
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What is 0.16666666666 as a simplified fraction
Answer:
[tex]0.16666666666=\frac{16666666666}{100000000000}[/tex]
Step-by-step explanation:
Given : Expression 0.16666666666.
To find : What is expression as a simplified fraction ?
Solution :
Expression 0.16666666666.
We have to remove decimal to convert into fraction,
By multiplying and divide by 10,
[tex]0.16666666666=\frac{0.16666666666\times 10}{10}[/tex]
[tex]0.16666666666=1.6666666666[/tex]
Similar approach we get,
[tex]0.16666666666=\frac{16666666666}{100000000000}[/tex]
52 thousandth scientific Notation
Help me with number 4...