please help out with the questions above, thank you very
much.
1. Are the following events 4.B C roulette independent? Find P(4B) and P(BA) in each case. a) A = Red, B=Even, b) A= {1,2,3,4}, B = {1,2,3,4,5,6,7,8,9}, c) A= {1,2,3,4,5), B= {6.7.8). 2. A generalisat
Answers
Since P(A and B) ≠ P(A) * P(B), the events A and B are not independent.
How to determine if the events A and B in r roulette independent1. To determine if the events A and B in roulette are independent, we need to check if the probability of one event is affected by the occurrence of the other event.
a) A = Red, B = Even
In roulette, there are 18 red numbers and 18 even numbers, out of a total of 38 numbers (including 0 and 00).
The probability of A (Red) is P(A) = 18/38, and the probability of B (Even) is P(B) = 18/38. To determine if they are independent, we need to check if P(A and B) = P(A) * P(B).
P(A and B) = P(Red and Even)
In roulette, there are 10 numbers that are both red and even: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20. So, P(A and B) = 10/38.
P(A) * P(B) = (18/38) * (18/38) = 324/1444 ≈ 0.2242
Since P(A and B) ≠ P(A) * P(B), the events A (Red) and B (Even) are not independent.
b) A = {1,2,3,4}, B = {1,2,3,4,5,6,7,8,9}
In this case, A and B are sets of numbers. A contains 4 numbers, and B contains 9 numbers. The probability of A is P(A) = 4/38, and the probability of B is P(B) = 9/38.
P(A and B) = P({1,2,3,4} and {1,2,3,4,5,6,7,8,9})
Since A and B have no numbers in common, P(A and B) = 0.
P(A) * P(B) = (4/38) * (9/38) ≈ 0.0234
Since P(A and B) ≠ P(A) * P(B), the events A and B are not independent.
c) A = {1,2,3,4,5}, B = {6,7,8}
In this case, A contains 5 numbers, and B contains 3 numbers. The probability of A is P(A) = 5/38, and the probability of B is P(B) = 3/38.
P(A and B) = P({1,2,3,4,5} and {6,7,8})
Since A and B have no numbers in common, P(A and B) = 0.
P(A) * P(B) = (5/38) * (3/38) ≈ 0.0034
Since P(A and B) ≠ P(A) * P(B), the events A and B are not independent.
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Related Questions
Cos(A) = ?
5/13
13/5
12/13
12/5
Answers
Answer: 5/13
Step-by-step explanation:
Cosine is adjacent over hypotenuse.
5/13
Hope this helps!
Classify thẹ following diferential equations. Write the order, linearity and the homogeneity of the equations. a) d^3y/dx^3+ex^2 d^2y/dx^2=x^3+5xy^2 b) x′′=x′+xsint
Answers
\(a) d^3y/dx^3+ex^2 d^2y/dx^2=x^3+5xy^2\)Classification of differential equationsDifferential equations can be classified into three types:1. Ordinary differential equations (ODE)2. Partial differential equations (PDE)3. Linear partial differential equations (LPDE)
There are several ways of classifying differential equations based on different properties, including order, linearity, and homogeneity.The order of a differential equation is defined as the highest order of the derivative present in the equation.
The linearity of a differential equation is defined as the degree of the polynomial that contains the derivative of the dependent variable.The homogeneity of a differential equation is defined as the degree of the polynomial that contains the dependent variable and its derivative. a) Given differential equation:d^3y/dx^3+ex^2 d^2y/dx^2=x^3+5xy^2The order of the differential equation is 3.
Since the highest order of the derivative present in the equation is 3.The differential equation is non-linear. Since the dependent variable y is raised to the power of 2, making the equation non-linear.The differential equation is non-homogeneous. Since x^3 is a function of x, not a function of y or its derivative.b) Given differential equation:x′′=x′+xsintThe order of the differential equation is 2. Since the highest order of the derivative present in the equation is 2.The differential equation is linear. Since the dependent variable is not raised to any power, making the equation linear.The differential equation is non-homogeneous. Since xsint is a function of x, not a function of y or its derivative.
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A jet travels 490 miles in 5 hours. At this rate, how far could the jet fly in 12 hours? What is the rate of speed of the jet?
Answers
Answer: 1,176 miles
Step-by-step explanation:
490 / 5 = 98 miles
98 mph X 12 hours is 1,176
Calculate the Laplace transform and its inverse using the second translation theorem.
Match the left column with the right column. You must provide the entire procedure to arrive at the answer.Paree: 1. L −1
{ e −35
s 5
} a) u(t−2)cos4(t−2) 2. L −1
{ s(s+1)
e −2s
} b) c) 4sinh3(t−4)u(t−4) 3. L −1
{ se −2s
s 2
+16
} c) (t−4)u(t−4)e x(−4)
4. L −1
{ 6e −3s
s 2
+4
} d) 3u(t−3)sin2(t−3) 5. L −1
{ 12e −45
s 2
−9
} e) 24
1
(t−3) 4
v(t−3) 6. L −1
{ (s−3) 2
+16
12e −2s
} f(1−e −(t−2)
)∥(t−2) 7. L −1
{ (s−3) 2
e −4s
} h) 3∥(t−2)e x(−2)
sin4(t−2)
Answers
To match the left column with the right column using the Laplace transform and its inverse, we will calculate the Laplace transform for each function in the left column and then find the inverse Laplace transform to match it with the correct answer in the right column. Here is the procedure for each case:
L^-1{e^(-3s) / s^5}: To calculate the Laplace transform inverse, we can use the second translation theorem. In this case, the inverse transform corresponds to t^n * F(s), where F(s) is the Laplace transform of the function and n is the order of the derivative. Applying this, we have:
L^-1{e^(-3s) / s^5} = t^4 * (1/4!) = (1/24) * t^4
L^-1{s(s+1) / e^(2s)}: Using partial fraction decomposition, we can write the expression as (A / s) + (B / (s+1)), where A and B are constants. Solving for A and B, we get A = -1 and B = 1. Then, applying the inverse Laplace transform, we have:
L^-1{s(s+1) / e^(2s)} = -u(t-2) + u(t-2) * e^(t-2) = u(t-2) * (e^(t-2) - 1)
L^-1{s * e^(-2s) / (s^2 + 16)}: This can be simplified using the second translation theorem. The inverse transform is given by t * F(s), where F(s) is the Laplace transform of the function. Applying this, we have:
L^-1{s * e^(-2s) / (s^2 + 16)} = t * (1/2) * sin(4(t-2)) * u(t-2)
L^-1{6 * e^(-3s) / (s^2 + 4)}: This can be simplified using the second translation theorem. The inverse transform is given by t * F(s), where F(s) is the Laplace transform of the function. Applying this, we have:
L^-1{6 * e^(-3s) / (s^2 + 4)} = 3 * u(t-3) * sin(2(t-3))
L^-1{12 * e^(-4s) / (s^2 - 9)}: This can be simplified using the second translation theorem. The inverse transform is given by t * F(s), where F(s) is the Laplace transform of the function. Applying this, we have:
L^-1{12 * e^(-4s) / (s^2 - 9)} = 24 * (t-3) * v(t-3) * sinh(3(t-3))
L^-1{(s-3)^2 / ((s-2)^2 + 16)}: This can be simplified using the second translation theorem. The inverse transform is given by F(t-a), where F(s) is the Laplace transform of the function and a is the constant inside the transform. Applying this, we have:
L^-1{(s-3)^2 / ((s-2)^2 + 16)} = (t-2) * e^(-2(t-2)) * sin^4(t-2)
By matching the calculated inverse Laplace transforms with the given options in the right column, we can determine the correct pairs.
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Find the area of the region that lies inside the curve r = 11 cos θ and outside the curve r = 5 cos θ.
Answers
The area of the region that lies inside the curve r = 11 cos θ and outside the curve r = 5 cos θ is \(48\int_{a}^{b}cos^2\theta d\theta\).
In the question, we are asked to find the area of the region that lies inside the curve, r = 11 cos θ and outside the curve, r = 5 cos θ.
The function r = n + a cos θ is a polar function, whose area under the curve can be calculated using integration with respect to dθ, with the formula, \(\int_{a}^{b}\frac{1}{2} r^2d \theta\), over the interval [a, b].
Thus, the area under the curve, r = 11 cos θ, using the stated formula, can be shown as:
\(\int_{a}^{b}\frac{1}{2} r^2d \theta\\=\int_{a}^{b}\frac{1}{2} (11 cos \theta)^2d \theta\\=\int_{a}^{b}\frac{121cos^2\theta}{2} r^2d \theta\)
The area under the curve, r = 5 cos θ, using the stated formula, can be shown as:
\(\int_{a}^{b}\frac{1}{2} r^2d \theta\\=\int_{a}^{b}\frac{1}{2} (5 cos \theta)^2d \theta\\=\int_{a}^{b}\frac{25cos^2\theta}{2} r^2d \theta\)
The area of the region that lies inside the curve, r = 11 cos θ, and outside the curve, r = 5 cos θ, can be shown as follows:
\(\int_{a}^{b}\frac{121cos^2\theta}{2} r^2d \theta - \int_{a}^{b}\frac{25cos^2\theta}{2} r^2d \theta\\=48\int_{a}^{b}cos^2\theta d\theta\)
Thus, the area of the region that lies inside the curve r = 11 cos θ and outside the curve r = 5 cos θ is \(48\int_{a}^{b}cos^2\theta d\theta\).
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If jamie completed 5 chores, about how much money did she earn?
Answers
Answer:
5(chore payment)
Step-by-step explanation:
since we dont know how much money the chore is worth it would be 5 times the money
-9x^2(-3x^5 +5x -5) what is the anwser
Answers
In developing patient appointment schedules , a medical centre wants to estimate the mean time that a staff member spends with each patient. How large a sample should be taken if the desired margin of error is 2 minutes at a 95 per cent level of confidence? How large a sample should be taken for a 99 per cent level of confidence ? Use a planning value for the population standard deviation of 8 minutes.
Answers
A. A sample size of 62 should be taken for a 95% level of confidence.
B. The sample size of 107 should be taken for a 99% level of confidence.
a. To estimate the sample size needed to estimate the mean time a staff member spends with each patient, we can use the formula for sample size calculation:
n = (Z^2 * σ^2) / E^2
Where:
n = required sample size
Z = Z-score corresponding to the desired level of confidence
σ = population standard deviation
E = desired margin of error
For a 95% level of confidence:
Z = 1.96 (corresponding to a 95% confidence level)
E = 2 minutes
σ = 8 minutes (population standard deviation)
Substituting these values into the formula:
n = (1.96^2 * 8^2) / 2^2
n = (3.8416 * 64) / 4
n = 245.9904 / 4
n ≈ 61.4976
Since we can't have a fraction of a sample, we round up the sample size to the nearest whole number. Therefore, a sample size of 62 should be taken for a 95% level of confidence.
b. For a 99% level of confidence:
Z = 2.58 (corresponding to a 99% confidence level)
E = 2 minutes
σ = 8 minutes (population standard deviation)
Substituting these values into the formula:
n = (2.58^2 * 8^2) / 2^2
n = (6.6564 * 64) / 4
n = 426.0096 / 4
n ≈ 106.5024
Rounding up the sample size to the nearest whole number, a sample size of 107 should be taken for a 99% level of confidence.
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if 1 liter ≈ 61 in3, then how many liters of soup will fit in a cylindrical can that measure by 18 inches tall by 5 inches wide? round to 2 decimal places.
Answers
The cylindrical can will fit 5.79 liters of soup. The value is the same with the volume of the can.
How to find the volume of a cylinder?To find the volume of a cylindrical can, we can use the formula of a cylinder.
V = πr²h
Where r is the radius and h is the height.
The radius is half the width, so in this case
r = ½(5 inches) = 2.5 inchesh = 18 inchesPlugging these values into the formula gives us:
V = π(2.5)²(18) ≈ 353.25 in³
Now we need to convert this volume from cubic inches to liters.
Since 1 liter ≈ 61 in³, we can use the conversion factor 1 L/61 in³ to find the volume in liters.
V = 353.25 in³ × (1 L/61 in³) ≈ 5.79 L
Hence, the cylindrical can will hold approximately 5.79 liters of soup.
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x2+5x+6 in quadratic trinomial
Answers
Therefore , the solution of the given problem of quadratic equation comes out to be (x−1)(x+6).
An explanation of a quadratic equationThe quadratic equation x ax2+bx+c=0 is an equations regression model in a single variable. a 0. According to the First Theorem of Algebra, this polynomial has at exactly one solutions because it is of second order. There could be simple or complex solutions. A four-variable equation is referred to as a quadratic equation. This implies that it must have at least one squared word. A typical formula for resolving math problems is "ax2 + bx + c = 0," where the numerical factors or constant a, b, and c stand in for the undefined variable "X."
Here,
Given : x²+5x+6
=> x²+bx+c.
Find two integers with the product c and the sum b.
Whose product in this instance is 6 and Whose summation is 5.
Put these integers to use in factoring the expression.
(x−1)(x+6)
Therefore , the solution of the given problem of quadratic equation comes out to be (x−1)(x+6).
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You toss a coin, what is the probability of having 5 heads in a row? 1/64 O 1/8 O 1/4 O 1/32 O 1/16
Answers
Answer:
Step-by-step explanation:
The Probability of Landing a heads is (1/2)
Now, to find the probability of landing it five times in a row, it is
1/2 x 1/2 x 1/2 x 1/2 x 1/2
( 1/2 is multiplied to the number of times to get a head )
The final answer will be,
Probability of landing heads 5 times in a row = 1/32
Pls answer I will mark brainliest
Answers
Step-by-step explanation:
I hope this will help you
Answer:
198
Step-by-step explanation:
the length of one side of a rectangle is p cm and width is 3(p-2) cm the perimeter is 44 cm find the length and width of rectangle
Answers
Answer:
Length = 7cm, Width = 15cm
Step-by-step explanation:
Length = p
Width = 3(p-2)
= 3p-6
Perimeter = length + width + length + width
= p + 3p-6 + p + 3p-6
= 8p-12
8p - 12 = 44
Isolate 8p.
8p = 44+12
= 56
Find p.
p = 56 ÷ 8
p = 7
Length = 7cm
Width = 3(7)-6
= 21-6
= 15cm
What is the slope of the line that goes through the points (-2, 5) and (0, 2)? Select the correct answer.
Answers
Answer:
Step-by-step explanation:
\(m=\frac{y_2-y_1}{x_2-x_1}\\ \\ m=\frac{2-5}{0+2}\\ \\ m=-\frac{-3}{2}\)
Answer:
3
Step-by-step explanation:
Find angle X.
I am not sure if it should add up to 360 degrees or 180 degrees
Answers
Answer:
195
Step-by-step explanation:
Since this figure is a quadrilateral you would be subtracting the inner angles from 360
360-87-40-38=195
How do you find the third side of an inequality of a triangle?
Answers
To find the third side of an inequality of a triangle, you must first use the Triangle Inequality Theorem.
This theorem states that for any triangle, the sum of any two sides of the triangle must be greater than the third side. This means that in order to find the length of the third side, you must subtract the sum of the two known sides from the smaller of the two sides, then the length of the third side will be equal to the difference between these two numbers. For example, if two sides of a triangle have lengths of 4 and 3, the third side must be greater than 1 (4 + 3 = 7 and 4 - 3 = 1). Therefore, the length of the third side must be greater than 1.
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An empty erlenmeyer flask that weighs 245.8 g is filled with 125 mL of carbon tetrachloride . The weight of the flask and carbon tetrachloride is found to be 444.6 g. From this information , calculate the density of carbon tetrachloride .
Answers
Answer:
The density is 1.59 g/mL. Therefore, the substance will NOT float in water.
Step-by-step explanation:
The following data were obtained from the question:
Mass of empty flask = 245.8 g
Mass of flask + CCl₄ = 444.6 g
Volume of CCl₄ = 125 mL
Density of CCl₄ =?
Next, we shall determine the mass of carbon tetrachloride, CCl₄. This can be obtained as follow:
Mass of empty flask = 245.8 g
Mass of flask + CCl₄ = 444.6 g
Mass of CCl₄ =.?
Mass of CCl₄ = (Mass of flask + CCl₄) – (Mass of empty flask)
Mass of CCl₄ = 444.6 – 245.8
Mass of CCl₄ = 198.8 g
Finally, we shall determine the density of carbon tetrachloride, CCl₄ as follow:
Mass of CCl₄ = 198.8 g
Volume of CCl₄ = 125 mL
Density of CCl₄ =?
Density = mass / volume
Density of CCl₄ = 198.8 / 125
Density of CCl₄ = 1.59 g/mL
The density of water is 1 g/mL. Since the density of carbon tetrachloride, CCl₄ (i.e 1.59 g/mL) is bigger than that of water, the substance will not float in water.
The density of carbon tetrachloride is 1.59 grams per milliliter.
Given that an empty erlenmeyer flask that weighs 245.8 g is filled with 125 mL of carbon tetrachloride, and the weight of the flask and carbon tetrachloride is found to be 444.6 g, to determine the density of carbon tetrachloride the following calculation must be performed:
Subtract the weight of the empty flask from the weight of the full flask, and then divide this result by 125 (the milliliters of carbon tetrachloride).
(444.6 - 245.8) / 125 = X 198.8 / 125 = X 1.59 = X
Therefore, the density of carbon tetrachloride is 1.59 grams per milliliter.
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James is making orange juice from concentrated frozen orange juice that he must mix with water. The concentrated juice is in 12 fluid ounce cartons. The ratio of orange juice concentrate to water is 12 fluid ounces to 36 fluid ounces. If James needs 4.5 gallon of orange juice, which is 576 fluid ounces, how many cartons of concentrated orange juice does he need?
Group of answer choices
Answers
In order to make 4.5 gallons of orange juice, she will need 12 cartons of concentrated orange juice.
The volume of concentrated orange juice is equal to 12 fluid-ounce cartons.Orange juice concentrate to water ratio = 12 fluid ounces to 36 fluid ouncesThe amount of orange juice required by James is 4.5 gallons (576 fluid ounces).So,
The orange juice concentrate to water ratio is 12:36.
Now, let's call 'x' the amount of concentrated orange juice in 4.5 gallons of orange juice and 'y' the amount of water in the 4.5 gallons of orange juice we have;
x + y = 4.5 (gallons) ...(1)x:y = 12:36 = 1:3∴ x/y = 1/33·x = y ...(2)We can conclude the following from equations (1) and (2):
x + y = 4.5x + 3·x = 4.5x = 4.5/4 = 1.125x = 1.125x = 1.125 gallons of concentrated orange juice in 4.5 gallons of orange juice:
y = 3 × x = 3 × 1.125 = 3.375y = 3.375y = 3.375, the amount of water in 4.5 gallons of orange juice.
As a result, we have;
4.5 gallons = 576 fluid ounces1.125 gallons = (576/4.5) × 1.125 = 144 fluid ouncesThe number of fluid ounces in a carton is 12 ounces.
The number of cartons in 144 fluid ounces = 144 fluidounces ÷ 12 fluidounces/carton = 12 cartonsIn 4.5 gallons of orange juice, x = 1.125 gallons = 144 fluidounces = 12 cartons of concentrated orange juice
x = 12 cartons of orange juice = the amount of concentrated orange juice she requires in 4.5 gallons of orange juiceThe amount of concentrated orange juice she requires in 4.5 gallons of orange juice, x = 12 cartons of orange juiceTherefore, in order to make 4.5 gallons of orange juice, she will need 12 cartons of concentrated orange juice.
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solve the equation 6(y+1.5)= -18. what is the value of y? y=
Answers
Answer:
y = -4.5
Step-by-step explanation:
Solve the equation 29 = v + 23 for v.
Answers
Answer:
6
Step-by-step explanation:
Solving steps
29v+23
Move the terms
- v =23 -29
Calculate
-V=-6
Change the signs
Solution
V = 6
Answer: 6
Step-by-step explanation: the guy above me has the best expanation
a film distribution manager calculates that 9%9% of the films released are flops. if the manager is right, what is the probability that the proportion of flops in a sample of 506506 released films would differ from the population proportion by greater than 3%3%? round your answer to four decimal places.
Answers
The probability that the proportion of flops in a sample of 506 released films would differ from the population proportion by greater than 3% is approximately 0.0192 or 1.92% (rounded to four decimal places).
Given:
Population proportion of flops: p = 9% = 0.09
Sample size: n = 506
First, let's calculate the standard deviation (σ) of the sampling distribution, which represents the standard error of the proportion:
σ = √[(p * (1 - p)) / n]
= √[(0.09 * (1 - 0.09)) / 506]
≈ √[(0.0819) / 506]
≈ √[0.000161955]
≈ 0.012736
Next, we need to find the z-score associated with a difference of 3% from the population proportion:
z = (0.03 - 0) / σ
= 0.03 / 0.012736
≈ 2.3542
Using a standard normal distribution table or calculator, we can find the probability associated with the z-score of 2.3542. However, since we are interested in the probability that the proportion differs from the population proportion by greater than 3%, we need to consider both tails of the distribution.
The probability of a difference greater than 3% is equal to the probability of a z-score less than -2.3542 or greater than 2.3542.
P(z < -2.3542) + P(z > 2.3542)
Looking up the values in the standard normal distribution table or using a calculator, we find:
P(z < -2.3542) ≈ 0.0096
P(z > 2.3542) ≈ 0.0096
Adding these probabilities:
0.0096 + 0.0096 ≈ 0.0192
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A contractor is required by a county planning department to submit one, two, three, four, five, six, or seven forms (depending on the nature of the project) in applying for a building permit. Let Y = the number of forms required of the next applicant. The probability that y forms are required is known to be proportional to y-that is, ply) = ky for y = 1, ..., 7. (Enter your answers as fractions.) (a)What is the value of k? [Hint: ∑ p(y) = 1] k= ____ (b) What is the probability that at most three forms are required? (c) What is the probability that between two and four forms (inclusive) are required? (d) Could p(y) = y^2 /138 for y = 1, ..., 7 be the pmf of Y?
_____ because ∑ p(y) = ______
Answers
(a) The value of k is 1/28
(b) The probability that at most three forms are required is 3/14
(c) The probability that between two and four forms (inclusive) are required is 9/28
(d) \(p(y) = \frac{y^2}{138}$ for $y = 1, ..., 7$\) is not the pmf of Y
What is probability?Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.
(a) To find the value of k, we use the fact that the sum of the probabilities for all possible values of Y must be equal to 1. Thus:
\($$\sum_{y=1}^{7} p(y) = k \sum_{y=1}^{7} y = k(28) = 1$$\)
Therefore, \(k = \frac{1}{28}$.\)
(b) The probability that at most three forms are required is the sum of the probabilities for Y = 1, Y = 2, and Y = 3. Thus:
\($$P(Y \leq 3) = P(Y = 1) + P(Y = 2) + P(Y = 3) = \frac{1}{28} + \frac{2}{28} + \frac{3}{28} = \frac{6}{28} = \frac{3}{14}$$\)
(c) The probability that between two and four forms (inclusive) are required is the sum of the probabilities for Y = 2, Y = 3, and Y = 4. Thus:
\($$P(2 \leq Y \leq 4) = P(Y = 2) + P(Y = 3) + P(Y = 4) = \frac{2}{28} + \frac{3}{28} + \frac{4}{28} = \frac{9}{28}$$\)
(d) To determine if \(p(y) = \frac{y^2}{138}$ for $y = 1, ..., 7$\) could be the pmf of Y, we need to verify that the probabilities sum to 1:
\($$\sum_{y=1}^{7} p(y) = \frac{1^2}{138} + \frac{2^2}{138} + \frac{3^2}{138} + \frac{4^2}{138} + \frac{5^2}{138} + \frac{6^2}{138} + \frac{7^2}{138} = \frac{1}{2}$$\)
Since the sum is not equal to 1, \(p(y) = \frac{y^2}{138}$ for $y = 1, ..., 7$\) cannot be the pmf of Y.
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COULD YALL PLEASE HELP ME WILL GIVE CROWN!!!
Answers
Answer:
5x+3x+11x which gives you 18x
Step-by-step explanation:
Might Help for a Answer:
13x-8+7x+4+3x=180
We move all terms to the left:
13x-8+7x+4+3x-(180)=0
We add all the numbers together, and all the variables
23x-184=0
We move all terms containing x to the left, all other terms to the right
23x=184
x=184/23
x=8
DERIVE the following problems and show show the complete solution.
1. √a+√x / √a-√x
2. a-x / √a-√x
3. √ax+b / cx+d
Answers
The simplified expression is (√(ax + b) * (cx - d)) / (c^2x^2 - d^2).
1. Deriving √a+√x / √a-√x:
To simplify the expression, we can multiply both the numerator and denominator by the conjugate of the denominator, which is √a+√x. This will help us eliminate the square roots in the denominator.
(√a+√x) / (√a-√x) * (√a+√x) / (√a+√x)
Expanding the numerator and denominator:
((√a)^2 + 2√a√x + (√x)^2) / ((√a)^2 - (√x)^2)
Simplifying further:
(a + 2√ax + x) / (a - x)
So, the simplified expression is (a + 2√ax + x) / (a - x).
2. Deriving a-x / √a-√x:
Again, to simplify the expression, we can multiply both the numerator and denominator by the conjugate of the denominator, which is √a+√x.
(a - x) / (√a - √x) * (√a + √x) / (√a + √x)
Expanding the numerator and denominator:
((a)(√a) + (a)(√x) - (√a)(√a) - (√a)(√x)) / ((√a)^2 - (√x)^2)
Simplifying further:
(a√a + a√x - a - √a√a - √a√x) / (a - x)
Grouping the like terms:
(a√a - a - √a√x) / (a - x)
So, the simplified expression is (a√a - a - √a√x) / (a - x).
3. Deriving √(ax+b) / (cx+d):
To simplify this expression, we can multiply both the numerator and denominator by the conjugate of the denominator, which is cx-d.
(√(ax + b) / (cx + d)) * (cx - d) / (cx - d)
Expanding the numerator and denominator:
(√(ax + b) * (cx - d)) / ((cx)^2 - (d)^2)
Simplifying the denominator:
(√(ax + b) * (cx - d)) / (c^2x^2 - d^2)
So, the simplified expression is (√(ax + b) * (cx - d)) / (c^2x^2 - d^2).
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3. if the 90% confidence limits for the population mean are 34 and 46, which of the following could be the 99% confidence limits a) (36,41) b) (39,41) c) (30,50) d) (39,43) e) (38,45) 4. given that the population standard deviation is 7500 and a 95% confidence level. what should be the sample size if we want the margin of error to be m
Answers
a) Option D, (39,43) could be the 99% confidence limit.
b) The determined minimum sample size is 166.
a) For a given sample size, the confidence interval is just the range of values including the real population mean. The confidence interval is interpreted as follows:
The real population mean are contained in around 95% of the estimated confidence intervals.
The breadth of the interval and the confidence level (including 95% or 99%) have a positive connection.
As the confidence level rises, the range of both the confidence interval expands, implying that the lower limit of the interval shrinks and the top bound of the interval expands.
Option B is the correct one among the available possibilities since it entirely follows the pattern. When compared to a 99% confidence interval, 33 should be less than 34, and 46 is more than 43.
b) s = Standard Deviation = $7,500 m = Margin of Error = $1,500 z = Empirical z-score at 95% CI = 2.575
The random sample for a 95% confidence interval is calculated as follows:
= (Z × s)² ÷ m²
= (2.575 × s)² ÷ m²
= (2.575 × 7500)² ÷ (1500)²
= 165.76
≈ 166
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Brett and Max are diving. Brett is 34 feet below the surface and Max is 25 feet below the surface. How many feet above Brett is Max?
Answers
Answer:
Max is 9 feet above Brett.
Step-by-step explanation:
If you subtract how far Max is below the surface to how far Brett is below the surface you find the difference of how much more above Brett Max is.
This would be the mathematical process:
34-25=9
Max is 9 feet above Brett.
What are Arithmetic operations?Arithmetic operations can also be specified by adding, subtracting, dividing, and multiplying built-in functions.
The operator that performs the arithmetic operation is called the arithmetic operator.
Operators which let do a basic mathematical calculation
+ Addition operation: Adds values on either side of the operator.
For example 4 + 2 = 6
- Subtraction operation: Subtracts right-hand operand from the left-hand operand.
for example 4 -2 = 2
* Multiplication operation: Multiplies values on either side of the operator
For example 4*2 = 8
Given that Brett is 34 feet below the surface and Max is 25 feet below the surface.
Max is more than twice as deep below the surface as Brett,
Thus we can determine this difference by subtracting Max's depth from Brett's.
The mathematical solution would be as follows:
⇒ 34 - 25
⇒ 9
Hence, Max is 9 feet above Brett.
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A. 6
B. ⟌50
C. ⟌34
D. 4
Which one?
Answers
Answer:
C
Step-by-step explanation:
3^2 + 5^2 = x^2
9 + 25 = x^2
x^2 = 34
x = sqrt(34)
so the answer is C
Gail made 7/8 quart of lemonade. Her sister drank 1/4 quart of the lemonade. How much lemonade is left?
Group of answer choices
2/8 quart
3/8 quart
4/8 quart
5/8 quart
Answers
Answer:
5/8 quarts
Step-by-step explanation:
First you want both fractions to have the same denominator so let’s keep 7/8 and multiply the 4 and the 1 in the fraction 1/4 which would now give you 2/8 now subtract the 7 in and the 2 and keep your denominator and your answer will be 5/8
Which property does each equation demonstrate? x2 + 2x = 2x + x2 (3z4 + 2z3) – (2z4 + z3) = z4 + z3 (2x2 + 7x) + (2y2 + 6y) = (2y2 + 6y) + (2x2 + 7x)
Answers
Answer:
1 . Closure
2. Distributive
3. Closure
Step-by-step explanation:
Here, we want to know the type of property exhibited or displayed by each of the equations in the question.
Equation 1 displays the closure property.
What this means that if we make an addition operation either way, we would get same answer. So we say that addition is closed for that equation.
Equation 3 exhibits closure property as well. If we go either way on the addition operation for that equation, we are bound to get the same answer.
Equation 2 exhibits the distributive property.
Each term in the bracket is multiplied by the subtraction symbol before we proceeded to complete the arithmetic operations
Answer:
1. Commutative property
2.Closure property
3.Commutative property
Step-by-step explanation: I just did it.
I know that in my time signature, I want a quarter note to get the beat and I want the four beats in each measure. What number should I have in the bottom of my time signature? What number should I put in the top of my time signature?
Answers
4/4 is the most commonly used time signature. You will have 4 beats per measure and the quarter note will be one beat.
What is time signature?Two numbers make up a time signature, which is similar to a fraction. The time signature may alter throughout a work, but it always appears at the beginning. The bottom number is the note value that corresponds to one beat, and the top number is the number of beats in a measure. A song in 4/4 time, for instance, will have four quarter notes every measure, whereas a song in 9/8 time will have nine eighth notes per measure.
Here,
The most popular time signature is 4/4. The quarter note is one beat, and each measure has four beats.
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