Suppose X has an exponential distribution with rate parameter λ1. Suppose Y has an exponential distribution with rate parameter λ2. Suppose X and Y are independent. Calculate P(X > Y).

Step-by-step explanation:

Expanding and simplifying 2(x + 7) + 3(x + 1):

2(x + 7) = 2x + 14

3(x + 1) = 3x + 3

Adding the two expressions:

2x + 14 + 3x + 3 = 5x + 17

So 2(x + 7) + 3(x + 1) = 5x + 17.

[tex] \sf2(x + 7) + 3(x + 1) \\ \sf2x + 14 + 3x + 3 \\ \sf5x + 17[/tex]

The equation that justifies why[tex]27^{(1/3)}[/tex] is equivalent to the cube root of 27 is:[tex]27^{(1/3)} = (27^{1)^{(1/3)}} = 27^{(1/3)}[/tex]

The cube root symbol is represented by the number "3". In the square root case, only the root symbol—also known as a radical—was employed. Therefore, the cube root of different numbers can be symbolically represented as follows: 5 divided by its cube = 3. 11 has a cube root of 311 and so on.

The cube root of three is the same as the number 1.442224957031. The cube root of three has the radical representations 33 and 31/3. " denotes the square root.

The cube root formula aids in computing the cube root of any given number that is represented by the symbol in radical form. It can be determined by first determining the number's prime factorization and then using the cube root formula. Assume that x is any number such that it equals y, y, and y.

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Marcus's father would require 189 if he wanted to completely redo the tent's cover, including the bottom.

He needs 55 to completely cover the tent's one rectangular side with the rip. 55

Marcus's father would require 189 if he wanted to completely redo the tent's cover, including the bottom.

3 rectangular sides = 165

2 triangular sides = 24

165 + 24 = 189

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Answer:

C is the answer

Step-by-step explanation:

The length of BD is approximately 8.62 cm and the length of CD is approximately 4.30 cm.

AB = 10 cm and BC = 18 cm and angle ADB = 56 degrees.

A: Length of BD:

Using the law of sines, BD can be calculated as:

BD = 10 * sin(56) = 8.62 cm (approx)

B: Length of CD:

Using the Pythagorean theorem, AD can be calculated as:

AD = sqrt(BD^2 + AB^2 - 2 * BD * AB * cos(56)) = 12.92 cm (approx)

And then, CD can be calculated as:

CD = AD - BD = 12.92 cm - 8.62 cm = 4.30 cm (approx)

So, the length of BD is approximately 8.62 cm and the length of CD is approximately 4.30 cm.

"

Complete question

ABCD is a trapezium AD and BC are parallel

where AB = 10cm and BC = 18cm and angle ADB = 56degree

Find

A: work out the length of BD

B:  work out the length of CD

"

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a) k/6 = 1 → k=6 is the distribution of the median of Y1,Y2,··· ,Yn when n is an odd integer

b) P(Y1 ≤ 3/4, Y2 ≥ 1/2) =  9/16

a) if distribution

f (y1, y2) = k(1 − y2), 0 ≤ y1 ≤ y2 ≤ 1,  0, elsewhere

for f to be a probability density function , has to comply with the requirement that the sum of the probability of all the posible states is 1 , then

P(all possible values) = ∫∫f (y1, y2) dy1*dy2 = 1

then integrated between

y1 ≤ y2 ≤ 1 and 0 ≤ y1 ≤ 1

∫∫f (y1, y2) dy1*dy2 =  ∫∫k(1 − y2) dy1*dy2 = k  ∫ [(1-1²/2)- (y1-y1²/2)] dy1 = k  ∫ (1/2-y1+y1²/2) dy1) = k[ (1/2* 1 - 1²/2 +1/2*1³/3)-  (1/2* 0 - 0²/2 +1/2*0³/3)] = k*(1/6)

then

k/6 = 1 → k=6

b)

P(Y1 ≤ 3/4, Y2 ≥ 1/2) = P (0 ≤Y1 ≤ 3/4, 1/2 ≤Y2 ≤ 1) = p

then

p = ∫∫f (y1, y2) dy1*dy2 = 6*∫∫(1 − y2) dy1*dy2 = 6*∫(1 − y2) *dy2 ∫dy1 =

6*[(1-1²/2)-((1/2) - (1/2)²/2)]*[3/4-0] = 6*(1/8)*(3/4)=  9/16

therefore

P(Y1 ≤ 3/4, Y2 ≥ 1/2) =  9/16

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1. f(-1) = 9

2. the domain of the function f(x) = (x+3)/(x-1) is: x ∈ R {1} or x ∈ R {- 1}

3. y = 3x + 2

4. y = 2/3x + 1

The formula for a straight line, written as y = mx + b, where m denotes the line's slope and b its y-intercept. When the slope of the line being studied is known, and the provided point is also the y-intercept, the slope-intercept formula, y = mx + b, is utilized (0, b). b  stands in for the y value of the y-intercept point in the formula.

1.

Given f(x) = 4x² - 3x + 2

f(-1) = 4(-1)² - 3(-1) + 2

f(-1) = 4 + 3 + 2

f(-1) = 9

2.

f(x) = x + 3/ x - 1

x - 1 ≠ 0

x ≠ 1

therefore, x ∈ R {1} or x ∈ R {- 1}

3.

Two points (1, 1) and (2, 4)

(x₁, y₁) = (1,1)

(x₂, y₂) = (2, 4)

Two points form an equation:

y - y₁ = {(y₂ - y₁) / (x₂ - x₁)} (x - x₁)

y - 1 = {(4 - 1) / (2 - 1)} (x - 1)

3x - y = 2

x/ (2/3) + y / (-2) = 1

intercept form: x/a + y/b = 1

y = 3x + 2

this is slope intercept form.

4.

given slope (m) = 2/3

y - intercept (c) = 1

y = mx + c

y = 2/3x + 1

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[tex]\huge\begin{array}{ccc}f(-3)=-33\to\boxed{A.}\end{array}[/tex]

We have the function:

[tex]f(x)=2x-3x^2[/tex]

We need

[tex]f(-3)=?[/tex]

Substitute [tex]x=-3[/tex] to [tex]f(x)[/tex]:

[tex]f(-3)=2\cdot(-3)-3\cdot(-3)^2=-6-3\cdot9=-6-27=-33\to\boxed{A.}[/tex]

The Answer is 2.557 when 17.9 is divided by 7

The roots of a polynomial are values that make the polynomial equal zero.

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The coordinates of point P along the directed line segment AB is (10, 13).

The midpoint of a line segment is given as,

x = (a + c)/2

y = (b + d) / 2

Where (x, y) is the midpoint and (a, b) and (c, d) are the two endpoints.

We have,

The line AB.

P is the point between the line AB.

Now,

A = (4, 10) = (a, b) and B = (14, 15) = (c, d)

m : n = 3 : 2

So,

P = (x, y)

The coordinates is given by:

x = (mc + na) / (m + n)

y = (md + nb) / (m + n)

So,

x = (42 + 8) / 5

x = 10

y = (45 + 20) / 5

y = 13

Now,

P = (10, 13)

Thus,

The coordinates of point P is (10, 13).

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For an nth root, there are n solutions of the equation z^n = ω.

To find these solutions, we use the polar form of z = r * e^(iθ). Substituting into the equation, we get:

r^n * e^(iθn) = s * e^iφ

Comparing the magnitude of both sides, we have:

r^n = s

Comparing the phase of both sides, we have:

nθ = φ + 2πk (where k is an integer)

So, we can set:

r = s^(1/n)

θ = (φ + 2πk) / n

Therefore, the n solutions are:

z = s^(1/n) * e^(i(φ + 2πk) / n)

for k = 0, 1, 2, ..., n-1.

--The question is not readable, answering to the question below--

"With ω = se^iφ, where s ≥ 0 and φ ∈ r , solve the equation z^n = ω in C where n is a natural number. How many solutions are there?"

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Answer:

x = 48

Step-by-step explanation:

x/12 = 4

Multiply both sides by 12:

[x = 48]

(a) The probability that an assembly will have exactly one defect is 0.2.

This can be calculated using the Poisson distribution formula, which states that the probability of a given number of events (in this case, defects) occurring in a given interval is equal to the mean number of events (in this case, defects) multiplied by the exponential of the mean number of events (in this case, defects).

And multiplied by the exponential of the mean number of events (in this case, defects) multiplied by the exponential of the mean number of events (in this case, defects) divided by the factorial of the given number of events (in this case, defects). Thus, the probability of an assembly having exactly one defect is 0.2.

(b) The probability of an assembly having one or more defects is 1 - 0.2 = 0.8. This can be calculated using the same formula as in (a).

(c) By reducing the occurrence rate of defects to λ = 0.1, the probability of an assembly having one or more defects is reduced to 1 - 0.1 = 0.9. This can be calculated using the same formula as in (a).

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Correct question:

A mechatronic assembly is subjected to a final functional test. Suppose that a defect occurs at random in the assemblies, and that defect occurs according to a Poisson distribution with parameter λ= 0. 2. (a) What i the probability that an assembly will have exactly one defect? (b) What i the probability that an assembly will have one or more defects? (c) Suppose that you improve the process o that the occurrence rate of defects i cut in half to λ=0. 1. What effect doe this have on the probability that an assembly will have one or more defects? \

If the medium drink cost $1. 50, the inequality that represents the cost of a popcorn is x ≤ 3.5. Hence, the most he can pay for each popcorn is $3.5.

To translate a word problem into an inequality:

In this problem, let:

x = the cost of 1 popcorn

Three popcorns means = 3x

The cost of a medium drink = 1.5

The amount he need to pay for a medium drink and 3 popcorn:

amount = 1.5 + 3x

However, he only has 12 dollars. Hence,

1.5 + 3x ≤ 12

Subtract both sides by 1.5

3x ≤ 12 - 1.5

3x ≤ 10.5

Divide both sides by 3

x  ≤ 10.5/3

x ≤ 3.5

Hence, the maximum price of a popcorn is $3.5

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The measure of the angle at the library is 90 degrees.

Since the library is the same distance from both Toru's house and the park, this means that the triangle formed by the three points is an isosceles triangle, with two sides of equal length and two congruent angles.

In an isosceles triangle, the two equal angles are always congruent and add up to 180 degrees. So, the measure of each angle at the library would be:

180 degrees / 2 = 90 degrees

So, the measure of the angle at the library is 90 degrees.

An isosceles triangle is a type of triangle where two sides are of equal length and two angles are congruent. The two equal sides are called the legs and the third side is called the base. The two equal angles are opposite the two equal sides and are located at the vertices that are connected to the base.

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The measure of the angle at the library is 90 degrees.

Since the library is the same distance from both Toru's house and the park, this means that the triangle formed by the three points is an isosceles triangle, with two sides of equal length and two congruent angles.

In an isosceles triangle, the two equal angles are always congruent and add up to 180 degrees. So, the measure of each angle at the library would be:

180 degrees / 2 = 90 degrees

So, the measure of the angle at the library is 90 degrees.

An isosceles triangle is a type of triangle where two sides are of equal length and two angles are congruent. The two equal sides are called the legs and the third side is called the base. The two equal angles are opposite the two equal sides and are located at the vertices that are connected to the base.

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20 feet per minute is equal to 400 yards/hour

What is unit rate?

A unit rate is the cost for only one of anything. This is expressed as a ratio with a denominator of 1. For instance, if you covered 70 yards in 10 seconds, you did so at an average speed of 7 yards per second. Although both of the ratios—70 yards in 10 seconds and 7 yards in one second—are rates, only the latter is a unit rate.

For 1 minute 20 feet

For 60 minutes , 60*20=1200 feet

1 hour = 60 minutes

Thus, we have 1200 feet per hour

3 feet = 1 yard

So, 1200 feet = 1200/3 yrads = 400 yards

Thus, 20 feet per minute is equal to 400 yards/hour

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The first three terms of the sequence are -4 , -1, 4. The 10th term of the sequence is given as 95

The general form of the nth term of a sequence can be represented as an expression involving n, such as n^2 - 5.

The first three terms of the sequence are:

n = 1, term = 1^2 - 5 = -4

n = 2, term = 2^2 - 5 = -1

n = 3, term = 3^2 - 5 = 4

The tenth term of the sequence is:

n = 10, term = 10^2 - 5 = 95

So, the first three terms are -4, -1, 4, and the tenth term is 95.

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Answer:

Step-by-step explanation:

I hope this helps you

Answer:

The equation 81a^2 + 5b^2 cannot be factored further as a polynomial expression because it is in the standard form of a sum of squares, and the coefficients are not perfect squares. Factoring a sum of squares means writing it as the product of two binomials, each of which is the square root of one of the terms. Since 81 and 5 are not perfect squares, the equation 81a^2 + 5b^2 cannot be written as the product of two binomials.

The equation  [tex]81a^2 + 5b^2[/tex]  cannot be written as the product of two binomials.

An equation is defined as an expression that shows the relationship between two or more numbers and variables.

Given equation as  [tex]81a^2 + 5b^2[/tex]  

Since we know that Factoring a sum of squares means writing it as the product of two binomials, each of that is the square root of one of the terms.

Hence, 81 and 5 are not perfect squares.

The given equation [tex]81a^2 + 5b^2[/tex] cannot be factored further as a polynomial expression because it is in the standard form of a sum of squares, and the coefficients are not perfect squares.

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formula for the tangent line is y=x-1 and differentiation of ln(x) is 1/x

A straight line without crossing the curve , it touches the curve at one single point is called tangent . Finding the derivative of a function or a variable in mathematics is called differentiation.

The ratio of the vertical to the horizontal distance between any two points on it  is called slope of ray or line or line segment in analytical geometry.

y-y1 = m(x-x1)

If the function passes through (1,0)  and the slope equals to 1 is:

y-0 = 1(x-1)

y=x-1

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Tangents are straight lines that only touch curves at a single spot rather than crossing them. Differentiation in mathematics refers to the process of determining a function's or variable's derivative.

The slope of a ray, line, or line segment in analytical geometry is the ratio of the vertical to the horizontal distance between any two locations on it.

y-y1 = m(x-x1) (x-x1)

If a function goes through the point (1, 0) and its slope is 1, then:

y-0 = 1(x-1) (x-1)

y=x-1

Answer:(2,6)

Step-by-step explanation: 4/1 is going rise/run. your rise would be 4 and your run would be 1. 4/1 is up 4 to the right 1. another point would be (0,-2). you are still gonne do the same thing as rise over run just go negavtive. -4/1 which is down 4 to the left 1.

Answer:

1 + 1 = 2.

Step-by-step explanation:

Answer NOBODY KNOWS THAT

Step-by-step explanation: MATHMATIONS HAVE BEEN TRYING TO FIND THAT OUT FOR YEARS  AND YOU THINK YOU'LL FIND IT ON BRAINLY THE EQUATION IS FAR TO COMPLEX FOR HUMAN MINDS THE ONLY WAY YOU'LL GET THE ANSWER IS IF YOU ASKED GOD HIMSELF: but i think 1 + 1 = 2

The average rate of change and the instantaneous rate of change are same for ƒ(x) = 2x + 5. The solution has been obtained by using the concept of rate of change.

What is rate of change?

The pace at which one quantity changes in relation to another is described by the rate of change function. Simply expressed, the amount of change in one item is divided by the same amount of change in another to determine the rate of change. The relationship between how one quantity changes in relation to a change in another quantity is provided by the rate of change formula.

The average rate of change is:

[tex]r_{avg} =\frac{f(b)-f(a)}{b-a}[/tex], on interval [a,b]

Here, we are given  ƒ(x) = 2x + 5

So,

[tex]r_{avg} =\frac{(2b+5)-(2a+5)}{b-a}[/tex]

[tex]r_{avg} =\frac{2b-2a}{b-a}[/tex]

[tex]r_{avg} =2[/tex]

The slope of f assessed at a single point, such as f′(c), where c is a predetermined point, is the definition of the instantaneous rate of change.

So, for ƒ(x) = 2x + 5,

f′(c) = 2

Therefore, instantaneous rate of change is 2.

Hence, the average rate of change and the instantaneous rate of change are same for ƒ(x) = 2x + 5.

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The equation which represents total pay P and number of copies sold N is P =1800 + 70N and the total pay for 28 copies sells will be $3760.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

From the question, we were given the following parameters

P = total pay

N = copies sold

P = 1800 +70N

replace N with 28

P=1800 + 70(28)

P=1800 + 1960

P= 3760 is her total pay selling 28 copies

Hence The equation which represents total pay P and a number of copies sold N is P =1800 + 70N and the total pay for 28 copies sells will be $3760

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Answer: She can buy 2 sweatshirts and 3 T-Shirts or 1 sweatshirt and 4 T-Shirts

Step-by-step explanation:

De Morgan's laws state: (A∪B)^c = A^c∩B^c and (A∩B)^c = A^c∪B^c.

What is Venn diagram ?

A Venn diagram is a widely used diagram style that shows the logical relation between sets, popularized by John Venn in the 1880s. The diagrams are used to teach elementary set theory.

The first law states that the complement of the union of two sets is equal to the intersection of their complements:

(A ∪ B)’ = A’ ∩ B’

This law can be illustrated with a Venn diagram, where the complement of a set is represented by shading the region outside the set. In this diagram, the shaded region outside the union of A and B is equal to the overlap of the shaded regions outside of A and B individually.

The second law states that the complement of the intersection of two sets is equal to the union of their complements:

(A ∩ B)’ = A’ ∪ B’

De Morgan's laws state: (A∪B)^c = A^c∩B^c and (A∩B)^c = A^c∪B^c.

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The answer to this question requires the use of the Poisson distribution and the cumulative distribution function.

(a) We are asked to find the probability that the fourth person weighed is the first person to be overweight. Since 63% of Americans are overweight, this means that the probability of a randomly selected American being overweight is 0.63. The probability of the first overweight person being the fourth person weighed is given by P(X=3) where X is the number of overweight people in the first 4 people weighed. Using the binomial distribution formula, we have:

[tex]P(X=3) = (4 choose 3) * (0.63)^3 * (0.37)^1\\\\ = 4 * (0.63)^3 * (0.37)[/tex]

(b) We are asked to find the probability that it takes more than 4 people to observe the first overweight person. This is equivalent to finding the probability that none of the first 4 people weighed are overweight. Using the complement rule, we have:

[tex]P(X=0) = 1 - P(X > 0)\\\\ = 1 - [P(X=1) + P(X=2) + P(X=3) + P(X=4)]\\\\ = 1 - [ (4 choose 1) * (0.63)^1 * (0.37)^3 + (4 choose 2) * (0.63)^2 * (0.37)^2 + P(X=3) ][/tex]

(c)  The expected value (mean) of a binomial distribution is given by μ = np, where n is the number of trials and p is the probability of success in each trial. In this case, n=4 and p=0.63. Thus, the mean number of overweight people in 4 trials is 4 * 0.63 = 2.52. The variance of a binomial distribution is given by σ^2 = np(1-p), so in this case the variance is 4 * 0.63 * 0.37 = 1.41. The standard deviation is the square root of the variance, so the standard deviation is approximately [tex]\sqrt{(1.41) } = 1.19[/tex]. This means that the number of overweight people in 4 trials is expected to be around 2.52, with a standard deviation of 1.19.

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160 ounces or 10 pounds of cheese is $ 15 and 84 cents.

The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.

Direct Variation

When there is a direct variation, an increase or decrease in one quantity will result in an equivalent rise or fall in the other. For instance, a rise in the quantity of commodities will result in higher costs.

Indirect Variation

A change in one quantity will directly affect a change in another, known as a direct variation. A rise in the quantity of goods, for instance, will result in higher costs.

We can say 1 pound = 16 ounces

10 pounds = 10 * 16 = 160 ounces

10 ounces of cheese is 99 cents

1 ounce of chess is 99/10 cents

160 ounces of cheese is 99*160/10 = 1584 cents = $ 15 and 84 cents.

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