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Answer:

5√9x645-9-5 3√5

Step-by-step explanation:

The final answer is: Mx(t) = E[e^(tx₂ + t4)], Mx₂(t) = E[e^(tx₂)], Px(t) = probability density function of XPx(x) = P(X=x).

Given:

X₁(t) → 4₁ (Y) = 1 8(T)NORMAL EX₁(0) = 2EX₂(0)=1P₁ = []X(t) = (x₂4+), X₂(t)W(t) ½s½s EW(t)=0

As X(t) = (x₂4+), we have to find Mx(t), Mx₂(t), Px(t), Px(x).

The moment generating function of a random variable X is defined as the expected value of the exponential function of tX as shown below.

Mx(t) = E(etX)

Let's calculate Mx(t).X(t) = (x₂4+)

=> X = x₂4+Mx(t)

= E(etX)

= E[e^(tx₂4+)]

As X follows the following distribution,

E [e^(tx₂4+)] = E[e^(tx₂ + t4)]

Now, X₂ and W are independent.

Therefore, the moment generating function of the sum is the product of the individual moment generating functions.

As E[W(t)] = 0, the moment generating function of W does not exist.

Mx₂(t) = E(etX₂)

= E[e^(tx₂)]

As X₂ follows the following distribution,

E [e^(tx₂)] = E[e^(t)]

=> Mₑ(t)Px(t) = probability density function of X

Px(x) = P(X=x)

We are not given any information about X₁ and P₁, hence we cannot calculate Px(t) and Px(x).

Hence, the final answer is:Mx(t) = E[e^(tx₂ + t4)]Mx₂(t) = E[e^(tx₂)]Px(t) = probability density function of XPx(x) = P(X=x)

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Answer:

A.

Step-by-step explanation:

when you distribute it you keep the subtraction sign and have to multiply 6 by 50 and then 6 by 1

The equation \(4x^2u^n + (1-x^2)u = 0\) has two solutions. One solution is given by \(u_1 = x^{1/2}\left(1 + \frac{x^2}{16} + \frac{x^4}{1024} + \dots\right)\). The other solution is not provided in the given question.

To find the solutions, we can rewrite the equation as \(u^n = -\frac{1-x^2}{4x^2}u\). Taking the square root of both sides gives us \(u = \pm\left(-\frac{1-x^2}{4x^2}\right)^{1/n}\). Now, let's focus on finding the positive solution.

Expanding the expression inside the square root using the binomial series, we have:

\[\left(-\frac{1-x^2}{4x^2}\right)^{1/n} = -\frac{1}{4^{1/n}x^{2/n}}\left(1 + \frac{(1-x^2)}{4x^2}\right)^{1/n}\]

Since \(|x| < 1\) (as \(x\) is a fraction), we can use the binomial series expansion for \((1+y)^{1/n}\), where \(|y| < 1\):

\[(1+y)^{1/n} = 1 + \frac{1}{n}y + \frac{1-n}{2n^2}y^2 + \dots\]

Substituting \(y = \frac{1-x^2}{4x^2}\), we get:

\[\left(-\frac{1-x^2}{4x^2}\right)^{1/n} = -\frac{1}{4^{1/n}x^{2/n}}\left(1 + \frac{1}{n}\cdot\frac{1-x^2}{4x^2} + \frac{1-n}{2n^2}\cdot\left(\frac{1-x^2}{4x^2}\right)^2 + \dots\right)\]

Simplifying and rearranging terms, we find the positive solution as:

\[u_1 = x^{1/2}\left(1 + \frac{x^2}{16} + \frac{x^4}{1024} + \dots\right)\]

The second solution is not provided in the given question, but it can be obtained by considering the negative sign in front of the square root.

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Answer:

C on edge 2021

Step-by-step explanation:

Answer:          GH

Step-by-step explanation:

Answer:

Whats the problem? and what class (algebra...)

Step-by-step explanation:

Answer:

sb

Step-by-step explanation:

Answer:

Option B is the best way to write the underlined parts of sentences 2 and 3.

Sentence 2: They have a special finish that helps.

Sentence 3: The finish helps the swimmer glide through the water.

Option B provides a clear and concise way to connect the two sentences and convey the idea that the special finish of the swimsuits helps the swimmer glide through the water. It avoids any ambiguity or redundancy in the language.

4 is greater than or equal to -5/4, it is in the domain of f(g(x)). Therefore, the correct statement is: 4 is in the domain of fᵒg.

To determine whether 4 is in the domain of the composite function fᵒg, we need to evaluate the composition of f(g(x)) and check if 4 is a valid input.

Given f(x) = √√x + 4 and g(x) = 4x + 5, we can find f(g(x)) by substituting g(x) into f(x):

f(g(x)) = √√(4x + 5) + 4

Now, let's see if 4 is in the domain of fᵒg. To be in the domain, the expression inside the square root (√) must be non-negative.

For f(g(x)), the expression inside the inner square root (√) is 4x + 5, and for the outer square root, we have √(√(4x + 5) + 4).

To determine the validity of 4 as an input, we set the expression inside the inner square root greater than or equal to 0:

4x + 5 ≥ 0

Solving this inequality for x, we get:

4x ≥ -5

x ≥ -5/4

This inequality tells us that x must be greater than or equal to -5/4 for the expression inside the inner square root (√(4x + 5)) to be non-negative.

The number 4 is in the domain of f(g(x)) since it is bigger than or equal to -5/4. The right answer is thus: 4 is in the area of fog.

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Answer:

(1st option) x>-3

Step-by-step explanation:

therefore, x is greater than negative three

x>-3

The probability of getting a king in one of the halves of a deck of cards that has been split into two halves of 26 cards each is 4/26 or 2/13.

There are 4 kings in a deck of 52 cards, which means that there are 2 kings in each half of the deck when it is split into two halves of 26 cards each.

The total number of cards in each half is 26, so the probability of getting a king in one of the halves is the number of kings in one half divided by the total number of cards in one half.

This can be expressed as follows:

Probability of getting a king in one half = Number of kings in one half / Total number of cards in one half

Probability of getting a king in one half = 2 / 26

Probability of getting a king in one half = 1 / 13

Probability of getting a king in one of the halves = Probability of getting a king in the first half + Probability of getting a king in the second half (because these are mutually exclusive events)

Probability of getting a king in one of the halves = 1/13 + 1/13

Probability of getting a king in one of the halves = 2/13

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Answer:

(-8, 11/2)

Step-by-step explanation:

1. The midpoint between two points can be found by averaging the x-values of both points and the y-values of both points. For example, if you had the points (x, y) and (m, n), then the midpoint would be (\(\frac{x+m}{2}\), \(\frac{y+n}{2}\))

2. Calculate your midpoint. In this specific case your x-value would be (-7+-9)/2 and your y-value would be (8+3)/2, or (-8, 11/2)

To find the estimated project completion time for the given project activities, we need to first calculate the earliest start and earliest finish times and then the latest start and latest finish times.

Using the activity times given, we can calculate the earliest start and earliest finish times for each activity as follows: Activity A: Earliest start time = 0

Earliest finish time = 1

Activity B: Earliest start time = 2

Earliest finish time = 5

Activity C: Earliest start time = 5

Earliest finish time = 11

Activity D: Earliest start time = 11

Earliest finish time = 17

Activity E: Earliest start time = 5

Earliest finish time = 8 Activity F:

Earliest start time = 8

Earliest finish time = 17

Now we can calculate the latest start and latest finish times for each activity using the backward pass.

Latest finish time = 5

Latest start time = 2

Activity A: Latest finish time = 1

Latest start time = 0

Now we can calculate the slack time for each activity as follows:Activity A:

Slack time = 0

Activity B: Slack time = 0

Activity C: Slack time = 0

Activity D: Slack time = 0

Activity E: Slack time = 3

Activity F: Slack time = 0

The critical path for this project is A -> C -> D, since these activities have zero slack time. Therefore, the estimated project completion time is 17 units of time.

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Answer:

3 pounds

Step-by-step explanation:

a pound is 16oz so 3x16=48

Let x be the principal of the first loan, and y be the principal of the second loan, then, we can set the following system of equations:

Solving the first equation for x, we get:

Substituting the above result in the second equation, we get:

Solving the above equation for y, we get:

Substituting y=5000, in x=12,000-y, we get:

Answer:

The principal of the 8% interest loan was $5000, and the principal of the other loan was $7000.

Answer:

(1/2)(4)(6)(12.5) = 12(12.5) = 150 ft²

To prove that the improper Riemann integral of e^((-x^2)/2) from 0 to infinity exists, we can compare it to another integral that converges. We will use the hint provided: for large x, e^((-x^2)/2) can be estimated by e^(-x).

First, note that 0 ≤ e^((-x^2)/2) ≤ e^(-x) for all x ≥ 0, since the exponent -x^2/2 is always less than or equal to -x when x is non-negative.

Now, we will evaluate the improper integral of e^(-x) from 0 to infinity:

∫(e^(-x)dx) from 0 to infinity

We can evaluate this integral by finding the antiderivative:

-∫(e^(-x)dx) = -e^(-x) + C

Now we evaluate the limits:

Lim(a→∞) [-e^(-x)] from 0 to a

= Lim(a→∞) [-e^(-a) + e^(0)]

As a approaches infinity, e^(-a) approaches 0, so the limit becomes:

= -0 + 1 = 1

Since the improper integral of e^(-x) from 0 to infinity converges to a finite value (1), and we have 0 ≤ e^((-x^2)/2) ≤ e^(-x) for all x ≥ 0, we can conclude that the improper Riemann integral of e^((-x^2)/2) from 0 to infinity also converges, according to the comparison test for improper integrals.

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true - searching for a value in a binary search tree takes O(log n) time.

a binary search tree is a data structure where each node has at most two children, and the left child is always smaller than the parent while the right child is always larger. This structure allows for efficient searching, as we can compare the value we are searching for with the value of the current node and traverse either the left or right subtree accordingly. By doing so, we can eliminate half of the remaining nodes with each comparison, leading to a time complexity of O(log n).

searching for a value in a binary search tree takes O(log n) time, which is a relatively efficient algorithmic complexity. However, it's important to note that this assumes the tree is balanced and does not take into account worst-case scenarios where the tree may be heavily skewed.

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To convert 21.73 m to customary units, we need to use the conversion factors as follows:

meter = 39.37 inches1

inch = 2.54

cm1 foot

= 12 inches

We have:

21.7.

3 m

= 21.73 x 39.37 inches (since 1 mete

r = 39.37 inches)

= 856.301 inches

= 71 feet 4.3 inches (since 1 foot = 12 inches)

The smallest tick mark on

1" = 1' 0"

architect’s scale is 1/16 inch.

This means that there are 16 tick marks in an inch. A fractional ruler was used for scale measurements of a line on the 1/4" = 1'-0" scale. The two ends of the line correspond to 6 2.7/4" and 9 6/8". To get the length of the line in inches, we need to convert the two ends to inches, then subtract them to get the length as follows:

\(6 2.7/4" \\= 6 x 12 + 2.7\\ = 74.7"  (since 1 foot\\ = 12 inches)\\9 6/8" = 9 x 12 + 6 \\= 114" (since 1 foo\\t = 12 inches)\)

Length of the line = 114 - 74.7 = 39.3 inches (rounded off to one decimal place)

Multiplying 3/5 by

\(17/13\\ gives:\\3/5 x 17/13\\= (3 x 17)/(5 x 13)\\= 51/65\)

This is already in its lowest form.

Therefore, the answer is:51/65 (an improper fraction)

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Answer:

The answer is 544 cm

Step-by-step explanation:

Hope this helps

Answer: x=-7

Step-by-step explanation:

The equation we are given is 2.5x+10=x-0.5. We can use out algebraic properties to solve for x.

2.5x+10=x-0.5       [move like terms into one side by adding and subtracting]

2.5x-x=-0.5-10       [combine like terms]

1.5x=-10.5              [divide both sides by 1.5]

x=-7

Answer: E. :)

Step-by-step explanation:

X be the number of successes and n be the sample size

When n = 80 and X = 40 then value of g is  0.506,

When n = 200 and X = 90 then value of g is 0.448

When n = 130 and X = 60 then value of g is 0.4631

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

We can find the values of p and ĝ using the following formulas:

p = X/n

ĝ = (X + 0.5)/(n + 1)

a. n = 80 and X = 40

p = 40/80 = 0.5

ĝ = (40 + 0.5)/(80 + 1) = 0.506

b. n = 200 and X = 90

p = 90/200 = 0.45

ĝ = (90 + 0.5)/(200 + 1) = 0.448

c. n = 130 and X = 60

p = 60/130 = 0.4615

ĝ = (60 + 0.5)/(130 + 1) = 0.4631

d. 25%

Let X be the number of successes and n be the sample size.

We are given that the sample proportion is 0.25, so we have:

p = 0.25

X = p × n = 0.25 × n

To find ĝ, we can substitute X and n into the formula for ĝ:

ĝ = (X + 0.5)/(n + 1) = (0.25n + 0.5)/(n + 1)

e. 42%

Using the same approach as in part (d), we have:

p = 0.42

X = p × n = 0.42 × n

ĝ = (X + 0.5)/(n + 1) = (0.42n + 0.5)/(n + 1)

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Answer:

C(4) is less

Step-by-step explanation:

Let C(x) represent Rule C and let D(x) represent Rule D.

C(x) = 10x + 15

D(x) = 80x

C(4) = 10(4) + 15 = 40 + 15 = 55

D(4) = 80(4) = 320

Thus, C(4) is less.

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False, each objective function line is unique and not necessarily parallel to every other objective function line in a problem.

In a multi-objective optimization problem, each objective function represents a different optimization criterion or goal. These objectives can have different slopes and directions, resulting in objective function lines that are not necessarily parallel to each other. The objectives may have conflicting or complementary relationships, leading to different trade-offs and possibilities in the optimization process. Therefore, it is incorrect to assume that all objective function lines are parallel in a problem.

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The driving time along this stretch was reduced by 36% for a person who always drives at the speed limit.

To calculate the percent reduction in driving time along the stretch, we need to consider the effects of both the distance decrease and the speed increase.

First, let's assume the original distance of the stretch was D. After the reconstruction, the distance is now 0.8D (since it was decreased by 20%).

Next, let's assume the original speed limit was S. After the reconstruction, the speed limit is now 1.25S (since it was increased by 25%).

To calculate the original driving time along the stretch, we would use the formula: time = distance / speed. So the original driving time would be D/S.

After the reconstruction, the driving time would be (0.8D) / (1.25S) = 0.64D/S.

To calculate the percent reduction in driving time, we can use the formula: (original time - new time) / original time * 100%.

Plugging in the values we calculated, we get:

(original time - new time) / original time * 100% = (D/S - 0.64D/S) / (D/S) * 100% = 36%.

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Answer:

(a)V=36πh

Explanation:

• Radius = 6 meters

Part A

An equation that represents the volume V as a function of the height h is:

Part B

Using 3.14 as an approximation for π

The graph of the function is attached below: (V is on the y-axis and h is on the x-axis).

Part C

The initial equation for volume is:

When h=1

If you double the height of a cylinder, h=2:

We observe that when the height is doubled, the volume of the cylinder is also doubled.

Part D

The initial equation for volume is:

If the height of the cylinder is multiplied by 1/3, we have:

The volume of the cylinder will be divided by 3.

Using the graph, we observe a horizontal stretch of the graph by 1/3.

The given statement "In a binomial experiment, any single trial contains only two possible outcomes and successive trials are independent" is true because a binomial experiment is a type of probability distribution where the experiment has only two possible outcomes, which are considered as a "success" or a "failure."

The characteristics of a binomial experiment are as follows:There are only two possible outcomes for each trial, which are success and failure.The trials are independent of each other.The probability of success remains constant throughout the experiment.The experiments are conducted for a fixed number of trials.The probability of success is equal for all trials.The outcomes of the trials are mutually exclusive.

The binomial distribution is frequently used in data analysis when the result of an experiment can be classified into one of two categories. It is frequently used in industries like finance, economics, and engineering, as well as for studying human behaviour. The binomial probability distribution is used to calculate the probability of a certain number of successes in a given number of trials.

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(a) Most calculators can find logarithms with base 10 and base e. To find logarithms with different bases, we use the change of base formula:

log_b(x) = log(x) / log(b)

Using this formula, we can find:

log_3(6) = log(6) / log(3) ≈ 1.631

log_5(258) = log(258) / log(5) ≈ 3.424

(b) No, the result is not the same. If we perform the calculation in part (a) using In in place of log, we get the natural logarithm instead of the base-10 logarithm. To find the logarithm with a different base, we need to use the change of base formula as shown above.

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The probability that fewer than 1690 blocks meet the specification in three or more of the six lots is  0.0000428%.

1. Let's calculate the probability of a single block meeting specification:

p(block meets spec) = 0.85

p(block doesn't meet spec) = 1 - 0.85

= 0.15

The number of blocks that meet the specification follows a binomial distribution with n = 2000 and p = 0.85.

Let X be the number of blocks that meet the specification.

Therefore, P(X < 1690) can be calculated using the binomial cumulative distribution function.Using a calculator or a software, we get:

P(X < 1690)

= 0.0006 (rounded to four decimal places)

Therefore, the probability that, in a given lot, fewer than 1690 blocks meet the specification is 0.0006 or 0.06%.

2. The number of blocks that meet the specification follows a binomial distribution with n = 2000 and p = 0.85.

We need to find the number of blocks k, such that

P(X < k) = 0.70

Using a calculator or a software, we get:

k = 1743

Therefore, the 70th percentile of the number of blocks that meet the specification is 1743.3.

The number of blocks that meet the specification in each lot follows a binomial distribution with n = 2000 and p = 0.85.

The probability that fewer than 1690 blocks meet the specification in a given lot is:

P(X < 1690) = 0.0006

From part 1, we know that the probability that fewer than 1690 blocks meet the specification in a given lot is 0.0006. Let Y be the number of lots with fewer than 1690 blocks meeting the specification.

Therefore, Y follows a binomial distribution with n = 6 and p = 0.0006.

We need to find P(Y ≥ 3).

Using a calculator or a software, we get:

\(P(Y ≥ 3) = 4.28 x 10^(-7)\) (rounded to nine decimal places)

Therefore, the probability that fewer than 1690 blocks meet the specification in three or more of the six lots is 4.28 x \(10^(-7)\) or 0.0000428%.

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Answer:

If it is expression than answer 6x-6

If it is an equation 5x-16=x+10 than answer is 13/2

Step-by-step explanation:

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\(\\ \sf \longmapsto 5x-16=x+10\)

\(\\ \sf \longmapsto 5x-x=10+16\)

\(\\ \sf \longmapsto 4x=26\)

\(\\ \sf \longmapsto x=\dfrac{26}{4}\)

\(\\ \sf \longmapsto x=\dfrac{13}{2}\)

(a) The least-squares equation for the given data pairs (2,4), (3,3), and (5,6) is ŷ = 1.143x + 0.857.

(b) The least-squares equation for the given data pairs (4,2), (3,3), and (6,5) is ŷ = 0.714x + 1.143.

(d) Solving the equation from part (a) for x gives x = 0.875y - 0.750

(a) To find the least-squares equation for the given data pairs, we first need to calculate the slope (m) and y-intercept (b) of the line that best fits the data. The slope is given by the formula:

m = (NΣ(xy) - ΣxΣy) / (NΣ(x^2) - (Σx)^2)

where N is the number of data points (in this case, 3). Plugging in the values from the data pairs, we get:

m = ((338) - (1013)) / ((3*38) - (10^2)) = 0.857

Next, we can use the point-slope formula to find the equation of the line:

y - y1 = m(x - x1)

Choosing the point (3,3) as our reference point, we get:

y - 3 = 0.857(x - 3)

Simplifying this equation, we get:

y = 1.143x + 0.857

which is the least-squares equation for the given data pairs.

(b) Following the same procedure as in part (a), we get:

m = ((314) - (134)) / ((3*29) - (10^2)) = 0.714

Choosing the point (3,3) again as our reference point, we get:

y - 3 = 0.714(x - 3)

Simplifying this equation, we get:

y = 0.714x + 1.143

which is the least-squares equation for the given data pairs

(d) Solving the equation from part (a) for x, we get:

y = 1.143x + 0.857

y - 0.857 = 1.143x

x = (y - 0.857) / 1.143

Simplifying this expression, we get

x = 0.875y - 0.750

which is the answer to part (d) of the question.

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