Differentiate each function with respect to x.
4) y = (3∛(x^2 )+ 1) (2x²+2)
5) y = (〖4x〗^(5 )+ 3)/(2 - x^(-5) )
6) y = ((5x^4 - 1)^5+ 3 )^4
Answers
In conclusion Final simplified answer: dy/dx = 400x^3 * ((5x^4 - 1)^5 + 3)^3 * (5x^4 - 1)^4
4) To differentiate y = (3∛(x^2) + 1) (2x^2 + 2) with respect to x, we will apply the product rule:
y = (3∛(x^2) + 1) (2x^2 + 2)
Using the product rule:
dy/dx = (3∛(x^2) + 1) * d/dx(2x^2 + 2) + (2x^2 + 2) * d/dx(3∛(x^2) + 1)
Taking the 4) To differentiate y = (3∛(x^2) + 1) (2x^2 + 2) with respect to x, we will apply the product rule:
y = (3∛(x^2) + 1) (2x^2 + 2)
Using the product rule:
dy/dx = (3∛(x^2) + 1) * d/dx(2x^2 + 2) + (2x^2 + 2) * d/dx(3∛(x^2) + 1)
Taking the derivatives of each term:
dy/dx = (3∛(x^2) + 1) * (4x) + (2x^2 + 2) * (d/dx(3∛(x^2))) + 0
Simplifying:
dy/dx = 4x(3∛(x^2) + 1) + (2x^2 + 2) * (d/dx(3∛(x^2)))
To find d/dx(3∛(x^2)), we can apply the chain rule:
d/dx(3∛(x^2)) = 3 * d/dx(x^(2/3)) * d/dx(x^2) = 3 * (2/3) * x^(-1/3) * 2x
Simplifying:
d/dx(3∛(x^2)) = 4x^(5/3)
Substituting this back into the previous equation:
dy/dx = 4x(3∛(x^2) + 1) + (2x^2 + 2) * (4x^(5/3))
Final simplified answer:
dy/dx = 4x(3∛(x^2) + 1) + 8x^(7/3) + 8x^2 + 2
5) To differentiate y = (4x^5 + 3)/(2 - x^(-5)), we will use the quotient rule:
y = (4x^5 + 3)/(2 - x^(-5))
Using the quotient rule:
dy/dx = [(2 - x^(-5)) * d/dx(4x^5 + 3) - (4x^5 + 3) * d/dx(2 - x^(-5))] / (2 - x^(-5))^2
Taking the derivatives of each term:
dy/dx = [(2 - x^(-5)) * (20x^4) - (4x^5 + 3) * d/dx(2 - x^(-5))] / (2 - x^(-5))^2
To find d/dx(2 - x^(-5)), we have:
d/dx(2 - x^(-5)) = 0 - (-5x^(-6)) = 5x^(-6)
Substituting this back into the previous equation:
dy/dx = [(2 - x^(-5)) * (20x^4) - (4x^5 + 3) * 5x^(-6)] / (2 - x^(-5))^2
Simplifying:
dy/dx = [(40x^4 - 20x^(-1)) - (20x^(-1) + 15x^(-6))] / (2 - x^(-5))^2
Final simplified answer:
dy/dx = (40x^4 - 35x^(-1) -
15x^(-6)) / (2 - x^(-5))^2
6) To differentiate y = ((5x^4 - 1)^5 + 3)^4, we will apply the chain rule multiple times:
y = ((5x^4 - 1)^5 + 3)^4
Using the chain rule:
dy/dx = 4 * ((5x^4 - 1)^5 + 3)^3 * d/dx((5x^4 - 1)^5 + 3)
To find d/dx((5x^4 - 1)^5 + 3), we can apply the chain rule again:
d/dx((5x^4 - 1)^5 + 3) = 5 * ((5x^4 - 1)^4) * d/dx(5x^4 - 1)
Taking the derivative of (5x^4 - 1):
d/dx(5x^4 - 1) = 20x^3
Substituting this back into the previous equation:
d/dx((5x^4 - 1)^5 + 3) = 5 * ((5x^4 - 1)^4) * (20x^3)
Simplifying:
d/dx((5x^4 - 1)^5 + 3) = 100x^3 * (5x^4 - 1)^4
Substituting this back into the original equation:
dy/dx = 4 * ((5x^4 - 1)^5 + 3)^3 * 100x^3 * (5x^4 - 1)^4
Final simplified answer:
dy/dx = 400x^3 * ((5x^4 - 1)^5 + 3)^3 * (5x^4 - 1)^4of each term:
dy/dx = (3∛(x^2) + 1) * (4x) + (2x^2 + 2) * (d/dx(3∛(x^2))) + 0
Simplifying:
dy/dx = 4x(3∛(x^2) + 1) + (2x^2 + 2) * (d/dx(3∛(x^2)))
To find d/dx(3∛(x^2)), we can apply the chain rule:
d/dx(3∛(x^2)) = 3 * d/dx(x^(2/3)) * d/dx(x^2) = 3 * (2/3) * x^(-1/3) * 2x
Simplifying:
d/dx(3∛(x^2)) = 4x^(5/3)
Substituting this back into the previous equation:
dy/dx = 4x(3∛(x^2) + 1) + (2x^2 + 2) * (4x^(5/3))
Final simplified answer:
dy/dx = 4x(3∛(x^2) + 1) + 8x^(7/3) + 8x^2 + 2
5) To differentiate y = (4x^5 + 3)/(2 - x^(-5)), we will use the quotient rule:
y = (4x^5 + 3)/(2 - x^(-5))
Using the quotient rule:
dy/dx = [(2 - x^(-5)) * d/dx(4x^5 + 3) - (4x^5 + 3) * d/dx(2 - x^(-5))] / (2 - x^(-5))^2
Taking the derivatives of each term:
dy/dx = [(2 - x^(-5)) * (20x^4) - (4x^5 + 3) * d/dx(2 - x^(-5))] / (2 - x^(-5))^2
To find d/dx(2 - x^(-5)), we have:
d/dx(2 - x^(-5)) = 0 - (-5x^(-6)) = 5x^(-6)
Substituting this back into the previous equation:
dy/dx = [(2 - x^(-5)) * (20x^4) - (4x^5 + 3) * 5x^(-6)] / (2 - x^(-5))^2
Simplifying:
dy/dx = [(40x^4 - 20x^(-1)) - (20x^(-1) + 15x^(-6))] / (2 - x^(-5))^2
Final simplified answer:
dy/dx = (40x^4 - 35x^(-1) -
15x^(-6)) / (2 - x^(-5))^2
6) To differentiate y = ((5x^4 - 1)^5 + 3)^4, we will apply the chain rule multiple times:
y = ((5x^4 - 1)^5 + 3)^4
Using the chain rule:
dy/dx = 4 * ((5x^4 - 1)^5 + 3)^3 * d/dx((5x^4 - 1)^5 + 3)
To find d/dx((5x^4 - 1)^5 + 3), we can apply the chain rule again:
d/dx((5x^4 - 1)^5 + 3) = 5 * ((5x^4 - 1)^4) * d/dx(5x^4 - 1)
Taking the derivative of (5x^4 - 1):
d/dx(5x^4 - 1) = 20x^3
Substituting this back into the previous equation:
d/dx((5x^4 - 1)^5 + 3) = 5 * ((5x^4 - 1)^4) * (20x^3)
Simplifying:
d/dx((5x^4 - 1)^5 + 3) = 100x^3 * (5x^4 - 1)^4
Substituting this back into the original equation:
dy/dx = 4 * ((5x^4 - 1)^5 + 3)^3 * 100x^3 * (5x^4 - 1)^4
Final simplified answer:
dy/dx = 400x^3 * ((5x^4 - 1)^5 + 3)^3 * (5x^4 - 1)^4
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Related Questions
If the mean of a data set is 47 with a standard deviation of 3.5, what is the z score of 45?
Answers
Step-by-step explanation:
z-score is the number of standard deviations away from the mean
45 is -2 away from the mean of 47
-2 / 3.5 = - . 571
Write the number with
scientific notation:
283 X 10^5
Answers
Answer:
2.83 x 10^5 = 283,000
Step-by-step explanation:
When you have the 10^5 multiplying to 2.83, you are moving the number further to the left of the decimal, making it larger every power of 10. if it was 4 powers of 10, the answer would be 28,300, 3 powers of 10 would be 2,830, etc.
PS. I think you forgot to add the decimal in 2.83, 283 x 10^5 is not written in Scientific Notation.
In a company which services air-conditioner units, the revenue,
$r, is given by the equation r = 20x, where x is the number of
units serviced. The operating cost, $c, is given by the equation
c= 3600 + 4x.
The profit, $P, is given by the expression, r — c.
(a) Find a formula for P in terms of x only.
(b) For each of the following cases, find the value of x if
(i) the revenue earned is twice that of the cost,
(ii)the profit earned is $292 more than one third of the revenue
earned.
Answers
Answer:
p(x) = 16x -3600600 units417 unitsStep-by-step explanation:
The problem statement gives expressions and relations for revenue, cost, and profit. Substitute and simplify or solve, as appropriate.
__
(a)Given: r(x) = 20x; c(x) = 3600+4x; p(x) = r(x) -c(x)
The formula for p(x) is ...
p(x) = (20x) -(3600 +4x) . . . . substitute for r(x) and c(x)
p(x) = 16x -3600 . . . . . . . . simplify
__
(b-i)r(x) = 2·c(x) . . . . given relation for revenue and cost
20x = 2(3600 +4x) . . . . substitute for each
12x = 7200 . . . . . . . simplify and subtract 8x
x = 600 . . . . . . . divide by 12
Revenue is twice the cost when x = 600 units.
__
(b-ii)p(x) = 292 +1/3r(x) . . . . given relation for profit and revenue
16x -3600 = 292 +1/3(20x) . . . . . substitute for each
28/3x = 3892 . . . . . . . . add 3600 -20/3x
x = 417 . . . . . . . . multiply by 3/28
Profit is $292 more than 1/3 the revenue earned for 417 units.
when a number is subtracted from 28 and the difference is divided by that number, the result is 3. what is the value of the number?
Answers
The value of the number is 7.
Let's assume that the number is x. The given equation is: $\frac{28-x}{x}=3$Multiplying both sides by x to remove the denominator, we get:28 - x = 3xAdding x to both sides, we get:28 = 4xDividing by 4 on both sides, we get: x = 7 Therefore, the value of the number is 7. The given equation is solved using simple algebraic manipulation. Here, we have to find the value of the number.
Let's assume the value of the number to be x. Using the given equation, we get $\frac{28-x}{x}=3$. We multiply both sides by x to remove the denominator. After doing so, we get 28-x=3x. We add x to both sides to get 28 = 4x. By dividing both sides by 4, we find that the value of x is 7.
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Find the value of x.
Answers
Answer:
x = 25
Step-by-step explanation:
One can use the Line Tangent to a Circle theorem to solve this problem. The Line Tangent to a Circle theorem states that when two non-parallel lines are tangent to a circle (the lines touch the circle at a single point), then the distance between the intersection point and the point of tangency is the same for both lines. This theorem does go by other names, but the actual theorem content is the same.
Using this one can form the equation;
BA = CA
Substitute,
2x + 3 = 53
Inverse operations,
2x + 3 = 53
-3 -3
2x = 50
/2 /2
x = 25
I really need help with this question !!!!!!!!!!!!!!!!!
Answers
Mutpliy please I need to finish this:)
Answers
Answer: 1. p^24 2. r^7 3. s^35 4. u^13
Step-by-step explanation: Hope this helps!
in the least squares regression line y=3-2x, the predicted value of y equals: a. 1.0 when x = −1.0 b. 2.0 when x = 1.0 c. 2.0 when x = −1.0 d. 1.0 when x = 1.0
Answers
The predicted value of y equals 1.0 when x = 1.0 in the given least squares regression line y=3-2x. So the correct answer is (D) 1.0 when x = 1.0.
The predicted value of y in the least squares regression line y=3-2x can be found by substituting the given values of x in the equation and solving for y.
a) When x = -1.0, the predicted value of y would be:
y = 3 - 2(-1)
y = 3 + 2
y = 5
So, the answer is not option a.
b) When x = 1.0, the predicted value of y would be:
y = 3 - 2(1)
y = 3 - 2
y = 1
So, the answer is option d.
c) When x = -1.0, we already found the predicted value of y to be 5. Therefore, the answer is not option c.
d) When x = 1.0, we already found the predicted value of y to be 1. Therefore, the answer is option d.
In summary, the predicted value of y equals 1.0 when x = 1.0 in the given least squares regression line y=3-2x.
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Find the distance between the two points in simplest radical form.
Answers
The distance bewteen the points (-3,5) and (3,1) in a simple radical form is 2√13.
What is the distance between the given points?The distance formula used in finding the distance between two points is expressed as;
d = √( ( x₂ - x₁ )² + ( y₂ - y₁ )² )
From the graph;
Point A: (-3,5)
x₁ = -3
y₁ = 5
Point B: (3,1)
x₂ = 3
y₂ = 1
Plug the given values into the distance formula and simplify.
\(d = \sqrt{( x_2 - x_1)^2 + (y_2 -y_1 )^2} \\\\d = \sqrt{( 3-(-3))^2 + (1 -5)^2} \\\\d = \sqrt{( 3+ 3)^2 + (1 -5)^2} \\\\d = \sqrt{( 6)^2 + (-4)^2} \\\\d = \sqrt{36 + 16} \\\\d = \sqrt{52}\\\\d = 2\sqrt{13}\)
Therefore, the distance between the points is 2√13.
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While shopping for clothes, Tracy spent $26 less than 2 times what Curtis spent. Tracy spent $12. Write and solve an equation to find how much Curtis spent. Let x represent how much Curtis spent.
Answers
Answer:
Curtis spent $76
(x=76)
Step-by-step explanation:
12 +26
Tracy spent 12 dollars, which was 26 dollars less two times what Curtis spent
(38)2
You then take 12+26 and multiply it by 2
76
brainliest pls?
Write a Haiku about science please! Have a great day :)
Answers
Answer:
in Earth, space, the trees
science is all around us
answer life's questions
Step-by-step explanation:
Haikus must be written with 5 syllables in the first line, 7 in the second, and 5 again in the 3rd, so they are naturally limited and simplistic. Hope this helps, and brainliest is always appreciated! Enjoy your day bro!
Zara is preparing a juice blend.In her recipe, the amount of water is twice the amount of strawberry juice, and amount of lemon juice is 1/5 the amount of strawberry juice. What is the ratio of the lemon water?
Answers
The ratio of the lemon water is 10:1
How to determine the ratioFrom the information, we have that;
The ratio of water to strawberry juice is 2 : 1
That of strawberry juice to lemon juice is 5: 1
The, we have that of water to lemon juice to be 10: 1 when compared
Hence, the ratio of the lemon water is 10: 1
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Please help!! Need the answer
Answers
In a town, 30% of the households own a dog, 20% own a cat, and 60% own neither a dog nor a cat. If we select a household at random, what is the chance that they own both a dog and a cat?. Please give a reason as to how you found the answer. Two steps, 1) find the answer and show step by step process and 2) this part is important, please explain in 200 words how you found the answer, give logical and statastical reasoning. Explain how you arrived at your answer.
Answers
To find the probability that a randomly selected household owns both a dog and a cat, we need to calculate the intersection of the probabilities of owning a dog and owning a cat. The probability can be found by multiplying the probability of owning a dog by the probability of owning a cat, given that they are independent events.
Step 1: Calculate the probability of owning both a dog and a cat.
Given that owning a dog and owning a cat are independent events, we can use the formula for the intersection of independent events: P(A ∩ B) = P(A) * P(B).
Let P(D) be the probability of owning a dog (0.30) and P(C) be the probability of owning a cat (0.20). The probability of owning both a dog and a cat is P(D ∩ C) = P(D) * P(C) = 0.30 * 0.20 = 0.06.
Therefore, the probability that a randomly selected household owns both a dog and a cat is 0.06 or 6%.
Step 2: Explanation and Reasoning
To find the probability of owning both a dog and a cat, we rely on the assumption of independence between dog ownership and cat ownership. This assumption implies that owning a dog does not affect the likelihood of owning a cat and vice versa.
Using the information provided, we know that 30% of households own a dog, 20% own a cat, and 60% own neither. Since the question asks for the probability of owning both a dog and a cat, we focus on the intersection of these two events.
By multiplying the probability of owning a dog (0.30) by the probability of owning a cat (0.20), we obtain the probability of owning both (0.06 or 6%). This calculation assumes that the events of owning a dog and owning a cat are independent.
In summary, the probability of a household owning both a dog and a cat is 6%, which is found by multiplying the individual probabilities of dog ownership and cat ownership, assuming independence between the two events.
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What is the 50th term of Arithmetic sequence 9,2,-5
Answers
Answer:
- 334
Step-by-step explanation:
There is a common difference between consecutive terms in the given sequence, that is
d = 2 - 9 = - 5 - 2 = - 7
This indicates the sequence is arithmetic with n th term
\(a_{n}\) = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = 9 and d = - 7 , thus
\(a_{50}\) = 9 + (49 × - 7) = 9 - 343 = - 334
There are 32 students mrs.Bennett ordered 512 pencils how many will each student receive draw an array
Answers
Answer:
16
Step-by-step explanation:
Factor.
y²-9 please help me with this
Answers
Since both terms are perfect squares, factor using the difference of squares formula,
a2−b2=(a+b)(a−b) where a=y and b=3.
(y+3)(y−3)
1) Please help. Given that line a is parallel to line b and the slope of line a is 2 ,what is the slope of line b?
Enter your answer as a number.
Answers
Answer: slope for line b is 2
Step-by-step explanation:
If a line is parallel to another, that means they have the same slope, different y-intercept.
Since it's given that a is parallel to b, that means the slope is the same, thus the slope of b is 2.
need help? will get brainlylist
Answers
Answer:
its the first answer.
hope this helps you a lot.
Chord is a line that joins any two points on the circle
AC,BC
OPTION A is the correct answer
20. For the data in the following sample: 10, 6, 8, 6, 5 a. Find the mean and the standard deviation. b. Now change the score of X 5 10 to X 5 0, and find the new mean and standard deviation. c. Describe how one extreme score influences the mean and standard deviation.
Answers
By replacing the extreme score of 10 with 0, the mean and standard deviation will be affected and will become 5 and 2.68 and the original mean and standard deviation were 7 and 1.79 respectively.
a. Mean: To find the mean, sum all the scores and divide by the number of scores. For the given data (10, 6, 8, 6, 5), the sum is 35, and since there are five scores, the mean is 35/5 = 7.
Standard Deviation: To find the standard deviation, we first calculate the deviations of each score from the mean. The deviations are (10-7), (6-7), (8-7), (6-7), and (5-7), which are 3, -1, 1, -1, and -2, respectively.
Then, square each deviation, resulting in 9, 1, 1, 1, and 4. The average of these squared deviations is (9+1+1+1+4)/5 = 16/5 = 3.2. Finally, take the square root of the average squared deviation to get the standard deviation, which is √3.2 ≈ 1.79.
b. Changing the score of 10 to 0, the new data set becomes (0, 6, 8, 6, 5).
New Mean: The sum of the new data set is 0+6+8+6+5 = 25, and since there are still five scores, the new mean is 25/5 = 5.
New Standard Deviation: Following the same steps as before, the deviations from the new mean are (-5, 1, 3, 1, 0), which result in squared deviations of 25, 1, 9, 1, and 0.
The average of these squared deviations is (25+1+9+1+0)/5 = 36/5 = 7.2. Taking the square root of the average squared deviation gives the new standard deviation, which is √7.2 ≈ 2.68.
c. One extreme score, such as the initial score of 10, has a significant impact on both the mean and standard deviation. The mean represents the central tendency of the data, and when an extreme score is present, it pulls the mean towards it.
In this case, the mean decreased from 7 to 5 when the extreme score was changed to 0. The standard deviation measures the spread or variability of the data, and extreme scores can widen the spread.
Thus, by replacing the extreme score of 10 with 0, the standard deviation increased from 1.79 to 2.68, indicating a greater dispersion in the data.
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the perimeter of a rectangle is 20cm. if the breadth of the rectangle is 2cm what is it's area
Answers
Answer:
perimeter =20cmbreadth=2cmlength=?we know that
perimeter =2*(l+b)
20=2*(l+2)
20=2l+4
2l=20-4
2l=16
l=16/2
l=8
Identify the action verb(s) in the sentence.
People in church prayed, and an angel woke Peter.
Answers
The bolded words represents the verbs in the statement as -
People in church prayed, and an angel woke Peter.
What is a verb?Verbs are words that show an action (sing), occurrence (develop), or state of being (exist).
Given is the statement as -
People in church prayed, and an angel woke Peter.
The verbs in the given statement are {bolded words} -
People in church prayed, and an angel woke Peter.
Therefore, the bolded words represents the verbs in the statement as -
People in church prayed, and an angel woke Peter.
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a radio station broadcasts a signal over an area with a 120-mile diameter. the population density of the area is 100 people per square mile. how many people are within receiving distance of the broadcast signal?
Answers
The radio station can reach around 1,030,400 people within its coverage area.
Using the equation, calculate the size of the circular circle that the radio station signal can cover.
A = πD²/4 is the area and D is the diameter. using the pi-number 3.14.
r = 120 / 2 = 60 miles
The density of the area: 100 people per sq. mile
A = r² π = 60² · 3.14 = 3600 · 3.14 = 11,304 sq. miles
11,304 · 100 = 1,030,400
or
A = (3.14)(120 mi) (120 mi)
² / 4 \s A = 11304 mi²
being aware that 100 individuals reside in each square mile.
total population receiving the signal =11304 mi² x (100 people / 1 mi²)
= 1,130,400
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Which of the following is not a type of effectiveness MIS metric?
Customer satisfaction
Conversion rates
Financial
Response time
Answers
"Financial" as it is not an effectiveness MIS metric.
To determine which one is not an effectiveness MIS metric, we need to understand the purpose of these metrics. Effectiveness MIS metrics measure how well a system is achieving its intended goals and objectives.
Customer satisfaction is a common metric used to assess the effectiveness of a system. It measures how satisfied customers are with the product or service provided.
Conversion rates refer to the percentage of website visitors who complete a desired action, such as making a purchase. This metric is often used to assess the effectiveness of marketing efforts.
Financial metrics, such as revenue and profit, are crucial indicators of a system's effectiveness in generating financial returns.
Response time measures the speed at which a system responds to user requests, which is an important metric for evaluating system performance.
Therefore, based on the given options, "Financial" is not a type of effectiveness MIS metric. It is a separate category of metrics that focuses on financial performance rather than the overall effectiveness of a system.
In summary, the answer is "Financial" as it is not an effectiveness MIS metric.
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I Need Help.
I'm on this worksheet, and the last question is the hardest.
The question is 3 + 5 = _
Lol it's a joke.
Answers
Answer:
haha 8 obvi
Step-by-step explanation
Answer:
8 eight ate late
Meeeep help I'm doing 6 the grade work cuz of my disabilities
Answers
Answer: Robinson's
hope my ans helps you
Step-by-step explanation:
pls mark me as brainly
You deposit $2500 in a bank account. Find the balance after 3 years for an account that pays 2.5% annual interest compounded monthly. Round to the nearest dollar.
Answers
The balance in the account after three years, rounded to the nearest dollar, is $2711.
To find the balance after three years for an account that pays 2.5% annual interest compounded monthly when $2500 is deposited in the account, you need to use the formula for compound interest.
A = P(1 + r/n)^(nt), whereA is the balance after three years, P is the principal amount ($2500), r is the annual interest rate (2.5%),
n is the number of times the interest is compounded per year (12 months), and t is the time in years (3 years).
Substituting the values in the formula,
we get:A = 2500(1 + 0.025/12)^(12*3)A
= 2500(1.00208333)^36A
= 2500(1.084297)A = $2710.74
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Erik is performing a marble experiment in math class. His teacher places an equal number of black, red, and white marbles in a bag. Then, Erik randomly takes out a marble, records the result, and puts the marble back in the bag. Each of the first four times Erik takes out a marble, he gets a black marble. A. What is the theoretical probability of Erik picking a black marble next time
Answers
Answer:
1/3
Step-by-step explanation:
The base of a rectangular pyramid has a length of 4 feet and a width of 3 feet. The height of the pyramid is 6 feet. Find the volume of the pyramid.
Answers
Answer:
24
Step-by-step explanation:
volume of the pyramid=length*width* height*1/3
Consider the following problem with 5 activities A1, A2, A3, A4, A5.
Activity A1 can be started immediately and take 2 days to complete.
Activity A2 depends on A1, and takes 2 days to complete.
Activity A3 depends on A2, and takes 2 days to complete.
Activity A4 depends on A3, and takes 2 days to complete.
Activity A5 depends on A4, and takes 2 days to complete.
Moreover, at the end of activity A4, there is 20% chance that we will have redo activity A3. Assume that this rework can happen only once.
Required:
What is the probability of completing the project in 10 or fewer days?
Answers
The variance of the project completion time is 0, which indicates that the probability of completing the project in 10 or fewer days is 0 or approximately 0 (rounded to four decimal places). The earliest completion time (ECT) of the project is the shortest time to complete the project by the most favorable scenarios.
The critical path is A₁→A₂→A₃→A₄→A₅, and the expected duration of the project is 10 days. The 20% chance of rework occurs only once, which will increase the duration of Activity A₃ by 2 days.
The resulting duration of Activity A₃ will be 4 days instead of 2 days. However, there is no impact on the expected duration of the entire project as there is a float of 2 days for Activity A₄.
The rework has no impact on the critical path of the project, which is A₁→A₂→A₃→A₄→A₅. The expected duration of the project is 10 days, which is calculated as follows: ECT = the sum of expected durations of the activities on the critical path
= 2 + 2 + 2 + 2 + 2
= 10 days
The variance of the project completion time is 0, which indicates that the probability of completing the project in 10 or fewer days is 0 or approximately 0 (rounded to four decimal places).
To know more about variance, refer
https://brainly.com/question/9304306
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