Answer:
b=80-8t
Step-by-step explanation:
"b" represents the charge remaining
"t" represents the number of hrs that have passed.
"80" is the reference we will be subtracting the hours from.
"8" is the percentage per hour we will be subtracting
therefore, the equation b=80-8t would solve for the remaining battery after "t" number of hours.
I'll mark you brainlyist, if I know how to do it, if you help me out real quick thx
Answer:
4 in
Step-by-step explanation:
as you see from the first rectangle it has been reduced 3 times of length
so the breadth also should be reduced 3 times
Answer:
x = 4
Step-by-step explanation:
the simplest way to do that is to divide
12 / 18 = 2 / 3
then we move to the another square:
x / 6 = 2 / 3
x = 6 x 2 / 3
x = 4
.. ..
You estimate the weight of an apple to be 6 ounces. The actual weight of an apple is 4 ounces. What is your percent error?
help
Answer:
150%
Step-by-step explanation:
I hope this helps
!!! WILL GIVE BRAINLIEST !! AND 15 POINTS PLS ANSWER !!!
Answer:
Yes, SASStep-by-step explanation:
As per diagram, the congruent sides/angles are:
HL ≅ KL - givenLJ ≅ JL - shared side∠HJL ≅ ∠KLJ - alternate interior angles are congruent as HJ║KLSo we have two sides congruent and included angle, this is Side-Angle-Side or SAS
Create a new Word doc for the elements of this assignment. Evaluate your process using 1 of the following: Use the lean concept to find ways to eliminate waste and improve the process. Use SPC or Six Sigma to reduce defects or variances in the process. Add your evaluation to your Word doc with the header "Process Evaluation." Continue to Step 2: Control Chart and Process Metrics.
this is for Starbucks
Evaluation of Control Chart and Process Metrics
Complete the following in Excel:
Calculate the defined process metrics including variation and process capability.
Develop and display a control chart for the process.
Evaluate the control chart and process metrics using Statistical Process Control (SPC) methods. Determine whether the process could benefit from the use of Six Sigma, Lean, or other tools. (Include all calculation and charts.)
Write your evaluation in your assignment Word doc under the header "Evaluation of Control Chart and Process Metrics."
question 2 also posted
The step 1 will process with beginning, mapping, and optimising. The step 2 will includes matrices calculation, creating control chart and analysis.
The steps to be followed for step 1 are as follows-
Begin with value identification which is the creation of word document. Map the value stream to remove redundant activites followed by waste elimination. Then work on to improve the efficiency by using templates, headers, using keyboard shortcuts and enabling autosave.
To proceed to step 2 and check if the process could benefit from other tools, consider these three actions: 1. Calculating the metrices that includes variation and process capability. 2. Formulate the control chart for process. 3. Analyse the metrices and control chart via the SPC method.
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If f(x) = x and g(x) = X + 2, which statement about the graphs of the functions is true?
A. g is a translation of f 2 units down.
B. g is a translation of f 2 units to the right.
C. g is a translation of f 2 units to the left and 2 units down.
D. g is a translation of f 2 units up.
PLEASE HELP ME DUE IN 10 minutes!!!
Answer: D
Step-by-step explanation: +2 would be an upwards translation
Any Suggestions on what to do here? I already restarted my PC twice, cleared my browsing data, and rebooted the wifi network....
Oh yea and whats 5 to the square root of 625
Answer:
Use a factor tree. For example, 625 = 5 x 125 = 5 x 5 x 25 = 5 x 5 x 5 x 5. Because there are 4 fives, and we are looking for the square root, (5 x 5) (5 x 5) = 625. Therefore the square root of 625 is 25.
given event a, event b, and event c. event a and event b are mutually exclusive. event a and event c are not mutually exclusive.
Event A and Event B being mutually exclusive means that they cannot occur simultaneously. On the other hand, Event A and Event C not being mutually exclusive means that they can occur together or overlap.
Mutually exclusive events refer to events that cannot happen at the same time. If Event A occurs, then Event B cannot occur, and vice versa. For example, if Event A represents "heads" in a coin toss, and Event B represents "tails," it is impossible for both events to happen simultaneously. Therefore, the occurrence of one event precludes the occurrence of the other.
Non-mutually exclusive events, as in the case of Event A and Event C, allow for the possibility of both events occurring together. For instance, if Event A represents "rain" and Event C represents "using an umbrella," it is possible for it to rain (Event A) and for someone to be using an umbrella (Event C) at the same time. In this case, the occurrence of Event A does not exclude the occurrence of Event C.
Understanding whether events are mutually exclusive or not is essential in probability theory, as it influences how probabilities are calculated. When events are mutually exclusive, the probability of either event occurring is simply the sum of their individual probabilities. However, when events are not mutually exclusive, the probability of both events occurring requires a different calculation, such as using conditional probabilities or the inclusion-exclusion principle.
In summary, Event A and Event B are mutually exclusive, meaning they cannot occur simultaneously, while Event A and Event C are not mutually exclusive, allowing for the possibility of both events occurring together.
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In ΔEFG, g = 34 inches, e = 72 inches and ∠F=21°. Find the area of ΔEFG, to the nearest square inch.
The area of triangle EFG, to the nearest square inch, is approximately 1061 square inches.
To find the area of triangle EFG, we can use the formula:
\(Area = (1/2) \times base \times height\)
In this case, the base of the triangle is FG, and the height is the perpendicular distance from vertex E to side FG.
First, let's find the length of FG. We can use the law of cosines:
FG² = EF² + EG² - 2 * EF * EG * cos(∠F)
EF = 72 inches
EG = 34 inches
∠F = 21°
Plugging these values into the equation:
FG² = 72² + 34² - 2 * 72 * 34 * cos(21°)
Solving for FG, we get:
FG ≈ 83.02 inches
Next, we need to find the height. We can use the formula:
height = \(EF \times sin( \angle F)\)
Plugging in the values:
height = 72 * sin(21°)
height ≈ 25.52 inches
Now we can calculate the area:
\(Area = (1/2) \times FG \times height\\Area = (1/2)\times 83.02 \times 25.52\)
Area ≈ 1060.78 square inches
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What is the surface area of a right circular cylindrical oil can, if the radius of its base is 4 inches and its height is 11 inches?
a. 85 pi in.2
b. 100 pi in.2
c. 120 pi in.2
d. 225 pi in.2
Answer:
c
Step-by-step explanation:
In a polynomial division problem, the dividend does not have an X^3-term. When the problem is written in long division form, what should be the coefficient of the x^3-term in the dividend? Α. 0 B.-1 C. 1 D. 3
Answer:
0
Step-by-step explanation:
When a number is not included or used, it can be considered 0.
This makes sense, because if it had a actualy value, it would effect the polynomial, and change the answer.
The only time it would not effect the polynomial is when it 0.
Hope this makes sense :D
a warehouse charges its customers per day for every cubic feet of space used for storage. the figure below records the storage used by one company over a month. how much will the company have to pay?
The company will have to pay $300,000 as warehouse charges for tis company.
Figure 1 is the original, but Figure 2 has been adjusted to make it easier to see a triangle and a rectangle.
The total number of cubic feet of storage multiplied by the number of days of storage usage is represented by the size of the triangle and rectangle.
Hence,
Total Area = Triangle Area + Rectangle Area
= 1/2 × base × height + length × breadth
= ½ 30 x (30,000 – 10,000) + 30 x 10,000
= 300,000 + 300,000
= 600,000
Because 10 cubic feet of storage costs $5 per day, the total amount the corporation must pay is
= (5 x 600,000) / 10 = $300,000
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Which is the largest group from among this list?a. Accessible population b. Control group c. Sample d. Target population
The largest group would be the target population as it encompasses all individuals or objects of interest, while the other groups are subsets or smaller samples of this larger group.
Out of the four groups listed, the largest group would be the target population. The target population is the total group of individuals or objects that the researcher is interested in studying or gathering information about. It is the group that the researcher wants to make conclusions about based on their study results.
The accessible population is a subset of the target population and refers to the group of individuals or objects that are accessible and available for the researcher to study. This group may be smaller than the target population if some individuals or objects are not accessible or willing to participate in the study. The sample is a smaller subset of the accessible population that is actually studied and analyzed. The sample is chosen to be representative of the accessible population and the target population.
The control group is a specific type of sample used in experimental research. It is a group that does not receive the intervention or treatment being studied and is used to compare against the group that does receive the intervention or treatment.
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Kindly help to solve questions
Applying notable products, the expanded expressions are given by:
a) (x + 1)² = x² + 2x + 1.
b) (x - 2)² = x² - 4x + 4.
c) (x + 3)² = x² + 6x + 9.
What is the notable product for the square of the sum?The notable product for the square of the sum is given by:
(a + b)² = a² + 2ab + b².
Hence:
a) (x + 1)² = x² + 2x + 1.
c) (x + 3)² = x² + 6x + 9.
What is the notable product for the square of the subtraction?The notable product for the square of the subtraction is given by:
(a - b)² = a² - 2ab + b².
That is, just the middle term changes compared to the square of the sum.
Hence:
b) (x - 2)² = x² - 4x + 4.
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assume that each of 2000 frogss living near a nuclear power plant is exposed to particles of a certain kind of radiation at an average rate of one per week. suppose that each hit by a particle is harmless with probability 1 - 10-5 , and produces a tumor with probability 10-5 . find the approximate distribution of
distribution of the total number of tumors produced in the whole population over a one-year period by this kind of radiation is 0, 1, 2, ..................104000.
let, x denote the total number of hits,
y denotes the number of hits by a particle in a year or an individual,
one per week ⇒ 52 per year
therefore, rate = 52 per year
since it is very rare to hit all individuals, we can use Poisson distribution.
therefore by using the formula p (x = x) = (e^(-rate) × rateˣ) ÷ x! ; x = 0, 1, 2, ............( 2000 × 52)
p (x = 2) = (e⁻⁵² × 52ˣ) ÷ x! ; x = 0, 1, 2, ............104000
now each hit has a harm of probability 10⁻⁵.
so p(total no. of tumors produced over a one year period)
= {e⁻⁵² × 52ˣ} ÷ x! × 10⁻⁵ ; x = 0, 1, 2, ............104000
therefore total no. of tumors = 2000 × (e⁻⁵² × \(52^{x.10^{-5} }\) ) ÷ x! × xⁿ ; x = 0, 1, 2, ............104000
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(complete question)
Assume that each of the 2000 individuals living near a nuclear power plant is exposed to particles of a certain kind of radiation at an average rate of one per week. Suppose that each hit by a particle is harmless with a probability of 1 - 10⁻⁵, and produces a tumor with a probability of 10⁻⁵. Find the approximate distribution of the total number of tumors produced in the whole population over a one-year period by this kind of radiation.
A project under consideration has a 10-year projected life. The initial investment for the project is estimated to have a mean of $10,000 and a standard deviation of $1,000. The annual receipts are independent, with each year’s expected return having a mean of $1,800 and a standard deviation of $200. MARR is 12 percent. Assuming that initial investment and annual receipts are independent and normally distributed, estimate the probability that the present worth is negative using NORM.INV function in excel.
This value represents the present worth below which the probability is 0.5, indicating a negative present worth.
To estimate the probability that the present worth is negative using the NORM.INV function in Excel,
we need to calculate the present worth of the project and then determine the corresponding probability using the normal distribution.
The present worth of the project can be calculated by finding the sum of the present values of the annual receipts over the 10-year period, minus the initial investment. The present value of each annual receipt can be calculated by discounting it back to the present using the minimum attractive rate of return (MARR).
Using the given information, the present value of the initial investment is $10,000. The present value of each annual receipt is calculated by dividing the expected return of $1,800 by \((1+MARR)^t\),
where t is the year. We then sum up these present values for each year.
We can use the NORM.INV function in Excel to estimate the probability of a negative present worth. The function requires the probability value, mean, and standard deviation as inputs.
Since we have a mean and standard deviation for the present worth,
we can calculate the corresponding probability of a negative present worth using NORM.INV.
This value represents the present worth below which the probability is 0.5. By using the NORM.INV function,
we can estimate the probability that the present worth is negative based on the given data and assumptions.
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Order each group of fractions from greatest least
Answer:
3/5, 1/5, 1/6
Step-by-step explanation:
3/5 is greater than 1/5 and is the largest of these three fractions.
Comparing 1/5 and 1/6, realize that the larger the denominator, the smaller the value of the fraction. Thus, 1/5 is greater than 1/6.
Then, in order from greatest to least: 3/5, 1/5, 1/6
I buy T stamps at Q cents each, S stamps at R cents each, and give the post-office clerk one dollar. If P = 8, Q = 7, R = 5, S = 2, and T = 6, how many stamps at P cents can I buy with the change? *
A. 4
B. 6
C. 7
D. 8
E. 9
Answer:
4 it's na answer the answer is 4
Olivia took out 8 glasses and poured juice from the pitcher. The capacity of each
glass is 3/10 liter. If there was enough juice for 6 glasses, how much juice was
there?
1.8 Liters
olivia took out 8 glasses and poured juice from the pitcher.
The capacity of each glass is 3/10 liter.
If there was enough juice for 6 glasses.
This means that the amount of juice will be the total quantity of juice poured in 6 glasses.
Since, capacity of 1 glass= 3/10 liters=0.3 liters
Capacity of 6 glasses= 6×0.3=1.8 liters.
Consider the curve below.y = x^80 ≤ x ≤ 1(a) Set up, but do not evaluate, an integral for the area of thesurface obtained by rotating the curve aboutthe x-axis.(b) Set up, but do not evaluate, an integral for the area of thesurface obtained by rotating the curve aboutthe y-axis.
For the curve, y = x⁸, 0≤ x ≤ 1
a) The area of the curve surface obtained by rotating the curve about the x-axis is equals to the \(A = \int_{a}^{b} 2π(x⁸)\sqrt(1+ 8x⁷)²dx .\)
b) The area of the surface obtained by rotating the curve about the y-axis is equals to the \(A = \int_{c}^{d} 2πx( \frac{ds}{dy})dy\).
We have, a curve equation, y = x⁸ ; 0≤x≤1.
a) We have to set up integral for area of the surface by the rotating about x -axis,
the arc of the curve y = f(x) from x = a to x = b is \(A = \int_{a}^{b} 2πyds
= \int_{a}^{b} 2πy(\frac{ds}{dx})dx \)
where \( \frac{ds}{dx}= \sqrt{(1 + \frac{dy} {dx})²}\)
Now, differentiating the curve equation, y = x⁸
=> dy/dx = 8x⁷
so, ds/dx = √(1 + 8x⁷)²
Therefore, Area of surface about rotating x-axis is \(A= \int_{a}^{b} 2π(x⁸)\sqrt(1+ 8x⁷)² dx.\)
b) Similarly, the area of the surface by the rotating about y -axis, of the arc of the curve x = f(y) from y = c to y = d is written as \(A = \int_{c}^{d} 2πx( \frac{ds}{dy})dy\).
Hence, we determined the integral for area of surface when rotating about x-axis and y-axis.
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U7L2 Cool Down
The measure of the arc from B to A not passing through C is 26 degrees.
1. What is the measure of angle BOA ?
2. What is the measure of angle BDA?
3. What is the measure of angle BCA ?
degrees
degrees
degrees
Using the inscribed angle theorems, the measure of the indicated angles are:
1. m∠BOA = 26°
2. m∠BDA = 13°
3. m∠BCA = 13°
What is the Inscribed Angle Theorems?Based on the inscribed angle theorem, the following relationships are established:
Inscribed angle = 2(measure of intersected arc)Central angle = measure of intersected arcGiven:
Intercepted arc BA = 26°
1. ∠BOA is central angle
Thus:
m∠BOA = 26° (inscribed angle theorems)
2. ∠BDA is inscribed angle.
m∠BDA = 1/2(30) = 13° (inscribed angle theorems)
3. m∠BCA = m∠BDA = 13° (inscribed angle theorems)
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Why is (4x-2)(3x+5) not an intelligent
guess for factoring this trinomial even though
4.3=12 and -2.5=-10?
Trinomials are expressions with three terms
The factor is not an intelligent guess, because the expression can be further simplified
Why the factor is not intelligent?
The factor is given as:
(4x - 2)(3x + 5)
The above factor can further be factorized.
This is shown below
(4x - 2)(3x + 5) = 2(2x - 1)(3x + 5)
Hence, the factor is not an intelligent guess, because the factor can still be further simplified
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1. A restaurant in Sri Lanka serves two popular desserts: watalappan and dodol.
Watalappan needs to be cooked for 20 minutes and dodol needs to be cooked for
25 minutes. If the restaurant wants to cook both desserts at the same time, what is
the least amount of time they need to cook to ensure both desserts are ready
together???
Answer:
They need at least 25 minutes to ensure both desserts are cooked together.
Step-by-step explanation
Watalappan can be cooked in 20 minutes.
Dodol can be cooked in 25 minutes.
So, under 25 minutes both the desserts can be cooked.
Answer:
25 minutes
Step-by-step explanation:
Watalappan takes 20 minutes
Dodol takes 25
By the time Dodol is finished, Watalappan would also be finished, so the least amount of time for both deserts to be finished would be 25 minutes.
Hope this helps!
The distance to your uncle's house is 444 miles, and the distance to Atlanta is 555 miles. If it took 12 hours to drive to your uncle's house, how long would you estimate the drive to Atlanta to take
It takes 15 hours to drive to Atlanta. Using the distance-time-speed formula the required time is calculated.
What is the distance-time-speed formula?The relation between distance 'd', time 't', and speed 's' is given by the formula,
s = d/t or
d = st or
t = d/s
Calculation:It is given that,
The distance to uncle's house = 444 miles
The time taken to drive to uncle's house = 12 hours
So,
speed = (444)/12 = 37 miles/hour
Then the time to drive 555 miles(to Atlanta) is calculated by,
time t = (555)/37 = 15 hours
Therefore, it takes 15 hours to drive to Atlanta at 555 miles of distance.
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Which of the following are key organizational data relevant to the production process? (2 Correct answers)
A. Purchasing Organization
B. Credit control area
C. Work center
D. Storage location
E. PLant
F. Bill of Material
The key organizational data relevant to the production process is:
(D) Storage location
(E) Plant
Organizational Structure:The organizational structure defines the entire direction of activities and tasks that lead towards the achievement of goals. Roles, responsibilities, procedures, plans are involved in activities and tasks. It also represents the hierarchy and flow of information at organizational levels.
The following are the important characteristics of organization: Specialization and division of work.
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Multiply the starting price by the right term that uses the compound average to show that the arithmetic mean does not recover the final price while the geometric and continuous means do. Convert the percent averages to fractions.
$53. 07 x (1 + arith mean) 3 = 53.07 x (1 + #21 %) 3 = #22
$53. 07 x (1 + geom mean) 3 = 53.07 x (1 + #23 %) 3 = $ #24
$53. 07 x e cont mean x 3 = 53.07 x e #25 % x 3 = $ #26
I need help filling out numbers #21 through #26
The values for numbers #21 through #26 are as follows:
#21: 2.33% or 0.0233. #22: $56.4842. #23: 1.85% or 0.0185. #24: $56.4148. #25: 3.64% or 0.0364. #26: $57.4397
#21: 2.33% (arithmetic mean as a fraction: 0.0233)
#22: $56.4842 (result of the calculation)
#23: 1.85% (geometric mean as a fraction: 0.0185)
#24: $56.4148 (result of the calculation)
#25: 3.64% (continuous mean as a fraction: 0.0364)
#26: $57.4397 (result of the calculation)
To fill out numbers #21 through #26, we need to calculate the values for each term using the given information and convert the percentages to fractions.
#21: The arithmetic mean is given as a percentage. Convert it to a fraction by dividing by 100. Therefore, #21 = 2.33% = 0.0233.
#22: Multiply the starting price ($53.07) by the compound factor (1 + arithmetic mean)^3. Substitute the value of #21 into the calculation. Therefore, #22 = $53.07 x (1 + 0.0233)^3 = $56.4842.
#23: The geometric mean is given as a percentage. Convert it to a fraction by dividing by 100. Therefore, #23 = 1.85% = 0.0185.
#24: Multiply the starting price ($53.07) by the compound factor (1 + geometric mean)^3. Substitute the value of #23 into the calculation. Therefore, #24 = $53.07 x (1 + 0.0185)^3 = $56.4148.
#25: The continuous mean is given as a percentage. Convert it to a fraction by dividing by 100. Therefore, #25 = 3.64% = 0.0364.
#26: Multiply the starting price ($53.07) by the continuous factor e^(continuous mean x 3). Substitute the value of #25 into the calculation. Therefore, #26 = $53.07 x e^(0.0364 x 3) = $57.4397.
Hence, the values for numbers #21 through #26 are as calculated above.
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Solve the linear equations
2y - 2x = - 30
x = 3y + 9
Answer:
1. Slope= 1.000
2. Slope= 0.333
Step-by-step explanation:
Hope this helps, If you need the x and y-intercepts just let me know and I can edit.
Brain-List?
Answer:
the solution is (18, 3)
Step-by-step explanation:
Let's first eliminate x. Multiply the second equation by 2, obtaining
2x = 6y + 18
Then add this result to the first equation 2y - 2x = -30:
2x = 6y + 18
2y - 2x = -30
-------------------- or
2x = 6y + 18
-2x = -30 - 2y
--------------------
0 = 4y - 12, which yields y = 3.
Substitute 3 for y in the second equation to obtain the value of x:
x = 3(3) + 9, or x = 18
Then the solution is (18, 3).
Note that we could do this faster by reducing 2y - 2x = -30 to y - x = -15
Then the second equation becomes x = 3(y) + 9, or
x = 3y + 9, with x = 18
Then 18 = 3y + 9, or 3y = 9, or y = 3 (as before)
point (x, y) is randomly picked from inside the rectangle with vertices (0, 0), (4, 0), (4, 1), and (0, 1). What is the probability that x < y
To solve this problem, let us first find the probability that x < y when point (x, y) is randomly selected from inside the rectangle. Then, using the area of the rectangle, normalize the probability.
The probability that x < y is 1/8.
To find the probability that x < y when a point is randomly chosen from within the rectangle. Let A be the area of the region where x < y, and B be the area of the rectangle. Then, the probability that x < y is given by P(x < y) = A/B. To find A and B, let us first look at the line x = y, which passes through (0,0) and (1,1) and separates the rectangle into two regions: Region I: The area to the right of the line x = y, where x > y. Region II: The area to the left of the line x = y, where x < y. region xy plane Region I has area B - A, and Region II has area A. Hence, B - A + A = B, which implies A/B = A/(B - A) = 1/2. Therefore, we only need to find A.
Let C be the triangle with vertices (0,0), (1,0), and (1,1). This triangle has area 1/2. Since the rectangle has height 1, the line x = y intersects the rectangle at a height of 1/2, which means that A is the area of the trapezoid with vertices (1/2, 0), (1, 0), (1, 1), and (1/2, 1/2).trapezoid xy plane. To find the area of this trapezoid, we can split it into a rectangle and a right triangle, as shown below: split trapezoid xy plane. The rectangle has base 1/2 and height 1, so its area is 1/2. The triangle has base 1/2 and height 1/2, so its area is 1/8. Hence, the area of the trapezoid is 1/2 + 1/8 = 5/8. Therefore, the probability that x < y is P(x < y) = A/B = (5/8) / 4 = 1/8.
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A bag of paper clips contains:
. 9 pink paper clips
• 7 yellow paper clips
• 5 green paper clips
• 4 blue paper clips
A random paper clip is drawn from the bag and replaced 50 times. What is a
reasonable prediction for the number of times a yellow paper clip will be
drawn?
Answer:
14 times
Step-by-step explanation: add all colors up for total which is 25
since 7 out of the 25 total paper clips are yellow you would have a 7/25 chance of getting yellow after 1 pick.
since you pick and replace 50 times do (7/25) X 50 which gives you 14 times yellow will be drawn.
A special deck of cards has 12 cards. four are green, three are blue, and five are red. When a card is picked, the color of it is recorded. An experiment consists of first picking a card and then tossing a coin. A. How many elements are there in the sample space? 12 B. Let A be the event that a green card is picked first, followed by landing a tail on the coin toss. P(A) = Present your answer as a decimal number rounded to two decimal places of accuracy. C. Let C be the event that a green or red is picked, followed by landing a tail on the coin toss. Are the events A and C mutually exclusive?(Yes or No) D. Let B be the event that a blue or red is picked, followed by landing a tail on the coin toss. Are the events A and B mutually exclusive? (Yes or No)
Answer:
A. Sample space = 6
B. 0.17
C. No
D. Yes
Step-by-step explanation:
A. The sample space of an experiment is the set of all possible outcomes of that experiment.
since there are three colours and 2 outcomes for a coin toss,
sample space = 3 * 2 = 6
B. Probability of picking a green first = 4/12 = 1/3
probability of a tail = 1/2
Probability of a green and a tail, P(A) = 1/3 * 1/2 = 0.17
C. No.
Considering the two events;
A; green card is picked first
C ; a green or red card is picked
There is an intersection point for the two events. Therefore, they are not mutually exclusive.
D. Yes.
Considering the two events;
A; green card is picked first
B ; a blue or red card is picked
There is no intersection point for the two events. Therefore, they are mutually exclusive.
Let f : R → R_3 be defined by f(u) = (u, u^2 , u^3 ) and let g : R_3 → R be defined by g(x, y, z) = 2x + y − z. Compute Df and Dg. Using the chain rule, compute D(f ◦ g).
The derivative of (f ◦ g) with respect to u is h'(u) = [2, 2g(u), \(-3g(u)^2].\) To compute the derivatives of the given functions, we'll start with finding the Jacobian matrices for each function.
For the function f(u) = \((u, u^2, u^3)\), the Jacobian matrix Df is:
Df = [∂f₁/∂u, ∂f₂/∂u, ∂f₃/∂u]
=\([1, 2u, 3u^2]\)
For the function g(x, y, z) = 2x + y − z, the Jacobian matrix Dg is:
Dg = [∂g/∂x, ∂g/∂y, ∂g/∂z]
= [2, 1, -1]
Next, we'll compute the derivative of the composition function (f ◦ g) using the chain rule. Let h(u) = (f ◦ g)(u), then:
h'(u) = D(f ◦ g)/du = Df(g(u)) * Dg(u)
Substituting the values we have:
\(h'(u) = [1, 2g(u), 3g(u)^2] * [2, 1, -1]\)
\(= [2, 2g(u), -3g(u)^2]\)
Therefore, the derivative of (f ◦ g) with respect to u is h'(u) = [2, 2g(u), \(-3g(u)^2].\)
Learn more about Jacobian matrix here:
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