find the total differential of the function w = e y cos(x) z^2 .
Answers
To find the total differential of the function w = e^y * cos(x) * z^2, we can take the partial derivatives with respect to each variable (x, y, and z) and multiply them by the corresponding differentials (dx, dy, and dz).
The total differential can be expressed as:
dw = (∂w/∂x) dx + (∂w/∂y) dy + (∂w/∂z) dz
Let's calculate the partial derivatives:
∂w/∂x = \(-e^{y} * sin(x) * z^{2}\)
∂w/∂y = \(e^{y} * cos(x) * z^{2}\)
∂w/∂z = \(2e^{y} *cos (x)* z\)
Now, let's substitute these partial derivatives into the total differential expression:
\(dw = (-e^{y} * sin(x) * z^{2} ) dx + (e^{y}* cos(x) * z^{2} ) dy + 2e^{y} *cos (x)*z) dz\)
Therefore, the total differential of the function w = e^y * cos(x) * z^2 is given by:
\(dw = (-e^{y} * sin(x) * z^{2} ) dx + (e^{y} * cos(x) * z^{2} ) dy + ( 2e^{y} * cos(x) * z) dz\)
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Related Questions
oliver has 5 pieces of string that are each 4 2 12 feet long. destiny has 4 pieces of string that are each 5 14 16 feet long. use an estimation strategy to determine who has the most string. choose the name and number to complete the statement. choose... is estimated to have choose... more feet of string.
Answers
Oliver has 5 pieces of string each of length 4 2 12 feet and Destiny has 4 pieces of string each of length 5 14 16 feet.
Now, let's use an estimation strategy to determine who has the most string by rounding the length of each string to the nearest whole number.The nearest whole number to 4 2 12 is 4The nearest whole number to 5 14 16 is 6Now, we can determine who has the most string by multiplying the rounded lengths of each string by the number of strings they have:Oliver has 5 strings, so he has about 5 × 4 = 20 feet of stringDestiny has 4 strings, so she has about 4 × 6 = 24 feet of string
Therefore, Destiny is estimated to have about 24 − 20 = 4 more feet of string than Oliver. Thus, Destiny is estimated to have 4 more feet of string than Oliver.
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suppose we want to test whether there is a difference between the room rates of luxury hotels in new york versus los angeles. we collect data from 20 random luxury hotels in new york and 30 random luxury hotels in l.a. what are the degrees of freedom associated with a pooled-variance two-sample t-test or confidence interval? type your answer here
Answers
The degrees of freedom associated with a pooled-variance two-sample t-test or confidence interval in the given case would be 48.
When a pooled-variance two-sample t-test or confidence interval is to be conducted on two groups, the degrees of freedom is calculated using the following formula: df = n1 + n2 - 2, where n1 and n2 are the sample sizes of the two groups being compared.
In the given scenario, data is collected from 20 random luxury hotels in New York and 30 random luxury hotels in Los Angeles. Therefore, the degrees of freedom for a pooled-variance two-sample t-test or confidence interval would be:df = 20 + 30 - 2df = 48. Hence, the degrees of freedom associated with a pooled-variance two-sample t-test or confidence interval are 48.
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Assistance required pleasssse help!
- Create your own piecewise function with at least two functions. Explain, using complete sentences, the steps for graphing the function. Graph the function by hand or using a graphing software of your choice
Answers
Answer:
system of function:
f(x)=.5x+6
f(x)=x^2; x > 2
Step-by-step explanation:
there's a screenshot attached. Explanation: I'm using desmos and just type the functions like what the screenshot did to graph the piecewise function made by two functions
Help look at the photo
Will mark the brainlest
Answers
Answer:
1. 6
2. 8
3. 10
4. 12
5. 14
Step-by-step explanation:
just solve
which of the following statements is true of the sample size for nonprobability samples
Answers
The statement that is true of the sample size for nonprobability samples is that it is typically small.
Nonprobability sampling methods are often used when it is not feasible or practical to obtain a large sample that is representative of the population.
Nonprobability samples are selected based on criteria other than random selection, such as convenience, judgment, or purposive sampling. These methods are commonly used in qualitative research or when studying hard-to-reach populations.
Since nonprobability samples do not guarantee representativeness, the focus is often on in-depth exploration rather than generalization to a larger population. As a result, researchers often work with smaller sample sizes that are more manageable and allow for in-depth analysis of the selected cases or individuals.
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please help me I dont know the answer
Answers
Answer:
2.71
Step-by-step explanation:
Its as simple as plugging in the values of y and z.
THis would give you
-1.46 + (-3.82) + 7.99
This plus^ you can think about having a 1 in front of it like
-1.46 + 1 (-3.82) +7.99
Multiple positive 1 with -3.82 1 times any value is that number, and positive times negative is negative. then looking like this:
-1.46 - 3.82 + 7.99 plug into a calculator and you get +2.71
Answer:
2.71
Step-by-step explanation:
We'll add the first value and the value in parentheses, being -3.82, then we'll add y, which is a negative because "-y", being -1.46. That becomes -5.28.
We'll then take our -5.28 and add 7.99, which will become 2.71.
Therefore, 2.71 is your answer.
HELP!! ASAP
Find the length of each line segment or object to the nearest half, fourth, or eighth inch.
Answers
12. Find the equation of the tangent line to f(x) = 2ex at the point where x = 1. a) y = 2ex + 4e b) y = 2ex + 2 c) y = 2ex + 1 d) y = 2ex e) None of the above
Answers
The equation of the tangent line to \(\(f(x) = 2e^x\)\) at the point where \(\(x = 1\)\) is \(\(y = 2e^x + 2\)\).
To find the equation of the tangent line, we need to determine the slope of the tangent at the point \(\(x = 1\)\). The slope of the tangent line is equal to the derivative of the function at that point.
Taking the derivative of \(\(f(x) = 2e^x\)\) with respect to x, we have:
\(\[f'(x) = \frac{d}{dx} (2e^x) = 2e^x\]\)
Now, substituting x = 1 into the derivative, we get:
\(\[f'(1) = 2e^1 = 2e\]\)
So, the slope of the tangent line at \(\(x = 1\)\) is 2e.
Using the point-slope form of a linear equation, where \(\(y - y_1 = m(x - x_1)\)\), we can plug in the values \(\(x_1 = 1\), \(y_1 = f(1) = 2e^1 = 2e\)\), and \(\(m = 2e\)\) to find the equation of the tangent line:
\(\[y - 2e = 2e(x - 1)\]\)
Simplifying this equation gives:
\(\[y = 2ex + 2e - 2e = 2ex + 2\]\)
Therefore, the equation of the tangent line to \(\(f(x) = 2e^x\)\) at the point where \(\(x = 1\)\) is \(\(y = 2e^x + 2\)\). Hence, the correct option is (b) \(\(y = 2e^x + 2\)\).
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All of the following are benefits (the "pro's") of having a credit card, EXCEPT which one?
a.
Credit cards are portable, and you won't have to carry as much cash.
b.
Credit cards are convenient to use, and you can buy now and pay later.
c.
Credit cards make it very easy to take on revolving debt.
d.
Credit cards are very helpful for emergency purchases.
e.
Credit cards can help build your credit rating if used responsibly.
Answers
asmita went to a blackjack table at the casino. at the table, the dealer has just shuffled a standard deck of 52 cards. asmita has had good luck at blackjack in the past, and she actually got three blackjacks with aces in a row the last time she played. because of this lucky run, asmita thinks that ace is the luckiest card. the dealer deals the first card to her. in a split second, she can see that it is a non-face card, but she is unsure if it is an ace. what is the probability of the card being an ace, given that it is a non-face card? answer choices are in a percentage format, rounded to the nearest whole number. 8% 10% 69% 77%
Answers
The probability of the card being an ace, given that it is a non-face card is option A: 8% .
What is the probability about?To find the probability of an event occurring, we can use the formula:
Probability = number of ways the event can occur / total number of outcomes.
In this case, we are trying to see the probability of drawing an ace from a standard deck of 52 cards, given that the card is a non-face card. There are 4 aces in a standard deck of 52 cards, so the number of ways the event (drawing an ace) can occur is 4. There are 52 total cards in the deck, and 48 of them are non-face cards. So, the total number of outcomes is 48.
Therefore, the probability of the card being an ace, given that it is a non-face card, is 4/48.
4/48 = 0.083
When converted to percentage, it is approximately 8.3%.
Therefore, This means that the probability of the card being an ace, given that it is a non-face card, is approximately 8%, which is seen as the closest to the answer choice "8%".
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amelie realizes she'll need to buy more crackers than necessary, since the crackers come in boxes of 20. now she wants to calculate how many graham crackers will be leftover in the final box, as she wants to see how many extras there will be for people that break their crackers (or get hungry and eat them). which line of code successfully calculates and stores the number of leftover crackers in the final box?
Answers
The line of code that successfully calculates and stores the number of leftover crackers in the final box is int leftoverCrackers = x % 20;
Let's assume Amelie needs to buy x number of crackers, and the crackers come in boxes of 20. We can first find out how many boxes Amelie needs to buy by dividing x by 20:
Number of boxes = x ÷ 20
Since Amelie has bought more boxes than necessary, the last box will not be completely full. To find out how many crackers will be left over in the final box, we can use the remainder of the division x ÷ 20. This is because the remainder represents the number of crackers that do not fit into the full boxes.
Number of crackers in the final box = x mod 20
Where "mod" is a mathematical operation that gives the remainder of the division.
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If the margin of error decreases and the sample size remains the same, the level of confidence.
Answers
Level of confidence decreases if the margin of error decreases(when the sample size is kept the same) Goes Down
What is level of confidence?A confidence interval is a range of estimates for an unknown parameter in frequentist statistics. The 95% confidence level is the most popular, but other levels, like 90% or 99%, are occasionally used when computing confidence intervals.
We are given asked when the sample size is kept the same,
What will happen to the level of confidence if the margin of error decreases?we know that the margin of error is nothing but a statistic which tells us how many percentage points our results will differ from the real population value.we know that when a greater error is allowed, the more will be the confidence(fundamental concept of confidence intervals)
Let Margin of Error be represented by E and the confidence level by C hence the relationship goes like this,
E↑⇔C↑and E↓⇔C↓
Here we are asked when the sample size is kept the same, what will happen to the level of confidence if the margin of error decreases .
The answer is that Level of confidence decreases if the margin of error decreases(when the sample size is kept the same) Goes Down.
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Find the exact values of the expression without a calculator
Answers
ANSWER:
\(\frac{3\sqrt{13}}{13}\)STEP-BY-STEP EXPLANATION:
We have the following expression:
\(\cos\left(\tan^{-1}\left(-\frac{2}{3}\right)\right)\)\(\begin{gathered} \cos\left(\tan^{-1}\left(-\frac{2}{3}\right)\right)=\cos\left(\arctan\left(-\frac{2}{3}\right)\right) \\ \\ \cos\left(-\arctan\left(\frac{2}{3}\right)\right)=\cos\left(\arctan\left(\frac{2}{3}\right)\right) \\ \\ \text{ we have the following} \\ \\ \cos \left(\arctan \left(x\right)\right)=\frac{\sqrt{1+x^2}}{1+x^2} \\ \\ \text{ we replacing:} \\ \\ \cos\left(\arctan\left(\frac{2}{3}\right)\right)=\frac{\sqrt{1+\left(\frac{2}{3}\right)^2}}{1+\left(\frac{2}{3}\right)^2}=\frac{\sqrt{1+\left(\frac{2}{3}\right)^2}}{1+\frac{2^2}{3^2}}=\frac{\sqrt{1+\frac{4}{9}}}{1+\frac{4}{9}}=\frac{\sqrt{\frac{13}{9}}}{\frac{13}{9}}=\frac{\frac{1}{3}\sqrt{13}}{\frac{13}{9}}=\frac{\sqrt{13}}{3\cdot\frac{13}{9}}=\frac{\sqrt{13}}{\frac{13}{3}}=\frac{3\sqrt{13}}{13} \end{gathered}\)the waiting times between a subway departure schedule and the arrival of a passenger are uniformly distributed between 0 and 8 minutes. find the probability that a randomly selected passenger has a waiting time greater than 4.25 minutes.
Answers
The probability that a randomly selected passenger has a waiting time greater than 4.25 minutes is 0.5278
The uniform distributed between a and b minutes.
The probability of finding a value above x is:
P(X > x) = \(\frac{b-x}{b-a}\)
The time is evenly distributed between 0 and 9 minutes.
This implies that a=0 , b=9
Determine the likelihood that a randomly selected passenger will have to wait longer than 4.25 minutes.
p(X > 4.25) = \(\frac{9-4.25}{9-0}\)
= 0.5278
There is a 52.78% chance that a randomly selected passenger will have to wait longer than 4.25 minutes.
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find the coordinates of A' after a reflection across the y-axis and then across the line y = -2. write your answer in the form (a, b).
Answers
Answer:
(3,1)
Step-by-step explanation:
When a point is reflected across the y axis, the sign of its x coordinate flips. Since point A is at (-3,-5), when it is reflected across the y axis its new position will be (3,-5). Now, point A is 3 units from the line y=-2, meaning that when it is reflected across it will be 3 units away from the other direction. (-2+(3))=1, meaning that the final coordinates of point A are (3,1). Hope this helps!
The student who traveled to states visited new states during a vacation. Does increasing the to change the median? If so, how?
Answers
Step-by-step explanation:
The exact question is as follows :
Given - The student who traveled to 3 states visited 6 new states during a vacation.
To find - Does increasing the 3 to 6 change the median? If so, how?
Proof -
Yes,
If we increase the 3 states to 6 states, it changes the median
Because
The median of the first 3 states is the middle state.
For example -
If we have 3 states X, Y, Z
Then the median is the state Y
Now,
The median of 6 states is the average of the 2 middle states.
For example -
If we have 6 states
X, Y, Z, U, V, W
Then
The median is not explicit.
Median is the average of the two middle states, Z and U.
And
Average of Z and U = half of the sum of Z and U.
i.e. (Z + U)/2.
And we can see that,
Median of 3 States is not equal to Median of 6 states
i.e. Y is not equal to (Z + U)/2.
So,
We can say that,
Increasing the state 3 to 6 changes the median.
What is the 5th root called?
Answers
A root of degree 5 is called a fifth root.
A radicand, or nth root, in mathematics is a number r that, when raised to the power n, equals the number x: rn = x, where n is a positive integer, also known as the degree of the root. A root of degree 5 is called a fifth root.
The required number is the result of multiplying a fifth root by itself five times.
Due to the fact that two multiplied by itself five times is 32, 532 = 2
Seven multiplied by itself five times is 16807.
Hence 516807 Equals 7 since 7 x 7 x 7 x 7 = 16807.
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plain why the statistic is misleading.
Wilson was 42 inches tall on Jan 1, 2000, and 51 inches tall on Jan 1, 2002. William was 5 feet tall on Jan 1, 2000, and 6 feet tall on Jan 1, 2002.
Conclusion: The difference between 42 and 51 is greater than the difference between 5 and 6, so Wilson grew more during one year.
Answers
Wilson and William were measured at various times, therefore drawing the inference that Wilson grew more over the course of a year than William is incorrect and the statistics is misleading.
What is descriptive statistics?Inferential statistics and descriptive statistics are two disciplines of statistics with distinct applications.
Summarizing and characterizing gathered data is the focus of descriptive statistics. It uses techniques including graphical presentations, measurements of variability, and measures of central tendency, such as mean, median, and mode (e.g., histograms, box plots). The purpose of descriptive statistics is to shed light on a sample's or population's properties, such as its distribution, dispersion, and shape.
Wilson and William were measured at various times, therefore drawing the inference that Wilson grew more over the course of a year than William is incorrect.
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You must decide whether to buy new machinery to produce product X or to modify existing machinery. You believe the probability of a prosperous economy next year is 0.7. Prepare a decision tree and use it to calculate the expected value of the buy new option. The payoff table is provided below (+ for profits and - for losses).
When entering the answer, do not use the $ symbol. Do not enter the thousand separator. Enter up to 2 decimal places after the decimal point. For example, $6,525.35 must be entered as 6525.35
N1: Prosperity ($) N2: Recession ($)
A1 (Buy New) $1,035,332 $-150,000
A2(Modify) $823,625 $293,648
Answers
The expected value of the "Buy New" option is 724732.60.
Decision Tree:
To solve the given problem, the first step is to create a decision tree. The decision tree for the given problem is shown below:
Expected Value Calculation: The expected value of the "Buy New" option can be calculated using the following formula:
Expected Value = (Prob. of Prosperity * Payoff for Prosperity) + (Prob. of Recession * Payoff for Recession)
Substituting the given values in the above formula, we get:
Expected Value for "Buy New" = (0.7 * 1,035,332) + (0.3 * -150,000)Expected Value for "Buy New" = 724,732.60
Therefore, the expected value of the "Buy New" option is 724,732.60.
Conclusion:
To conclude, the decision tree is an effective tool used in decision making, especially when the consequences of different decisions are unclear. It helps individuals understand the costs and benefits of different choices and decide the best possible action based on their preferences and probabilities.
The expected value of the "Buy New" option is 724,732.60.
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A math tutor earns $40 an hour tutoring teenagers. Sometimes he will meet with two students at once and get paid $80 per hour total. Is this a linear model or an exponential model?
Answers
Answer:
It should be linear if you let the variable t represent the time tutoring for ONE student, so y = 40*t where t = number of hours for ONE student
so if the tutor taught 2 students for 2 hours together, then t = 2*2 = 4 hours
Step-by-step explanation:
y = 40t
t = tutoring hours for ONE unique student...
#21, what is this answer ?
Answers
Answer:
18 ft
Step-by-step explanation:
Height of the cable pole and it's shadow's length will be in direct proportion with the height of man and its shadow.
Let the height of the cable pole be x feet
\(\therefore \frac{x}{12} = \frac{6}{4} \\ \\ x = \frac{ \cancel{12} \times 6}{ \cancel4} \\ \\ x = 3 \times 6 \\ \\ x = 18 \: ft\)
Write the sum as a product. \[ \cos (5 x)-\cos (9 x) \]
Answers
The given expression \(\cos (5x) - \cos (9x)\) represents the difference between two cosine functions. The expression \(\cos (5x) - \cos (9x)\) cannot be simplified as a product.
The given expression \(\cos (5x) - \cos (9x)\) represents the difference between two cosine functions. The sum or difference of trigonometric functions cannot be simplified into a single product.
Trigonometric identities exist for sum-to-product and product-to-sum transformations, but they apply to sums or products of the same trigonometric function, not different ones. In this case, \(\cos (5x)\) and \(\cos (9x)\) are distinct functions with different arguments, so they cannot be combined into a single product. Hence, the expression \(\cos (5x) - \cos (9x)\) remains as it is and cannot be further simplified.
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the length of a rectangle is 3 more than twice its width. the total area of the rectangle is 54 square units. what is the width and length of the rectangle?
Answers
The width and length of the rectangle is 4.5ft and 12ft.
Width of a rectangle = b = x ft.
Length of a rectangle = l = (2x+3) ft.
Area of the rectangle = l×b = 54 sq.ft.
= x (2x + 3) = 54
= 2x² + 3x = 54
(2x-9)(x+6) = 0
The size of a patch on a surface is determined by its area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.
Area can be interpreted as the quantity of material with a specific thickness required to create a model of the shape or as the quantity of paint required to completely cover a surface in a single coat.
It is the two-dimensional equivalent of the volume of a solid or the length of a curve, both of which are one-dimensional concepts (a three-dimensional concept).
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suppose that AB is invertible then (AB)^−1 exists. We also know (AB)^−1=B^−1A^−1. If we let C=(B^−1A−^1A) then by the invertible matrix theorem we see that since CA=I(left inverse) then B is invertible. Would this be correct?
Answers
The invertible (AB)^-1 exists and is equal to B^-1A^-1. Yes, that is correct.
CA = (B^-1)(A^-1)A = (B^-1)I
Multiplying both sides by B, we get:
(B)(B^-1)(A^-1)A = B
IA = B
Therefore, B = IA, which means B is invertible. From here, we can use the given information that (AB)^-1 = B^-1A^-1 to show that (AB)^-1 exists. Since we know that B is invertible, we can multiply both sides of (AB)^-1 = B^-1A^-1 by B to get:
B(AB)^-1 = (BB^-1)(A^-1)
B(AB)^-1 = I(A^-1)
(BA)(B(AB)^-1) = BA(A^-1)
I = B(A^-1) Therefore, (AB)^-1 exists and is equal to B^-1A^-1.
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ashley drove 605 miles in 11 hours at the same rate how long would it take her to drive 495 miles
Answers
Answer:
9 hours
Step-by-step explanation:
605 miles/11 hours = 55miles/hour
495 miles (time) = 495 / 55 =9
So, 9 hours
What is the solution to the equation 3x+2=x+8
Answers
Answer:
x=3
Step-by-step explanation:
3x+2=x+8
Subtract x from both sides.
3x+2−x=x+8−x
2x+2=8
Subtract 2 from both sides.
2x+2−2=8−2
2x=6
Divide both sides by 2.
2x/2=6/2
x=3
Jane has 9 cups of sugar. A batch of cookies uses 1 ¹⁄₂ cups of sugar. How many batches of cookies can Jane make?
Answers
Answer:
6 batches
Step-by-step explanation: because 9 divided by 1 1/2 cups of sugar is 6
If 1+1 =2 than what does 3x+5x equal
Answers
Answer:
If 1 + 1 = 2, then we can say that 1 = 2 - 1. Now, if we have 3x + 5x, we can factor out the common term of x to get: 3x + 5x = (3 + 5)x = 8x So, 3x + 5x = 8x.
in what situations would you want to change from rectangular to cylindrical or to spherical coordinates?
Answers
what is the probability that a five card hand contains four 2s
Answers
The probability of getting a hand with all four 2's is approximately 0.00648
The probability of drawing a single 2 from a deck of 52 cards is 4/52, or 1/13. Since there are four 2's in the deck, the probability of drawing all four 2's in a five-card hand is:
(4/52) × (3/51) × (2/50) × (1/49) = 0.000002641
This is a very small probability, which makes sense because it is highly unlikely to draw all four 2's from a deck of cards.
However, we also need to consider the number of possible five-card hands that can be drawn from a deck of 52 cards. This is given by the combination formula:
C(52,5) = 52! / (5! × (52-5)!) = 2,598,960
Therefore, the probability of drawing a five-card hand that contains all four 2's is:
(4/52) × (3/51) × (2/50) × (1/49) × (2,598,960) = 0.00648
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The given question is incomplete, the complete question is:
A simple random sample of size five is selected from 52 cards. Find the probability of five-card hand contains all four 2's