The value of dw/dt is [tex]e^\frac{y}{z}(7t^6- \frac{x}{z} + \frac{-9xy}{z^2} )[/tex]
To find dw/dt using the Chain Rule, we need to differentiate each component of the function [tex]w = xe^\frac{y}{z}[/tex] with respect to t and then multiply them together.
Given:
[tex]w = xe^\frac{y}{z}[/tex]
x = t⁷
y = 6 - t
z = 4 + 9t
Let's find dw/dt step by step:
x = t⁷
Taking the derivative of x with respect to t:
dx/dt = 7t⁶
y = 6 - t
Taking the derivative of y with respect to t:
dy/dt = -1
z = 4 + 9t
Taking the derivative of z with respect to t:
dz/dt = 9
[tex]w = xe^\frac{y}{z}[/tex]
Taking the derivative of w with respect to x:
[tex]\frac{dw}{dx} =e^\frac{y}{z}[/tex]
[tex]w = xe^\frac{y}{z}[/tex]
Taking the derivative of w with respect to y:
[tex]\frac{dw}{dy} = (\frac{x}{z} )e^\frac{y}{z}[/tex]
[tex]w = xe^\frac{y}{z}[/tex]
Taking the derivative of w with respect to z:
[tex]\frac{dw}{dz} = (\frac{-xy}{z^2} )e^\frac{y}{z}[/tex]
Apply the Chain Rule to find dw/dt:
dw/dt = (dw/dx)(dx/dt) + (dw/dy)(dy/dt) + (dw/dz)(dz/dt)
Substituting the derivatives we found earlier:
dw/dt [tex]= (e^\frac{y}{z})(7t^6) + (\frac{x}{z} )e^\frac{y}{z}(-1) + (\frac{-xy}{z^2} )e^\frac{y}{z}(9)[/tex]
dw/dt [tex]= e^\frac{y}{z}(7t^6- \frac{x}{z} + \frac{-9xy}{z^2} )[/tex]
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Jackson Brothers Auto Dealers sells two brands: Honda and GMC. Over the last 3 months, they have sold 175 autos. The company makes $300 profit on each GMC sold and $450 profit on each Honda. If the company has made $60,750 profit in that time, how many of each type of car have they sold?
Let x be the number of GMC sold
Let y be the number of Honda soldAccording to the given data, we can form the following equations: x+y = 175 ............ (1)300x + 450y = 60,750 ............ (2)
Multiplying equation (1) by 300 on both sides, we get:300x + 300y = 52,500Subtracting this equation from equation (2), we get:150y = 8,250Solving for y, we get:y = 55Substituting the value of y in equation (1),
we get:x + 55 = 175x = 120Therefore, the number of GMCs sold is 120 and the number of Hondas sold is 55.
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The company have sold 50 GMC and 125 Honda for this profit.
Let the number of GMC sold be x and the number of Honda sold be y.
Then:
[tex]x + y = 175[/tex]----------------------(1)
GMC: Profit on one car sold = $300
Therefore, the total profit on x GMC cars sold = $300x
Honda: Profit on one car sold = $450
Therefore, the total profit on y Honda cars sold = $450y
Total profit on x GMC and y Honda sold = $60,750
Therefore, we can write:
[tex]300x + 450y = 60,750[/tex]----------------(2)
Multiplying (1) by 450 and subtracting it from (2) multiplied by 100, we get:
[tex]-150x = 7,500⇒ x = 50[/tex]
Substituting the value of x in (1), we get:
[tex]y = 175 - 50= 125[/tex]
Therefore, the number of GMC sold is 50 and the number of Honda sold is 125.
They have sold 50 GMC and 125 Honda.
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For the given margin of error and confidence level, determine the sample size required. Show your answer in the integer form. You wish to estimate the proportion of shoppers that use credit cards. Obtain a sample size that will ensure a margin of error of at most 0.065 for a 92.5% confidence interval.
The sample size required to ensure a margin of error of at most 0.065 for a 92.5% confidence interval is 523.
To estimate the proportion of shoppers using credit cards with a desired margin of error and confidence level, determining the appropriate sample size is crucial.
In this scenario, we aim to achieve a margin of error of no more than 0.065 for a 92.5% confidence interval. The sample size required to fulfill these criteria is 523.
To comprehend the significance of these calculations, it's essential to understand the concepts of margin of error and confidence level. The margin of error represents the maximum amount of uncertainty we can tolerate in our estimate.
In this case, we want our estimate of the proportion of shoppers using credit cards to be accurate within ±0.065. A smaller margin of error indicates greater precision in our estimate.
The confidence level, on the other hand, reflects the level of certainty we have in the accuracy of our estimate.
A confidence level of 92.5% implies that if we were to repeat the sampling process numerous times, we would expect approximately 92.5% of the resulting confidence intervals to contain the true proportion of credit card-using shoppers.
The formula to calculate the sample size required for a proportion estimation is based on the desired margin of error, confidence level, and an assumed proportion (usually 0.5 for maximum variability).
This formula incorporates a z-value, which corresponds to the desired confidence level. For a 92.5% confidence level, the z-value is approximately 1.81.
By plugging the values into the formula and solving for the sample size, we find that a sample size of 523 is necessary to estimate the proportion of shoppers using credit cards with a margin of error no greater than 0.065 and a confidence level of 92.5%.
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What is the ratio of yellow butterflies to total butterflies? Choose the correct option
Answer:2/3
Step-by-step explanation: there is 2 yellow out of 3 butterfiles
In a large population of college-educated adults, the mean IQ is 112 with standard deviation 50.62. Suppose 30 adults from this population are randomly selected for a market research campaign. The distribution of the sample mean IQ is: a. approximately Normal, with mean 112 and standard deviation 1.443. b. approximately Normal, with mean 112 and standard deviation 4.564. c. approximately Normal, with mean equal to the observed value of the sample mean and standard deviation 25. d. approximately Normal, with mean 112 and standard deviation 9.241.
Given: Population mean IQ = 112Population standard deviation IQ = 50.62Sample size (n) = 30To find: Distribution of the sample mean IQ
The Central Limit Theorem states that for a large sample size, the distribution of sample means will be approximately Normal with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size . Let's calculate the standard deviation of the sample mean IQ:
Standard deviation of sample mean IQ = (Population standard deviation IQ) / √n= 50.62 / √30= 9.241 (approx.)Therefore, the distribution of the sample mean IQ is approximately Normal, with mean 112 and standard deviation 9.241. The correct option is (d).
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What is the mode of the data set? {102, 102, 100, 94, 102} Enter your answer in the box.
Answer:
102
Step-by-step explanation:
The mode is the number that appears the most in the data set. 102 appears 3 times while the others only once
HELPPPPPPPPPPPPP meeeee please
Step-by-step explanation:
5. 4b = b + b + b + b (A)
4b = 2b + 2b (C)
6. 111 = 14a
a = 111/14
a = 7.92
#CMIIWHelp me with this asp please
The x-coordinate of the endpoint of the line segment is 2.
The y-coordinate of the endpoint is -6.
To find the x-coordinate of the endpoint of the line segment, we can use the midpoint formula.
Given that one endpoint is at (10, 12) and the midpoint is at (6, 9), we can denote the coordinates of the other endpoint as (x, y).
Using the midpoint formula, we have:
x-coordinate of the endpoint = 2 * x-coordinate of the midpoint - x-coordinate of the known endpoint
x = 2 * 6 - 10
x = 12 - 10
x = 2
To find the y-coordinate of the endpoint of the line segment, we can use the midpoint formula. We know that the midpoint of the line segment is (6, 9) and one endpoint is (10, 12).
Let the coordinates of the other endpoint be (x, y). Using the midpoint formula, we can set up the following equation:
(10 + x) / 2 = 6
Simplifying the equation, we have:
10 + x = 12
Subtracting 10 from both sides:
x = 2
Therefore, the x-coordinate of the endpoint is 2. Now, we need to find the y-coordinate. Since we know that the endpoint is (2, y), we can use the given endpoint (10, 12) to find the y-coordinate:
12 + y / 2 = 9
Subtracting 12 from both sides:
y / 2 = -3
Multiplying both sides by 2:
y = -6
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Simplify each radical expression, if possible 3v/7-5^4v/7
Answer:
cannot be simplified
Step -by-step explanation:
[tex]3\sqrt{7} - 5\sqrt[4]{7} \\[/tex]
The indexes are not the same so the radicals cannot be combined.
cannot be simplified
(3/2)^4= in fraction form help pls
Answer:
81/16
Step-by-step explanation:
While taking inventory at her pastry shop, Aisha realizes that she had 1/4 of a box of baking powder yesterday, but the supply is now down to 1/6 of a box. How much more baking powder did Aisha have yesterday?
Answer:
1/12
Step-by-step explanation:
[tex]\frac{1}{4} - \frac{1}{6}[/tex]
[tex]\frac{6 - 4}{24}[/tex]
[tex]\frac{2}{24}[/tex]
Converting to its simplest form, divide numerator and denominator by 2 = 1/12
find the slope. (no units needed)
Answer: 4/5
Step-by-step explanation: It is 8/10, but if you simplify it, it is 4/5.
Assuming that the sample variances are continuous measurements, find the probability that a random sample of 30 observations, from a normal population with variance 92= 5, will have a sample variance of s2 that is a) greater than 7.338; b) between 2.766 and 7.883.
a) chi-square = (30-1) * 7.338 / 5 = 42.456 b) The probability of having a sample variance between 2.766 and 7.883 is the difference between the cumulative probabilities of chi-square2 and chi-square1.
Answer to the aforemention questionsTo find the probability in both cases, we need to use the chi-square distribution with n-1 degrees of freedom, where n is the sample size.
a) To find the probability that the sample variance is greater than 7.338, we need to find the upper tail probability of the chi-square distribution.
The chi-square statistic is calculated as:
chi-square = (n-1) * s^2 / sigma^2
In this case, n = 30, s^2 = 7.338, and sigma^2 = 5.
chi-square = (30-1) * 7.338 / 5 = 42.456
b) To find the probability that the sample variance is between 2.766 and 7.883, we need to find the cumulative probability within that range.
First, we calculate the chi-square statistics for both values:
chi-square1 = (30-1) * 2.766 / 5 = 15.359
chi-square2 = (30-1) * 7.883 / 5 = 43.179
The probability of having a sample variance between 2.766 and 7.883 is the difference between the cumulative probabilities of chi-square2 and chi-square1.
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Flow many years after the tree is planted does the model predict the tree will reach a height of 65 feet?
B
this is the answer
-6x - 14 > 10 what is the answer to this problem, please helt
Answer:
Inequality Form:
x < - 4
Interval Notation:
( − ∞ , − 4 )
Step-by-step explanation:
[5 points) X is places in an account which carries a nominal annual interest rate of 2.5% compounded monthly. After five years, the accumulated value is places in an account which earns a nominal annual interest rate of 3.2% compounded quarterly. The value of this account in eight years is $10,000. Find X.
The initial value of X can be determined using compound interest calculations. X is invested in an account with a nominal annual interest rate of 2.5%, compounded on a monthly basis, for a period of five years. After the initial period, X is then transferred to another account with a nominal annual interest rate of 3.2%, compounded on a quarterly basis, for a total duration of eight years. The approximate value of X at the end of this investment period is $6,573.83.
To solve for X, we will substitute the first equation into the second equation and solve for X. Let's proceed with the calculations:
The first equation is: FV = X(1 + 0.025/12)^(12*5)
The second equation is: $10,000 = X(1 + 0.032/4)^(48)(1 + 0.025/12)^(125)
We can substitute the first equation into the second equation:
$10,000 = [X(1 + 0.025/12)^(125)] * (1 + 0.032/4)^(48)
$10,000 = X * (1 + 0.025/12)^(125) * (1 + 0.032/4)^(48)
Now we can simplify the equation:
$10,000 = X * (1.002083)^60 * (1.008)^32
Divide both sides of the equation by [(1.002083)^60 * (1.008)^32] to solve for X:
X = $10,000 / [(1.002083)^60 * (1.008)^32]
Using a calculator, we can find the value of X:
X ≈ $10,000 / (1.138877 * 1.335893)
X ≈ $10,000 / 1.521364
X ≈ $6,573.83
Therefore, the value of X is approximately $6,573.83.
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Solve the problem. Use synthetic division and the remainder theorem to determine if [x−(3−2i)] is a factor of f(x)=x2−6x+13. Select one: a. No b. Yes
Using synthetic division and the remainder theorem, we can determine if [x−(3−2i)] is a factor of f(x)=x^2−6x+13.
To determine if [x−(3−2i)] is a factor of f(x)=x^2−6x+13, we can use synthetic division. First, we need to rewrite the given factor in the form x - c, where c is the conjugate of 3 - 2i, which is 3 + 2i.
Performing synthetic division with 3 + 2i as the divisor: f(x)=x^2−6x+13, we can use synthetic division. First, we need to rewrite the given factor in the form x - c, where c is the conjugate of 3 - 2i, which is 3 + 2i.
Performing synthetic division with 3 + 2i as the divisor:
3 - 2i | 1 -6 13
__________________
(remainder)
If the remainder is zero, then [x−(3−2i)] is a factor of f(x). However, if the remainder is nonzero, then [x−(3−2i)] is not a factor of f(x). Therefore, based on the result of the synthetic division, we can determine if [x−(3−2i)] is a factor of f(x).
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if f(x) = 1/4x 1 and g(x) = 4(1/4x 1), what is the slope of the graph of g?
The slope of the graph of the function g(x) is 1, indicating that for every unit increase in x, the corresponding value of g(x) increases by 1.
To find the slope of the graph of the function g(x), we can use the power rule of differentiation. Let's differentiate g(x) step by step:
Step 1: Express g(x) in a simplified form.
g(x) = 4(1/4[tex]x^1[/tex])
Step 2: Simplify the expression.
g(x) = x
Step 3: Differentiate g(x) to find the slope.
The derivative of g(x) with respect to x is simply 1, as the derivative of x with respect to itself is 1.
Therefore, the slope of the graph of g(x) is 1.
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Can someone help me on this I’m struggling to figure it out...
Answer:
It's D
Step-by-step explanation:
PLEASE HELP!
The blank of y in 17y is 17.
Its either term, variable or coefficient
In the term, 17y 17 is the coefficient of 17y.
What are coefficients and like terms?A quantity or number that is combined with a variable is known as a coefficient. The variable is often multiplied by an integer, which is then printed next to it.
Terms that have the same variables raised to the same power are referred to as like terms. The only difference is in the numerical coefficients.
The term 17y together is a variable, In 17y 'y' is also a variable.
In front of 'y' the constant number is 17 and it is called the coefficient of 'y'.
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HELP ASAP!!! question in picture!!!
Answer:
Y=3x-17
Step-by-step explanation:
I graphed it
Find the area of the larger sector.
Round to the nearest tenth.
2559
13.4 miles
Area = [ ? ]miles2
Enter
Step-by-step explanation:
the formula for the area of a sector is
(x°(r^2)π)/360
with x being the angle
r bring the radius of the circle
(255(13.4)^2π)/360
399.6
Hope that helps :)
Answer:
The answer is 399.6 not 399.4. I put 399.6 as my answer on acellus and I got it right.
What is the distance between A(7, 4) and B(2, −8)?
Answer:
The distance would 13 square units
Step-by-step explanation:
Well follow the formula
=√(2−1)^2+(2−1)^2
Plug in everything and solve, remeber to follow order of operations
what is the true solution to 3 l n 2 l n 8 = 2 l n (4 x)x = 1x = 2x = 4x = 8
The true solution to the equation is x ≈ 0.688. By simplifying the equation and solving for x, we find the approximate value.
To find the true solution to the equation 3ln(2ln8) = 2ln(4x)x = 1x = 2x = 4x = 8, we need to simplify the equation and solve for x.
First, let's break down the equation step by step:
3ln(2ln8) = 2ln(4x)x = 1x = 2x = 4x = 8
By simplifying each expression, we have:
3ln(ln8) = 2ln(4x)x = x = 2x = 4x = 8
Now, let's focus on the middle expression, 2ln(4x)x. Using the properties of logarithms, we can rewrite it as:
ln((4x)^2) = x
Simplifying further:
ln(16x^2) = x
Exponentiating both sides:
16x^2 = e^x
This is a transcendental equation that cannot be solved algebraically. However, using numerical methods or a graphing calculator, we find the approximate solution:
x ≈ 0.688
Therefore, the true solution to the equation is x ≈ 0.688.
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Factor 8b^3 – 4b^2 a - 18b + 9a completely.
Answer:
85
Step-by-step explanation:
Answer:
(2b-a)x(2b-3)x(2b+3)
Step-by-step explanation:
Warm-Up: Perpendicular Bisector
1.
What is WY? Explain your reasoning.
Answer: WY = 27
Step-by-step explanation:
Due to WX being a Perpendicular Bisector WY = WZ
4x - 5 = 2x + 11
Add 5 to both sides
4x = 2x + 16
Subtract 2x from both sides
2x = 16
Divide by 2
x = 8
So 4x - 5 of x = 8
4*8 = 32 - 5 =27
Answer:
27
Step-by-step explanation:
WY = WZ because XZ = XY
[tex]2x + 11 = 4x - 5\\(2x + 11) - 11 = (4x - 5) -11\\2x = 4x - 16\\-2x = -16\\x = 8\\\\WY = 4x - 5\\WY = 4(8) -5\\WY = 32 - 5\\WY = 27[/tex]
A delivery company purchases a $20,000 van. The value of the van depreciates at a rate of 19% per year. How many years will it take before the van is worth half its original purchase price? Round to the nearest tenth of a year.
A 1.7 years
B 4.0 years
C 3.3 years
The longest run way at an airport has the shape of a rectangle and an area of 1,573,000 sq ft. This run way is 130 feet wide. How long is the run way?
Answer:
12,100 feet
Step-by-step explanation:
The longest run way at an airport has the shape of a rectangle and an area of 1,573,000 sq ft. This run way is 130 feet wide. How long is the run way?
The area of a rectangle = Length × Width
Width = 130 feet
Area = 1,573,000 sq ft
The Length = Area/Width
= 1,573,000 sq ft/130 feet
= 12,100 feet
Therefore, the runaway is 12,100 feet long.
A car salesman sells cars with prices ranging from $5,000 to $45,000. The box plot shows the distribution of the numbers of cars he expects to sell over the next 10 years.
The salesman has observed that many students are looking for cars that cost less than $5,000. If he decides to also deal in cars that cost less than $5,000 and projects selling 200 of them over the next 10 years, how will the distribution be affected?
A. The mean and the median will be the same.
B. The median will shift to the right.
C. The mean will shift to the left.
D. The mean will shift to the right.
please help me .......
Answer:
A
Step-by-step explanation:
Use one step of Euler's Method with Ar = .3 to approximate y(1.3) where y(x) is the solution of the differential equation y'(x) = 2xeª — y, with initial data y(1) = 0.
Using Euler's Method with a step size of 0.3 and the given initial data and differential equation, the approximate value of y(1.3) is 0.3 × 2[tex]e^{0.3[/tex].
To approximate the value of y(1.3) using Euler's Method, we need to take one step with a step size of h and update the y-value accordingly. Here's how to do it step by step:
Determine the step size, h. In this case, we want to approximate y(1.3) using the initial data at y(1). Since we know that x increases from 1 to 1.3, the step size is h = 1.3 - 1 = 0.3.
Calculate the slope at the initial point (x0, y0). The slope can be found using the given differential equation y'(x) = 2x[tex]e^a[/tex] - y. Plugging in the values x0 = 1 and y0 = 0, we get:
y'(1) = 2(1)[tex]e^{0.3[/tex] - 0 = 2[tex]e^{0.3[/tex].
Compute the approximate value of y at the next step. Using Euler's Method, we can update the y-value as follows:
y1 = y0 + h × y'(x0, y0)
= 0 + 0.3 × 2[tex]e^{0.3[/tex].
Evaluating the expression:
y1 = 0.3 × 2[tex]e^{0.3[/tex].
This gives us the approximate value of y(1.3) using Euler's Method with the given initial data and differential equation.
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