PART I. Simplify the following expression. Your final answer is to have fractions reduced, like terms combined, and as few exponents as possible. An exponent that has more than one term is still a single exponent. For example: x3x2bx−a, which has 3 exponents, should be re-expressed as x3+2b−a, which now has only 1 exponent. Problem 1. (20\%) 3yx+exy−(21eln(a)+x+e−xyx−e2xy+3e−x2a)e−x (x2+2x)2x+(x+26e−x−exxe−ln(x))e−x−x−a(x−2a−1)+32 (2y+e−ln(y)4x3e−ln(x))2y−(x2−(53−46))4y2+(yx2e−ln(x4)1)2y
Answers
Simplification of the given expression:3yx + exy - (21/eln(a)+x+e−xyx−e2xy+3e−x2a)e−x (x2+2x)2x+(x+26e−x−exxe−ln(x))e−x−x−a(x−2a−1)+32 (2y+e−ln(y)4x3e−ln(x))2y − (x2 − (5/3 − 4/6))4y2 + (yx2e−ln(x4)1)2y
The simplified expression is:(3yx + exy - 21/eln(a) e−x)/(x2+2x)2x + e−xyx−e2xy+3e−x2a + (x+26e−x−exxe−ln(x))e−x - (x−2a−1)−a+32/(2y+e−ln(y)4x3e−ln(x))2y - (x2 − 5/6)4y2 + yx2e−ln(x4)12yAnswer more than 100 words:Simplification is the process of converting any algebraic or mathematical expression into its simplest form. The algebraic expression given in the problem statement is quite complicated, involving multiple variables and terms that need to be simplified. To simplify the expression,
we need to follow the BODMAS rule, which means we need to solve the expression from brackets, orders, division, multiplication, addition, and subtraction. After solving the brackets, we have the following expression: (3yx + exy - 21/eln(a) e−x)/(x2+2x)2x + e−xyx−e2xy+3e−x2a + (x+26e−x−exxe−ln(x))e−x - (x−2a−1)−a+32/(2y+e−ln(y)4x3e−ln(x))2y - (x2 − 5/6)4y2 + yx2e−ln(x4)12yNow, we need to solve the terms with orders and exponents, so we get:(3yx + exy - 21/eln(a) e−x)/(x2+2x)2x + e−x(y−x−2xy)+3e−x2a + (x+26e−x−x e−ln(x))e−x - (x−2a−1)−a+32/(2y+4x3/y)e−ln(x)2y - (x2 − 5/6)4y2 + yx2e−ln(x4)2yNow, we need to simplify the terms with multiplication and division, so we get:(3yx + exy - 21/eln(a) e−x)/(x2+2x)2x + e−x(y−3x)+3e−x2a + e−x(x+26e−x−x e−ln(x)) - (x−2a−1)−a+32/(2y+4x3/y)e−ln(x)2y - (x2 − 5/6)4y2 + yx2e−ln(x4)2yFurther simplification of the above expression gives the following simplified form:(3yx + exy - 21/eln(a) e−x)/(x2+2x)2x + (3e−x2a + 26e−x + x e−ln(x))e−x + (x−2a−1)−a+32/(2y+4x3/y)e−ln(x)2y - (5/6 − x2)4y2 + yx2e−ln(x4)2yThe above expression is the simplest form of the algebraic expression given in the problem statement.
The algebraic expression given in the problem statement is quite complicated, involving multiple variables and terms. We have used the BODMAS rule to simplify the expression by solving the brackets, orders, division, multiplication, addition, and subtraction. Further simplification of the expression involves solving the terms with multiplication and division. Finally, we get the simplest form of the expression as (3yx + exy - 21/eln(a) e−x)/(x2+2x)2x + (3e−x2a + 26e−x + x e−ln(x))e−x + (x−2a−1)−a+32/(2y+4x3/y)e−ln(x)2y - (5/6 − x2)4y2 + yx2e−ln(x4)2y.
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The simplified form of the equation is : 2(xy + \(e^x\)y) - 7/6a
Given equation,
3yx + \(e^{x}\)y - (1/2\(e^{ln(a) + x}\)+ yx/\(e^{-x}\) −\(e^{2x}\)y+2a/\(3e^{-x}\))\(e^{-x}\)
For the simplification, the basic algebraic rules can be applied.
Therefore,
3xy + \(e^{ x}\) y - (1/2 \(e^{ln(a) + x}\) + xy / \(e^{-x}\) - \(e^{2x}\) y + 2 a/3\(e^{-x}\))\(e^{-x}\)
Taking \(e^{-x}\) inside the bracket ,
= 3xy + \(e^{x}\)y - (1/2a + xy - \(e^{x}\)y + 2/3 a)
Now the given equation reduces to ,
= 3xy + \(e^{x}\)y -(1/2a + xy - \(e^{x} y\) + 2/3a)
= 2(xy + \(e^x\)y) - 7/6a
Therefore, the given equation is simplified and the simplified equation is
2(xy + \(e^x\)y) - 7/6a
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Related Questions
Two cards are dealt from a standard deck of cards, after it is dealt the first card IS REMOVED from the deck. Is this a Dependent or Independent probability problem?
Answers
Answer:
Dependent. The probability of what the second card will be changes based on what the first card is
Step-by-step explanation:
I need help understanding how to solve this problem .
Answers
10*|x|-6=24
10*|x|=30
Divided both sides of the equation by 10
|x|=3
X=3 X=-3
let x be a uniformly distributed random variable on [0,1] then x divides [0,1] into the subintervals [0,x] and [x,1]. by symmetry
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When x is a uniformly distributed random variable on [0,1], it divides the interval [0,1] into two subintervals: [0,x] and [x,1]. This division exhibits symmetry, as explained in the following paragraphs.
Consider a uniformly distributed random variable x on the interval [0,1]. The probability density function of x is constant within this interval. When x takes a particular value, it acts as a dividing point that splits [0,1] into two subintervals.
The first subinterval, [0,x], represents all the values less than or equal to x. Since x is randomly distributed, any value within [0,1] is equally likely to be chosen. Therefore, the probability of x falling within the subinterval [0,x] is equal to the length of [0,x] divided by the length of [0,1]. This probability is simply x.
By symmetry, the second subinterval, [x,1], represents all the values greater than x. The probability of x falling within the subinterval [x,1] can be calculated as the length of [x,1] divided by the length of [0,1], which is equal to 1 - x.
The symmetry arises because the probability of x falling within [0,x] is the same as the probability of x falling within [x,1]. This symmetry is a consequence of the uniform distribution of x on the interval [0,1].
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find and sketch the domain of the function. f(x, y, z) = ln(81 − 9x2 − 9y2 − z2)
Answers
The function is defines for all (x,y,z) ∈ R³
Hence the domain of this equation is,
D = {(x, y, z) | 9x² + 9y² + z² ≤ 81
The function is bound by sphere.
The set of inputs that a function will accept is known as the domain of the function in mathematics. (f), " (f), where f is the function, are other ways to refer to it.
More specifically, the domain of f is X given a function Xto Yfcolon Xto Y. It should be noted that in contemporary mathematical terminology, a function's domain is a component of its definition rather than a quality.
The function f can be graphed in the Cartesian coordinate system in the particular situation where X and Y are both subsets of R In this instance, the graph's x-axis shows the domain as the projection.
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Which is the factor in this operation 13x 2 yz
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The factors in the expression 13x²yz are 13, x², y, and z.
What are the factors?A factοr is a number that divides anοther number withοut leaving a remainder. Fοr example, the factοrs οf 12 are 1, 2, 3, 4, 6, and 12, because these numbers divide 12 withοut leaving a remainder.
The expressiοn 13x²yz is a multiplicatiοn οf several terms. The factοrs in this expressiοn are:
13 is a cοnstant quantity. This means that its value dοes nοt change and it dοes nοt depend οn any variables. It is simply a number that is being multiplied with the οther terms.
x² is a variable quantity raised tο the pοwer οf 2. This means that x is a variable and the 2 as an expοnent indicates that it is being multiplied with itself. In οther wοrds, x² is the same as x multiplied by x. This is knοwn as "x squared".
y and z are alsο variable quantities, but they dο nοt have any expοnents attached tο them. They are simply variables that are being multiplied with the οther terms.
When we put all of these terms together and multiply them, we get the expression 13x²yz. So, to summarize, the factors in this expression are:
13, which is a constant factor
x², which is a variable factor raised to the power of 2
y, which is a variable factor
z, which is a variable factor
Therefore, the factors in the expression 13x²yz are 13, x², y, and z.
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Which equation represents a line which is parallel to the line 8x – 7y = 35?
Answers
Answer:
anything with a slope of 8/7
Step-by-step explanation:
A greengrocer buys 20 cases of oranges at a cost of $15 per case. Each case contains 10 kg of oranges. If he sells the oranges at $4/kg, how many kilograms must he sell before he makes a profit? If he sells all the oranges what will be his profit?
Answers
Answer:greengrocer should Dell 17 kg before profit. 500$ profit
Step-by-step explanation:
Timmy is trying to run a marathon, which is 26 miles, at the end of the year. Every month, he adds 2 miles to how far he can run. If he starts the year able to run 4 miles, at least how many months does he have to train before he can run a marathon?
Answers
Answer:
if he starts at four, add two until you get to 26 or you can add by 4 or 8 to go faster.
4+4+4+4+4+4+2 = 26 so it'll take him 11 months
Step-by-step explanation:
Suppose y, ... Yn ~ N(u,02), with y known. Use the non-informative prior p(02) « 1/02. Obtain the sampling distribution (likelihood) and the posterior distribution.
Answers
To obtain the sampling distribution (likelihood) and the posterior distribution for this scenario, we can use Bayesian inference.
The sampling distribution (likelihood) can be represented as:
p(y|u,02) = (1/sqrt(2*pi*02)^n) * exp(-(1/(2*02)) * sum((yi-u)^2))
where y is the observed data, u is the mean of the normal distribution, and 02 is the variance of the normal distribution.
The non-informative prior for 02 can be represented as:
p(02) « 1/02
Using Bayes' theorem, we can obtain the posterior distribution:
p(u,02|y) = p(y|u,02) * p(02) / p(y)
where p(y) is the marginal likelihood. To simplify the calculation, we can integrate out u from the joint distribution:
p(02|y) = (p(y|02) * p(02)) / p(y)
where p(y|02) is the marginal likelihood for 02:
p(y|02) = (1/sqrt(2*pi*02)^n) * exp(-(n-1)/2)
We can then obtain the posterior distribution for 02:
p(02|y) « 1/02 * exp(-(n-1)/2)
This is a gamma distribution with shape parameter (n-1)/2 and scale parameter 1/2. Therefore, the posterior distribution for 02 is:
02|y ~ Gamma((n-1)/2, 1/2)
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what is the surface area!!
Answers
Answer:
450
Step-by-step explanation:
find perimeter of bases and then the area. then find Lateral Surface area to get Surface area
who runs the fastest
Answers
Answer:
Ron run faster then other
Bob’s employer covers 23% of his family’s annual health insurance premium. The balance of the premium is deducted in equal amounts from Bob’s paycheck 26 times over the calendar year. If $185.30 is withheld from each of Bob’s paychecks, what is his family’s annual health insurance premium?
a.
$805.65
b.
$4,817.80
c.
$6,256.88
d.
$20,946.96
Answers
Answer:
4817.8
Step-by-step explanation:
185.30 x 26
185 x 26 is 4810
and 30 x 26 is 780 so
7.8 from 780
and
481.0 so
we add them together we get 4817.8
The wheel of a shopping cart that must be replaced is 3.5 inches in diameter. However, the only wheel you have is 2.75 inches in diameter. To keep the cart level, you must brace it out with a piece of metal. How much should you extend the new wheel out?
Answers
Answer:
you should extend the new wheel out by .75 cm
Step-by-step explanation:
2.75 + .75 = 3.5
A tree is currently
2
feet tall and grows
1.3
feet per year. Which inequality represents the time, in
x
years, when the tree will have a height of at least
20
feet?
Answers
The inequality expression for the number of years when tree will be atleast 20 feets tall is x ≥14
Current height = 2 Growth rate = 1.3 feets per yearThe height of the tree after x years can be represented as a linear equation thus :
Height = 2 + 1.3xNumber of years when the tree will be 20 feets tall :
20 = 2 + 1.3x 20 - 2 = 1.3x 1.3x = 18x = 13.84The tree would be atleast 20 feets tall in 14 years x this can be expressed thus
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The following chips are placed in a bucket: 4 red, 1 yellow, 5 blue, and 5 green. One chip is randomly selected from the bucket.
What is the probability that the chip is blue?
Answers
Answer:Red
Step-by-step explanation:
Answer:
Step-by-step explanation:
5 blue out of 15 chips
a store prints a request on each receipt asking customers to fill out a satisfaction survey online if they are willing. what type of sample is this?
Answers
The type of sample that a store prints a request on each receipt asking customers to fill out a satisfaction survey online if they are willing is a voluntary response sample.
In the statistics world, a voluntary response sample is a research sample that relies on individual self-selection. This is in opposition to random sampling, in which the samples are gathered in a way that ensures everyone in a particular population has an equal chance of being chosen. This method of self-selection is also known as self-selection bias or sampling bias.Voluntary response samples are subject to a variety of flaws. The responses may not be representative of the population as a whole, and they may be skewed by numerous factors, such as which individuals are most likely to volunteer, how these volunteers differ from the population as a whole, and how the survey questions are phrased.The results of a voluntary response survey may be useful in generating hypotheses or gaining a general sense of how individuals feel about a particular subject. However, they are not reliable enough to draw any conclusions or to be taken seriously in the scientific sense.
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Solve Question!
6 = 2y/3
Y=
Answers
Y = 9
Answer:
y=9
Step-by-step explanation:
So 2y=19
y=9
What is the y-intercept of y=-3x + 6?
A. -6
B. -3
C. 3
D. 6
Answers
Answer:
D. 6
Step-by-step explanation:
the last number in the equation is the y-intercept. The answer properly written would be (0,6). Hope this helped!
Answer:
D
Step-by-step explanation:
billy took a 3/4 mile hike in the woods. if the stopped every 1/4 of a mile to drink from his water bottle, how many times did the top?
Answers
A 2kg bag of flour provides enough flour for 25 rolls. How much flour is needed for 8 rolls in grams?
Answers
Answer:
640 gram 8 rolls
Step-by-step explanation:
2000 ÷ 25 = 80 gram 1 roll
80 × 8 = 640 gram 8 rolls
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HELP AND HURRY PLEES
Answers
Answer:
(7, -3) d.
Step-by-step explanation:
You move 7 to the right, and 3 units down on the graph, starting from the origin (0,0).
and you get the correct answer : D.
how would you determine real gdp if you only knew the gdp
Answers
This can be done by finding the CPI or another price index for the same period. Once you have the GDP deflator, you can use the formula above to calculate the real GDP.
If you only know the nominal GDP, you cannot determine the real GDP. In order to determine the real GDP, you need to take into account inflation. This is done by adjusting the nominal GDP for inflation using a price index, such as the Consumer Price Index (CPI).The formula for calculating real GDP is:Real GDP = Nominal GDP / GDP DeflatorThe GDP deflator is a measure of inflation that takes into account changes in the prices of all goods and services produced in an economy. It is calculated by dividing nominal GDP by real GDP and multiplying by 100. This gives us a ratio of the current price level to the base year price level.
The base year price level is assigned a value of 100.Using this formula, we can see that if we know the nominal GDP and the GDP deflator, we can calculate the real GDP. For example, if the nominal GDP is $10 trillion and the GDP deflator is 120, the real GDP would be:Real GDP = $10 trillion / 1.2 = $8.33 trillionTherefore, in order to determine the real GDP if you only know the nominal GDP, you need to obtain the GDP deflator.
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Please need answers please
Answers
Answer:
The absolute value is the distance between a number and zero. The distance between −13 - 13 and 0 0 is 13 13 . −1⋅13 - 1 ⋅ 13. Multiply −1 - 1 by 13 13 .
Step-by-step explanation:
Happy to Help 13
A yoga instructor collected student data. He found that students who had less sleep did not tend to burn more or fewer calories during class. What can he conclude
Answers
the correct conclusion is: 1) There is no correlation between the amount of sleep and the number of calories burned.
Based on the information provided, the yoga instructor can conclude:
1) There is no correlation between the amount of sleep and the number of calories burned during class.
Since the instructor found that students who had less sleep did not tend to burn more or fewer calories during class, it suggests that the amount of sleep and the number of calories burned are not related or correlated. The data does not indicate any significant relationship between these variables.
Therefore, the correct conclusion is:
1) There is no correlation between the amount of sleep and the number of calories burned.
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Given question is incomplete, the complete question is below
A yoga instructor collected student data. He found that students who had less sleep did not tend to burn more or fewer calories during class. What can he conclude?
1)There is no correlation between amount of sleep and number of calories burned.
2)There may or may not be causation. Further studies would have to be done to determine this.
3)There is a correlation between amount of sleep and number of calories burned. There is probably also causation. This is because there is likely an increase in the number of calories burned with an increase in the amount of
I really need this a please help me
Answers
Answer:
The amount of water it gets?? I'm just going for an answer here, cause it s talking about water
Step-by-step explanation:
In triangle ABC, m/ A=z and m/ B=y. Which of these can be proved using the triangle sum theorem?
O A m/C= 180° - (x + y)
O B. m/C=y
O c. m/C=x+y
O D. m/C= 180° − x+y
Answers
The formula that can prove the triangle sum theorem is m ∠ C = 180°-(x + y)
What is a triangle?A polygon with three sides, angles and vertices is called a triangle.
Given that, a triangle with two angels A and B are x and y respectively,
We need to choose an expression from the options which can be a proof of the sum of interiors angles of a triangle is 180°
So,
According to the angle sum property of a triangle, we will have,
∠ A + ∠ B + ∠ C = 180°
Put the given values of A and B.
x + y + ∠ C = 180°
∠ C = 180°-(x+y)
Hence, the formula that can prove the triangle sum theorem is m ∠ C = 180°-(x + y)
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3. 5-6x = 17 - 8x what’s the answer
Answers
Answer:
x=6
Step-by-step explanation:
5-6x=17-8x 5-6x=17-8x
5-6(6)=17-8(6) or 5+2x=17 added 8x to both sides
5-36=17-48 2x=12 subtracted 5 from both sides
-31=-31 x=6 divided both sides by 2
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Help ASAP! Find x: 4−x/5 + x+2/3 =6 Thank you!
Answers
Answer:
x=44
Step-by-step explanation:
Pretty straightforward!
4-x/5 +x+2/3=6
3(4-x) + 5(x+2) = 90 (Multiply both sides of the equation by 15, a multiple of both 5 and 3)
12-3x+5x+10=90 (Use Distributive property to multiply across parentheses)
-3x+5x=90-12+10 (Bring like terms together/Signs change when moved to the other side)
2x=88
x=44
Thank you for your time!
Answer: x=44
Step-by-step explanation: Pretty straightforward!
4-x/5 +x+2/3=6
3(4-x) + 5(x+2) = 90 (Multiply both sides of the equation by 15, a multiple of both 5 and 3)
12-3x+5x+10=90 (Use Distributive property to multiply across parentheses)
-3x+5x=90-12+10 (Bring like terms together/Signs change when moved to the other side)
2x=88
x=44
Thank you for your time!
The points (2,5), (3, 3) and (k, 1) all lie in a straight line.
(a) Find the value of k.
(b) find the equation of the line
Answers
Answer:
(a) k = 4 (b) y = -2x+9
Step-by-step explanation:
I know I solved it in reverse, but I hope you still be able to understand the way I solved.
If you have any questions about the way I solved it, don't hesitate to ask me in the comments below ;)
And if you find my answer helpful, please consider marking it Brainliest. Thnx
the NEW HDI is created from combining a number of different indices as described in the textbook. the value of each sub-index used in the creation of the HDI is created using a dimension index. Calculate the Dimension index if the Actual Value=8.5 , The Minimum Value=4.0 and the Maximum value=19.3
Answers
The Dimension Index is 0.322.
How is the Dimension Index calculated?The Dimension Index is calculated using the formula:
\[ \text{Dimension Index} = \frac{\text{Actual Value} - \text{Minimum Value}}{\text{Maximum Value} - \text{Minimum Value}} \]
Given that the Actual Value is 8.5, the Minimum Value is 4.0, and the Maximum Value is 19.3, we can plug these values into the formula:
\[ \text{Dimension Index} = \frac{8.5 - 4.0}{19.3 - 4.0} = \frac{4.5}{15.3} \approx 0.294 \]
So, the Dimension Index is approximately 0.294.
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