The 95% confidence interval that estimates proportion of 8th graders that are involved in an after school activity (0.745, 0.895) , the correct option is (a) .
In the question ,
it is given that ,
simple random sample of 100 8th graders is taken ,
that means ,
n = 100 ,
also given that , 82% of them are involved with some type of after school activity.
means ; p = 0.82 .
the level of significance (α) = 100 - 95 = 5% = 0.05 .
the critical value= [tex]Z_{\alpha /2}[/tex] = [tex]Z_{0.025}[/tex] = 1.959964 ......from the Z table .
the lower limit of the 99% confidence interval is = p - [tex]Z_{\alpha /2}[/tex]*SE
and the upper limit for the 99% confidence interval is= p + [tex]Z_{\alpha /2}[/tex]*SE .
the standard error is √(p(1-p)/n
= √(0.82(1 - 0.82)/100
= 0.0384
So , the lower limit is ⇒ 0.82 - 1.959964*0.0384
On simplification ,
we get ,
lower limit is = 0.7447006 ≈ 0.745 .
the upper limit is = p + [tex]Z_{\alpha /2}[/tex]*SE
= 0.82 + 1.959964*0.0384
On Simplification ,
we get ,
upper limit is = 0.8952994 ≈ 0.895 .
Therefore , the confidence interval is (0.745, 0.895) .
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Fifteen less than twice a number is the same as the number plus two. What is the number?
The number is 17.
The first part is "Fifteen less than twice a number".
Let us say that n represents the unknown number.
Twice a number is the same as two times the number or 2n, and fifteen less than 2n is 2n−15.
The next part "is the same as the" part of the word problem indicating that the two parts are equal. So we use an equal sign to represent it⇒2n−15 =
The third part of the problem is "the number plus two". This is the same as n+2
The final equation is 2n-15=n+2
To solve for n, we would add 15 to both sides: 2n=n+17
Then subtract 1n from both sides: n=17
The number is 17.
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The Girl Scouts sponsor a Movie Night each year. In the first year, there were 26 participants. In the fourth year, there were 89 participants. Write an equation in slope-intercept form modeling this situation where y, number of participants, is a function of x, number of years. How many participants are predicted for the 6th year?
The required Slope-intercept form is y = 21x + 5 and the number of participants in the 6th year is 131.
Slope-intercept form:The slope-intercept form is One of the most common ways to describe a line's equation. The general form of a slope-intercept form is given by
y = mx + cWhere m is the slope and c is the y-intercept
And the formula for Slope is given by
Slope (m) = (y₂ - y₁)/ (x₂ - x₁)Here we have
Number of participants in 1st year = 26
Number of participants in 4th year = 89
Take number of years as x - coordinate
Number of participants as y - coordinate
As we know for 1 year, number of participants is 26
=> The pair of coordinates = (1, 26)
For 4th year, number of participants is 89
=> The pair of coordinates = (4, 89)
Now we will find the slope-intercept form for the situation
using the coordinates (1, 26) (4, 89)
As we know slope m = (y₂ - y₁)/(x₂- x₁)
Slope m = (89 - 26)/(4 - 1) = 63/3 = 21
As we know slope intercept form, y = mx + c
=> y = 21x + c --- (1)
As per the situation, Line (1) will pass through (1, 26)
=> 26 = 21(1) + c
=> c = 26 - 21
=> c = 5
=> y = 21x + 5
Therefore,
The required Slope-intercept form is y = 21x + 5
To find the number of participants in the 6th year, take x = 6
=> y = 21(6) + 5
=> y = 126 + 5
=> y = 131
Therefore,
The required Slope-intercept form is y = 21x + 5 and the number of participants in the 6th year is 131.
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the question is in the screen shot need this answered by 11:59 pm
Based on the line of best fit that models the data points, the y-value when x = 24 is equal to 20.
How to determine a line of best fit for the data set?In order to determine a linear equation for the line of best fit that models the data points described above, we would have to calculate the slope of the trend line.
Mathematically, the slope of a straight line can be calculated by using this formula;
Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope, m = (y₂ - y₁)/(x₂ - x₁)
From the information provided, we have the following points:
Points on x-axis = (4, 8).
Points on y-axis = (5, 8).
Substituting the given points into the formula, we have;
Slope, m = (8 - 5)/(8 - 4)
Slope, m = 3/4
Slope, m = 0.75
Mathematically, the slope-intercept form of a straight line is given by;
y = mx + c
Where:
x and y are the points.m represents the slope.c represents the y-intercept.Note: The y-intercept is equal to 2 based on the ordered pair (0, 2).
A linear equation for the line of best fit in slope-intercept form is given by:
y = 0.75x + 2
When x = 24, the value of y is;
y = 0.75(24) + 2
y = 18 + 2
y = 20.
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At a particular restaurant, each mini hotdog has 60 calories and each mozzarella stick has 70 calories. A combination meal with mini hotdogs and mozzarella sticks is shown to have 1080 total calories and 5 more mini hotdogs than mozzarella sticks. Write a system of equations that could be used to determine the number of mini hotdogs in the combination meal and the number of mozzarella sticks in the combination meal. Define the variables that you use to write the system.
Answer:
the combination meal contains 18 mini hotdogs and 13 mozzarella sticks.
Step-by-step explanation:
To determine the number of mini hotdogs and mozzarella sticks in the combination meal, we can use the following system of equations:
Let x be the number of mini hotdogs in the combination meal.
Let y be the number of mozzarella sticks in the combination meal.
The first equation represents the total number of calories in the combination meal: 60x + 70y = 1080
The second equation represents the difference between the number of mini hotdogs and mozzarella sticks: x - y = 5
Thus, the system of equations is:
60x + 70y = 1080
x - y = 5
To solve this system, we can use a variety of methods, such as substitution or elimination. For example, we can eliminate x by adding the equations together, which yields:
60x + 70y = 1080
x - y = 5
60x - x + 70y - y = 1080 - 5
59x + 69y = 1075
Dividing both sides by 59, we find that x = 18.
Substituting this value into the second equation, we find that y = 18 - 5 = 13.
Therefore, the combination meal contains 18 mini hotdogs and 13 mozzarella sticks.
Answer:
There are 9 pizza rolls and 12 mini hotdogs in the combination meal.
Step-by-step explanation:
We are given the following in the question.
Let x be the number of pizza rolls sold and y be the number of mini hotdogs in the combination meal.
Total number of items in combination meal = 21
Thus, we can write the equation
Calorie in a pizza roll = 60
Calorie in a mini hotdog = 70
Total calories = 1380
Thus, we can write the equation
Solving the two equations, we get,
Thus, there are 9 pizza rolls and 12 mini hotdogs in the meal.
Why is square a regular polygon?
A Polygon is a closed figure made up of line segments (not curves) in a two-dimensional plane. Polygon is the combination of two words, i.e. poly (meaning many) and gon (meaning sides). Usually , a minimum of three line segments is required to connect end to end, to make a closed figure. In terms of geometry, a polygon is a plane figure that is described by a finite number of straight line segments (greater than 3) connected to form a closed polygonal chain.
A regular polygon is a polygon with sides equal in length and angles equal in measure. For example, a square has all four sides equal and all four angles equal to 90 degrees. Hence, it is a regular polygon.
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(1 point) in the 6/51 lottery game, a player picks six numbers from 1 to 51. how many different choices does the player have if repetition is not allowed? note that the order of the numbers is not important. your answer is :
There are 18 million different choices for a player to pick six numbers from 1 to 51. By using the combinations formula, the required value is obtained.
What is the formula for finding the number of combinations?The combinations formula is as follows:
ⁿCₓ = n!/(n - x)!x!
Where n is the total number of things and x is the required number of things.
Calculation:It is given that,
In a 6/51 lottery game, a player picks six numbers from 1 to 51.
So, the number of different choices the player has if repetition is not allowed is
ⁿCₓ = n!/(n - x)!x!
Here, n = 51 and x = 6
On substituting the values, we get
⁵¹C₆ = 51!/(51 - 6)!6!
⇒ ⁵¹C₆ = 51!/45!6!
⇒ ⁵¹C₆ = (51 × 50 × 49 × 48 × 47 × 46 × 45!)/45! × 6!
⇒ ⁵¹C₆ = (51 × 50 × 49 × 48 × 47 × 46)/6 × 5 × 4 × 3 × 2 × 1
⇒ ⁵¹C₆ = 17 × 10 × 49 × 47 × 46 = 170 × 105938 = 18,009,460
Therefore, there are 18 million choices for the player to pick six numbers from a set of 51 numbers.
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Maria was given this absolute value graph and needs to come up with the equation, domain, range and intercepts.
function is y = |x|..and from her knowledge with translations she knows that it has translated horizontally to the right 4 units.
So she says the new equation must be y = |x+4|. The domain is all values of x. The range is all values of y greater u
to zero. The y-intercept is (0,4). There isn't an x intercept, because it just sits at (4,0). can you find any errors in her solution?
Maria wrote incorrectly the function, it is:
y = |x - 4|
And:
Domain: all real numbers.Range: all real numbers equal to or larger than zero.y-intercept: (0, 4)x-intercept: (4, 0).There are errors in her solution?She started with the parent absolute value function:
y = |x|
And wrote a translation to the right as:
y = |x + 4|
That is her mistake, a translation to the right of N units is written as:
g(x)= f(x - N)
So for a translation to the right of 4 units, we need to subtract 4 to the input, the actual function that we can see on the graph is written as:
y = |x - 4|
Now, the y-intercept is what we get when we evaluate in x = 0:
y = |0 - 4| = 4
So the y-intercept is (0, 4).
The x-intercept is the value of x such that y = 0, so we need to solve:
|x - 4| = 0
x - 4 = 0
x = 4
The x-intercept is (4, 0).
Finally, the domain (like in all absolute value functions) is the set of all real numbers, and the range is the set of all real numbers equal to or larger than zero.
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3/5w=4
Pls hurrrrrrrrrrry with this one thank u!
Answer:
w = [tex]\frac{20}{3}[/tex]
Step-by-step explanation:
[tex]\frac{3}{5}[/tex] w = 4 ( multiply both sides by 5 to clear the fraction )
3w = 20 ( divide both sides by 3 )
w = [tex]\frac{20}{3}[/tex]
how to construct a confidence interval of the population proportion given at the level of confidence
Answer:
Step-by-step explanation:
what i do not undersante
evaluate. (3/8 3/4)−(1/3 1/6) enter your answer as a fraction in simplest form by filling in the boxes. $$
The value of (3/8+3/4)(1/3+1/6) in its most basic form of fraction is 5/8.
What is fraction?Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English. In mathematics, a fraction is used to denote a portion or component of the whole. It stands for the proportionate pieces of the whole. Numerator and denominator are the two components that make up a fraction. The numerator is the number at the top, and the denominator is the number at the bottom.
Here,
(3/8+3/4)−(1/3+1/6)
=3/8+3/4
=(3+6)/8
=9/8
=1/3+1/6
=(2+1)/6
=3/6
=1/2
=9/8-1/2
=(9-4)/8
=5/8
The value of (3/8+3/4)−(1/3+1/6) is 5/8 in the simplest form of fraction.
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The standard deviation of a sample of 100 observations equals 64. The variance of the sample equals 10 6400 4096 Question 15 (1 point) The interquartile range is the 50th percentile the difference between the third quartile and the first quartile another name for variance the difference between the largest and smallest values
The variance of a sample is 4,096. And for interquartile, the difference between the largest and smallest values. The correct answer is option D
To calculate the variance we have a small formula:
v=s^2-----(1)
v=variance
s=Standard deviation
so, given that s=64
substitute in equation(1)
v=64*64
v=4096.
variance: The variance is a measure of variability. It is calculated by taking the average of squared deviations from the mean.
Variance is denoted by a symbol: σ2.
Interquartile range (IQR) is a measure of statistical dispersion, which is used to spread the data. The IQR is also called midspread.
To calculate the IQR, the data set is divided into quartiles. These quartiles are denoted by Q1 (another name is the lower quartile), Q2 (the median), and Q3 (also called the upper quartile). The lower quartile corresponds with the 25th percentile and the upper quartile corresponds with the 75th percentile, so IQR = Q3 − Q1
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What is the measure of angle B in this triangle?
Enter your answer in the box.
m∠B=
By using the fact that the sum of all internal angles must be equal to 180°, we will see that the measure of angle B is 70°.
How to find the measure of angle B?Remember that the sum of the internal angles of a triangle is always equal to 180°, then we can write the linear equation:
40° + (2x - 30°) + (x + 20°) = 180°
(2x - 30°) + (x + 20°) = 180° - 40°
2x + x - 30° + 20° = 140°
3x = 140° + 30° - 20°
3x = 150°
x = 150°/3
x = 50°
Then the measure of angle B is (2x - 30°) = (2*50° - 30°) = 70°.
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The correct answer is 70
(9x-6)ln(3)=(12x-8)ln(4)
solve for x with steps
Answer:
x = 2/3
Step-by-step explanation:
ln3^(9x-6) = ln4^(12x-8)
9x - 6 = 12x - 8
12x - 9x = -6 + 8
3x = 2
3/3 x = 2/3
x = 2/3
suppose the interval [-4,4]is divided into n=4 equal subintervals. what are the right endpoints, left endpoints, and midpoints of these intervals?
For the subintervals -
right endpoints: [2,4]left endpoints: [-4,-2]midpoints: [-2,0] and [0,2]Explain the term subintervals?Either of numerous smaller intervals through which a larger interval is divided. A division of an interval into subintervals is called a partition; the subintervals are the subintervals that make up the partition, in a sense. The width of a widest subinterval, not the partition's sidest subinterval, serves as the partition's norm.For the stated intervals;
interval [-4,4]
Total interval length;
= 4 - (-4)
= 4 + 4
= 8
Divide the interval in n=4 equal subintervals.
8/ 4 =2
First subinterval; [-4,-2]
Second subinterval; [-2,0]
Third subinterval; [0,2]
Fourth subinterval; [2,4]
Thus,
right endpoints: [2,4]
left endpoints: [-4,-2]
midpoints: [-2,0] and [0,2]
Thus, the subintervals of the given interval [-4,4] is obtained.
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find the exact values of x and y. (let r = 10.)
Using Pythagoras' theorem, we know that the exact values of x and y are (A) 2√3 and 4√3 respectively.
What is Pythagoras' theorem?In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relationship in Euclidean geometry between the three sides of a right triangle.
According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.
So, the trigonometric ratio formula:
Tanθ = opp. sides of θ/adj. sides of θ
Tan60° = 6/x
We know 60° = √3:
√3 = 6/x
Multiply both LHS and RHS by x as follows:
√3 * x = 6/x * x
√3 * x = 6
Divide both LHS and RHS by √3 as follows:
√3 * x/√3 = 6/√3
x = 2√3
Use of Pythagoras' theorem:
y² = 6² + (2√3)²
y² = 36 + 12
y² = 48
y = 4√3
Therefore, using Pythagoras' theorem, we know that the exact values of x and y are (A) 2√3 and 4√3 respectively.
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What is the image point of ( -1, -5) after a translation left 1 unit and up 4 units?
if a regulation basketball is randomly selected, what is the probability that it will weigh between 20.5 and 23.5 ounces?
Therefore, the probability that basketball will weigh between 20.5 and 23.5 is 0.866
What is probability ?Probability is the concept that describes the likelihood of an event occurring. In real life, we frequently have to make predictions about how things will turn out. We may be aware of the result of an occurrence or not. When this is the case, we refer to the likelihood that the event will occur or not.
Here,
X υ N (22,1)
Probability that basketball will weigh between 20.5 and 23.5
is:
=> P(20.5 < x < 23.5)= P[ 20.5-22/1 < z < 23.5-22/ 1 ]
=> P(20.5 < x < 23.5) = P(-1.5 < z < 1.5)
=> P(20.5 < x < 23.5) = 0.866
Therefore, the probability that basketball will weigh between 20.5 and 23.5 is 0.866
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a researcher states that he expects that there will be a significant difference between 20- and 30-year- olds after a 12-week exercise training program using exercise heart rates and myocardial oxygen consumption as measures of performance. what kind of hypothesis is being used in this study?
The kind of hypothesis is being used in this study is Research hypothesis
Hypothesis
In statistics, a testable statement about the relationship between two or more variables or a proposed explanation for some observed phenomenon is known as hypothesis.
Given,
Here we know that a researcher states that he expects that there will be a significant difference between 20- and 30-year- old's after a 12-week exercise training program using exercise heart rates and myocardial oxygen consumption as measures of performance.
And we need to find the kind of hypothesis is being used in this study.
While we looking into the given question we know that a researcher contacts the research on 20- and 30-year- old's after a 12-week exercise training program using exercise heart rates and myocardial oxygen consumption as measures of performance.
And her record the result accordingly.
Basically this one refers his research hypothesis.
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bailey tried to prove that \triangle fgj\sim \triangle fhi△fgj∼△fhitriangle, f, g, j, \sim, triangle, f, h, i in the following figure, but her proof is wrong.
The first error Bailey made was in the justification for his initial statement. The correct term to use is reflexive property.
What is the Reflexive Property of Congruence?An angle, line segment, or shape is always congruent to itself, according to the reflexive characteristic of congruence in geometry.
If A is an angle, then A is an angle.
Angle A intersects Angle A.
An angle will always be equal to or congruent to itself, according to the reflexive property of congruence.
So, for instance, given an angle, B, so:
∠B ≅ ∠B
Based on the reflexive property of congruence and the illustration provided:
∠F ≅ ∠F
Therefore, the first error Bailey made was in the justification for his initial statement. The correct term to use is reflexive property.
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Complete question;
Bailey tried to prove that FGJ~FHI in the following figure, but her proof is wrong. What is the first mistake Bailey made in the proof?
What is the value of x in the
equation 2x+3y = 36, when y = 6?
8
9
27
36
3x + 1.5 = 2.5x + 4.7
Answer:
x = 6.4
Step-by-step explanation:
Answer: x=6.4
Step-by-step explanation:
Fill in the blank random variable has either a finite or a countable number of values A discrete random variable has either a finite or a countable number of values. probability continuous discrete required
A discrete random variable has either a finite or a countable number of values.
Discrete random variables are defined as variables that can only take on a finite number of values. If any random variable takes a countable number of all the possible values, it is referred to be a discrete random variable. For instance, while flipping a coin, the random variable X will take the values 0, 1, and 2 depending on the number of heads.
If the value of any variable, such as X, is uncertain, that variable is said to be a random variable. It may also be defined as a function that is crucial in giving values to the results of any random experiment. Depending on the sort of numeric values they include, random variables can be either discrete or continuous.
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A store receives `12` boxes that contain many different numbers of lemons. They weigh each box and then count the lemons. The data is in the scatter plot. A new box weighs `30` pounds. Approximately how many lemons are in the box?
answer - UR MOTHERRRRR
Answer:
12*30 is the answer
if u multiply it
jenny buys 222222 sports drinks for her soccer team. they are on sale for \$0.35$0.35dollar sign, 0, point, 35 off per drink. jenny paid \$18.70$18.70dollar sign, 18, point, 70 for the 222222 sports drinks. what question does the equation 22(x-0.35)
The original cost of each sports drink that Jenny bought for her soccer team was $1.20.
Number of sports drink that Jenny bought for her soccer team
= 22
The amount of discount that Jenny got on each drink as they were on sale
= $0.35
Amount that Jenny paid for 22 sports drinks
= $18.70
Let the original cost of each sports drink be $x
Amount that Jenny paid for each drink
= $(x-0.35)
Therefore, amount that Jenny paid for 22 sports drink
= 22× (x-35) = 18.70
(x-0.35) = 18.70/22
x = 0.85 + 0.35
x = $1.20
The question is incomplete, the complete question is:
Jenny buys 22 sports drinks for her soccer team, they are on sale for $0.35 off per drink. Jenny paid $18.70 for 22 sports drink. How much does each drink cost originally?
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2. There are 108 feet in 36 yards. What is the
constant of proportionality that relates y, the
number of yards to x, the number of feet?
Answer:
x=36
Step-by-step explanation:
Based on the given conditions, formulate: x = 108 / 3
Cross out the common factor: x = 36
get the result: x = 36
Answer: x = 36
Answer: 36
Step-by-step explanation:
if a sample of items is taken and the mean of the sample is outside the control limits, the process is:
If a sample of items is taken and the mean of the sample is out of control and the cause should be established producing high quality products.
The correct option is option (A).
When Statistical Process Control (SPC) samples an item and the mean of the sample is outside the control limits, the process is as follows. You don't have to worry within certain control limits using only natural sources of variation to produce under control within certain control limits. The process is said to be out of control and the cause should be investigated. That is, many sample points are outside the control limits, a sample of the item is taken, and the average of the samples is outside the control limits.
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Complete question:
In Statistical Process Control (SPC), if a sample of items is taken and the mean of the sample is outside the control limits, the process is:
a) out of control and the cause should be established producing high quality products b)in control and capable of producing within the established control limits in control,
c)there is no need for concern
d)within the established control limits with only natural causes of variation
(-4,-2) and (4,0) in linear equations
Answer:
y = 1/4 x - 1
Step-by-step explanation:
y = mx + b
m = slope = (-2 - 0)/(-4 - 4) = -2/(-8) = 1/4
y = 1/4 x + b
0 = 1/4 × 4 + b
0 = 1 + b
b = -1
y = 1/4 x - 1
undergraduate students at a college belong to one of four groups depending on the year in which they are expected to graduate. each student must choose one of 21 differ- ent majors. how many students are needed to assure that there are two students expected to graduate in the same year who have the same major?
Maximum number of distinct majors/groups: 84 therefore, the 85th student must be the same as one of the 84 students.
What would a typical graduation date be?Date of anticipated graduation: May 15, 2020, or Spring 2020 for graduation (expected). Instead of expected or anticipated, you can use the word pending if you're presently working to finish your final semester.
Do I need to mention my anticipated graduation date on my resume?Employers may be able to see that you are actively pursuing your degree even though you haven't graduated by seeing your anticipated graduation date on your resume.
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Is quadrilateral ABCD a rectangle? Provide justification for your decision using the grid or by explanation.
As per the rules in geometry the given figure is rectangle
what is geometry?
Studying the dimensions, sizes, positions, angles, and shapes of objects is the subject of the mathematical branch known as geometry.
explanation:
1. ABC = 90 ................ other angles can be of any value.
2. AB = CD ............... AC and BD might not be equal.
For rectangle, all angles have to be equal (hence, 90) and opposite sides should be equal. Neither of the two statement helps in determining if the two requirements are satisfied or not.
Hence the given figure is Rectangle
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Find the derivative for y=eu(x); u(x) is a function in terms of x.
The derivative for y=eu(x); u(x) is a function in terms of x is dy/dx = eu'(x) + u(x)e .
A derivative is the rate of change of a function with respect to a certain variable . There are certain rules of differentiation which help us to evaluate the derivatives of some particular functions. :
Power Rule.Sum and Difference Rule.Product Rule.Quotient Rule.Chain Rule.This equation can be solved using the product rule of derivatives :
According to the product rule derivative of uv will be taken as -
u(v)' + v(u)'
where (') represents derivative of the variable.
Therefore accordingly -
y = eu(x)
differentiating with respect to x
dy/dx = e(u(x))' + u(x)(e)'
dy/dx = eu'(x) + u(x)e ( derivative of e=e)
Therefore the derivative in terms of x is dy/dx = eu'(x) + u(x)e .
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