Answer:
Anna the teacher bought 54 child tickets and 19 adult tickets
Step-by-step explanation:
Find the value of c ( x + 1 ) factor of the polynomial p ( x ) = 5 x 4 + 7 x 3 − 2 x 2 − 3 x + c
Step-by-step explanation:
I think the actual equation you meant to write was 5x⁴ + 7x³ - 2x² - 3x + c.
You're going to equate the whole equation to 0 and replace x for -1( because x + 1 is a factor)
= 5(-1)⁴ + 7(-1)³ - 2(-1)² - 3(-1) + c = 0
= 5 - 7 - 2 + 3 + c = 0
= - 1 + c = 0
Therefore c = 1
Let x and y be independent random variables with pdfs given by f and g, respectively. let h be the pdf of the random variable Z = X + Y
The pdf of the random variable Z = X + Y is given by the convolution of the pdfs of X and Y. The convolution is denoted by h(z) = (f * g)(z) = ∫f(x)g(z-x)dx. It represents the probability of the sum of two random variables taking on a certain value.
In other words, it is the probability of X taking on a certain value x and Y taking on a certain value z-x simultaneously. The convolution is only defined if X and Y are independent random variables, and the integral converges. It is also important to note that the convolution of two pdfs does not necessarily result in a pdf, it can also result in a cdf, if integral from minus infinity to z is taken instead of from minus infinity to infinity.
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Among all the vectors in Rn whose components add up to 1, find the vector of minimal length. In the case n=2, explain your solution geometrically.
The unit circle has a radius of 1, so it is the shortest distance from the origin to (x1,x2).
The vector of minimal length in Rn whose components add up to 1 is called the unit vector. The unit vector is calculated by dividing each component of the vector by the sum of all components. Thus, in Rn, the unit vector is given by (x1/s, x2/s, ..., xn/s), where s is the sum of all components.
In the case n=2, the unit vector is given by (x1/s,x2/s). Geometrically, this vector is the vector from the origin to the point (x1,x2) on the unit circle. This vector has minimal length because the unit circle has a radius of 1, so it is the shortest distance from the origin to (x1,x2).
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Angie bought a shirt that was priced at $16.50. She paid $18.82 at the counter. Find the tax rate.
Answer:
The price: 16.5
The total payment: 18.82
The amount of tax: 18.82-16.5 = 2.32
Tax rate = The amount of tax / The price = 2.32/16.5 = 0.14 = 14%
If packages of shredded cheese in the refrigerator case are lined up in 7 rows with 8 packages of shredded cheese in each row, how many packages of shredded cheese are there all together?
Using multiplication operation, the total number of packages of shredded cheese is 56.
What is multiplication operation?Multiplication operation is one of the four basic mathematical operations, including subtraction, division, and addition.
Multiplication operation has the following parts: multiplicand (the number being multiplied), the multiplier (the number doing the multiplication), the equal symbol, and the product (the result of the multiplication operation)
The number of rows = 7
The number of packages of shredded cheese per row = 8
The total number of packages = 56 (7 x 8)
Thus, the number of packages in the refrigerator is 56 shredded cheese.
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the whole numbers are written consecutively in rows as shown. each row contains two more numbers than the previous row. $123{,}000$ is the $m$th number in the $n$th row (counting from the left). enter the values of $m$ and $n$ in this order, separated by a comma. \[\begin{array}{lccccccccc} \text{row 1}
The values of m and n are m = 123,000 and n = (123,000 - m1) / 2 + 1.
The given number is 123,000 which is the mth number in the nth row.
The rows contain two more numbers than the previous row.
Let us assume that the first row has m1 numbers.
Therefore, the second row has m1 + 2 numbers, the third row has m1 + 4 numbers, and so on.
We can represent the above information in a general formula as;
m1 + 2 (n - 1) = m
where m1 is the number of elements in the first row and n is the row number in which 123,000 is present.
By solving the above equation, we get
m1 = m - 2 (n - 1)
Now, we can calculate the value of n as;
n = (m - m1) / 2 + 1
Substituting the values of m and m1, we get
n = (123,000 - m1) / 2 + 1
Therefore, the values of m and n are m = 123,000 and n = (123,000 - m1) / 2 + 1.
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How to find period with two midline’s picture is below
first off, next time make sure your screenshot is sharp enough and clear enough.
so if we notice the two points on the midline that you took, the horizontal distance will be from -4.5 to 3.6 which gives us a distance over the x-axis of 8.1 units, now half of that will be to the "orange" area, half of 8.1 is 4.05. Now, the ending of the "orange" part is not really clear, but that'd be the period, because that is the part that's repeating.
How long is it?
well, our 4.05 half ends after the "2", so without a better calibration of the picture, hmmm 2.20 or thereabouts, let's make an assumption the "orange" section ends at 16, so that'd be 4.05 + (16 - 2) ≈ 18.05.
How much water do you add to make each concentration? 25% sugar using 15 g sugar
Answer:
You can add 45 grams of water to 15 grams of sugar to make a 25% sugar solution.
Step-by-step explanation:
To make a 25% sugar solution, you need to add a certain amount of water to 15 grams of sugar. To determine this amount, you can use the following formula:
(desired concentration / 100) x total volume = amount of solute (in this case sugar)
We know that the desired concentration is 25%, and the amount of solute is 15 grams. To find the total volume, we can use the following formula:
amount of solute / desired concentration = total volume
15 grams / 0.25 = 60 grams
So the total volume of the solution is 60 grams, and the amount of water you need to add to make a 25% sugar solution using 15 grams of sugar is 45 grams.
You can add 45 grams of water to 15 grams of sugar to make a 25% sugar solution.
Another way to think of it is to add 3 times the amount of water as the amount of sugar, since 25% of 60g is 15g
Find the slope and y-intercept (if possible) of the equation of the line. (If an answer does not exist, enter DNE.)
y − 6 = 0
The slope of the equation of the line is 0 and the y-intercept is 6. To find the slope and y-intercept of the equation of the line, we need to first rewrite the equation in the standard form of y = mx + b.
The slope of the equation of the line is 0 and the y-intercept is 6.
Slope: 0
y-intercept: 6
To find the slope and y-intercept of the equation of the line, we need to first rewrite the equation in the standard form of y = mx + b.
In this equation, m is the slope and b is the y-intercept.
The equation is given as y − 6 = 0.
We can rewrite this equation as y = 0 + 6.
This can be rewritten as y = 0x + 6, where 0 is the slope and 6 is the y-intercept.
Therefore, the slope is 0 and the y-intercept is 6.
The slope of the equation of the line is 0 and the y-intercept is 6.
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What are the domain and range of f(x) = -24 ?
Domain: {-24} Range: All real numbers
Domain: {-24} Range: {-24}
Domain: All real numbers Range: All real numbers
Domain: All real numbers Range: {-24}
The domain of the function is, All real numbers.
And, The range of the function, {- 24}
What is Domain?The set of all inputs of the function is called Domain of set.
We have to given that;
The function is,
⇒ f (x) = - 24
Now, We know that;
The domain is where the function is defined.
Hence, The domain of function f (x) = - 24 is,
⇒ Domain = (- ∞, ∞)
And, The range is the set of values that correspond with the domain.
Hence, The range of the function, {- 24}.
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Sai buys $12,500 worth of music equipment. He finances his purchase
at a 2.5% simple interest rate and sets up a 24-month payment plan.
How much interest will Sai pay?
The amount of interest Sai will pay is $312.50.
What is intrest?Interest is the cost associated with borrowing money, or the return earned for lending money. It is typically expressed as a percentage of the principal amount borrowed or lent, and is usually paid periodically over the life of the loan. Interest can also be earned from investments, such as savings accounts, bonds, and other financial instruments. The rate of interest charged or earned varies depending on the nature of the loan or investment, the risk associated with the transaction, and the creditworthiness of the borrower or investor.
This is calculated by multiplying the principal amount of $12,500 by the interest rate of 2.5%, which equals 0.025. Then, the 0.025 is multiplied by the loan period of 24 months to come up with the total interest. Therefore, $12,500 x 0.025 x 24 = $312.50.
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A coffee shop is having a sale on prepackaged coffee and tea. Yesterday they sold 34
packages of coffee and 27 packages of tea, for which customers paid a total of $420. The day
before, 41 packages of coffee and 45 packages of tea was sold, which brought in a total of
$606. How much does each package cost?
Polynomial equations are those created by combining variables, exponents, and coefficients.The cost of coffee is 8 and the cost of tea is 4.
How much does each package cost?The higher exponent, known as the degree of the equation, might have several exponents.
When there is at least one algebraic term with at least one variable and all of the exponents are integers that are equal to or larger than zero, the equation is said to be a polynomial equation.
Coffee cost = Rs 8
Tea cost = Rs 4
Let the price of coffee be X
and the price of Tea be y , then
45 x + 41 y = 524
20 x + 11y = 204
y = 524 - 45 x /41=
= 20 x + 11( 524 -45 x)/41)
= 204
820 x + 5764- 495 x = 204* 41
325x = 2600
x = 8 y = 524 - 8* 45/45
y = 4
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Polynomial equations are those created by combining variables, exponents, and coefficients. The cost of coffee is 8 and the cost of tea is 4.
How much does each package cost?The higher exponent, known as the degree of the equation, might have several exponents.
When there is at least one algebraic term with at least one variable and all of the exponents are integers that are equal to or larger than zero, the equation is said to be a polynomial equation.
Coffee cost = Rs 8
Tea cost = Rs 4
Let the price of coffee be X
and the price of Tea be y , then
45 x + 41 y = 524
20 x + 11y = 204
y = 524 - 45 x /41=
= 20 x + 11( 524 -45 x)/41)
= 204
820 x + 5764- 495 x = 204* 41
325x = 2600
x = 8 y = 524 - 8* 45/45
y = 4
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The following scenario represents a proportional relationship.
Jerome's dry cleaning fee was $19.50 for 3 pairs of pants.
What is the constant of proportionality?
Answer:
6.5
Step-by-step explanation:
Proportional relationship:
[tex]y \propto x \implies y=kx[/tex]
where k is the (non-zero) constant of proportionality.
To determine the constant of proportionality, substitute the given values into the equation and solve for k:
x = 3y = 19.50[tex]\implies 19.50=3k[/tex]
[tex]\implies k=6.5[/tex]
Therefore, the constant of proportionality is 6.5.
Review: geometry are the lines represented by the equations at right parallel? support your reasoning with convincing evidence. homework help
Yes, the lines represented by the equations at right are parallel. This can be seen by examining the slopes of the equations. The slope of the first equation is -3/5 and the slope of the second equation is -3/5. Since the slopes are equal, the lines are parallel.
To determine if two lines are parallel, we need to compare their slopes. The equation of the first line is y = -3x/5 and the equation of the second line is y = 5x/3. To calculate the slope of the first line, we need to take the coefficient of x (-3/5) and divide it by the coefficient of y (1).
The resulting slope is -3/5. To calculate the slope of the second line, we need to take the coefficient of x (5/3) and divide it by the coefficient of y (1). The resulting slope is also -3/5. Since the slopes of both lines are equal, the lines are parallel.
The equation of the first line is y = -3x/5 and the equation of the second line is y = 5x/3. To calculate the slope of the first line, we need to take the coefficient of x (-3/5) and divide it by the coefficient of y (1).
The resulting slope is -3/5. To calculate the slope of the second line, we need to take the coefficient of x (5/3) and divide it by the coefficient of y (1). The resulting slope is also -3/5. Since the slopes of both lines are equal, the lines are parallel.
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in each of problems 1 through 4 show that the given differential equation has a regular singular point at x =0 and determine two for x >0.
A regular singular point is a point at which the differential equation has a non-removable singularity. The point x=0 is a regular singular point for problems 1-4. Two solutions for x>0 can be found by solving the differential equation around x=0.
A regular singular point is a point at which the differential equation has a non-removable singularity. In order to identify a regular singular point, we must first identify the point at which the equation has a non-removable singularity. For problems 1-4, the point x=0 is a regular singular point. To find two solutions for x>0, we can solve the differential equation around x=0. First, we must identify the coefficients of the equation, which will allow us to determine the order of the equation. Once we have determined the order, we can use the properties of regular singular points to find two solutions for x>0. For example, the equation may be of the form y' + P(x)y = Q(x), where P(x) and Q(x) are functions of x. Using the properties of regular singular points, we can solve for two solutions of the form y = x^r*F(x), where F(x) is a function of x and r is the order of the equation.
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The new bookcase for your future dorm room has the dimensions of 24 in. wide by 12 in. deep by 36 in.
tall. If one average textbook has the dimensions of 8.5 in wide by 11 inches long by 1.5 in. tall, how
many books could you fit on your bookshelf with no shelving?
On solving the provided question, we can say that since it is a cuboid books could you fit on your bookshelf = 24*12*36/8.5*11*1.5 = 10368/140.25 = 73.9251336898 = 73 books
what is cuboid?A cuboid is a solid or three-dimensional form in geometry. A cuboid is a convex polyhedron having 8 vertices, 12 sides, and 6 rectangular faces. Another name for a cuboid is a cuboid. A cube is a cuboid with six square faces. Boxes include things like books and bricks. The following are the key variations between cubic and cubic: In contrast to a cube, which has rectangular faces, a cube has six equally sized square faces. Even though the cube and cuboid structures have a similar appearance, they differ in some ways in terms of side length, diagonal, and area.
since it is a cuboid
books could you fit on your bookshelf = 24*12*36/8.5*11*1.5 = 10368/140.25 = 73.9251336898 = 73 books
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Ben scores 50 runs more than Chris in a cricket match if Chris scores x runs how much is ben score
Can you give me the step by step explanation too
Answer:
x+50
Step-by-step explanation:
I hope it helps
thanks
Find the indicated real nth root(s) of a.
n = 2, a = 400
Root: ?
Answer:
20 or +-20
Step-by-step explanation:
They are asking for an nth root. This is generic-speak for square root, third root, fourth root, etc.
Since n is 2, they are talking about 2th root...really 2nd root. But we commonly call that square root.
Square root of 400 is 20. (That's the principal square root because its positive) They asked for real roots, so, technically -20 is also a square root of 400.
20^2 = 400 and
(-20)^2 = 400
So square root of 400 is +- 20.
Or if this is an intro class, then just 20 is probably a good enough answer.
A theme park in Florida wants to attract more visitors. They post a survey on a travel website asking viewers which attractions they would like to see at the park. Identify the Sample for this situation. O Visitors to the theme park O People who responded to the survey O People visiting the website O Citizens of Florida
The sample for this situation is People who responded to the survey.
What is the sample?
A sample is a group of elements chosen from the population. The features that describe the population are called the parameters and the properties of the sample data are known as statistics. Population and sample both are important parts of statistics.
A sample is a subset of the population that is selected for a study.
In this case, the population is the group of people who might be interested in visiting the theme park in Florida.
The park wants to attract more visitors, so they post a survey on a travel website asking viewers which attractions they would like to see at the park.
The sample is the group of people who responded to the survey, as it represents the subset of the population that the park is trying to gather information from.
Hence, The sample for this situation is People who responded to the survey.
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Helppp!!! Pleaseeeeee
Answer:
f = 2÷7. I hope this helped your experience
Jake said you can compare two fractions with same denominator by only comparing the numerators
Jake said you can compare two fractions and determine which fraction is larger when two fractions have the same denominator by only comparing the numerators.
What is fraction?An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.
Given:
Two fractions have the same denominator.
Then,
you can determine which fraction is larger when two fractions have the same denominator by only comparing their numerators.
That means,
1/n and 2/n are the two fractions.
Then,2 > 1.
So, 2/n > 1/n.
Therefore, you can determine which fraction is larger when two fractions have the same denominator.
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Maureen spends 4 hours editing a 3 minute long video.
At this rate, how long will it take Maureen to edit a 9 minute long video?
Enter your answer in the box.
hours
Answer:
hi
Step-by-step explanation:
Find the determinant of the coefficient matrix
3x+4y=0
-2x+3y=-17
Answer:
17
Step-by-step explanation:
You want the determinant of the coefficient matrix for the equations ...
3x +4y = 0-2x +3y = -17Coefficient matrixThe matrix of coefficients is formed by listing the coefficients of the equation variables on rows of the matrix, in the same order for each row.
Here it is:
[tex]\left[\begin{array}{cc}3&4\\-2&3\end{array}\right][/tex]
DeterminantThe determinant of a 2×2 matrix is the difference between the product of terms on the down diagonal and that on the up diagonal.
det = (3)(3) -(-2)(4) = 9 + 8 = 17
The determinant of the coefficient matrix is 17.
__
Additional comment
Many scientific and graphing calculators can find this for you. A spreadsheet can be useful for this purpose, too.
The determinant is only defined for a square matrix. For sizes larger than 2×2, the arithmetic is a little different.
20,45,70,97 25th term
The 25th term in the sequence is 620.
How to find the 25th term in the sequence?To find the 25th term in the sequence, we can use the formula for the nth term of an arithmetic sequence:
aₙ = a1 + (n-1)d
where a1 is the first term, d is the common difference, and n is the term number.
Substituting the known values:
aₙ = 20 + (25-1) × 25
aₙ = 20 + (24 ×25)
aₙ = 20 + 600
aₙ = 620
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given a solid whose cross-section is defined by a(x), the volume of the solid is given by group of answer choices
A solid whose cross-section is defined by a(x), the volume of the solid given by [tex]\int\limits^a_b {A(x)} \, dx[/tex]
How do you measure volume in solids?The amount of space occupied by three-dimensional objects is measured by a solid's volume.Water displacement can be used to determine the volume of these items. A graduated cylinder is filled with enough water to completely cover the object, and the volume is then measured. After adding the item to the cylinder, the volume is once more read. The volume of the object is the difference between the two volumes.Matter exists in three different states: solid, liquid, and gas. Solids have a distinct volume and shape. Although they have a specific volume, liquids adopt the shape of the container. Gases lack a distinct volume or shape.Learn more about Volume of solid refer to :
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in the figure below, there are three right triangles. complete the following. (a)write a similarity statement relating the three right triangles. (b)complete each proportion.
The three right triangles are all similar. The ratios of the sides of the triangles are AB/BC = 3/4, BC/CD = 2/3, and AD/DC = 5/6.
a) All three of the right triangles are similar.
b) Triangle ABC: AB/BC = 3/4
Triangle BCD: BC/CD = 2/3
Triangle ADC: AD/DC = 5/6
a) All three of the right triangles are similar because they all have three sides and two angles that are equal.
b) To find the ratios of the sides of the triangles, we use the Pythagorean Theorem.
Triangle ABC: AB^2 + BC^2 = AC^2. Therefore, AB/BC = (3/4)^2/(5/4)^2 = 3/4.
Triangle BCD: BC^2 + CD^2 = BD^2. Therefore, BC/CD = (2/3)^2/(4/3)^2 =2/3.
Triangle ADC: AD^2 + DC^2 = AC^2. Therefore, AD/DC = (5/6)^2/(7/6)^2 = 5/6.
The three right triangles are all similar. The ratios of the sides of the triangles are AB/BC = 3/4, BC/CD = 2/3, and AD/DC = 5/6.
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Which of the following scatterplots provides evidence that the condition of equal variance for inference for the slope of a regression line has not been met?
Such a plot is evidence of a linear relationship between the explanatory and response variables, which is a condition for these inference procedure
These are the four presumptions: Relatively linear residuals Continuity of residuals The residuals are distributed normally. residual variance is same.
Linearity: We plot the residuals and y values in a scatter plot. Y values are shown on the horizontal x axis and standardized residuals, or ZRESID in SPSS, are derived from the vertical y axis. The linearity assumption is satisfied if the scatter plot displays a linear pattern (rather than a curved pattern).
We generally have two types of data: cross sectional and longitudinal. Cross -sectional datasets are those where we collect data on entities only once. For example we collect IQ and GPA information from the students at any one given time.
Independence is a concern when working with longitudinal datasets. With a longitudinal dataset, observations are gathered from the same subject across time. For example, in stock price information, we gather price information on the same stock, the subject, throughout time.
The two forms of data that we typically use are longitudinal and cross sectional. Datasets that are cross-sectional are those for which entities' information is only collected once. For instance, we constantly get IQ and GPA data from the kids.
We gather GPA data from the same student over time in a longitudinal data set.
We do not need to worry about the Independence assumption in cross-sectional datasets. It is "assumed" that it will be.
Normality: First, we create a histogram of the residuals, and then we check to see if they are normal. The assumption is met if the residuals do not exhibit skewness.
A scatterplot of the residuals vs the explanatory variable values shows a haphazard distribution of dots around the line.
Correct. This inference technique requires a linear relationship between the explanatory and response variables, which is demonstrated by a plot like this.
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.
The following dot plots show the numbers of people per table at a bingo hall on two nights. Each
dot represents one of the 20 tables.
●●
H
H
0 1 2 3 4 5 6 7 8 9
People per table Tuesday
H
+
0 1 2 3 4 5 6 7 8 9
People per table Wednesday
Compare the typical number of people per table.
In general, there were more people per table on Select day
Select typical number of people ✓
per table.
with
In general, there were more people per table on Tuesday with 8 number of people per table.
What is a dot plot?In Mathematics, a dot plot can be defined as a type of line plot that is typically used for the graphical representation of a data set above a number line, especially through the use of dots.
By critically observing the given dot plots which is used to illustrate the numbers of people per table at a bingo hall on two nights, we can reasonably infer and logically deduce that there were more people per table on Tuesday than on Wednesday.
In conclusion, there were 8 number of people per table on Tuesday while there were 5 number of people per table on Wednesday.
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A counter records people entering a fast-food restaurant. The data below shows the number of customers that enter the restaurant for each two-hour period starting at 8:00 am. Estimate the rate at which the customers are entering the store at 5:00p.m. (t=9). Use correct units (3 pts.) Hours after 8:00 am 0 2 4 6 8 10 12 Number of Customers 0 21 42 36 | 14 | 58 23
The rate of customer entry into the store at 5:00 p.m. (t = 9) is -3 customers/hour.
What is meant by fraction?In Maths, a fraction is used to represent the portion/part of the whole thing. It represents the equal parts of the whole. A fraction has two parts, namely numerator and denominator. The number on the top is called the numerator, and the number on the bottom is called the denominator.
A fraction is a part of a whole number, and a way to split up a number into equal parts. It is written as the number of equal parts being counted, called the numerator, over the number of parts in the whole, called the denominator.
Given the number of patrons entering the restaurant every two hours beginning at 8:00 am.
To find the rate of customer entry into the store at 5:00 p.m. (t = 9).
[tex]$\frac{36-42}{6-4}=\frac{-6}{2}=-3$[/tex]
Therefore, the rate of customer entry into the store at 5:00 p.m. (t = 9) is -3 customers/hour.
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Identify the open intervals on which the function is increasing or decreasing. (Enter your answers using interval notation.) h(x) = 5 squareroot xe^-x increasing decreasing
The function h(x) = 5 square root x e^-x is increasing on the interval (0, ∞) and decreasing on the interval (-∞, 0).
1. Calculate h'(x) = 5 (1/2 x^-1/2 e^-x - x^1/2 e^-x)
2. Set h'(x) = 0 to find the critical points.
3. Since h'(x) < 0 for x < 0 and h'(x) > 0 for x > 0, h(x) is decreasing for x < 0 and increasing for x > 0.
4. Therefore, h(x) is increasing on the interval (0, ∞) and decreasing on the interval (-∞, 0).
The derivative of h(x) = 5 square root xe^-x is h'(x) = 5 (1/2 x^-1/2 e^-x - x^1/2 e^-x). Setting h'(x) = 0 gives the critical points of the function. Since h'(x) is negative for x < 0 and positive for x > 0, this tells us that the function is decreasing for x < 0 and increasing for x > 0. So, h(x) is increasing on the interval (0, ∞) and decreasing on the interval (-∞, 0). We can also conclude from the graph of the function that it is concave down for x < 0 and concave up for x > 0.
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