Find the indicated real nth root(s) of a.

n = 2, a = 400

Root: ?

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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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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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

Using multiplication operation, the total number of packages of shredded cheese is 56.

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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Answer:

f = 2÷7. I hope this helped your experience

The rate of change of the angle of elevation is the rate at which the angle between the rope and the horizon changes over time.

The angle of elevation is the angle formed by the rope attached to the boat and the horizon. It is measured from the horizon line and can be used to measure the height of the boat relative to the horizon. The rate of change of the angle of elevation is the rate at which the angle between the rope and the horizon changes over time. This rate of change can be calculated by measuring the change in the angle over a specific time period and dividing it by the time period. This rate of change can be used to determine the speed at which the boat is moving up or down relative to the horizon. It can also be used to measure the rate of acceleration or deceleration of the boat.

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The complete question is

What is the rate of change of the angle of elevation, which is the angle formed by the rope attached to the boat and the horizon, given the speed of the boat and the distance from the boat to the horizon?

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:

[tex]\implies 19.50=3k[/tex]

[tex]\implies k=6.5[/tex]

Therefore, the constant of proportionality is 6.5.

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]

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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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Answer:

x+50

Step-by-step explanation:

I hope it helps

thanks

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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The rate of customer entry into the store at 5:00 p.m. (t = 9) is -3 customers/hour.

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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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%

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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The domain of the function is, All real numbers.

And, The range of the function, {- 24}

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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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.

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.

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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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

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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.

In general, there were more people per table on Tuesday with 8 number of people per table.

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 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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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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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

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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The 25th term in the sequence is 620.

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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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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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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Answer:

  17

Step-by-step explanation:

You want the determinant of the coefficient matrix for the equations ...

The 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]

The 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.

Answer:

[tex]f(a)=8a+5\\\\f(x+h)=8x+8h+5\\\\\frac{f(x+h)-f(x)}{h}=8[/tex]

Step-by-step explanation:

When we're asked to write what f(x+h) or f(a) is equal to, all we really have to do is substitution. The original function is provided as [tex]f(x)=8x+5[/tex], and all that "x" represents is input, now we can manipulate what that input is by simply substituting in new input. So if we want to write f(x+h), we substitute in "x+h" for "x".

For this problem, we just do what was stated about and replace all of the x's, with a's, meaning: [tex]8x+5\to 8a+5[/tex].

We essentially do the same thing here, although we will have to simplify more, but the first step is as follows: [tex]8x+5\to 8(x+h)+5[/tex], now from here we want to expand out the [tex]8(x+h)[/tex] by using the distributive property, so it becomes: [tex]8x+8h[/tex] and plugging this into our equation we get: [tex]8x+8h+5[/tex]

For this last question, I think it's also important to note that this is the formula to calculate the slope between point "x" and the point "h units away" or "x+h".

We already know what f(x+h) is and what f(x) is, so let's plug those into the equation:

[tex]\frac{(8x+8h+5)-(8x+5)}{h}[/tex]

Now let's distribute the negative sign to get:

[tex]\frac{8x+8h+5-8x-5}{h}[/tex]

Now let's group like terms:

[tex]\frac{(8x-8x)+(5-5)+8h}{h}[/tex]

Now let's simplify the grouped terms

[tex]\frac{8h}{h}[/tex]

Now let's divide by h to get:

[tex]8[/tex]

And this is our answer!

Answer:

hi

Step-by-step explanation:

The amount of interest Sai will pay is $312.50.

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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