Let f be a continuous function such that f changes from increasing to decreasing, and the graph of f changes fro concave up to concave down. Which of the following is true about the midpoint Riemann sum approximation for definite integral from 1 to 3 of f(x^2 + x) using 4 subintervals?a. The midpoint Riemann sum approximation underestimates the definite integral.b. The midpoint Riemann sum approximation overestimates the definite integral.c. The midpoint Riemann sum approximation cannot be determined to be an underestimate or an overestimate.

The complete table for the function f(x)=x^2-2 is given below.

What is a function?

A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and co-domain or range. A function is generally denoted by f(x) where x is the input. The general representation of a function is y = f(x).

There are several types of functions in math. Some important types are:

Injective function or One to one function: When there is mapping for a range for each domain between two sets.

Surjective functions or Onto function: When there is more than one element mapped from domain to range.

Polynomial function: The function which consists of polynomials.

Inverse Functions: The function which can invert another function.

Now,

Given

f(x)=x^2-2

The table will be filled as

x                f(x) =x^2-2                     (x,y)

-2                  2                                (-2,2)

-1                   -1                                (-1,-1)

0                    -2                               (0,-2)

1                     -1                                 (1,-1)

2                    2                                  (2,2)

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Right question is in image.

Answer:

25 r12

Step-by-step explanation:

first, u ask yourself how many times can 30 go in 7, well it can't so you do 30 can go in 76, 2 times because. 30x2 is 60 and it doesn't go over 76.

30x2 is 60 so on the first box u put 2. Then u multiply again 30x2 which is 60 so u put the 60 on the box below the 76. U subtract

Next, you would subtract it which would turn out to be 16. Since 16 can't go in 30 equally, u would drop down the 2 in the 762 now you can do 30 into 162 which is 5 times bc 30x5 is 150 and doesn't go over so u put the 5 in the box next to the 2.

30x5 is 150, u put that in the box below 162. Then u subtract 162-150 which is 12. So you have a remainder of 12.

Answer: a (x – x1) + b (y– y1) + c (z –z1) = 0.

Step-by-step explanation:

Recall that the general form of the equation of a straight line in two dimensions is

++=0.

This can also be written in the form 

=+, where  is the gradient and  is the -intercept, which we can determine by knowing two points on the line.

If (,) is a point that lies on the line, we can determine  from the general form as =−(+); thus, the equation of the line can be written as

+−(+)=0.

The equation of the line can also be realized as a dot product of two vectors as (,)⋅(−,−)=0.

Now, if we define the position vectors,⃑=(,),⃑

then the equation of the line can be written in vector form as⃑ ⋅⃑=⃑⋅⃑,where ⃑=(,) is called a normal vector of the line and ⃑−⃑ will lie completely on the line.

A property of the dot product states that two vectors are perpendicular to each other if their dot product is zero. This equation of the line in vector form shows that the normal vector ⃑ and the vector ⃑−⃑ are perpendicular to each other by this property.

The general equation of a plane in three-dimensional space can be represented as Ax + By + Cz = D.

What is the plane?

A plane is a two-dimensional doubly ruled surface spanned by two linearly independent vectors. The generalization of the plane to higher dimensions is called a hyperplane. The angle between two intersecting planes is known as the dihedral angle.

Where A, B, and C are coefficients and D is a constant.

The coefficients A, B, and C represent the components of the normal vector to the plane, and D represents the distance of the plane from the origin.

The equation defines a set of all points (x, y, z) in space that satisfy the equation and lie on the plane.

Hence, The general equation of a plane in three-dimensional space can be represented as Ax + By + Cz = D.

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In nature, there are various constraints on population number and expansion. Some are depending on the density, whereas others are not.

A population's per capita growth rate changes—typically declines—with rising population density due to density-dependent limiting constraints. One illustration is how individuals in a group compete for scarce food.

Independent of population density, several factors impact the per capita growth rate. Natural catastrophes like forest fires are examples.

Diverse limiting variables can combine in intricate ways to generate different patterns of population expansion. Some populations exhibit cyclical oscillations, where the population size varies cycle by cycle in a predictable manner.

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Answer:

Below

Step-by-step explanation:

Remember the trig identity    sin^2 + cos^2 = 1

.6157^2 + cos ^2 = 1

cos^2 = 1 - .6157^2

cos^2 = .6209

cos = ~  ± .7879

There are an infinite number of planes that are orthogonal to a given plane in space, and this is due to the fact that a plane can be thought of as a flat surface that extends indefinitely in all directions.

Orthogonal Planes in Space: In three-dimensional space, a plane is said to be orthogonal to another plane if the two planes are perpendicular to each other, i.e., their normal vectors are perpendicular. Since the normal vectors of two orthogonal planes are perpendicular to each other, this means that the angle between them is equal to 90 degrees.

Given a plane in space, there are an infinite number of planes that are orthogonal to it. This is because a plane can be thought of as a flat surface that extends indefinitely in all directions.

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Option A. is the correct answer.

Sample space = watermelon, lemon-lime, lemon-lime, grape, grape, grape.

A sample space is a set of potential results from a random experiment. The letter "S" is used to denote the sample space. Events are the subset of possible experiment results. Depending on the experiment, a sample area could contain a variety of results.

here, we have,

Given that, Julia had a bag filled with gumballs. There were 1 watermelon, 2 lemon-lime, and 3 grape gumballs.

now,

Sample space contains,

2 lemon-lime: Elements in sample space are lemon-lime, lemon-lime,

1 watermelon: Elements in sample space are watermelon,

3 grape: Elements in sample space are grape, grape, grape,

In total there are 13 elements in sample space.

Therefore, option A . is the correct answer.

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Answer:

Step-by-step explanation:

Option A. is the correct answer.

Sample space = watermelon, lemon-lime, lemon-lime, grape, grape, grape.

y = 2 is the solution of  differential equation .

What exactly does differential equation mean?

An equation that connects one or more unknown functions and their derivatives is known as a differential equation in mathematics.

                               Applications typically use functions to describe physical quantities, derivatives to indicate the rates at which those quantities change, and differential equations to define a relationship between the two.

( x logx )dy/dx + y = 2xlogx

dividing by xlogx, we get

  dy/dx + y/xlogx  = 2

   d(IF × Y ) = 2logx dx

  IF  =  e∫1/xlogx dx

        = [tex]e^{log(logx)} = logx[/tex]

rightarrow Multiplying by IF, we get

      d(IF * Y ) = 2logx dx

   By integrating, we get

y logx = ∫2 logx dx

 By using Product Rule on RHS, we get

   ylogx = 2[logx ∫ 1 - ∫((∫1) d/dx(logx)) dx

  ylogx =  2[x(logx - 1 )] + c

  Put x = 1, we get

   0 = 2[1(0 - 1 )] + c

    c = 2

ylogx = 2[x[logx - 1 )] + 2

  at x = e

 y = 2

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An equation for the population, p, years after 2003 is 45000 + 1700t .

The population of a town has been increasing linearly. The population was 21,000 in 2003. 1700 persons have been added to the population annually.

Locate the necessary equation:

An equation for the population, p, years after 2003.

Given: Population in 2003 was 45,000.

Additionally, annual population growth equals 1,700.

After t years, the population will expand by 1,700t because it has been rising linearly.

Population t years later = 45000 + 1700t, then.

P(t) = 45000 + 1700t is the needed equation as a result.

An equation for the population, p, years after 2003 is 45000 + 1700t .

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Answer:

C. (-5,0) ( -2, 0)

Step-by-step explanation:

The X-intercept is when the y = 0

We see the x-intercept on the graph is located at (-5,0) and (-2,0), so the answer is C.

The area of the circle is 346.5 cm² while the area of the square is 272.25 cm². The figure that encloses more area is the circle.

If a wire of length 66cm is bent into the shape of a circle and square, then this length will be its circumference and perimeter, respectively.

C = 66cm = 2πr

r = 10.5 cm

P = 4s = 66cm

s = 16.5 cm

The area of the circle is given by the formula

A = πr²

A = π(10.5 cm)²

A = 346.5 cm²

So, the area of the circle is 346.5 cm².

The area of the square is given by the formula

A = s²

A = (16.5 cm)²

A = 272.25 cm²

So, the area of the square is 272.25 cm².

Therefore, the figure that encloses the greater area is the circle.

The problem seems unreadable, it must have been...

"a wire of length 66 cm is bent into the shape of a circle. find its area. if the same wire is bent into the shape of a square, what will be its area? which figure enclose more area, the circle or the square? take π = 22/7."

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The correct line of best fit is y = -1/3x + 2. Option C

A line of best fit is a line that is used to approximate the underlying pattern or relationship between two variables in a scatterplot. The line of best fit is drawn so that the number of points above the line and below the line are approximately equal (and the line passes through as many points as possible).

The line of best fit is used to make predictions about the response variable based on the predictor variable, and to understand the strength and direction of the relationship between two variables.

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Answer:

Here are the completed ratio tables for both classes:

Mrs. Washington's class:

Band: 2

Chorus: 3

Total: 2 + 3 = 5

Band-to-Chorus ratio: 2 : 3

Mr. Utley's class:

Band: 5

Chorus: 7

Total: 5 + 7 = 12

Band-to-Chorus ratio: 5 : 7

Based on the ratios, it appears that Mr. Utley's class has a greater ratio of students in band to students in chorus. The ratio in Mr. Utley's class is 5 : 7, while the ratio in Mrs. Washington's class is 2 : 3.

Step-by-step explanation:

Step-by-step explanation:

radius are a special form of fractions. but they are fractions, and a such all rules of calculation and comparison apply.

mrs. Washington's class has a ratio of 2/3 (or 2:3 or 2÷3).

2/3 = 0.666666666...

mrs. utley's class has a ratio of 5/7.

5/7 = 0.714285714...

so, the class of mrs. Utley had a greater ratio.

to compare the ratios (like any fraction) within calculating their decimal value, we need to bring them to the same denominator :

.../3 and .../7

we need to bring both to .../21 :

2/3 × 7/7 = 14/21

5/7 × 3/3 = 15/21

so, we can clearly see that the ratio of mrs. Utley's class is greater, as 15 is greater than 14.

There are 12,804,280,000 ways to select 10 countries in the United Nations to serve on a council.

The number of ways to select 3 countries from a block of 52 is given by the combination formula:

        C(62, 1) = 62.

        C(75, 6) = 75! / (6! * (75 - 6)!) = 178,365.

Finally, to find the number of ways to select 10 countries in total, we multiply the number of ways to select 3, 1, and 6 countries:

19600 * 62 * 178365 = 12,804,280,000.

So there are 12,804,280,000 ways to select 10 countries in the United Nations to serve on a council.

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Step-by-step explanation:

x

x+2

x+4

x+6

x+8

these are the 5 consecutive odd integers.

when starting with an odd number as x, with every added 2 we get again an odd number.

the sum of the last 3 integers is 3 more than the sum of the 2 greatest :

x+4 + x+6 + x+8 = x+6 + x+8 + 3

we can subtract (x+6) abd (x+8) from both sides :

x + 4 = 3

x = -1

so, the 5 numbers are

-1

1

3

5

7

3 + 5 + 7 = 15

5 + 7 + 3 = 15

correct.

Answer:

0.89

Step-by-step explanation:

6.1/3.9=28/10x/x+81/10

61/39=28x(x)/10+8.1

61/39-81/10=28x(x)/10

610/390_3159/390=28x(x)/10

2469/390=28x(x)/10

2469/390=14/5x(x)

2.51=14/5x

12.55=14x

x=0.89

The two digit number is 38.

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

Le x be the number at the ten's place and y be the number at the unit's place.

So, the number is 10x+y

The sum of digits of a two-digit number is 11.

That is, x+y=11 -------(i)

If the digit at tens place is increase by 5 and the digit at unit place is decreased by 5, the digits of the number are found to be reversed.

10(x+5(y-5)=10y+x

9x-9y=-45

x-y=-5 -------(ii)

Add equation (i) and (ii), we get

2x=6

x=3

Substitute x=3 in equation (i), we get

y=8

So, the number is 38

Therefore, the two digit number is 38.

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Answer:

4.5

Step-by-step explanation:

Distance that James has to travel = 4.32 km

Distance that Megan has to travel = 0.96 km

How many times as long  
==> 4.32/0.96 = 4.5

Therefore,

The distance James lives from school is 4.5 times, as long as the distance Megan lives from school

4.5 is the answer which goes into the blank

16y6/x2 is the corresponding formula.The necessary equivalent expression is therefore 16y6/x2.

Expressions in mathematics are made up of variables combined with the use of operations and predetermined rules. An equation, some numbers, etc., could be used as examples.

Expressions in mathematics are made up of variables combined with the use of operations and predetermined rules.

Expressions in mathematics are made up of variables combined with the use of operations and predetermined rules. An equation, some numbers, etc., could be used as examples.

There is a phrase that says,

{4xy³/x²}²

Expressed more succinctly,

{4xy³/x²}²

= {4y³/x}²

= 16y⁶/x².

The necessary equivalent expression is therefore 16y6/x2.

The complete question is,

Which of the following expressions is the same as the one given?

(4xy^3/x^2)

^2

A. 16y^6 \sB. 16y

5 x 2, 16 x 2, 5 y, and 16 y.

^6/x^2

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The percent change of the data set is 10%.

Percentage change is a way to describe the difference between an old value and a new value, expressed as a ratio and then multiplied by 100.

If the price of a product was $5 last month and it increased to $5.50 this month, we can calculate the percentage change as

=> (5.50 - 5) / 5 x 100 = 10%.

This means that the price of the product has increased by 10% compared to last month. If the price had gone down, we would have a negative percentage change.

Percentage change is a useful tool to compare data sets, especially when dealing with large numbers.

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Answer:

dfgss sdffcfsgdbebgndnngsageqfetehashqrvdqhqdhtqi

The equation that represent the value of the computer in years is: computer cost at (n-1) year - 1/5 (n-1cost) and the computer be worth less than $100 at 10 year

They are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.

According to the data problem,

The cost of computer = $ 800

It lost 1/5 of value every year.

The value of computer after 0 years = cost of computer = $ 800

The value after 1 year = 800 - (1/5*800) = $640

The value after 2 years = 640 - (1/5*640) = $512

The value after 3 years = 512- (1/5*512) = $409.6

Continue with the formula we have:

The value after 9 years = 134.21 - (1/5*134.21) = 107.37

The value after 10 years = 107.37 - (1/5*107.37) = 85.90

The value after n years = computer cost at (n-1) year - 1/5 (n-1cost)

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Total area of Ruby’s model for a Fourth of July party hat is 182.75 square centimeter.

The area of Rectangle is length times of width.

Let us find the area of the red colour right triangle.

Area of red triangle=1/2×13.5×9

=60.75 square cm.

Area of blue triangle=1/2×8×9

=36 square cm.

Area of rectangle=Length×breadth

=(13.5+8)4

=21.5×4

=86 square cm.

The total area of Ruby’s model for a Fourth of July party hat is

60.75+36+86

182.75 square centimeter.

Hence, total area of Ruby’s model for a Fourth of July party hat is 182.75 square centimeter.

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The value of x is -0.03125 or - 1/32.

Solving equations involves finding the value of the unknown variables in the given equation. The condition that the two expressions are equal is satisfied by the value of the variable. Solving a linear equation in one variable results in a unique solution, solving a linear equation involving two variables gives two results.

Solving equations is computing the value of the unknown variable still balancing the equation on both sides. An equation is a condition on a variable such that two expressions in the variable have equal value.

[tex]2^{-5} - x = \frac{1}{16}[/tex]

[tex]x =2^{-5} - \frac{1}{16}[/tex]

[tex]x = \frac{1}{2^{5} } - \frac{1}{16}[/tex]

[tex]x = \frac{1}{32} } - \frac{1}{16}[/tex]

x = (16 - 32) / (16 x 32)

x =  -16 / 512

x = -0.03125

0r

x = [tex]-\frac{1}{32}[/tex]

Therefore, the value of x is -0.03125 or - 1/32.

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The scale factor is 1/5 inch per foot.

The scale factor of the drawing can be found by dividing the length of the rug in real life by the length of the rug in the drawing.

4 feet / (5 inches/12 inches/foot) = 4 * 12 / 5 = 9.6 inches

So the scale factor is 9.6 inches / 4 feet = 1/5 inch per foot.

The method used to find the scale factor is applicable to any drawing or model where the size of an object is known in both the real-life version and the drawing or model. As long as the ratio of the size of the object in the real-life version to the size of the object in the drawing or model is constant, the scale factor can be found using the same method.

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Note that from the graph given above and their slopes, it is correct to state that mRT = mTV.

First, note that the slope or gradient of a line in mathematics is a quantity that specifies both the direction and the steepness of the line.

Here, Slope RT = Δy/Δx = SR/ST = 2/4 = 1/2

Slope TV =  Δy/Δx = UT/UV = 1/2

Thus, since the Slope of RT = 1/2 and the Slope of TV = 1/2 it i correct to state that mRT = mTV.

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If the function is f(x) = eˣ Cos(x) where (0≤ x ≤2π) , then the function will be increasing in interval (0, π/4) U (7π/4, 2π), and decreasing in interval (π/4, 7π/4) .

In order to find the intervals where function f(x) = eˣ Cos(x) is increasing and where it is decreasing, we find the points where the derivative of the function, f'(x), is positive and negative,

The derivative of function : f(x) = eˣ cos(x) is:

⇒ f'(x) = eˣ cos(x) + eˣ (-sin(x))

⇒ eˣ (cos(x) - sin(x))

So , To find the intervals where f'(x) is positive or negative, we can use the sign of the derivative to determine if the function is increasing or decreasing.

we  know that ;

⇒ When f'(x) > 0, the function is increasing.

⇒ When f'(x) < 0, the function is decreasing.

For function  " eˣ (cos(x) - sin(x)) " ,

we can see that f'(x) is positive when cos(x) > sin(x) and negative when cos(x) < sin(x).

By using a unit circle, we can see that the inequality cos(x) > sin(x) is satisfied for x in the interval (0, π/4) U (7π/4, 2π), and

the inequality cos(x) < sin(x) is satisfied for x in the interval (π/4, 7π/4) .

The given question is incomplete , the complete question is

Determine the intervals where the function f(x) = eˣ Cos(x) where (0≤ x ≤2π) is increasing and where it is decreasing ?

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9) △MST is not similar to △DJZ

10) △ARP is not similar to △TRY.

11) △XYZ is not similar to △RVW

12) △ADE is not similar to △ABC.

What are similar triangles?

Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent.

"If in two triangles, sides of one triangle are proportional to (i.e., in the same ratio of) the sides of the other triangle, then their corresponding angles are equal and hence the two triangles are similar," states the Side-Side-Side (SSS) criterion.

The length of the sides of △MST are 16, 12, 5.

The length of the sides of △DJZ are 10, 7, 3

The ratio of sides is

16/10 ≠ 12/7 ≠ 5/3.

The length of the sides of △ARP are 15, 12, 5.

The length of the sides of △TRY are 54, 43.2, 18

The ratio of sides is

15/54 ≠ 12/43.2 ≠ 5/18.

The length of the sides of △XYZ are 17, 15, 8

The length of the sides of △RVW are 30.6, 27,4

The ratio of sides is

30.6/17 ≠ 27/15 ≠ 4/8.

The length of the sides of △ABC are 9, 8, 6.

The length of the sides of △ADE are 24, 12+8 = 20, 9+6=15

The ratio of sides is

24/9 ≠ 20/8 ≠ 15/6.

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