Estimate the sum of 202 and 57.
​

By using fundamental theorem of calculus  The exact value of the definite integral [tex]\int {1}^{\pi}\left(3x^{-1} \sqrt{x}\right)\ dx[/tex] is 6(√(π) - 1).

First, we can find an antiderivative of the integrand by using the power rule and the constant multiple rule of integration:

∫(3x^(-1/2)) dx = 3 ∫(x^(-1/2)) dx = 3 (2x^(1/2)) + C = 6√(x) + C

where C is the constant of integration.

Now, we can use the fundamental theorem of calculus to evaluate the definite integral \int {1}^{\pi}\left(3x^{-1} \sqrt{x}\right)\ dx. The theorem states that if f(x) is continuous on the interval [a, b] and F(x) is an antiderivative of f(x), then

∫[a, b] f(x) dx = F(b) - F(a)

In this case, f(x) = 3x^(-1/2) and F(x) = 6√(x) + C. Therefore,

∫{1}^{π} (3x^(-1/2)) dx = F(π) - F(1) = 6√(π) + C - 6√(1) - C = 6√(π) - 6√(1) = 6(√(π) - 1)

So the exact value of the definite integral [tex]\int {1}^{\pi}\left(3x^{-1} \sqrt{x}\right)\ dx[/tex] is 6(√(π) - 1).

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The system of equations has infinitely many solutions.

What is a system of equations?

A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, often known as a system of equations or an equation system.

Here, we have

Given:

-2x - 3y + z = 7

-x - y + 3z = -10

-2x - y - z = 13

We have to how many solutions the system of equations has.

Arranging the above equations in form of a matrix and finding the determinant, we get,

Δ = [tex]\left|\begin{array}{ccc}-2&-3&1\\-1&-1&3\\-2&-1&-1\end{array}\right|[/tex]

= -2(1+3) +3(1+6) +1(1-2)

= - 4 + 21 -1 = 16

Δ₁ = [tex]\left|\begin{array}{ccc}7&-3&1\\-10&-1&3\\13&-1&-1\end{array}\right|[/tex]

= 7(1+4) +3(10-39) +1(10+13)

= 35 - 87 + 23

= -29

Hence, the system of equations has infinitely many solutions.

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The rod's linear density at 1 metre from the left end and a point x meters to the right is 8 x 3 kg is = 8(1)2 = 8 kg/m.

We can start by using the definition of linear density, which is the mass per unit length of a rod or wire. Let's assume that the linear density of the rod at a distance of 1 meter from the left end is ρ kg/m.

Then, the mass of the part of the rod that lies between 0 meters and 1 meter to the right is:

m1 = ρ * 1 kg

Similarly, the mass of the part of the rod that lies between 0 meters and x meters to the right is:

m2 = 8x^3 kg

The mass of the part of the rod that lies between 1 meter and x meters to the right is:

m2 - m1 = (8x^3 - ρ) kg

Since we know that this mass is equal to ρ times the length of the rod segment, which is (x-1) meters, we can write:

ρ * (x-1) = 8x^3 - ρ

By condensing this solution, we obtain:

ρ * (x-1+1) = 8x^3

ρ * x = 8x^3

ρ = 8x^2 kg/m

As a result, the rod's linear density at 1 metre from the left end is = 8(1)2 = 8 kg/m.

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The total area of both triangles is the product of the height and base of the flag.

The connecting of three noncolinear points results in a triangle, which is a three-sided closed-plane object. Triangles can be classified into three categories based on their side properties: equilateral, scalene, and isosceles.

Given, Anthony painted 2triangles of the same size on the top corners of his house flag for sports day.

We are aware of A parallelogram can be divided into two comparable triangles by dividing it along its diagonal.

A planar figure with opposite sides that are parallel and of equal length is called a parallelogram.

Since the area of a parallelogram is equal to its base times its height, the combined area of the two triangles will be the same.

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Answer:

[tex]l = 30[/tex]     OR     [tex]l=-60[/tex]

Step-by-step explanation:

We can solve this problem with a system of equations by creating 2 equations from the information given.

1. "a length of 30 feet less than 5 times its width"

[tex]l = 5w - 30[/tex]

2. "the area of the rectangle is 360 ft²"

[tex]l\cdot w = 360[/tex]

To solve for the rectangle's length, we can create a substitution for w by dividing both sides of the second equation by length ([tex]l[/tex]).

[tex]l\cdot w = 360\\\overline{\ \ l\ \ } \ \ \ \: \ \overline{\ l \ \ }[/tex]

[tex]w = \dfrac{360}{l}[/tex]

Then, we can substitute this value back into the first equation and solve for [tex]l[/tex].

[tex]l = 5(\dfrac{360}{l}) - 30[/tex]

↓ distribute the 5

[tex]l(l) = \left(\dfrac{1800}{l} - 30\right)l[/tex]

↓ multiply both sides by [tex]l[/tex]

[tex]l^2 = 1800 - 30l[/tex]

↓ move all [tex]l[/tex]'s to one side

[tex]l^2 + 30l = 1800[/tex]

To solve this quadratic, we can complete the square.

    ↓ add (30/2)² to both sides

    [tex]l^2 + 30l + \left(\dfrac{30}{2}\right)^2 = 1800 + 15^2[/tex]

    ↓ simplify 15²

    [tex]l^2 + 30l + 225 = 1800 + 225[/tex]

    ↓ factor the left side as a perfect square

    [tex](l + 15)^2 = 2025[/tex]

    ↓ take the square root of both sides

    [tex]l + 15 = \pm \sqrt{2025}[/tex]

    [tex]l + 15 = \pm 45[/tex]

↓ split into 2 equations

[tex]l + 15 = 45[/tex]     OR     [tex]l + 15 = -45[/tex]

[tex]\boxed{l = 30}[/tex]          OR     [tex]\boxed{l=-60}[/tex]

Answer:

You just want to find what 25% of 450 is. To do so, you can change 25% into a decimal, and then multiply:

25% as decimal is 0.25.

0.25 * 450 = 112.5

The discount is $112.50.

Step-by-step explanation:

Hope it helps! =D

120 is the number divisible by 6, 8, and 10.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

The common multiples to 6, 8, and 10.

6 x 20 =  120

8 x 15 = 120

10 x 12 = 120

So,

120 is divisible by 6, 8, and 10.

Thus,

120 is the number.

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The total amount of cash collected is $10,418.6.

A percentage is expressed as a number or ratio that can be expressed as fraction of 100. It is denoted by % symbol.

The amount of cash collected at the time of making a cash sale of $9,220 worth of merchandise subject to 13 % HST is,

Rate of interest on the sales amount is 13%

13% of 9220 = [tex]\frac{13}{100}*9220=1198.6[/tex]

Here, sales price = $9,220

The total amount of cash collected = 1198.6+9220

                                                          = 10,418.6

Hence, the total amount of cash collected is $10,418.6.

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The ratio of the volume of a paraboloid (a parabola rotated about the y axis) to the volume of a cylinder with the same height and base radius is 1/2

We know that the formula for the volume of a paraboloid is:

V = 1/2 × π × r²  × h

where r is the Radius of Paraboloid

and h is Height of Paraboloid

Let us assume that V₁ represents the volume of a paraboloid (a parabola rotated about the y axis)

So, V₁ = 1/2 × π × r²  × h

Also, we know that the formula for the volume of a cylinder is:

V = π × r²  × h

Let us assume that V₂ be the volume of a cylinder with the same height h and base radius r.

So, V₂ =  π × r²  × h

consider the ratio of the volume of a paraboloid to the volume of a cylinder with the same height and base radius,

V₁ / V₂

= (1/2 × π × r²  × h) / (π × r²  × h)

= 1/2

Therefore, the required ratio is 1/2

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Answer:

Jakaur7889 on inta

Step-by-step explanation:

Babahaja

The cost for each person is $12.

So, each person paid $12 for a movie ticket.

The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.

Given:

The cost of going to the movie theater for Elissa and 11 of her friends is $144.

The total cost is divided equally among each person.

The number of total people is 12.

So, the cost of each person,

= total cost/ the number of total people

= 144/12

= 12

Therefore, 12 is the required value.

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Answer:

--------------------------------

Given line:

We know that perpendicular lines have opposite-reciprocal slopes.

Perpendicular line to the given has a slope of m = - 1 / (1/4) = - 4.

Let the y-intercept be b, then the line is:

Given line:

We know parallel lines have equal slopes.

The parallel line to the given has a slope of m = - 3 and passes through point (3, 8).

Set the point-slope equation:

Convert this into slope-intercept form:

Answer:

60 dollars

Step-by-step explanation:

I say this because it's simple math 199.90 - 139.99 its obviously 60

The height of the triangle is 20 and base of the triangle is 12.

"Information available from the question"

The base of a triangle is 8 ft. less than its height.

If the area is 120 [tex]ft^2.[/tex]

We have to find the base and the height of this triangle.

Now, According to the question:

Let the height be x then if the base is 8 ft. less, then the base is x - 8.

We know that:

Area of the triangle is :  (b × h)/2

Area of the triangle is : (x (x - 8)) /2

120 [tex]ft^2[/tex] = ([tex]x^{2} -8x[/tex])/2

240 = [tex]x^{2} -8x[/tex]

[tex]= > x^{2} -8x-240=0[/tex]

For solving equation, Use the quadratic formula :

x = (-b ± [tex]\sqrt{b^2-4ac}[/tex]) / 2a

a = 1

b = -8

c = -240

x = (-(-8) ± [tex]\sqrt{(-8)^2-4.1(-240)})/2.1[/tex]

By solving, we get

x = (8 ± 32)/2

We get the values :

x = 20 and x = -12

We know x = −12 can't be a solution as length can't be negative.

Base = x - 8

Base = 20 - 8

Base = 12

Hence, The height of the triangle is 20 and base of the triangle is 12.

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The volume of the parallelepiped formed by the adjacent edges u=i+j, v=j+k, and w=i+k is: 1.

The triple scalar product can be used to find the volume of the parallelepiped formed by three non-coplanar vectors u, v, and w. The triple scalar product is defined as:

where × represents the cross product and · represents the dot product.

Given that u=i+j, v=j+k, and w=i+k, we can first find the cross product of v and w as:

= i x (j+k) + k x (j+k)

= i x j + i x k + k x j + k x k

= -k + i -j

Next, we can find the dot product of u with the cross product of v and w as:

= i · (-k) + i · i + i · (-j) + j · (-k) + j · i + j · (-j)

= -ik + i^2 - ij - jk + ji - j^2

= i^2 - j^2 - k(i+j)

= 1 - 0 - (1+0)

= -1

The absolute value of this result gives the volume of the parallelepiped, so the volume is:

Therefore, the volume of the parallelepiped formed by the adjacent edges u=i+j, v=j+k, and w=i+k is 1.

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Answer:

120

Step-by-step explanation:

18 = .15x  Divide both sides by .15 (15% as a decimal is .15)

[tex]\frac{18}{.15}[/tex] = [tex]\frac{.15x}{.15\\}[/tex]

120 = x

Using unitary method, we can calculate the number of 0.04s boxes between R-R intervals on an ECG trace for our chosen event.

The unitary method is a mathematical technique that involves finding the value of one unit of a given quantity and then using it to find the value of a different quantity. In this case, we want to find the change in heart rate per second, so we need to determine how many beats per second our chosen event increases our heart rate by.

To calculate the duration of each R-R interval, we can use the following formula:

R-R interval duration = 1 / heart rate (in seconds)

Assuming our starting heart rate is 90 bpm and our event increases our heart rate by y beats per second, we can calculate the new heart rate as follows:

New heart rate = 90 bpm + (y * 60) bpm

We can then calculate the duration of each R-R interval using the formula above.

Finally, to find the number of 0.04s boxes between R-R intervals on an ECG trace, we can convert the R-R interval duration to a number of 0.04s boxes. Each 0.04s box on an ECG trace represents 0.04 seconds, so we can use the following unitary method:

1 second = 25 0.04s boxes

R-R interval duration (in seconds) = x seconds

Number of 0.04s boxes = x * 25

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(a) The value of E(Y) will be = 0.8

(b)  The expected amount of the surcharge is $165.

(a) The expected value of Y is given by:

E(Y) = 0(0.5) + 1(0.25) + 2(0.2) + 3(0.05)

= 0.25 + 0.4 + 0.15

= 0.8

Therefore, the expected number of moving violations for which the individual was cited during the last 3 years is 0.8.

(b) The amount of the surcharge for an individual with Y violations is $110[tex]y^{2}[/tex]. The expected surcharge is given by:

E($110[tex]y^{2}[/tex]) = $110 * E([tex]y^{2}[/tex])

To calculate E([tex]y^{2}[/tex]), we use the formula:

E([tex]y^{2}[/tex]) = Σ [tex]y^{2}[/tex] p(y)

where the sum is taken over all possible values of Y.

E([tex]y^{2}[/tex]) = [tex]0^{2}[/tex](0.5) + [tex]1^{2}[/tex](0.25) + [tex]2^{2}[/tex](0.2) + [tex]3^{2}[/tex](0.05)

= 0 + 0.25 + 0.8 + 0.45

= 1.5

Therefore, the expected surcharge is:

E($110[tex]y^{2}[/tex]) = $110 * E([tex]y^{2}[/tex])

= $110 * 1.5

= $165

So, the expected amount of the surcharge for an individual with moving violations is $165.

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a) The factors that impact a person's credit score and history include:

b) To raise or improve a credit score and history, you must undertake the following actions:

A credit score is a numerical rating or expression of an individual's credit history to determine their creditworthiness.

Credit scores are presented on credit reports, which are regularly prepared by credit bureaus.

On the other hand, a credit history is an official record of an individual's credit management.

Thus, one must understand the credit history and meet payment obligations to improve a person's credit score.

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The proof method to show that the statement "The average of any three odd integers is an odd integer" is true is "Prove true by direct proof."

To prove that the statement is true by direct proof, we can assume that the three odd integers are a, b, and c, where a = 2k + 1, b = 2m + 1, and c = 2n + 1 for some integers k, m, and n. Then, the average of these three odd integers is:

(a + b + c)/3 = (2k + 1 + 2m + 1 + 2n + 1)/3

= (2k + 2m + 2n + 3)/3

= 2(k + m + n) + 1

Since k, m, and n are integers, k + m + n is also an integer. Therefore, the average of any three odd integers is of the form 2x + 1, where x is an integer, which is an odd integer.

The reason the attempted proof of the statement "The difference between any odd integer and any even integer is odd" is not correct is "The proof violates the parity property." The student incorrectly subtracted an even integer from an odd integer and concluded that the result is odd. However, the difference between an odd integer and an even integer is always odd, which can be proven directly as follows:

Let n be any odd integer and m be any even integer. Then, by definition, n = 2k + 1 and m = 2j for some integers k and j. The difference between n and m is:

n - m = (2k + 1) - 2j

= 2k - 2j + 1

= 2(k - j) + 1

Since k and j are integers, k - j is also an integer. Therefore, the difference between any odd integer and any even integer is of the form 2x + 1, where x is an integer, which is an odd integer.

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In accordance with Side-Angle-Side theorem of congruence, the triangles seen in choices A and C are congruent.

In this problem we need to determine what triangles are congruent, that is, two triangles whose sides and angles are the same in measure and distribution. We can prove congruence by means of Side-Angle-Side theorem, where given angle is between two given sides.

Then, by direct inspection, the triangles from choices A and C are congruent, because sides and in-between angle are the same in measure and distribution.

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The triangles that are certainly congruent in the diagram are triangle A and triangle C.

Congruent triangles are triangles that have the same size and shape, such that the lengths of the three sides in one triangle are equivalent or have same length as the lengths of the three sides of the other triangle.

The congruent triangles can be obtained by using the congruence rules, or conditions for congruence, which includes; ASA, SAA, SSS, SAS

Where;

ASA is an acronym for Angle-Side-Angle

SAA is an acronym for Side-Angle-Angle

SSS is an acronym for Side-Side-Side

SAS is an acronym for Side-Angle-Side

The lengths of two sides and the measure of the included angle in triangle A are congruent to the length of two sides and the measure of the included side between the two sides in triangle C.

Therefore, the triangle in option A is congruent to the triangle in option C by the Side-Angle-Side, SAS, congruency rule.

The angle 62° is the non included angle to the 14 m and 10 m long side in option B and D, while the 14 m long side is the adjacent side to the 62° angle in option B. In option D the 10 m long side is adjacent to the 62° angle, which the orientation of triangles B and D to be different

The only two congruent triangles are triangles in option A and option C

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The total area of the canvas needed would be 21.4 square yards.

The formula to calculate the total surface area of a triangular pyramid is -

T.S.A. = {1/2}(a × b) + {1/2}(b × s).

Given is a tent is in the shape of a triangular prism.

The total area of the canvas would be -

A{C} = 2{1/2 x 2 x 1.7} + 2{3 x 2} + {3 x 2}

A{C} = (2 x 1.7) + 12 + 6

A{C} = 3.4 + 18

A{C} = 21.4 square yards

Therefore, the total area of the canvas needed would be 21.4 square yards.

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Answer:6

Step-by-step explanation:beacuse it it

Answer:

x = 12

Step-by-step explanation:

The exterior angle is equal to the sum of the opposite interior angles.

5x+20 = 20 + 6x-12

Combine like terms.

5x+20 = 6x +8

Subtract 5x from each side.

5x+20-5x = 6x+8-5x

20 = x+8

Subtract 8 from each side.

20-8 = x+8-8

12 =x

The difference of  8/3x+5 -2x/3x+5 is (8 - 2x) / (3x+ 5).

The correct option is (A).

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator)

We have the Expression as:

8/3x+5 -2x/3x+5

Now, Simplifying the expression as:

=  8/3x+5 -2x/3x+5

= (8 - 2x) / (3x+ 5)

= 8/(3x+ 5) - 2x/ (3x+ 5)

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If W is a subspace of V, then ax + by is an element of W since it satisfies the closure axioms of a vector space. Specifically, scalar multiplication closure confirms that ax and by are in W, and additive closure confirms that their sum, ax + by, is also in W.

Conversely, if ax + by is an element of W for all scalars a and b and all vectors x and y in W, then W must be closed under both addition and scalar multiplication.

To demonstrate this, we can assign a particular value to a or b, set the other to 1, and substitute the corresponding vectors x and y from W to get the equation ax + by = a(x) + b(y). This equation confirms that W is closed under addition and scalar multiplication, making it a subspace of V.

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The value of the test statistic z is, 2.31.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

It is claimed that less than 25% of adults prefer Italian food as their favorite ethnic food.

And,  A survey of 1122 adults resulted in 314 who say that Italian food is their favorite ethnic food.

Now,

⇒ P = 25%

⇒ q = 100% - 25% = 75%

⇒ n = 1122

Hence, We get;

⇒ z = (314/1122 - 25%) / √(25% 75% / 1122)

⇒ z = 2.31

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As per the information provided, option B) The errors e1,e2, e; have the same variance is the assumptions for linear regression.

Regression analysis is a linear technique used to model the relationship between a scalar response and/or one or more explanatory variables, also known as the dependent and independent variables here.

Simple linear regression and multiple linear regression are two terms used to describe the process when there is only one explanatory variable present. This statement is different from multivariate linear regression, which thus predicts multiple correlated dependent variables as opposed to a single scalar variable present.

The first regression analysis technique that attracted a lot of research attention and was frequently applied in practical situations was linear regression. This is because models with linear rather than non-linear dependence on their unknown parameters are easier to fit, and it is also easier to determine the statistical properties of the resulting estimators.

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The way to transform the function such that the bond goes from quarterly compounding interest to annually compounding interest is = 1 + ( 1 + rate / 4 )ⁿ ˣ ⁴.

The bond is said to be compounded quarterly. There would therefore be four compounding periods in a single year because there are four quarters in a year.

The formula would have been:

= Initial investment + ( 1 + rate ) ^ number of years

The adjusted formula to account for the quarters becomes :

= 1  + ( 1 + rate / 4 )ⁿ ˣ ⁴

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