consider the function f(x)={2xif x<2if x≥2 evaluate the definite integral ∫6−1f(x)dx

[tex]~~~~~~ \stackrel{\textit{\LARGE Quarterly}}{\textit{Compound Interest Earned Amount}} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$7000\\ r=rate\to 9\%\to \frac{9}{100}\dotfill &0.09\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &12 \end{cases}[/tex]

[tex]A = 7000\left(1+\frac{0.09}{4}\right)^{4\cdot 12} \implies A=7000(1.0225)^{48}\implies \boxed{A \approx 20367.48} \\\\[-0.35em] ~\dotfill[/tex]

[tex]~~~~~~ \stackrel{\textit{\LARGE Annually}}{\textit{Compound Interest Earned Amount}} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$7000\\ r=rate\to 9\%\to \frac{9}{100}\dotfill &0.09\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &12 \end{cases}[/tex]

[tex]A = 7000\left(1+\frac{0.09}{1}\right)^{1\cdot 12}\implies A=7000(1.09)^{12} \implies \boxed{A \approx 19688.65} \\\\[-0.35em] ~\dotfill\\\\ 20367.48~~ - ~~19688.65 ~~ \approx ~~ \text{\LARGE 678.83}[/tex]

The only one carton of pear is not enough because the sum of both Jo and Max requirement is max than the one.

There is only one carton of pear.

Jo want to buy 3/4 of it, and Max to buy 1/3 of it.

To check whether one carton of pear is enough for both Jo and Max we firstly add the part of Jo and Max to find the total pear they want. Then we check the one pear is enough y subtracting.

Now finding the total pear that Jo and Max want:

Total Pear they want = Jo want + Max want

Total Pear they want = 3/4 + 1/3

To add we equal the denominator.

Multiply and divide by 12 on both number

Total Pear they want = 3/4 × 12/12 + 1/3 × 12/12

Total Pear they want = 9/12 + 4/12

Total Pear they want = (9 + 4)/12

Total Pear they want = 13/12

Total Pear they want = 1 1/12

As we can see that the sum of both Jo and Max requirement is max than the one pear. So the only one carton of pear is not enough.

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The second order differential equation:-

[tex]\frac{d^2y}{dx^2}+P(x)\frac{dy}{dx}+Q(x)y[/tex].

Now, According to the question:

A differential equation is an equation that consists of a function and its derivative. A differential equation that consists of a function and its second-order derivative is called a second order differential equation. Mathematically, it is written as y'' + p(x)y' + q(x)y = f(x), which is a non-homogeneous second order differential equation if f(x) is not equal to the zero function and p(x), q(x) are functions of x. It can also be written as F(x, y, y', y'') = 0. Further, let us explore the definitions of the different types of the second order differential equation.

Hence, The second order differential equation.

[tex]\frac{d^2y}{dx^2}+P(x)\frac{dy}{dx}+Q(x)y[/tex].

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Answer:

isosceles, equilateral, scalene, obtuse, acute, and right triangles.

Step-by-step explanation:

isosceles, equilateral, scalene, obtuse, acute, and right triangles.

Triangles can be classified into six different shapes: right, obtuse, acute, equilateral, scalene, and isosceles. A triangle is said to be isosceles if two of its sides are congruent and one of its sides and angle is distinct.

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The maximum number of people who can stand in each side of the boat is equal to the buoyant force divided by the average mass of a person multiplied by the acceleration due to gravity.

The maximum number of people who can stand in each side of a boat can be determined using Archimedes' Principle. This principle states that the buoyant force on an object is equal to the weight of the fluid it displaces. In the case of a boat, the buoyant force is equal to the weight of the water it displaces.

Using this principle, the maximum number of people who can stand in each side of a boat can be calculated using the equation:

F_B = m_p * g

Where F_B is the buoyant force, m_p is the total mass of all the people standing in the boat, and g is the acceleration due to gravity.

To determine the maximum number of people, we must first calculate the mass of the boat, m_b. We can do this by multiplying the volume of the boat (V) by the density of the material the boat is made of (ρ).

m_b = V * ρ

Next, we can calculate the total mass of all the people standing in the boat, m_p. This can be calculated by multiplying the total number of people (n) by the average mass of a person (m).

m_p = n * m

Finally, we can calculate the maximum number of people who can stand in each side of the boat by rearranging the equation for F_B and solving for n.

n = (F_B) / (m * g)

Therefore, the maximum number of people who can stand in each side of the boat is equal to the buoyant force divided by the average mass of a person multiplied by the acceleration due to gravity.

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Answer:  40 divided  by 2 (half) = 20+16 = 36

Step-by-step explanation:

The standard deviation of the distribution of price increases over this period is 0, and the modal price increase during this period is $2.

a) The standard deviation of the distribution of price increases over this five-year period can be calculated using the formula for the standard deviation of a population:

SD = √(Σ(x - μ)²/N)

Where x is each price increase, μ is the mean of the price increases, and N is the number of price increases.

First, we find the mean:

μ = (4 + 2 - 1 + 2 + 2) / 5 = 9/5

Next, we calculate the standard deviation:

SD = √(((4 - 9/5)^2 + (2 - 9/5)^2 + (-1 - 9/5)^2 + (2 - 9/5)^2 + (2 - 9/5)^2) / 5) = √(0 / 5)

= 0

b) The modal price increase during this period is the one that occurs most frequently. In this case, the modal price increase is $2, as it occurs thrice.

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Answer: 3 rose bushes

Step-by-step explanation:

1. First we must identify the unknown. We do not know how many rose bushes he can get, we will use "x" to represent this number.

2. We must set up an equation with the given information. We know the delivery fee will remain constant.

3. 15+18.75(x)=80

4. Subtract 15 from both sides and it leaves you with 18.75x=65

5. Then you must divide both sides by 18.75, which leaves you with x=3.46

6. We cannot buy .46 of a plant so we must round down to 3

7. Jim can buy 3 rose bushes

(a) Kenton is running 2.5 miles per day.

(b) An equation that illustrates the relationship between the day number and the total number of miles since Kenton began training is t = 2.5d

Equations whose variables have a power of one are called linear equations. One example with one variable is where ax+b = 0, where a and b are real values and x is the variable.

Given:

The table describes Kenton’s running progress during his training.

In the table, d represents the day number, and t represents the total number of miles he ran since he began training.

From the table,

In a day Kenton ran = 5/2 = 2.5 miles.

2.5 is a common difference.

(a) Kenton is running 2.5 miles per day.

(b) An equation that illustrates the relationship between the day number and the total number of miles since Kenton began training is t = 2.5d

Therefore, the equation is t = 2.5d

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Answer:

P = (-6, 4)

Step-by-step explanation:

A = (x1,y1) = (-7,5)

B = (x2,y2) = (-2,0)

m:n = 1:4

P = (x, y)  

= (    mx2 + nx1/ m + n       ,       my2 + ny1/ m + n     )

= (        1(-2) + 4(-7)/1+4       ,         1(0) + 4(5)/ 1+4       )

= (       -2 - 28 / 5                ,             20 / 5                )

= (         - 30 / 5                   ,                 4                   )

= ( -6 , 4)

P = (-6, 4)

Answer:

See below

Step-by-step explanation:

This is very easy once you understand what to do kiddo. They give you a x term, in this case -2, all you have to do is plug in this value into the equation y = x² -2x -3 which will give you your y value in this case +5 not - 5.

Heres the extra work

[tex]y = x^2 - 2x -3\\y = (-2)^2 -2(-2) -3\\y = 4 + 4 -3\\y = 5[/tex]

The nearest whole number is 814. The value of 338/698 < 0.5

What is whole number?

Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the corresponding positive numbers are the negative numbers. The boldface Z is a common way to represent the set of integers in mathematical terms.

Given mixed number is [tex]814\frac{338}{698}[/tex].

The fraction part of the mixed number is 338/698.

2 times of 338 is 676 < 698.

Thus the value of 338/698< 0.5.

It is necessary to look at the first digit following the decimal point in order to round a number to the nearest whole number. We don't need to do anything if this digit is less than 5 (1, 2, 3, 4), but we must round up if it is 5 or higher (5, 6, 7, 8, 9).

This means the decimal value of the given number is less than 814.5.

Since the digit in the tenth place is less than 5, thus the nearest whole number of the given mixed number is 814.

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Answer:

See below

Step-by-step explanation:

The graph is of f(x) is shifted 1 unit to the LEFT to get g(x)

          so  4^x     is now  4^(x+1)

                                   then    4^(x+1) = 4^(x-h)

                                         would mean h = - 1

The recursive rule for the given sequence 1, 3, 4, 7, 11 ... is aₙ₊₁ = aₙ + aₙ₋₁.

The next two term of the sequence 1, 3, 4, 7, 11, is equal to 18 , 29.

Recursive rule for the sequence 1, 3, 4, 7, 11, ...... is represented by :

Let us consider before 1 it is 0.

Next term is sum of previous two terms :

0 + 1 = 1

1 + 3 = 4

3 + 4 = 7

4 + 7 = 11

Recursive rule for the given sequence is equal to :

3rd = 2nd + 1st term

4th term = 3rd term + 2nd term .....

aₙ₊₁ = aₙ + aₙ₋₁

Next two terms for the above sequence is equal to:

7 + 11 = 18

11 + 18 = 29

Therefore, the recursive formula to represents the sequence 1, 3, 4, 7, 11 is equal to aₙ₊₁ = aₙ + aₙ₋₁ and next two terms are 18, and 29.

The above question is incomplete, the complete question is:

Write a recursive rule for the sequence. Then write the next two term of the sequence. For 1,3,4,7,11

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Answer:

Ответ:

Пошаговое объяснение:

Ответ : Пошаговое объяснение : - 1

Answer: x =13

Step-by-step explanation:

subtract 7 from both sides

7-7= 0

-7+20=13

x=13

Answer:

[tex] \sf \: x = 13[/tex]

Step-by-step explanation:

Given equation,

→ x + 7 = 20

Now the value of x will be,

→ x + 7 = 20

→ x = 20 - 7

→ [ x = 13 ]

Hence, the value of x is 13.

Answer:

A)  The perimeter of the figure is 19 units (nearest unit).

B)  The area of the figure is 23 square units (nearest square unit).

Step-by-step explanation:

The given figure is part of a circle and part of a square.

From inspection of the diagram, the circular part is a quarter circle.

Therefore, the length of the curved part of the figure is a quarter of the circumference of a circle (with radius 3 units).

[tex]\boxed{\begin{aligned}\textsf{Circumference of a circle}&=2 \pi r\\\\\implies \textsf{Circumference of a $\frac{1}{4}$ circle}&=\dfrac{1}{4} \cdot 2 \pi r\\\\&=\dfrac{1}{2}\pi r\end{aligned}}[/tex]

The perimeter of the figure is the sum of the length of the curved part and the measures of the straight edges.

[tex]\begin{aligned}\textsf{Perimeter}&=\dfrac{1}{2} \pi \cdot 3+2 \cdot 2+2 \cdot 5\\&=\dfrac{3}{2}\pi+4+10\\&=18.7123889...\\&=19\; \sf units\end{aligned}[/tex]

Therefore, the perimeter of the figure is 19 units to the nearest unit.

The area of the curved part of the figure is a quarter of the area of a circle (with radius 3 units).

[tex]\boxed{\begin{aligned}\textsf{Area of a circle}&=\pi r^2\\\\\implies \textsf{Area of a $\frac{1}{4}$ circle}&=\dfrac{1}{4} \pi r^2\end{aligned}}[/tex]

The area of the part of a square can be separated into two rectangles (see attachment).  The area of a rectangle is the product of its width and length.

The area of the figure is the sum of the area of the curved part and the two rectangles.

[tex]\begin{aligned}\textsf{Area}&=\dfrac{1}{4}\pi \cdot 3^2+3 \cdot 2+2 \cdot 5\\&=\dfrac{1}{4}\pi \cdot 9+6+10\\&=\dfrac{9}{4}\pi +6+10\\&=23.0685834...\\&=23\; \sf square\;units\end{aligned}[/tex]

Therefore, the area of the figure is 23 square units to the nearest square unit.

The perimeter of the figure, which is part circle and part square, can be found to be 18. 71 units.

The area of the figure would be 23. 07 units ².

The perimeter is the distance around the shape so we can add up the sides given and then find out the missing dimensions around the quarter circle.

The distance of that quarter circle is:

= ( Pi x Diameter ) / 4 quarters

= ( π x ( 3 + 3 )) / 4

= 4. 71 units

The perimeter then is:

= 2 + 5 + 5 + 2 + 4. 71

= 18. 71 units

To find the area, you can divide the figure into three shapes which would be two rectangles and one quarter circle.

The area of the rectangles would be:

= Length x Width                                                = 5 x 2

= 3 x 2                                                                 = 10 units ²

= 6 units ²

The area of the quarter circle would be:

= ( π x radius ² ) / 4

= ( π x 3 ² ) / 4

= 7. 07 units ²

Sum them all up:

= 6 + 10 + 7. 07

= 23. 07 units ²

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The equation has one solution at (0, -2) for the system of linear equations represented in the graph.

The points where the lines representing the intersection of two linear equations intersect are referred to as the solution of a linear equation. In other words, the set of all possible values for the variables that satisfy the specified linear equation constitutes the solution set of the system of linear equations.

Given the graph,

and the line passes from (0, -2) and (4, 0)

since the line passes from  (0, -2) and (4, 0),

so one of the solutions is at (0, -2),

and another solution is at (4, 0).

according to the options equation has  (0, -2) as one of the solutions.

Hence option B is correct.

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The expression (4/9) - (5/7)[(2/3) x (2/3)] in the simplified form will be 8/63.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

The expression is given below.

⇒ (4/9) - (5/7)[(2/3) x (2/3)]

Simplify the expression, then we have

⇒ (4/9) - (5/7)[(2/3) x (2/3)]

⇒ (4/9) - (5/7)(4/9)

⇒ (4/9) - (20/63)

⇒ (28 - 20) / 63

⇒ 8 / 63

The expression (4/9) - (5/7)[(2/3) x (2/3)] in the simplified form will be 8/63.

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Percentage multiplier calculates the percentage of an amount. It is also used to increase or decrease an amount by a percentage.

In order to find the percentage multiplier of 26% of an amount we can multiply the number by a multiplier.

26% = [tex]\frac{26}{100}[/tex] = 0.26

Hence, 0.26 is the multiplier.

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The price of each pair of skates is given as follows:

$8.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

For which the parameters are given as follows:

A skating rink charges a rate of $4, hence the intercept b is given as follows:

b = 4.

Hence:

y = mx + 4.

A family rents 2 pairs of skates and pays a total of $20, meaning that when x = 2, y = 20, then the slope m, representing the cost of each pair, is obtained as follows:

20 = 2m + 4

2m = 16

m = 16/2

m = 8.

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================================================

Work Shown:

Solve the first equation for y.

3x+y = 0

y = -3x

Then substitute that into the other equation to solve for x.

x-6y = 19

x-6(-3x) = 19

x+18x = 19

19x = 19

x = 19/19

x = 1

Once we determine x, we can determine y.

3x+y = 0

3*1+y = 0

3+y = 0

y = -3

Or you could say:

x-6y = 19

1-6y = 19

-6y = 19-1

-6y = 18

y = 18/(-6)

y = -3

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

In summary we get x = 1 and y = -3 pairing up together.

The ordered pair solution is (x,y) = (1, -3)

To confirm the answer, plug the coordinates back into the original equations. Simplify both sides. You should get the same thing on both sides. I'll let you do these confirmation steps.

Visually you can use something like Desmos or GeoGebra to note that the two lines intersect at (1, -3)

Given:-

Multiply the given eqⁿ ( 1 ) to 6

now , add the eqⁿ ( 3 ) to eqⁿ ( 2 )

18x + 6y = 0

x - 6y = 19

————————

19x = 19

x = 19/19

x = 1

now , put the value of x = 1 in eqⁿ ( 1 )

━━━━━━━━━━━━━━━━━━━━━━━━━━

hope it helps! :)

relational algebra is a sufficient tool for manipulating data in a distributed system because it provides a uniform and consistent way to access and manipulate data.

Regardless of where it is stored in the system, and because it is a declarative language that abstracts away implementation details, making it easier to maintain and evolve the system.

Relational algebra is a powerful mathematical tool used to manipulate data in a relational database. It provides a way to perform operations on data in a structured and organized manner.

In a distributed system, where multiple nodes store and process data, relational algebra is still sufficient because it provides a uniform and consistent way to access and manipulate data across the entire system.

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The length of the arc of the circle formed by the central angle of 90° is approximately 12.57 units

The length of an arc in a circle can be found using the formula:

Arc Length = (Central Angle / 360) * (2 * π * Radius)

Given a central angle of 90° and a radius of 8, the arc length can be found as follows:

Arc Length = (90 / 360) * (2 * π * 8)

Arc Length = (1/4) * (16π)

Arc Length = 4π

So, we have

Arc length = 12.57

So, the length of the arc of the circle is 12.57 (rounded to two decimal places).

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The number of tiles that must be sold in a quarter for Belleterre Tile to earn $15,210 in quarterly operating profit is 138000 tiles .

To calculate the number of tiles needed to be sold in order to earn $15,210 in quarterly operating profit, you need to first find the unit variable cost (the cost of producing each tile),

The average variable cost per tile is = 357556/125900 = $2.84  ;

the average selling price per tile is = 463312/125900 = $3.68   ;

So , Average contribution margin per tile is = $3.68 - $2.84 = $0.84  ;

The Number of tiles to earn  earn $15,210 in quarterly operating profit is calculated as : (total fixed costs + profit) / (contribution margin)

⇒ (100800+15120)/0.84

⇒ 115920/0.84 = 138000 tiles .

Therefore , to earn $15,210 in quarterly operating profit , 138000 tiles should be sold .

The given question is incomplete , the complete question is

Belleterre Tile Revenue and Costs for Third Quarter is :

Total Revenue sold   : 125900 tiles  ;

Total revenue            : $462312   ;

Total Variable costs  : 357556    ;

Total Fixed Costs      : 100800  ;

The CFO tells you that the company owner have said that unless the quarterly operating profit exceeds $15210, they will liquidate the company. How many tiles would have to be sold in a quarter for Belleterre Tile to earn $15,210 in quarterly operating profit ?

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The actual length of the swing set area is 0.5 * 20 feet = 10 feet.

Since the scale drawing represents the actual dimensions of the park,

We can use the ratio of the scale drawing dimensions to the actual dimensions to find the actual length of the swing set area.

Let's call the actual length of the swing set area L.

Then, on the scale drawing, the length of the swing set area is 0.5 inches.

The ratio of the actual length to the scale drawing length is 20 inches : L feet.

We can set up an equation to find L:

L * (20 inches / L feet) = 0.5 inches

Solving for L, we find:

L = (0.5 inches * L feet) / (20 inches / L feet)

= (0.5 * L feet) / (20 / L feet)

= (0.5 * L feet) / (20 / L feet)

= 0.5 * (L feet / 12 inches/foot)

= 0.5 * 20 feet

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Answer:

The answer is 100 feet. I took the quiz and it was 100 feet.

Step-by-step explanation:

The image of 8,12 after dilation by a scale factor of 1/4 will be 2,3.

Given that the image of (8,12) after dilation by a scale factor of 1/4 centered at the origin.

The image of the dilated point will be:-

x : - 8 ⇒ 8 / 4 = 2

y : - 12 ⇒ 12 / 4 = 3

Therefore, the image of 8,12 after dilation by a scale factor of 1/4 will be 2,3.

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The Probability P(Green and odd) for given Sample Space is 1/5.

The likelihood of an event is expressed by probability. A random event's occurrence is the subject of this mathematical field of study. From zero to one, the value is available. In mathematics, probability is used to forecast the likelihood that events will take place.

The likelihood of something happening is referred to as a probability. The probability distribution also makes use of this basic concept in probability theory. We must first ascertain the total number of possibilities before calculating the likelihood of a specific event occurring.

Event's likelihood of occurring P(E) = The number of positive outcomes divided by the total number of outcomes

Now,

Total number of outcomes=10

No. of Box that are green and marked odd=2

Hence, the probability

           P(Green and odd)=2/10=1/5

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Answer:

Yes.

Step-by-step explanation:

They will be either side of the 2 circles.

Answer: -6x + 21y = -42Now we can solve for y:21y = -42 + 42

y = 0Substitute y = 0 back into one of the original equations:-3x + 14(0) = -28

-3x = -28

x = 9/1So the solution to the system of equations is (x, y) = (9, 0).

Step-by-step explanation: