Please help ASAP!!!!!!!! :)

√9 - 3x⁄x + 4x2 - x3⁄2 + y2 - 2xy + 2⁄2 + 9 - x2⁄2 from 0 to √9

To find the area bounded by the given functions, we will need to solve the following integrals:

1. Integral of √9 - 3x⁄x from 0 to √9
2. Integral of 4x2 - x3⁄2 from 0 to √9
3. Integral of y2 - 2xy + 2⁄2 from 0 to √9
4. Integral of 9 - x2⁄2 from 0 to √9

The area bounded by the given functions is then equal to the sum of the four integrals, or:

Area = √9 - 3x⁄x + 4x2 - x3⁄2 + y2 - 2xy + 2⁄2 + 9 - x2⁄2 from 0 to √9

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The required value of a + b is 35.

The area of the shadow can be calculated by finding the area of the regular hexagon. The formula for the area of a regular hexagon is:

    A = (3√3)/2 * s^2,

where s is the length of one side of the hexagon.

Since the cube is balanced on one of its vertices, the length of one side of the hexagon is equal to the length of one edge of the cube, which is 8.  Therefore, the area of the shadow is A = (3√3)/2 * 8^2 = 64√3/2 = 32√3.

The value of a is 32 and the value of b is 3, so the value of a + b is 32 + 3 = 35. Therefore, the answer is 35.

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Box plot of the given data for the scores of the statistics is represented by minimum value = 51, maximum value = 93, Median = 75, lower quartile = 67 and upper quartile = 87.

Box plot is attached.

Scores of the statistics test  is equal to

83,72,91,73,74,51,62,52,76,93

Arrange the scores into ascending order we get,

51, 52, 62, 72, 73, 74, 76, 83, 91, 93

Minimum value = 51

Maximum value = 93.

Median= Average of the two middle values.

Two middle values are 74 and 76

Median

= (74 + 76) / 2

= 75

Lower quartile = Median of the lower half of the data

Upper quartile = Median of the upper half of the data

Lower half= 51, 52, 62, 72, 73

Upper half = 76, 83, 91, 93

Lower quartile

= (62 + 72) / 2

= 67

Upper quartile

= (83 + 91) / 2

= 87

Constructed box plot is attached.

Therefore, to construct box plot minimum value = 51, maximum value = 93, Median = 75, lower quartile = 67 and upper quartile = 87 for the given test scores.

Box plot is attached.

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Step-by-step explanation:

So, let's say that we have 5/20. 5 and 20 can divide by a similar number (5) so you divide each variable by 5. in the end, you get 1/4.

The after-tax cost of the tennis racket is $101.70.

To calculate the after-tax cost of the tennis racket, we first need to find the sale price of the racket, then add on the HST.

Step 1: Find the sale price of the racket. To do this, we need to find 25% of $120, then subtract that amount from the original price.

25% of $120 = 0.25 × $120 = $30

Sale price = $120 - $30 = $90

Step 2: Add on the HST. To do this, we need to find 13% of the sale price, then add that amount to the sale price.

13% of $90 = 0.13 × $90 = $11.70

After-tax cost = $90 + $11.70 = $101.70

Therefore, the after-tax cost of the tennis racket is $101.70.

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Answer:

Below

Step-by-step explanation:

x^2 -x + 1      Use Quadratic Formula    a = 1    b = -1    c = 1

  to find zeroes   1/2 ±  i sqrt(3) / 3

Sooo.... Not sure you could find it by factoring:

         (x -1/2 +i sqrt(3) /2) (x - 1/2 - i sqrt (3)/2)    would be hard to see !!

The solution to the given system of equations, 3x+2y=4; 2x−3y=7 is (2, -1).

To solve the given system of equations graphically, we need to first graph each equation on the same coordinate plane and then find the point of intersection.

The first equation is 3x+2y=4. We can rearrange this equation to get y in terms of x:
2y = -3x + 4
y = (-3/2)x + 2

The second equation is 2x−3y=7. We can also rearrange this equation to get y in terms of x:
3y = 2x - 7
y = (2/3)x - (7/3)

Now we can graph both equations on the same coordinate plane. The first equation has a y-intercept of 2 and a slope of -3/2, while the second equation has a y-intercept of -7/3 and a slope of 2/3.

After graphing both equations, we can see that they intersect at the point (2, -1). This means that the solution to the system of equations is x = 2 and y = -1.

Therefore, the solution to the given system of equations is (2, -1).

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Answer:

2/10

Step-by-step explanation:

7/ 10 of the distance on Saturday

Remaining distance is 3/10

2/3 of remaining distance is 2/3 x 3/10 = 2/10

Saturday 7/10

Sunday 2/10

The linear velocity of the bicycle is approximately 6.68 miles per hour.

a) The angular velocity of the wheel can be found by using the formula:
ω = v / r
where ω is the angular velocity, v is the linear velocity, and r is the radius of the wheel.
In this case, v = 115 m/sec and r = (8 cm / 2) = 4 cm = 0.04 m.
So, the angular velocity of the wheel is:
ω = (115 m/sec) / (0.04 m) = 2875 radian per second.

b) The linear velocity of the bicycle can be found by using the formula:
v = ω * r
where v is the linear velocity, ω is the angular velocity, and r is the radius of the wheel.
In this case, ω = 125 revolutions per minute = (125 * 2π) / 60 = 13.09 radian per second and r = (18 inches / 2) = 9 inches = 0.75 feet.
So, the linear velocity of the bicycle is:
v = (13.09 radian per second) * (0.75 feet) = 9.82 feet per second.
To convert this to miles per hour, we can use the conversion factor 5280 feet = 1 mile:
v = (9.82 feet per second) * (60 seconds / 1 minute) * (60 minutes / 1 hour) * (1 mile / 5280 feet) = 6.68 miles per hour.
So, the linear velocity of the bicycle is approximately 6.68 miles per hour.

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Answer: 55

Step-by-step explanation: 13 -7 = 16. 16/2 = 8. 8 + 7 = 15. 8 X 5 = 40

The number representing the 6th grader participated in the field event is 120

A sample space is a collection or a set of possible outcomes of a random experiment.

The sample space is represented using the symbol, “S”. The subset of possible outcomes of an experiment is called events.

Given is a graph, showing the number of class students taking parts in different events,

We need to find the number of the 6th graders who participated in field event.

The sample size is 20 for who participated in field event, that means one unit is representing 20 participants

The sample number for 6th graders who participated in field event = 6

That means, the total number of the 6th graders who participated in field event = 20 x 6 = 120

Hence, the number representing the 6th grader participated in the field event is 120

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Answer:6

Step-by-step explanation:

the perimeter of the orange square is 18

4+4+5+5=18

3+3=6

18-6=12

12/2=6

6+6=12

3+3=6

6+12=18

18=18

The velocity of the pendulum is approximately -2.45 inches/second.

The acceleration of the pendulum is approximately 5.13 inches/second².

To find the velocity and acceleration of the pendulum, we need to find the first and second derivatives of the function d(t).

a. The velocity of the pendulum is given by the first derivative of the function d(t):

v(t) = d'(t) = 7 * (π/3) * cos(πt/3 - 2)

To find the velocity at t = 6 seconds, we simply plug in 6 for t:

v(6) = 7 * (π/3) * cos(π(6)/3 - 2) = 7 * (π/3) * cos(4) ≈ -2.45 inches/second

So the velocity of the pendulum at 6 seconds is approximately -2.45 inches/second.

b. The acceleration of the pendulum is given by the second derivative of the function d(t):

a(t) = d''(t) = -7 * (π/3)² * sin(πt/3 - 2)

To find the acceleration at t = 6 seconds, we simply plug in 6 for t:

a(6) = -7 * (π/3)² * sin(π(6)/3 - 2) = -7 * (π/3)² * sin(4) ≈ 5.13 inches/second²

So the acceleration of the pendulum at 6 seconds is approximately 5.13 inches/second².

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The original value of the oranges is 143.75.

A percentage is a number or a ratio that is expressed as a fraction of 100 i.e. out of 100.

In formula, x% of amount y = y*(x/100)

Given :

Tax paid by Rekha : 15%

Final Price paid by Rekha : 165.31

Let the original price of the oranges = x

The additional tax amount on oranges

           = 15% of original price of x

           = 15 * x / 100

           = 0.15 x

Total price paid by Rekha = Original price of orange + Tax amount

165.31 = x + 0.15x

165.31 = (1 + 0.15)x

165.31 = 1.15x

x = 165.31/1.15

x = 143.75

Thus, the original value of the oranges is 143.75.

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Answer- 1:8

The original length of the board was 32 inches. Since it reduced we can divide 32 into 4. 32/4 is 8. This means that the scale factor of the dilation  is 1:8. 32 is 8/1 of 4, so that means in ratio 1 whole is divided into 8 parts, hence 1:8.

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To run 6 miles it takes 2880 seconds of time.

The speed formula can be defined as the rate at which an object covers some distance. Speed can be measured as the distance travelled by a body in a given period of time. The SI unit of speed is m/s.

Given that, a runner records his rate of speed along the first mile of a 6 mile path that winds through the park.

We know that, speed =Distance/Time

Here, Distance= 1/4 mile and time=120 seconds

Speed = 1/4 ÷120 =1/480 miles per seconds

Time taken to run 6 miles

We know that, Time =Distance/Speed

Time = 6 ÷ 1/480

= 6×480

= 2880 seconds

Therefore, to complete 6 miles it takes 2880 seconds.

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Answer:

He bought more turkey

Step-by-step explanation:

Simple way is to check how close both numbers are to a whole number or convert to fraction

0.75 =75/100

0.57= 57/100

The value of a is 20, b is 40, c is 10 and d is 10√3

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

By using sine function we find the value of a

sin 45=a/20√2

1/√2 = a/20√2

20√2=a√2

a=20

Now let us find c

cos 45=c/(20√2)

1/√2×20/√2=c

10=c

sin30=a/b

1/2=20/b

b=40

Now we have to find d by cosine function

cos30=d/a

√3/2=d/20

d=10√3

Hence, the value of a is 20, b is 40, c is 10 and d is 10√3

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Answer:

z=5/138

Step-by-step explanation:

15 1/3z=5

46/3z=5

3z=5/46

z=5/138

a) The sales of the cooking club will be $80, while the expenditures will be $80 when the number of cakes sold will cover their expenditures (break-even point).

b) The number of cakes that the members of the cooking club will sell at the street fair at this point (break-even point) is 10.

The break-even point is the sales units that will equate to the expenditures.

At the break-even point, there is no profit or loss because the total sales revenue equals the total costs (fixed and variable).

The selling price per unit = $8

The fixed cost for a booth at the fair = $20

The variable cost price per unit = $6

Contribution margin per unit = $2 ($8 - $6)

The break-even point in units = Fixed Cost/Contribution margin per unit

= 10 units ($20/$2)

Total sales revenue at the break-even point = $80 ($8 x 10)

Total variable cost = $60 ($6 x 10)

Total fixed and variable costs = $80 ($20 + $60)

Thus, at the break-even point, the cooking club will have sold 10 units making revenue to equal the total costs.

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Answer: [tex]x^{2}[/tex]+2x-5

Step-by-step explanation:

(g+f)(x) = g(x)+f(x)

g(x) = 2x-2

f(x) = [tex]x^{2}[/tex]-3

g(x)+f(x) = (2x-2) + ([tex]x^{2}[/tex]-3)

g(x)+f(x) =  [tex]x^{2}[/tex]+2x-5

Below is the exact match for public good or service of Local Government and Federal Government.

Goods and services are two distinct types of economic products that are exchanged in the marketplace.

Goods are tangible, physical products that can be seen, touched, and stored. They are typically manufactured or produced and can be traded in the marketplace.

Services are usually produced and consumed simultaneously and involve an activity performed by one person or group for the benefit of another. Examples of services include healthcare, education, transportation, banking, consulting, and entertainment.

Local Government                                Federal Government

Sewage system                                    Financial aid for college

Traffic light                                            Internal Revenue Service (IRS)

Hospitals                                               Hospitals  

                                                              Currency

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The number of servings that a 1.5 liter (1500ml) bottle of soda will make is 6 servings of 0.25 liter (250ml).

To find the number of servings, you can divide the total volume of the bottle by the volume of each serving.
Step-by-step explanation:
1. Convert the volume of the bottle to milliliters: 1.5 liters = 1500 milliliters
2. Convert the volume of each serving to milliliters: 0.25 liters = 250 milliliters
3. Divide the total volume of the bottle by the volume of each serving: 1500 milliliters / 250 milliliters = 6 servings
Therefore, a 1.5 liter (1500ml) bottle of soda will make about 6 servings of 0.25 liter (250ml).

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Jody needs to walk 3.5 miles on Sunday to reach her goal.

What is Multiplication?

Multiplication is a mathematical operation that combines two or more numbers to produce a result called the product. It is a repeated addition of the same number.

To reach her goal of 25 miles per week, Jody would have already walked a total of:

4.5 miles/day x 4 days = 18 miles

3.5 miles on Saturday = 3.5 miles

The total distance walked from Monday to Saturday is:

18 + 3.5 = 21.5 miles

To reach her goal of 25 miles per week, she needs to walk an additional:

25 - 21.5 = 3.5 miles

Therefore, Jody needs to walk 3.5 miles on Sunday to reach her goal.

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427.

The proof for the question is as follows:

A(n) is the arithmetic mean of the (positive) factors of n.

We want to find the n for which A(n) = 124.

Let F be the set of (positive) factors of n, and let f1, f2,..., fm be the elements of F.

The arithmetic mean of F is defined as A(n) = (f1 + f2 + ... + fm)/m.

Now, we have A(n) = 124. So, 124 = (f1 + f2 + ... + fm)/m.

Therefore, 124m = f1 + f2 + ... + fm.

This implies that f1 + f2 + ... + fm = 124m = 427.

Thus, n = 427.

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A 12-ft high flagpole is standing vertically at the edge of the roof of a building with angle of elevation of 78°50'.  The height of the building is 312.2 ft (option c)

To find the height of the building, we can use the tangent function of the angle of elevation. The tangent function relates the opposite side (height of the building + flagpole) to the adjacent side (distance from the base of the building) of a right triangle.

The angle of elevation is given as 78° and 50'. We can convert this to decimal form by dividing the minutes by 60:

78° + (50'/60) = 78.833°

Let H = height of the building + height of the flagpole

Then,

tan(78.833°) = opposite/adjacent
tan(78.833°) = H/64 ft
H = 64 ft * tan(78.833°)
H = 324.2 ft

Therefore,

the height of the building = H - 12

                                            = 324.2 - 12 = 312.2 ft (option c)

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Answer:

1.5 inches of stell will make 1 spring

Step-by-step explanation:

If 450 inches of steel are used to make 300 springs, we can simply divide the inces by the spring count to obtain a unit of inches/(1 spring).

(450 inches of steel)/(300 springs) = (1.5 inches of steel)/)1 spring)

You can calculate the average value of the data set by summing all the data points and dividing by the number of data points. This will give you the average value of the data set for the reservoir simulation grid block or for comparison with a good test.

To provide an average of the given data for reservoir simulation grid block or for comparison with a well test, you would need to consider the following factors:

The range of data: You need to consider the range of data, from the minimum to the maximum value, to determine the average value of the data set.

The number of data points: You also need to consider the number of data points in the data set, as this will affect the calculation of the average value.

The type of data: You need to consider the type of data, whether it is porosity or horizontal permeability, as this will affect the calculation of the average value.

The variation of data with depth: You need to consider the variation of data with depth, as this will affect the calculation of the average value.

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In interval notation, the domain and range of the function are:
Domain: (-∞, ∞)
Range: [1, ∞)

The domain of a function is the set of all possible values of x that can be plugged into the function. The range of a function is the set of all possible values of f(x) that can be obtained by plugging in values of x into the function.

For the given function f(x) = 9x² + 1, the domain is all real numbers, because any value of x can be plugged into the function. Therefore, the domain is (-∞, ∞).

The range of the function is the set of all possible values of f(x) that can be obtained by plugging in values of x into the function. Since the function is a quadratic with a positive leading coefficient (9), the graph of the function will be a parabola that opens upward. The minimum value of the function will occur at the vertex of the parabola, which is (0, 1). Therefore, the range of the function is [1, ∞).

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The slope of line A is -1/2 and the slope of line B is -3/5. The slope of line A is greater than the slope of line B.

What is slope?

A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.

First, let's rewrite the equation of line A in slope-intercept form (y = mx + b) where m is the slope and b is the y-intercept -

y - 1 = - 1/2(x + 10)

y = 1/2(x + 10) + 1

y = 1/2x + 6

So, the slope of line A is - 1/2.

For line B, we can use the formula for finding the slope of a line given two points (m = (y2 - y1) / (x2 - x1)).

Let's use the first and last points to find the slope -

m = (-3 - 6) / (-10 - 5) = -9 / -15 = 3/5

So, the slope of line B is 3/5.

Therefore, the slope of line B is smaller as compared to slope of line A.

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