Find the area of the shaded portion.

The area of the region enclosed by the given curves is 1/6.

The area of the region enclosed by a curve can be determined by doing a definite integral between the two points. The area under the curve y = f(x) is determined by integrating y = f(x) between the limits of a and b.

When the area of the region enclosed by two curves needs to be calculated the difference the function is integrated for the limits which are represented by the solution of the curves. The given curves are y = f(x) = x and y = g(x) = x^2. The solutions of the curves from the figure attached is (0,0) and (1,1).

Hence, the area is given as:

A = ∫_a^b▒〖((f(x)-g(x))〗 dx

A = ∫_0^1▒(x-x^2 )  dx

A = |1/2 x^2-1/3 x^3 |1¦0

A = 1/2 (1)^2-  1/3 (1)^3-(1/2 (0)^2- 1/3 (0)^3 )

A = 1/6

Note: The question is incomplete. The complete question probably is: Find the area enclosed between the curves y = x and y=x^2.

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Answer:

x^2=1

3x=+3

2=+2

Step-by-step explanation:

answers

1

3x

+2

hope it helps

Answer:  √8

Step-by-step explanation:

Step 1: Find the mean.

(5+7+9+11+13)/5 --> 45/5 = 9

Step 2: Find each score's deviation from the mean.

5-9= -4

7-9= -2

9-9= 0

11-9= 2

13-9= 4

Step 3: Square each deviation from the mean.

-4^2 = 16

-2^2= 4

0^2 = 0

2^2 = 4

4^4 = 16

Step 4: Find the sum of squares.

16+4+0+4+16 = 40

Step 5: Find the variance.

40/5 = 8

Step 6: Find the square root of the variance.

the square root of 8 is √8

Take the vertices as A(2,1), B(0,2), C(-1,1) and D (x2,y2) The fourth coordinate is (1, 1)

Let the vertices ABCD represent the  parallelogram.

The diagonals AC and BD bisect each other [property of parallelogram]

Mid point of AC = Mid point of BD               ……….. 1

Mid point of AC =  (x1+x2)/ 2 and (y1+y2) /2)

=(2-1)/2, (1+1)/2

=(1/2 , 1)

Mid point of BD= (x1+x2)/2, (y1+y2)/2

=(0+x2)/2, (2+y2)/2)

From equation 1

(1/2 , 1)=(0+x2)/2, (2+y2)/2)

{(1/2 , 1/1)} = {(0+x₂)/2 , (1+y₂)/2}

This implies that

1/2 = x₂/2 and 1/1 = (2+y₂)/2

Cross and multiplying we have

2x₂=2 and 2=2+y₂

Making x and y the subject of the relations

x₂=1 and y₂= 1

Therefore the fourth vertex D is (1,1)

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The correct explanation of each step is 1. Assume n is not even, that is, it is odd.  - Negation of the conclusion. 2.Then n = 2k + 1 for some integer k.  - Definition of an odd integer.

When one is familiar with the inverse statement, it is simple to comprehend how to construct a contrapositive statement. Take the negation of the hypothesis and the conclusion to produce the conditional statement's opposite. Create the inverted statement first, then swap the hypothesis and conclusion to create the contrapositive of the conditional statement.

3.5n + 3 = 5(2k + 1) + 3 = 10k + 8 = 2(5k + 4) - Definition of an even number

1. Assume n is not even, that is, it is odd.  - Negation of the conclusion.

2.Then n = 2k + 1 for some integer k.  - Definition of an odd integer.

3.5n + 3 = 5(2k + 1) + 3 = 10k + 8 = 2(5k + 4) - Definition of an even number Arithmetic.

4. Hence, 5n + 3 is even.

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Answer:

16-3y

Step-by-step explanation:

9+7= 16

16-3y. first u do the ones that the same and don't have a letter after them. then you do the letter which in this case u just put the minus sign befor and it cokes out to 16-3y.

Answer:

he y-intercept of the line is the point (0,-41)

Step-by-step explanation:

Hope this is right!

Answer:

get a life

Step-by-step explanation:

The present value of the estimated toll revenue for the proposed highway construction is approximately $31,333,333.33.

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

To Calculate the percent of a number , divide the number by whole number and multiply by 100.

Now, Using the formula for the present value of an annuity, with a rate of 6% and 20 years, we get:

Present Value = $2,000,000 [ (1 - (1+0.06)⁻²⁰) / 0.06 ]

                      = $2,000,000 [ (1 - 0.312) / 0.06 ]

                       = $31,333,333.33

So, the present value of the estimated toll revenue for the proposed highway construction is approximately $31,333,333.33.

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The best estimate for the blue shark population would be = 234.

The total number of blue sharks that was tagged and released = 36 blue sharks.

The total number of sharks that the government corral = 130.

The number of sharks among the corral sharks that are tagged = 20

Since 130 = 20

X. = 36

Make X the subject of formula;

X = 130× 36/20

= 468/20

= 234.

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The coordinates of the figure after the rotation of 180° will result in a 180° clockwise and counterclockwise rotation: (x, y) becomes (-x,-y)

The measure of the amount a figure is rotated about the center of rotation is called the angle of rotation. The angle of rotation is usually measured in degrees. We specify the degree measure and direction of a rotation.

90° clockwise rotation: (x,y) becomes (y,-x)

90° counterclockwise rotation: (x,y) becomes (-y,x)

180° clockwise and counterclockwise rotation: (x, y) becomes (-x,-y)

270° clockwise rotation: (x,y) becomes (-y,x)

270° counterclockwise rotation: (x,y) becomes (y,-x)

Given data ,

Let the figure be represented as JKL

Now , the rotated figure be represented as J'K'L'

The coordinates of JKL be J ( x₁ , y₁ ) , K ( x₂ , y₂ ) and L ( x₃ , y₃ )

Now , let the rotation angle be d = 180°

For a rotation of 180° clockwise and counterclockwise rotation: (x, y) becomes (-x,-y)

Substituting the values in the equation , we get

The coordinates of J'K'L' is J' ( -x₁ , -y₁ ) , K' ( -x₂ , -y₂ ) and L' ( -x₃ , -y₃ )

Hence , the rotation is solved

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The average yearly salary of an individual with each of these final degrees is,

Master's individual earns average of $66,000 while the Bachelor's individual earns $55,000.

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

Given that;

The average yearly salary of an individual whose final degree is a​ master's is ​$44 thousand less than twice that of an individual whose final degree is a​ bachelor's.

And, Combined, two people with each of these educational attainments earn ​$121 thousand.

Now, The total amount earned by a Bachelor's person be $x:

And, amount earned by a masters person will be; $(2x - 44)

Hence, Total amount earned by the two individuals will be;

⇒ x + (2x - 44) = 121

Solve for x as;

⇒ x + 2x - 44 = 121

⇒ 3x - 44 = 121

⇒ 3x = 121 + 44

⇒ 3x = 165

⇒ x = 165/3

⇒ x = 55

And, (2x - 44) = 2 × 55 - 44

                     = 110 - 44

                     = 66

Therefore we conclude that; master's individual earns average of $66,000 while the Bachelor's individual earns $55,000.

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Store A sells at cheaper rate.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the

change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

Given:

Store A: y= 0.40 x

so, the unit rate is 0.40.

Store B:

The cots of 3 pound carrot= 20.16

and, the cost of 48 ounce carrot = 20.16

and, cost per ounce= 20.16 /48= 0.42

So, the unit rate is 0.42.

Thus, store A sells at cheaper rate.

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The bearing of L from C is 50°.

First  we need to use the concept of transitive bearings. Given the bearing of the ship R from lighthouse L as 220°, and the fact that canoe C is equidistant from R and L,

we can set up a pair of complementary angles to find the bearing of L from C.

Since C is due North of R, the bearing of R from C is 90°. Then, the bearing of L from R is 90° + 220° = 310°.

To find the bearing of L from C, we subtract this angle from 180°.

Therefore, the bearing of L from C is 180° - 310° = 50°.

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Answer:

Step-by-step explanation:

The profitability index (PI) is a measure used in capital budgeting to evaluate the financial viability of an investment. It is calculated by dividing the present value of the future cash flows by the initial investment. The formula for calculating the profitability index is:

PI = Present value of future cash flows / Initial investment

To calculate the present value of the future cash flows, we need to discount each cash flow to its present value using the required return of 8.4 percent. The present value of each cash flow is as follows:

Year 0: -$249,000 (no discounting necessary for the initial investment)

Year 1: $147,100 / (1 + 0.084)^1 = $135,870.37

Year 2: $164,600 / (1 + 0.084)^2 = $137,672.76

Year 3: $129,700 / (1 + 0.084)^3 = $100,636.20

The present value of the future cash flows is the sum of the present values of each cash flow:

PV = $135,870.37 + $137,672.76 + $100,636.20 = $374,179.33

Now we can calculate the profitability index:

PI = $374,179.33 / $249,000 = 1.5035

Therefore, the profitability index for this project is 1.5035. This means that for every dollar invested in the project, the project is expected to return $1.50 in present value of future cash flows. A profitability index greater than 1.0 indicates that the project is expected to generate positive net present value and is therefore a good investment.

Answer: C. 10

Step-by-step explanation:

931 / 7 = 133

so, 133 units per hour

133x = 1,330

1,330 / 133 = 10

Your answer is 10 hours, or option C

15.05 + 2.5x 2.05 is the second operation and 13.95 ÷ 5 x (8.34 − 6.09) value is 6.2775, Option A is correct.

An expression is combination of variables, numbers and operators.

The given expression is 15.05 + (6.25 − 3.75) x 2.05.

By using BODMAS rule we apply the operations.

15.05 + (6.25 − 3.75) x 2.05.

Firstly we solve the expression in parenthesis.

15.05 + 2.5x 2.05.

The other expression is 13.95 ÷ 5 x (8.34 − 6.09).

2.79 x (2.25)

6.2775

Hence,  15.05 + 2.5x 2.05 is the second operation and 13.95 ÷ 5 x (8.34 − 6.09) value is 6.2775, Option A is correct.

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Answer:

B

Step-by-step explanation:

she purchased 9 units at $30 each (= she spent 9×$30), and she received $8 credits for each of 5 units she returned.

so, the total money spent was

9×$30 - 5×$8 = $270 - $40 = $230

because we are looking at the money spent, any credit is then entering the calculation as '-', because it reduces the amount of money spent.

The graph backs up the assertion that India is unlikely to be a serious competitor in the steel production industry in the future because China, Japan, and the US have far more experience producing steel than India does.

A group of businesses or organisations that offer comparable goods or services is referred to as an industry. A few examples of the factors that can be used to define an industry include the kind of products or services they offer, their manufacturing procedures, the technology they use, or the customers they aim to serve. Development of industries was a result of the Industrial Revolution.

The graph shows that China, Japan, and the US all have a lot more experience making steel than India does, and India is not expected to become a significant competitor in the near future. Notwithstanding the nation's economic crisis, the industry—despite being one of the sectors that suffered the most—continues to play a vital role in the expansion of the economy.

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Answer: To convert liters of fuel oil burned in hours to gallons, we can use the conversion factor that 1 gallon is equal to 3.785 liters. The formula for the conversion can be represented as a function:

def liters_to_gallons(liters):

   return liters / 3.785

Here, the input liters represents the number of liters of fuel oil burned in hours, and the output of the function is the equivalent number of gallons. The function performs the conversion by dividing the input value (in liters) by the conversion factor (3.785).

Answer:

y = -15/18 x - 12

Step-by-step explanation:

The linear equation that passes through the points (-12, 14) and (6, -1) can be found by using the point-slope form of a line. The point-slope form of a line is given by:

y - y1 = m(x - x1)

where (x1, y1) is a point on the line, m is the slope of the line, and (x, y) are the coordinates of any other point on the line. To find the equation of the line passing through the points (-12, 14) and (6, -1), we can use either of the two points as (x1, y1) and find the slope m using the other point.

Let's use the point (-12, 14) as (x1, y1):

m = (y2 - y1) / (x2 - x1)

= (-1 - 14) / (6 + 12)

= -15/18

y - 14 = -15/18 (x + 12)

Simplifying the equation, we get:

y = -15/18 x - 12

This is the linear equation that passes through the points (-12, 14) and (6, -1).

Answer:

First you need to find the slope of the line joining the two points

Slope = [tex]\frac{(14-(-1))}{((-12)-6)}[/tex] =[tex]\frac{15}{-18}[/tex]

then find the equation

y-(-1) = 15/-18 (x-6)

y+1 = 15/-18 x +5

y = -15/18 x + 4

you can present the equation in the above way or multiply the whole equation by 18 if you do not want any fractions

By substituting the values and solving the equation for x, the value of x in both the subparts is as follows:

(A) x = 5/2

(B) x = 1

They are connected by using the equal sign.

An example formula might be 3x - 5 = 16. We discover that the variable x has a value of 7 after solving this equation.

So, we have:

5x - 7

-3x + 3

(A) f(x) + g(x)

5x - 7 + -3x + 3

5x - 7 -3x + 3

2x - 5

2x = 5

x = 5/2

(B) g(x) - f(x)

-3x + 3 - (5x - 7)

-3x + 3 - 5x + 7

-8x + 8

-8x = -8

x = 1

Therefore, by substituting the values and solving the equation for x, the value of x in both the subparts is as follows:

(A) x = 5/2

(B) x = 1

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The beam has diverged from its target by approximately 2097.80 miles when it reaches the moon.

What is the tangent function?

The tangent function is one of the main six trigonometric functions and is generally written as tan x. It is the ratio of the opposite side and the adjacent side of the angle in consideration in a right-angled triangle.

To calculate the distance the beam has diverged from its target, we need to find the horizontal distance the beam has traveled.

To do this, we'll use the tangent function:

tan(0.5°) = horizontal_distance / 240,000 miles

Rearranging the equation and solving for the horizontal distance, we get:

horizontal_distance = 240,000 miles * tan(0.5 degrees) = 240,000 miles * 0.008726646 = 2097.80 miles

Therefore, the beam has diverged from its target by approximately 2097.80 miles when it reaches the moon.

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Answer:

Step-by-step explanation:

The range of the brain volumes is:

Range = highest value - lowest value = 1498 cm³ - 906 cm³ = 592 cm³

According to the range rule of thumb, the standard deviation can be estimated as:

Standard deviation ≈ Range / 4

Standard deviation ≈ 592 cm³ / 4 ≈ 148 cm³

The estimate of the standard deviation is within 15 cm³ of the exact standard deviation of 171 cm³, so it can be considered accurate according to the given criteria. However, note that the range rule of thumb is a very rough estimate and may not be very accurate in all cases.

Answer:

The range rule of thumb suggests that the estimated standard deviation is approximately 18.2 cm³. This estimate is within 15 cm³ of the exact standard deviation of 171 cm³, indicating that it is accurate.

Answer: The markup percentage of 100% means the store added an amount equal to the original cost of the chair to its price, so the selling price of the chair before tax was 494.47 * 2 = $989.94.

The sales tax is calculated as 5.5% of the selling price before tax, which is 5.5/100 * 989.94 = $54.45.

The total amount paid by Sally for the leather chair, including tax, is 989.94 + 54.45 = $1044.39.

Step-by-step explanation:

The answer is 9 11/16 inches.

Distance is the total movement of an object without any regard to direction.

To find the distance on the map, we need to convert the actual distance of 125 miles into the equivalent distance on the map, using the scale of 1:1 200 000.

Let's call the distance on the map d. Then, using the scale, we can write the relationship:

d = (1/1 200 000) * 125 miles

d = 0.0001041667 miles

Since one inch on the map represents 1/1 200 000 miles in real life, the distance on the map can be calculated as:

d (in inches) = 0.0001041667 miles * (1 inch/0.0001041667 miles)

d (in inches) = 9.672

Rounding to the nearest sixteenth of an inch, the answer is 9 11/16 inches.

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He has to replace around 1775 square feet of yard, therefore after adding the 4 inches, he will require a total of 592 cubic feet of earth.

An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure. The square unit, which is frequently expressed as square inches, square feet, etc., is the accepted unit of area.

My calculations show that my Neighbour would save $20 by collecting the soil themselves. According to my calculations, he has to replace around 1775 square feet of yard, therefore after adding the 4 inches, he will require a total of 592 cubic feet of earth.

On the other hand, the man's truck can hold 110,400 cubic inches of dirt, and we know that we need 1,023,000 cubic inches of dirt, so we did a cubic feet to cubic inches calculation and found that it will take us 10 loads to get all the dirt. The shipping company charges $30 to deliver 18 cubic yards of dirt, but our neighbour needs about 22 cubic yards, so they will need to take 2 trips totaling $60 to get all the dirt. Since the store is 9 miles away, it will take 18 miles to transport each load of dirt.

With a total distance of 180 miles to travel and my neighbor's truck getting 17 miles per gallon, our estimated gas consumption is 10.6 gallons. At $3.79 per gallon, the 10.6 gallons of gas we'll need will cost us about $40. This indicates that we will save $20 by picking up the dirt ourselves rather than having it delivered.

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Work Shown:

(r+b-g)(b+g)

(9+5-(-6))(5-6)

(9+5+6)(5-6)

(20)(-1)

-20

Answer:

a

Step-by-step explanation:

Congruent shapes are shapes that are exactly the same. The corresponding sides are the same and the corresponding angles are the same. To do this we need to check all the angles and all the sides of the shapes. as you can see they are exactly the same

Answer:

Step-by-step explanation:

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