Prove that the real vector space of all continuous real-valued functions on the interval [0,1] is infinite-dimensional.
Please use the theorem related to linear algebra

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.

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 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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Answer:

x^2=1

3x=+3

2=+2

Step-by-step explanation:

answers

1

3x

+2

hope it helps

The Scientific notation of [tex]$0.09 \cdot\left(9 \times 10^{-4}\right)$[/tex] be 0.000081.

Very big or very small numbers can be written using scientific notation. Once a number between 1 and 10 has been multiplied by a power of 10, it is then expressed in scientific notation.

Simple numerical writing is what scientific notation is. Because it is shorter and more efficient and indicates magnitude very easily, it is particularly helpful for expressing very large or very small values. Every real number can be expressed as the product of two parts: an integer power of ten and a decimal part.

Let the equation be [tex]$0.09 \cdot\left(9 \times 10^{-4}\right)$[/tex]

Apply exponent rule: [tex]$\quad a^{-b}=\frac{1}{a^b}$[/tex]

[tex]$=9 \times 0.09 \times \frac{1}{10^4}$$[/tex]

Multiply fractions: [tex]$\quad a \times \frac{b}{c}=\frac{a \times b}{c}$[/tex]

[tex]$=0.09 \times \frac{1 \times 9}{10^4}[/tex]

[tex]$& \frac{1 \times 9}{10^4}=\frac{9}{10000} \\[/tex]

simplifying the above equation, we get

= 0.09 × 9/10000

Multiply fractions: [tex]$\quad a \times \frac{b}{c}=\frac{a \times b}{c}$[/tex]

= 9 × 0.09/10000

= 0.81/10000

Divide the numbers: 0.81/10000 = 0.000081

= 0.000081

Therefore, the Scientific notation of [tex]$0.09 \cdot\left(9 \times 10^{-4}\right)$[/tex] be 0.000081.

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Answer: E. x > 3

Step-by-step explanation:

Step 1: Subtract 20 from both sides.

−5x +20 − 20 < 5 − 20

−5x < −15

Step 2: Divide both sides by -5.

−5x/−5 < −15/−5x

x > 3

On a number line, it would look like this:

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.

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: 80%

Step-by-step explanation:

Large Buttons=64

Small buttons = 16

64+16=80 (the total amount of buttons she got)

64/80 * 100%

0.8 * 100%

80%

Eva got an 80% of large buttons

The solution of the system is X = -73/53 and Y = -2/53.

One or many equations having the same number of unknowns that can be solved simultaneously called as simultaneous equation. And simultaneous equation is the system of equation.

Given:

System of equations,

5X + 3Y = -7  {equation 1}

6X - 7Y = -8   {equation 2}

From equation 1,

Y = (-7-5X)/3

Substituting the value to the equation 2,

6X - 7{(-7-5X)/3} = -8

18X + 49 + 35X = -24

53X = -24 - 49

53 X = -73

X = -73/53

And Y = -2/53

Therefore, X = -73/53 and Y = -2/53.

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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.

The future value of the loan is $1,333.86

A quick and easy method of calculating the interest charge on a loan is called a Simple interest.

Given that;

Values are,

P = 1250, r = 3.31 and t = 2 years

Now, We know that;

⇒ Amount = P (1 + r)ⁿ

Substitute all the values we get;

⇒ Future value = 1250 (1 + 3.31/100)²

⇒ Future value = 1250 (1 + 0.033)²

⇒ Future value = 1250 (1.033)²

⇒ Future value = 1250 × 1.067

⇒ Future value = $1,333.86

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Answer:

x = 9

Step-by-step explanation:

⅔x = 6

3/2 × ⅔x = 3/2×6

½ × 2 = 3×3

x = 9

According to the dendrogram, the complete linkage distance between the cluster containing {10, 13} and the cluster containing {4, 20} is 2.577 units.

A dendrogram is a type of diagram that is used to represent the structure of a set of objects, where the objects are linked together in a hierarchy.

Now, let's take a closer look at the dendrogram that displays the complete linkage distance between the cluster containing {10, 13} and the cluster containing {4, 20}.

In this case, the maximum distance is

=> 20 - 4 = 16 units.

Next, we need to normalize the distance by dividing it by the square root of the number of data points in the two clusters. In this case, there are 4 data points in total, so the normalized distance is

=> 16 / √4 = 4.

Finally, we can use the formula for the complete linkage distance, which is given by

D = √2 * (1 - x),

where x is the normalized distance. Plugging in our values, we get

D = √2 * (1 - 4) = √2 * -3 = -2.236 units.

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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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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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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:

Similar

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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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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The surface area of the pyramid is 25 + 10h.

A three-dimensional shape is a pyramid. A pyramid's flat triangular faces unite at a common point known as the apex and have a polygonal base. The bases are joined to the peak to create a pyramid. The lateral face is a triangle face formed by the connection of each edge of the base to the apex.

Given:

A pyramid with the square base.

The side of the base is 5 unit.

So, the surface area of the pyramid,

= base area + 1/2 x perimeter of base x slant height

= (5 x 5) + 1/2 x (4 x 5) + h

= 25 + 10h

Hence, surface area is 25 + 10h.

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The Euclidean distance between (1.0, 6.1) and (3.3, 8.7) is 3.48, rounded to 1 decimal place.

The Euclidean distance formula  is used to calculate the distance between two points in a two-dimensional plane. The formula for Euclidean distance between two points (x1, y1) and (x2, y2) is given by:

[tex]d = √(x2-x1)2 + (y2-y1)2[/tex]

For our two points, (1.0, 6.1) and (3.3, 8.7), the Euclidean distance is:

[tex]d = √(3.3-1.0)2 + (8.7-6.1)2 \\ = √(2.3)2 + (2.6)2 \\ = √5.29 + 6.76 \\ = √12.05 \\ = 3.48[/tex]

Therefore, the Euclidean distance between (1.0, 6.1) and (3.3, 8.7) is 3.48, rounded to 1 decimal place.

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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 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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Work Shown:

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

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

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

(20)(-1)

-20

Answer:

8.468579573930919e+40

2.768574091477416e 41

Step-by-step explanation:

Answer:

Step-by-step explanation:

You want a system of equations and their solution for the number of shots of each type if the total number is 52 and the points from 1- and 2-point shots total 89.

Let x and y represent the numbers of 1- and 2-point shots, respectively. The problem description tells of two relations:

  x + y = 52 . . . . . . . total of shots is 52

  x + 2y = 89 . . . . . . total of points is 89

Subtracting the first equation from the second, we get ...

  (x +2y) -(x +y) - (89) -(52)

  y = 37

Then the first equation tells us ...

  x = 52 -y = 52 -37 = 15

The team made 15 1-point shots and 37 2-point shots.

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: 1,2,4,8,16

Step-by-step explanation: All of the factors of a number multiply to equal a certain number.

Answer:

The trip took 2.5 hours

Step-by-step explanation:

Answer:

1. 8 minutes and 30seconds

Step-by-step explanation:

Divide 17*2= 8.5