Fill in the blanks to make the statement true.

Pi the ratio of the (choose your answer...) of a circle to its ( choose your answer....)​

The closest projection will have a value of -29/360.

we will follow these steps to use the Gram-Schmidt orthonormalization procedure for producing an orthonormal basis for the subspace spanned by 1, x, and x²,

Set u₁ = 1, a unit vector.

Set v₂ = x and u₂ = v₂ / ||v₂||.

Set v₃ = x² - (x², u₁)u₁ - (x², u₂)u₂, and u₃ = v₃ / ||v₃||.

Thus we get the orthonormal basis for the subspace spanned by 1, x, and x² to be {u₁, u₂, u₃}.

Now we will use the formula for the projection of a vector onto a subspace to find the closest-point projection of x³ into this subspace,

proj_subspace(x³) = (x³, u₁)u₁ + (x³, u₂)u₂ + (x³, u₃)u₃

The inner products will be calculated as follows:

(x³, u₁) = ∫x³ X 1 dx = 1/4

(x³, u₂) = ∫ x³ X x dx = 1/5

(x³, u₃) = ∫ x³ * (x² - (x², u₁)u₁ - (x², u₂)u₂) dx

Here all the integrals will have limits of 0 and 1.

Hence we get

= 1/9 - 1/4 X 1/2 - 1/5 X 1/3

= 1/9 - 1/8 - 1/15

= (40 - 45 - 24)/360

= -29/360

Thus, the projection of x³ onto the subspace spanned by 1, x, and x² is:

proj_subspace(x³) = 1/4 X u₁ + 1/5 X u₂ + (1/9 - 1/4 X 1/2 - 1/5 X 1/3) X u₃

This projection is the closest point in the subspace to x³, in the sense that the distance between x³ and proj_subspace(x³) is minimized.

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Answer:

a) 5  b) 1  c) 0  d) -4

Explanation:

a) 10[(1/2+1/4) + 2(1/8)] ÷ 2

Ok, there's a lot going on. You will want to follow PEMDAS, the acronym of the Order of Operations. It stands for Parentheses, Exponents, Multiplication/Division, and Addition/Subtraction. The M/D can be switched depending on what comes first from left to right, and same goes for A/S.

First, start off by doing everything in the brackets.

Let's add 1/2 and 1/4. To add fractions, they have to have a common denominator. I'm making 1/2 into 2/4 but multiplying the top and bottom by 2. Now it is 2/4 + 1/4 so we can add to get 3/4.

The other thing inside the brackets is 2(1/8). We can just multiply straight across and get 2/8. This can be simplified to 1/4.

Now, we add 3/4 and 1/4. The denominators are already the same, so we can just add them together to get 4/4 or 1.

Rewriting the equation, we now have 10(1)÷2

10•1 = 10

10 ÷ 2 = 5

The answer to question a is 5.

b) √(0.6)² + (0.8)²

First, we need to square both terms. Squaring is the same as multiplying the number by itself.

0.6 • 0.6 = 0.36

0.8 • 0.8 = 0.64

Add them together: 0.36 + 0.64 = 1

√1 = 1

The answer to question b is 1.

c) (1/5 - 3/5) • √6•3/2 + (√36 ÷ √5²)

Let's start with the first bit: (1/5 - 3/5)

The denominators are the same, so just subtract and you get -2/5

The second bit now: \(\sqrt{6 *\frac{3}{2} }\)

Multiply across and you get 18/2, which can be simplified to 9

√9 = 3

The third section: (\(\sqrt{36}\)÷ \(\sqrt{5^{2} }\))

The square root of 36 = 6 (because 6•6=36, so it's right)

The square root and the square cancel each other out, so the second part is 5.

6 ÷ 5 = 1.2

Now put it all together: -2/5 • 3 + 1.2

I'm making the 1.2 into a fraction so it is the same as the fraction: 1.2 = 6/5

We now have -2/5 • 3 + 6/5

First we multiply -2/5 and 3 across:

-2/5 • 3 = -6/5

Now we add -6/5 and 6/5 across:

-6/5 + 6/5 = 0

d) [-1.5 + √0.25 - (-0.75)] • 2^4

Doing the brackets first:

The square root of 0.25 = 0.5 (because 0.5 • 0.5 = 0.25)

-1.5 + 0.5 - -0.75

-1 + 0.75 (subtracting a negative make a positive)

-0.25

-0.25 • 2^4

2^4 = 16 (this is saying 2•2•2•2 which is 16)

-.25 • 16 = -4

Answer:

a(1,4)

Step-by-step explanation:

This is the point where the two lines meet.  When x = 1 and y = 4

(1,4)

Answer:

The area of the drawing is 12 Squares

Answer:

y=5 is the correct answer

Step-by-step explanation:

it would be paralell because the x variable goes across in a straight line

Answer:

A) x=5

Step-by-step explanation:

I would recommend using desmos as well :)

Answer:

13 feet of cable

Step-by-step explanation:

Convert 8 ft to inches (96 in)

96+39+21= 156

156/12= 13

Answer:11.1 feet

Step-by-step explanation:

Answer:

1000 tiles

Step-by-step explanation:

Determine total floor space
800 x 10 = 8000 squared cm total floor space.
Divide floor space by size of tile
8000 / 8 = 1000 tiles now required to cover the floor.

Answer: D

Step-by-step explanation:

Range affects y-coordinates

Range starts from -8 and ends at 7. -8 is included in the range, but 7 isn't.

Hence, the answer is -8<=y<7, but the best matching answer is -8<=y<8 since these two inequalities share the most number of solutions.

Hence, the answer is D

answer: the range is 41.

to find the range of this data set, we first need to find the minimum and maximum values - which are 59 and 100.

then we subtract the minimum from the maximum.

59 - 100 = 41.

\(8 - 4( {3}^{3} ) + 11 \\ 8 - 4(27) + 11 \\ 8 - 108 + 11 \\ 8 - 97 \\ - 89\)

Answer:

43

Step-by-step explanation:

Green:  9 - 2(-3) = 9 + 6 = 15

Red:  -2(-3) + 4 = 6 + 4 = 10

Dark blue:  7x + 5 = 19

7x = 19 - 5 = 14

x = 14/7 = 2

Light blue:  6x + 3 = 21

6x = 21 - 3 = 18

x = 18/6 = 3

Red(Lt blue) - Dk blue + Green = 10(3) - 2 + 15 = 43

3.76 many times large is 7.9 x 10⁴ than 2.1 x 10³. This can be solved using scientific notation method.

A method of writing numbers that combines a power of 10 with a number between 1 and 10. Using scientific notation, one may express extremely big or extremely small values. Once a number between 1 and 10 has been multiplied by such a power of 10, it is then expressed in scientific notation. For instance, 6.9 × 10⁸ can be used to represent the number 690,000,000.

The main goal of scientific notation is to simplify computations using numbers that are abnormally big or tiny. When a number is written in scientific notation, all of the digits are important since zeros are no longer utilized to set the decimal point.

For: 7.9 x 10⁴

= (79/10) x 10⁴

= 79 x 10³

on the other hand for: 2.1 x 10³

Thus, 3.76 many times large is 7.9 x 10⁴ than 2.1 x 10³.

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Answer:

17%

Step-by-step explanation:

Let's say Carissa spent $100 on her English reading book. Shane spent 25% less, so she spent $75. John spent 8% less than Carissa, so he spent $92. John spent $17 more than Shane, so the answer is 17%

Answer:

1372 cm^3

Step-by-step explanation:

\(\frac{4}{3} (3)(7^3)=\frac{4}{3} (3)(343)=\frac{4}{3} (1029)=1372\)

The percentage error is approximately 10%

We have:

Estimated = 1242

Actual = 1378

The change in the measurement is:

Change = Actual - Estimate

So, we have:

Change = 1378 - 1242

Evaluate

Change = 136

The percentage error is then calculated as:

Percentage error = Change * 100%/Actual

This gives

Percentage error = 136 * 100%/1378

Evaluate

Percentage error = 9.869%

Approximate

Percentage error = 10%

Hence, the percentage error is approximately 10%

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The linear function graphed is defined as follows:

y = 3x/2 - 3.

(third option).

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

y = mx + b.

In which:

The graph crosses the y-axis at y = -3, hence the intercept b is given as follows:

b = -3.

When x increases by 2, y increases by 3, hence the slope m is given as follows:

m = 3/2.

Then the function is defined as follows:

y = 3x/2 - 3.

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Answer:

The magnitude of the vector is 9.165 and it's direction is 40.6°

Step-by-step explanation:

A vector quantity is a quantity that has both size (magnitude) and direction. Examples of vector quantities are force, velocity and impulse.

Magnitude of vector v is given by

|v| = √6²+7²

= √36+49

= √84

= 9.165

Direction of vector v is obtained by:

\( \tan( \theta) = \frac{x}{y} \)

\(\theta = {tan}^{ - 1} ( \frac{6}{7}) \)

\(\theta = {40.6°}\)

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Answer:

3×8 =24

24÷2=12

Area of triangle=12m²

Step-by-step explanation:

3×8 =24

24÷2=12

Answer: the answer is :z^3+5z-7

Step-by-step explanation:

The only matrix that is certainly symmetric is a)\((a^2 - b^2).\)

We know that a matrix A is symmetric if it is equal to its transpose, that is \(A = A^T.\)

a) \((a^2 - b^2)\)

We can write the transpose of this matrix as

\((a^2 - b^2)^T = (a^2)^T - (b^2)^T = a^2 - b^2\), which is equal to the original matrix. Therefore, this matrix is symmetric.

b) (A+B)(A-B)

Expanding this expression, we get \((A+B)(A-B) = A^2 - AB + BA - B^2.\)

Taking the transpose of this, we get \((A^2)^T - (AB)^T + (BA)^T - (B^2)^T = A^2 - BA + AB - B^2.\)

Since AB and BA may not be equal, we cannot say for certain that this matrix is symmetric.

c) ABA

Taking the transpose of this matrix, we get\((ABA)^T = A^T B^T A^T\). Since \(A^T and B^T\) may not commute, we cannot say for certain that this matrix is symmetric.

d) ABAB

Taking the transpose of this matrix, we get \((ABAB)^T = B^T A^T B^T A^T\). Again, since \(A^T and B^T\) may not commute, we cannot say for certain that this matrix is symmetric.

Therefore, the only matrix that is certainly symmetric is a) \((a^2 - b^2).\)

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Answer:

3 rounds of bingo

Step-by-step explanation:

Let x represent the number of bingo rounds

For adults, the total cost can be represented by 2x + 13, since it is $2 per game and there is a $13 entry fee

For children, the cost can be represented by 3x + 10, since it is $3 per round and there is a $10 entry fee

To find how many rounds are needed to make the cost the same, set these expressions equal to each other and solve for x:

2x + 13 = 3x + 10

13 = x + 10

3 = x

So, costs will be the same with 3 rounds of bingo

The value of x in the parallelogram is 112°.

In a parallelogram, adjacent angles are always supplementary. This means that the sum of two adjacent angles in a parallelogram is always 180 degrees.

To understand this concept, let's consider a parallelogram ABCD. The opposite sides of a parallelogram are parallel and equal in length, and the opposite angles are congruent. Adjacent angles are those that share a side. Let's say angle A and angle B are adjacent angles in the parallelogram.

Since opposite angles of a parallelogram are congruent, we have angle A is congruent to angle C, and angle B is congruent to angle D.

Now, let's consider angle A and angle B. The sum of angle A and angle B is equal to the sum of angle C and angle D because opposite angles are congruent.

Therefore, we can conclude that angle A + angle B = angle C + angle D = 180 degrees.

This property holds true for all parallelograms. So, in any parallelogram, the adjacent angles are always supplementary, meaning their sum is 180 degrees.

For the given question, we know x° + 68° = 180°.

Then x° = 180° - 68°

x° = 112°

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Answer:

OMG IM ON THE SAME QUESTION

Step-by-step explanation:

SOLUTION

From Distributive property, we have that

So apply this to the question, we have that

Becomes

Hence the answer is option B

Given, Option A: Hourly wage is $19 and the salesperson works 40 hours per week. So, he will earn in a week \(\sf = 19 \times 40 = \$760\)

Now, according to option b, he will get 8% commission on weekly sales.

Let. x = the amount of weekly sales.

To earn the same amount of option A, he will have to equal the 8% of x to $760

So, \(\sf \dfrac{8x}{100}=760\)

Or, \(\sf 8x= 76000\)

Or, \(\sf x= \dfrac{76000}{8}=9500\)

the salesman needs to make a weekly sales of $9,500 to earn the same amount with two options.

The Orthogonal projection of A on Z i.e subspace formed by X and Y is A cos (90- θ) = A sin (θ).

A figure projected in parallel rays. In this projection, tangencies are preserved. On parallel lines, parallel lines converge. Both the length-to-area ratio and the length-to-area ratio of parallel segments are maintained. Any triangle can be positioned so that an orthogonal projection results in an equilateral shadow.

Let's say we have a vector. A and vector X and Y

Consider the subspace that is vector-formed. X and Y are perpendicular to the subspace vector Z, where Z = X + Y.

Cos = (X * Y) can be used to calculate the angle between X * Y and A.

A/|(X * Y)| * |A|

Now, Z and A are at a 90° angle.

As a result, A's projection onto Z, or the subspace created by X and Y, is given by A cos (90 - ) = A sin ().

The angle between the subspace and the vector whose projection we are trying to find must be determined in order to find the projection.

Use MATLAB Code for locating a projection on vector a on the subspace defined by vectors x and y. so that it will be more easy to understand

% cross product of x and y vector

xCrossY = cross(x, y);

% angle between xCrossY and vector 'a'

angle_radian = dot(xCrossY,a)/(norm(xCrossY)*norm(a));

% angle in degrees

angle_deg = rad2deg(angle_radian);

% projection of a on subspace made by x and y is asin(angle_deg)

projection = norm(a)*sin(angle_deg);

A cos (90- ) = A sin () is the orthogonal projection of A on Z, i.e. the subspace created by X and Y.

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Answer:

3/4 a pan

Step-by-step explanation:

2 - 1 1/4 = 3/4

two seperated into fourths would look like this

1/4 1/4 1/4 1/4

1/4 1/4 1/4 1/4

one seperated into fourths would look like this

1/4 1/4 1/4 1/4

so take one and one extra fourth away from two and you're left with

1/4 1/4 1/4

add that together and you have 3/4

Answer:

133

Step-by-step explanation:

100/.75 = 133.33 = 133