The figure i made up of 4 identical rectangle that form a quare at the center. The area and the breadth of each rectangle are 4/18 m2 and 1/9 m repectively

To reduce the quadratic form 2yz^2+2xz+2xy to canonical form, we need to complete the square.

First, we factor out the coefficient of z^2 from the yz^2 term:

2yz^2 = 2z(yz)

Next, we add and subtract the square of half the coefficient of z from the resulting expression:

2z(yz + (x/y)^2 - (x/y)^2)

= 2z((y + x/y)^2/4 - (x/y)^2)

= z(y + x/y)^2/2 - zx^2/y

Now, we can see that the quadratic form can be written in the canonical form:

q(x,y,z) = (y + x/y)^2/2 - x^2/y

To find the rank, we need to count the number of non-zero eigenvalues. In this case, we have two non-zero eigenvalues, so the rank is 2.

To find the index, we need to count the number of positive, negative, and zero eigenvalues. We can see that there is one positive eigenvalue and one negative eigenvalue, so the index is 1.

Finally, to find the signature, we subtract the index from the rank. In this case, the signature is 1.
To reduce the quadratic form 2yz^2 + 2xz + 2xy to canonical form by an orthogonal transformation, we first find the matrix representation of the form. The given quadratic form can be written as Q = [x, y, z] * A * [x, y, z]^T, where A is a symmetric matrix:

A = | 0  1  1 |
    | 1  0  1 |
    | 1  1  2 |

Now, we find the eigenvalues and eigenvectors of A. The eigenvalues are λ₁ = 3, λ₂ = -1, and λ₃ = 0, with corresponding eigenvectors:

v₁ = [1, 1, 1]
v₂ = [-1, 1, 0]
v₃ = [-1, -1, 2]

Normalize the eigenvectors to form an orthogonal matrix P:

P = |  1/√3   1/√2  -1/√6 |
    |  1/√3  -1/√2  -1/√6 |
    |  1/√3    0    2/√6 |

Now, we can transform A to its canonical form using the orthogonal matrix P:

D = P^T * A * P
D = | 3  0  0 |
    | 0 -1  0 |
    | 0  0  0 |

So, the canonical form of the quadratic form is:

Q canonical = 3x'^2 - y'^2

The rank of the quadratic form is the number of non-zero eigenvalues in the diagonal matrix D. In this case, the rank is 2.

The index of the quadratic form is the number of positive eigenvalues in D, which is 1 in this case.

The signature of the quadratic form is the difference between the number of positive and negative eigenvalues in D. In this case, the signature is 1 - 1 = 0.

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The maintenance cost expected to be incurred during July is $9,400. This corresponds to option C in the given choices.

To determine the maintenance cost expected to be incurred during July, we need to substitute the planned machine time of 9,000 hours into the cost formula Y = $5,800 + $0.40X.

Plugging in X = 9,000 into the formula, we get:

Y = $5,800 + $0.40(9,000)

Y = $5,800 + $3,600

Y = $9,400

Therefore, the maintenance cost expected to be incurred during July is $9,400. This corresponds to option C in the given choices.

The cost formula Y = $5,800 + $0.40X represents the fixed cost component of $5,800 plus the variable cost component of $0.40 per machine-hour. By multiplying the planned machine time (X) by the variable cost rate, we can determine the additional cost incurred based on the number of machine-hours. Adding the fixed cost component gives us the total maintenance cost expected for a given level of machine-time. In this case, with 9,000 hours of planned machine time, the expected maintenance cost is $9,400.

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The eigenvalues of T are λ₁ = 2 and λ₂ = 0. The corresponding eigenvectors are v₁ = (1, 0, 0) and v₂ = (0, 1, 0).

To find the eigenvalues and eigenvectors of the linear transformation T: R³ → R³, we need to solve the equation T(v) = λv, where v is a non-zero vector and λ is a scalar (the eigenvalue).

Let's consider an arbitrary vector v = (x, y, z) and apply T to it:

T(v) = T(x, y, z) = (2x, 3z, 0)

Now, we set up the equation T(v) = λv:

(2x, 3z, 0) = λ(x, y, z)

This gives us the following system of equations:

2x = λx

3z = λy

0 = λz

From the first equation, we can see that λ = 2 or x = 0. If x = 0, then the entire vector v is zero, which is not allowed for an eigenvector. Therefore, we consider λ = 2.

From the second equation, we have 3z = λy. Since λ = 2, this simplifies to 3z = 2y.

From the third equation, we have 0 = λz. Again, since λ = 2, this gives us 0 = 2z.

From the second and third equations, we can see that z = 0 and y can be any real number. Therefore, the eigenvectors corresponding to λ = 2 are of the form v₁ = (x, y, 0), where x and y are arbitrary.

Now, let's consider the case where λ = 0. In this case, we have:

2x = 0

3z = 0

0 = 0

From these equations, we can see that x and z can be any real numbers, and y must be zero. Therefore, the eigenvectors corresponding to λ = 0 are of the form v₂ = (0, 0, z), where z is an arbitrary real number.

The eigenvalues of T are λ₁ = 2 and λ₂ = 0. The corresponding eigenvectors are v₁ = (1, 0, 0) and v₂ = (0, 1, 0).

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The value of  (x - µ) / σ is the z factor.

We have:

x is the random number

µ is the mean

σ  is the standard deviation,

Now,

we need to evaluate, (x - µ) / σ

(x - µ) / σ = z factor

The Z factor is computed by dividing the dynamic range by the separation band (i.e., the difference between the sample mean and the control mean).

The difference in a value's z-score between it and the set mean is measured in standard deviations. By deducting the value from the mean and dividing the result by the standard deviation, you may determine it.

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Answer:

19

Step-by-step explanation:

The population proportion who participated in voting (63%) is higher than the sample proportion from this survey (58.91%).

To determine whether the population proportion who participated in voting or the sample proportion from the survey is higher, we need to compare the percentages.

The population proportion who participated in voting is given as 63% of all registered voters.

This means that out of every 100 registered voters, 63 participated in voting.

In the survey of retired voters, 162 out of 275 participants voted. To calculate the sample proportion, we divide the number of retired voters who participated (162) by the total number of retired voters in the sample (275) and multiply by 100 to get a percentage.

Sample proportion = (162 / 275) \(\times\) 100 ≈ 58.91%, .

Comparing the population proportion (63%) with the sample proportion (58.91%), we can see that the population proportion who participated in voting (63%) is higher than the sample proportion from this survey (58.91%).

Therefore, based on the given data, the population proportion who participated in voting is higher than the sample proportion from this survey.

It's important to note that the sample proportion is an estimate based on the surveyed retired voters and may not perfectly represent the entire population of registered voters.

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Given statement solution is :- The t-statistic associated with the test is approximately -0.28.

The t-statistic, which is used in statistics, measures how far a parameter's estimated value deviates from its hypothesised value relative to its standard error. Through the Student's t-test, it is utilised in hypothesis testing. In a t-test, the t-statistic is used to decide whether to accept or reject the null hypothesis.

To find the t-statistic associated with the test, we need to calculate the test statistic using the estimated slope coefficient, the null hypothesis, and the standard error.

The estimated slope coefficient is 4.93.

The null hypothesis is H₀: β₁ ≥ 5.14 (stating that the true slope coefficient is greater than or equal to 5.14).

The predicted slope's standard error is 0.74.

The formula to calculate the t-statistic is:

t = (estimated slope - hypothesized slope) / standard error

Plugging in the values:

t = (4.93 - 5.14) / 0.74

t = -0.21 / 0.74

t ≈ -0.28 (rounded to two decimal places)

Therefore, the t-statistic associated with the test is approximately -0.28.

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Answer:

(13.5)/4 = 3.375

step-by-step explanation

Answer:

Yes

Step-by-step explanation:

Answer:

292

Step-by-step explanation:

1752 dollars for 6 computers so you divide the dollars between the 6 computers, (1752 divided by 6)

Answer:

Answer:

292

Step-by-step explanation

1,752 dollars for 6 computers so you divide the money between the 6 computers, So 1,752 divided by 6 is 292.

Answer:

\( \frac{3}{8} \)

Step-by-step explanation:

\( \frac{3}{4} \div 2 = \frac{3}{4} \div \frac{2}{1} = \frac{3}{4} \times \frac{1}{2} = \frac{3}{8} \)

For a sample of 36 bearings is collected with measured diameter, the approximate probability that sample mean of bearings will fall between \((\mu - 0.0001)\) and \((\mu + 0.0001)\) inch is equals to 0.4514.

We have a metal lathe that produces machine bearings is properly adjusted.

Sample size for diameter , n = 36

Standard deviations, s = 0.001

We have to determine probability that the mean diameter of the sample of 36 bearings will fall between \((\mu - 0.0001)\) and \((\mu + 0.0001)\) inch. Let X be a random variable for mean diameter of sample. There is normal distribution of X random variable, \(X \: \tilde \: N( \mu, \frac{\sigma²}{n})\).

Now, probability that sample mean of diameter will fall between \((\mu - 0.0001)\) and \((\mu + 0.0001)\)

\(= P( \mu - 0.0001 < \bar x < \mu - 0.0001) \\ \)

\(= P( \frac{\mu - 0.0001 - \mu }{\frac{\sigma} {\sqrt{n}}}< \frac{\bar x - \mu}{\frac{\sigma} {\sqrt{n}}}<\frac{ \mu + 0.0001 - \mu } { \frac{\sigma} {\sqrt{n}}}) \\ \)

\(= P( \frac{- 0.0001 }{\frac{0.001} {\sqrt{36}}}< z <\frac{ 0.0001} { \frac{0.001} {\sqrt{36}}})\)

\(= P( \frac{- 0.0006}{0.001} < z <\frac{ 0.0006}{0.001})\)

= P( -0.6 < z < 0.6)

= P(z< 0.6) - P( z < - 0.6)

Using the p-value calculator or normal table or Excel command, the values of are calculated.

= 0.4514

Hence, required value is 0.4514.

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Answer:

Step-by-step explanation:

Mason would have, after 12 years, about $83.86 more in his account than Logan.

The amount of money in each account after 12 years can be calculated using the compound interest formula:

For Mason's account:

\(A = P(1 + r/n)^(nt)\)

Where

Here,\(P = $230, r = 6.625%,\) \(n = 12\) (since the interest is compounded monthly), and t = 12.

Plugging these values into the formula, we get:

\(A = 230(1 + 0.06625/12)^(12*12) = $546.56\) (rounded to the nearest cent)

For Logan's account:

A = \(Pe^(rt)\)

Here, \(P = $230, r = 5.875%\),\(and t = 12.\) Plugging these values into the formula, we get:

\(A = 230e^(0.0587512) = $462.70\)

Therefore, the difference in the amounts is:

\(546.56 - 462.70 = $83.86\)

Therefore, Mason would have, after 12 years, about $83.86 more in his account than Logan.

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Answer:

11

Step-by-step explanation:

You can find the amplitude (high) when x = 1 and x = 12, so the period is 12-1=11

Answer:

B

Step-by-step explanation:

B

The functions which are graphed below are  1-2x51 1.4.> 1, the correct option is D.

For a solution to be solution to a system, it must satisfy all the equations of that system, and as all points satisfying an equation are in their graphs, so solution to a system is the intersection of all its equation at single point(as we need common point, which is going to be intersection of course)(this can be one or many, or sometimes none)

We are given that;

The graph of the function

Now,

Let’s apply these steps to your question. The given piecewise function has three pieces:

f (x) = {−2x, x < −1 −|x|, −1 ≤ x ≤ 1 2−x2, x > 1 f ( x) = { − 2 x , x < − 1 − | x | , − 1 ≤ x ≤ 1 2 − x 2 , x > 1

The first piece is a linear function with slope -2 and y-intercept 0. It is defined for all values of x less than -1. To graph this piece, we can use two points: (-2,4) and (-1,-2). We use an open circle at (-1,-2) because this point is not included in this interval.

The third piece is a quadratic function with vertex at (0,2). It is defined for all values of x greater than 1. To graph this piece, we can use three points: (0.5, 3/4), (1,0), and (2,-2). We use an open circle at (0.5,3/4) because this point is not included in this interval.

The final graph looks like this:

To find which option matches the given graph, we can compare their equations with the given pieces.

Option A has f(x) = -|x| when -∞ < x < ∞. This does not match any of the pieces.

Option B has f(x) = -|x| when -∞ < x ≤ -3 or -3 < x ≤ ∞. This does not match any of the pieces.

Option C has f(x) = -|x| when -∞ < x ≤ ∞. This matches only one of the pieces.

Option D has f(x) = {−2x,x<−12−x,x≥−12 f(x)=−2xx<−12−xx≥−12​ . This matches none of the pieces.

Therefore, by the given graph the answer will be  1-2x51 =1.4.> 1

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Answer: The answer is 3 units

Step-by-step explanation:

In order to answer this question we have to apply the formula for the sphere volume

The missing information in the square is option(b) x = 4y = 4 √(2) and y = 4.

Given square PQRS, the task is to determine the missing information. A square is a quadrilateral with four equal sides and four equal angles.

The coordinates of the vertices of a square are (x,y), (x+4,y), (x+4,y+4) and (x,y+4).

The missing information, x and y, can be found by solving the equations that represent the sides of the square. We can start by solving for x.

The equation for the side PQ is x + 4y = 2 √(2). Solving this equation for x gives x = 4y - 8 √(2).

Similarly, the equation for the side RS is x + 4y = 4 √(2). Solving this equation for x gives x = 4y = 4 √(2).

Therefore, the missing information is x = 4y = 4 √(2) and y = 4.  

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Answer:

104

Step-by-step explanation:

260x.4=104

Answer:

156

Step-by-step explanation:

Answer:

Step-by-step explanation:

this is were they should go

Isolate the variable by dividing each side by factors that don't contain the variable.

Inequality Form:

k < 4

Interval Notation:

(−∞, 4)

Answer: that’s the answer

Step-by-step explanation:

Answer:

\(\boxed{\sf sin\ C =\frac{40}{41}}\)

Step-by-step explanation:

We need to find out the value of sinC using the given triangle . Here we can see that the sides of the triangle are 40 , 41 and 9 .

We know that the ratio of sine is perpendicular to hypontenuse .

\(\sf\longrightarrow sin\theta =\dfrac{ perpendicular}{hypontenuse}\)

Here we can see that the side opposite to angle C is 40 , therefore the perpendicular of the triangle is 40. And the side opposite to 90° angle is 41 . So it's the hypontenuse . On using the ratio of sine ,

\(\sf\longrightarrow sinC =\dfrac{ p}{h}\\\\\sf\longrightarrow sin\ C =\dfrac{AB}{AC}\)

Substitute the respective values ,

\(\sf\longrightarrow \boxed{\blue{\sf sin\ C =\dfrac{40}{41}}}\)

Hence the required answer is 40/41.

Answer:

1003003001

Step-by-step explanation:

1001x1001x1001=1003003001

Answer:

1,003,003,001

Step-by-step explanation:

\(1001^3=1,003,003,001\)

Answer: unit of account

Step-by-step explanation:

I learned this in Macro Chapter 34.

Answer:

\( {x}^{3} + 5 {x}^{2} - x - 5 \\ {x}^{2} (x + 5) - 1(x + 5) \\ (x + 5)( {x}^{2} - 1)\)

As 945.55 divided by 0.4 equals 378.22, the proper statement is that Lucinda placed $378.22 into her savings account.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

Lucinda deposited $945.55 into her checking account.

The same day, she deposited 0.4 times as much money into her savings account.

So, She deposited in Saving account

= 945.55 x 0.4

= $378.22.

Hence, Lucinda deposited $378.22 into her savings account, because 945.55 × 0.4 = 378.22.

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Answer:

k = 8.4, j = 13.1

Step-by-step explanation:

Solve for k:

\(tan(40)=\frac{k}{10}\\10(tan(40))=k\\8.4=k\)

Solve for j:

\(8.4^2+10^2=j^2\\70.56+100=j^2\\170.56=j^2\\13.1=j\)

Answer:

k = 10 tan (40) = 8.39 (to 2 decimals)

J = 10 / cos(40) = 13.05 (to 2 decimals)

Step-by-step explanation:

It is SOH CAH TOA, or

Sin = Opposite / Hypotenuse

Cos = Adjacent / Hypotenuse

Tan = Opposite / Adjacent

Using SOH CAH TOA,

tan(40) = k/10, so k = 10 tan (40) = 8.39 (to 2 decimals)

cos(40) = 10 / j, so J = 10 / cos(40) = 13.05 (to 2 decimals)

Answer:

D- 5hrs

Step-by-step explanation:

If the family can hike 3 miles per hour,
for 15 miles: 15/3 = 5 hours.

Every hour they cover 3 miles per hour, so to cover 15 miles, they will take 5 hours

Answer:

D. 5 hours

Step-by-step explanation:

3 miles per 1 hour so 3/1

15 miles per x hours so 15/x

3/1 = 15/x or 3 = 15/x

get x by itself so

3 divided by 3 and 15 divided by 3

x = 5 hours