If x is a nontrivial solution of Ax=0​, then every entry in x is nonzero. T/F?

Y and (Xi - Y) are independent.

To show that Y and (Xi - Y) are independent, we need to demonstrate that their joint moment-generating function (MGF) factors into the product of their individual MGFs. Let's denote Y as the sample mean and Xi as the individual observation from a random sample of size n.

First, let's find the distribution of (Xi - Y). Since Y is the sample mean, it can be expressed as Y= (1/n) * ΣXi, where ΣXi represents the sum of all the observations. We can rewrite (Xi - Y as (1 - 1/n) * Xi - (1/n) * ΣXj, where j ≠ i.

Now, (1 - 1/n) * Xi is a constant multiplied by Xi, and (1/n) * ΣXj is a linear combination of the other random variables Xj. Since Xi and Xj are independent and identically distributed (IID) according to the given assumption, (Xi - Y) is also normally distributed.

The joint MGF of Y and (Xi -Y) can be expressed as M(Y, (Xi - Y))(s, t) = M(Y)(s) * M((Xi - Y))(t). By substituting the MGFs of Y and (Xi - Y) into the joint MGF equation, we can verify that the joint MGF factors into the product of their individual MGFs.

Therefore, we can conclude that Y and (Xi - Y) are independent based on their joint and marginal MGFs.

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Answer:

i think 10 or 5

Step-by-step explanation:

Answer:

1*2(3-2n) = 2(n-2)

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The value of cos (x + pi) is -✓3/2, based on the stated information and known trigonometric values.

As per the known fact, the value of x wil be 30° as it is the specific value whose cosine or cos is ✓3/2. Now, we also know that π represents 180°. Also, the formula for cos (a + b) is cos A cos B - sin A sin B.

So, cos (x + pi) will be -

cos x cos pi - sin x sin pi

Keeping the values and solving -

cos (x + pi) = cos 30 cos 180 - sin 30 sin 180

cos (x + pi) = (✓3/2 × -1) - (1/2 × 0)

cos (x + pi) = -✓3/2

Hence, the value of cos (x + pi) is -✓3/2.

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Answer:

C

Step-by-step explanation:

percentage of adults who use the toothpaste =

\( \frac{0.008}{0.75} \times 100\% = 10.66666666666 \%\)

Approximately it is 11%

percentage of children who use the toothpaste =

\( \frac{0.06}{0.25} \times 100\% = 24\%\)

The soil productivity is 7.5 tons per hectare.

The teacher asks Marvin to calculate soil productivity. The following data are given: "The farmer Mahlzahn owns 8 hectares of land. With this land he has a potato yield of 60 tons."

Yield per hectare = Total yield / Total land area Yield per hectare

= 60 tons / 8 hectares

Yield per hectare = 7.5 tons per hectare

Therefore, the correct answer would be 7.5 tons per hectare.

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The measure of angles inside the rhombus are:

∠1 = 56

∠2 = 56

∠3 = 34

∠4 = 34

We have,

In a rhombus,

The opposite angle is congruent.

So,

(56 + 56) = ∠1 + ∠2

And,

∠1 and ∠2 are equal angles.

So,

112 = 2∠1

∠1 = 56

∠2 = 56

Now,

All four angles in side the rhombus = 360

112 + 112 + ∠x + ∠x = 360

2∠x = 360 - 224

2∠x = 136

∠x = 68

This ∠x is the angle inside the rhombus.

And, ∠x/2 = ∠3 = ∠4

So,

∠3 = 68/2 = 34

∠4 = 34

Thus,

The measure of angles inside the rhombus are:

∠1 = 56

∠2 = 56

∠3 = 34

∠4 = 34

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Answer:

Step-by-step explanation:

You want the area of a 16-unit circle using different values for pi.

The formula for the area of a circle is ...

  A = πr² . . . . . . where r is half the diameter

For the different values of pi, this will be (in square units) ...

  π(8²) = 64π . . . . exact

  3.14(8²) = 200.96 . . . . using 3.14 for π, slightly low

  22/7(8²) = 201 1/7 . . . . using 22/7 for π, slightly high

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Answer:

50h+25.5=154

Step-by-step explanation:

Answer:

17/12

Step-by-step explanation:

3/4 = x - 4/6

Add 4/6 to both sides

3/4 + 4/6 = x - 4/6 + 4/6

simplify

17/12 = x

switch sides:

x = 17/12

In linear equation , 24 new girls were added.

What are a definition and an example of a linear equation?

Total no. Of students = 432

Ratio of boys(b) to girls(g)=> b:g = 5:4

Let the common factor be x

Therefore,

5x + 4x = 432

9x =432

x = 48

Therefore ,

Original no. Of boys = 5×48= 240

Original no. Of girls = 4× 48 = 192

After addition of students:

New no. Of boys= 240 + 12 = 252

Let no. Of girls added be y

New total no. Of students = 432+12+y = 444+y

New ratio: b:g = 7:6

Therefore , equating no. Of boys:

7/(7 + 6) × (444 + y) = 252

7/13 × (444 + y) = 252

444 + y = (444 × 13) / 7

444 + y = 468

y = 24

Therefore, 24 new girls were added.

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\(~\hspace{7em}\textit{rational exponents} \\\\ a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n} ~\hspace{10em} a^{-\frac{ n}{ m}} \implies \cfrac{1}{a^{\frac{ n}{ m}}} \implies \cfrac{1}{\sqrt[ m]{a^ n}} \\\\[-0.35em] ~\dotfill\\\\ \left( x^{\frac{8}{15}} \right)^3\implies \left( x^{\frac{8}{15}\cdot 3} \right)\implies x^{\frac{8}{5}}\implies x^{1+\frac{3}{5}}\implies x\cdot x^{\frac{3}{5}}\implies x\sqrt[5]{x^3}\)

Answer:

Whats the rest of the question?

Step-by-step explanation:

Answer:

Applied force

Step-by-step explanation:

Answer:

y= 77

Step-by-step explanation:

Write down the equation for direct proportion.

y= kx, where k is a constant.

Find the value of k.

When x= 12, y= 84,

84= k(12)

12k= 84

k= 84 ÷12

k= 7

Substitute the value of k into the equation.

y= 7x

When x=11,

y= 7(11)

y= 77

The opinion on the fairness of a travel​ professional's salary is not independent of gender.

Given,

A total of 284 travel​ professionals, 108 males and 176 ​females, participated in the survey.

Here,

Null Hypothesis , H0: The opinion on the fairness of a travel​ professional's salary is independent of gender.

Alternative Hypothesis , H1: The opinion on the fairness of a travel​ professional's salary is not independent  of gender.

For expected frequencies , the formula is as follows :

Eij = Ri x Cj/ T

where Ri​ corresponds to the total sum of elements in row i, Cj​ corresponds to the total sum of elements in column j, and T is the grand total.

Here , number of rows and columns are 3 and 2 respectively . thus , The degrees of freedom of \chi²   is (3-1) * (2-1) = 2*1 = 2

\(Test Statistic\chi^2 =\sum_{i} \frac{(O_{ij}-E_{ij})^2}{E_{ij}}\)

where , Oij is the observed frequency and Eij is the expected frequency .

X² = 6.522 + 3.814 + 1.097 + 4.002 + 2.34 + 0.673

X² = 18.448

Thus , the test statistic value i.e.   \(\chi^2 = 18.448\)

P-value:

P-value = 0.0001( Round to four decimal places )

Using the P-value calculator

Thus , p- value for the test is 0.0001 .

Given  α=0.10

Using the P-value approach  ,  P-value = 0.0001 is less than the α = 0.10, it is then concluded that the null hypothesis is rejected.

The required tabular data is attached in the image below .

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area of rectangle = length×breadth

area of square = side×side

As the side length increases by 1, the area does not increase or decrease by an equal amount.

What is the area?

A two-dimensional figure's area is the amount of space it takes up. In other terms, it is the amount that counts the number of unit squares that span a closed figure's surface. In general, square units such as square inches, square feet, etc. are used as the standard unit of area.

As shown in the graph, the area values are not constantly increasing or decreasing, at 2 values of side length, area is same, at the side length= 9 inches, there is no area at all..

So,  

As the side length increases by 1, the area does not increase or decrease by an equal amount.

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The option B) yields the highest value for Z, which is 56.5. Therefore, the correct answer is B) x1 = 5, x2 = 5.25, Z = 56.5

To determine the correct answer, we can substitute each option into the objective function and check if the constraints are satisfied. Let's evaluate each option:

A) x1 = 5, x2 = 4.63, Z = 52.78

Checking the constraints:

17x1 + 8x2 = 17(5) + 8(4.63) = 85 + 37.04 = 122.04 ≤ 136 (constraint satisfied)

3x1 + 4x2 = 3(5) + 4(4.63) = 15 + 18.52 = 33.52 ≤ 36 (constraint satisfied)

B) x1 = 5, x2 = 5.25, Z = 56.5

Checking the constraints:

17x1 + 8x2 = 17(5) + 8(5.25) = 85 + 42 = 127 ≤ 136 (constraint satisfied)

3x1 + 4x2 = 3(5) + 4(5.25) = 15 + 21 = 36 ≤ 36 (constraint satisfied)

C) x1 = 5, x2 = 5, Z = 55

Checking the constraints:

17x1 + 8x2 = 17(5) + 8(5) = 85 + 40 = 125 ≤ 136 (constraint satisfied)

3x1 + 4x2 = 3(5) + 4(5) = 15 + 20 = 35 ≤ 36 (constraint satisfied)

D) x1 = 4, x2 = 6, Z = 56

Checking the constraints:

17x1 + 8x2 = 17(4) + 8(6) = 68 + 48 = 116 ≤ 136 (constraint satisfied)

3x1 + 4x2 = 3(4) + 4(6) = 12 + 24 = 36 ≤ 36 (constraint satisfied)

From the calculations above, we see that options B), C), and D) satisfy all the constraints. However, option B) yields the highest value for Z, which is 56.5. Therefore, the correct answer is: B) x1 = 5, x2 = 5.25, Z = 56.5.

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Mortgage loan= P = $100,000

Rate= r = 6% and the rate interest is

For a period of 30 years, i.e

The formula to find monthly mortgage payment is

Answer:

\(33 units^{2}\)

I counted the squares.

Answer:

Probability that a customer complains in percentage = 4% (Approx)

Step-by-step explanation:

Given:

Total number of customers = 669

Total number of complaints = 27

Find:

Probability that a customer complains

Computation:

Probability that a customer complains = 27 / 669

Probability that a customer complains in percentage = [27 / 669]100

Probability that a customer complains in percentage = [0.040358]100

Probability that a customer complains in percentage = 4.0358%

Probability that a customer complains in percentage = 4% (Approx)

Answer:

m+ p+ q= 180°

m+76°+72°=180°

m+ 148=180°

m=180°-148

m=32°

Given a profit-maximizing level of output, Qm, the monopoly price is the price on the demand curve that corresponds to Qm units of output

The monopoly price is the price on the demand curve that corresponds to the profit-maximizing level of output, Qm units of output. At the profit-maximizing level of output, the marginal revenue (MR) equals the marginal cost (MC). The price corresponding to the profit-maximizing level of output is found by looking at the demand curve at that level of output. The demand curve shows the relationship between the price and the quantity demanded by consumers. The price that corresponds to Qm units of output is the monopoly price.

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Answer:

I cant tell you the answer but think of this formula.

Step-by-step explanation: