Let R be an n × n orthogonal matrix.1. What values can the determinant of R take?2. What values can the real eigenvalues take?

The results of the expressions involving logarithms are listed below:

Case 1: 1 / 2

Case 2:

Subcase a: 0

Subcase b: 11 / 2

Subcase c: - 11 / 2

In this problem we have a case of an expression involving logarithms that must be simplified and three cases of expressions involving logarithms that must be evaluated. Each case can be solved by means of the following logarithm properties:

㏒ₐ (b · c) = ㏒ₐ b + ㏒ₐ c

㏒ₐ (b / c) = ㏒ₐ b - ㏒ₐ c

㏒ₐ cᵇ = b · ㏒ₐ c

Now we proceed to determine the result of each case:

Case 1

㏒ ∛8 / ㏒ 4

(1 / 3) · ㏒ 8 / ㏒ 2²

(1 / 3) · ㏒ 2³ / (2 · ㏒ 2)

㏒ 2 / (2 · ㏒ 2)

1 / 2

Case 2:

Subcase a

㏒ [b / (100 · a · c)]

㏒ b - ㏒ (100 · a · c)

㏒ b - ㏒ 100 - ㏒ a - ㏒ c

3 - 2 - 2 + 1

0

Subcase b

㏒√[(a³ · b) / c²]

(1 / 2) · ㏒ [(a³ · b) / c²]

(1 / 2) · ㏒ (a³ · b) - (1 / 2) · ㏒ c²

(1 / 2) · ㏒ a³ + (1 / 2) · ㏒ b - ㏒ c

(3 / 2) · ㏒ a + (1 / 2) · ㏒ b - ㏒ c

(3 / 2) · 2 + (1 / 2) · 3 + 1

3 + 3 / 2 + 1

11 / 2

Subcase c

㏒ [(2 · a · √b) / (5 · c)]⁻¹

- ㏒ [(2 · a · √b) / (5 · c)]

- ㏒ (2 · a · √b) + ㏒ (5 · c)

- ㏒ 2 - ㏒ a - ㏒ √b + ㏒ 5 + ㏒ c

- ㏒ (2 · 5) - ㏒ a - (1 / 2) · ㏒ b + ㏒ c

- ㏒ 10 - ㏒ a - (1 / 2) · ㏒ b + ㏒ c

- 1 - 2 - (1 / 2) · 3 - 1

- 4 - 3 / 2

- 11 / 2

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Answer:

a1 = 4

a2 = 40

a3 = 400

a4 = 4000

Step-by-step explanation:

First substitute n with 1.

1. 4 ⋅ 10^1  - 1

4 ⋅ 10^0

4 ⋅ 1 = 4

Second substitute n with 2.

2. 4 ⋅ 10^2 - 1

4 ⋅ 10^1

4 ⋅ 10 = 40

Next substitute n with 3.

3. 4 ⋅ 10^3 - 1

4 ⋅ 10^2

4 ⋅ 100 = 400

Finally, substitute n with 4.

4. 4 ⋅ 10^4 - 1

4 ⋅ 10^3

4 ⋅ 1000 = 4000

It's simple. Just plug in 1, 2, 3, and 4 into n and solve the equation.

Step-by-step explanation:

write the function in module in real where how does standard it's easy how do you have to do is think in your mind and there's follow like if it had some if it have some notes or something like that you could actually read it and then you can get ideas in your head and complete answers and you will get it

Answer:

The snowiest city receive 347.7 inches on average each year.

Step-by-step explanation:

We want to find the amount of snow the snowiest city receives on average every year, "x". It is known that this city receives 113.9 more inches than the second snowiest, which receives 223.8 inches on average every year. Therefore, the expression for "x" is:

\(x = 233.8 + 113.9\\x = 347.7 \text{ inches}\)

The snowiest city receive 347.7 inches on average each year.

The three digit number is 727 while the one digit number is 4

Given data

The sum of a three-digit number and a one-digit number is 731.

The product of the numbers is 2,908

let three digit number be x, y, and z

let the one digit be w

The sum

xyz + w =731

xyz * w = 2,908

making xyz the subject of formula

xyz = 731 - w

plugging in xyz into xyz * w = 2,908

( 731 - w ) * w = 2908

731w - w^2 = 2908

w^2 - 731w + 2908 = 0

solving the quadratic equation gives

w = 727 or 4

since w is a one digit number then w = 4

plugging in w = 4 into xyz + w =731 we have

xyz + w =731

xyz + 4 =731

xyz =731 - 4

xyz  = 727

Hence the three digit number is 727 while the one digit number is 4

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Answer:

$-17

Step-by-step explanation:

Answer:

im pretty sure the other person got it correct

the answer is yes they will use the same amount

Yes, I would consider VFITX to be a good investment choice because it has  total return of 9.39%.

For long-term stock market investments, the majority of investors would consider an average annual rate of return of 10% or above to be a decent ROI.

It shoud be noted that VFINX  is been seen as an investment having 5-year annualized total return of 9.39%  which can b e seen as  top third among its category peers and it has risk tolerance because VFITX are generally considered to be less risky  when it is been place side b y side to equity funds.

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Answer:

OPTION A

I CHOSE OPTION A AS THE ANSWER BECAUSE OPTI0N D CANNOT BE TRUE ACCORDING TO THE QUESTION AND OPTION B AND C ARENT TRUE BECAUSE IT WAS MENTIONED THAT AT 3 HOURS THE COST WOULD BE 140 $ BUT IN OPTION B IT SHOWS THAT THEY ALREADY ACHIEVED 200$ BEFORE IT EVEN BECAME 3 HOURS AND IT ISNT OPTION C BECAUSE IT  CROSSED 150$ WHILE IT WAS 3 HOURS SO MOST LIKELY THE ANSWER IS TO BE OPTION A.

HOPE THIS HELPS YOU....

Answer:

$5

Step-by-step explanation:

if 5 leis are worth $25, each lei would be 25/5

25/5 is 5/1, when the denominator is one, that is unit price

the unit price is $5

Answer:

y=-2x+7

enter the point into point slope form to find the slope and then use one of the points in point slope form  and rearrange it to have y by itself

Answer:

8/21    ≈0.381

Explanation:

if you need the explanation message/comment under this answer for it :)

Answer:

39

Step-by-step explanation:

(15 / 5)+9+(14 - 5 )*3

Answer: 39

Step-by-step explanation:

I started with simplifying 15/5 to 3

3+9+(14 - 5)*3

Than Simplified (14 - 5) to 9

3+9+9*3

Next, I did 9*3 due to PEMDAS

3+9+27

Finally, I added it all together to get 39

The decimal number of bits required to store a + b or a - b is 17 bits.

The number of bits required to store the result of the operations equal.

For the given 4-digit hex numbers a and b, convert them to binary to determine the number of bits required. Each hexadecimal digit corresponds to 4 binary bits.

Therefore, the number of bits required to store a is 4 ×4 = 16 bits, and the number of bits required to store b is also 16 bits.

To calculate the number of bits required to store a + b or a - b, to consider the maximum value that can result from these operations. The maximum value will occur when both a and b have their highest possible values.

For a 4-digit hex number, the highest value is "FFFF" in hexadecimal or 65535 in decimal. When performing addition or subtraction, the maximum result will be 2 ×65535 = 131070, which represented by 17 bits.

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Answer:

6/250, 9/375, etc...

Step-by-step explanation:

multiply(GIANT ONE)

3/125 x 2/2 = 6/250

3/125 x 3/3 = 9/375

The probability is a very small value, and when expressed as a decimal rounded to the nearest millionth, it is approximately 0.000011

The probability that the four flavors chosen consist of each of their favorite flavors can be calculated by considering the total number of possible outcomes and the number of favorable outcomes.

First, let's determine the total number of possible outcomes. Since there are 40 flavors in total and they are randomly choosing four flavors, the total number of possible outcomes can be calculated using combinations. We can use the formula for combinations: nCr = n! / (r!(n-r)!), where n is the total number of flavors (40) and r is the number of flavors they are choosing (4).

nCr = 40! / (4!(40-4)!)

    = 40! / (4!36!)

    = (40 * 39 * 38 * 37) / (4 * 3 * 2 * 1)

    = 91390

Next, let's determine the number of favorable outcomes, which is the number of ways they can choose one flavor from each of their favorites. Since each person has a different favorite flavor, the number of favorable outcomes is simply 1 for each person.

Therefore, the probability of choosing four flavors consisting of each of their favorite flavors is:

Probability = Number of favorable outcomes / Total number of possible outcomes

           = (1 * 1 * 1 * 1) / 91390

           = 1 / 91390

The probability is a very small value, and when expressed as a decimal rounded to the nearest millionth, it is approximately 0.000011.

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The surface area of the box is 272 square inches.

A cuboid is a solid in three dimensions with six rectangular faces, eight vertices, and twelve edges. Three dimensions, including length, breadth, and height, define a cuboid. A cuboid with integer edges is referred described as being perfect.

Given:
The dimensions for a US postal office box that you are wrapping as a gift.

The height of the cuboid is 2 inches.

And the length of the cuboid is 8 inches.

The width of the cuboid is 12 inches.

The surface area of the cuboid is,

= 2lw+2lh+2hw.

Where h is the height, l is the length and w is the width.

= 2(8 x 12) + 2(12 x 2) + 2 (2 x 8)

= 192 + 48 + 32

= 272 square inches.

Therefore, the surface area is 272 square inches.

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The power series representation for the given function centered at x = 0 is Σ (-1)ⁿxⁿ from n = 1 to ∞.

The given function is

f(x) = 7/(1 - x²).

We know that

1/(1 - x) = Σ xⁿ, for |x| < 1.

Hence,

f(x) = 7/(1 - x²)

= 7/(1 - x)(1 + x)

= 7[1/(1 - x) - 1/(1 + x)]

∴ f(x) = 7[x + x² + x³ + .... - x - x² - x³ - ... ]

∴ f(x) = 7(x - x² + x³ - x⁴ + .... )

Therefore, the power series representation for the given function centered at x = 0 is Σ (-1)ⁿxⁿ from n = 1 to ∞.

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The probability that the student receives a grade above C is 0.75

The probability that an event will occur is measured by the ratio of favorable examples to the total number of situations possible

Probability = number of desirable outcomes / total number of possible outcomes

The value of probability lies between 0 and 1

Given data ,

Let the probability that the student receives a grade above C be P ( C )

And , the equation will be

Let the probability you will get an A in this class is P ( A ) = 0.25

Let the probability you will get a B in this class is P ( B ) = 0.50

Now , the events P ( A ) and P ( B ) are mutually exclusive events

So , P ( A ∩ B ) = 0

And , P ( A ∪ B ) = P ( A ) + P ( B ) - P ( A ∩ B )

On simplifying the equation , we get

P ( A ∪ B ) = P ( C )

And , probability that the student receives a grade above C = P ( A ) + P ( B )

The probability that the student receives a grade above C = 0.25 + 0.50

The probability that the student receives a grade above C = 0.75

Hence , the probability is 0.75

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The interior volume of the tent where the cross sections are triangles is given is 120ft³.

There are two cross sectional triangles

The  one smaller triangle with the height and base of 2ft

The other bigger triangle has a base and height of 4 ft

And the total length of the Tent is given as 6 ft.

Therefore,

Area of smaller triangle = 2 x 2 = 4m²

Area of bigger triangle = 4 x 4 = 16 ft²

So the Volume of the tent is given by ,

Total length x (Area of smaller triangle + Area of bigger triangle)

= 6 x ( 4 + 16 )

=6 x ( 20 )

= 120 ft ³

A measurement of three-dimensional space is volume.  Numerous imperial or US customary units, as well as SI-derived units (such the cubic metre and litre), are frequently used to quantify it numerically (such as the gallon, quart, cubic inch). Volume and length (cubed) have a symbiotic relationship. The capacity of a container is typically regarded to be its volume.

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Answer:

Hello,

Step-by-step explanation:

\(\overrightarrow{x}=\overrightarrow{-c}+\overrightarrow{a}+\overrightarrow{b}\\\\=-\overrightarrow{c}+\overrightarrow{a}+\overrightarrow{b}\)

Answer:

its 63

Step-by-step explanation:

Answer:

\( \frac{15.75}{0.25} = \frac{1575}{25} \\ = 63\)

...............................

The probability of selecting two Harry Potter DVDs at random, one after the other, is 1/110.

The probability of selecting a Harry Potter DVD at random is dependent on the total number of DVDs and the number of Harry Potter DVDs in the collection. Let's assume there are a total of 100 DVDs and 10 of them are Harry Potter films.

When selecting the first DVD, the probability of picking a Harry Potter film is 10/100 = 1/10.

After selecting the first DVD, there are 99 DVDs left, with 9 Harry Potter films remaining.

When selecting the second DVD, the probability of picking another Harry Potter film, while keeping the first one in hand, is 9/99 = 1/11.

To find the probability of both DVDs being Harry Potter films, we multiply the probabilities: (1/10) * (1/11) = 1/110.

Therefore, the probability that both DVDs will be Harry Potter films is 1/110.

In conclusion, the probability of selecting two Harry Potter DVDs at random, one after the other, is 1/110.

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Answer:

15.28 - 8.73 = 6.55

Step-by-step explanation:

Given - Here is Tylers strategy to find 15.28 – 8.73 . First, I add 0.27 to 8.73, then I add 6 more and 0.28 more.

To find - Explain why Tylers method works and use it to find the difference of 15.28 – 8.73

Proof -

If we add 0.27 to 8.73 , we get

8.73 + 0.27 = 9

Then add 6, we get

9 + 6 = 15

Then add 0.28 we get

15 + 0.28 = 15.28

As after adding 0.27 and 6 and 0.28 more to 8.73 gives the value 15.28.

So,

Tylers method works

Now,

By using Tylers method , we get

15.28 - 8.73 = 0.27 + 6 + 0.28

                    = 6.55

i.e. we get

15.28 - 8.73 = 6.55

Answer:

  1)  6

  3)  -6

Step-by-step explanation:

You want to solve the equation x² = 36 by the square root method.

This method finds the solution by taking the square root of both sides of the equation.

  \(x^2=36\\\\\sqrt{x^2}=\sqrt{36}\\\\|x|=6\qquad\text{positive square root}\\\\x=\pm6\)

The solutions are x = 6 and x = -6.

__

Additional comment

We often "cut to the chase" and write the result of taking the square root as x = ±√36 = ±6. It is worth noting that the square root symbol indicates the positive square root. That's what the absolute value bars also indicate: the positive value of the number.

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Measure of angle:

∠A  = 36.86°

∠B = 90°

∠C = 53.13 °

Measure of side ,

AB =  28

BC = 21

CA = 35

Given triangle ABC.

Right angled at B.

Now, using trigonometric ratios to find angle A , B , C .

Right angled at B : ∠B = 90°

Angle A,

SinA = 21/35

∠A = 36.86

Angle C,

SinC = 28/35

∠C = 53.13

Now measures of side.

To find the length of side use sine rule .

Sine rule:

a/sinA = b/sinB = c /sinC

a = opposite side of angle A .

b = opposite site of angle B .

c = opposite side of angle C.

AB = 28

BC = 21

CA = 35

Hence the sides and angles of the triangles are measured .

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Answer:

c = 16

Step-by-step explanation:

We have (a + b)² = a² + 2ab + b²

x² + 8x + c is of the form a² + 2ab + b²

where x² = a²

8x = 2ab

and c = b²

⇒ x² + 8x + c = (x + √c)² which is a perfect square

x² = a² ⇒ x = a

8x = 2ab

⇒ 8x = 2xb

⇒ b = 8x/(2x)

⇒ b = 4

c = b²

⇒ c = 4²

⇒ c = 16

(x + √c)² = (x + √16)²

= (x + 4)²

= x² + 2(x)(4) + 4²

= x² + 8x + 16

Therefore, c = 16 makes the expression a perfect square

The area of the acute triangle can be found by the formula: area of acute triangle = (1/2) × b × h.

According to Pythagoras theorem the triangle is termed as acutely angled if the square of its longest side is less than the sum of the squares of two other smaller sides. Let a, b, and c are the length of sides of a triangle, where side "a" is the longest, then the given triangle is acutely angled if and only if a^2 < b^2 + c^2.

The area of the acute triangle can be calculated by the formula:

         area of acute triangle = (1/2) × b × h

         b = base, and

         h = height

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