imaginary number i^32

In summary solution for this question  the value of x is 10.

Angles u and v are complementary, which means their measures add up to 90 degrees.

Given:

Angle u = 3x + 4

Angle v = 56

To find the value of x, we can set up an equation using the fact that the sum of the angle measures is 90 degrees:

Angle u + Angle v = 90

Substituting the given values:

(3x + 4) + 56 = 90

Now, we can solve for x:

3x + 4 + 56 = 90

3x + 60 = 90

3x = 90 - 60

3x = 30

x = 30/3

x = 10

Therefore, the value of x is 10.

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The predicted gain (or loss) from a single trial is 53 cents per game on average.

A roulette wheel has the number 1 through 36, as well as 0 and 00. If you wager $1 that an odd number would show up, you will win or lose $1 depending on whether or not that occurrence occurs. If random variable X represents your net benefit, X=1 with probability 18/38 and X=-1 with probability 20/38.

E(X) = 1(18/38) – 1 (20/38) = -$.053

On average, the casino wins  5 cents for each game.

If the stakes are raised, the casino makes even more money:

E(X) = 10(18/38) – 10 (20/38) = -$.53

If the cost is $10 for each game, the casino wins an averaged of 53 cents per game. If 10,000 games are played in a single night, that's a cool $5300.

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Answer:

Step-by-step explanation:

980

Distance is increasing with a speed of 0.2 Miles/Min

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Time in Minutes      Distance in Miles

0                              0.0

2                              0.4

4                              0.8

6                              1.2

8                              1.6

Here, Myra’s distance is increasing as time increase with a constant Speed.

Now, In every 2 mins distance traveled = 0.4 Miles

Hence, In every 1 min Distance traveled = 0.4/2 = 0.2 Miles/Min

Thus, Distance is increasing with a speed of 0.2 Miles/Min.

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1. For sample 1:

  - Percent of water: 48.85%

2. For sample 2:

  - Percent of water: 35.14%

3. For sample 3:

  - Percent of water: 34.97%

4. Average percent of water for all three samples: 39.65%

5. Median percent of water: 35.14%

6. Range of percent of water: 13.88%

7. Relative percent range: 35.04%


To find the percent of water in a compound, we can use the following steps:

⇒ Calculate the mass of water lost during heating.
- Subtract the mass of the beaker after the 2nd heating from the mass of the beaker sample after the 2nd heating. This gives you the mass of water lost during heating.

⇒ Calculate the mass of the compound.
- Subtract the mass of the beaker sample after the 2nd heating from the mass of the beaker sample. This gives you the mass of the compound.

⇒ Calculate the percent of water.
- Divide the mass of water lost during heating by the mass of the compound.
- Multiply the result by 100 to get the percent.

Now, let's calculate the percent of water for each sample:

For sample 1:
- Mass of water lost = 10.915 g - 10.615 g = 0.300 g
- Mass of the compound = 10.615 g - 10.001 g = 0.614 g
- Percent of water = (0.300 g / 0.614 g) x 100 = 48.85%

For sample 2:
- Mass of water lost = 10.771 g - 10.571 g = 0.200 g
- Mass of the compound = 10.571 g - 10.002 g = 0.569 g
- Percent of water = (0.200 g / 0.569 g) x 100 = 35.14%

For sample 3:
- Mass of water lost = 10.821 g - 10.621 g = 0.200 g
- Mass of the compound = 10.621 g - 10.050 g = 0.571 g
- Percent of water = (0.200 g / 0.571 g) x 100 = 34.97%

To calculate the average, add up the percent of water for all three samples and divide by 3:
- (48.85% + 35.14% + 34.97%) / 3 = 39.65%

To find the median value, arrange the percent of water values in ascending order and find the middle value:
- 34.97%, 35.14%, 48.85%
- The median value is 35.14%.

To calculate the range, subtract the smallest value from the largest value:
- Largest value: 48.85%
- Smallest value: 34.97%
- Range: 48.85% - 34.97% = 13.88%

To calculate the relative percent range, divide the range by the average and multiply by 100:
- Relative percent range = (13.88% / 39.65%) x 100 = 35.04%

Please note that these calculations are based on the given data and are accurate to three significant figures.

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1) The amplitude c+ is c+l

2) The expectation value is 0

3) The uncertainty ΔSX is √(3/7) c+.

Now, we know that any wave function can be written as a linear combination of two spin states (up and down), which can be written as:

Ψ = c+ |+> + c- |->

where c+ and c- are complex constants, and |+> and |-> are the two orthogonal spin states such that Sx|+> = +1/2|+> and Sx|-> = -1/2|->.

Hence, we can write the given wave function as:Ψ = c+|+> + i/√7|->

Now, we know that the given wave function has been defined in Sx basis, and not in the basis of |+> and |->.

Therefore, we need to write |+> and |-> in terms of |l> and |r> (where |l> and |r> are two orthogonal spin states such that Sy|l> = i/2|l> and Sy|r> = -i/2|r>).

Now, |+> can be written as:|+> = 1/√2(|l> + |r>)

Similarly, |-> can be written as:|-> = 1/√2(|l> - |r>)

Therefore, the given wave function can be written as:Ψ = (c+/√2)(|l> + |r>) + i/(√7√2)(|l> - |r>)

Therefore, we can write:c+|l> + i/(√7)|r> = (c+/√2)|+> + i/(√7√2)|->

Comparing the coefficients of |+> and |-> on both sides of the above equation, we get:

c+/√2 = c+l/√2 + i/(√7√2)

Therefore, c+ = c+l

The amplitude c+ is a real number and is equal to c+l

The expectation value of the operator Sx is given by: = <Ψ|Sx|Ψ>

Now, Sx|l> = 1/2|r> and Sx|r> = -1/2|l>

Hence, = (c+l*) + (c+l) + (i/√7) - (i/√7)(c+l*)= -i/√7(c+l*) + i/√7(c+l)= 2i/√7 Im(c+)

As c+ is a real number, Im(c+) = 0

Therefore, = 0

The uncertainty ΔSX in the state |Ψ> is given by:

ΔSX = √( - 2)

where = <Ψ|Sx2|Ψ>and2 = (<Ψ|Sx|Ψ>)2

Now, Sx2|l> = 1/4|l> and Sx2|r> = 1/4|r>

Hence, = (c+l*) + (c+l) + (i/√7) - (i/√7)(c+l*)= 1/4(c+l* + c+l) + 1/4(c+l + c+l*) + i/(2√7)(c+l* - c+l) - i/(2√7)(c+l - c+l*)= = 1/4(c+l + c+l*)

Now,2 = (2i/√7)2= 4/7ΔSX = √( - 2)= √(1/4(c+l + c+l*) - 4/7)= √(3/14(c+l + c+l*))= √(3/14 * 2c+)= √(3/7) c+

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Answer:

Step-by-step explanation:

Answer:

1.5 or 3/2

Step-by-step explanation:

\(\frac{2x+1}{2x-1} =2\\(\frac{2x+1}{2x-1} )(2x-1)=2(2x-1)\\2x+1 = 4x-2\\2x+1-4x=4x-2-4x\\-2x+1=-2\\-2x+1-1=-2-1\\-2x=-3\\x=\frac{-3}{-2} \\=1.5 or \frac{3}{2}\)

     A loan calculator is an automated instrument that enables you to comprehend what your potential monthly loan payments and total loan cost might be. Online, you can find a variety of loan calculators, such as those for mortgages or other kinds of specialized loans.

The amount due each month is $4000.

Detailed explanation:

Given: $4168.79 in total interest has been paid for a loan with a two-year term at 4% interest compounded monthly.

Identify: What is the loan's monthly payment?

Answer: $4168.79 in total interest for a two-year loan compounded monthly.

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The sequence is defined recursively as a₁ = 3 and an+1 = 5an - 1. The first five terms of the sequence are 3, 20, 75, 375, and 1875.

The given sequence is defined recursively, meaning that each term is calculated based on the previous term. The first term, a₁, is given as 3. To find the subsequent terms, we use the recursive formula an+1 = 5an - 1.

To find a₂, we substitute n = 1 into the formula, giving us a₂ = 5a₁ - 1 = 5(3) - 1 = 15 - 1 = 14.

To find a₃, we substitute n = 2 into the formula, giving us a₃ = 5a₂ - 1

5(14) - 1 = 70 - 1 = 69.

Continuing this process, we can find a₄ and a₅. Using the formula, a₄ = 5a₃ - 1 = 5(69) - 1 = 345 - 1 = 344, and a₅ = 5a₄ - 1 = 5(344) - 1 = 1720 - 1 = 1719.

Hence, the first five terms of the sequence are 3, 14, 69, 344, and 1719.

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Answer: x=20

Step-by-step explanation:

3(20)+50= 110

6(20)-10= 110

Answer:

x=20

Step-by-step explanation:

3x+50 = 6x-10

we put all the variables in one side and the numbers in one side

so 3x-6x = -50-10

-3x = -60

x=20

so ( 3×20+50) = (6×20 - 10 )

110=110 ✓

so the answer is 20

The differential equation is a mathematical equation that relates a function to its derivatives.

Differential equations are of two types: ordinary differential equations (ODEs) and partial differential equations (PDEs).

Ordinary differential equations (ODEs) deal with the functions of a single variable and its derivatives.

Partial differential equations (PDEs) are equations that involve partial derivatives of functions of multiple variables. Linear Differential Equation: If the dependent variable and its derivatives occur in the differential equation linearly, then it is called a linear differential equation.

Nonlinear Differential Equation: A differential equation is nonlinear if it is not a linear equation.

Homogeneous Differential Equation: A homogeneous equation is a type of differential equation in which all the terms have the same degree of the dependent variable and its derivatives. Non-Homogeneous Differential Equation: A differential equation is non-homogeneous if it is not a homogeneous equation.

\(The differential equation dx2 d2y/dx2 - 6dy/dx + 13y = 0\) given is the Ordinary Linear Homogeneous Differential Equation of the Second Order.

Therefore the order of the given Differential Equation is 2. y=e3xcos(2x) can be verified as a solution to the given differential equation dx2 d2y/dx2 - 6dy/dx + 13y = 0 as follows: Given, y = e3xcos(2x)Let us differentiate y twice:dy/dx = 3e3xcos(2x) - 2e3xsin(2x)And, d2y/dx2 = 9e3xcos(2x) - 12e3xsin(2x) - 12e3xsin(2x) - 4e3xcos(2x)

\(Hence the differential equation can be verified by substituting y=e3xcos(2x)\)

\(Putting the values we getdx2 d2y/dx2 = -13e3xcos(2x)\) and \(-6dy/dx = -6(3e3xcos(2x) - 2e3xsin(2x))= -18e3xcos(2x) + 12e3xsin(2x)And 13y = 13e3xcos(2x)\)

\(By substituting the values, we getdx2 d2y/dx2 - 6dy/dx + 13y = -13e3xcos(2x) + 18e3xcos(2x) - 12e3xsin(2x) + 13e3xcos(2x)=0\)

Therefore the indicated function y=e3xcos(2x) is a solution to the given differential equation.

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Answer: the last one

Step-by-step explanation:

Answer:

Width x length

Step-by-step explanation:

Find the width or how wide it is

Then find the length or how long it is

multiply those

Step-by-step explanation:

a) 4x 12+n = There are no like terms )

b) (4x12) +n = There are no like terms )

c) 4x (12+ n)  = 4nx+48x

d) 4+ (12 x n) =12nx+4

( I hope this was helpful ) >;D

Answer:

I feel like this question would be easier when given a few starting values. I'm sorry man but I've been sitting here for 30 minutes trying to figure this out.

Step-by-step explanation:

The true statements regarding the construction are statement 2) and statement 5)

"Construction" in Geometry means to draw shapes, angles or lines accurately. These constructions use only compass, straightedge (i.e. ruler) and a pencil.

Given that, A design began from the construction of a regular hexagon.

The true statements made on the construction is;

2) When JKLO is reflected across segment OJ, JKLO is taken to JIHO. So, quadrilateral JKLO is congruent to quadrilateral JIHO.

5) When JKLO is reflected across segment OL, JKLO is taken to HGLO. So, quadrilateral JKLO is congruent to quadrilateral HGLO.

Hence, The true statements regarding the construction are statement 2) and statement 5)

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Answer:

given and explained below.

Step-by-step explanation:

b)

opposite/ adjacent = tan(∅)

tan(∅) = 8 /5

∅ = \(tan^{-1}( 8/5)\)

∅ = 58.99°

c)

opposite/hypotenuse = sin(x)

sin(x) = 7 / 12

x = \(sin^{-1} (7/12)\)

x = 35.68°

adjacent/hypotenuse = cos(y)

cos(y) =   7/12

y=\(cos^{-1} (7/12)\)

y = 54.31°

d)

cos(T) = adjacent / hypotenuse

cos(T) = 7.5/9

T =      \(cos^{-1}(7.5 / 9) \)

∠T=33.56°

Step-by-step explanation:

the 3 main tools we need here :

- the sum of all angles in a triangle is always 180°.

- Pythagoras : c² = a² + b²

- the law is sine : a/sin(A) = b/sin(B) = c/sin(C)

b)

in order to be able to use the law of sine, we need to get the length of the baseline.

Pythagoras

baseline² = 8² + 5² = 64 + 25 = 89

baseline = sqrt(89)

8/sin(angle) = sqrt(89)/sin(90) = sqrt(89)/1 = sqrt(89)

sin(angle) = 8/ sqrt(89) = 0.847998304...

angle = 57.99461679...° ≈ 58° (or 57.99° officially rounded to the nearest hundredths)

c)

7/sin(x) = 12/sin(90) = 12/1 = 12

sin(x) = 7/12 = 0.583333333...

x = 35.68533471...° ≈ 35.69°

y = 180 - 90 - 35.69 = 54.31°

d)

9² = RG² + 7.5²

81 = RG² + 56.25

RG² = 24.75

RG = sqrt(24.75) = 4.974937186...

sqrt(24.75)/sin(T) = 9/sin(90) = 9/1 = 9

sin(T) = sqrt(24.75)/9 = 0.552770798...

T = 33.55730976...° ≈ 33.56°

\(4x - 8 < 12 \\ 4x < 12 + 8 \\ 4x < 20 \\ \frac{4x}{4} < \frac{20}{4} \\ x < 5 \\ \\ or \\ \\ 4x - 8 > - 12 \\ 4x > - 12 + 8 \\ 4x > - 4 \\ \frac{4x}{4} > \frac{ - 4}{4} \\ x > - 1 \\ \\ = - 1 < x < 5\)

I hope this helps!!!!

AS PER THE LAST STATEMENT YOU GAVE I CANNOT SEE THROUGH IF THE DETAILS ARE COMPLETE OR WRITTEN IN THE CORRECT FORM..THIS WILL GIVE YOU A DETAILED HINT TO CHOOSE THE CORRECT ONE!!!!!!!

Answer:

6. 24

Step-by-step explanation:

A) Use pythogaras theoram

8x8 - 5x5 = axa - bxb = c

64-25= 39

39 square root =6.24

Answer:

\(y = 2(2) {}^{x} \)

Step-by-step explanation:

It ask us to create a exponential function. A exponential function is represented by a equation like this

\(y = ab {}^{x} \)

where a is the vertical stretch, b is the constant rate of growth, and x is the nth exponet.

Using the point 0,2

we can plug that in to find a part of the equation above.

let x=0 and y=2

\(2 = ab {}^{0} \)

\(b {}^{0} = 1\)

\(2 = a \times 1\)

\(a = 2\)

Let update the equation now since a equal 2

\(y = 2b {}^{x} \)

Now let use point 2,8 to find the b value

let x=2 and y=8

\(8 = 2b {}^{2} \)

Divide both sides by 2

\(4 = {b}^{2} \)

take the sqr root of 4

\(b = 2\)

Let update the equation

\(y = 2(2) {}^{x} \)

Answer:

its 5 boxes

Step-by-step explanation:

Probability that the waiting time at the median line is at most 6 seconds is approximately 0.596 and more than 6 seconds is approximately 0.404 and between 4 and 8 seconds is approximately 0.336.

To calculate the probability, we need to integrate the probability density function (PDF) within the specified range.

(a) To find the probability that the waiting time is at most 6 seconds (P(X ≤ 6)), we need to integrate the PDF from 1 to 6:

P(X ≤ 6) = \(\int\limits^1_6 {0.55e^{(-0.55(x-1)} } \, dx\)

Evaluating the integral, we get P(X ≤ 6) ≈ 0.596.

To find the probability that the waiting time is more than 6 seconds (P(X > 6)), we can subtract the probability of X ≤ 6 from 1:

P(X > 6) = 1 - P(X ≤ 6) ≈ 1 - 0.596 ≈ 0.404.

(b) To calculate the probability that the waiting time is between 4 and 8 seconds, we need to integrate the PDF from 4 to 8:

P(4 ≤ X ≤ 8) = \(\int\limits^4_8 {0.55e^{(-0.55(x-1)} } \, dx\)

Evaluating the integral, we find P(4 ≤ X ≤ 8) ≈ 0.336.

Therefore, the probability that the waiting time at the median line is at most 6 seconds is approximately 0.596, the probability of it being more than 6 seconds is approximately 0.404, and the probability of the waiting time being between 4 and 8 seconds is approximately 0.336.

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Answer:

x=-1/6

I luv u

Answer:Solve for x 2x-4=10 2x − 4 = 10 2 x - 4 = 10 Move all terms not containing x x to the right side of the equation. Tap for more steps... 2x = 14 2 x = 14 Divide each term in

Step-by-step explanation:

The equivalent expression for the given expression is 3x⁴√2.

An expression is formed by using the variables, coefficients and constants that represents an arithemtic operation.

Two or more equations that have the same values on simplifying are said to be equivalent expressions.

The given expression is 18x²\(\sqrt{14x^8}\) ÷ 6\(\sqrt{7x^4}\)

On simplifying, we get

18x²\(\sqrt{14x^8}\) ÷ 6\(\sqrt{7x^4}\) = 18x²\(\sqrt{14(x^4)^2}\) ÷ 6\(\sqrt{7(x^2)^2}\)

⇒ (18x² × x⁴ × √14) ÷ (6 × x² × √7)

⇒ (18 × x⁶ × √2× √7)/(6 × x² × √7)

⇒ 3x⁴√2

Therefore, the equivalent expression for the given expression is 3x⁴√2.

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\( - 6x - 42 = - 10x + 62\)

Add sides 42

\( - 6x - 42 + 42 = - 10x + 62 + 42 \\ \)

\( - 6x = - 10x + 104\)

Add sides 10x

\( 10x - 6x =10x - 10x + 104 \)

\(4x = 104\)

Divided sides by 4

\( \frac{4}{4}x = \frac{104}{4} \\ \)

\(x = 26\)

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Done ♥️♥️♥️♥️♥️