what is 2/3i-3 simplified?

Answer:

Given Equation

\( \bf \: 25 {x}^{2} - 64\)

we have to factorise the given equation .

We will use the following identity here

Let's factorise it

\(\sf \longrightarrow \: 25 {x}^{2} - 64 \\ \\ \\ \sf \longrightarrow \: {5x}^{2} - {8}^{2} \\ \\ \\ \sf \longrightarrow \:(5x + 8)(5x - 8)\)

Therefore,

So, your answer is (5x+8) ( 5x-8)

The width of the rectangle is 9 meter.

Now, According to the question:

The perimeter of a rectangle is defined as the sum of all the sides of a rectangle. For any polygon, the perimeter formulas are the total distance around its sides. In case of a rectangle, the opposite sides of a rectangle are equal and so, the perimeter will be twice the width of the rectangle plus twice the length of the rectangle and it is denoted by the alphabet “p”.

Now, Solving the problem:

Perimeter of rectangle is 50 meter sq.

Length of the rectangle(L) is 16 meter.

We have to find the width (W) of the rectangle.

We know that,

Perimeter of rectangle is = 2 (L + W)

50 = 2(16 + W)

50 = 32 + 2W

2W = 50 - 32

2W = 18

W = 18/2

W = 9

Hence, The width of the rectangle is 9 meter.

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Answer:

\(y=-\frac{1}{2}x+5\)

Step-by-step explanation:

\(\frac{y-5}{x-0}=\frac{3-5}{4-0} \\\frac{y-5}{x}=-\frac{2}{4}\\2y-10=-x\\2y=-x+10\\y=-\frac{1}{2}x+5\)

Answer: vertical

Step-by-step explanation:

Answer: its A

Step-by-step explanation:

Given:

The inequality is:

\(y>5x+3\)

To find:

The y-intercept, slope and type of line (solid or dotted).

Solution:

The slope intercept form of a line is:

\(y=mx+b\)            ...(i)

Where, m is the slope and b is the y-intercept.

We have,

\(y>5x+3\)

The relation equation is:

\(y=5x+3\)             ...(ii)

On comparing (i) and (ii), we get

\(m=5\)

\(b=3\)

It means the slope is 5 and the y-intercept is 3.

The sign of the inequality in the given inequality is ">". It means the boundary line is not included in the solution set. So, the boundary line is a dotted line.

Therefore, the slope is 5, the y-intercept is 3 and the line is a dotted line.

Answer:£15.80

Step-by-step explanation: £4.40 for a 2-litre carton is the best buy since it is £2.20 for every litre.

So to fulfil the 7 litres for 7-days requirement the lowest price would be buying the best buys possible. Then it would be 3 2-litre cartons and 1 1-litre carton which would cost £15.80.

Answer:

Step-by-step explanation:

Given expressions:

Their difference is:

If the first expression is equal to 1, then the second one will be 5 more as found above:

To find a recursive Nevill's method when interpolating a table using a polynomial at x = 4.1, we can use the following steps:

Step 1: Set up the given data in a table with two columns, one for f(x) and the other for x.

f(x)             x

36               1.16164956

3.80201036       4.0

0.30663842       4.2

0.35916618       -123926000.4

Step 2: Begin by finding the first-order differences in the f(x) column. Subtract each successive value from the previous value.

Δf(x)            x

-32.19798964     1.16164956

-3.49537194      4.0

-0.05247276      4.2

Step 3: Repeat the process of finding differences until we reach a single value in the Δf(x) column. Continue subtracting each successive value from the previous one.

Δ^2f(x)          x

29.7026177       1.16164956

3.44289918       4.0

Step 4: Repeat Step 3 until we obtain a single value.

Δ^3f(x)          x

-26.25971852     1.16164956

Step 5: Calculate the divided differences using the values obtained in the previous steps.

Divided Differences:

Df(x)             x

36                1.16164956

-32.19798964     4.0

29.7026177       4.2

-26.25971852     -123926000.4

Step 6: Apply the recursive Nevill's method to find the interpolated value at x = 4.1 using the divided differences.

f(4.1) = 36 + (-32.19798964)(4.1 - 1.16164956) + (29.7026177)(4.1 - 1.16164956)(4.1 - 4.0) + (-26.25971852)(4.1 - 1.16164956)(4.1 - 4.0)(4.1 - 4.2)

Solving the above expression will give the interpolated value at x = 4.1.

Q2: To construct an approximation polynomial using the Hermite method, we follow these steps:

Step 1: Set up the given data in a table with three columns: f(x), f'(x), and x.

f(x)             f'(x)              x

2.572152         7.615964          1.2

3.602102         13.97514          1.3

5.797884         34.61546          1.4

14.101442        199.500           1.5

Step 2: Calculate the divided differences for the f(x) and f'(x) columns separately.

Divided Differences for f(x):

Df(x)            \(D^2\)f(x)           \(D^3\)f(x)

2.572152         0.51595           0.25838

Divided Differences for f'(x):

Df'(x)           \(D^2\)f'(x)

7.615964         2.852176

Step 3: Apply the Hermite interpolation formula to construct the approximation polynomial.

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Answer:

false

Step-by-step explanation:

Answer:

False

Step-by-step explanation:

Quadratic equations have the highest degree on x as 2 (a squared value). The given equation has x^3 (assuming x3 is x^3 and not 3x), meaning that the equation is a cubic equation.

When testing the null hypothesis with an alpha value of 0.05, the critical value will be larger than if you were testing with an alpha value of 0.01.

If you are testing the null hypothesis with an alpha value of 0.05, the critical value will be smaller than if you were testing the alpha value of 0.01. This is because a smaller alpha value means a more stringent test of significance, which requires stronger evidence to reject the null hypothesis.

Therefore, the critical value is larger for a smaller alpha value to reflect the higher level of evidence required for rejection. Conversely, a larger alpha value allows for a less stringent test of significance, requiring weaker evidence to reject the null hypothesis, which results in a smaller critical value.

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Answer:A1/d1 And A/B

Sorry i dont really know how to do that just a guess

The number of people who understand hexadecimal would be zero, as it is restricted to individuals who are deceased.

The statement "only dead people understand hexadecimal" implies that living people do not understand hexadecimal.

Assume that understanding hexadecimal is limited to only those who have passed away.

This means that among the current living population, no one understands hexadecimal.

Therefore, the number of people who understand hexadecimal would be zero, as it is restricted to individuals who are deceased.

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Answer:

it us 67%

Step-by-step explanation:

:))))))) good luck

To find two nonnegative numbers x and y such that xy = 162 and 4x +2y is minimized, we need to use the concept of the Arithmetic-Geometric Mean.The main answer is:x = 9√2y = 9/√2

Explanation: Arithmetic-Geometric Mean: Let a and b be positive numbers.The Arithmetic Mean (AM) is a + b / 2. The Geometric Mean (GM) is √ab.The Arithmetic-Geometric Mean is the following:a_n = (a_n−1 + b_n−1) / 2  b_n = √a_n−1 * b_n−1  a_0 = a  b_0 = b

Let's solve the problem using the Arithmetic-Geometric Mean.√(4xy) = √(4 * 162) = 36xy/36 = 162/36xy = 9√2 * 9/√2xy = 81The numbers that will minimize 4x + 2y are 4x = 36, and 2y = 18. Therefore, x = 9√2, and y = 9/√2

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The inverse of the given matrix is not defined.

To find the inverse of a matrix, we need to check if the matrix is invertible or non-singular. For a square matrix to be invertible, its determinant must be non-zero.

Let's calculate the determinant of the given matrix:

Det(Matrix) = (1 * 0 * 2) + (2 * 2 * 1) + (1 * 3 * 8) - (2 * 0 * 1) - (1 * 2 * 8) - (1 * 3 * 0)

= 0 + 4 + 24 - 0 - 16 - 0

= 12

Since the determinant of the given matrix is non-zero (12 ≠ 0), it implies that the matrix is invertible.

Next, we can proceed to find the inverse of the matrix by using the formula:

Matrix^(-1) = (1/Det(Matrix)) * Adjoint(Matrix)

However, before calculating the adjoint of the matrix, let's check for any possible errors in the matrix elements. The elements of the matrix you provided are not consistent, and it seems there might be a mistake. The matrix you provided (121, 302, 182) does not conform to the standard 3x3 matrix format.

In conclusion, based on the given matrix, the inverse is not defined. Please make sure to provide a properly formatted 3x3 matrix to find its inverse.

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The probability of drawing a blue or yellow ball at random is 3/4.

To find the probability of drawing a blue or yellow ball at random, we need to determine the total number of favorable outcomes (blue or yellow balls) and the total number of possible outcomes (all the balls in the box).

The total number of favorable outcomes is the sum of blue and yellow balls, which is 7 + 5 = 12.

The total number of possible outcomes is the total number of balls in the box, which is 16.

Therefore, the probability of drawing a blue or yellow ball at random is 12/16, which can be simplified to 3/4.

So, the probability of drawing a blue or yellow ball at random is 3/4.

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Answer:

3

Step-by-step explanation:

as u add 2 + 1 from the 6 and 7 hours

Answer:

y=x+15

Step-by-step explanation:

Answer:

El costo es:

Primero tenemos un cargo fijo de $140.

Luego tenemos un $25 por cada m^3 consumido.

Entonces, si tenemos x m^3 consumidos en un mes, el cargo de ese mes va a ser:

C(x) = $140 + $25*x.

Esto es una relación linear.

A) En este caso tendríamos x = 140

C(140) = $140 + $25*140 = $3640

B) La formula es, como ya escribimos arriba, C(x) = $140 + $25*x.

C) El grafico estará al final.  En el podemos ver que la linea corta el eje vertical en y = $140, que seria lo minimo que se puede pagar al mes, en el caso de que el consumo sea x = 0.

D) La ordenada al origen es $140, representa el cargo fijo que no depende de la variable x.

Answer:

Angle 1 is = 54° ( vertically opposite angles)

Angle 2 is = Angle 1 (corresponding angles are equal)

therefore Angle 2 = 54°

Standard Deviation of given set of numbers is 0.71

The two key areas in statistics are variance and standard deviation. It is a metric for statistical data dispersion. The degree to which values in a distribution deviate from the distribution's average is known as dispersion.

The standard deviation is a metric that reveals how much variance from the mean there is, including spread, dispersion, and spread. A "typical" variation from the mean is shown by the standard deviation. Because it uses the data set's original units of measurement, it is a well-liked measure of variability. When data points are closely spaced from the mean, there is a small variation, and when they are far spaced from the mean, there is a large variation.

Standard Deviation Formula:

σ=\(\sqrt{\frac{sigma(xi-m)^2}{n} }\)

Given 6,4,5,5

m=\(\frac{6+4+5+5}{4}\)=5;

⇒σ=\(\sqrt{\frac{(6-5)^2+(4-5)^2+(5-5)^2+(5-5)^2}{4} }\)=0.707≅0.71

Standard Deviation of given set of numbers is 0.71

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\(\text{Given that,} \\\\f(x) = 18 \cdot 3^x \\\\f(-2) = 18 \cdot 3^{-2} = 2\\\\f(1) = 18 \cdot 3^1 = 54\\ \\\text{So,}~ (x_1,y_1) = (x_1, f(-2)) = (-2,2) ~\text{and}~ (x_2,y_2) = (x_2, f(1)) = (1,54)\\ \\\text{Slope,}~ m = \dfrac{y_2 -y_1}{x_2 -x_1} = \dfrac{54-2}{1+2} = \dfrac{52}3 \\\\\)

\(\text{Equation of line,}\\\\~~~~~~~y - y_1 = m (x-x_1)\\\\\\\implies y-2 = \dfrac{52}3(x+2)~~~~~~~~~~~;[\text{Point-Slope form.]} \\\\\\\implies y-2 = \dfrac{52}3x + \dfrac{104}3\\\\\\\implies y = \dfrac{52}{3}x + \dfrac{104} 3 +2\\\\\\\implies y = \dfrac{52}3 x +\dfrac{110}3 ~~~~~~~~~~~~~~~;[\text{Slope -Intercept form}]\)

Answer:

linear function

Step-by-step explanation:

not constant function as it have variable

The  distance between the ships is increasing at a rate of approximately 18.71 km/h.

To solve this problem, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. In this case, the two sides are the distance traveled by ship A and the distance traveled by ship B.

Let's start by calculating the distance traveled by ship A from noon to 4:00 p.m., which is 4 hours:

distance = rate × time = 40 km/h × 4 h = 160 km

Now let's calculate the distance between the two ships at noon:

distance = √(170² + 0²) = √28900 ≈ 170.13 km

At 4:00 p.m., ship A has traveled 160 km east, and ship B has traveled 25 km/h × 4 h = 100 km north. We can use the Pythagorean theorem to calculate the new distance between the two ships:

distance = √(170² + 160² + 100²) ≈ 244.95 km

Therefore, the distance between the ships at 4:00 p.m. is approximately 244.95 km. To find the rate of change of this distance, we can subtract the initial distance from the final distance and divide by the time interval:

rate of change = (244.95 km - 170.13 km) / 4 h ≈ 18.71 km/h

Therefore, the distance between the ships is increasing at a rate of approximately 18.71 km/h.

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The measure of angle ABC is given as follows:

m < ABC = 145º.

Two angles are defined as supplementary angles when the sum of their measures is of 180º.

In a parallelogram, we have that the opposite angles are supplementary.

The opposite angles for this problem are given as follows:

Hence the measure of angle ABC is given as follows:

m < ABC + 35º = 180º.

m < ABC = 145º.

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Answer:

58

Step-by-step explanation:

do the right first

then subtract

Answer:

a. 21 = u1 + 6·d

b. 29 = u1 + 10·d

c. d = 2, u1 = 9

Step-by-step explanation:

a. The given parameters are;

The amount of therapeutic drug Kiri receives on her first at the hospital = u1 milligrams

The amount of drug increase received by Kiri each day = d

The amount of drug Kiri received on the seventh day = 21 mg

The amount of drug she received on the eleventh day = 29 mg

Therefore, we have an arithmetic progression with the formula for the nth term given as follows;

aₙ = a₁ + (n - 1)·d

Where;

a₁ = u1

n = The number of terms

Therefore, for the 7th day, the amount of drugs she receives, which is 21 milligrams, is given as follows;

a₇ = u1 + (7 - 1)·d = u1 + 6·d = 21

The equation for the amount of drugs she receives in terms of u1 and d on the seventh day is given as follows;

21 = u1 + 6·d

b. For the eleventh day, the amount of drugs she receives, which is 29 milligrams, is given as follows;

a₁₁ = u1 + (11 - 1)·d = u1 + 10·d = 29

Therefore, the equation for the amount of drugs she receives in terms of u1 and d on the  eleventh day is given as follows;

29 = u1 + 10·d

c. Therefore, we have two equations which are given as follows;

21 = u1 + 6·d................(1)

29 = u1 + 10·d..............(2)

Subtracting equation (1) from equation (2) gives;

29 - 21 = (u1 + 10·d) - (u1 + 6·d)

8 = 4·d

d = 8/4 = 2

d = 2

From equation (1), we have;

21 = u1 + 6·d = u1 + 6×2 = u1 + 12

21 = u1 + 12

21 - 12 = u1

∴ u1 = 9

d = 2, u1 = 9.

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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The correct interpretation for a 95% confidence interval is (c) 95% of the confidence intervals created around sample means will contain the population mean.

The confidence interval is a range of values that has been set up to estimate the value of an unknown parameter, such as the mean or the standard deviation, from the sample data. Confidence intervals are usually expressed as a percentage, indicating the probability of the actual population parameter falling within the given interval. Therefore, a 95% confidence interval, for example, indicates that we are 95% confident that the population parameter lies within the interval range.

The following interpretations for a 95% confidence interval are accurate:(a) The population mean will fall in a given confidence interval 95% of the time. This interpretation is incorrect because the population parameter is fixed, and it either falls within the confidence interval or it does not. Therefore, it is incorrect to say that it will fall within the interval 95% of the time.

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Answer:

The answer is 9

Step-by-step explanation:

27^2 =729

729/27^4/3