=
Given g(x) = -x +4, solve for x when g(x) = -3.

Answer: \(- \frac{62}{5}\)

Convert the decimal number into a fraction

Multiply by 10

\((- \frac{12.40}{1} ) (\frac{10}{10})\)

\(- \frac{124}{10}\)

Divide the fraction by 2

\(- \frac{62}{5}\)

the correct answer is: Vout after 5 minutes is approximately -173.2 volts.

To find the value of Vout after 5 minutes when the resistance voltage is given by 200 \( \cos (t) \), we need to evaluate the expression 200 \( \cos (t) \) at t = 5 minutes.

Given that 1 minute is equal to 60 seconds, 5 minutes is equal to \( 5 \times 60 = 300 \) seconds.

So, we need to calculate 200 \( \cos (300) \).

Evaluating this expression using a calculator, we find:

200 \( \cos (300) \approx -173.2 \) volts.

Therefore, the correct answer is:

Vout after 5 minutes is approximately -173.2 volts.

Please note that the negative sign indicates a phase shift in the cosine function, which is common in AC circuits.

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Answer:

\(x > 0\)

Step-by-step explanation:

The x-values (domain/input) are greater than 0

In other words, the graph covers the x-axis on all points greater than 0

Answer: the function is defined for all real values of x. Therefore, the domain of the function is the set of all real numbers, which can be denoted as:

Domain = (-∞, ∞) or (-∞, +∞)

Using the triangle inequality theorem, the largest possible whole-number length for the third side is 4.

The third side of a triangle must be shorter than the sum of the other two sides and longer than the difference between the other two sides.

So, for a triangle with sides of length 1, 4, and x (where x is the length of the third side), we have:

1 + 4 > x

4 + x > 1

1 + x > 4

Simplifying these inequalities, we get:

5 > x

x > 3

x > -3 (this inequality is always true)

The largest possible whole-number length for the third side is 4, since it is the largest integer that satisfies the above inequalities.

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A function f(z) = u(x, y) + iv(x, y) is considered analytic on a set G if the first partial derivatives of u and v satisfy the Cauchy-Riemann equations on G.

The Cauchy-Riemann equations are given by:
1. ∂u/∂x = ∂v/∂y
2. ∂u/∂y = -∂v/∂x

To determine if the function is analytic on G, follow these steps:
1. Calculate the first partial derivatives of u with respect to x and y, denoted as ∂u/∂x and ∂u/∂y.
2. Calculate the first partial derivatives of v with respect to x and y, denoted as ∂v/∂x and ∂v/∂y.
3. Check if the calculated partial derivatives satisfy the Cauchy-Riemann equations mentioned above.
4. If both equations are satisfied, the function f(z) is analytic on the set G.

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The expressions formed are,

Formation of expressions in 1, 2 and 3:

In 1, twelve times f is, 12f

Taking away 5, it becomes (12f-5)

In 2, sum of k and 6 is, (k+6)

One-half of the above quantity is, (k+6)/2

In 3, sum of 5 with x is, (x+5)

Now, x squared minus the above expression indicates (x²-x+5)

Formation of expressions in 4 and 5:

In 4, product of a and b, is ab and 3 times c is 3c

Sum of the expressions evaluated in the previous statement = ab+3c

In 5, 24 times the product of x and y is, 24xy

Adding, g in the above computed expression, we get, 24xy+g

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To represent decimal values ranging from 0 to 12,500, we need 14 bits.

To determine the number of bits needed to represent decimal values ranging from 0 to 12,500, we need to find the smallest number of bits that can represent the largest value in this range, which is 12,500.

The binary representation of a decimal number requires log base 2 of the decimal number of bits. In this case, we can calculate log base 2 of 12,500 to find the minimum number of bits needed.

log2(12,500) ≈ 13.60

Since we can't have a fraction of a bit, we round up to the nearest whole number. Therefore, we need at least 14 bits to represent values ranging from 0 to 12,500.

Using 14 bits, we can represent decimal values from 0 to (2^14 - 1), which is 0 to 16,383. This range covers the values 0 to 12,500, fulfilling the requirement.

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Answer:

The angle between the diagonal of the rectangle is \(\frac{\pi }{2}\).

Given:

The vertices of the rectangle are

a = (1, 0), b = (0, 3), c = (3, 4), and d = (4, 1)

To find:

The objective is to find the angle between the diagonals.

Step 1 of 3

Consider the diagram attached.

Step 2 of3

The position vector of diagonal AC is-

=(3-1)î+(4-0)j=2î+4j

And the position vector of diagonal BD is-

=(4-0)î+(1-3)j=4î-2j

Step 3 of 3

cosθ=\(\frac{AC.BD}{|AC|.|BD|}\)

cosθ=\(\frac{(2i-4j)(4i-2j)}{\sqrt{2^2+4^2} \sqrt{4^2+(-2)^2\\} }\)

=\(\frac{8-8}{\sqrt{20}.\sqrt{20} }\)

=0

θ=\(cos^{-1}\)(0)

θ=\(\frac{\pi }{2}\)

Therefore the angle between the diagonal of the rectangle is \(\frac{\pi }{2}\)

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The angle between the diagonals of a rectangle is π/2

The vertices of the rectangle are

a = (1, 0), b = (0, 3), c = (3, 4),  d = (4, 1)

The diagonal position vector AC  

=(3-1)î+(4-0)j=2î+4j

And the diagonal position vector BD  

=(4-0)î+(1-3)j=4î-2j

cos Ф = (AC.BD) / (|AC| . |BD|)

cos Ф = (8-8) / (root20 -roo20)

= 0

Ф = π/2

Therefore the angle between the diagonals of the rectangle is π/2

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The value of x is 19.44

Similar triangles are triangles that have the same shape, but their sizes may vary.

For two triangles to be similar, the corresponding angles must be congruent and also, the ratio of the corresponding sides of similar triangles are equal,

therefore,

27/9x-13 = 15/90

27 × 90 = 15(9x-13)

2430 = 135x - 195

collecting like terms

2430+195 = 135x

2625 = 135x

divide both sides by 135

x = 2625/135

x = 19.44

therefore the value of x is 19.44

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Accoreding to the given statement,

The simple method to find the value of √20 is to factorise the number under the root.

The process of breaking or decomposing an entity (such as a number, a matrix, or a polynomial) into a product of another entity, or factors, whose multiplication results in the original number, matrix, etc., is known as factorisation or factoring.

According to the given value;

The prime factorisation of 20 = 2 x 2 x 5 = 2 2 x 5

Thus, here we can see, 20 is not a perfect square, because we cannot pair digit 5 after factoring 20.

Only 2 2 can be taken out of the root.

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Answer:

Sorry if this is wrong I haven't done this in like a year or two but it should be B.

Step-by-step explanation:

Would take seven years to type out and not sure if I even did the math right

Answer:

Interest = Rs 2000

Amount = Rs 7000

Step-by-step explanation:

Amount = Principal + Interest

Given

Principal = Rs 5000

Interest= PRT/100

Interest = 5000*8*5/100

Interest = 50*40

Interest = Rs 2000

Amount after 5years = 5000 + 2000

Amount after 5years = Rs 7000

\(~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 2000\\ P=\textit{original amount deposited}\dotfill &\$1800\\ r=rate\to 4.8\%\to \frac{4.8}{100}\dotfill &0.048\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years \end{cases}\)

\(2000 = 1800\left(1+\frac{0.048}{12}\right)^{12\cdot t} \implies \cfrac{2000}{1800}=(1.004)^{12t}\implies \cfrac{10}{9}=1.004^{12t} \\\\\\ \log\left( \cfrac{10}{9} \right)=\log(1.004^{12t})\implies \log\left( \cfrac{10}{9} \right)=t\log(1.004^{12}) \\\\\\ \cfrac{\log\left( \frac{10}{9} \right)}{\log(1.004^{12})}=t\implies 2.20\approx t\qquad \textit{about 2 years and 73 days}\)

The volume trapped below the cone and over the semicircular disk can be calculated using the given equation z = Vx^2 + y^2 = r. The integral to evaluate the volume is ∫∫(0 to 1)(0 to 0.5 + √(7/2 - r^2))(r dr do).

To find the volume, we first need to understand the geometry of the problem. The equation z = Vx^2 + y^2 = r represents a cone with its vertex at the origin and its axis along the z-axis. The parameter V determines the slope of the cone, while r represents the radial distance from the origin. The semicircular disk lies in the xy-plane and is defined by the inequality 0 ≤ r ≤ 0.5 and 0 ≤ θ ≤ π.

To calculate the volume, we need to express the volume element in terms of the cylindrical coordinates r, θ, and z. In cylindrical coordinates, the volume element is given by dV = r dr do dz. However, in this case, since we are integrating over a semicircular disk, the range of θ is limited to π. Thus, the volume element becomes dV = r dr do dz, where r ranges from 0 to 0.5, θ ranges from 0 to π, and dz ranges from 0 to 0.5 + √(7/2 - r^2).

Now, we can set up the integral to evaluate the volume trapped below the cone and over the semicircular disk. The integral becomes ∫∫∫(0 to 1)(0 to π)(0 to 0.5 + √(7/2 - r^2))(r dr do dz). Evaluating this integral will give us the desired volume.

In conclusion, the volume trapped below the cone z = Vx^2 + y^2 = r over the semicircular disk is given by the integral ∫∫∫(0 to 1)(0 to π)(0 to 0.5 + √(7/2 - r^2))(r dr do dz), where V is the slope of the cone and r ranges from 0 to 0.5.

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The expected value of the discrete distribution, for each case, is given as follows:

a) Amount won by one entry: $0.075.

b) If the cost is the cost of a postage stamp:  -$0.525.

The expected value of a discrete distribution is obtained with the sum of each outcome multiplied by it's probabillity.

In this problem, the distribution for the prizes is given as follows:

Hence the expected value for the prizes is:

E(X) = 10,000,000 x 1/300,000,000 + 350,000 x 1/150,000,000 + 50,000 x 1/10,000,000 + 20,000 x 1/1,000,000 + 400 x 1/200,000 + 75 x 1/6,000 = $0.075.

The cost of a postage stamp is of $0.6, hence the expected value considering this cost would be of:

0.075 - 0.6 = -$0.525.

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Answer:

2n+7

Step-by-step explanation:

First lets find the common difference which is 2, now we can use this formula to find the nth term.

an = a1 + (n - 1 ) d

an= 9+(n-1)2

=9+2n-2

=2n+7

To check let's insert n=5, 2(5)=10+7=17.

15+2=17!

Value of r is different for every series

let

a , b , c , d ..... be geometric series then

r = b/a or d/c and so on

where r is common ratio

Answer:

It was 50%

Step-by-step explanation:

Another possible values for a and b are a = 12 and b = 4

A variation is a relation between a set of values of one variable and a set of values of other variables

Given that:  a is inversely related to the square of b, and a = 3 when bis

8.

This can be written as:

a α 1/b²

a = k/b²               (where k is  a constant)

k = ab²

since a = 3 and b = 8.

Thus, k = 3 × 8² = 3 × 64 = 192

For a value to be another possible value for a and b, they must give k = 192 when substituted into the equation k = ab²:

a = 4, b = 12: k = 4 × 12² = 576

a = 12, b = 4: k =  12 × 4² = 192

a = 8, b = 3:  k =  8 × 3² = 72

a = 2, b = 4: k =  2 × 4² = 32

a = 6, b = 4: k =  6 × 4² = 96

The values that produce k = 192 are a = 12 and b = 4. Therefore, another possible value for a and b is a = 12 and b = 4. So option B is the answer

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Step-by-step explanation:

Andrew paid 30% in taxes, which means he has 70% remaining

30% Cash Prize + 70% Cash Prize = 100% Cash Prize

If C = Original Cash Price

Remaining Cash = 70% x C = $28,000

C = $28,000 / 70% = 28000/0.7 = $40,000

The property of real numbers illustrated by the equation -10+4 = 4+(-10) is the commutative property of addition. This property states that changing the order of the numbers being added does not change the sum.

In this equation, both sides are equal because the order of the numbers being added is changed, but the sum remains the same. Therefore, the commutative property of addition is being illustrated.The property of real numbers illustrated by the equation:

-10 + 4 = 4 + (-10)

is the Commutative Property of Addition.

The Commutative Property of Addition states that the order of the numbers being added does not affect the sum. In other words, when adding two real numbers, changing the order of the numbers being added does not change the result.

In the given equation, both sides of the equation have the same sum (-6), even though the order of the terms has been reversed. This demonstrates the Commutative Property of Addition.

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Answer:

Do you need all 6 of them?

Answer and Step-by-step explanation:

w = -1

x = 6

y = 3

z = -2

32. Plug -2 for z and 6 for x.

(9(-2)) / 6

-18 / 6

3

33.

\(6^{2} - 3^{2}\)

36 - 9

27

34.

\(3^{2} - (-2)^{2}\)

9 - 4

5

35.

\(\frac{2(6)+3}{-2 + -1} \\\\\frac{12+3}{-3}\\\\\frac{15}{3} \\\\5\)

36.

\(\frac{3(6)-(-2)}{-(-1)} \\\\\frac{18 + 2)}{1)} \\\\\frac{20}{1} \\\\20\)

37.

\(\frac{6 + -1}{3 - (-2)} \\\\\frac{5}{5}\\\\1\)

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Answer:

On melissa's 6th birthday, she gets a $4000 cd that earns 3% interest, compounded quarterly. If... | like | dislike ... The amount accumulated in a certificate of deposit (CD) is found using the compound interest formula as a CD also earns compounding interest. ... The number of years between the 6th and 12th birthdays is 6

Step-by-step explanation:

There will be $41142.87 available on Melissa's 16th birthday.

Interest accrued on both the principal sum of money and the interest already earned.

The formula for compound interest is p(1+r/100)ⁿ - p

Where p is principal, r is rate and n is time.

Given that,

Amount that Melissa gets on her 6th birthday = $4000

Rate of interest = 6% compounded quarterly.

Melissa gets amount on her 16th birthday, time = 6 years

The amount that Melissa will get on her 16th birthday

= 4000(1+6/100)¹⁰ˣ⁴

= 4000 (106/100)⁴⁰

= 4000 x 10.2857

= 41142.87

Melissa will get $41142.87 on her 16th birthday.

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Answer:

y = 1.3x + 10

Step-by-step explanation:

as, y = 1.3 * 5 + 10

= 16.5

Answer: y = 1.3x + 10

Step-by-step explanation: 1.3 x 0 = 0→ 0 + 10 = 10

1.3 x 5 = 6.5→ 6.5 + 10 = 16.5
1.3 x 10 = 13→ 13 + 10 = 23

1.3 x 15 = 19.5→ 19.5 + 10 = 29.5

1.3 x 20 = 26→ 26 + 10 = 36

Hope this helps.

Answer:

1,2.5

3,4.5

4,5.5

6,7.5

8,9.5

Step-by-step explanation:

For the linear equation y = 2x 4, if x increases by 1 pointThe value of y will increase by 2 points(A).

The equation y = 2x + 4 represents a linear relationship, where the coefficient of x, which is 2, represents the slope of the line. The slope indicates how much y changes when x increases by 1. In this case, the slope is 2, meaning that for every increase of 1 in x, y will increase by 2.

Therefore, For the linear equation y = 2x 4, if x increases by 1 point,the value of y will increase by 2 points(A). This means that correct option is A.

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Regenerate response

a) The values of alpha and beta are: α = 4,  β = 5

b) The probability that a student uses the terminal for at most 24 min = 0.7149

c) The probability that a student spends between 20 and 40min useing the terminal =  0.3911

We know that the theorem: The limiting distribution of the gamma(α, β) distribution is the N(μ, σ²) distribution where μ = αβ and σ² = αβ²

Here, mean (μ) = 20 min and variance (σ²) = 80 min²

After solving these equation for α and β we get,

α = 80/20

α = 4

and β = 20/4

       β = 5

The formula for the gamma distribution is shown in attached image.

And the formula for the gamma function is Γ(α) = ∫_{0-∞} (\(y^{\alpha -1}e^t\))dy

The probability that a student uses the terminal for at most 24 min:

P(X ≤ 24) = F(24; α, β)              

               = F(24/α , β)

               = F(6, 5)

               = 0.7149        ............(Using the gamma distribution formula)

The probability that a student spends between 20 and 40min using the terminal.

= P(X ≥ 20) - P(X ≥ 40)

= F(20/α , β) - F(40/α , β)

= F(5, 5) - F(10, 5)

= 0.43347 - 0.04238     ............(Using the gamma distribution formula)

= 0.3911

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Elise's number is 29.

If you think of multiplying a value by -3 to get -33, it would obviously be 11.

So in this case, you would want to add 18 to 11 to get Elise's number, which is 29. Subtracting 18 from 29 would get you back to the value of 11, which you can then multiply it by  -3 again to get -33.

9514 1404 393

Answer:

  5/3

Step-by-step explanation:

The reciprocal of any fraction is obtained by swapping the numerator and denominator, turning it "upside down."

  the reciprocal of the fraction 3/5 is 5/3

Arithmetic average return of the company is 2.57%.Geometric average return of the company is 13%.Variance of the company is 56.Standard deviation of the company is 7.48%.

Given, Returns of the company for the last few years are 5%, 10%, -15%, 20%, -12%, 22%, 8%
Arithmetic Average return:
Arithmetic Average return = (sum of all returns) / (total number of returns)
Arithmetic Average return = (5 + 10 - 15 + 20 - 12 + 22 + 8) / 7= 18 / 7= 2.57
Therefore, the arithmetic average return of the company is 2.57%.
Geometric average return:
Geometric average return = [(1+R1) * (1+R2) * (1+R3) * …….. * (1+Rn)]1/n - 1
Geometric average return = [(1.05) * (1.1) * (0.85) * (1.2) * (0.88) * (1.22) * (1.08)]1/7 - 1= 0.13
Therefore, the geometric average return of the company is 13%.
Variance:
Variance = (sum of (return - mean return)2) / (total number of returns)
Mean return = (5 + 10 - 15 + 20 - 12 + 22 + 8) / 7= 18 / 7= 2.57
Variance = [(5-2.57)2 + (10-2.57)2 + (-15-2.57)2 + (20-2.57)2 + (-12-2.57)2 + (22-2.57)2 + (8-2.57)2] / 7= 392.12 / 7= 56
Therefore, the variance of the company is 56.
Standard Deviation:
Standard Deviation = Square root of Variance
Standard Deviation = √56= 7.48
Therefore, the standard deviation of the company is 7.48%.

Thus, Arithmetic average return of the company is 2.57%.Geometric average return of the company is 13%.Variance of the company is 56.Standard deviation of the company is 7.48%.

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