Write the expression in standard form: (3) / (3-12i).

The car will cost $ 800 after a depreciation time of approximately 6 years.

Herein we are informed about the case of a car bought in 2011 at a cost of $ 36,000 and that depreciates linearly every year. Then, the depreciation function is described below:

c(t) = c' + m · t

Where:

If we know that c(0) = 36,000, c(4) = 12,000 and c(t) = 800, then the depreciation rate is:

m = (12,000 - 36,000) / (4 - 0)

m = - 24,000 / 4

m = - 6,000

800 = 36,000 - 6,000 · t

6,000 · t = 35,200

t = 35,200 / 6,000

t = 5.867

The expected depreciation time is approximately 6 years.

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The values of ∂z/∂r and ∂z/∂s. These partial derivatives will depend on the specific function F(u, v, w) provided.

To find ∂z/∂r and ∂z/∂s, we need to differentiate z = F(u, v, w) with respect to r and s.
Given that u = r^2, v = -2s^2, and w = ln(r) + ln(s), we can substitute these values into z = F(u, v, w).
So, z = F(r^2, -2s^2, ln(r) + ln(s)).
To find ∂z/∂r, we differentiate z with respect to r while treating s as a constant. This gives us:
∂z/∂r = ∂F/∂u * ∂u/∂r + ∂F/∂w * ∂w/∂r.
Similarly, to find ∂z/∂s, we differentiate z with respect to s while treating r as a constant. This gives us:
∂z/∂s = ∂F/∂v * ∂v/∂s + ∂F/∂w * ∂w/∂s.
Since we don't have the specific function F(u, v, w) mentioned in the question, we cannot determine the values of ∂z/∂r and ∂z/∂s. These partial derivatives will depend on the specific function F(u, v, w) provided.

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Answer:

C) g(x) = f(x) + 4

Step-by-step explanation:

A vertical shift is where you shift, slide or translate the whole graph up or down (on a graph) The way this shows up in the equation is just a number tacked on to the end of the equation. A +anumber (like the +4 in the answer) slides the function UP four units. A

-anumber would slide the function DOWN instead.

As for the other answers:

A) the 3multiplied in front is a vertical STRETCH.

D) the 1/2 multiplied in front is a vertical shrink (smash)

B) The -3 in close tight with the x is a horizontal shift(slide, translate) It is a RIGHT shift. A +anumber would be a LEFT shift. Horizontal shift seem kind of backwards. + goes LEFT and - goes RIGHT.

Answer:

A. Determine 1% of 56, both of them

Step-by-step explanation:

The ratio of false positives to true positives is 8 over 54.

According to the Question

Results of a strep throat test performed on a sample of 400 ill people are displayed in the table's data. People who have the flu and those who don't are separated into two categories. The patients are then separated into groups based on whether they tested positive or negative for strep throat within each of these categories.

We must first define what a true positive and a false positive are in order to calculate the ratio of false positives to true positives. A patient who tests positive for strep throat but does not actually have the illness is said to have a false positive. The 8% of patients in this instance who tested positive for strep throat but did not have the flu would fall under that category. A patient who tests positive for strep throat and truly has the illness is said to have a true positive. That would be the 54% of patients who tested positive for both the flu and strep throat in this instance.

We divide the percentage of false positives (8%) by the percentage of true positives (54%), which gives us the ratio of false positives to true positives.

As a result, the ratio becomes 8% / 54%, or 8/54.

It's critical to remember that this ratio is dependent on the sample and test performed and may not be the same for different populations or testing methodologies.

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Answer:

\(m\angle Y=30^{\circ}\)

Step-by-step explanation:

In any right triangle, the cosine of an angle is equal to its adjacent side divided by the hypotenuse, or longest side, of the triangle.

Therefore, we have:

\(\cos Y=\frac{42\sqrt{3}}{84},\\Y=\arccos(\frac{42\sqrt{3}}{84})=\boxed{30^{\circ}}\)

The 3-point differentiation rule is computationally efficient because it requires evaluating the function at three points and performs a simple arithmetic calculation to estimate the derivative.

The 3-point differentiation rule, also known as the central difference method, provides a good balance between computational efficiency and accuracy. It approximates the derivative of a function using three points: one point on each side of the desired differentiation point.

In the 3-point differentiation rule, the derivative is calculated using the formula:

f'(x) ≈ (f(x + h) - f(x - h)) / (2h)

where h is a small step size.

Compared to other methods, such as the forward or backward difference rules, the 3-point rule provides better accuracy as it takes into account information from both sides of the differentiation point. It reduces the error caused by the step size and gives a more accurate approximation of the derivative.

Additionally, the 3-point differentiation rule is computationally efficient because it requires evaluating the function at three points and performs a simple arithmetic calculation to estimate the derivative. This makes it a practical choice for differentiating functions, providing a good trade-off between accuracy and computational performance.

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There can be 144 unique sandwiches created.

To determine the Possibility of unique sandwiches that can be created, we multiply the number of options for each category: 3 types of bread, 6 meats, and 8 toppings.

To calculate the total number of unique sandwich combinations, we multiply these numbers together:

\(3 (bread\ options) * 6 (meat\ options) *\ 8 (topping\ options) = 144.\)

Therefore, it is possible to create 144 distinct sandwiches by selecting one item from each category, considering the given options.

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Answer: To find the remainder when 4x^3 - 8x^2 + 3x - 7 is divided by 4x - 3, we can use polynomial long division.

Here's how:

 4x^3 - 8x^2 + 3x - 7

÷ 4x - 3

4x^2  

4x^2  

______

0x^3 + 4x^2 - 8x^2 + 3x - 7

-4x^2 -12x^2  

-12x^2  

-12x^2  

________

0x^2 - 8x^2 + 3x - 7

+12x^2 -36x^2

-24x^2  

-24x^2  

________

-24x^2 + 3x - 7

+24x^2 +72x^2

48x^2  

48x^2  

________

48x^2 - 3x + 1

-48x^2 +144x^2

192x^2  

________

192x^2 + 1

The remainder is 192x^2 + 1.

Step-by-step explanation:

The statement is true. Simple random sampling is a method of selecting a sample from a larger population in which every member of the population has an equal chance of being selected for the sample.

This method is associated with a high degree of generalizability because it ensures that the sample is representative of the population. When a sample is representative of the population, the findings from the sample can be generalized to the entire population with a high level of confidence.

Simple random sampling is considered to be one of the most reliable and unbiased methods of sampling, making it a popular choice in many research studies.

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Answer:

Step-by-step explanation:

Given linear equation:

Meaning of each term is:

According to above details the correct answer choise is B

Answer:

b

Step-by-step explanation:

bc i did the schoolnet thingy

The score at 35th percentile is 469.6 marks according to standard deviation and mean.

What is standard deviation?

Standard Deviation could be a measure that shows what quantity variation (such as unfold, dispersion, spread,) from the mean exis

Main body:

Given:

mean of μ = 500  and standard deviation of σ = 80

To answer this, we must find the z-score that is closest to the value 0.35 in the z table. This value turns out to be -0.38:

We can then plug this value into the percentile formula:

Percentile Value = μ + zσ

35th percentile = 500 + (-0.38)*80

35th percentile = 469.6

the score at the 15th percentile weighs about 469.6 marks.

Hence marks at 35th percentile is 469.6

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Answer:

I would say c and b

Step-by-step explanation:

I would say this because with out the number it would be that same thing and the same eqaution and  formation

The sum of Peter, Richard, and John's ages is 191.

We know that the ratio of Peter's age to Richard's age is = 5/8 --(i)

The ratio of John's age to Peter's age is = 7/12 --(ii)

Similarly, the ratio of John's age to Richard's age is = (5*7)/(8*12)= 35/96 -(iii)

Using the value of (i),(ii),(iii), we get -

Age of Peter = (5*12)/(8*12) = 60/96

= 60 years of age

Age of John = (7*5)/(12*5) = 35/60

=35 years of age

From the value of (iii), since no one is over 100 years of age, the age of Richard= 96 years of age

Hence the sum of their ages is = 96+35+60

= 191

Therefore, we know that the sum of their ages is 191.

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We can associate each maximal ideal (f(x)) with the complex number x, where x is a complex number in the upper-half plane. This establishes a one-to-one correspondence between the two sets.

To show a bijective correspondence between the maximal ideals of R[x] (the ring of polynomials with coefficients in R) and the upper-half of the complex plane, we can make use of the fact that every complex number z in the upper-half plane can be written as z = x + iy, where x and y are real numbers and y is positive.

First, let's consider the maximal ideals of R[x]. An ideal in R[x] is maximal if and only if it is of the form (f(x)), where f(x) is an irreducible polynomial over R. So, to establish a bijective correspondence, we need to find a way to associate each maximal ideal with a unique complex number in the upper-half plane.

One way to do this is by considering the polynomial f(z) = z - x. The ideal (f(z)) generated by this polynomial consists of all polynomials in R[x] that have x as a root. Now, notice that if x is a real number, then z - x = 0 implies z = x, which corresponds to a point on the real axis. However, if x is a complex number, then z - x = 0 implies z = x, which corresponds to a point in the upper-half plane.

Therefore, we can associate each maximal ideal (f(x)) with the complex number x, where x is a complex number in the upper-half plane. This establishes a one-to-one correspondence between the two sets.

In summary, there is a bijective correspondence between the maximal ideals of R[x] and the upper-half of the complex plane, where each maximal ideal corresponds to a unique complex number in the upper-half plane.

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The Moon and Sun's gravitational pull on the waters of Earth is what causes tides.

The Moon and Sun's gravitational pull on the waters of Earth is what causes tides. The gravitational pull between any two objects is determined by both their masses and their separation from one another. Although having a far larger mass than the Moon, the Sun is located much distant from Earth. This indicates that the Moon's gravitational pull on the oceans of Earth is greater than that of the Sun.

The water on the side of the Earth that faces the Moon is drawn towards it by the Moon's gravitational attraction, creating a high tide. Another high tide results from simultaneous pulls on the opposite side of the Earth's water towards the Moon.

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The moon has a greater effect on Earth's tides than the sun because it is much closer to Earth.

Gravitational pull is the force by which a planet or other body draws objects toward its center. The force of gravity keeps all of the planets in orbit around the sun. It also keeps the moon in orbit around Earth.

The Moon and Earth exert a gravitational pull on each other. On Earth, the Moon's gravitational pull causes the oceans to bulge out on both the side closest to the Moon and the side farthest from the Moon. These bulges create high tides. The low points are where low tides occur.

The moon has a greater effect on Earth's tides than the sun because it is much closer to Earth. The gravitational force between two objects decreases as the distance between them increases, so the moon's gravitational pull on Earth's oceans is much stronger than the sun's. However, during certain times of the year, when the sun and moon are aligned, their combined gravitational pull can create especially high or low tides, known as spring tides.

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Answer:

Part 1; The point (m, 4) divides the line externally in the ratio 3:2

Part 2; m = -19

Step-by-step explanation:

Part 1

The given point dividing the line = (m, 4)

The given points on the line = (5, 1) and (-3, 2)

Let A and B, represent the points (5, 1) and (-3, 2) respectively, and let P represent the point, (m, 4)

Therefore, we have;

The vertical distance from 4 to 1 = 4 - 1 = 3 units

The vertical distance from 4 to 2 = 4 - 2 = 2 units

Given that the point 4 is over the given points joined by the line, (5, 1) and (-3, 2), we have that the point (m, 4) divides the line in the ration -3:2 or externally in the ratio AP:PB = -3:2

Part 2

Therefore, we have;

(m - 5)/(m - (-3)) = 3/2

3·m + 9 = 2·m - 10

m = -19

The standard deviation of the data set is found as  19.13.

The formula used -

For the given data set:

12, 30, 54, 36, 60, 18

Total Numbers N = 6

Mean = 12, +  30 + 54 + 36 + 60+  18 / 6

Mean = 35

Variance = (12- 35)² +  (30- 35)² + (54- 35)² + (36- 35)² + (60- 35)² + (18- 35)²)/(6 - 1)

Variance = 366

Standard deviation  σ = √Variance

Standard deviation  σ =√366 = 19.13

Thus, the standard deviation of the data set is found as  19.13.

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Table a:    y  = x + 3

Table b:    y = -x²

Table c:    y = x² + 3

Table d:    y = 3x - 1

For table a:

x = 1, 0, -4, 2, -2, -1

y = 4, 3, -1, 5, 1,  2

Each value of y is gotten by adding 3 to the corresponding value of x.

Therefore, the equation representing the data is y  =  x  +  3

For table b:

x = -1, 3, 1,  0, -2, 2

y = -1, -9, -1, 0, -4, -4

Each value of y is gotten by finding the square of the corresponding value of x and negating the result

Therefore, the equation representing the data is y = -x²

For table c:

x = 3, -2, 1, 0, 2, -3

y = 12, 7, 4, 3, 7, 13

Each value of y is gotten by adding 3 to the square of the corresponding value of x

Therefore, the equation representing the data is y = x² + 3

For table d:

x = -3, 4, 2, -2, 0, -10

y = -10, 11, 5, -7, -1, -31

Each value of y is gotten by subtracting 1 from thrice the corresponding value of x

Therefore, the equation representing the data is y = 3x - 1

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Answer:

Step-by-step explanation:

let a be the first term and r be common ratio.

\(a_{3}=ar^2=-45\\a_{5}=ar^4=-405\\divide\\\frac{ar^4}{ar^2} =\frac{-405}{-45} =9\\r^2=9\\r=\pm3\\9a=-45\\a=-5\\a_{7}=ar^{7-1}=ar^6=ar^4 \times r^2=-405 \times 9=-3645\)

We can plot the vector r(t) and the vector N(T) at the given value of t = T.

To find the principal unit normal for the vector-valued function r(t) = sin(t)i + tcos(t)j + tk, we need to compute the derivative of r(t) with respect to t and then normalize it to obtain a unit vector.

First, let's find the derivative of r(t):

r'(t) = cos(t)i + (cos(t) - tsin(t))j + k

Next, we'll normalize the vector r'(t) to obtain the unit vector:

||r'(t)|| = sqrt((cos(t))^2 + (cos(t) - tsin(t))^2 + 1^2)

Now, we can find the principal unit normal vector by dividing r'(t) by its magnitude:

N(t) = r'(t) / ||r'(t)||

Let's evaluate the principal unit normal at t = T:

N(T) = (cos(T)i + (cos(T) - Tsin(T))j + k) / ||r'(T)||

To sketch the situation, we can plot the vector r(t) and the vector N(T) at the given value of t = T.

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Answer:

2. (1) \(30\)

3. (1) \(y=\frac{1}{4}x\)

4. a) \(y=x+6\)   b) \(42\)

Step-by-step explanation:

In a proportional relationship, y=2 when x=8, the following lines will show this relationship,

1.   y = 1/4x

2.  y = x - 6

4.  y =  1/2x - 2

The equation of a straight line is a relationship between x and y coordinates, The general equation of a straight line is y = mx + c, where m is the slope of the line and c is the y-intercept.

Given that,

The point,

x = 8 and  y = 2

We have to check all the given options,

1.   y = 1/4x

     y  = 1/4 × 8

     y  =  2

2.  y   = x - 6

         = 8 - 6

    y   =  2

3.  y   = 4x

         = 4 × 8

    y   = 32

4.  y   = 1/2x - 2

         = 1/2 × 8 - 2

         =  2

Hence, Option 1, 2, & 4 satisfies the given condition

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Answer:

  see attached

Step-by-step explanation:

The two different triangles can be formed by placing the 90° angle adjacent to, or opposite the given side.

__

In the attached diagram, the two triangles are ABC and ABD. The right angles are at vertex C and vertex B, respectively.

Answer:

g(x) = x(x - 5)(x + 4)

Step-by-step explanation:

Here the binomial is x + 4, indicating that a root is -4.  Note that x is common to all terms of g(x)=x3−x2−20x, so we can immediately write g(x) in partially factored form as

g(x) = x(x^2 - x - 20).  Since -20 = -5*4,

g(x) = x(x - 5)(x + 4)

Answer:

x(x-5)(x+4)

Step-by-step explanation:

Checked. Answer submitted prior to mine is correct on BIM.

Answer:

7^4

Step-by-step explanation:

to divide exponents we just subtract what the exponent is so we can write it like this

7^5/7^1= 7^5-1=7^4

Hopes this helps please mark brainliest

Answer: 3(m+3n)

Step-by-step explanation:

3m + 9n=

3*m + 3*3n=3(m+3n)