I need help on this asap please don't take the points if you do know the answer.

Answer: Plain:  the product is 24 ∠ 15° in polar form. This means that the magnitude of the product is 24 and the angle between the positive real axis and the line connecting the origin and the product is 15°, measured counterclockwise.

Step-by-step explanation: To multiply complex numbers in polar form, we multiply their magnitudes and add their angles. We can start by converting the given complex numbers from rectangular form to polar form:

6√5 - 6i = 6(√5 - i) = 12 ∠ -30°

(√3 + √3i) = √3(1 + i) = 2 ∠ 45°

where we have used the fact that ∠θ is the angle between the positive real axis and the line connecting the origin and the complex number a + bi, measured counterclockwise.

Now, we can multiply the two complex numbers in polar form:

(6√5 - 6i)(√3 + √3i) = 12 ∠ -30° * 2 ∠ 45°

= 24 ∠ 15°

Therefore, the product is 24 ∠ 15° in polar form. This means that the magnitude of the product is 24 and the angle between the positive real axis and the line connecting the origin and the product is 15°, measured counterclockwise.

To determine the quadrant of the complex plane in which the product lies, we note that the angle 15° is in the first quadrant (between 0° and 90°). Therefore, the product lies in the first quadrant of the complex plane.

The equation x^2 + 24 = -11x can be solved to find the roots of the equation. The roots of the equation are x1 = -6 and x2 = -5. To find the roots of the given equation x^2 + 24 = -11x, we first rewrite it in the standard quadratic form, which is ax^2 + bx + c = 0.

By moving all the terms to one side, we get x^2 + 11x + 24 = 0. Now we can use the quadratic formula to solve for x, where a = 1, b = 11, and c = 24. The quadratic formula states that x = (-b ± √(b^2 - 4ac)) / (2a). Substituting the values, we have x = (-(11) ± √((11)^2 - 4(1)(24))) / (2(1)). Simplifying this equation gives us x = (-11 ± √(121 - 96)) / 2, which further simplifies to x = (-11 ± √25) / 2. Taking the square root of 25, we have x = (-11 ± 5) / 2. This yields two possible solutions: x1 = (-11 + 5) / 2 = -6 and x2 = (-11 - 5) / 2 = -5. Therefore, the roots of the equation are x1 = -6 and x2 = -5.

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Answer:

x1= -3

x2= -8

Step-by-step explanation:

Answer:

5½ this is the correct answer

Therefore , the solution of the given problem of triangle comes out to be x = Tan⁻¹(15/8) .

Because a triangle has two or so more extra parts, it is a polygon. It has a straightforward rectangular shape. Only two of a triangle's three sides—A and B—can differentiate it from a regular triangle. Euclidean geometry produces a single area rather than a cube when boundaries are still not perfectly collinear. Triangles are defined by their three sides and three angles. Angles are formed when a quadrilateral's three sides meet. There are 180 degrees of sides on a triangle.

Here,

Given :

=> AS =15 and AN = 8

So,

We have to find m∠N = x

=> Tanx = 15/8

=> x = Tan⁻¹(15/8)

Therefore , the solution of the given problem of triangle comes out to be  x = Tan⁻¹(15/8) .

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Usually, six to twelve equally wide categories are a decent number to use when trying to understand how the data is distributed for drawing a histogram.

One common graphing tool is the histogram. It is employed to present interval-scaled summaries of discrete or continuous data. It is frequently used to conveniently depict the main characteristics of the data distribution.

A histogram is a graphic representation of data that uses bars of various heights. Each bar in a histogram divides numbers into ranges. More data falls inside that range, as shown by taller bars. The form and distribution of continuous sample data are shown in a histogram.

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Answer:

X=45

Step-by-step explanation:

90 - 45 = 45

Answer:

P = 47.1 units

Step-by-step explanation:

the perimeter of the pair of straight opposite sides is 11+11, or 22

now you have 2 semi-circles, which equals 1 full circle which, if we find the circumference to then we just add it to 22 to get the entire answer

Circumference of circle with diameter of 8:

C = 2πr

C = 2π(4)

C = 8π

C = 25.13

now add 22 + 25.13 to get 47.1 rounded to nearest tenths place

Answer: y=-(3/4)x-1/2

Step-by-step explanation: To be in standard form the equation or the line must look like y=mx+b

m=the gradient or slope of the line and can take on both positive and negative values and can also be in fraction form

b= where the graph cuts the y axis it can also take on positive and negative values and can also be in fraction form

In this case m=-3/4 and b=-1/2

Solution

Step 1:

Write the function

Step 2:

5.30 % rate of return would you expect on a 5-year treasury security, assuming the pure expectations theory is valid.

To reflect the true cost and purchasing power of money that is borrowed or invested, an interest rate is called a real interest rate that has been adjusted for inflation. The nominal interest rate depicts the cost of money and reflects the state of the market. A good's nominal value is its price in terms of money. Its value in relation to another good, service, or collection of goods is what determines its true worth. Given that it is the current interest rate in the economy, it is frequently referred to as the market interest rate (usually charged by banks and other institutions). Depending on the bank or the type of loans or deposits, this nominal interest rate may be 8%, 10%, or 12%.

Nominal interest rate = Real interest rate + Inflation rate

= 2.5% + 2.8%

= 5.30%

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Answer:

multiplying by 2.3 is the opposite

\(2x*(5x^{2} +17+10)\) is the answer I think

The requirement f(x1) * f(x2) < 0 for choosing initial guesses x1 and x2 with opposite signs ensures the validity and convergence of certain numerical root-finding methods such as the bisection method or the regula falsi method.

The statement you provided is true for certain numerical methods used to find roots of equations, such as the bisection method or the regula falsi method. These methods are iterative and require an initial interval or range where the root is expected to be found. To ensure convergence and a valid solution, it is necessary to choose initial guesses x1 and x2 such that the function f(x) evaluated at those points have opposite signs, i.e., f(x1) * f(x2) < 0.

The rationale behind this requirement is based on the Intermediate Value Theorem, which states that if a continuous function f(x) changes sign over an interval [x1, x2], then there exists at least one root within that interval. By ensuring that f(x1) and f(x2) have opposite signs, we guarantee the existence of a root within the interval [x1, x2].

The bisection method works by repeatedly bisecting the interval and selecting a new subinterval that contains the root. At each iteration, the method narrows down the interval by halving it, based on the sign change observed in the function evaluations.

Similarly, the regula falsi (or false position) method also operates by iteratively refining the interval based on the linear interpolation between the function values at the endpoints. The method adjusts the interval based on the sign change of the function, converging to the root.

Both methods rely on the property of opposite signs to guarantee convergence and avoid getting stuck in a non-converging or incorrect solution. If the initial guesses do not satisfy the condition f(x1) * f(x2) < 0, it is possible that the method fails to converge or converges to a different root or solution.

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The correct conclusions about the triangle reflections are -

        {y} - axis.

        {x} - axis.

In statistics, a quartile is a type of quantile which divides the number of data points into four parts, or quarters, of more-or-less equal size. The data must be ordered from smallest to largest to compute quartiles.

Given is the boxplot as shown in the image.

From the box - plot, we can write the results as -

Therefore, We c

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Answer:

that not a thing

Step-by-step explanation:

The linear approximation, denoted as l(x), to the function f(x) = 1/x near x = 4 is given by the equation l(x) = f(a) + f'(a)(x - a). In this case, a = 4, so we need to find f(a), f'(a), and substitute them into the equation to obtain the linear approximation.

First, we find f(a) by substituting a into the function f(x). Thus, f(4) = 1/4.

Next, we need to determine f'(a), which represents the derivative of f(x) with respect to x, evaluated at x = a. The derivative of f(x) = 1/x is found by applying the power rule of differentiation. The derivative f'(x) = -1/x^2. Substituting a = 4, we get f'(4) = -1/(4^2) = -1/16.

Now, we can substitute f(a) and f'(a) into the linear approximation equation. Therefore, l(x) = 1/4 - (1/16)(x - 4).

In summary, the linear approximation l(x) to the function f(x) = 1/x near x = 4 is given by l(x) = 1/4 - (1/16)(x - 4). This approximation provides an estimate of the function's behavior in the vicinity of x = 4 using a linear equation.

To derive the linear approximation, we first determine f(a) by substituting a = 4 into the original function f(x) = 1/x. This yields f(4) = 1/4. Then, we find f'(x), the derivative of f(x) with respect to x, using the power rule of differentiation. The derivative f'(x) = -1/x^2. Evaluating this at x = 4 gives us f'(4) = -1/(4^2) = -1/16. Finally, we substitute f(a) and f'(a) into the linear approximation equation l(x) = f(a) + f'(a)(x - a) to obtain the final expression l(x) = 1/4 - (1/16)(x - 4). This equation provides an approximate representation of the original function near x = 4, allowing us to estimate its behavior using a simpler linear function.

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Answer:

Step-by-step explanation:

Answer:

The area is 77

Step-by-step explanation:

7*11=77

Answer:

area = 77

Step-by-step explanation:

if 7 is one side, and 11 is the other, and we know that length times width is the area of a rectangle or a square, we can set up a simple equation to solve for the area:

7 x 11 = ?

when looking at multiplying by 11s, the pattern is 2 of the number your multiplying it by until you exceed 9 (ex. 11 x 5 = 55, 11 x 4 = 44, 11 x 9 = 99, etc.) so:

7 x 11 = 77. which is your answer.

i hope this helped :))

Answer:

15x - 6

Step-by-step explanation:

To solve this, Given the expression 12 x + 3 ( x − 2 )

To simplify, expand

12 x + 3 * x −3 * 2

Knowing that

- * + = -

then the expression becomes

= 12 x + 3x - 6

= 15x - 6

The expression given is equivalent to 15x - 6

For the year in which they earned $176,500, the partners will receive $52,950, $35,300, and $88,250 respectively.

Here let the partners be A, B, and C.

According to the question, A: B: C = 3: 2: 5

This implies that if the profits are divided into

3 + 2 + 5 = 10 equal parts, 3 of those parts will go to A, 2 of those parts will go to B and 5 of those parts will go to C.

Here the profits for the year are $176,500.

Now dividing them into 10 equal parts will give us the value of each part to be

$176, 500/10 = $17,650

Hence A will receive $17,650 X 3 = $52,950

B will receive $17,650 X 2 = $35,300

C will receive $17,650 X 5 = $88,250

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Answer:

6/9, 12/18 (just 6 then 12)

Step-by-step explanation:

Please mark brainlest

Answer:

6/9  

12/18

Step-by-step explanation:

Hopefully this is correct

We need to first find the equation of the line l1 in vector form or parametric form. Without the equation of the line, we cannot determine if it lies on, intersects or does not intersect the surface.

Once we have the equation of the line, we can substitute the coordinates of the line into the equation of the surface, and see if there exists a solution.

Please provide more information about the line l1 so that we can solve the problem.

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A 95% confidence interval for the population mean rating for Miami International Airport is (5.34, 7.16).

To calculate the confidence interval, we can use the following formula:

sample mean ± (t-value)(standard error)

First, we need to calculate the sample mean and standard error. The sample mean is the average of the ratings, which is:

x bar = (4+8+9+10+1+1+1+8+8+8+8+7+6+7+8+8+10+9+1+8+7+8+7+9+8+10+6+4+8+1+1+8+8+7+10+9+7+1+7+5+8+4+1+9+8+9+1+1+7+7)/50 = 6.00

The standard error is the standard deviation of the ratings divided by the square root of the sample size.

Using a calculator or software, we find that the standard deviation is 2.98, so the standard error is:

SE = 2.98/√50 = 0.42

Next, we need to find the t-value for a 95% confidence interval with 49 degrees of freedom. Using a t-table or calculator, we find that the t-value is 2.01.

Finally, we can calculate the confidence interval:

6.00 ± 2.01(0.42) = (5.34, 7.16)

Therefore, we are 95% confident that the population mean rating for Miami International Airport falls between 5.34 and 7.16. This means that if we were to repeat the survey many times, 95% of the resulting confidence intervals would contain the true population mean rating.

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Answer:

x=2 and y=5

Step-by-step explanation:

Steps:

I will solve your system by substitution.

x=y−3;2x+y=9

Step: Solve x = y − 3 for x:

Step: Substitute y − 3 for x in 2x + y = 9:

2x+y=9

2(y−3)+y=9

3y−6=9(Simplify both sides of the equation)

3y−6+6=9+6(Add 6 to both sides)

3y=15

3y/3=15/3  (Divide both sides by 3)

y=5

Step: Substitute 5 for y in x = y − 3 :

x=y−3

x=5−3

x=2(Simplify both sides of the equation)

Answer:

x=2 and y=5

Answer:

x = 2          y = 5

Step-by-step explanation:

Since we know that

x = y - 3

We can insert that into the equation above:

2(y-3) + y = 9

After having this equation, we can start by multiplying the numbers/variables in the parenthesis by 2.

2y - 6 + y = 9

Then add the common multiples (2y and y)

That makes:

3y - 6 = 9

We need to get 3y on a side by itself, so to do this, we can add 6 to (-6) and (9)

That makes:

3y = 15

Divide the 3 by 3 and 15 to get the y on its own:

y = 5

Now we need to find x, and to do this we can insert y into the equation:

2x + 5 = 9

Now subtract the 5 from the (5) and (9) and you'll get

2x = 4

Then you divide the 2 on both sides and get

x = 2

You can check your work by inserting x and y into the equation

2(2) + 4 = 9  

Sorry for this super long explanation, and hope this helps

Answer:

wait.. almost done...

Step-by-step explanation:

Answers:

Larger bottle = 44 gallons

Smaller bottle = 33 gallons

=====================================================

Explanation:

L = capacity of larger bottle

S = capacity of smaller bottle

Capacities are in gallons

We're told the ratio of these capacities is 4 to 3, meaning L/S = 4/3. Note how L goes first on top since 4 is the first number and it's larger than 3.

Cross multiply to get 3L = 4S. We can solve for S to get S = 3L/4.

----------------------------

We're also told that the larger bottle has 11 more gallons than the smaller one, so,

Larger = Smaller + 11

L = S+11

L = (3L/4) + 11 .... plug in S = 3L/4

4L = 4*(3L/4) + 4*11 ... multiply every term by 4

4L = 3L + 44 .... the fraction goes away afterward

4L-3L = 44 .... subtract 3L from both sides

L = 44

The larger bottle can hold 44 gallons

S = 3L/4

S = 3*44/4

S = 3*11

S = 33

The smaller bottle can hold 33 gallons

Note that L-S = 44-33 = 11 to show there's an 11 gallon difference between the larger and smaller bottles. We can also see that L/S = 4/3 is also true because 44/33 = 4/3. This confirms our answers.

All of the above factors - confidence level, required precision (margin of error), and the degree of variation in the population as measured by its standard deviation - are used to determine sample size.

When determining the sample size for a study or survey, several factors need to be considered: confidence level, required precision (margin of error), and the degree of variation in the population as measured by its standard deviation. Let's break down each factor and understand how they contribute to determining the sample size:

Confidence Level: The confidence level represents the degree of certainty or confidence desired in the results. It is typically expressed as a percentage (e.g., 95% or 99%). The higher the confidence level, the more confident we can be that the estimated result falls within a certain range. For example, a 95% confidence level means that if the study were repeated 100 times, we would expect the true population parameter to fall within the estimated range in 95 out of those 100 times.

Required Precision (Margin of Error): The required precision, also known as the margin of error, defines the acceptable amount of uncertainty or error allowed in the estimation. It represents the maximum difference between the estimated result and the true population parameter that is considered acceptable. A smaller margin of error indicates higher precision and vice versa. For instance, if you want to estimate the proportion of people supporting a particular political candidate with a margin of error of ±3%, it means that the estimated proportion should be within 3% of the true proportion.

Degree of Variation (Standard Deviation): The degree of variation in the population, quantified by its standard deviation, reflects how much the values within the population differ from the population mean. If the population has a high standard deviation, it suggests a larger spread of values, indicating greater heterogeneity. Conversely, a low standard deviation implies less variability and more homogeneity in the population. The standard deviation helps determine how much information is needed from the sample to make accurate estimates of the population parameters.

These factors are interrelated in determining the sample size. As the confidence level increases, the margin of error becomes smaller, requiring a larger sample size to achieve the desired precision. Similarly, a higher degree of variation in the population (larger standard deviation) necessitates a larger sample size to capture that variability accurately.

In summary, the confidence level, required precision (margin of error), and degree of variation (standard deviation) are essential factors used in determining the appropriate sample size for a study or survey. The balance between these factors ensures that the sample is representative enough to provide reliable estimates of the population parameters with the desired level of confidence and precision.

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Answer: 71.25 meters

Step-by-step explanation:

1. 498.75/7

2. 71.25

Mia made 7 trips to visit her grandmother. she walked 498.75 meters in all, mia walks on each trip is 71.25 m

Mia made 7 trips to visit her grandmother

she walked 498.75 meters in all

In order to calculate the distance she walks on each trip, we calculate it by dividing the total distance by the number of trips

The total distance is 498.75

The number of trips is 7

walk on each trip is 498.75/ 7 = 71.25

Therefore, mia made 7 trips to visit her grandmother. she walked 498.75 meters in all, mia walks on each trip is 71.25 m

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