Pls help me with this question!!!

The value of the given complex number is 0.641 ∠ 180°.

By multiplying the numerator and denominator, we may make the complex number expression (5 ∠ 10°)(10 ∠ -40°)/(13 ∠ -80°)(6 ∠ -130°) easier to evaluate.

We multiply the magnitudes and add the angles when multiplying complex numbers in polar form.

The numerator can be summed up as follows:

(5 ∠ 10°)(10 ∠ -40°) = (5 * 10) ∠ (10° - 40°) = 50 ∠ -30°

The denominator simplifies as follows:

(13 ∠ -80°)(6 ∠ -130°) = (13 * 6) ∠ (-80° - 130°) = 78 ∠ -210°

Now, we divide the numerator by the denominator:

(50 ∠ -30°)/(78 ∠ -210°) = (50/78) ∠ (-30° - (-210°)) = (25/39) ∠ 180°

The value of the given complex number is (25/39) ∠ 180°, which can also be written as approximately 0.641 ∠ 180°.

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The complete question is:

Evaluate the complex number (5∠10°)(10∠-40°)/13∠-80°)(6∠-130°). The value of the given complex number is ________.

Answer: 12

Step-by-step explanation:

Answer:

419/1000

Step-by-step explanation:

\( \frac{(0.419 \times 1000)}{(1 \times 1000)} = \frac{419}{1000} \)

If a political candidate has asked you to conduct a poll to determine what percentage of people support him. if the candidate only wants a 5% margin of error at a 99.5% confidence level, The size of sample is needed is:  787.92.

Margin of error = 5% or 0.05

99.5% confidence interval = 2.807

p = 0.5 (default because no value was given)

Let n represent the sample size

5% error means z× SE =0.05

z (0.995)= 2.807

SE =√(.5×.5/n)

2.807 × √(.25/n)=0.05

Square both sides

7.879 × .25=0.0025×n

Move  the n across

1.9698 = 0.0025×n

n = 1.9698 / 0.0025

n= 787.92

Therefore we can conclude that 787.92 is the sample size that is needed.

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Answer:

\(\frac{6}{7}\)

Step-by-step explanation:

Given a number n then the multiplicative inverse is \(\frac{1}{n}\)

Thus

the multiplicative inverse of \(\frac{7}{6}\) is \(\frac{1}{\frac{7}{6} }\) = \(\frac{6}{7}\)

As per the unitary method, the amount of grape juice does Sarah use for each cup of water is 11/48

The term unitary method in math refers the process of finding the value of a single unit and then find the value of more or fewer units by multiplying their quantity with the value of a single unit.

Here we have given that Sarah dilutes grape juice for her two-year-old sister. she uses 1/4 cup of grape juice for every 2/3 cup of water.

And we need to find the amount of grape juice does Sarah use for each cup of water

In order to find the solution, we have to add the two fraction first to determine the total ratio

=> ¹/4 + ²/3 = ¹¹/12

Now, we know that she uses ¼ cup grape juice for ¹¹/12 cup full of diluted grape juice, then it can be written as,

=> ¼ : ¹¹/12

So, the amount of grape juice does Sarah use for each full cup of water, that is ¹²/12, so it can be written as,

=> (x) : ¹²/12

Now, we have to cross multiply the ratios;

=> ¹²/12 * ¼ = ¹¹/12 * x

=> ³/12 = ¹¹/12 x

=> ³/12 * ¹²/11 = x

=> ¹¹/48 = x

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Answer:

The simplified version of 6/2 is 2squareroot of 2

Step-by-step explanation:

The value of K is 2.

Let's denote the scale factor as K. The surface area of a solid after dilation is directly proportional to the square of the scale factor.

We are given that the initial surface area of the solid is 50 units^2, and after dilation, the surface area becomes 200 units^2.

Using the formula for the surface area, we have:

Initial surface area * (scale factor)^2 = Final surface area

50 * K^2 = 200

Dividing both sides of the equation by 50:

K^2 = 200/50

K^2 = 4

Taking the square root of both sides:

K = √4

K = 2

Therefore, the value of K is 2.

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It will not be reasonable to use regression line to predict the final exam score , the reason is explained below .

What is Regression Line ?

If data shows a linear relationship between two variables, then line that best fits this linear relationship is known as least-squares regression line.

it is given that ,

the student has missed 10 class periods .

we have to check whether it will be reasonable to use the least-squares regression line to predict the final grade for a student .

So , No , it will not be reasonable to use the least-squares regression line to predict the final grade for a student who has missed 10 class periods because 10 absent is outside the scope of the model.

Therefore , the correct option is (c) .

The given question is incomplete , the complete question is

Would it be reasonable to use the​ least-squares regression line to predict the final exam score for a student who has missed 10 class​ periods? Why or why​ not?

(a) No, because the absolute value of the correlation coefficient is less than the critical value for a sample size of n=10.

(b) ​Yes, because the purpose of finding the regression line is to make predictions outside the scope of the model.

(c) ​No, because 10 absent is outside the scope of the model.

(d) ​Yes, because the absolute value of the correlation coefficient is greater than the critical value for a sample size of n=10.

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AnswerAnwser key

Step-by-step explanation:

Answer:

1) -6

2) -8

3) 125185623/1000000000 ( i didn't really understand this one but i hope i got it right)

4) 1

5) 0.94736842

6) 4/5 = 5/4

I can only do up to there for now .... sorry

but i can do the second part in a few mins.

Step-by-step explanation:

i really hope this is right....

Answer:

The third one

Step-by-step explanation:

it number 3 one no prob

Step-by-step explanation:

The equation to predict how many hours, x, the second part of the trip will take is :x = (total distance - distance traveled in the first part) / average speed x = (125 - 75) / 50  x = 1

To predict how many hours, x, the second part of the trip will take, we can use the equation:

x = (total distance - distance traveled in the first part) / average speed

In this case, the total distance of the trip is 125 miles, and the distance traveled in the first part is the product of the average speed and the time taken for the first part, which is 50 miles/hour * 1.5 hours = 75 miles.

Substituting these values into the equation, we have:

x = (125 - 75) / 50

Simplifying the equation, we get:

x = 50 / 50

x = 1

Therefore, the equation to predict how many hours, x, the second part of the trip will take is:

x = (total distance - distance traveled in the first part) / average speed

x = (125 - 75) / 50

x = 1

This means that the second part of the trip will take 1 hour to complete after the bus stops to refuel.

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The term that refers to the fact that the distance between two or more points is equal is "equidistant".

In geometry, the concept of equidistance is important when dealing with circles, which are sets of points that are equidistant from a single point called the center. This property is what allows circles to be defined in terms of their radius, which is the distance between the center and any point on the circle.

Equidistance is also important in other areas of mathematics and science. For example, in physics, equidistant points can be used to define a plane or surface that is perpendicular to a given line or axis. This is useful in many applications, such as designing electronic circuit boards or constructing buildings.

The concept of equidistance is not limited to mathematics and science, however. It can also be applied in everyday life. For instance, if you are planning a road trip and want to visit several destinations that are equidistant from your starting point, you can use this information to help plan your route and estimate your travel time.

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The perimeter of square ABCD is 8 \(\sqrt{13}\)  units.

Coordinates of the vertices are A(-2, 1), B(2, 7), C(8, 3) and D(4, -3)

A square's perimeter is equal to the sum of its four sides or the product of four and one of its sides.

Therefore, the square's perimeter is equal to a + b + c + d.

4 × any of the sides because the sides of a square are equal to one another.

Since ABCD is a square:

Perimeter of a square = 4 × (length of a side)

=4 × AB

Formula to calculate the distance between two points \($\left(x_1, y_1\right)$\) and \($\left(x_2, y_2\right)$\) is, \($\mathrm{d}=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}$\)

Therefore, distance between two points A(-2, 1) and B(2, 7) will be,

AB = \(\sqrt{(2+2)^2+(7-1)^2} \\\)

AB = \(\sqrt{4^2+6^2} \\\)

AB = \(\sqrt{52} \\\)

AB = 2\(\sqrt{13}\)

Hence the perimeter of square ABCD can be calculated as 4 × AB

Now Perimeter of a square ABCD = 4 × 2\(\sqrt{13}\)

= 8 \(\sqrt{13}\)  units

Therefore the answer is 8 \(\sqrt{13}\)  units

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Square ABCD has vertices at A(−2,1), B(2,7), C(8,3), and D(4,−3). How many units is the perimeter of square ABCD?

Here we would be using the midpoint formula to find the co-ordinates of the line segment joining the two given points.

Given points,

★ We have :

★ Midpoint of two points:-

Now, refer to the attachment.

Additional Information :

★ Centroid of a triangle :-

★ Distance Formula :-

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A binary tree is a structure in which each node is capable of having two successor nodes, called "left child" and "right child."

In a binary tree, each node can have at most two successor nodes, known as the left child and the right child. These successor nodes branch out from the parent node, forming two distinct paths or branches. The left child represents the left branch, and the right child represents the right branch. This hierarchical structure allows for efficient organization and traversal of data, as each node can connect to two other nodes, creating a branching pattern throughout the tree. The concept of left and right children enables various operations and algorithms to be performed on the binary tree, such as insertion, deletion, searching, and sorting.

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Answer:

They can run 32 times down the court

Step-by-step explanation:

Answer:

84

Step-by-step explanation:

\(-2(-42)\\2(42)\\84\)

two negatives cancel out.

Hope this helps plz hit the crown :D

Answer:

its 84

Step-by-step explanation:

because when minus multiplies minus it's becomes + and 2× 42 is 84

Answer:

not equivalent to meteorologists ratio

Step-by-step explanation:

meteorologists ratio is

rainy days : sunny days = 2 : 5

last months weather is

rainy days : sunny days

= 10 : 20 ( divide both parts by LCM of 10 )

= 1 : 2 ← not equivalent to 2 : 5

Yes, the given curves are orthogonal.

In mathematics, an orthogonal trajectory is a curve, which intersects any curve of a given pencil of (planar) curves orthogonally.

Given equation is,

x²+y²=ax

Differentiating,

2x+2yy'=a

y' = (a-2x)/2y = m1

Again,

x²+y²=by

Differentiating,

2x+2yy'=by'

y' = -2x/(2y-b) = m2

For both curves are orthogonal, we have

m1*m2 = -1

(a-2x)/2y*-2x/(2y-b)  = -1

-2ax+4x² = -4y²+2yb

4(x²+y²) = 2ax+2yb

Since, ax = (x²+y²)

by = (x²+y²)

Then,

4(x²+y²) = 2(x²+y²) +2(x²+y²)

4(x²+y²) = 4(x²+y²)      (true)

Hence, the above response is appropriate.

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Answer:

c/sin(60°) = 14/sin(25°)

c = 14sin(60°)/sin(25°) = 28.7

Greetings from Brasil...

Rewriting the problem sets

A = {-7, 4, 2, 14, 21, 34, 42}

B = {...; 2; 4; 6; 8; 10; 12; 14; 16; 18; 20; 22; 24; 26; 28; 30; 32; 34; 36; 38; 40; 42;...}

C = {...; -14; -7; 0; 7; 14; 21; 28; 35; 42; 49; 56; 63; 70; 77;...}

So, according to the statement, it is desired:

A ∩ B ∩ C - the intersection between the 3 sets, that is, which numbers are present simultaneously in the 3 sets....

Looking at the sets we conclude that

Answer:

x=-4 :D yw

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Patterns where the output is addition or subtraction the same value is Linear

Patterns where the output is multiplying or dividing the same value is Exponential.

A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept.

Given:

We know In a linear relationship the y-values have equal differences.

Then, we can say that linear relation support addition and subtraction.

Thus, Patterns where the output is addition or subtraction the same value is Linear

Now, In an exponential relationship, the y-values have equal ratios.

Then, we can say that exponential relation support multiplying or dividing.

Thus, Patterns where the output is multiplying or dividing the same value is Exponential.

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Answer:

your new grade is 88%

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According to Zaller's Receive-Accept-Sample (RAS) model, individuals who are most susceptible to the message of a political action committee launching a new advertisement aimed at expanding health insurance to low-income Americans through increased government funding would be those who both receive and accept the message.

The RAS model suggests that individuals have varying levels of political knowledge and are exposed to different sources of information. Those who are more likely to receive the message are individuals who are politically interested and engaged, while those who are more likely to accept the message are individuals who have limited political knowledge and are less critical of the information presented to them.

Therefore, in the context of the advertisement aiming to expand health insurance to low-income Americans, the most susceptible individuals would be those who are politically interested but have limited political knowledge. These individuals may be more likely to accept the message without critically evaluating its content.

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