find the area of the region enclosed by one loop of the curve. r = sin(12θ)

Answers

Answer 1

The area of the region enclosed by one loop of the curve r = sin(12θ) is π/48.

We have to find the area of the region enclosed by one loop of the curve.

The given curve is:

r = sin(12θ)

Consider the region r = sin(12θ)

The area of region bounded by the curve r = f(θ) in the sector a ≤ θ ≤ b is

A =

Now to find the area of the region enclosed by one loop of the curve, we have to find the limit by setting r=0.

sin(12θ) = 0

sin(12θ) = sin0   or    sin(12θ) = sinπ

So θ = 0             or      θ = π/12

Hence, the limit of θ is 0 ≤ θ ≤ π/12.

Now the area of the required region is

A = [tex]\int ^{\pi/12}_{0} \frac{1}{2}(\sin12\theta)^2d\theta[/tex]

A = [tex]\frac{1}{2}\int ^{\pi/12}_{0}\sin^212\thetad\theta[/tex]

A = [tex]\frac{1}{2}\int ^{\pi/12}_{0}\frac{1-\cos24\theta}{2}d\theta[/tex]

A = [tex]\frac{1}{4}\int ^{\pi/12}_{0}(1-\cos24\theta)d\theta[/tex]

A = [tex]\frac{1}{4}\left[(\theta-\frac{1}{24}\sin24\theta)\right]^{\pi/12}_{0}[/tex]

A = [tex]\frac{1}{4}\left[(\frac{\pi}{12}-\frac{1}{24}\sin24\frac{\pi}{12})-(0-\frac{1}{24}\sin24\cdot 0)\right][/tex]

A = [tex]\frac{1}{4}\left[(\frac{\pi}{12}-\frac{1}{24}\sin2\pi)-(0-\frac{1}{24}\sin0)\right][/tex]

A = 1/4[(π/12-0)-(0-0)]

A = 1/4(π/12)

A = π/48

Hence, the area of the region enclosed by one loop of the curve r = sin(12θ) is π/48.

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Related Questions

an agriculturalist working with australian pine trees wanted to investigate the relationship between the age and the height of the australian pine. a random sample of australian pine trees was selected, and the age, in years, and the height, in meters, was recorded for each tree in the sample. based on the recorded data, the agriculturalist created the following regression equation to predict the height, in meters, of the australian pine based on the age, in years, of the tree. Predicted height = 0.29 + 0.48(age) Which of the following is the best interpretation of the slope of the regression line?

Answers

The height increases by 0.48  meters each year.

The available regression equation is: Predict height= 0.29 + 0.48 (age).

Here, the predict height is dependent variable and the  age is in-dependent variable.

Intercept = 0.29

Slope      = 0.48

The given regression equation indicates the y on x model and the intercept coefficients of the regression equation is 0.29 and the slope is 0.48.

The height increases, an average, by 0.48 m per year.

Because co-efficient of slope variable indicate the positive sign and we increase 1 year in age then automatically height increased is 0.48 m.

The height increases, on average, by 0.48 meter each year.

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The available regression equation is: Predict height= 0.29 + 0.48 (age).

Here, the predict height is dependent variable and the  age is in-dependent variable.

Intercept = 0.29

Slope      = 0.48

The given regression equation indicates the y on x model and the intercept coefficients of the regression equation is 0.29 and the slope is 0.48.

Pls help I’ll put in a picture

Answers

Answer:

2 < x < 26

Step-by-step explanation:

The length of the side of a triangle must be less than the sum of the lengths of the other two sides of a triangle.
Therefore:

12+14>x

x<26

However, the following must also be true:

x+12>14 (The sum of x and 14 will always be greater than 12 because 14>12, so we don’t need to include that in the inequality)

So, x>2.
This means that the answer is 2<x<26

Three years ago Joseph was three times older than Agnes in 2 years times the sum of their ages will be 75 years. Determine their present ages

Answers

Answer:

Hey, answer is attached.

Step-by-step explanation:

Hope this helps.

Write an equation that represents the line. Use exact numbers. hurry please!!

Answers

Answer:

y=3/4x-9/2

Step-by-step explanation:

y=mx+c

m=dy/dx

=-3/-4

=3/4

-3=(3/4*2)+c

-3=3/2+c

-9/2=c

If this trapezoid is moved through the translation (x+3,y-2), what will the coordinates of B be?

Answers

The coordinate of the vertex B after the transformation of the given trapezoid is (-2, 2).

How to transform a graph of the function?

The graph of a function can be transformed by either shifting it in the right, left, up or down.

When the transformation is rightwards, the function becomes as f(x - a).

For left shifting it is f(x + a).

As per the given graph, the coordinate of vertex B is (-5, 4).

After the translation (x, y) → (x + 3, y - 2), the new coordinate can be obtained as,

(-5, 4) → (-5 + 3, 4 - 2)

⇒ (-2, 2)

Hence, the coordinate of B after the transformation is (-2, 2).

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PLEASE HURRY!
Write and solve the inequality that represents negative one eighth is less than the product of negative two thirds and a number.

A: negative one eighth is less than negative two thirds y where y is less than three sixteenths
B: negative one eighth is less than or equal to negative two thirds y where y is greater than negative three sixteenths
C: negative two thirds is less than negative one eighth y where y is less than one twelfth
D: negative two thirds is greater than negative one eighth y where y is greater than negative one twelfth

Answers

The solution to the inequality statement is x < 3/16

How to determine the solution to the inequality?

From the question, we have the following parameters that can be used in our computation:

negative one eighth is less than the product of negative two thirds and a number.

Express as numbers and operators

So, we have

-1/8 < -2/3x

Divide both sides by -2/3

So, we have the following representation

1/8* 3/2 > x

Evaluate the produdts

3/16 > x

Rewrite as

x < 3/16

Hence, the solution is x < 3/16

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Solve the inequality 3(x-2) + 1 ≥x + 2(x + 2).
O A. x≤ 4
OB. x ≥-5
OC. no solution
OD. all real numbers

Answers

Answer: no solution

Step-by-step explanation:

1. distribute through both sides to get 3x-6+1 ≥ x+2x+4

2. then combine like terms to get 3x-5 ≥ 3x+4

3. then make sure like terms are together on either side -> 3x -3x ≥ 4+5 ->

4. since the 3x-3x = 0, there are no solutions

Quadrilateral ABCD with vertices A (-3,3), B (8,8), C (6,2), and D (0,0) is shown. You want to reflect quadrilateral ABCD in the vertical
line that passes through the midpoint of CD. Graph the line of reflection and the image after the reflection.
Polygon
here to search
Line
14
13-
12-
11-
10-
9
7
6
5
Undo
Redo
x Reset
13
calculate
gra

Answers

The line of reflection and the image of after reflection graph is attached below  

What is line of reflection ?

The picture is consistent with the preimage when reflecting a figure in a line or a point. Every point on a figure is translated into an image by a reflection across a set line. The term "line of reflection" refers to the fixed line.

The line of reflection is a line across which an image will reflect. Every point in a figure is said to reflect the other figure if and only if it is equally spaced from every corresponding point in the other figure. The image that is reflected should be identical in size and shape but face the opposite way.

Graph the quadrilateral. By inspection, you can tell where the midpoint is. (see attachment 1)

Now, I'll draw a line through it. (see attachment 2)

To reflect across a line, think about the points traveling across the line the same number of spaces the point is from the line. For example, point A is three away from the line. So, A' will be 3 away from the other side. The coordinates will be at (-3,2). (see attachment 3).

Do the same for the other points, and you'll have your image.

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Paul pent $72 on 4 day-lilie and 7 geranium. Megan pent $128 on 10 day-lilie and 11 geranium. Find the cot of one day-lily and the cot of one geranium

Answers

The cost of one day-Lilly is found to be $4 and the cost of one geranium is found to be $8. Therefore, Paul spent about $16 for day-Lilly and $56 for geranium. And Megan spent about $40 for day-Lilly and $88 for geranium.

Two or more algebraic equations that have a common variable and are solved simultaneously are referred to as simultaneous equations. We can find the answers to both unknowns if we have two separate equations with the same two unknowns in each. Here, we'll employ the addition-and-subtraction or elimination method.

Let's consider the cost of day-Lilly as x and the cost of geranium as y. The cost spent by Paul is written as 4x+7y=$72 and Megan is written as 10x+11y=$128.

Solving these two equations for x and  y,

[tex]\begin{aligned}40x+70y = \$720\\\underline{40x+44y=\$512}\\26y=\$208\\y=\$8 \end{aligned}[/tex]

Substitute the value of y in equation 4x+7y=$72 to get the value of x,

[tex]\begin{aligned}4x+7(8)&=\$72\\4x&=\$16\\x&=\$4\end{aligned}[/tex]

The answers are $4 and $8.

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Draw a line PQ and take a point A outide it. Uing ruler and compa , draw a line through A parallel to PQ

Answers

Using a ruler and compass, draw a line through point A parallel to line PQ by first drawing a line segment from A to any point on PQ. Then, use the compass to draw an arc from the other end of the line segment to the other point on PQ. Finally, use the ruler to draw a line through the arc, parallel to PQ.

Drawing a line parallel to an existing line can be done using a ruler and compass. First, draw a line segment from point A to any point on line PQ. Then, use the compass to draw an arc from the other end of the line segment to the other point on PQ. This arc should intersect with the first line segment. Finally, use the ruler to draw a line through the arc, parallel to PQ. This line will be parallel to PQ since it is the same distance from each point on the original line. The use of the compass ensures that the resulting line is the same distance away from the original line throughout, thus resulting in a line parallel to PQ.

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10. dice when a pair of dice is rolled, what is the probability tha tthe sum of the dice is 5, given that exactly one of the dice shows a 3?

Answers

The probability sum of the dice is 2/11.

Let A be the event that the sum of dots is 5, then

A={(1,4), (2,3), (3,2), (4,1)}

n(A)=4

And, B is the event that one die shows a "one"

B={(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (3,1), (4,1), (5,1), (6,1)}

n(B)=11

The Event that some of the dots are five and one of the die shows "one".

A intersection B = {(1,4), (4,1)}

Since n(A) = 36 (thirty-six possible samples of two dice)

P(A)=4/36

P(B)=11/36

P(A intersection B)=2/36

So, the required probability is

P(A|B)=P(A intersection B)/P(B) =2/11

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A group of students is asked if they travel
Students travelling Students not by car
travelling by car 14 to school by car. Here
are the results. 11 a) What percentage of
these students do not travel to school by
car? % No of students b) 14 of these
students travel by car. Number of cars in
one car Some of these travel in the same
car. Fill the missing frequency in the table.
c) Work out the mean number of students
in each car

Answers

The percentage of those that don't travel by car will be 44%.

How to calculate the percentage?

It's important to note that a percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.

In this case, 14 students travel by car and 11 don't travel by car. The total number of students will be:

= 11 + 14.

= 25

Therefore, the percentage of those that don't travel by car will be:

= 11 / 25 × 100

= 44%

The percentage is 44%.

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you round_trip drive to work is 4 3/10 miles how many miles do you drive to and from work in 3 days?​

Answers

Answer:

12.9 or 12 9/10

Step-by-step explanation:

4 3/10 or 4.3 x 3

12.9 or 12 9/10

PLS HELP

What is the range of f(x) = |x| + 7?

−7 ≤ y < ∞
−∞ < y ≤ −7
0 ≤ y < ∞
7 ≤ y < ∞

Answers

The range of the function f(x) = |x| + 7 is given by the option presented as follows:

7 ≤ y < ∞.

How to obtain the range of a function?

The range is composed by the set containing all the values assumed by the output of the function, that is, all the numeric values assumed by the function.

In the context of this problem, the function is defined as follows:

f(x) = |x| + 7.

The parent function is the absolute value function g(x) = |x|, which gives the distance of a point x from the origin, assuming real values of at least 0, as a distance cannot be negative.

The addition by 7 means that the parent function was translated up seven units, meaning that the minimum value assumed by the range is seven, and the range of the function is given by the last option given as follows:

7 ≤ y < ∞.

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Joe asked a bank teller to cash a $570 check using $20 bills and $50 bills, If the teller gave him a total of 15 bills, how many of each type of bill did he receiver

Answers

Answer:

9 $50 bills and 6 $20 bills

Step-by-step explanation:

Let f = number of $50 bills.

Let t = number of $20 bills.

f + t = 15

50f + 20t = 570

f = 15 - t

50(15 - t) + 20t = 570

750 - 50t + 20t = 570

-30t = -180

t = 6

f + t = 15

f + 6 = 15

f = 9

Answer: 9 $50 bills and 6 $20 bills

Is anyone good at this math

Answers

Answer:

x = 3

Step-by-step explanation:

4 + x = 7  Subtract 4 from both sides of the equation

4 - 4 - x = 7 - 4  Simplify

x = 3  X equals 3

Answer:

x = 3

Step-by-step explanation:

4 + x = 7

x + 4 - 4 = 7-4 = 3

x = 3

To solve for x, subtract 4 from both side of the equation.  This leaves x by itself on the left side of the equation.  Next subtract 4 from 7 to get the solution, x = 3.

What is a written description of x − 14?

Answers

Answer:   The written description of x - 14 is given as the difference of variable x and integer 14 gives x -14.

Step-by-step explanation:

Calculate the answer using a math operator is referred to as a mathematical operation.

Basic mathematical operations are addition, multiplication, subtraction and division.

Let x be a variable,

And 14 is an integer.

By using mathematical operations,

The difference of x and 14 can be given as,

x - 14.

You buy the following from Walmart:
1 puzzle for $8, 1 TV for $350, 1 cutting board for $9, and 1 blender for $25
What is the Subtotal: $
You have a 10% off coupon, how much do you save: $
What is the new Subtotal: $
Sales tax is 5%: $
What is the total: $
4

Answers

Answer:

You buy the following from Walmart:

1 puzzle for $8, 1 TV for $350, 1 cutting board for $9, and 1 blender for $25

$8 + $350 + $9 + $25What is the Subtotal: $392

You have a 10% off coupon,  

392 * 0.1 = $39.2How much do you save: $39.2

What is the new Subtotal:

$392 - $39.2 = $352.8$352.8

Sales tax is 5%: $

352.8 * 0.05 = $17.64$17.64

What is the total:

$352.8 + $17.64 = $370.44$370.44

Step-by-step explanation:

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which of the three methods of assigning probabilities is used when we are dealing with sampling (as a method of determining probabilities)? no need to explain.

Answers

Random sampling methods of assigning probabilities is used when we are dealing with sampling.

Random sampling is a method of assigning probabilities used when dealing with samples of a population. It involves randomly selecting a sample from the population and then using that sample to estimate the probabilities of different outcomes. This is done by calculating the proportion of the sample that falls into each category. For example, if you are trying to determine the probability of a certain outcome, you would randomly select a sample from the population and then count how many of the individuals in the sample fall into that category. The probability of the outcome would then be calculated by dividing the number of individuals in that category by the total number of individuals in the sample.

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If f(x)=|x−5| 2, find f(3). responses 10 10 6 6 4 4 0

Answers

If the function f(x) = |x-5| + 2, then the value of f(3) is 4

The function

f(x) = |x-5| + 2

The function is defined as the mathematical statement that shows the relationship between the independent variable and the dependent variable. The function consist of different variables, numbers and mathematical operators

Here the function consist of the absolute value symbol.

|-a| = a

The absolute value of the positive and the negative number will be always positive.

The function is f(x) = |x-5| + 2

Then,

f(3) = |3-5| + 2

= |-2| + 2

= 2 + 2

= 4

Therefore, the value of f(3) is 4

I have answered the question in general, as the given question is incomplete

The complete question is:

If f(x)=|x−5| + 2, find the value of f(3).

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According to the american dental association, 8% of adults have never had a cavity. A dental graduate student contacts an srs of 1000 adults and calculates the proportion p in this sample who have never had a cavity

Answers

The proportion of people who never had a cavity is 0.92.

What are ratio and proportion?

A ratio is a comparison between two similar quantities in simplest form.

Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant k and vice versa.

In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.

Given,  8% of adults have never had a cavity. A dental graduate student contacts an srs of 1000 adults.

8% of 1000 is,

= (8/100)×1000.

= 80.

Now, The proportion of people who never had a cavity is (1000 - 80)/100.

= 920/1000.

= 92/100.

= 0.92 proportion of people never had a cavity.

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A company makes a loss of 2 million dollars in its first year of trading. In the following two years it makes a profit of $625 000 per year. What is the average profit or loss per year made by the company over the three years?

Answers

Answer: They lose $250000 per year over the three years!

Step-by-step explanation:

First, find the total profit for the two following years

Take $625000 times 2 = $1250000

Next, find the total they made in 3 years

Take -$2000000 of the first year + $1250000 = - $750000

Now we find their average profit per year

Take -$750000 divided by 3 = -$250000

They lose $250000 per year over the three years

What is the product of 5x(x - 8) ?

Answers

Answer:

5x^2 - 40x

Step-by-step explanation:

5x (x-8)

5x^2 - 40x

5x(x-8)
5(x -8) x(x-8)
5x - 40 x^2 - 8x
Answer: x^2 - 40x - 40

A rectangular yard measuring 40ft by 53ft is bordered (and surrounded) by a fence. Inside, a walk that is 4ft wide goes all the way along the fence. Find the area of this walk. Be sure to include the correct unit in your answer. helpppppp plssss for my final

Answers

Area of the walk that goea around the rectangular yard is 680 sq. ft.

What is a Rectangle ?

A quadrilateral with parallel sides that are equal to one another and four equal vertices is known as a rectangle. It is also known as an equiangular quadrilateral for this reason.

Rectangles can also be referred to as parallelograms since their opposite sides are equal and parallel.

The rectangle's characteristics are listed below:

There are four vertices and four sides.Every vertex has an angle of 90 degrees.Equal and parallel sides are on the opposing sides.Intersect each other diagonallyThe perimeter is equal to double the length plus width of the object.the product of its length and width determines its area.It has four right angles and is a parallelogram.All inner angles added together equal 360 degrees.

Dimension of the yard is

width = 40 ft

length = 53ft

Dimension of the yard without the walkway is

Width =40 - 4*2 = 40 - 8 = 32 ft

Length = 53 - 4*2 = 53 - 8 = 45 ft

Area of the yard = Width * Length = 40 * 53 = 2120 sq. ft

Area of the yard wtihout the walk = 32 * 45 = 1440 sq. ft

Therefore the area of the walk is = Area of yard - Area of yard without walk = 2120 = 1440 = 680 sq. ft.

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How many lines of symmetry does the figure have?

0
1
2
3

Answers

Answer:

1

Step-by-step explanation:

because you can only cut it in a certain way that both pieces are the same measurements

What D
Evaluate each expression for the giver
3x² when x is 10

Answers

Answer:

3x²

= 3(10)²

= 3(100)

= 300

Step-by-step explanation:

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someone with great knowledge of this please help its due asap please help.

Answers

Answer: x = 2 hours y= 7 hours = 9 hours a week, 80$ a week

Step-by-step explanation:

5$x2=10$   10$x7=70$ 70$ + 10$ = 80 $.

hopefully, maybe that helps for the first question.

What is the answer to this question

Answers

Answer:

Step-by-step explanation:

a because if you divide  everything under the fraction number you get answer a

The solution for the given expression is x = 4³/₅. The correct option is B.

What is an expression?

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the expression is x - 17⁴/₅ = -13¹/₅. The given expression will be solved as,

x - 17⁴/₅ = -13¹/₅

x = 17⁴/₅ -13¹/₅

x = 89 / 5 - 66 / 5

x = 23 / 5

x = 4³/₅

The expression will be equivalent to x = 4³/₅.

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What i the equation of the line that pae through the point (-1,5)(−1,5) and ha a lope of -3

Answers

The equation of the line is y = -3x + 2.

What is the slope of a line?

A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate.

Both the net change in the y-coordinate and the net change in the x-coordinate are represented by Δy and Δx, respectively.

As a result, m = change in y/change in x = Δy/Δx is the formula for the change in y-coordinate with respect to the change in x-coordinate.

where "m" represents a line's slope.

Given that, the line passes through the point (-1,5) with slope of -3.

The equation of line passes through (x₁, y₁) with slope m is

y -  y₁ = m(x - x₁)

Putting x₁ = -1, y₁ = 5 and m = -3.

y - 5 = -3(x - (-1))

y - 5 = -3x - 3

y = -3x  + 2

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Graph the image of this figure after a dilation with a scale factor of 3 centered at
(−7, −6). Use the polygon tool to graph the dilated figure. *picture Below*

Answers

Answer:

See the picture below

Step-by-step explanation:

You start from the center given (-7,-6),  then count how many spaces from the center to that point.  Take that number and triple it to find the new point.  I drew lines so that you could see the path of two of the points.  

The path that I did not draw was from the point (-3,-2).  If you start at (-7,-6) you will have to move 4 spaces to the right and 4 spaces up to get to (-3,-2)  Now triple that.  You will move 12 spaces to the right and 12 spaces up for the new point of (5,6)

Other Questions
Which of the following statements about the nucleus is true? magine you are Violet from the Goalden Girls and mentoring a new UMA student when using the steps of the scientific method, which step would you use immediately after the development of a hypothesis? during her interview, margo realized that the organization seemed to foster an aggressive culture. what three characteristics would indicate this? Python formats all floating-point numbers to two decimal places when outputting with the print statement. True or False if the cost of direct aggression is too high, the aggression may be redirected toward whomever or whatever is available. this type of response is known as which of the following represents the maximum amount of time that a dns server or resolver is allowed to cache the result of a forward lookup? select the correct statement about executive compensation plans involving stock. the total amount of compensation expense for a restricted stock award plan is recognized when the stock is issued. the total amount of compensation expense for a restricted stock award plan is determined at the grant date. for stock-appreciation rights plans payable in cash, compensation expense is recognized only during the service period. for stock-appreciation rights plans payable in cash, compensation expense recognized in any given reporting period cannot be negative. a sociologist encounters a group of people and wants to study whether their group constitutes a religion. which question incorporates a sociological definition of religion? Select the statements below that correctly describe the flow of costs in a merchandiser's accounting cycle. (check all that apply.)O Merchandise that is sold becomes an asset reported on the balance sheet. O Beginning inventory net purchases Merchandise available for sale For the following pairs of voltages and currents, indicate whether the element involved is a capacitor, an inductor, or a resistor, and find the value of C, L, or R if sufficient data are given:a.v = 550 sin(377t + 50) i = 11 sin(377t - 40)b.v= 36 sin(7541 - 80) i = 4 sin(754t - 170) c.v = 10.5 sin(wt - 13) i = 1.5 sin(wt - 13) 2, 7, 4, 2, 3, 6, 11MEAN:MEDIAN:MODE:RANGE: If you have an average of 31 and you have the numbers 63,53,20,10, what is the missing value? Which of the following techniques is the best fit for monitoring traffic on switches with large volumes of traffic? A) SFTP;B) portTAP C)SRTP a nurse is caring for a client diagnosed with schizoid personality trait. when developing a plan of care for the client, which would a nurse most likely include? type of loan/investment annual rate of return (%) automobile loans 9 furniture loans 11 other secured loans 12 signature loans 13 risk-free securities 10 What is true about an iris scan?O It picks out the unique characteristics of each person's iris.OIt would not require a database.O Many police departments are currently using iris scans for identifying missing persons.O All of the above jose lives in florida. there are laws in the state to protect him from being forced to join a union in order to obtain or keep a job. what kind of laws are these? write a program that reads the student information from a tab separated values (tsv) file. the program then creates a text file that records the course grades of the students. each row of the tsv file contains the last name, first name, midterm1 score, midterm2 score, and the final score of a student. a sample of the student information is provided in studentinfo.tsv. assume the number of students is at least 1 and at most 20. assume also the last names and first names do not contain whitespaces. the program performs the following tasks: read the file name of the tsv file from the user. open the tsv file and read the student information. compute the average exam score of each student. assign a letter grade to each student based on the average exam score in the following scale: a: 90 Diego is making sandwiches for a picnic. He uses 2 slices of cheese to make each sandwich,and he has a package of cheese with 24 slices.Write an equation that shows how the number of slices of cheese remaining, y, depends onthe number of sandwiches Diego makes, x.