please help me with this question
step by step please

The area enclosed in the figure of the graph of r² = sin(2θ) is

1 square units.

A polar equation of a curve is usually expressed in polar coordinates and written with {r} as a function of {θ}.

Given is a polar equation as follows -

r² = sin(2θ)

Area enclosed in the figure is equivalent to -

{A} = 2{∫1/2r²dθ}

{A} = ∫r²dθ

{A} = ∫sin(2θ) dθ

{A} = {- cos(2θ)/2}     (integral limit -> 0 to π/2)

{A} = {- cos(π)/2 + cos(0)/2}

{A} = 1/2 + 1/2

{A} = 1

Therefore, the area enclosed in the figure of the graph of r² = sin(2θ) is

1 square units.

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Four types of discontinuity of a function are as follow:

Jump discontinuity , infinite discontinuity, endpoint discontinuity, and Mixed discontinuity.

As given in the question,

Four types of discontinuity are given by :

1. Jump discontinuity :

In this type of discontinuity both side of limit that left hand side and right hand side limit exist but both represents the different value .

2. Infinite discontinuity :

In this case both the side of limit exist but are reaches to infinity.

3. Endpoint discontinuity:

In this case only one side either left or right side of limit exist.

4. Mixed discontinuity:

In this case at least one side of limit either right or left does not exist.

Therefore, the four types of discontinuity are :

Jump discontinuity , infinite discontinuity, endpoint discontinuity, and Mixed discontinuity.

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Answer:

Last one

Step-by-step explanation:

Answer:

The slope of this line (m) is 5

Step-by-step explanation:

Slope is the change in y over the change in x.

The y values are 80 and 50 (6,50) (12,80)  You find the change by subtracting these values

80 -50 = 30

The x values are 12 and 6 (6,50) (12,80)  You find he change by subtracting these values.

12 - 6 = 6

[tex]\frac{30}{6}[/tex]  this reduces to 5

The probability that Sid takes one counter of each color is 0.5.

To find the probability that Sid takes one counter of each color, we need to know the total number of possible outcomes when Sid takes two counters from the bag. Since the order in which Sid takes the counters does not matter, there are two cases to consider:

Sid takes a green counter first and a blue counter second. There are 8 green counters and 3 blue counters, so there are a total of 8 * 3 = <<8*3=24>>24 outcomes in this case.

Sid takes a blue counter first and a green counter second. There are 3 blue counters and 8 green counters, so there are a total of 3 * 8 = <<3*8=24>>24 outcomes in this case.

In total, there are 24 + 24 = <<24+24=48>>48 outcomes when Sid takes two counters from the bag.

To find the probability that Sid takes one counter of each color, we divide the number of successful outcomes (24 in each case) by the total number of outcomes (48). This gives us a probability of 24/48 = 1/2 = 0.5.

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The equations y = 0 and y = -6 have no solution.

Given equation,

y = 0

y = -6

We will plot these lines on the graph.

According to the graph, the x-axis is represented by the equation y = 0, and a line parallel to the x-axis is represented by the equation y = 6. Thus, it is clear that both lines are parallel, and even if we extended either line in either direction, there was no chance that the two lines would ever collide. However, we are aware that the intersection of the two lines is where the solution of the pair of lines is defined.

Hence, No solution to the lines can be found here.

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The number where the digit 6 have a value that is 10 times as great as the digit 6 in the number 62,045 is A. 640,488.

It should be noted that a place value is the value that is represented based on the position of a number.

In this case, the digit of 6 in 62,045 is 60000. From the options, the digit of 6 in 640488 is 600000. This is 10 times the value.

Therefore, the number where the digit 6 have a value that is 10 times as great as the digit 6 in the number 62,045 is 640,488. The correct option is A.

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Find the total digits' factorial. Add the factorial together and save it as a variable (s). Compare the total to the specified number (N). The number (N) is a special number if the total equals the number, else it is not.

An element that can be represented by the sum of two numbers, one of which is the opposite of the other, is referred to as a peculiar element. similar to Array is 22 and 121. In this case, 22 = 11 + 11, and 121 = 92 + 29. Consequently, both elements are unique. The PHP count() or sizeof() functions can be used to determine the number of values or elements in an array.

When a variable is initialized with an empty array, the count() and sizeof() functions return 0, but they may also return 0 when a variable is not set.

How many special integers are there in an array:

function findMagicNumber(arr[0...n])

spell n:= NaN

Then magic n:=arr[0] if n = 1

If n is more than 1,

then quicksort(arr) old n:= arr[0]

for i:= 1 to n cur n:= arr[i] repeat:= 0

repeat:=repeat plus one

If repeat is 1,

then magic n:=old n, old n:=cur n, and magic n:=repeat:=0

return magic n.

If cur n old n,

then repeat is 1,

then if repeat = 1

then magic n:=old n, cur_;

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Yes, 5 is a all real number.

A real number is a number that can take on any value on the real number line, which is an infinite line that extends from negative infinity to positive infinity. Real numbers are used in mathematics to represent quantities such as distance, area, and time. They can also be used to represent irrational numbers, such as pi, and numbers with recurring decimals, such as 1/3.

A real number is any number that is either a rational number (fractions and whole numbers) or an irrational number (numbers that cannot be expressed as a fraction or a whole number). This includes all integers, fractions, and decimals. 5 is an integer, so it is included as a real number.
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Answer:

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

Given:

Perimeter is:

or

The perimeter is at most 96 cm (not greater than):

The matching choice is A.

To graph a function with two variables, you need to plot the points that satisfy the function in a coordinate system.

For example, suppose you have a function f(x,y) = x^2 + y^2. To graph this function, you can choose a set of values for x and y that satisfy the function, and plot these points in the coordinate system.

For example, if you choose x = 1 and y = 2, then the point (1,2) satisfies the function because f(1,2) = 1^2 + 2^2 = 1 + 4 = 5. Similarly, if you choose x = -2 and y = 3, then the point (-2,3) satisfies the function because f(-2,3) = (-2)^2 + 3^2 = 4 + 9 = 13.

You can repeat this process for a range of values for x and y to plot more points in the coordinate system. As you plot more points, you will start to see a pattern emerge, which is the graph of the function.

Note that the graph of a function with two independent variables will be a surface in three-dimensional space, rather than a curve in two-dimensional space like the graph of a function with only one variable.

--The question is incomplete, answering to the question below--

"How do you graph a function with two variables?"

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The graph of  k x = 5 will be a line parallel to Y axis and the graph of k x < 5 will be the region where the value of x does not exceed 5/k.

Linear Inequalities are the expressions which have a left and a right hand side connected with inequality signs like >, <, ≥ and ≤.

Consider k x = 5

⇒ x = 5/k

This means that, for a nonzero constant k, the value of x will be the same throughout, which is 5/k.

If k = 1, then the value of x will be 5 throughout.

If k = 2, then the value of x will be 5/2 = 2.5 throughout.

and so on.

So the graph of k x = 5 will be a line parallel to the Y axis passing through the point x = 5/k for some constant k.

Now let us consider k x < 5.

⇒  x < 5/k

This means that for any nonzero constant k, the value of x will not be equal or never exceed 5/k.

If k = 1, then the value of x will be less than 5 throughout.

If k = 2, then the value of x will be less than 5/2 = 2.5 throughout.

and so on.

So the graph of k x < 5 includes the region where value of x does not exceed 5/k.

Hence the graph of  k x = 5 and k x < 5 is a line parallel to Y axis and the region which does not exceed 5/k respectively.

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The total length of ribbon that Leah bought is equal to 358.4 inches.

In Mathematics, measurement can be defined as an act or process through which the size, weight, magnitude, quantity, volume (capacity), dimensions (length and width), or distance traveled by a physical object or body is taken, especially for the purpose of an experiment.

In order to determine the total length of ribbon that was purchased by Leah, we would have to multiply the length of the strips of ribbon by the length of each of the strips as follows;

Total length of ribbon = Length of the strips of ribbon × Length of each of the strips

Substituting the given parameters into the formula, we have;

Total length of ribbon = 32 × 11.2 inches

Total length of ribbon = 358.4 inches.

In this context, we can reasonably infer and logically deduce that total length of ribbon that was purchased by Leah is equal to 358.4 inches.

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To solve a 2x2 matrix equation of the form Ax = b, where A is a 2x2 matrix, x is the variable (a column vector), and b is a known column vector.

You can use the following steps:

A^(-1) = (1/det(A)) * adj(A)

where det(A) is the determinant of matrix A and adj(A) is the adjugate of matrix A. The transposition of a matrix's cofactor matrix is adjugate. The cofactor matrix is a matrix of the determinants of the minors of the original matrix, each of which is multiplied by a cofactor (-1)^(i+j). The minors of a matrix are the determinants of the square submatrices formed by deleting one row and one column from the matrix. The determinant of a matrix is a scalar value that can be computed from its elements.

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Given that value of y exceeds a, then value of a must be smaller than -8.2.

The provided equation is-

(13-20- A* 13y)= 168* 13-22

We get,

By 260, divide both sides.

Y has a value of -8.265.

Thus, provided that y exceeds a, then value of a must be smaller than -8.2

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The correct question is-

What is the value of (a,y) in (13-20- A* 13y)= 168* 13-22?

The acceleration of the box is 4m/s².

Acceleration is a vector quantity as it has both magnitude and direction. It is also the second derivative of position with respect to time or it is the first derivative of velocity with respect to time. The change in the velocity of an object could be an increase or decrease in speed or a change in the direction of motion.

We know the frictional force f=μN where N=normal force = mg

Given that,

Frictional force μ = 250N

Hence F(net)= F(app)- f = 450 - 250 = 200 N

We know Force(F)=ma

a=200/50 = 4m/s²

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We know the frictional force f=μN where N=normal force = mg

Given that,

Frictional force μ = 250N

Hence F(net)= F(app)- f = 450 - 250 = 200 N

We know Force(F)=ma

a=200/50 = 4m/s²

Answer:

Squares have to have the same shape and size to be congruent. Therefore, not all squares are congruent, since not all of them are the same size. … This means that they have the same shape, although not necessarily the same size.

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Step-by-step explanation:

As per the unitary method, the linear equation represents the number of minutes Denzel still has to practice is N(x) = 210 - 30x

The term unitary method refers a process of finding the value of a single unit, and based on this value.

Here we have given that Denzel must practice the piano for 210 min each week. he practices for 30 min each day

And we need to find linear equation represent the number of minutes Denzel still has to practice after x days

As from the given question we know that Denzel must practice piano for 210 minutes each week.

Therefore, the total practice needed = 210 minutes

And the total minutes practicing per day = 30 minutes

Here let us consider x be the number of days practiced

Then the total minutes practices after n days = 30x

So, the total remaining minutes is calculated as,

=> 210 - 30x

Therefore, the number of minutes Denzel still has to practice after x days is written as, N(x) = 210 - 30x

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It would cost 0.72 pounds to buy the envelopes from VALUEWORLD

first of all, we would have to calculate what the cost would be for LETTER 2GO

This is 450 / 25 x 3.29

= 59.22 dollars

The next option would be for us to solve for the cost for Value 2 world.

This is given as 450 / 30 * 1.95*2

= 58.50 dollars

The cost of getting the envelope from value world would be given as 59.22 - 58.50

= 0.72 pounds

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The total of their age be in three years time is 40 years.

As per the given data:

The total of the age of Ann, Bob and Chri is 31 years.

Let the present age of Ann is 'x' years.

Then the age of Ann after 3 years will be x+3

Let the present age of Bob is 'y' years.

Then the age of Bob after 3 years will be y+3

Let the present age of Chri is 'z' years.

Then the age of Chri after 3 years will be z+3.

The total of the age of Ann, Bob and Chri is 31 years.

x + y + z = 31.....(i)

The total of the age of Ann, Bob and Chri after 3 years is ( x + 3 + y + 3 + z + 3 ) years.

= ( x + 3 + y + 3 + z + 3 )

= ( x + y + z + 9 )

From equation (i)..... ( x + y + z = 31 )

= 31 + 9

= 40 years

Therefore the answer is 40 years.

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Answer:

Fair dice mean that each of the faces has the same probability of landing facing up. A standard 6-sided die, for example, can be considered “fair” when each of the faces has the same probability of ⅙.

Step-by-step explanation:

Answer:

22/7 or 3.14

the value of pie is 22/7 or if you write it in decimals it will be 3.14.

The indicated critical value of z₀.₁₁ is 0.54.

What does it mean round to two decimal places?

The second place to the right of the decimal point, or the hundredths place, is used to round a decimal value to two decimal places. For instance, you can round 2.83620364 to two decimal places as 2.84 and 0.7035 to two decimal places as 0.70.

A crucial value is the test statistic's value that establishes a confidence interval's upper and lower boundaries or the level of statistical significance for a given test.

The critical value of z₀.₁₁ is z₀.₁ ₊ ₀.₀₁ = 0.5438

The round to two decimal places of 0.5438  is 0.54.

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A unit rate is a rate with a denominator of one.

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A equation of the tangent line to the curve is y = 3x + 3

The term tangent line in math is calculated as an equation of the tangent line we have to find the derivative of the function and its value at the given point.

And then we have to the function given is a product of an exponential and cosine function. We will have to use product rule.

Finally, we have to write the equation of tangent line by point slope form.

Here we have the curve equation as,

=> y = 3eˣcos(x)

Now, we have to calculate the derivative y' from the given equation, then we get,

=> y' = = 3(eˣ (−sin x) + (cos x) eˣ)

Now, it can be simplified as,

=>y' = 3eˣ(cos x − sin x)

Here we have given that the the slope of the tangent line at (0, 3), then the value of

=> 3e⁰(cos0−sin0) = 3(1−0) = 3

Then the equation is written as

=> y − 3 = 3(x − 0)

=> y = 3x + 3

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The answer is data labels tool.Data Labels tool is used make chart 1 look like chart 2.When you select the chart and right click and select the option to add data labels.So the required labels will be displayed.

A chart is a visual display of data in which the data is displayed by symbols such as bars in a bar chart or lines in a chart.It can help people to understand information easily.

There are following types  of charts.

column charts

line charts

bar  charts

area charts

pie charts

Now for opening chart tools in excel.you can

click the insert tab and then click the arrow next to chart.click chart type and then double click the chart you want to add.So you can insert chart into excel sheet.

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If the incomes in a certain larger population of college teachers have a normal distribution with mean of $60,000 and standard deviation of $5,000.the probability that their average salary exceeds $65,000 is 0.0228.

Probability is the tendency or likelihood that an event will happen.

First step is to find the standard deviation

Standard deviation= $5,000/√4

Standard deviation= $5,000/2

Standard deviation= $2,500

Second step is to find the z -score

Z= 65,000 - 60,000/2500

Z= 5,000/2500

Z= 2

Now let find the  pvalue of 2

pvalue of 2 = 0.0228

Therefore the probability is 0.0228.

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The given equation represents a straight line equation with slope [m] = 2 and [y] - intercept as 8.

Given is the linear equation as follows -

y = 2x + 8

The given equation is as follows -

y = 2x + 8

The given equation is a straight line with a slope of [m] = 2. The [y] - intercept is equivalent to 8. This means that the graph cuts the [y] axis at the point (0, 8).

Therefore, the given equation represents a straight line equation with slope [m] = 2 and [y] - intercept as 8.

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Answer:

The roots are imaginary.

Step-by-step explanation:

⭐ What is "the nature of the roots"

⭐What are the different types of "the nature of the roots"?

⭐How do we determine "the nature of the roots"?

To solve this problem, substitute the values of the coefficients of the given quadratic equation into the quadratic formula:

[tex]x =\frac{ -6+/-\sqrt{6^2-4(2)(30)} }{2(2)}[/tex]

Now, compute only the discriminant ([tex]b^2-4ac[/tex]).

[tex]b^2-4ac = 36-4(60)[/tex]

[tex]b^2-4ac = 36-240[/tex]

[tex]b^2-4ac = -204[/tex]

[tex]b^2-4ac[/tex]< 0. Therefore, the roots are imaginary.