find the area of the region enclosed by one loop of the curve. r = sin(6θ)

Answer:

Step-by-step explanation:

Two right-angled triangles are said to be congruent to each other if the hypotenuse and one side of the right triangle are equal to the hypotenuse and the corresponding side of the other right-angled

Answer:

[tex]\displaystyle x < \frac{12}{7}[/tex]

Step-by-step explanation:

This is an inequality, not an equation. Notice the sign is a "less than" sign and not an "equal" sign. You still solve it like a normal equation, however:

[tex]\displaystyle 7x-2 < 10\\\\\rightarrow 7x < 12\\\\\rightarrow x < \frac{12}{7}[/tex]

The order of the quantities in an inequality matters. Therefore, it is true.

An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The most frequent application is to size-compare two numbers on a number line.

When resolving an inequality, you can do one of the following: Add the same amount to each side; Subtract the same amount from each side; Multiply or divide each side by the same positive amount. You must flip the inequality symbol if you multiply or divide each side by a negative number.

Therefore, the order matters.

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Therefore , the solution of the given problem of trigonometry comes out to be  B = arcsin(9/14) - 180° = 140.0°.

Correlations between triangles' angles and sides are studied in the branch of mathematics known as trigonometry. Since every straight-sided form may be reduced to a collection of triangles, trigonometry can be found throughout geometry. The relationships between trigonometry and other branches of mathematics, in particular calculus, real or complex, infinite series, logarithms, and infinite series, are astonishingly complicated.

Here,

There are two potential solutions because the supplied angle is opposite the given side that is the shortest.

Using the sine law,

B = b/asin(A)arcsin(9/7sin(30°))arcsin(9/14)

Angle B may take on the following values:

B is equal to arcsin(9/14) = 40.0°.

B = arcsin(9/14) - 180° = 140.0°

Therefore , the solution of the given problem of trigonometry comes out to be  B = arcsin(9/14) - 180° = 140.0°.

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Answer : if each topping is 1.25 then multiply that by 3 because there's 3 toppings on the pizza and if the total was 16.25 the original price of the pizza is 12.5. I hope this was the answer you were looking for a good luck :)

Step-by-step explanation:

The distance that Nick has to drive to reach Kansas will be at least 250 miles.

Inequalities are simply created through the connection of two expressions. In this case, it should be noted that the expressions in an inequality are not always equal. Inequalities implies that the expressions are not equal. Here, they are denoted by the symbols ≥ < > ≤.

Since Nick is driving from Brookville to Kansas City, a distance of more than 325 miles and after driving 75 miles, Nick stops for gas.

An inequality to determine how much farther Nick has to drive to reach Kansas City will be:

x > 325 -75

x > 250

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Plotting method is the graphical representation of mathematical expression.

A plot is a graphical representation of a list of data. Besides, a plot is the graphical analysis of mathematical expressions and equations because plot can show the relationship between two or more variables. There are many plotting methods such as hand plotting method, computer aided plotting method and so on.

At first, we need to choose the coordinate system by which we plot the point.

suppose we choose a XY coordinate plane. At first identify the horizontal or X axis and vertical or Y axis.

besides, we need to determine the required value that will be plotted on the plan.

if we have a list of X and Y value then find the value of X on the x axis and next find the value of Y on the Y axis.

we will notice some points for every pair of x and y value. Finally, we will join the points to achieve a required shaped graph.

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Using trigonometric functions, we can  find a side length of a right triangle with an angle and a side.

Trigonometric ratios are the ratios of a right triangle's sides. The sine (sin), cosine (cos), and tangent (tan) are three often used trigonometric ratios. There are other trigonometric ratios which are reciprocals of these ratios.

Trigonometric ratios can be computed either using the provided acute angle or by calculating the ratios of the right-angled triangle's sides.

You can determine the hypotenuse by dividing the length of the side by sin(θ) if you have an angle and the side opposite to it. Alternatively, to find the length of the side next to the angle, divide the length by tan(θ).

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Each person will pay $49.056. The value must be divided by the entire value, and the resulting number must then be multiplied by 100 to get the percentage.

A percentage, often known as percent, is a division by 100. Percentage, which meaning "per 100," designates a portion of a total sum. 45 out of 100 is represented by 45%, for instance. Finding the percentage of a whole in terms of 100 is what percentage calculation is. Both manual calculation and the use of internet calculators are options.

Amount of bill = $124.72

and tip they left = 18% of $124.72

total amount is =$124.72 + $124.72*18%=$147.1696

so, each person pay= $147.1696/3=$49.056

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Approximately 66(2s f) percentage of the logo does the circle cover.

What is percentage?

A percentage is a number or ratio expressed as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent sign, "%," is frequently used to indicate it. A percentage is a number without dimensions and without a standard measurement.

To find the percentage we must first find the area of the circle:

We can find the radius of the circle using the distance formula;

⇒ [tex]d=\sqrt{(x_2-x_1)^2 +(y_2-y_1)^2}[/tex]

⇒  [tex]r = \sqrt{(6.3-0)^2+(1.6-0)^2}[/tex]

⇒   r = 6.5

Now we calculate the area;

⇒ [tex]A = \pi r^2[/tex]

⇒  [tex]A = \pi (6.5)^2[/tex]

⇒  [tex]A = \frac{169}{4} \pi[/tex]

To get the percentage we divide the area of the circle by the square’s are and multiply by 100;

⇒ Percentage = [tex]\frac{42.25*\pi }{200}*100[/tex]

⇒ Percentage = 66(2s f)

Hence, approximately 66(2s f) percentage of the logo does the circle cover.

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Note that the resultant expression after simplifying simplify square root of 3y² if y<0 is: y√3

Note that we need to take a factor out of the square root:  √(3y²) , where y<0.

The given expression is  √(3y²)

Recall that to take out a factor out of the square root that factor must have a degree in multiple of 2 such as x², x⁴, (x-2)⁴, thus,

√(3y²)  = √3y²

⇒ √3 √y²

⇒  √3 (y²)[tex]^\frac{1}{2}[/tex]

⇒ √3 (y)[tex]^\frac{2}{2}[/tex]

= y √3

Thus, having simplified the expression √(3y²), the result is:  y √3.

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The probability that the distance is at most 100m is 0.749926 and at most 200 m is 0.9375 between 100 and 200 m is 0.1876 and the probability that distance exceeds the mean distance by more than 2 standard deviations is 0.04979

What is Probability ?

probability can be defined as the ratio of the number of favourable outcomes and the total number of outcomes.

We are given with an exponential distribution with

λ=0.01386.

The probability distribution function is:

F(x)=λ * e power (−λx)

Cumulative distribution function is

F(x) = 1- e power (−λx)

The mean of the exponential distribution function

E(X) = 1 / λ

= 1/0.01386

= 72.15

Hence, E(X) = 72.15

The variance of the exponential distribution function

V(X) = 1 / λ ^{2}

= 1/0.01386*0.01386

= 5205.63

V(X) = 5205.63

Probability that the distance is at most 100m

P(X <= 100 ) = F (100)

= 1- e power (−λx)

= 1 - e power (-0.01386*100)

= 1- e power (-1.386)

= 1-0.25007

= 0.749926

Therefore, P(X<=100) = 0.749926

probability that the distance is at most 200m

P ( X<= 200) = F(200)

=1-e power (−λx)

=1-e power (-0.01386*200)

= 1 - e power (-2.772)

= 1-0.06253

= 0.9375

P(X<= 200) = 0.9375

Probability that the distance is between 100 and 200m

P(100<= X <= 200) = F(200) - F(100)

= 0.9375-0.7499

=01876

P(100 <= X <= 200) = 0.1876

Probability that the distance exceeds the mean distance by more than 2 standard deviation.

P( X + P>μ+2σ) = P(X>72.15+2√5205.63)

= P(X > 72.15 +144.3)

P(X>216.45)

= 1-P(X<= 216.45)

1 - (1- e power (-0.01386*216.45)

=  e power (-2.9999)

= 0.04979

P( X + P>μ+2σ) = 0.04979

Hence , The probability that the distance is at most 100m is 0.749926 and at most 200 m is 0.9375 between 100 and 200 m is 0.1876 and the probability that distance exceeds the mean distance by more than 2 standard deviations is 0.04979

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The length of the rope is  2√29 meters.

What is an isosceles triangle?

An isosceles triangle has two equal sides as well as two equal angles. The Greek words iso (same) and skelos are the source of the name (leg). An equilateral triangle is one in which all of its sides are equal, whereas a scalene triangle is one in which none of its sides are equal.

Given that the distance between two trees is 2 meters. A boy hangs on a rope tied to the trees in the middle of the rope.

it sags so that the center is 2 meters below the level of the ends.

Thus it forms an isosceles triangle. △ACD and △BCD are two right triangles.

Since △ABD is isosceles triangle and AD = BD.

In △ACD, Hypotenouse = AD, Base = AC = 10/2 = 5 cm, Height = CD = 2 meters

Apply Pythagorean theorem on △ACD:

AD² = AC² + CD²

AD² = 5² + 2²

AD² = 29

AD = √29

Therefore, BD = √29

The length of the rope is AD + BD = 2√29 meters.

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The estimated IQR for the males dataset is 24 , the estimated difference between median value of each dataset is 14.

What is median ?

The median is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution in statistics and probability theory. It can be regarded as "the middle" value for a set of data.

When a dataset is ordered, the median value is the one that appears exactly in the middle of the dataset. Depending on whether you have an odd or an even number of data points, there are different processes to take when calculating the median.

In a collection of numbers, the median is the value in the middle. A series of numbers must first be sorted, or arranged, in value order from lowest to highest or highest to lowest in order to find the median value.

A. IQR  for male dataset

The IQR is calculated as follows:

IQR = Q3 - Q1

      =

For the male's data:

IQR = Q3 - Q1

      = 25 - 1

      = 24

Hence, the IQR of the male dataset is 24.

B. Difference in median values

We have:

median = 20 ----- Male dataset                                                    

median = 6  ----- Female dataset

So, the difference (d) is:

d = 20 - 6

  = 14

Hence, the difference in median of both dataset is 14.

C. Best measure of center

The female box plot has an outlier. This means that the measure of center to use for the female dataset is the median.

The male box plot has no outlier; this means that the mean can be used as a measure of center for the male box plot

D. Reason for outlier

There are several reasons that could cause an outlier in a dataset. One of the reasons is human error during data entry.

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The total number of servings of chicken the food bank can provide is 70 servings.

Per-unit is a technique of expressing a quantity's value in terms of a base or reference quantity. Each system variable or quantity in a per-unit system is normalized in relation to its own base value.

Two chickens make up the main course of a plate of food, according to the table's content. Each chicken served by the food bank weighs 12.6 ounces. 110.9 pounds of chicken are available at the food bank (1,774.4 ounces of chicken)

Thus,

The mass of chicken per serving = 2 × 12.6 = 25.2 oz/serving

The total number of servings of chicken the food bank can provide = (The quantity of chicken the food bank has)/(The mass of chicken per serving)

∴ The total number of servings of chicken the food bank can provide = (1,774.4 oz)/(25.2 oz/serving) ≈ 70.413

Given that the servings are in whole numbers, we have;

therefore, To the nearest whole number, the food bank can offer a maximum of 70 servings of chicken.

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Therefore , the solution of he given problem of linear equation comes out to be x = 5.

A linear equation is one that has the form y=mx+b in algebra. B is the slope, and m is the y-intercept. It's usual to refer to the previous clause as a "linear equation with two variables" because y and x are variables. The two-variable linear equations known as bivariate linear equations. There are several instances of linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. It is referred to as being linear when an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept.

Here,

Given : 2x-4=6

To prove x =5

Thus,

We have to find the value of x

=> 2x =10

=> x =10/2

=> x =5

Therefore , the solution of he given problem of linear equation comes out to be x = 5.

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On solving the provided question we can say that  so the value of the data from histogram graphs will be x [tex]\alpha[/tex] 0.123 * 125 / 100  = 0.15375

Mathematicians use graphs to logically convey facts or values using visual representations or charts. A graph point will typically reflect a relationship between two or more things. Nodes, or vertices, and edges make form a graph, a non-linear data structure. Glue together the nodes, often referred to as vertices. This graph has vertices V=1, 2, 3, 5, and edges E=1, 2, 1, 3, 2, 4, and (2.5), (3.5). (4.5). Statistical charts (bar charts, pie charts, line charts, etc.) graphical representations of exponential growth. a logarithmic graph in the shape of a triangle

the best way to describe the data that was used to create this histogram (keep in mind that there is no scale on the horizontal axis, so you must choose based simply on the appearance of the histogram graphs

so the value of the data from histogram graphs will be

z = 0.123

u = 100

x = 125

x [tex]\alpha[/tex] 0.123 * 125 / 100  = 0.15375

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Therefore ,As a result, the answer to the above  equation is: She starts at (19,8), travels 8 blocks back in 2 minutes, and ends up at (21,0).

An equation in mathematics is a representation of two equal variables, one on each side of a "equals" sign. To tackle common issues, equations can be used. We commonly seek pre algebra help to overcome obstacles in real life. Math fundamentals are covered in pre-algebra lessons.

Here,

Given :

At time zero, Kadeesha stepped outside and drove 3 minutes at a speed of 1 block per minute to the store.

after traveling six blocks at her normal speed of three blocks per minute

She spent 5 minutes stopping at the bank as a result. She then sped home at a rate of three blocks per minute.

She therefore begins at (19,8), travels 8 blocks back in 2 minutes, and ends at (21,0).

Therefore ,As a result, the answer to the above  equation is: She starts at (19,8), travels 8 blocks back in 2 minutes, and ends up at (21,0).

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y = -1/2x is the equation of example of the direct variation.

A polynomial is a mathematical equation that solely uses the operations addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Variables are sometimes known as indeterminates in mathematics. Polynomials come in various varieties. Monomial, binomial, and trinomial, respectively.

Given four linear equations in them we need to state which equation is an example of direct variation.

The direct variation equation has the form y = kx, where k is the constant proportionality. It is a linear equation with two variables. In a coordinate plane, the direct variation graph is a straight line. A constant is the ratio of two quantities that vary directly. Or in other words, the direct variation equation always passes through the origin point of a cartesian plane or (0, 0).

Therefore, in the given options y = -12/x is the only equation that is an example of direct variation.

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The area of bedroom rug is 15 square feet. the longer side measures 5 feet. his living room rug is twice as long and twice as wide as the bedroom rug.

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For the given Augmented Matrix ,the correct option is :

A) The solution set has exactly one element.

The exact solution is x = -25 , y = 2 and z = 2.

Augmented Matrix:

An augmented matrix is ​​a means of solving simple linear equations. Coefficients and constant values ​​of linear equations are represented as matrices called augmented matrices. Simply put, an augmented matrix is ​​a combination of two simple matrices along columns. If the first matrix has m columns and the second matrix has n columns, then the augmented matrix has m + n columns.

Now, as given the Augmented matrix:

[1 7 3 -5]

[0 0 0 3]

[0 0 1 2]

[0 1 -1 4]

From this system we get:

y - z = 4       --------------------------- (1)

    z = 2

and, z = 3

and, x + 7y + 3z =-5   ---------------- (2)

Now, Solving the equation with z = 2,

    y - 2 = 4

⇒ y = 6

and, putting y = 6 and z = 2

   x + 7× 6 + 3×2 = -5

⇒ x + 42 + 6 = -5

⇒ x +48 = -5

⇒ x = -53

Therefore, x = -53, y=6 and z =2

Now, for z = 3 in equation (1)

   y - 3= 4

⇒ y = 7

Putting y =7  and z =3, we get:

   x + 7 × 7 + 3×3 = -5

⇒ x + 49 + 9 =-5

⇒ x + 58 = -5

⇒ x = -63

Therefore, x = -63, y =7 and z =3

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Answer:

Step-by-step explanation:

Given the value function v(t) = 20000·0.86^t, you want the value after 4 years and 10 years.

Put the value of t in the formula where t is, and do the arithmetic.

The attached calculator output tells us ...

  value after 4 years: $10,940

  value after 10 years: $4,426

__

Additional comment

When you are asked to do the same evaluation with different numbers, it is convenient to process them as a list, or using a spreadsheet.

Answer:

x - intercept = (15, 0)

y - intercept = (0, 6)

Step-by-step explanation:

x-int. is when y = 0

y-int. is when x=0

Plug in y = 0 and x = 0 to get intercepts.

FOR X-INT.:

12x + 30(0) = 180

12x = 180

x = 15

x-int. is (15, 0)

FOR Y-INT. :

12(0) + 30y = 180

30y = 180

y = 6

y-int. is (0, 6)

The mean of her sales over the week is 29 and the median is 27.

The arithmetic mean, arithmetic average, or simply the mean or average, is the sum of a collection of numbers divided by the number of numbers in the collection in mathematics and statistics. The collection is frequently a collection of results from an experiment, observational research, or survey. The mean is the average of a set of variables in mathematics and statistics. The mean may be calculated in a variety of methods, including the simple arithmetic mean (add the numbers and divide the total by the number of observations), geometric mean, and harmonic mean.

Here,

To find the mean you need to sum all daily sales and then divided by the number of days. If we called daily sales as xi and the number of days evaluated as N, we have that the mean can be expressed as

mean = (∑xi)/N ⇒ media = (23 + 25 + 32 + 35 + 36 + 25 + 27 )/7

⇒mean = 29.

To find the mediana you have to put the number of sales in increasing orden and then look which is the number in the middle of the serie. So

23 - 25 - 25 - 27 - 32 - 35 - 36

⇒median = 27.

Summarizing, the mean of the sales is 29 and the median 27.

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The probability that the top card is a suit of heart as calculated from the data given is found to be 4 / 663.

We are given that ,

The number of cards in the deck = 52

Number of 3's in the deck = 4

Number of 8's in the deck = 4

As because all the card deck's have 4 cards of same number in different suits.

Probability is calculated as ,

P = required outcome / Total possible outcomes

Therefore, when we can choosing cards without replacing them we get,

P(top card is a 3) = 4 / 52

P(second being 8) = 4 / 51

P(top card is a 3 and second 8)

=4/52 x 4/51

= 16 / 2652

= 4 / 663.

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Answer:

Y-intercept: (0, -7)

X-intercept: (-14,0)

Step-by-step explanation:

To find the y-intercept, we need to put 0 in for x

0 + 2y = -14

2y = -14

y = -7

So, the y-intercept is located at (0, -7)

To find the x-intercept, we need to put 0 in for y

x + 2(0) = -14

x = -14

So, the x-intercept is located at (-14,0)

Step-by-step explanation:

To find the y-intercep, we need to put 0 in for x

0 + 2y= -14

2y = -14

y = - 7

So, the y - intercept is located at ( 0, - 7)

If the value of y = 0, then it make the straight line on the graph.

The term graph in math is defined as the way that is used to represent a set of data to make it easier to understand and interpret statistical information.

Here we have the expression y = 0.

And here we know that the y coordinate is constant which is 0 for given equation and only x coordinate is variable.

Therefore it represent the x-axis.

Therefore, basically y=0 is the linear equation to denote the x - axis, here as all the points on the x- axis, then we have their y co-ordinate = 0.

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The total surface area of the hemisphere is 108 pi cm^2.

Surface area is the amount of space covering the outside of a three-dimensional shape. We calculate the surface area for three dimensional objects. The surface area of a 3-D object is not same as its volume.

The surface area of a sphere with the radius r is 4 pi r^2

The surface area of a hemisphere with the radius r = 2 pi r^2 +   pi r^2

where pi r^2 represents the area of the circular base of the hemisphere of radius r.

The surface area of a hemisphere sphere with the radius r is 3 pi r^2

For radius r=6cm

TSA of  the hemisphere is 3 pi (6x6) cm^2

TSA = 108 pi cm^2

108 pi cm^2 is the total surface area of a hemisphere with the radius 6 cm.

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The perimeter of the right triangle is 228 inches

What is a right-angle triangle?

It is a triangle in which one of the angles is 90 degrees and the other two are sharp angles. The sides of a right-angled triangle are known as the hypotenuse, perpendicular, and base.

The complete length of a shape's edge serves as its perimeter in geometric terms. Adding the lengths of all the sides and edges that surround a form yields its perimeter.

Since it is a right triangle,

c² = 57² +76²

c² = 3249 + 5776

c² =  9025

c=  √ 9025 = 95

Perimeter is the sum of all sides

Perimeter = 57+76+95 = 228 inches

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