Circle O shown below has a radius of 30 inches. To the nearest tenth of an inch,
determine the length of the arc, x, subtended by an angle of 1.8 radians.
30 inches
0=1.8 rad

Angle A is 154.2857 degrees, angle B is 77.1429 degrees, and angle C is 25.7143 degrees.

What is the sum of the three angles in a triangle?

A triangle's angles add up to 180 degrees because one exterior angle is equal to the sum of the other two angles in the triangle.

Given that 2 angle A = 3 angle B = 6 angle C, we can set up the following equations:

2A = 3B

3B = 6C

We know that in any triangle, the sum of the three angles is always 180 degrees. We can set up the equation:

A + B + C = 180

We can substitute the values of A and B from the first two equations into this third equation:

2A + 3B + C = 180

2(3B) + 3B + C = 180

6C + C = 180

7C = 180

We can solve for C:

C = 180/7 = 25.7143

We can use the value of C to find the value of B:

B = 3C = 3(25.7143) = 77.1429

We can use the value of B to find the value of A:

A = 2B = 2(77.1429) = 154.2857

Therefore, angle A is 154.2857 degrees, angle B is 77.1429 degrees, and angle C is 25.7143 degrees.

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The given equation system has the following solution: (10, 11).

A finite set of equations for which common solutions are sought is referred to as a set of simultaneous equations, often known as a system of equations or an equation system.

Given the system of equations below:

2x+3y=53

3x-y=19

From equation 2, y = 3x - 19 .......... 3

Substitute equation 3 into 1 to have;

2x+3y=53

2x + 3(3x - 19) = 53

2x + 9x - 57 = 53

11x = 110

x = 10

Substitute x = 10 into equation 3 to have:

y = 3x - 19

y = 3(10) - 19

y = 30 - 19

y = 11

Hence the solution to the given system of equation is (10, 11).

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Therefore , the solution to the given problem of percentage comes out to be  total number of student  = 182 (approx).

In mathematics, a percentage is a number or ratios that is expressed as a portion of 100. Occasionally, the acronyms "pct.," "percent growth," & "pc" are also used. But it is commonly indicated by the percent sign, "%." The % amount has no dimensions. Percentages are essentially fractions when the denominator is 100. Use the percent sign (%) to indicate that a quantity is a percentage by placing it next to it.

Here,

Given :  22% of x is 40

thus,

To find the value of x , where x is the total number of students in that class.

=>  22/100* x = 40

=> x = 40 * 100 /22

=> x = 4000/22

=> x =181.81

So, x = 182 (approx)

Therefore , the solution to the given problem of percentage comes out to be   total number of student  = 182 (approx).

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Answer:

see the picture attached

Step-by-step explanation:

To graph this, we will count to a negative five on the graph. This means that we will move to the left five spaces and plot a point at (-5,0). Now, we will create a vertical line at -5 to encapsulate all of the values found at x = -5. This is essentially an infinite line, but the picture I included shows it on a 10 x 10 plane. Hope this helps!

Answer:

What is X= -5 graphed

Step-by-step explanation:

Graph x=-5 x = −5 x = - 5 Since x = −5 x = - 5 is a vertical line, there is no y-intercept and the slope is undefined.

The fundamental theorem of algebra states that you will have ‘n’ roots for an nth-degree polynomial, including multiplicity. So, your roots for f(x) = x^3 are 0 (multiplicity 3). The total number of roots is still 3 because you have to count 0 thrice.

A polynomial can be defined as an expression which consists of variables, constants and exponents, that are combined using mathematical operations such as addition, subtraction, multiplication and division. 
·[tex]f(x)= ax^{n}+bx^{n-1}+cx^{n-2} +k[/tex]

We can also phrase it as there are going to be ‘n’ values of x for which it will make polynomial f(x)=0.

For Example: [tex]p(x)= x^{2}-6x+9[/tex]

                   ⇒   n = 2

                   ∴ Total number of roots = 2

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The required rate of change of the surface area of the cube is 66 sq,feet/second.

The momentum of a variable is represented by the rate of change, which is used to mathematically express the percentage change in value over a specified period of time. R = (D2 - D1)/T is a general formula for calculating the rate of change.

[tex]\frac{V}{dt}[/tex] = 1327 cubic feet per second

volume(V) = 528528 cubic feet

We know that

V = a^3

528528 = a^3

a = 80.85

Differentiate w, r, t

[tex]\frac{V}{dt}[/tex] = 3a^2[tex]\frac{da}{dt}[/tex]

1327 = 3(80.85)^2da/dt

da/dt = 0.068

Now,

Surface area(S) = 6a^2

Differentiate w, r, t

dS/dt = 12a(da/dt)

dS/dt = 12(80.85)(0.068)

dS/dt = 66 Sq.feet/second

Thus, required rate of change of the surface area of the cube is 66.

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The probability that her 10th roll is her last roll in the expression of a decimal to the nearest thousandth is 0.039.

As per information given, the condition of the event will be:

As we can find the value of each probability, the probability of the tenth roll is the last roll will be:

Last roll in tenth = 1 x (5/6)⁸ x 1/6

Last roll in tenth = 0.03876133989

Since, the question is asking for the nearest thousandth, the answer will be 0.039

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Answer:

Step-by-step explanation:

maybee the 2ed one

the fox population in a certain region has an annual growth rate of 8 percent per year. it is estimated that the population in the year 2000 was 7600.

(a) function model for the t year after 2000 (exponential model):

[tex]p(t) = 7600 (1.08)^t[/tex]

The function is a mathematical phrase, rule, or law that establishes the connection between an independent variable and a dependent variable (the another variable).

A function is described as a relationship between a group of inputs and one output each. A function is, to put it simply, a connection between inputs in which each input is connected to exactly one output.

Population in 2000,

P(0) = 7600

Growth rate = 8% each year

(a) function model for the t year after 2000 (exponential model):

[tex]p(t) = 7600 (1.08)^t[/tex]

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No, 22/7 is not a repeating decimal. The fraction 22/7 is an estimate for pi, but since pi is an irrational number, it does not repeat and 22/7 is not an exact representation of pi.

1. The ratio of the distance around a circle to the distance across a circle through its center is represented by the number pi.

2. The number pi is a decimal that does not repeat.

3. The fraction 22/7 is sometimes used as an estimate for pi.

4. 22/7 is not a repeating decimal because pi is an irrational number, meaning it does not repeat and 22/7 is not an exact representation of pi.

No, 22/7 is not a repeating decimal. The fraction 22/7 is an estimate for pi, but since pi is an irrational number, it does not repeat and 22/7 is not an exact representation of pi.

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There are two types of roots for an equation: real roots and complex roots. Real roots are the solutions of the equation where the values of the variables are real numbers, and complex roots are the solutions of the equation where the values of the variables are complex numbers.

There are two types of roots for an equation: real roots and complex roots. Real roots are the solutions of the equation where the values of the variables are real numbers. To find the real roots of an equation, one can use various methods such as graphing, factoring, completing the square, and the quadratic formula. If the equation is a linear equation, one can also use the slope-intercept form to find the real root. Complex roots are the solutions of the equation where the values of the variables are complex numbers. Complex roots are usually found using the quadratic and cubic formulas. These formulas involve complex numbers and can be used to solve equations with complex coefficients. The roots can also be found graphically by plotting the equation on a complex plane and finding the intersecting points. The real and imaginary parts of the root can then be determined.

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The total cost of the entertainment center after six years, if Zebina must pay it off, would be $9,203.19.

When a person purchases an item using a deferred payment plan with interest, the total cost of the item will be greater than the original purchase price due to the added interest.

To calculate the total cost of the entertainment center after six years, we need to use the formula for compound interest:

A = P(1 + r/n)^(nt)

where A is the total cost, P is the original purchase price, r is the annual interest rate (expressed as a decimal), n is the number of times the interest is compounded per year, and t is the number of years.

In this case, P = $2,798, r = 0.2195 (21.95% expressed as a decimal), n = 1 (because the interest is compounded annually), and t = 6. Plugging these values into the formula gives:

A = 2798(1 + 0.2195)^6

A = $9,203.19

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Answer:

  3√7 ≈ 7.937 units²

Step-by-step explanation:

You want to know the area of the isosceles triangle with congruent sides 4 units and base 6 units.

The perimeter of the triangle is ...

  P = 4 + 4 + 6 = 14

so the semiperimeter is ...

  s = P/2 = 14/2 = 7

By Heron's formula, the area of the triangle is ...

  A = √(s(s -a)(s -b)(s -c))

  A = √(7(7 -4)(7 -4)(7 -6)) = 3√7

The area of the triangle is 3√7 ≈ 7.937 square units.

__

Additional comment

You can also compute the area after finding the altitude (the length of the dashed line) using the Pythagorean theorem. The figure consists of two right triangles, each with leg 3 and hypotenuse 4. The missing leg (the triangle height) is then ...

  h = √(4² -3²) = √7

The area is ...

  A = 1/2bh = 1/2(6)(√7) = 3√7 . . . . square units

Answer:that doesn’t seem possible to figure out

Step-by-step explanation:

?

The interval of increase for the given function is (-1 , 0) (0 , infinity).

The real-valued functions that tend to rise and decrease with changes in the value of the function's dependant variable are increasing and decreasing intervals of real numbers. You must ascertain the function's first derivative in order to identify intervals of rise and decline.

This is done to determine whether the function's sign is positive or negative. If the value of the function f (x) rises as the value of x rises, the function interval is said to be positive. Instead, if the value of the function f (x) drops as the value of x increases, the function interval is said to be negative.

The given function is:

C(x) = x1/5(x + 6)

Find the derivative of the given function to get calculate the interval of increase and decrease.

The interval of increase is (-1 , 0) (0 , infinity).

Th graph is concave up when derivative of, f is greater than 0. The intervals in which the function depicts this behavior will be the interval that will have a concave up curve.

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The test statistic of -0.03 is compared to a critical value to determine if the null hypothesis can be rejected. If the test statistic is less than or equal to the critical value, the null hypothesis is rejected and the 90% figure is not accurate.

Calculate the sample proportion:

Sample Proportion

= 657/750

= 0.87

Calculate the test statistic:

Test Statistic

= 0.87 - 0.90

= -0.03

Compare the test statistic to a critical value:

If the test statistic is less than or equal to the critical value, then we can reject the null hypothesis. If the test statistic is greater than the critical value, then we cannot reject the null hypothesis.

The null hypothesis is that the percentage of adults in the region who drink milk is equal to 90%, while the alternative hypothesis is that the percentage is not equal to 90%. A sample of 750 adults is polled and the sample proportion is calculated to be 0.87.

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So the shortest distance he must walk to return to his house is approximately 10.8 miles.

The man walks 6 miles south and 9 miles east from his house. To find the shortest distance he must walk to return to his house, we need to use the Pythagorean theorem.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In this case, the man's walk can be represented by a right triangle, where the length of one side is 6 miles (the distance he walked south), the length of the other side is 9 miles (the distance he walked east), and the length of the hypotenuse is the shortest distance he must walk to return to his house.

Using the Pythagorean theorem, we can calculate the length of the hypotenuse as:

hypotenuse = √(6^2 + 9^2) = √(36 + 81) = √117

So the shortest distance he must walk to return to his house is approximately 10.8 miles.

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The parallelogram's surface area is 24 square units as a result.

A quadrilateral with the opposing sides parallel is called a parallelogram (and therefore opposite angles equal). A parallelogram with all right angles is known as a rectangle, and a quadrilateral with equal sides is known as a rhombus. A quadrilateral is referred to as a parallelogram in geometry.

The opposite sides of a parallelogram are parallel and of equal length. Rhombus, rectangle, and square are a few instances of parallelograms.

Here points are a(−3, 0), b(−1, 5), c(7, 4), and d(5, −1).

= 1/2 [-3 (4 + 1) - 1 (- 7 - 20)]

= 1/2 [-3 (5) - 1 (-27)]

= 1/2 [-15 + 27]

= 1/2 [12]

= 6 sq units

Area of parallelogram abcd = Area of triangle abc + Area of triangle acd

= 18 + 6

= 24 sq units.

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a. The value of h'(3) is 45.

b. The value of H'(1) is 36.

The complete table is in the attachment. h' and H are derivates from function h(x) and H(x). Using the Chain Rules to derivate the function.

Calculate the h'(x) function

h(x) = f(g(x))

h'(x) = d/dx {f(g(x))}

h'(x) = f' (g(x)) × g'(x)

h'(3) = f' (g(3)) × g'(3)

h'(3) = f'(2) × 9

h'(3) = 5 × 9

h'(3) = 45

Calculate the H'(x) function

H(x) = g(f(x))

H'(x) = d/dx {g(f(x))}

H'(x) = g' (f(x)) × f'(x)

H'(1) = g' (f(1)) × f'(1)

H'(1) = g'(3) × 4

H'(1) = 9 × 4

H'(1) = 36

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The TQ is a chord, PR is a secant line and WU is a tangent line.

Circle is a two dimensional figure which consist of set of all the points which are at equal distance from a point which is fixed called the center of the circle.

A chord of a circle is the line segment joining two points on the circle.

Line segments TQ and QV are chords.

TV is also a chord, which is the diameter.

A secant line is a line which intersects the circle at two different points.

Line PR is a secant line which intersects the circle at T and Q.

A tangent line is a line which intersects the circle at exactly one point.

Line WU is a tangent line which intersects the circle at V.

Hence the chords in the given figure are TQ and QV, secant line is PR and tangent line is WU.

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Answer:

(- 3, 2 )

Step-by-step explanation:

to find the start, do the reverse, that is move 1 unit to the right.

this means adding 1 to the x- coordinate

start = (- 4, 2 ) → (- 4 + 1, 2 ) → (- 3, 2 )

Answer:

In this problem, we need to add a point to this graph which creates a right triangle with the given points.

The easiest way to do this is to find a point that is perpendicular to both of the points; more simply put, it has to have the x-coordinate of one of the given points and the y-coordinate of the other given point.

For example, adding the point (50, -14) to the graph satisfies this criteria, using the x-coordinate of (50, 25) and the y-coordinate of (130, -14). However, you could also use the y-coord of the first point and the x-coord of the second to add the point (130, 25). Both points in bold satisfy the criteria.

See the attached image for a graph of these points and the right triangles they create.

The particular solution of y = f(x) to the given differential equation [tex]\frac{dy}{dx} = y (xlnx)[/tex] with the initial condition f(1) = 4 is [tex]y = 4e^{\frac{1}{2}x^{2} lnx } - \frac{1}{4} x^{2} + \frac{1}{4}[/tex].

dy/dx = y(x lnx)

1/y dy = x lnx dx      Eqn (1)

Let u =  lnx, dv = x dx

Differentiate u = lnx

du = 1/x dx

Integrate dv = x dx

v = (1/x)x²

Now, integrate equation(1), we get

∫1/y dy = ∫x lnx dx

ln y = 1/2 x² ln x - 1/4 x² + C       Eqn (2)

Now, put the value of x and y to calculate the value of C

ln 4 = 1/2 ln 1 - 1/4 + C

ln 4 + 1/4 = C

Put the value of C in equation (2), and we get

ln y = 1/2 x² ln x - 1/4 x² + ln 4 + 1/4

[tex]y = 4e^{\frac{1}{2}x^{2} lnx } - \frac{1}{4} x^{2} + \frac{1}{4}[/tex]

--The given question is incorrect, the correct question is

''Find the particular solution y = f (x) to the given differential equation [tex]\frac{dy}{dx} = y (xlnx)[/tex] with the initial condition f(1) = 4."--

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The three comparisons are Beta had a higher percentage of listeners than group alpha, Beta had a higher mean number of hours listening than group alpha and Beta had a higher range of number of hours listening than group alpha.

The first comparison states that the Beta group had a higher percentage of listeners than the Alpha group. This means that out of all the people who listened to the radio station that day, a larger proportion of them belonged to the Beta group, compared to the Alpha group.

The second comparison is saying that the Beta group had a higher mean number of hours listening than the Alpha group. This means that on average, people in the Beta group listened to the radio station for more hours than people in the Alpha group.

The third comparison states that the Beta group had a higher range of number of hours listening than the Alpha group. This means that the difference between the minimum and maximum hours of listening in the Beta group is larger than the Alpha group. Which means that the listeners of Beta group have a greater variability in terms of hours of listening than the Alpha group.

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There are six different positive integers divisible by 4 that can be formed using each of the digits 1, 2, 3, and 4 at most once and no other digits: 12, 24, 32, 42, 43, and 124.

1. 12: 1 and 2

2. 24: 2 and 4

3. 32: 3 and 2

4. 42: 4 and 2

5. 43: 4 and 3

6. 124: 1, 2 and 4

The six different positive integers divisible by 4 that can be formed using each of the digits 1, 2, 3, and 4 at most once and no other digits are 12, 24, 32, 42, 43, and 124. To find these numbers, we begin by examining all the possibilities that can be formed using the digits 1, 2, 3, and 4. We can form 12, 24, 32, 42, 43 and 124 by combining different combinations of the digits. For example, 12 is made up of the digits 1 and 2. 24 is made up of 2 and 4. 32 is made up of 3 and 2. 42 is made up of 4 and 2.

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the height intercept would be 0 given the pool has no water at the beginning.

Which is the vertical intercept?

The vertical intercept (y-intercept) is found by evaluating the function when the input variable, x, is 0 and is always the same as the constant b. It can be thought of as the original value of the function. The horizontal intercept (x-intercept) is the value of the variable x when the function value is 0.

according to the constant dividend growth model

price = d1 / (r - g)

d1 = next dividend to be paid

r = cost of equity

g = growth rate

$2.5 / (0.1 - 0) = $25

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Number Zero is neither positive nor negative.

A whole number, an integer can be positive, negative, or zero but cannot be a fraction or a decimal because it is a whole number. The natural numbers (1, 2, 3,...), their opposites (-1, -2, -3,...), and zero are all considered to be integers. Numerous branches of mathematics use integers, but number theory and algebra place a special emphasis on them.

Zero is not an integer that may be either positive or negative. It is regarded as a non-negative or neutral number. The absolute value of zero is also zero in terms of magnitude. |0| = 0. In the set of integers, zero is also regarded as the identity element of addition and the absorbing element of multiplication.

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The greatest integer that does not exceed S/10 is 2.

1000 can be factored as 1000 = 2^3 * 5^3. The positive divisors of 1000 are the numbers of form 2^i * 5^j, where i and j are non-negative integers and i <= 3, j <= 3.

The sum of all numbers of the form a/b, where a and b are relatively prime positive divisors of 1000, is the sum of all numbers of the form 2^i * 5^j / (2^k * 5^l), where i, j, k, and l are non-negative integers and i, j, k, l are non-negative integers and i <= 3, j <= 3 and (i,j) is not equal to (k,l).

There are total 24 such terms in the sum.

We can evaluate the sum as:

(1/1 + 1/2 + 1/4 + 1/5 + 1/8 + 1/10 + 1/20 + 1/25 + 1/40 + 1/50 + 1/80 + 1/100 + 1/125 + 1/200 + 1/250 + 1/400 + 1/500 + 1/625 + 1/1000 + 2/5 + 4/25 + 8/125 + 16/625)

S = (1 + 0.5 + 0.25 + 0.2 + 0.125 + 0.1 + 0.05 + 0.04 + 0.025 + 0.02 + 0.0125 + 0.01 + 0.008 + 0.005 + 0.004 + 0.0025 + 0.002 + 0.0016 + 0.001 + 0.0004 + 0.0008 + 0.00016 + 0.000064)

S = (2.93120)

Therefore, the greatest integer that does not exceed S/10 is 2.

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The plot of 2 1/3, −5/6, and −3 1/2 on the number line is attached below

Generally, The uneven distribution of resources, opportunities, and advantages among different persons or groups in a society is what we mean when we talk about inequality.

This may manifest itself in a variety of ways, such as economic inequality (differences in income or wealth), social inequality (differences in status or access to resources), or political inequality (differences in power or influence) (differences in power or representation).

inequality, A statement in mathematics that establishes an order connection between two numbers or algebraic expressions, such as "greater than," "greater than or equal to," "less than," or "less than or equal to."

The mathematical symbol for "equals" has been substituted by an arrowhead in the statement "5x - 4 > 2x + 3," which gives it the appearance of an equation. It is an illustration of the concept of inequality. This indicates that the section on the left, which reads 5x minus 4, is more significant than the section on the right, which reads 2x plus 3.

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Answer:

Below in bold.

Step-by-step explanation:

R(x) = 8x/(x + 19)

When x = -19 the denominator = zero so there is a vertical asymptote which is

x = -19.

If we divide 8x by x + 19 we get  8 remainder -152.

So horizontal asymptote is R(x) = 8.

As the degree of the numerator and denominator are the same ( both 1) there is no oblique asymptote.