The circle has center O. Its radius is 4 ft, and the central angle a measures 110°. What is the area of the shaded region?
Give the exact answer in terms of it, and be sure to include the correct unit in your answer.

The expression (r-s)(x) is 4x² - x + 5, (r.s)(x) is 4x³ - 20x² and value of (r-s)(-1) is 10.

To find the expression (r-s)(x), we subtract the function s(x) from the function r(x):

(r-s)(x) = r(x) - s(x)

Substituting the given functions, we have:

(r-s)(x) = 4x² - (x-5)

Simplifying further:

(r-s)(x) = 4x² - x + 5

To find the expression (r.s)(x), we multiply the functions r(x) and s(x):

(r.s)(x) = r(x) × s(x)

Substituting the given functions, we have:

(r.s)(x) = (4x²)×(x-5)

Expanding and simplifying:

(r.s)(x) = 4x³ - 20x²

Now, let's evaluate (r-s)(-1) by substituting x = -1 into the expression (r-s)(x):

(r-s)(-1) = 4(-1)² - (-1) + 5

(r-s)(-1) = 4 - (-1) + 5

(r-s)(-1) = 4 + 1 + 5

(r-s)(-1) = 10

Therefore, (r-s)(-1) equals 10.

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The solution is the point (0, 1/6) y = 1/6

Given the equation y = (-3/4)x + 1/6, which represents a linear equation, there is no "system" of equations involved since there is only one equation.

In this case, the equation is in slope-intercept form (y = mx + b),

where m represents the slope (-3/4) and b represents the y-intercept (1/6).

The slope-intercept form allows us to determine various properties of the equation.

Since there is only one equation, the solution to this equation is a single point on the Cartesian plane.

Each pair of x and y values that satisfy the equation represents a solution.

For example, if we choose x = 0, we can substitute it into the equation to find the corresponding y value:

y = (-3/4)(0) + 1/6

y = 1/6

Therefore, the solution is the point (0, 1/6).

In summary, the given equation has a unique solution, represented by a single point on the Cartesian plane.

Any value of x plugged into the equation will yield a corresponding y value, resulting in a unique point that satisfies the equation.

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If 5sinA=3 and cosA is smaller than 0  , the value of 2tanAcosA is -6/5.

To determine the value of 2tanAcosA, we need to find the values of tanA and cosA first. We are given that 5sinA = 3 and cosA is smaller than 0.

Let's start by finding sinA. Since sinA = opposite/hypotenuse, we can set up a right triangle with the opposite side as 3 and the hypotenuse as 5. Using the Pythagorean theorem, we can find the adjacent side:

adjacent^2 = hypotenuse^2 - opposite^2

adjacent^2 = 5^2 - 3^2

adjacent^2 = 25 - 9

adjacent^2 = 16

adjacent = 4

Now we can find cosA using the adjacent side and hypotenuse:

cosA = adjacent/hypotenuse

cosA = 4/5

Since cosA is smaller than 0, it means that cosA is negative. Therefore, cosA = -4/5.

Next, we can find tanA using the given information. tanA = opposite/adjacent = 3/4.

Now, we can calculate the value of 2tanAcosA:

2tanAcosA = 2 * (3/4) * (-4/5) = -24/20 = -6/5

Therefore, the value of 2tanAcosA is -6/5.

To aid in visualizing the situation, it would be helpful to draw a right triangle with the appropriate side lengths based on the given values of sinA and cosA. The opposite side would be 3, the adjacent side would be 4, and the hypotenuse would be 5. Additionally, since cosA is negative, we can indicate the direction of the adjacent side to be in the negative x-axis direction. This diagram would provide a visual representation of the values and relationships involved in solving the problem.

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Answer:

a. 140°

b. 230°

Step-by-step explanation:

In Circle

m arc PTR=180° Being linear Pair

m arc PU+ m arc UT + m arc TS+m arc SR=180°

substituting value

40°+ m arc UT+40°+50°=180°

m arc UT=180°-130°

m arc UT=50°

Now for question

a.

m arc RSU= m arc TU+m arc TS+m arc SR=50°+40°+50°=140°

b.

we have

m arc RQ=m arc PQ=90° being right angle reflective

Now

m arc PQS= m arc PQ+ m arc QR+m arc RS=90°+90°+50°=230°

The test statistic and critical value needed to test the claim that the success is independent of the type of treatment are 9.750 and critical value is 6.635.

The expected value for each cell is calculated as follows:

E = row total * column total / grand total

The grand total is 150.

The row totals are 83 and 67.

The column totals are 86 and 64.

The expected values are as follows:

Successful: 60 * 86 / 150 = 36.4

Unsuccessful: 60 * 64 / 150 = 29.6

Surgery treatment

Successful: 67 * 86 / 150 = 49.6

Unsuccessful: 67 * 64 / 150 = 27.4

The test statistic is calculated as 9.750

The critical value is calculated as follows:

α = 0.01

df = (r-1)(c-1) = (2-1)(2-1) = 1

x²(α, df) = 6.635

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Answer:

44 m2

Step-by-step explanation:

The area of the rhombus can be divided into 4 equal triangles.

The area of one triangle is A=bh/2

so:

A = 5.5*2

A = 11 squared m

Since there are four (4) triangles in the rhombus we just need to multiply 11 by 4 so:

A = 11 * 4

A = 44 squared m

The pine cone is 20 feet above the ground after about 1.58 seconds.

To solve the equation h = -16t² + 60 for t, we can rearrange the equation as follows:

-16t² + 60 = h

Subtract 60 from both sides:

-16t² = h - 60

Divide both sides by -16:

t² = (h - 60) / -16

Take the square root of both sides:

t = ±√((h - 60) / -16)

Since time cannot be negative in this context, we can ignore the negative square root:

t = √((h - 60) / -16)

We are given that the pine cone is 20 feet above the ground, so we substitute h = 20 into the equation:

t = √((20 - 60) / -16)

Simplifying:

t = √(-40 / -16) = √(2.5)

t = 1.58 seconds

Therefore, the pine cone is 20 feet above the ground after about 1.58 seconds.

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The integer number that represents the change in Lily's account balance is given as follows:

-25.

Integer number are numbers that can have either positive or negative signal, but are whole numbers, meaning that they have no decimal part.

For the balance of the bank account, we have that:

Lily withdrew $25 from her savings account to buy a birthday gift for her grandfather, hence the integer number is given as follows:

-25.

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Answer:

250πcm³

Step-by-step explanation:

Length of bigger = k X length of smaller (k is a constant)

Area of bigger = k² X area of smaller (k is a constant)

Volume of bigger = k³ X volume of smaller (k is a constant)

ratio of 3:5 means that there are 3 + 5 = 8 parts.

Length of bigger = k X length of smaller

5 = 3k

k = 5/3.

Volume of bigger = k³ X volume of smaller

= (5/3)³ 54π

= 250πcm³

Answer:23/93.

Step-by-step explanation:

The length of FE is equal to 35 units.

In Mathematics and Geometry, the triangle midpoint theorem states that the line segment which connects the midpoints of two (2) sides of a triangle must be parallel to the third side, and it's congruent to one-half of the third side.

By applying the triangle midpoint theorem to the triangle, we have the following:

AE = 1/2(FE)

BD ≅ FE (midpoints of AC and CE)

BD = FE = 35 units.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The given picture with Midpoints B, D, and F, AC is 50 units, CE is 60 units, and BD is 35 units. The length of segment FE is determined to be 35 units.

In the given picture, let's label the points as A, B, C, D, E, and F. It is mentioned that points B, D, and F are midpoints.

Given information:

AC = 50

CE = 60

BD = 35

Since B, D, and F are midpoints, we know that BD is equal to half of AC and half of CE. Therefore, BD = AC/2 and BD = CE/2.

We are given that BD = 35, so we can set up the equations:

35 = AC/2    ...(Equation 1)

35 = CE/2    ...(Equation 2)

Let's solve Equation 1 for AC:

AC = 35 * 2

AC = 70

Similarly, solving Equation 2 for CE:

CE = 35 * 2

CE = 70

Now, let's consider triangle AFE. Since B and D are midpoints, we know that BD is parallel to FE, and FD is parallel to AE. Therefore, triangle AFE is similar to triangle ADC.

In similar triangles, corresponding sides are proportional. Hence, we can write the following ratios:

FE/AC = FD/AD

Substituting the known values, we get:

FE/70 = 35/AC

Cross-multiplying, we have:

FE * AC = 70 * 35

Since we know AC is 70, we can solve for FE:

FE = (70 * 35) / 70

FE = 35

Therefore, the length of FE is 35 units.

the given information, in the given picture with midpoints B, D, and F, AC is 50 units, CE is 60 units, and BD is 35 units. The length of segment FE is determined to be 35 units.

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Answer:

3.999 millimeters.

Step-by-step explanation:

To find the height of the cylinder, we can use the formula for the volume of a cylinder:

V = πr²h

Given that the radius (r) of the cylinder is 4 millimeters and the volume (V) is 200.96 cubic millimeters, we can substitute these values into the formula and solve for the height (h).

200.96 = π(4²)h

200.96 = 16πh

To solve for h, we can divide both sides of the equation by 16π:

200.96 / (16π) = h

Using a calculator, we can calculate the approximate value of h:

h ≈ 200.96 / (16 × 3.14159)

h ≈ 3.999

Therefore, the height of the cylinder is approximately 3.999 millimeters.

The correct formula for finding the break-even point is option C:

Break even point = (0.01)(#of points)(P)/monthly savings.

In this formula, the break-even point is calculated by multiplying the number of points (#of points), the price per unit (P), and a factor of 0.01, then dividing it by the monthly savings.

It's important to note that the break-even point is the level of sales or production at which total costs and total revenue are equal, resulting in neither profit nor loss. The formula above provides a way to determine the break-even point by considering the relevant variables.

Regarding your explanation of posting the answers in your questions, I understand your situation. If you encounter any issues or limitations with the platform, feel free to provide any necessary context or information in the questions. I'm here to assist you further if needed.

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Answer:

Decrease in temp.

Step-by-step explanation:

Here is the reason:

Initially, at an altitude of 3,000 meters above sea level, the temperature was 12 degrees Celsius. As the altitude increased, the temperature dropped to 4 degrees Celsius. Since the temperature decreased from 12 degrees Celsius to 4 degrees Celsius, there was a decrease in the temperature

The amount that Mark will pay monthly if the house's original price is 15,000,000 pesos for 20 years at 13.75% monthly compounded interest is 183,810.81 pesos.

The monthly payment can be computed using an online finance calculator that incorporates the compound interest system.

The compound interest system charges interest on both the principal and the accumulated interest for each period.

N (# of periods) = 240 months

I/Y (Interest per year) = 13.75%

PV (Present Value) = 15,000,000 pesos

FV (Future Value) = 0

Results:

Monthly Payment (PMT) = 183,810.81 pesos

The sum of all periodic payments = 44,114,593.72 pesos

Total Interest = 29,114,593.72 pesos

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Answer:

Step-by-step explanation:

please what grade this if you answer i will help you

The simplified expression in the context of this problem is given as follows:

[tex]5\sqrt{5}(\sqrt{10} - 3) = 25\sqrt{2} - 15\sqrt{5}[/tex]

The expression in the context of this problem is given as follows:

[tex]5\sqrt{5}(\sqrt{10} - 3)[/tex]

Applying the distributive property, we multiply the outer term by each of the inner terms, hence:

[tex]5\sqrt{50} - 15\sqrt{5}[/tex]

The number 50 can be written as follows:

50 = 2 x 25.

Hence the square root is simplified as follows:

[tex]\sqrt{50} = \sqrt{2 \times 25} = 5\sqrt{2}[/tex]

Hence the simplified expression is given as follows:

[tex]25\sqrt{2} - 15\sqrt{5}[/tex]

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The ratio of the surface area to the volume of a cylinder is (2rh + 2r²) / (r²h).

The formula for the surface area of a cylinder is:

Surface Area = 2πrh + 2πr²

Volume of Cylinder: The volume of a cylinder is given by the formula:

Volume = πr²h

Ratio of Surface Area to Volume:

Ratio = (2πrh + 2πr²) / (πr²h)

Simplifying the expression, we can cancel out the common factors of π and r:

Ratio = (2rh + 2r²) / (r²h)

So, the ratio of the surface area to the volume of a cylinder is (2rh + 2r²) / (r²h).

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Tamara should expect the sum of the two cubes to be equal to 7 around 30 times when rolling the two number cubes 180 times.

To determine how many times Tamara should expect the sum of the two number cubes to be equal to a certain value, we need to analyze the chart and calculate the probabilities.

Let's examine the chart and count the number of times each sum occurs:

Sum: 2, Occurrences: 1

Sum: 3, Occurrences: 2

Sum: 4, Occurrences: 3

Sum: 5, Occurrences: 4

Sum: 6, Occurrences: 5

Sum: 7, Occurrences: 6

Sum: 8, Occurrences: 5

Sum: 9, Occurrences: 4

Sum: 10, Occurrences: 3

Sum: 11, Occurrences: 2

Sum: 12, Occurrences: 1

Now, let's calculate the probabilities of each sum occurring.

Since there are 36 possible combinations when rolling two number cubes, the probability of each sum is the number of occurrences divided by 36:

Probability of sum 2 = 1/36

Probability of sum 3 = 2/36

Probability of sum 4 = 3/36

Probability of sum 5 = 4/36

Probability of sum 6 = 5/36

Probability of sum 7 = 6/36

Probability of sum 8 = 5/36

Probability of sum 9 = 4/36

Probability of sum 10 = 3/36

Probability of sum 11 = 2/36

Probability of sum 12 = 1/36

To find out how many times Tamara should expect a certain sum when rolling the two number cubes 180 times, we can multiply the probability of that sum by 180.

For example, to find the expected number of times the sum is 7:

Expected occurrences of sum 7 = (6/36) [tex]\times[/tex] 180 = 30

Similarly, we can calculate the expected occurrences for all other sums.

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Applying the tangent ratio, the value of x in the image, rounded to the nearest thousandth is: 15.824.

The tangent ratio, commonly referred to as "tangent," is a trigonometric function that relates the ratio of the length of the side opposite an angle to the length of the side adjacent to that angle in a right triangle. It is expressed as:

tan (∅) = opposite/adjacent

We have the following:

Reference angle (∅) = 53 degrees

Length of opposite side = 21

Length of adjacent side = x

Plug in the values:

tan 53 = 21/x

x * tan 53 = 21

x = 21 / tan 53

x = 15.824

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Answer:

A. 144

D. √9 * √16.  

Step-by-step explanation:

The product property of square roots states that for any two numbers (a and b), where both are greater than or equal to 0, the square root of a product is equal to the product of the square root:

[tex]\sqrt{ab}=\sqrt{a} *\sqrt{b}[/tex]

Thus, √(9 * 16) is equivalent to √9 * √16.  

We can see this mathematically if we evaluate the expressions:

[tex]\sqrt{(9*16)}=\sqrt{9}*\sqrt{16}\\ \sqrt{144}=3*4\\ 12=12[/tex]

Thus, the answers are A and D.

If you can only choose one answer, choose D because the question didn't explicitly ask us to evaluate √(9 * 16).

If you can choose multiple answers, choose A and D.

The Quadratic equation in standard form that corresponds to the given parabola is (x + 1)^2 = 12y.

The quadratic equation in standard form that corresponds to the graph of the parabola passing through the points (2, 0) and (-4, 0), we can use the vertex form of a parabola equation, which is (x - h)^2 = 4a(y - k). the vertex of the parabola. The vertex is the midpoint of the line segment connecting the two given points.

The x-coordinate of the vertex is the average of the x-coordinates of the two points:

(2 + (-4))/2 = -2/2 = -1

The y-coordinate of the vertex is the same as the y-coordinate of both given points:

y = 0

Therefore, the vertex of the parabola is (-1, 0).

Now, let's find the value of 'a', which represents the coefficient in front of the y-term. We know that the distance from the vertex to either of the given points is equal to 'a'. In this case, the distance from the vertex (-1, 0) to either (2, 0) or (-4, 0) is 3 units.

So, 'a' = 3.

Now, we can write the quadratic equation in standard form:

(x - h)^2 = 4a(y - k)

Plugging in the values we found:

(x - (-1))^2 = 4(3)(y - 0)

Simplifying:

(x + 1)^2 = 12y

Therefore, the quadratic equation in standard form that corresponds to the given parabola is (x + 1)^2 = 12y.

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To find the derivative matrix of the composition of functions f∘g, we need to compute the partial derivatives of f with respect to u and v, and then evaluate them at the point (u(x, y), v(x, y)). Let's calculate the partial derivatives first:

∂f/∂u = cos(u)cos(v)

∂f/∂v = -sin(u)sin(v)

Now, let's substitute u = 4x^2 - 5y and v = 3x - 5y into the partial derivatives:

∂f/∂u = cos((4x^2 - 5y))cos((3x - 5y))

∂f/∂v = -sin((4x^2 - 5y))sin((3x - 5y))

The derivative matrix D(f∘g)(x, y) is a 1x2 matrix (a row vector) where each entry represents the partial derivative of f∘g with respect to x and y, respectively.

D(f∘g)(x, y) = (∂f/∂u ∂f/∂v) evaluated at (u(x, y), v(x, y))

D(f∘g)(x, y) = (cos((4x^2 - 5y))cos((3x - 5y)), -sin((4x^2 - 5y))sin((3x - 5y)))

Answer:

True

Step-by-step explanation:

If the discriminant [tex]D=b^2-4ac < 0[/tex], then there are two complex roots

If the discriminant [tex]D=b^2-4ac > 0[/tex], then there are two real roots

If the discriminant [tex]D=b^2-4ac=0[/tex], then there is only one real root

At a price of $3, the total revenue will be the greatest, and the company will sell 3 units at that price.

To find the total revenue at each price, we can multiply the price by the corresponding quantity.

Price        Quantity          Total Revenue

$6                0                      $0

$5                 1                       $5

$4                 2                       $8

$3                 3                        $9

$2                 4                         $8

$1                  5                          $5

To find the price at which total revenue is the greatest, we look for the highest value in the Total Revenue column.

In this case, the highest total revenue is $9, which occurs when the price is $3.

At a price of $3, the company will sell 3 units (as indicated in the Quantity column).

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Answer:

Step-by-step explanation:

The system of equations with no solution is:

y + 3x = -7

4z - 2y = 10

The system of equations with exactly one solution is:

y = 6z+8

y = 6x-4

y = 3x + 2

2z-y = 5

y=-2z+8

The system of equations with infinitely many solutions is:

4z + y = 8

The area of the parallelogram of triangle would be listed below as follows:

19A.) = 336mm²

19B.) = 416in²

To calculate the area of the parallelogram of triangle, the formula for the area of the parallelogram should be used and it is given as follows:

Area of parallelogram = base×height

For A.)

Base = 18+10 = 28mm

height = 12mm

Area = 28×12 = 336mm²

For B.)

Base = 26in

Height = 16(using the sine rule)

Area = 26×16 = 416in²

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Therefore, we would predict that a catfish with a length of 33 inches would weigh approximately 26.5 pounds.

Jin has decided to research the relationship between the length in inches and the weight of a certain species of catfish. He measures the length and weight of a number of specimens he catches, then throws back into the water. After plotting all his data, he draws a line of best fit.

The given problem is related to a scatter plot, which depicts the relationship between the length in inches and the weight of a certain species of catfish. Based on the scatter plot, it is clear that there is a positive correlation between length and weight.

The correlation between the two variables can be measured using the correlation coefficient, r, which ranges between -1 and 1, where -1 denotes a perfect negative correlation, 1 denotes a perfect positive correlation, and 0 denotes no correlation.

The line of best fit can be determined using the method of least squares.

This method minimizes the sum of the squared errors between the observed values and the predicted values.

The equation of the line of best fit is

y = mx + b,

where m is the slope of the line and b is the y-intercept.

To predict the weight of a catfish with a length of 33 inches, we need to use the equation of the line of best fit.

Let's assume that the equation of the line of best fit is

y = 0.5x + 10,

where y is the weight of the catfish in pounds and x is the length of the catfish in inches.

Then, we can substitute x = 33 into the equation to obtain:

y = 0.5(33) + 10

   = 16.5 + 10

   = 26.5

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4. The x-intercept of g(x) is 2.

The y-intercept of g(x) is -4.

5. The minimum value of g(x) is -8.

The maximum value of g(x) is 17.

In Mathematics and Geometry, the x-intercept is also referred to as horizontal intercept and the x-intercept of the graph of any function simply refers to the point at which the graph of a function crosses or touches the x-coordinate (x-axis) and the y-value or the value of "f(x)" is equal to zero (0).

By critically observing the table representing the function g(x), we can logically deduce the following x-intercept and y-intercept:

Question 5.

By critically observing the table representing the function g(x), we can logically deduce the following minimum value and maximum value over the interval [-2, 3];

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To find the area of a parallelogram in the coordinate plane, we need to determine the base and the height of the parallelogram.

Using the given coordinates, we can find the length of one side of the parallelogram as the distance between points A and B.

The length of AB = sqrt((6 - 7)^2 + (5 - 5)^2) = sqrt((-1)^2 + 0^2) = sqrt(1) = 1

The height of the parallelogram can be found as the distance between point D and the line passing through points A and B. We can use the formula for the distance between a point and a line to find the perpendicular distance.

The equation of the line passing through A and B can be found using the point-slope form:

y - 5 = (5 - 5)/(7 - 6) * (x - 7)

y - 5 = 0 * (x - 7)

y - 5 = 0

y = 5

The perpendicular distance from point D(-9, -2) to the line y = 5 is the difference in their y-coordinates:

Perpendicular distance = |-2 - 5| = 7

Now, we have the base length AB = 1 and the height = 7.

The area of the parallelogram is given by the formula: Area = base * height.

Area = 1 * 7 = 7 square units.

Check the picture below.

[tex]\textit{area of a trapezoid}\\\\ A=\cfrac{h(a+b)}{2}~~ \begin{cases} h~~=height\\ a,b=\stackrel{parallel~sides}{bases~\hfill }\\[-0.5em] \hrulefill\\ a=1\\ b=13\\ h=7 \end{cases}\implies A=\cfrac{7(1+13)}{2}\implies A=49[/tex]