Find the exact value of cos (2theta), given tan A = -8/15, and theta lies in Quadrant II.

Please show steps and thank you in advance!

If cosA = 24/25 tanB = 4/3 and angles A and B are in Quadrant I. The value of tan(A-B) is -23/33.

We can start by using the identity: tan(A - B) = (tan A - tan B)/(1 + tan A tan B)

From the given information, we have:

cos A = 24/25, which means sin A = sqrt(1 - cos^2 A) = 7/25 (since A is in Quadrant I)

tan B = 4/3, which means sin B = 4/sqrt(4^2 + 3^2) = 4/5 and cos B = 3/sqrt(4^2 + 3^2) = 3/5

Now, we can use the definitions of sine and cosine to find tan A:

tan A = sin A / cos A = (7/25)/(24/25) = 7/24

Substituting the values we have found into the formula for tan(A - B), we get:

tan(A - B) = (tan A - tan B)/(1 + tan A tan B)

= [(7/24) - (4/3)]/[1 + (7/24)(4/3)]

= (-13/72)/(25/72)

= -13/25

Therefore, tan(A - B) = -13/25.

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The drive-thru that typically has more wait time is

Burger Quick, because it has a larger median.

Option A is correct.

Because Burger Quick's box plot displays a higher interquartile range (from 9.5 to 24) than Super Fast Food (from 8.5 to 15.5), Burger Quick often has longer wait times.

Additionally, Burger Quick's median (15.5) is greater than Super Fast Food's median (12), demonstrating that Burger Quick's middle value of reported wait times is higher than Super Fast Food's middle value of reported wait times.

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Answer:

19,188

Step-by-step explanation:

hope this helps ;)

Answer: 1.7(repeating) OR 1.78

Step-by-step explanation:

Divide 4 by 2.25 (2 1/4)

Given the polynomial 4x2y4 − 9x2y6, rewrite as a product of polynomials. (2xy2 − 3xy3)(2xy2 + 3xy3). So, correct answer is A.

To multiply two binomials, we use the FOIL method which stands for First, Outer, Inner, Last. For option A, using the FOIL method, we get

(2xy² - 3xy³)(2xy² + 3xy³) = (2xy²)² - (3xy³)² = 4x²y⁴ - 9x²y⁶

This is the given polynomial, so option A is correct.

For other option, we have two identical binomials multiplied together, which would give us a trinomial with three terms, so it cannot be a product of two binomials.

Option C is also incorrect because when we multiply the two binomials, we do not get the given polynomial. Option D is incorrect as well because the signs are incorrect and we would get a different polynomial when we multiply the two binomials.

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--The given question is incomplete, the complete question is given

" Given the polynomial 4x²y⁴ − 9x²y⁶, rewrite as a product of polynomials. a. (2xy² − 3xy³)(2xy² + 3xy³) b. (2xy² − 3xy³)(2xy² − 3xy³) c. (4xy² + 9xy³)(xy² − xy³) d. (4xy² − 9xy³)(xy² − xy³)"--

The sum of the expression is simplified to give x² + 11x - 6/(x-3)(x+3)

Algebraic expressions are simply defined as expressions that consist of terms, factors, constants, variables and coefficients.

These mathematical expressions are also made up of arithmetic operations such as;

From the information given, we have the expression as;

x-2/x-3  + 10x/x² - 9

Find the lowest common factor, we have;

(x-2)(x+3) + 10x/(x-3)(x+3)

expand the bracket

x² + 3x - 2x - 6 +10x/(x-3)(x+3)

Now, add the like terms, we get;

x² + 11x - 6/(x-3)(x+3)

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The new cost after the discount and tax are applied is $872.10, which is option (d).

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data.

First, let's calculate the amount of discount Angel will receive using the coupon code:

Discount = 15% of $950 = 0.15 x $950 = $142.50

Next, let's calculate the new price of the jacket after the discount is applied:

New price = $950 - $142.50 = $807.50

Now, let's calculate the amount of tax that will be applied to the new price:

Tax = 8% of $807.50 = 0.08 x $807.50 = $64.60

Finally, let's add the tax to the new price to get the total cost:

Total cost = $807.50 + $64.60 = $872.10

Therefore, the new cost after the discount and tax are applied is $872.10, which is option (d).

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The circumferences and areas of the circles are listed below:

Case 2: s = 54.689 cm

Case 3: 16257.980 ft²

Case 4: 26.999 mm

In this problem we need to determine the circumference and the area of the circle, whose equations are introduced below:

Circumference

s = 2π · R

Area

A = π · R²

Where:

Case 2 (A = 238 cm²)

R = √[(238 cm²) / π]

R = 8.704 cm

s = 2π · (8.704 cm)

s = 54.689 cm

Case 3 (s = 452 ft)

R = (452 ft) / 2π

R = 71.938 ft

A = π · (71.938 ft)²

A = 16257.980 ft²

Case 4 (A = 58 mm²)

R = √[(58 mm²) / π]

R = 4.297 mm

s = 2π · (4.297 mm)

s = 26.999 mm

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The equation of the given circle is;Option D; x² + y² = 9

The general formula for the equation of a circle is expressed as;

(x - h)² + (y - k)² = r²

Where;

We are told that;

Circle is at the origin with coordinates (0, 0)

r = 3

Substitute the known values in the above equation, so, we have the following representation

(x - 0)² + (y - 0)² = 3²

Evaluate the exponents and open the brackets

x² + y² = 9

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The equation of the circle is; Option D: x² + y² = 9

The general formula for expressing the equation of a circle is :

(x - h)² + (y - k)² = r²

Where;

(h, k) is the coordinate of the center of the circle

r is the radius of the circle

From the given image of the circle, we see that the center of the circle is at the origin. Thus, the coordinates of the center of the circle is (0, 0)

We also see that from the origin to the circumference is 3. Thus:

r = 3

Plugging in the relevant values into the circle equation, we have:

(x - 0)² + (y - 0)² = 3²

Simplifying further gives us:

x² + y² = 9

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The matrix of dependent coefficients and the vector column of independent variables of the system of linear equations are:

[tex]\vec A = \left[\begin{array}{ccc}1&-2&3\\-4&5&-6\\7&-8&9\end{array}\right][/tex]

[tex]\vec {b} =\left[\begin{array}{ccc}6\\8\\1\end{array}\right][/tex]

In this question we find a representation of a system of three linear equations with three variables {x, y, z}. This system can be described by following expression according to linear algebra:

[tex]\vec A \,\bullet \,\vec x = \vec B[/tex]

Where:

Please notice that operator "•" represents a dot product.

Then, the matrix of dependent coefficients and the vector column of independent variables are, respectively:

Matrix of dependent coefficients

[tex]\vec A = \left[\begin{array}{ccc}1&-2&3\\-4&5&-6\\7&-8&9\end{array}\right][/tex]

Vector column of independent variables

[tex]\vec {b} =\left[\begin{array}{ccc}6\\8\\1\end{array}\right][/tex]

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the ratio of Nonfiction novels to all novels is: Nonfiction novels : Total novels  [tex]= 2 : 11[/tex]  So the correct answer is  [tex]2:11.[/tex]

The ratio of Nonfiction novels to all novels can be calculated by dividing the number of Nonfiction novels by the total number of novels.

The total number of novels is the sum of Nonfiction, mystery, and fiction novels:

Total number of novels = Nonfiction + Mystery + Fiction [tex]= 2 + 4 + 5 = 11[/tex]

The ratio of nonfiction novels to all novels is not a fixed value, as it depends on the specific set of novels being considered. However, it can be calculated if we have the appropriate data.

Therefore, the ratio of Nonfiction novels to all novels is: Nonfiction novels : Total novels  [tex]= 2 : 11[/tex] So the correct answer is 2:11.

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Answer:

0.2 oz

Step-by-step explanation:

We Know

1g ≈ 0.035oz

5 gram = ? oz

We Take

0.035 x 5 ≈ 0.175 oz

So, 5 grams ≈ 0.2 oz

I hope this helps you .

A normal curve is symmetrical, with the mean, median, and mode being equal and located at the center of the curve.

It is not skewed (left or right) nor uniform.

A normal curve is a) symmetrical.

A normal curve, also known as a Gaussian curve or a bell curve, is a symmetrical probability distribution curve that represents the distribution of a set of data.

In a normal curve, the mean, median, and mode are equal and located at the center of the curve.
Because the curve is symmetrical, it has the following characteristics:
It is unimodal, meaning it has a single peak.

The tails of the curve extend infinitely in both directions, but the probability of data points at the tails decreases as we move further away from the mean.
The area under the curve equals 1, representing the total probability of all possible outcomes.
In contrast, skewed distributions (left or right) have an asymmetrical shape where the tail extends more prominently in one direction.

A left-skewed distribution has a longer tail on the left side, while a right-skewed distribution has a longer tail on the right side.

Skewed distributions can lead to inaccurate conclusions when using measures of central tendency like the mean.
A uniform distribution is another type of probability distribution where all outcomes have equal probabilities.

In this case, the curve appears as a horizontal line (a rectangle), with no peak or skewness.

A normal curve is a) symmetrical.

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The answer is a) Symmetrical. A normal curve is symmetrical, meaning that it has the same shape on both sides of the central axis.

This is also referred to as a bell curve, as it forms a bell-shaped curve. The term uniform refers to a distribution where all values are equally likely, which does not apply to a normal curve.

A normal curve is a symmetrical bell-shaped curve that represents the probability distribution of a continuous random variable. It is often used as an approximation to the graph of scores or measurements consisting of many bunched values near the average in the middle and a few large and a few small values arranged toward the opposite ends. A normal curve has a mean, median, and mode that are equal and located at the center of the curve. The standard deviation determines how spread out the values are from the mean

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Answer:

90 km/h

Step-by-step explanation:

There are 3600 seconds in an hour. So, let's multiply the unit rate by 3600.

[tex]3600*25=90000[/tex]

So, after 3600 seconds (or an hour), the car will have traveled 90000 meters.

Or, the car's rate is 90000 meters per hour.

1 meter is 0.001 kilometer. Let's multiply 90000 by 0.001 to find how many kilometers the car travels after an hour.

[tex]90000*0.001=90[/tex]

So, the car's speed is 90 km/h.

Answer:

Step-by-step explanation:

One minute is equal to 60 seconds modeled by the ratio 1:60 one hour is equal to 60 minutes modeled by the ratio 1:60 therefore using substitution 1hour:60minutes(1):60seconds(60) therefore 1:[tex]60^{2}[/tex] or 3,600 so in this instance 25m/s = 25:1 and because a km is equal to 1,000 meters as denoted by the prefix kilo. One can understand that multiplying by 1,000 is the same as dividing by 1,000 less therefore instead of doing (25*3600)/1000 you can simply do 25*3.6 which yields 90.

Therefore 2.5m/s = 90km/h

PS. For future reference, you can reference a free conversion tool if you find that easier to use.

An observed effect (the difference between the observed value and the claimed value) is statistically significant if it is unlikely to have occurred due to chance variation.

An observed effect is statistically significant if it is unlikely to be due to chance variation, which means that the probability of observing such a large difference between the observed value and the claimed value purely by chance is very small.

In statistical hypothesis testing, this probability is quantified by a p-value, which is the probability of obtaining a test statistic at least as extreme as the one observed, assuming the null hypothesis is true.

If the p-value is less than a pre-specified significance level (e.g., 0.05), the null hypothesis is rejected, and the observed effect is deemed statistically significant.

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C21 represents 4 senior boys.

A matrix, which is used to represent a mathematical object or an attribute of one, is a rectangular array or table containing numbers, symbols, or expressions that are organized in rows and columns. is a matrix having two rows and three columns, for instance

Given:

[tex]\left[\begin{array}{ccc}5&6\\4&3\\\end{array}\right][/tex], [tex]\left[\begin{array}{ccc}c11&c12\\c21&c22\\\end{array}\right][/tex]

[tex]\left[\begin{array}{ccc}\ Junior boy&Junior girl\\Senior boy&Senior girl\\\end{array}\right][/tex]

4 Senior boys is c21 represented.

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Answer:

The choice that provides the greatest advantage for a career as an art teacher is:

enjoys children, is flexible, competent in a variety of art forms, and is energetic

Here are the key reasons why this is the best choice:

• Enjoys children - Working with students is core to being a teacher. An art teacher needs to enjoy interacting with and assisting children.

• Is flexible - The role of a teacher requires adapting to different students' needs, interests, abilities and challenges. Flexibility is important.

• Competent in a variety of art forms - An art teacher needs to be knowledgeable and skilled across different art mediums, subjects, techniques to support students.

• Is energetic - Teaching requires passion, enthusiasm and energy to keep students engaged and motivated.

In contrast, the other options lack important characteristics for an art teacher:

• Dislikes children, dislikes mess, intolerant of noise, and creates computer graphics - These indicate unsuitable qualities for a teacher.

• Organized, neat, quiet, and likes to paint houses in spare time - While organized and detail-oriented are good, the other traits do not reflect the key responsibilities of art instruction and supporting students.

• Enjoys art museums, reads often, hard worker, is a part-time photographer - An interest in art is relevant but not sufficient. Important teaching qualities like flexibility, working with children, knowledge of art forms are missing.

So in summary, the choice that highlights enjoying children, flexibility, competence across art forms, and energy are the characteristics that would provide the greatest advantage for a career as an art teacher. Art knowledge and skills are prerequisite but a passion for instructing students and learning is essential.

Step-by-step explanation:

The third outer loop execution (i = 3), the loop compares the third element (12) with the remaining elements in the list (13, 14, 15) for a total of 3 comparisons

Assuming the outer loop is a standard loop that iterates through the list from the first to the second-to-last element, the number of comparisons made during the third outer loop execution (i = 3) would be 3.

During the first outer loop execution (i = 1), the loop compares the first element (10) with the rest of the elements in the list (11, 12, 13, 14, 15) for a total of 5 comparisons.

During the second outer loop execution (i = 2), the loop compares the second element (11) with the remaining elements in the list (12, 13, 14, 15) for a total of 4 comparisons.

During the third outer loop execution (i = 3), the loop compares the third element (12) with the remaining elements in the list (13, 14, 15) for a total of 3 comparisons.

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Assuming you are using a standard bubble sort algorithm, during the third outer loop execution (i = 3), there will be 3 comparisons made.

The given list (10, 11, 12, 13, 14, 15) and the number of comparisons made during the third outer loop execution (i = 3):

In the first outer loop iteration (i = 1), there will be 5 comparisons (comparing elements at positions 1-2, 2-3, 3-4, 4-5, and 5-6).

In the second outer loop iteration (i = 2), there will be 4 comparisons (comparing elements at positions 1-2, 2-3, 3-4, and 4-5).

In the third outer loop iteration (i = 3), there will be 3 comparisons (comparing elements at positions 1-2, 2-3, and 3-4).

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Answer:

  144 m²

Step-by-step explanation:

You want to know the surface area of a square base pyramid with a side length of 6 m and a slant height of 9 m.

The area of the given net is the sum of the areas of 4 congruent triangles and one square. The areas of these can be found using the relevant formulas.

  SA = square area + 4 × triangle area

  SA = 6² + 4 × 1/2(6)(9) = 36 +108

  SA = 144 . . . . square meters

__

Additional comment

The area of a square of side s is A = s².

The area of a triangle with base b and height h is A = 1/2bh.

Answer:

Let's denote:

M: the set of students who like maths

S: the set of students who like science

n(M): the number of students who like maths

n(S): the number of students who like science

n(M ∩ S): the number of students who like both maths and science

n(M ∪ S): the number of students who like maths or science (or both)

We can use the principle of inclusion-exclusion to find n(M ∪ S):

n(M ∪ S) = n(M) + n(S) - n(M ∩ S)

From the problem statement, we know:

n(M) = 10

n(S) = 15

n(M ∩ S) = ? (unknown)

We also know that 10 students like neither maths nor science, which means that:

n(M ∪ S)' = 10

where (M ∪ S)' denotes the complement of M ∪ S, i.e., the set of students who do not like maths or science.

We can use the formula:

n(A') = N - n(A)

where N is the total number of students (N = 50).

n(M ∪ S)' = n((M ∪ S))' = N - n(M ∪ S) = N - (n(M) + n(S) - n(M ∩ S))

Substituting the known values:

n((M ∪ S))' = 50 - (10 + 15 - n(M ∩ S)) = 25 + n(M ∩ S)

Simplifying:

n(M ∩ S) = n((M ∪ S))' - 25 = 10

Therefore, we have:

n(M ∪ S) = n(M) + n(S) - n(M ∩ S) = 10 + 15 - 10 = 15

The ratio of the students who like maths or science is:

n(M ∪ S) / N = 15 / 50 = 3/10

So the required ratio is 3:10.

Step-by-step explanation:

The value of the system in which newton's law of motion is applicable is (a) 25 (b) 10 (c) if output is x , 4y -x-15 =0

What about newton's law of motion?

Newton's laws of motion are three fundamental laws in classical physics that describe the behavior of objects in motion. They were first presented by Sir Isaac Newton in his work "Philosophiee Naturalis Principia Mathematica" in 1687. The three laws are:

According to the given information:

a) When input is 10.

   output= 10×4 - 15 =25

b) From the question output is 25

  Because input* 4 -15= output. So (output +15) / 4= input

  so input =[tex](25+15)/4[/tex] =10

c) if output is x. So y × 4 - 1 5 = x , 4y - x - 15 = 0

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The value of the system in which newton's law of motion is applicable is (a) 25 (b) 10 (c) if output is x , 4y -x-15 =0

What about newton's law of motion?

Newton's laws of motion are three fundamental laws in classical physics that describe the behavior of objects in motion. They were first presented by Sir Isaac Newton in his work "Philosophiee Naturalis Principal Mathematical" in 1687. The three laws are:

The Law of Inertia: An object at rest will remain at rest, and an object in motion will continue in a straight line with constant velocity, unless acted upon by an external force.

The Law of Acceleration: The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. Mathematically, F = ma, where F is the net force, m is the mass of the object, and a is the acceleration.

The Law of Action-Reaction: For every action, there is an equal and opposite reaction. This means that when an object exerts a force on another object, the second object exerts an equal and opposite force back on the first object.

According to the given information:

a) When input is 10.

  output= 10×4 - 15 =25

b) From the question output is 25

 Because input* 4 -15= output. So (output +15) / 4= input

 so input = =10

c) if output is x. So y × 4 - 1 5 = x , 4y - x - 15 = 0

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The amount of juice that can be poured into 6 cups with a diameter of 4.4 inches and a height of 7 inches is 638.30 cubic inches (rounded to the nearest hundredth).

Solution:We can use the formula to find the volume of a cylinder,V = πr²hwhere V is the volume of the cylinder, r is the radius of the base, h is the height of the cylinder, and π is the mathematical constant approximately equal to 3.14.To begin solving this problem, we must first find the radius of the base of the cylinder.

Since the diameter of each cup is given as 4.4 inches, the radius is half of this, or 2.2 inches.Now we can use the formula for the volume of a cylinder, with r = 2.2 inches and h = 7 inches.V = πr²hV = 3.14(2.2)²(7)V ≈ 106.38 cubic inches

This is the volume of juice that can be poured into a single cup. To find the total volume of juice that can be poured into 6 cups, we multiply this by 6.6(106.38) ≈ 638.30 cubic inches

Therefore, the answer is 638.30 cubic inches.

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The amount of money earned over six weekends is best described as decreasing. The Option A.

Decreasing income refers to a situation in which an individual or household experiences a reduction in the amount of money earned over a certain period of time.

This can be caused by a variety of factors, such as job loss, reduction in work hours, or a decrease in wages. When income decreases, individuals may find it more difficult to meet their financial obligations, such as paying bills, making rent or mortgage payments, and purchasing basic necessities like food and clothing.

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The z-score associated with an observed age at first marriage of 25.50 is 0.35.

To calculate the z-score associated with an observed age at first marriage of 25.50, we use the formula:

z = (x - μ) / σ

where:

x = the observed age at first marriage (25.50)

μ = the mean age at first marriage (23.33)

σ = the standard deviation of age at first marriage (6.13)

Substituting the given values, we get:

z = (25.50 - 23.33) / 6.13

z = 0.35

Therefore, the z-score associated with an observed age at first marriage of 25.50 is 0.35.

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The equation of the quadratic function that models the height of the ball h(t) at time t is h(t) = -2(t-3)^2 + 46. So, correct option is D.

The height of the ball at time t can be modeled by a quadratic function in the form h(t) = at^2 + bt + c, where a, b, and c are constants that we need to find.

We know that after 1 second, the height of the ball is 10 feet. This gives us the point (1, 10), which we can substitute into the quadratic equation to get:

10 = a(1)^2 + b(1) + c

10 = a + b + c --------------- (1)

We also know that after 4 seconds, the ball reaches its maximum height of 46 feet. This gives us the point (4, 46), which we can substitute into the quadratic equation to get:

46 = a(4)^2 + b(4) + c

46 = 16a + 4b + c --------------- (2)

Finally, we know that after 7 seconds, the height of the ball is back to 10 feet. This gives us the point (7, 10), which we can substitute into the quadratic equation to get:

10 = a(7)^2 + b(7) + c

10 = 49a + 7b + c --------------- (3)

Now we have a system of three equations (equations 1, 2, and 3) with three unknowns (a, b, and c) that we can solve. Using algebraic manipulation or substitution, we can solve for a, b, and c to get:

a = -2, b = 12, and c = 28

Therefore, the equation of the quadratic function that models the height of the ball h(t) at time t is:

h(t) = -2t^2 + 12t + 28

The answer is not listed among the choices, but if we simplify the equation we can see that it matches with option D:

h(t) = -2(t-3)^2 + 46

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The probability of drawing two red balls in a row from one of the two boxes, given that the first ball drawn is red, is 1/7.

The first step in solving this problem is to determine the probability of selecting the red box versus the other box. Since we have two boxes and each one has an equal chance of being selected, the probability of selecting the red box is 1/2.

Now we can put all of these probabilities together to determine the overall probability of drawing two red balls in a row from one of the two boxes.

We know that the probability of selecting the red box is 1/2, the probability of drawing a red ball on the first try is 4/7, and the probability of drawing a red ball on the second try, given that we've already drawn one red ball, is 1/2.

To find the overall probability, we simply multiply these three probabilities together:

(1/2) x (4/7) x (1/2) = 1/7

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The probability that the second ball will be red, given that the first ball is red, is 3/7.

To find the probability that the second ball will also be red given that the first ball is red, we need to consider two cases.

Case 1: Selecting a box with 4 red balls and 3 purple balls.

Case 2: Selecting a box with 4 green balls and 3 red balls.

Now, we calculate the overall probability by adding the probabilities of the two cases: (4/7) * (3/6) + (3/7) * (2/6) = 12/42 + 6/42 = 18/42 = 3/7.

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Answer: An arc whose measure equals 180 degrees is called a semicircle, since it divides the circle in two. Every pair of endpoints on a circle either defines one minor arc and one major arc, or two semicircles. Only when the endpoints are endpoints of a diameter is the circle divided into semicircles.

A semicircle is a two-dimensional geometric shape that consists of a curved arc and a straight line segment that connects the two endpoints of the arc. Here are the steps to identify a semicircle:

Look for a curved arc that forms a half-circle shape.

Locate the center point of the arc, which is also the midpoint of the line segment connecting the two endpoints.

Check that the line segment connecting the endpoints is a diameter of the circle.

Confirm that the arc and line segment together form a continuous, closed shape that divides the circle into two equal halves.

Finally, compare the shape to a circle to make sure that it is only half of a complete circle.

If all of these conditions are met, then the shape is a semicircle.