Which of the following results in the difference of two squares?

Using arithmetic operations it is obtained that there were approximately 76 female animals in the herd.

What is arithmetic operation?

A subject of mathematics known as arithmetic operations deals with the study and use of numbers in all other branches of mathematics. Basic operations including addition, subtraction, multiplication, and division are included.

If 32% of the animals were males, then 100% - 32% = 68% of the animals were female.

To find the number of female animals in the herd of 112 animals, multiply the total number of animals by the percentage that were female -

68% = 68/100 = 0.68

Number of female animals = 0.68 x 112

Number of female animals = 76.16

Rounding this to the closest whole number gives -

Number of female animals ≈ 76

Therefore, the number of female animals is 76.

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The option that is incorrect is option (b) Because each sample includes exactly one graduate student and four undergraduate students, this is not a random sample.

A simple random sample is a type of probability sampling method used in statistics, where each member of a population has an equal chance of being selected for the sample.

In other words, in a simple random sample, every possible sample of a given data will have has an equal probability of being selected from the population.

Here we have

A statistics class has 10 graduate and 40 undergraduate students.

We want to randomly sample 10% of the students in the class.

Even though one graduate student and four undergraduate students are selected at random, the percentage selecting both categories is the same.

Hence, this is a simple random sample.

Therefore,

The option that is incorrect is option (b) Because each sample includes exactly one graduate student and four undergraduate students, this is not a random sample.

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Answer:

15 oz

Step-by-step explanation:

1/10 of 30 = 30/10 = 3 oz

2/5 of 30 = 30 * 2/5 = 60/5 = 12 oz

add those up to get 3 + 12 = 15 oz eaten

there are thus 30-15 = 15 oz left in the box

The values of m for the given inequality should be in the interval

(-∞, -18/19).

What is meant by inequality?

In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa. Literal inequalities are relationships between two algebraic expressions that are expressed using the inequality symbols. Typically, we use the "not equal" sign to indicate that two values are not equal. However several inequalities are utilised to compare the numbers, whether it is less than or higher than.

Given the inequality,

8m + 95 < -87m +5

We are asked to solve the inequality.

this means we have to find the value of m.

8m + 95 < -87m +5

8m + 87m < 5 - 95

95m < -90

m < -90/95

m< -18/19

Therefore the values of m for the given inequality should be in the interval (-∞, -18/19).

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Answer:

The expression "sine squared theta over the quantity 1 plus cosine theta end quantity" can be simplified to "1 - cos θ".

Answer:

1 - cos θ

Step-by-step explanation:

Therefore , the solution of the given problem of graph comes out to be

option c is correct it shows an association of the distribution of different mode of transportation among the same age of group.

Academics use graphs to visually represent or chart happenings or quantities in a logical manner. The interaction between a number of objects is frequently represented by a graph point. A graph is a non-linear storage structure made up of nodes, also known as vertices, and edges. The vertices, sometimes referred to as nodes, should be joined together with glue. Vertex numbers in this graph are 1, 2, 3, or 5, while edge numbers are 1, 2, 1, 3, 2, 4, etc. (2.5). (3.5). (4.5). (4.5). (4.5).

Here,

Given : A graph having choices of adult , child , teen  and senior mode of transportation ,

In different age the mode of transportation preferred by among the same ages .

Thus ,

it shows an association of the distribution of different mode of transportation among the same age of group.

So , option c is the correct answer.

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The variable which is always positive will be a, b, c, d, p, and q. The constant that lies between 0 to 1 will be 'b'. And the two constants that are definitely equal will be 'a' and 'c'.

Let 'a' is the leading coefficient and 'b' is the factor.

The exponent is given as,

y = a(b)ˣ

Some points regarding the exponent function:

The variable which is always positive will be a, b, c, d, p, and q. The constant that lies between 0 to 1 will be 'b'. And the two constants that are definitely equal will be 'a' and 'c'.

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Answer:

Step-by-step explanation:

50% of 366 is 183, therefore your answer is 366.

The constant of proportionality (k) for the graph is 11.7.

The proportional equation for the graph is y = 11.7x.

In Mathematics, a proportional relationship can be defined as a type of relationship that generates equivalent ratios and it can be modeled or represented by the following mathematical expression:

y = kx

Where:

Next, we would determine the constant of proportionality (k) for money earned per hour as follows:

Constant of proportionality, k = y/x

Constant of proportionality, k = 35.1/3 = 81.9/7

Constant of proportionality, k = 11.7.

Therefore, the required equation is given by:

y = kx

y = 11.7x

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(a) Ann used 4/10 blue beads i.e. 80.

(b) Ann had 160 beads in the end.

The solution has been obtained by using arithmetic operations.

What are arithmetic operations?

According to mathematicians, any real number may be expressed using the four basic operations, also referred to as "arithmetic operations." The four mathematical operations that produce quotient, product, sum, and difference, respectively, are divide, multiply, add, and subtract.

(a) We are given that Ann had a total of 285 red and blue beads, and she used 45 red beads and 40% of the blue bead.

Let the red beads be x and blue beads be y

So, we get

x + y = 285

x = 285 - y

After using the beads, we get another equation as

⇒(x - 45) / (y - 0.4y) = 1/3

⇒(285 - y - 45) / (y - 0.4y) = 1/3

⇒(240 - y) / (0.6y) = 1/3

⇒720 - 3y = 0.6y

⇒720 = 3.6y

⇒y = 200

So, x = 85

Blue beads used = 40% of 200 = 80

(b) Since, Ann has used 80 blue beads and 45 red beads, so

Beads in the end = 285 - 45 - 80 = 160

Hence, Ann had 160 beads in the end.

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Answer:

  15.8%

Step-by-step explanation:

You want the percentage of world bike production represented by 13.239 million bikes out of a world production of 84 million bikes.

A fraction is converted to a percentage by multiplying it by 100%.

  13.239/84 × 100% ≈ 15.8%

Germany contributed about 15.8% of the world's bike production in 2006.

Answer:

6 times

HOPE THE ANSWER HELPS

There are 120 different ways to create a path to 3 different roller coasters at Six Flags.

There are a total of 10 choose 3 ways (120) to choose 3 roller coasters out of the 10 available at Six Flags. To calculate this, we can use the combination formula.

The combination formula is:

In this case, n is 10 and r is 3, so the total number of possible combinations is

To calculate the number of combinations without using a formula, we can use the following method: Start with the first roller coaster, then add a second roller coaster, then a third. There are 10 choices for the first roller coaster, then 9 for the second, and 8 for the third. This results in:

which is 6 times more than the 120 calculated by the combination formula. This is because the combinations ABC and CBA are the same, and so are other combinations that are just permutations of each other.

Therefore, there are 120 different ways to create a path to 3 different roller coasters at Six Flags.

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Answer:

Three days from Tuesday is Friday.

Answer:

(x - 1)^2 + (y + 3)^2 = 400.

Step-by-step explanation:

Your equation is correct.

The center of the circle is (1, -3), which is the midpoint of the diameter. The diameter is 20, so the radius is 10. The equation of a circle with center (h, k) and radius r is given by:

(x - h)^2 + (y - k)^2 = r^2

Substituting the values, we get:

(x - 1)^2 + (y + 3)^2 = 10^2

Simplifying the right side, we get:

(x - 1)^2 + (y + 3)^2 = 100

Therefore, the equation of the circle is (x - 1)^2 + (y + 3)^2 = 400.

The return on total assets (ROTA) can be calculated using the formula:

ROTA = Net Income / Average Total Assets

Using the given information, we have:

ROTA = $386,760 / $5,230,000 = 0.0739 or 7.39%

Therefore, the return on total assets for the company is 7.39%. Note that this answer is rounded to two decimal places.

The approximate area between the x-axis and the graph of f(x) =x² +3

over the interval [0, 2] is 9.75.

introducing intervals, bounded collections of numerical values that are highly helpful in explaining domain and range. To demonstrate where a value lies in relation to two endpoints, we can use interval notation.

To approximate the area between the x-axis and the graph of

 f(x) = x² + 3 over the interval [0, 2].

The heights of the rectangles in the right rectangle method are determined by the function's value at the right endpoint of each subinterval. The right endpoints of each subinterval would be 0.5, 1, 1.5, and 2 if the range [0, 2] were divided into 4 equal subintervals, each of width 0.5.

The height of the first rectangle

f(0.5) = 0.5² + 3

f(0.5) = 3.25

and, the height of the second rectangle

f(1) = 1² + 3

f(1) = 4

and, the height of the third rectangle

f(1.5) = 1.5² + 3

f(1.5) = 5.25

and, the height of the fourth rectangle

f(2) = 2² + 3

f(2) = 7

So, sum of the areas of the rectangles

= (0.5) × (3.25+4+5.25+7)

= (0.5) × 19.5

= 9.75

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The value of "a" will be 30 for the given Algebraic expression.

Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.

Given, a algebraic expression 6a -4a +5a = 210

Simplifying the equation in terms of a

6a -4a +5a = 210

adding or subtracting the terms with the same variables

7a = 210

divide by 7 on both sides

a = 30

Therefore, the value of "a" will be 30 for the given Algebraic expression.

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The original price of the game card was approximately $46.58.

When the game can be effectively described by a numerical "characteristic function," such as v(S), which expresses how much any coalition S of players may win with certainty, regardless of the behaviour of the other players, then we can most readily determine the value of the game.

Let x represent the game card's initial cost. So 1 - 0.27 = 0.73, the price would be 0.73x after a 27% drop.

We are aware that 34.00 = 0.73x. We can divide both sides by 0.73 to find x:

x = 34.00 ÷ 0.73

x ≈ 46.58

Thus, the game card's initial cost was only about $46.58.

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1. Point - Corner of a Vaccination room

2. Plane  - Face mask

3. Line - The long chain of children for pediatric vaccination

Point:

A point is represented as a "dot" on paper. There will be no length, width, or height existing for a point. It simply identifies a certain position. Zero dimensions apply to it.

Line:

The line is a one-dimensional shape in geometry. A line, thus, has length but neither width nor height. In any direction, a line never stops. Two end points of lines act as the fundamental determinants of a line.

Plane:

The coordinate plane, which is used to plot points in algebra, is an example of a plane. The number lines on the coordinate plane stretch eternally from left to right and from up to down, respectively. The coordinate plane cannot be seen entirely.

Here we have

Corner of a Vaccination room,  Face mask, The long chain of children for pediatric vaccination

Where

The corner of a Vaccination room represents a point.

Face mask represents a plane

The long chain of children for pediatric vaccination represents a line.

Therefore,

1. Point - Corner of a Vaccination room

2. Plane  - Face mask

3. Line - The long chain of children for pediatric vaccination

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Answer:

The ordered pair that is a solution is (2, 10)

Step-by-step explanation:

2x + 6 = 4x + 2  Subtract 2x from both sides

2x - 2x + 6 = 4x - 2x + 2

6 = 2x + 2  Subtract 2 from both sides

6 - 2 = 2x + 2 -2

4 = 2x  Divide both sides by 2

2 = x

Substitute 2 for x in either of the two original equations.

y = 2x + 6

y = 2(2) + 6

y = 4 + 6

y = 10

The ordered pair that is a solution is (2, 10)

To calculate your available credit, you need to subtract your current balance and the amount of cash advance you want from your credit limit:

Available credit = credit limit - current balance - cash advance amount

Given that your credit limit is $7,500 and your current balance is $2,200, the available credit can be calculated as follows:

Available credit = $7,500 - $2,200 - cash advance amount

Now, if you want a cash advance of $1,000, for example, your available credit will be:

Available credit = $7,500 - $2,200 - $1,000 = $4,300

Therefore, your available credit is $4,300 if you want a cash advance of $1,000.

To calculate the transaction fee, you need to multiply the cash advance amount by the transaction fee percentage. In this case, the transaction fee is 2.5%. So, if you want a cash advance of $1,000, the transaction fee will be:

Transaction fee = $1,000 x 0.025 = $25

Therefore, if you want a cash advance of $1,000, you will owe a transaction fee of $25. It's important to note that cash advances usually come with a higher interest rate than regular credit card purchases, so it's best to use them only when absolutely necessary and pay them off as soon as possible to avoid accruing interest charges.

Answer:

Hopefully this is the answer you are looking for.

For the trapezoid ABCD following statements are true -

Statement 2: The length of AB can be found using 3²+4²=c².

Statement 3: The perimeter of the trapezoid shown is 22 units.

What is a trapezoid?

A polygon with only one set of parallel sides is called a trapezoid. The parallel bases of a trapezoid are another name for these parallel sides. Trapezoids have two additional sides that are not parallel and are referred to as their legs.

Statement 2 is true because AB is a horizontal side and its length can be found using the Pythagorean theorem -

(Hypotenuse)² = (Base)² + (Perpendicular)²

AB = √((4 - 1)² + (7 - 3)²)

AB = √((3)² + (4)²)

AB = √(9 + 16)

AB = 5

Statement 3 is true because the perimeter of a trapezoid is the sum of the lengths of its four sides, so the perimeter of this trapezoid is

Perimeter = AB + BC + CD + DA

Perimeter = 5 + 5 + 4 + 8

Perimeter  = 22

Therefore, second and third statement is true.

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The sinusoidal function is y = 2sin(2x) - 1

The general form of a sinusoidal function is given by:

y = A sin(Bx + C) + D

where:

We know that the period is π and the amplitude is 2.

So, we have

A = 2

B = (2π)/(π) = 2

So, we have

y = 2sin(2x + C) + D

The point (-11π/4, 1) implies that, the function is shifted down by 1 unit

So, we have

y = 2sin(2x) - 1

Hence, the function is y = 2sin(2x) - 1

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The length of q is approximately is 0.4 cm.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

To solve for the length of q in triangle AOPQ, we can use the law of sines, which states:

a/sin A = b/sin B = c/sin C

where a, b, and c are the lengths of the sides opposite the angles A, B, and C, respectively.

In triangle AOPQ, we know that:

Side p = 6.3 cm (opposite angle P)

Angle O = 149° (opposite side q)

Angle P = 29° (opposite side p)

Let use angle sum property of triangles to find the measure of angle Q:

Angle Q = 180° - Angle O - Angle P

Angle Q = 180° - 149° - 29°

Angle Q = 2°

Now we can use the law of sines to solve for the length of q:

q/sin Q = p/sin P

q/sin(2°) = 6.3/sin(29°)

q = sin(2°) × (6.3/sin(29°))

q=0.034 × (6.3/0.484)

q = 0.442 cm

Therefore, the length of q is approximately is 0.4 cm.

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Answer: Approximately 34.17%.

Step-by-step explanation: Let's divide 41 by 120. Doing so, we get 0.3466666 looping forever. We can simplify that to .3417, and then turn that into a percentage giving us 34.17%

The values are :

What is trigonometry ?

Trigonometry is a branch of mathematics that deals with the relationships and properties of angles and the trigonometric functions such as sine, cosine, and tangent. It is based on the study of the geometric properties of triangles and is used extensively in fields such as physics, engineering, architecture, and astronomy.

In trigonometry, the relationships between the sides and angles of a triangle are expressed using the six trigonometric functions: sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), and cotangent (cot). These functions describe the ratios between the sides of a right triangle, where one angle is 90 degrees. Trigonometric functions can also be defined for any angle, not just those in a right triangle, using the unit circle or other methods.

Trigonometry has many practical applications, such as in navigation, surveying, and the design of structures such as bridges and buildings. It is also used extensively in science and engineering, particularly in fields such as physics, mechanics, and electromagnetics.

If tan x = 0, then tan(-x) = 0.

The tangent function is an odd function, which means that tan(-x) = -tan(x). However, since tan x = 0, this means that -tan(x) = 0 as well. Therefore, tan(-x) = 0.

If sin x = 0.3, then sin(-x) = -0.3.

The sine function is an odd function, which means that sin(-x) = -sin(x). Since sin x = 0.3, this means that -sin(x) = -0.3. Therefore, sin(-x) = -0.3.

If cos x = 0.3, then cos(-x) = 0.3.

The cosine function is an even function, which means that cos(-x) = cos(x). Since cos x = 0.3, this means that cos(-x) = 0.3 as well.

If tan x = -2, then tan(pi+x) = tan(pi + atan(-2)) = tan(2.0344 + pi) = -2.

To find tan(pi + x), we need to use the identity tan(a + pi) = -tan(a). In this case, a = atan(-2), which is the inverse tangent of -2. Using a calculator or a table, we can find that a is approximately 2.0344 radians. Therefore, tan(pi + x) = -tan(2.0344) = -(-2) = 2.

Hence, values are

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The number of days it will take for him to kick 100 goals is given as follows:

45 days.

The slope-intercept definition of a linear function is presented as follows:

y = mx + b.

In which:

The parameters for this problem are given as follows:

Hence the function giving the number of goals on day x is given as follows:

y = 2x + 10.

The number of days for him to score 100 goals is then obtained as follows:

100 = 2x + 10

2x = 90

x = 90/2

x = 45 days.

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The statement "an exterior angle of a triangle will always be obtuse" is actually false.

Why it is?

An exterior angle of a triangle is formed by extending one of the sides of the triangle, and it is the angle between that extended side and the adjacent side of the triangle.

The measure of an exterior angle is equal to the sum of the measures of the two interior angles that are not adjacent to it.

Now, consider a triangle with interior angles of 70, 60, and 50 degrees. If we extend the side opposite the 70-degree angle, we get an exterior angle of 110 degrees. However, 110 degrees is not obtuse, since an angle is obtuse if and only if it is greater than 90 degrees. Therefore, we have shown that an exterior angle of a triangle does not always have to be obtuse.

In summary, the statement "an exterior angle of a triangle will always be obtuse" is false, and we have provided a counterexample to show why this is the case.

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