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Write and simplify a polynomial expression to find the area of 4 circles. Each circle has a radius of (4a-6)

Answer:

-9

Step-by-step explanation:

[tex](-9)^3 = -729[/tex]

[tex]-9 = \sqrt[3]{-729}[/tex]  (taking cube root on both sides)

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The percentage change in the birth rate of a nation from 1990 to 2000 is -35%.

Percentage change is the relative difference between two values expressed as a percentage of one of the values, where the value of the latter is used as the reference point.

It can be calculated by using the following formula:

Percentage change = ((new value - old value) / old value) x 100

Given the birth rate of a nation in 1990 as 20 and the birth rate in 2000 as 13, the percentage change can be calculated as follows: Percentage change = ((13 - 20) / 20) x 100= (-7 / 20) x 100= -0.35 x 100= -35%

Hence, the percentage change is -35%.

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The value of [tex]e^{In 5}[/tex] is equal to 5 which of option B. According to the property of logs and logarithm rules the given equation is done.

The natural log, or log to the base e, is denoted by ln. ln can also be written as [tex]log_{e}[/tex].

So, we can write the given expression as:

[tex]e^{log_{e}^(5) }[/tex]

The property of logs is:

[tex]a^{log_{a}^(x) } = x[/tex]

This means that if the number an is raised to a log whose base is the same as the number a, the answer will be equal to the log's argument, which is x.

The number e and the base of log are the same in the given case. As a result, the answer to the expression will be the log argument, which is 5.

Therefore, the value of [tex]e^{log_{e}^(5) }[/tex] = [tex]e^{In 5}[/tex] = 5. Correct option is option B.

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The conclusion of the test is the calculated z-test value of -1.5 falls within the acceptable limits of +/- 2 sigma.

To interpret the results of the run test, we need to compare the calculated z-test value with the acceptable limits for the test. The acceptable limits for the run test are +/- 2 sigma, which means that the process is considered acceptable if the z-test value falls within this range.

Since the z-value of -1.5 falls within the acceptable limits of +/- 2 sigma, we can conclude that the process is acceptable according to the run test. This means that there is no evidence of non-randomness or nonconformity in the process, and the process is functioning as expected.

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a continuous random variable x is normally distributed with a mean of 0 and a standard deviation of 1. the probability of an observation that lies within the range of -1.0 < x <1.0 is 0.6827.

       The explanation for normal distribution is described by two parameters, the mean (μ) and the standard deviation (σ).

         A continuous random variable X that is normally distributed has the probability density function, (X is a normally distributed variable):

                   f(x)=1σ√2π×e−12((x−μσ)2)

        A normal distribution with a mean of 0 and standard deviation of 1 is called standard normal distribution or Z-distribution. The probability for the standard normal distribution can be found using the standard normal distribution table.

   In this case, we have a continuous random variable x which is normally distributed with a mean of 0 and a standard deviation of 1. We are asked to find the probability of an observation that lies within the range of -1.0 < x < 1.0.

  In other words, we want to find: P(-1.0 < x < 1.0)

  To do this, we need to transform the interval (-1.0, 1.0) to a standard normal distribution as follows:

             Z=(X−μ)/σ = (X−0)/1

                              = X

   Next, we use a standard normal distribution table to find the probability for Z as follows:

             P(-1.0 < x < 1.0) = P(-1 < Z < 1)

                                      = P(Z < 1) - P(Z < -1)

    From the standard normal distribution table,

    We have P(Z < 1) = 0.8413 and

                   P(Z < -1) = 0.1587

   Therefore: P(-1.0 < x < 1.0) = 0.8413 - 0.1587

                                               = 0.6827

   Thus, the probability of an observation that lies within the range of -1.0 < x < 1.0 is 0.6827.

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According to the question, the exact value of side x in the Trina are  34.641016151377546in.

Value is an intangible concept that refers to the worth of something, whether it is tangible or intangible. It is based on the perceived benefits and costs associated with the thing in question. Value can be subjective, as different people may place different worth on the same item. Value can also be objective, as there may be a set market price for a certain item.

The exact value of side x in the triangle can be determined by using the law of sines. The law of sines states that the ratio of the length of a side to the sine of its opposite angle is the same for all sides of a triangle.

Therefore, we can set up the following equation:

(20in/sin30°) = (x/sin60°)

Solving for x, we get:

x = 20in×(sin60°/sin30°)

x = 20in×(√(3)/1)

x = 20in×√(3)

x = 34.641016151377546in

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The exact value of side x in the Trina, according to the question, is 34.641016151377546in.

Where you cannot predict the value, you must be specific. An exact number is a value that can be determined with absolute precision. Counted quantities of objects or sure unit conversions are examples of exact numbers.

The term "approximate number" refers to a number that is close to the precise number, and there is always a difference among exact and approximate numbers. For instance, are exact integers because no approximation is required.

As a result, we can construct the following equation:

(20in/sin30°) = (x/sin60°)

Solving for x, we get:

x = 20in×(sin60°/sin30°)

Simplify the above equation,

x = 20in×(√(3)/1)

x = 20in×√(3)

The value of x is,

x = 34.641016151377546in

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The complete question is,

What is the exact value of side x in the Trina for below? 20in 30 degree and X? Determine the exact value of side x.

After solving the given equation, the value of variable a is 6.81 respectively.

Every equation is a formula.

Not all equations have formulas. It is the purpose of equations to be solved for a variable.

We analyze formulas.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.

For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

2/3a  -7 + 7/18a - 5 1/6 = 0

2/3a + 7/18a = 7 + 6/31

12a+7a/18 = 7+6/31

19a/18 = 7+6/31

19a = (7+6/31)18

19a = (217+6/31)18

19a = (223/31)18

19a = 4,014/31

a = 4014/31*19

a = 4014/589

a = 6.81

Therefore, after solving the given equation, the value of variable a is 6.81 respectively.

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Complete question:

Solve the given equation: 2/3a  -7 + 7/18a - 5 1/6 = 0

Professor Salton's measure for work is the number of hours worked for a non-academic job, as reported by respondents in his survey.

This measure is a simple but effective way to gain an understanding of how work can impact a student's academic studies. It provides a direct measure of the amount of time that students spend working outside their academic pursuits, and can be used to quantify the potential effects of working on their educational success.

By taking this measure, Professor Salton has provided an effective way of analyzing the relationship between work and study. It allows researchers to determine whether working has an impact on student performance and academic outcomes. It also allows researchers to investigate whether certain types of work, such as part-time or full-time employment, have more of an impact than others.

Ultimately, this measure is an invaluable tool for researchers to gain a better understanding of the effects of work on student success.

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The value of the determinants of the matrix | 5 3 | |7 9 | is 24

A matrix is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns which is used to represent a mathematical object or a property of such an object.

Also, It provides two benefits: compact notation for describing sets of data and sets of equations as well as efficient methods for manipulating sets of data and solving sets of equations.

For the given matrix, the determinant Det is:

Det = (5*9) - (7*3)

So, we have

det. = 45 - 21

Evaluate the difference

det = 24

herefore the determinant is equal to 24

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Point A is three units left and three units up from the origin, so its coordinates are (-3, 3). Therefore, the correct answer is option 2) (-3, 3).

The topic of coordinate geometry involves the use of the Cartesian plane, also known as the coordinate plane or xy-plane, to graph and analyze relationships between points, lines, and shapes. The plane consists of two perpendicular number lines called the x-axis and the y-axis.

The origin, denoted by the point (0, 0), is the point where the two axes intersect. Points on the plane are represented by ordered pairs of numbers (x, y), where x is the distance from the y-axis and y is the distance from the x-axis. Lines on the plane can be represented by their slope and y-intercept, while shapes like circles, rectangles, and triangles can be graphed and analyzed using their respective formulas.

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Answer: (−3, −3)

Step-by-step explanation:

A shape's perimeter is calculated by adding the lengths of all of its sides and edges. The V's direction is [tex](-5, -12)[/tex]  .

The complete length of a shape's boundary is referred to as the perimeter in geometry. Its dimensions are expressed in linear units like centimetres, metres, inches, and feet.

We need to know the lengths of all the sides of Fard ZH in order to calculate its perimeter. We can see from the diagram that  [tex]ZF = ZD + DF = 24 + 28 = 52[/tex]  and [tex]FH = ZG = 30 and ZH = 36.[/tex]

As a result, Fard ZH's perimeter is as follows:

perimeter = [tex]= ZF + FH + ZH + ZG[/tex]

perimeter  [tex]= 52 + 30 + 36 + 30[/tex]

perimeter  [tex]= 148[/tex]

So the perimeter of Fard ZH is [tex]148[/tex]  .

(3) The vector that connects points A and B must be identified in order to determine the direction of V, and it can be written as follows:

[tex]V = (xB - xA, yB - yA)[/tex]

Where xA and yA represent point A's x and y coordinates, and xB and yB represent point B's x and y coordinates.

Plugging in the given values, we get:

[tex]V = (5 - 10, 2 - 14)[/tex]

[tex]V = (-5, -12)[/tex]

Therefore, The V's direction is [tex](-5, -12)[/tex] .

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The area of the bedroom in the terms of p and q is (6p7q)² square units.

What is the area of square?

The amount of square units required to fill a square is referred to as the area of a square. In general, the region contained within a flat object's or 2D figure's boundary is referred to as the area. The unit of measurement is square, with square metres serving as the default.

We are given that a bedroom is in the shape of a square with the length as 6p7q.

We know that area of a square is the square of the side.

So, from this we get

⇒ Area = (6p7q)² square units

Hence, the area of the bedroom in the terms of p and q is (6p7q)² square units.

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linear Equation to represent the description "8 more than 4 times number 28" is: y = 4x + 8

What is linear equation ?

A linear equation is an algebraic equation that describes a straight line relationship between two variables, typically denoted as x and y. The general form of a linear equation is:

y = mx + b

where y is the dependent variable, x is the independent variable, m is the slope of the line, and b is the y-intercept (the point at which the line crosses the y-axis).

The slope, m, represents the rate of change of y with respect to x, or how steep the line is. It is calculated as the change in y divided by the change in x between any two points on the line.

According to the question:
a. An equation to represent the description "8 more than 4 times number 28" is:

y = 4x + 8

where x represents the number 28, and y represents the result of multiplying 28 by 4 and then adding 8.

b. A real-world situation that this equation could represent is the cost of purchasing a certain number of items. For example, if the price of one item is $28, and there is a discount of 8 dollars for every four items purchased, the equation y = 4x + 8 could be used to calculate the total cost y of purchasing x items. The 4x term represents the cost of the items before the discount, and the +8 term represents the discount. For instance, if a customer wants to purchase 12 items, they would pay 4 * $28 = $112 for the first 12 items, minus $8 for the discount, resulting in a total cost of $104.

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where P is the principal amount, r is the interest rate, and n is the number of years. In this case, A is $1,000,000, r is 0.05, and n is 119. Thus, P = [tex]$1,000,000/(1+0.05)119 = $66,059.19.[/tex]

A. The investment of $1,000 in 1900 would be worth $97,792.96 today. This can be calculated by using the compound interest formula A=P(1+r)n, where P is the principal amount, r is the interest rate, and n is the number of years. In this case, P is $1,000, r is 0.05, and n is 119.

Thus, A = [tex]$1,000(1+0.05)119 = $97,792.96.[/tex]

B. If the investment has grown to $1 million in 2019, the principal amount invested in 1900 would be $66,059.19. This can be calculated by using the compound interest formula [tex]A=P(1+r)n[/tex]

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The probability of at least one visit during a given minute is 86.47%.

Given that the average rate of visits per minute is two.

To find the probability of at least one visit during a given minute, we can use Poisson distribution.

Poisson distribution is a probability distribution that is used to determine the probability of a certain number of events occurring in a fixed time period when the events are rare and random.

The Poisson probability distribution is given by;

[tex]P(X=x) = (e^{-\lambda} \times \lambda ^x) / x![/tex]

Where; λ is the average rate of events, x is the number of events that occurred, and e is the base of the natural logarithm,

e ≈ 2.7183

We can find the probability of at least one visit in a minute using the complement rule.

The complement rule states that the probability of an event happening is equal to 1 minus the probability of the event not happening.

Therefore;

P(at least one visit) = 1 - P(no visit)P(no visit)

= P(X=0)   = [tex](e^{-\lambda} \times \lambda^0) / 0![/tex]  = [tex]e^{-\lambda}[/tex] = [tex]e^{-2}[/tex] = 0.1353

Therefore;

P(at least one visit) = 1 - P(no visit)

= 1 - 0.1353

= 0.8647 = 86.47%

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Answer:

The density of the wood is 0.6 g/cm^3

Step-by-step explanation:

The density of an object can be calculated by dividing the mass of the object by its volume. In this case, the mass of the block of wood is 120g and its volume is 200cm^3.

Density = mass / volume

Density = 120g / 200cm^3

Density = 0.6 g/cm^3

Therefore, the density of the wood is 0.6 g/cm^3.

The probability that a male passenger can fit through the doorway without bending is approximately 0.9599, or 95.99%.

What is probability?

Probability is a branch of mathematics that deals with the study of random events and their likelihood of occurrence. It is used to quantify uncertainty and to make informed decisions in the face of incomplete or uncertain information.

We can assume that the heights of male passengers follow a normal distribution with a mean of 69.0 in and a standard deviation of 2.8 in. Let X be the height of a male passenger in inches. Then, we need to find the probability that X is less than or equal to 74 in, which represents the height of the airliner's doors.

(a) Using the standard normal distribution, we can standardize X as follows:

z = (X - μ) / σ

where μ is the mean and σ is the standard deviation of the distribution, and z is the corresponding z-score.

Substituting the values, we get:

z = (74 - 69.0) / 2.8 = 1.75

Using a standard normal distribution table or calculator, we can find the probability that a standard normal random variable is less than or equal to 1.75:

P(Z ≤ 1.75) ≈ 0.9599

Therefore, the probability that a male passenger can fit through the doorway without bending is approximately 0.9599, or 95.99%.

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The height is either 10 cm,12 cm,14 cm.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The base of the parallelogram has a length of 10 cm.

Here, area is not given so the height may be anything.

suppose h = 10

Hence, We get;

Area = base * height

      = 10 * 10

       = 100 cm²

if h = 12

area = 10 * 12

       = 120 cm²

if h = 14

area = 10 * 14

        = 140 cm²

Therefore, the height is either 10 cm,12 cm,14 cm.

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The midline is 1500. The midline in this context represents the average volume of air in a person's lungs over a period of time.

The midline of a periodic function is the horizontal line that passes through the middle of the function's range.

For a function of the form V(t) = A cos(B(t - C)) + D, the midline is given by the equation y = D, which represents the average value of the function over a period.

In this case, the function is V(t) = 500 cos(²(t - 0.25)) + 1500, so the midline is given by the equation:

y = 1500

This represents the average volume of air in a person's lungs over a period of time.

Since the cosine function oscillates between -1 and 1, the actual volume of air in the person's lungs will oscillate around the midline, between 1500 - 500 = 1000 mL and 1500 + 500 = 2000 mL.

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This equation fits the given data: Oy = -2x + 10. The equation creates a linear relationship between the x and y values, with each x value increasing by 1 resulting in a decrease in the y value by 2.

Linear refers to a type of relationship between two or more variables. It is a straight line relationship where the output is directly proportional to the input. Linear relationships can be observed in the natural world such as in the relationship between distance and time. They can also be observed in mathematical equations and models, where the output is directly related to the input. Linear relationships are also used to represent real-world problems in the form of linear equations and models.

The equation satisfies the data points, as plugging in each x value will result in the corresponding y value. For example, when x = 0, the equation produces y = 10, which is the given data point. Similarly, when x = 2, the equation produces y = 6, which is also the given data point.

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This equation fits the given data: y = 1/3x + 2. The equation creates a linear relationship between the x and y values. Hence the correct option is b.

Linear refers to a type of relationship between two or more variables. It is a straight line relationship where the output is directly proportional to the input. Linear relationships can be observed in the natural world such as in the relationship between distance and time. They can also be observed in mathematical equations and models, where the output is directly related to the input. Linear relationships are also used to represent real-world problems in the form of linear equations and models.

The equation satisfies the data points, as plugging in each x value will result in the corresponding y value. For example, when x = 0, the equation produces y = 10, which is the given data point. Similarly, when x = 2, the equation produces y = 6, which is also the given data point.

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The maximum amount of §179 expense TDW may deduct for 2022 is $257,000.

To determine the maximum amount of §179 expense that TDW Corporation can deduct for 2022, we first Add up the cost of all the assets acquired in 2022:

$2,270,000 (machinery) + $263,000 (computer equipment) + $880,000 (furniture) = $3,413,000

Now we determine the amount of the §179 deduction limit for the tax year.

For tax year 2022, the §179 deduction limit is $1,050,000.

Check if the cost of the assets exceeds the §179 deduction limit.

Since the cost of the assets ($3,413,000) is greater than the §179 deduction limit ($1,050,000), we need to calculate the phase-out limit.

Now we determine the phase-out limit.

For tax year 2022, the phase-out limit is $2,620,000.

Calculate the §179 expense deduction.

Since the cost of the assets ($3,413,000) is greater than the phase-out limit ($2,620,000), we need to reduce the §179 deduction by the excess over the phase-out limit.

The excess over the phase-out limit is $793,000 ($3,413,000 - $2,620,000).

The §179 expense deduction is the lesser of the §179 deduction limit and the cost of the assets reduced by the excess over the phase-out limit.

The §179 expense deduction is $1,050,000 - $793,000 = $257,000.

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We can see that this corresponds to the point (4, 10). Therefore, there were 4 people in the group that popped 10 balloons.

Correlation refers to the relationship between two variables in a dataset. It is a statistical measure that quantifies the degree to which two variables are related to each other.

There are two types of correlation: positive and negative. Positive correlation exists when the two variables move in the same direction, meaning that as one variable increases, the other variable also increases. Negative correlation exists when the two variables move in opposite directions, meaning that as one variable increases, the other variable decreases.

The strength of the correlation can be measured using a correlation coefficient, which ranges from -1 to +1. A correlation coefficient of +1 indicates a perfect positive correlation, while a correlation coefficient of -1 indicates a perfect negative correlation. A correlation coefficient of 0 indicates no correlation between the two variables.

From the given graph, we can see that there is a positive correlation between the number of people in a group and the total number of balloons they pop. As the number of people in the group increases, the total number of balloons they pop also tends to increase.

We are asked to find the number of people in the group that popped 10 balloons. From the graph, we can see that this corresponds to the point (4, 10). Therefore, there were 4 people in the group that popped 10 balloons.

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Answer:270

Step-by-step explanation: 3pm + 12am = 15am

15 am - 10:26 pm = 4 hours 34 minutes

4 hours 34 minutes = 4x60 +30 mins = 270 mins

Each pack should weigh 11.5 oz when the seeds are redistributed equally.

Since Mr. Salinger wants to redistribute the seeds in such a way that each pack weighs the same, he needs to find the common weight of all the packs. To do this, he can find the total weight of all the packs and divide it by the number of packs.

Using the line plot, we can see that the weights of the 8 packs are:

12 oz

8 oz

10 oz

10 oz

12 oz

14 oz

10 oz

16 oz

To find the total weight of all the packs, we can add these weights together:

12 + 8 + 10 + 10 + 12 + 14 + 10 + 16 = 92 oz

So the total weight of all the packs is 92 oz.

To find the weight of each pack, we need to divide the total weight by the number of packs:

92 ÷ 8 = 11.5 oz

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Step-by-step explanation:

y is a corresponding angle to the 35 degree angle so  y = 35°

'x' + the 35 degree angle form a straight line = 180 degrees

x + 35 = 180

x = 145°  

Format your answer as needed

The taxi driver charges an initial fare of $3.00 plus $0.40 for each 1/5 of a mile driven. If the total charge for a ride is $27.00, the distance traveled, in miles is 9.

  The data given in the question is, The taxi driver charges an initial fare of $3.00 plus $0.40 for each 1/5 of a mile driven. The total charge for a ride is $27.00.

   Let's calculate the distance traveled:

                  Let d be the distance traveled. The given data in the problem is in dollars and cents. Therefore, let's first change it to the same units (cents). We know that 1 dollar is equal to 100 cents. Thus $27.00 is equal to 27 * 100 cents.

    Therefore, $27.00 is equal to 2700 cents.

     Now, we know that the driver charges $3.00 as an initial fare.

                    So, he charged 300 cents. Therefore, the remaining amount of money he charged for the distance is (2700 - 300) cents.

      Hence, he charged 2400 cents for the distance traveled. The driver charges $0.40 for each 1/5 of a mile. That is 40 cents for each 1.2 km.

     Therefore, he charges 200 cents for each 1.2 km of distance traveled.

      Hence, he charges (2400/200) * 1.2 km of distance traveled.

       Therefore, the distance traveled is 14.4 km or 9 miles. Accordingly, the distance traveled, in miles, is 9.

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Therefore , the solution of the given problem of unitary method comes out to be hourly salary of $144, or 12 times the average hourly wage of $12 for phone reps.

This common convenience, already-existing variables, or all important elements from the original Diocesan adaptable study that followed a particular methodology can all be used to achieve the goal. Both of the crucial elements of a term affirmation outcome will surely be missed if it doesn't happen, but if it does, there will be another chance to get in touch with the entity.

Here,

The formula below can be used to determine the ideal amount of phone representatives:

=>  MR = MC

Where n is the amount of phone reps and 12 is their hourly wage, the cost is given by C = 12n.

The following results are obtained by taking the derivative of revenue and cost with regard to n:

=> MR=dR/dn = k

=>  dC/dn = 12 for MC.

When we set MR equal to MC, we obtain:

=> k = 12

Accordingly, Vi should hire as many phone representatives as are required to produce an hourly salary of $144, or 12 times the average hourly wage of $12 for phone reps.

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The answer is in numerator = 3 and denominator = 5

Numbers are present in every part οf οur everyday lives, including the number οf laps we cοmplete οn the racetrack, the number οf hοurs we sleep at night, and many οther things.

In math, a number can be even, οdd, prime, cοmpοsite, decimal, fractiοnal, ratiοnal, irratiοnal, natural, integer, real, whοle, οr any cοmbinatiοn οf these.

Numbers are the basis οf mathematics

We must learn abοut numbers if we are tο understand math.

There are many different kinds οf numbers.

There is a lengthy list that includes whοle numbers, οrdinal numbers, οrdinal numbers, natural numbers, οdd numbers, even numbers, cοnsecutive numbers, and sο οn.

3*3 = 9

5*4=20

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Answer:

Step-by-step explanation:

The total revenue from selling 300 tickets for £5 each is:

300 x £5 = £1500

The profit will be the difference between the total revenue and the cost of prizes:

£1500 - £400 = £1100

The amount of profit that goes to Charity A is:

55% x £1100 = £605

The amount of profit that goes to Charity B is:

45% x £1100 = £495

Therefore, Charity A receives £605 and Charity B receives £495.

Answer:

17.8

Step-by-step explanation:

a^2+b^2=c^2

To find the distance between Tallahassee and Miami we need to find the distance from...

(10,17) and (10,3)

as well as (10,3) and (21,3)

The distance from the point (10,17) to (10,3) is the difference in y or 17-3, which gives you 14

The distance from the point (10,3) to (21,3) is the difference in x or 21-10, which gives you 11

Now you can plug in the values in the pythagorean theorem like so:

14^2+11^2=c^2

196+121=c^2

317=c^2

Square root both sides

The sqrt of 317 is approximately 17.804, rounding to 17.8 to the nearest tenths place.