The radius of a circle is 21 m. Find its area to the nearest whole number.

1. Cosx = 5/√(41)

2. An equation {tan(x) + cot(x)}/{tan(x)} =csc²(x)

Equations using trigonometric functions that hold true for all possible values of the variables are known as trigonometric identities.

Given:

1. tanx = -4/5

and tanx = perpendicular/adjacent leg

So, P = -4 and A = 5

So, H = √(-4)² + (5)²

H = √(41)

So, Cosx = 5/√(41)

2. A trigonometric identity,

{tan(x) + cot(x)}/{tan(x)}

Simplifying,

= {tan(x)/tan(x) + cot(x)/{1/tan(x)}

= 1 + cot²(x)

= csc²(x)

Therefore, Cosx = 5/√(41)

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The snow on the lawn after 5 hours is 14.50 inches.

The snow on the lawn after tt hours is 12 + 0.5tt inches

The equation that represents the amount of snow after a number of hours is a linear equation. A linear equation is an equation that has a single variable that is raised to the power of one.

The form of the equation is:

Total snow = snow on the lawn + (rate at which the snow falls x number of hours)

Snow after 5 hours = 12 + (0.5 x 5)

= 12 + 2.5 = 14.50 inches

Snow after tt hours = 12 + (0.5 x tt)

= 12 + 0.5tt inches

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The amount of Tylenol remaining after 8 hours is 47.1g

half-life, in radioactivity, the interval of time required for one-half of the atomic nuclei of a radioactive sample to decay (change spontaneously into other nuclear species by emitting particles and energy), or, equivalently, the time interval required for the number of disintegrations per second of a radioactive.

R = A(0.5)^t/3

R = 300(0.5)^8/3

R = 300( 0.157)

R = 47.1

therefore after 8 hours 47.1 g of Tylenol is is left

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The costs and areas of the mat are

Represent the dimensions of the frame with

Length = x

Width = y

So, the frame area is

Area = xy

When the mat is 1 inch from the frame, we have

Whole Area = (x + 1 + 1) * (y + 1 + 1)

Whole Area = (x + 2) * (y + 2)

Expand

Whole Area = xy + 2x + 2y + 4

So, the mat area is

Mat area = xy + 2x + 2y + 4 - xy

Mat area = 2x + 2y + 4

The cost is

Cost = 0.05 * (2x + 2y + 4)

Cost = 0.1x + 0.1y + 0.2

When the mat is 2 inches from the frame, we have

Whole Area = (x + 4) * (y + 4)

Expand

Whole Area = xy + 4x + 4y + 16

So, the mat area is

Mat area = xy + 4x + 4y + 16 - xy

Mat area = 4x + 4y + 16

The cost is

Cost = 0.05 * (4x + 4y + 16)

Cost = 0.2x + 0.2y + 0.8

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The equation b = 3.99a has a slope of 3.99 and the y intercept is 0.

An equation is an expression that shows the relationship between numbers and variables using mathematical operators like addition, subtraction, multiplication and division. Equations can be linear, quadratic.

The standard form of a linear equation is:

y = mx + b

Where y, x are variables and b is the y intercept

Given an equation:

b = 3.99a

Comparing with the standard linear equation:

The slope is 3.99 and the y intercept is 0.

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The description of the graph of the system of inequalities, including shading and the types of lines graphed, and the description of the solution set is given below:

2x + y <= 8 is the inequality for the cost.

x + y >= 4 is the inequality for the number of cupcakes or pieces of fudge that she wants to buy.

using the desmos dot com calculator, you would graph the OPPOSITE of the inequalities.

the area on the graph that is NOT shaded is the feasible region

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Answer:

8x3 + 2x − 5

Step-by-step explanation:

Using the formula to convert pounds to kilogram,

We know that :

1 lb/ Pound = 0.453592 kilogram

therefore,

250 lbs/ Pound = 113.398 kilogram.

Using the formula to convert pounds to kilograms, you find that 250 pounds equals 113.398 kilograms

To convert 250 pounds (pounds) to kilograms (kg), you must use the conversion factor 1 pound = 113.398 kilogram.

Therefore,

we multiply 250 pounds by 86.18 kg/lb to get the equivalent weight in kilograms:

250 pounds x 0.45359237 kg/lb = 113.398 kilogram

Therefore,

250 pounds is 113.4 kilogram.

To understand the conversion factor, you need to know that pounds and kilograms are units of mass, but are used in many parts of the world. In the United States and some other countries, the accepted unit of mass is the pound, while most other countries use the kilogram.

A conversion factor connects the number of pounds to the number of kilograms, so you can easily convert from one unit of measure to another. It is important to use the correct conversion factor for accurate conversion.

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Answer: To determine which vehicle received the greater force, we need to calculate the momentum change for each vehicle during the collision. The force experienced by a vehicle during a collision is equal to the rate of change of its momentum.

First, let's calculate the initial momentum for each vehicle:

The car has a mass of 1,000 kg and a velocity of 30 m/s, so its initial momentum is 1,000 kg * 30 m/s = 30,000 kg m/s.

The truck has a mass of 2,000 kg and a velocity of 20 m/s, so its initial momentum is 2,000 kg * 20 m/s = 40,000 kg m/s.

Next, let's calculate the final momentum for both vehicles after the collision:

The car and truck collide head-on, so their velocities will become zero after the collision. So the final momentum for both vehicles will be zero.

Finally, we can calculate the rate of change of momentum for each vehicle:

The rate of change of momentum for the car is equal to its final momentum minus its initial momentum, or 30,000 kg m/s - 0 kg m/s = 30,000 kg m/s.

The rate of change of momentum for the truck is equal to its final momentum minus its initial momentum, or 0 kg m/s - 40,000 kg m/s = -40,000 kg m/s.

Since the magnitude of the rate of change of momentum for the truck is greater than the magnitude of the rate of change of momentum for the car, the truck has received the greater force.

Step-by-step explanation:

The height of the kite is 56 feet.

Trigonometric ratio is used to show the relationship between the sides of a triangle and its angles.

Let h represent the height of the kite. Hence, using trigonometric ratios:

[tex]sin(30)=\frac{h}{112}[/tex]

h = 56 feet

Therefore, the height of the kite is 56 feet.

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The solution of the system of equations is (4, 3)

Here we want to solve the system below:

8x+2y=38

2x-4y=-4

If we add 2 times the first equation and the second equation we will get:

2*(8x + 2y) + (2x - 4y) = 2*38 - 4

16x + 4y + 2x - 4y = 72

18x = 72

x = 72/18  = 4

And the vale of y is given by inputing x = 4 in one of the two equations.

2*4 - 4y = -4

8 - 4y = -4

-4y = -4 - 8

y = -12/-4 = 3

The solution is (4, 3)

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The phrase to describes the algebraic expression Three-fourths x + 2 is three-fourths of a number plus two.

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

Given in question;

The algebraic expression;

Three-fourths x + 2

Now,

The phrase that describes the algebraic expression Three-fourths x + 2;

three-fourths of a number plus two.

Therefore, the phrase of expression will be three-fourths of a number plus two.

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If Elish was required to write a 600 word Literature essay and word count on her computer showed that she had typed 240 words Elish still needs to complete 3/5 of the essay.

To find the fraction of the essay that Elish still needs to complete, we need to determine how many words she has left to write. We can do this by subtracting the number of words she has already written from the total required word count:

Words left to write = Total word count - Words already written

Words left to write = 600 - 240

Words left to write = 360

Now, to find the fraction of the essay that Elish still needs to complete, we can express the remaining words as a fraction of the total word count:

Fraction of essay left to complete = Words left to write / Total word count

Fraction of essay left to complete = 360 / 600

We can simplify this fraction by dividing both the numerator and denominator by their greatest common factor, which is 120:

Fraction of essay left to complete = (360 ÷ 120) / (600 ÷ 120)

Fraction of essay left to complete = 3 / 5

This means that she has completed 2/5 of the essay so far (which is the equivalent fraction of 240/600).

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In order to guide learners to move from the concrete level to the semi-concrete and finally to the abstract level in relation to their understanding of the more than/less than concept, I would use a step-by-step approach.

At the concrete level, I would introduce the concept of more than/less than with a hands-on activity. For example, I would have students compare the number of counters or blocks and have them determine which group has more or less. This would help them develop a fundamental understanding of the concept.At the semi-concrete level, I would introduce the concept of more than/less than with written numerals. I would have students compare numbers on paper, such as 4 and 6, and have them determine which number is more or less. I would also ask them to use concrete objects to represent the numbers, such as using four counters for 4 and six counters for 6.At the abstract level, I would introduce the concept of more than/less than with larger numbers. I would ask students to compare numbers such as 12 and 15, and determine which number is more or less. I would also ask them to use abstract symbols, such as 12 + and 15 -, to represent the numbers.By using this step-by-step approach, students will be able to move from the concrete level to the semi-concrete and finally to the abstract level of understanding the more than/less than concept. This will help them develop a strong foundation of the concept, which will allow them to solve more complex problems in the future.

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Answer:

v = 21

Step-by-step explanation:

Suppose v varies directly as g, meaning that there is a constant k such that v = kg. If v = 70 when g = 30, then we can use this information to find the value of k:70 = k * 30k = 70 / 30k = 7 / 3Now that we have the value of k, we can use it to find v when g = 9:v = kgv = (7 / 3) * 9v = 21So when g = 9, v = 21.In conclusion, by finding the value of the constant of proportionality k and using the formula v = kg, we determined that when g = 9, v = 21.

Answer:

3,975.16 United States Dollar

Step-by-step explanation:

To sit comfortably, the students need a total of 6 tables. The correct option is 3.

There are 32 students in a classroom. In 5th grade. Now to sit comfortably, the students need 6 tables. In each table, a total of 6 students can fit. In 5 tables, only 30 students can sit but two students will remain table less. With 1 extra table, 2 students can sir and each student from a table can sit in the las bench, i.e., 6th table.

The number of pupils in the classroom is 32. in grade five. The pupils now require 6 tables in order to sit comfortably. A total of 6 pupils can fit at each table. Only 30 pupils can fit at 5 tables, however 2 students will be tableless. With one extra table, two students can sit at the sixth table and each student from a table can use the last bench. Therefore, students need a total of 6 tables.

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Answer:

Step-by-step explanation:

The value of t is,

⇒ t = 28

Multiplication means to add number to itself a particular number of times. Multiply will be viewed as a process of repeated addition.

Given that;

The circle is shown in figure.

Now, From the figure we can formulate;

t = 1/2 (3t - 28)

2t = 3t - 28

3t - 2t = 28

t = 28

Thus, The value of t is,

⇒ t = 28

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The false statement is (a) P( A^c n B^c)=P(A^c) P(B^c). The probability of the intersection of complements is generally not equal to the product of individual complements.

The misleading assertion including p, and the erratic occasions An and B is (a) P( A^c n B^c)=P(A^c) P(B^c).

This assertion is bogus in light of the fact that by and large, the likelihood of the convergence of the supplements of two occasions, A^c and B^c, isn't equivalent to the result of their singular supplements.

For instance, assume we flip a fair coin. Let A be the occasion of getting heads and B be the occasion of getting tails. Then, P(A) = P(B) = 1/2, so P(A^c) = P(B^c) = 1/2. In any case, A^c and B^c are a similar occasion (getting heads or tails, separately), so P(A^c n B^c) = P(A^c) = 1/2. Then again, P(A^c) P(B^c) = (1/2)(1/2) = 1/4, which isn't equivalent to P(A^c n B^c).

Consequently, proclamation (a) is misleading.

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Josh will do more push ups than Charis in 2 1/2 minutes. This can be solved by using the concept of multiplication.

Along with addition, subtraction, and division, multiplication is one of the four fundamental mathematical operations. Multiply in mathematics refers to the continual addition of sets of the same size. One of the fundamental mathematical processes is multiplication. The result of multiplying two or more integers together is known as the product. The first number used in a multiplication operation between two numbers is referred to as the multiplicand.

Given that,

Josh did 36 push ups in 30 seconds

Josh did push ups in 2 1/2 minutes:

= (36/30) × 150

= 180 push ups

Chris did 56 push ups in 50 seconds

Chris did push ups in 2 1/2 minutes:

= (56/50)× 150

= 168 push ups

Thus, Josh will do more push ups than Charis in 2 1/2 minutes.

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The requried representative sample for the survey would consist of 385 people randomly selected from the city's population.

The statistic is the study of mathematics that deals with relations between comprehensive data.

Here,
To obtain a representative sample of the population, the sample should be randomly selected to ensure that each person in the city has an equal chance of being chosen. The size of the sample will depend on the level of precision required, the confidence level desired, and the margin of error that is acceptable. However, as a general rule, a sample size of at least 385 people would be required to obtain a margin of error of plus or minus 5% with a 95% confidence level.

Therefore, a representative sample to the survey would consist of 385 people randomly selected from the city's population.

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The expression that represents the area of each section is 14.2z - 9.8.

What is area ?

To find the area of each section, we need to divide the total area of the garden plot by the number of sections, which in this case is six.

The expression for the area of each section can be obtained by dividing the expression for the total area by 6:

(area of each section) = (total area of garden plot) / 6

(area of each section) = (85.2z - 58.8) / 6

Simplifying this expression, we can divide both terms by 6:

(area of each section) = 14.2z - 9.8

Therefore, the expression that represents the area of each section is 14.2z - 9.8.

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495.95

convert the percentage into a decimal

0.09

then do b=1-r

1 - 0.09 = 0.91

Now do 545 x 0.91

Answer: 495.95

Let's assume that the original price of the antique was x.

We know that the antique was sold at a profit of 9%, which means that the selling price is 109% of the original price:

[tex]Selling \: price = Original \: price + Profit[/tex]

[tex]£545 = x + 0.09x \\ £545 = 1.09x[/tex]

[tex]x = 500[/tex]

Answer:

y=3x-2

Step-by-step explanation:

Answer:

$14

Step-by-step explanation:

i multiplied 2.80 times 5 and got 14.

i hope this helped :)

The magic number is calculated as G + 1 − [tex]W_{A}[/tex] − [tex]L_{B}[/tex], where G represents the season's overall number of games. The total victory for Team A is represented by the WA. LB is the total number of defeats Team B has suffered this year.

The "magic number" in baseball is used to estimate how likely a club is to advance to the postseason or win the division. Every year, in September, when teams get closer to clinching, it gains attention. The total number of victories and losses that must occur by a team's closest rival in order for that team to achieve a certain goal is known as its magic number. A team's magic number drops by one with each victory. The magic number additionally drops by one each time the team's closest rival for the division (or Wild Card) loses.

This is the precise formula: Games left in season: +1 (Losses by second place team - losses by first place team)

The magic number changes to reflect any further changes in the second-place team.

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Answer: a = (2S)/(n + l)

Step-by-step explanation:

a = (2S)/(n + l)

In this equation, 'a' is the subject, which means that it is the value being solved for. To solve for 'a', we can divide both sides by the denominator of the fraction on the right-hand side (n + l). This leaves us with the answer of a = (2S)/(n + l).

Answer:

84 square inches

Step-by-step explanation:

The shaded region comprises of two same trapeziums:

∴Area of shaded region = 2 × (Area of a trapezium)

    = 2 × [tex]\frac{1}{2}[/tex] × (Sum of parallel sides) × (perpendicular height of trapezium)

    = [tex]\frac{2}{2}[/tex] × (4 + 8) × (6)

    = 84 square inches