put them in order from least to greatest:
2.71 2.819 2.7 2.87 2.824 2.89

The area of the circle created by the paint is given by the expression 4πt².

The area of the circle is 100π, which is approximately 314.16 in².

The circle will be at least 300 in² in 5 minutes. Yes.

To find the area of the canvas, we multiply the lengths of its sides:

Area = (3x + 5) × (2x + 1)

Expanding the expression:

Area = 6x² + 3x + 10x + 5

Combining like terms:

Area = 6x² + 13x + 5

The area of the canvas is given by the expression 6x² + 13x + 5.

Now, let's find the area of the circle created by the paint.

The area of a circle is given by the formula A = πr², where r represents the radius.

The radius is given by the spreading of paint, which is r(t) = 2t.

Substituting the value of r(t) into the formula, we have:

A[r(t)] = π(2t)²

Simplifying:

A[r(t)] = π(4t²)

A[r(t)] = 4πt²

Now, let's determine if the area of the circle will be at least 300 in² in 5 minutes.

Substitute t = 5 into the area formula:

A[r(5)] = 4π(5)²

A[r(5)] = 4π(25)

A[r(5)] = 100π

Since 314.16 in² is larger than 300 in², the circle created by the paint will be larger than 300 in² in 5 minutes.

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The domain of the exponential function is all real numbers.

The domain of a function refers to the set of all possible input values (also known as the independent variable) for which the function is defined.

For the exponential function y = 2ˣ + 6, the domain includes all real numbers.

This is because there are no restrictions on the input values that can be plugged into the function.

We can take any real number x, substitute it into the expression 2ˣ, and then add 6 to get a corresponding output value y.

Hence,  the domain of the exponential function is all real numbers.

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Answer:

Step-by-step explanation:

i am working on the assumption that nobody does all three of them

i got 4 because including the people that do swimming and park, the total number of people that do swimming is 22.

the same logic goes for cycling: including the people that do swimming and visit the national park, the total is 23.

so that means that find how many people do swimming and cycling, we have to add the people doing only swimming, with the people doing both swimming and park and then subtract that answer from 22 which gives you 4

The Canal's price/earnings ratio is 2.92.

To calculate Canal's price/earnings ratio, we need to find the earnings per share (EPS) first. The EPS can be calculated by dividing the net income by the weighted average number of common shares outstanding.

The weighted average number of common shares outstanding can be calculated as follows:

Weighted average number of common shares outstanding = Total number of common shares - Weighted average number of treasury shares

Weighted average number of common shares outstanding = 24,200 - 4,200 = 20,000

EPS = Net income / Weighted average number of common shares outstanding

EPS = $260,000 / 20,000 = $13

Finally, the price/earnings ratio can be calculated by dividing the market price per share by the EPS:

Price/earnings ratio = Market price per share / EPS

Price/earnings ratio = $38 / $13 = 2.92

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Answer:

2.17

Step-by-step explanation:

if you subtract 3 1/2 by 1 1/3 it equals 2.1666667 and 2.1666667 rounds to 2.17 and thats how you get your answer.

Answer:

x

__

140

Step-by-step explanation:

all i could get sorry

Answer:

x = 11

Step-by-step explanation:

Answer:

Step-by-step explanation:

  =

can make 11 batches with 1/3 stick butter left over

Answer:

1 5/8

Step-by-step explanation:

Hello there!

Answer:

16

Step-by-step explanation:

\( |x| = x \: \: \: if \: \: x \: \geqslant 0 \\ |x| = - x \: \: \: if \: \: \: x \: \leqslant 0\)

-12 < 0 so |-12| = -(-12) = 12

4 > 0 so |4| = 4

|-12| + |4| = 12 + 4 = 16

Answer:

16

Step-by-step explanation:

Hello! This question is looking for the absolute value of integers. The absolute value is the distance the number has from zero. For example, -12 as twelve numbers away from zero, twelve away in the negative direction. The absolute value of -12, then, is just twelve. An easy way to remember this is to take away the negative sign when taking the absolute value, since an absolute value can never be negative. The absolute value sign is represented by a squarish bracket [ and ].

This question says to find the absolute value of each integer and then add the two. First we have [-12]. This is 12 away from zero, and we can take away the - sign from the asked integer and we get 12.

The second integer given is 4, and when we take the absolute value of 4, [+4], we get positive four. This is because four is four spaces away from zero on the number line.

Thus, we have +12 and +4 as are values to add since they are the absolute values and we can form this equation

12+4=16

Thus, the answer is 16.

Hope this helps! Remember the hint, when something has brackets like that or asks for the absolute value, take away a negative sign and make it positive! Have a great day!

Answer:

The second option

Step-by-step explanation:

Here, we need to multiply each part of the matrix by -10.

This will give us: [ -230 380 ]

                           [ -170    60 ]

So, the answer is the second option.

Answer:

1.704 x 10⁹ people

Step-by-step explanation:

    Population of China = 1.381 x 10⁹

    Population of US = 3.23 x 10⁸

Problem:

Number of people in both countries combined = ?

Solution

   To solve this problem, simply add them together;

Let us make the exponents the same for easy addition;

      Population of China = 1.381 x 10⁹ = 13.81 x 10⁸

      Poplation of US =  3.23 x 10⁸

Adding both:

                   (13.81 x 10⁸)  + (3.23 x 10⁸)

             ⇒ (13.81 + 3.23) x 10⁸

             ⇒ 17.04 x 10⁸

             ⇒ 1.704 x 10⁹

The scale factor and the value of x for each figure is given as follows:

A) Scale factor of 1/3, x = 7 m.

B) Scale factor 0.4747, x = 4.5 in.

For Figure A, we have that the ratio between the areas is given as follows:

510/4590 = 1/9.

As the area is measured in square units, while the side lengths are measured in units, the scale factor is the square root of 1/9, hence it is given as follows:

1/3.

Then the value of x is obtained as follows:

x = 21 x 1/3

x = 7 m.

For Figure B, we have that the ratio between the areas is given as follows:

16/71 = 0.22535.

The scale factor is then the square root of 0.22535, which is given as follows:

0.4747.

Then the value of x is given as follows:

x = 9.5 x 0.4747

x = 4.5 in.

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Answer:

Therefore, the correct statements are A, B, and E.

Explanation:

Based on my knowledge, a vector is a quantity that has both magnitude and direction. A scalar is a quantity that has only magnitude. When a vector is multiplied by a scalar, the magnitude of the vector is multiplied by the absolute value of the scalar, and the direction of the vector is either preserved or reversed depending on the sign of the scalar.

To answer your question, we need to find the component form, magnitude, and direction of the scalar product –4⇀

.

- The component form of −4⇀

is obtained by multiplying each component of ⇀

by –4. Therefore, −4⇀

= ⟨–8, –12⟩. This means that statement A is true.

- The magnitude of −4⇀

is obtained by multiplying the magnitude of ⇀

by 4. The magnitude of ⇀

is √(2^2 + 3^2) = √13. Therefore, the magnitude of −4⇀

is 4√13. This means that statement B is true.

- The direction of −4⇀

is opposite to the direction of ⇀

because the scalar –4 is negative. This means that statement C is false.

- The vector −4⇀

is in the third quadrant because its components are both negative. This means that statement D is false.

- The direction of −4⇀

is 180° greater than the inverse tangent of its components because it is opposite to ⇀

. The inverse tangent of its components is tan^(-1)(–12/–8) = tan^(-1)(3/2). Therefore, the direction of −4⇀

is 180° + tan^(-1)(3/2). This means that statement E is true.

Therefore, the correct statements are A, B, and E.

Answer:

Step-by-step explanation:

a, e, f

Answer:

c = 3

Step-by-step explanation:

\( 32^{2c} = 8^{c + 7} \)

\( (2^5)^{2c} = (2^3)^{c + 7} \)

\( 2^{10c} = 2^{3c + 21} \)

\( 10c = 3c + 21 \)

\( 7c = 21 \)

\( c = 3 \)

Answer:x=12

i hope im right have a good rest of your day or night :)

Step-by-step explanation:

Step-by-step explanation:

-4×8= -32

-4×-3x= 12x

-32 + 12x = 112

+32. +32

12x = 144

\(12x \div 12x = 0\)

\(144 \div 12x = 12\)

Answer: 12

It is possible to find out the number of people who attended the event. Hence option B is correct.

What is the system of equations?

System of equations, also known as simultaneous equations, Two or more equations to be solved together in algebra (i.e., the solution must satisfy all the equations in the system). The number of equations must equal the number of unknowns for a system to have a unique solution.

Given that, a total of 24 cases of forks and each case of forks contains 36 packages each containing 12 forks.

Form about information, calculate the number of forks.

A total of 24 cases of spoons and each case of spoons contains 45 packages each containing 12 spoons.

Form about information, calculate the number of spoons.

Given that at the end of the event, 12 forks and 18 spoons were not given out to guests.

Form these we can get information that how many spoon used.

Since each guest will receive 2 forks and 3 spoons at the beginning of the event.

Using this information we can get the number of people who attend the event.

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Answer:

Step-by-step explanation:

Answer:

A) 44

Step-by-step explanation:

The given angle measurements are same side interior angles. Therefore, the summation of the two angle measurements will equal 180° (Forming a straight line).

Set the two angle measurements equal to 180:

\((3x + 3) + (45) = 180\)

Simplify. First, combine like terms. Like terms are terms that share the same amount of the same variables. In this case, combine 3 with 45:

\(3x + 3 + 45 = 180\\3x + (3 + 45) = 180\\3x + (48) = 180\)

Next, isolate the variable, x. Note the equal sign, what you do to one side of the equation, you do to the other. Do the opposite of PEMDAS.

PEMDAS is the order of operations, and stands for:

Parenthesis

Exponents (& Roots)

Multiplications

Divisions

Additions

Subtractions

~

First, subtract 48 from both sides of the equation:

\(3x + 48 = 180\\3x + 48 (-48) = 180 (-48)\\3x = 180 - 48\\3x = 132\)

Next, divide 3 from both sides of the equation:

\(\frac{3x}{3} = \frac{132}{3} \\x = \frac{132}{3} \\x = 44\)

A) 44 is the value for x.

~

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Answer:

(k, -2k+21) where k is any integer

Explanation:

Given the following simultaneous equation;

2x+y=21 ..... 1

y=-2x+21 ..... 2

Subtitute equation 2 into 1:

2x + (-2x+21) = 21

2x -2x+21 = 21

0x = 21-21

0x = 0

x = 0/0

Since the variables cannot be determined, we will subtitute x = k

Substitute x = k into equation 2;

From 2: y = -2x+21

y = -2k+21

Hence the solution to the system of equation is (k, -2k+21) where k is any integer

The length of the line segment AB is 5 units.

Unfortunately, you haven't provided any information about PQ such as its location or any other data to help solve the question.

Therefore, it's impossible to determine the length of PQ using the given options. However, here is an explanation of how to find the length of a line segment using the distance formula, which may help you in solving similar questions in the future.

The distance formula is used to find the distance between two points in a coordinate plane, such as the length of a line segment. The formula is:

d = √((x₂ - x₁)² + (y₂ - y₁)²)

where d is the distance, (x₁, y₁) and (x₂, y₂) are the coordinates of the two points.

To use the distance formula, you first need to find the coordinates of the two points that make up the line segment. Then, substitute these coordinates into the formula and simplify to find the distance.

For example, let's say you have two points: A(1, 2) and B(4, 6), and you want to find the length of the line segment AB. Using the distance formula:

d = √((4 - 1)² + (6 - 2)²)
d = √(3² + 4²)
d = √(9 + 16)
d = √25
d = 5

Remember, the distance formula can be applied to any two points in a coordinate plane to find the distance between them.

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When applying the some rule, we only combine two equal ratios at once. Consequently, we deal with pairs of sides and angles that have equivalent ratios.

When two ratios are equal, a percentage is formed; alternatively, two equal ratios can be said to produce a proportion. When we understand that two ratios are equal, you can write a proportion. The ratios of these two numbers are equal.

When two variables are correlated in a manner that their ratios are equal, this is known as a proportional relationship. In a proportional connection, one variable is always a constant value multiplied by the other, which is another way to think of them. The "constant of proportionality" is the term used to describe that constant. Two angles are said to be complimentary if their sum is 90 degrees. Alternatively put, two angles are said to be complimentary if they combine to make a right angle.

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Answer:

The maximum number of intersection is Six

Step-by-step explanation

The triangle has three sides, for intersection to occur with "no sides of the triangle are on the same line" then each of the sides of the triangle will cross the second triangle making (2×3) = 6 intersection point

Hence, The maximum number of intersection is Six

The state spelled out with letter tiles depends on the probability of picking the letter O, and the possible states are Ohio,  Colorado and  Oregon respectively.

To solve this problem, we need to consider the frequency of the letter O in each state's name.

If the probability of picking the letter O is 1/2, then the state must have two O's in its name. The only state that meets this criteria is OHIO.

If the probability of picking the letter O is 3/8, then the state must have three O's in its name. The only state that meets this criteria is COLORADO.

If the probability of picking the letter O is 1/3, then the state must have at least three O's in its name. The only state that meets this criteria is OREGON.

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Using the concept of word problems and quadratic equation it will take 1 year until the sum of square of their ages be 45.

Word problems are mathematical problems that are delivered in ordinary words, instead of mathematical symbols.

Part of the problem with dealing with word problems that they first need to be translated into mathematical equations, and then the equations need to be solved.In this problem;

let x represent the number of years from now when the sum of square of their respective age will be

45.(x + 2)² + (x + 5)² = 45

Expanding the brackets;

x² + 4x + 4 + x² + 10x + 25 = 45

2x² + 14x + 29 = 45

2x² + 14x + 29 - 45 = 0

2x² + 14x - 16 = 0

Solving the quadratic equation for x;

x = 1, x = -8

Taking the positive value, the value of x is 1

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Using the formula for the margin of error, it is found that a smaller confidence interval would be obtained as follow:

D. Increase the sample size to 64.

It is given by the following formula:

\(M = z\frac{s}{\sqrt{n}}\)

In which:

For a smaller interval, we need to decrease the margin of error, which is possible increasing the sample size, hence option D is correct.

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Answer:

\(7\frac{7}{15}\)

Step-by-step explanation:

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