Mr. Lucy has 10 1/4 feet of rope. If he needs 1/8 OF the rope
for a project, how many feet of rope will he use?

The volume of a rectangular prism is -

V = Length x width x height

V = L x B x H

Volume is a collection of two - dimensional points enclosed by a single dimensional line. Mathematically, we can write -

V = ∫∫∫ F(x, y, z) dx dy dz

Given is a rectangular prism.

The volume of a rectangular prism is the measurement of the total space inside it. Since the image of the prism is not given, we can write the volume of a rectangular prism as -

V = Length x width x height

V = L x B x H

Therefore, the volume of a rectangular prism is -

V = Length x width x height

V = L x B x H

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Answer:

The object falls 4.9 meters in the first second, 14.7 meters in the second second, 24.5 meters in the third second, and 34.3 meters in the fourth second. We can see that the object is falling 9.8 meters per second per second, which is the acceleration due to gravity.

To find how far the object falls in 10 seconds, we can use the formula for the sum of an arithmetic sequence:

S = n/2(2a + (n-1)d)

where S is the sum of the sequence, n is the number of terms, a is the first term, and d is the common difference between the terms.

In this case, we have:

n = 10 (since we want to find the total distance in 10 seconds)

a = 4.9 (the first term is the distance fallen in the first second)

d = 9.8 (the common difference is the acceleration due to gravity)

Plugging in these values, we get:

S = 10/2(2(4.9) + (10-1)9.8) = 10/2(9.8 + 88.2) = 10/2(98) = 490

Therefore, the object will fall a total of 490 meters in 10 seconds.

The object will fall 495 meters in 10 seconds.

It is a sequence where the difference between each consecutive term is the same.

We have,

We can see that the object is falling with a constant acceleration of 9.8 meters per second squared (which is the acceleration due to gravity near the surface of the Earth).

Each second, the distance the object falls increases by an additional 9.8 meters.

So, during the fifth second, the object will fall 44.1 meters (34.3 + 9.8), during the sixth second it will fall 53.9 meters, during the seventh second it will fall 63.7 meters, during the eighth second it will fall 73.5 meters, during the ninth second it will fall 83.3 meters, and during the tenth second it will fall 93.1 meters.

The total distance the object will fall in 10 seconds is:

= 4.9 + 14.7 + 24.5 + 34.3 + 44.1 + 53.9 + 63.7 + 73.5 + 83.3 + 93.1

= 495 meters

The object will fall 495 meters in 10 seconds.

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The hypothesis of this research is that there is a positive correlation between the independent variables (hours slept on the night of the test, hours spent studying the week before the test, and student's IQ) and the dependent variable (test scores). As such, the null hypothesis states that there is no relationship between the independent variables and the dependent variable, while the alternative hypothesis states that there is a relationship between the independent variables and the dependent variable. Symbolically, this can be written as:

H0: There is no relationship between the independent variables and the dependent variable

H1: There is a relationship between the independent variables and the dependent variable

Given the hypothesis, the independent variable (number of hours of sleep, number of hours spent studying, and IQ) are quantitative and discrete, and the dependent variable (test scores) is ratio, an f test is the most appropriate statistical test to use. An f test will allow us to compare the independent variables to see if there is a statistically significant difference between the independent variables and the dependent variable. By using an f test, we can determine if the independent variables are actually associated with the dependent variable and how strong that association is.

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The value of x is approximately 7.21 and the side lengths do not form a pythagorean triple.

The figure in the image is a right traingle.

We can use the Pythagorean theorem to solve for the missing leg of the right triangle:

a² + b² = c²

Where a and b are the legs of the triangle and c is the hypotenuse.

Plugging in the given values, we get:

12² + b² = 14²

144 + b² = 196

Subtracting 144 from both sides:

b² = 52

Taking the square root of both sides:

b = 7.21

Therefore, the second leg of the right triangle is approximately 7.21 units long.

This is not a Pythagorean triple because the three sides (12, 7.21, and 14) do not form a set of integers that satisfy the Pythagorean theorem.

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terms of time t.

A. The function A(r)=πr2 gives the area of the ripple in terms of the radius r, and (A∘r)(t)=πr(t)2=π(4t)2=16πt2 gives the area of the ripple in terms of time t.

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There is no way for the student to take 4 classes next semester, given that she needs 8 more classes to complete her degree and has already met 5 pre-requisites.

Since the student needs to take 8 more classes to complete her degree and has already taken 5 pre-requisites, she has 8 - 5 = 3 classes that she can choose from for next semester.

To calculate the number of ways she can take 4 classes next semester, we can use the combination formula:

nCr = n / (r × (n-r))

where n is the number of classes she can choose from (which is 3), and r is the number of classes she will take next semester (which is 4).

Plugging in the values, we get:

3C4 = 3 / (4 × (3-4)) = 0

Since we cannot choose 4 classes from a set of 3 classes, the answer is 0.

Therefore, there is no way for the student to take 4 classes next semester, given that she needs 8 more classes to complete her degree and has already met 5 pre-requisites.

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Answer:

35° and 55°

Step-by-step explanation:

(x - 20) and x form a right angle (90° ) and are complementary

complementary angles sum to 90° , then

x - 20 + x = 90

2x - 20 = 90 ( add 20 to both sides )

2x = 110 ( divide both sides by 2 )

x = 55

then the 2 angles are

x = 55°

x - 20 = 55 - 20 = 35°

We can be 90% confident that the true population variance of unemployed workers' math test scores falls between 65.61 and 197.57.

The first step in finding a 90% confidence interval for the population variance is to find the degrees of freedom for the sample. In this case, the degrees of freedom is 18 - 1 = 17.

Next, we need to find the critical value for a 90% confidence interval with 17 degrees of freedom. We can do this using a chi-squared distribution table. The critical values for a 90% confidence interval with 17 degrees of freedom are 8.671 and 27.488.

Now we can use the formula for a confidence interval for the population variance:

CI = [(n-1) * s²] / X²

Where n is the sample size, s is the sample standard deviation, and X^2 is the critical value from the chi-squared distribution table.

Plugging in the values we have:

CI = [(17) * (10.4)²] / X²

For the lower bound of the confidence interval, we use the smaller critical value:

CI = [(17) * (10.4)²] / 8.671

CI = 197.57

For the upper bound of the confidence interval, we use the larger critical value:

CI = [(17) * (10.4)²] / 27.488

CI = 65.61

So the 90% confidence interval for the population variance is (65.61, 197.57).

In conclusion, we can be 90% confident that the true population variance of unemployed workers' math test scores falls between 65.61 and 197.57.

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Hence, to convert a number of months to a fractional portion of a year, linear function divide the number of months by either 6 or 12 to get the answer in terms of half-years or complete years.

In mathematics, the term "linear function" is used to describe two separate but related ideas. Calculus and related fields classify polynomial functions of degree 0 or 1 as linear if their graphs are straight lines. A straight line on a coordinate plane represents any function, which is referred to as linear. Since it represents a straight line in the coordinate plane, the linear function y = 3x - 2 is an example. As the function may be connected to y, it can be represented as f(x) = 3x - 2.

You may divide a number of months by 12, which is the number of months in a year, to get a fractional portion of a year.

Consider the case when you have nine months. Nine months are equal to 0.75 years when you divide nine by twelve. But, if you divide 9 by 6, you obtain a result of 1.5, indicating that 9 months are equal to 1.5 half-years or 1 year and 6 months.

Hence, to convert a number of months to a fractional portion of a year, divide the number of months by either 6 or 12 to get the answer in terms of half-years or complete years.

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To reduce 95 ounces of a 27% solution of potassium chloride to a 19% solution, you must add 28.6 ounces of water.

To calculate this, you can use the formula M1V1 = M2V2, where M1 is the initial concentration, V1 is the initial volume, M2 is the desired concentration, and V2 is the desired volume.

So, M1 = 27%, V1 = 95 ounces, M2 = 19%, and V2 = (95 + V2) ounces.

Plugging this into the formula, you get 27(95) = 19(95 + V2). Solving for V2, you get V2 = 28.6 ounces, which is the amount of water you must add.

The equation (M1V1=M2V2) represents the dilution equation in chemistry. “Dilution is the process of decreasing the concentration of a solute in a solution, usually simply by mixing with more solvent like adding more water to the solution.”

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The area of the shaded segment is:= 16π - 32 cm² (exact value)

= 30.849 cm² (approximate value, rounded to three decimal places)

Area is the measurement of the surface inside a two-dimensional figure. It is expressed in square units, such as square meters or square inches.

To find the area of the shaded segment, we need to subtract the area of the triangle formed by the two radii and the chord from the area of the sector.

formula:

A = (θ/360)πr²

where A is the area of the sector, θ is the central angle in degrees, π is pi (approximately 3.14), and r is the radius of the circle.

Here, the central angle is 90 degrees and the radius is 8 cm.

area of sector is:

sector = (90/360)π(8)²

= 16π cm²

To find the area of the triangle, we need to find its base and height. The base is the chord, which is also the diameter of the circle and has a length of 16 cm (twice the radius). The height is half of the length of the chord (since the central angle is 90 degrees), which is 4 cm.

So the area of the triangle is:

A_triangle = (1/2)bh

= (1/2)(16)(4)

= 32 cm²

the area of shaded segment is:

shaded = sector - triangle

= 16π - 32

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The CRB (Cramér-Rao Bound) of variance estimation is a lower bound on the variance of an unbiased estimator of a parameter. The CRB of variance estimation for this system is (02 +0)^2/(02 +0 + (02 +0)^2). This is the minimum variance that an unbiased estimator of the parameter 8 can achieve.

In this case, the parameter we are trying to estimate is 8. To derive the CRB for estimating the parameter 8, we first need to find the Fisher Information matrix, which is defined as:
I(8) = E[(d log f(X; 8)/d8)^2]
where f(X; 8) is the probability density function of X and E is the expectation operator.

Since X~N(0,02 +0), the probability density function of X is:
f(X; 8) = (1/sqrt(2*pi*(02 +0)))*exp(-X^2/(2*(02 +0)))

Taking the derivative of the log of this function with respect to 8, we get:
d log f(X; 8)/d8 = -(1/(02 +0))*((X^2)/(02 +0) - 1)

Squaring this and taking the expectation, we get:
I(8) = E[(1/(02 +0))^2*((X^2)/(02 +0) - 1)^2]

Simplifying and using the fact that E[X^2] = 02 +0, we get:
I(8) = (1/(02 +0))^2*(02 +0 + (02 +0)^2)

Finally, the CRB for estimating the parameter 8 is given by the inverse of the Fisher Information matrix:
CRB(8) = 1/I(8) = (02 +0)^2/(02 +0 + (02 +0)^2)

Therefore, the CRB of variance estimation for this system is (02 +0)^2/(02 +0 + (02 +0)^2). This is the minimum variance that an unbiased estimator of the parameter 8 can achieve.

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The results of the SPSS INDEPENDANT T TEST can help to determine whether the effect of sugar on activity is statistically significant.

Yes, sugar has an effect on activity. In order to determine this, you can use an SPSS INDEPENDANT T TEST. This is a statistical test used to determine whether there is a significant difference between two groups of data, in this case, the control (water) and experimental (juice) groups.

The T Test requires that the two data sets are of equal length and are both normally distributed. The data provided above meet these criteria. The results of the T Test will tell us if the difference between the two sets is statistically significant at the 5% level (α=.05).

Therefore, the results of the SPSS INDEPENDANT T TEST can help to determine whether the effect of sugar on activity is statistically significant.

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Answer:

D. 432

Step-by-step explanation:

To find out this question you need to find out how many cookies you have of each type. we know we have 120 chocolate chip cookies. There are 42 fewer oatmeal cookies than chocolate chip cookies so we take 120 and minus 42.

120 - 42 = 78

There are 78 oatmeal cookies. now we want to find out how many peanut butter cookies we have. There are 3 times as many peanut butter cookies than oatmeal cookies so we times 77 with 3.

78 × 3 = 234

Now we know how many cookies are in all the types, we need to find the total number of all cookies in the grocery store.

120 + 78 + 234 = 432

therefore the answer will be D. 432

Hope this helps :)

If Colin wants to make 2 batches of Lavender soap and 2 batches of Vanilla soap, then he will need $9.57 for the oils

Here, Colin needs 1.5 ounces of Scented oil to make a batch of soap.

He wants to make 2 batches of Lavender soap and 2 batches of vanilla soap.

So, the amount of scented oil for 2 batches would be:

1.5 × 2 = 3 ounces

The cost of an ounce of Lavender oil is $1.54

So, using unitary method the cost of oil for the 2 batches of Lavender soap would be:

C₁ = 3 × 1.54

C₁ = 4.62 dollars

The cost of an ounce of Vanilla oil is $1.65

So,  using unitary method the cost of oil for the 2 batches of Vanilla soap would be:

C₁ = 3 × 1.65

C₁ = 4.95 dollars

Thus, the total cost would be,

C = C + C

C = 4.62 + 4.95

C = 9.57 dollars

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The degree of the function (1)/(2)=(x+2)(x-1)^(2)(5x-2) is 4, as there are 4 total x terms in the equation.

The end behavior of the function is determined by the leading term, which is (1/2)(5x^4). As the degree is even and the leading coefficient is positive, the end behavior is that the function will rise to the right and rise to the left.

The x-intercepts of the function are the values of x that make the function equal to zero. These can be found by setting each factor equal to zero and solving for x:

x+2=0 -> x=-2

x-1=0 -> x=1

5x-2=0 -> x=2/5

The x-intercepts are -2, 1, and 2/5.

The y-intercept is the value of the function when x=0. Plugging in 0 for x gives:

(1/2)(0+2)(0-1)^2(5(0)-2) = (1/2)(2)(-1)^2(-2) = -2

The y-intercept is -2.

The zeroes of multiplicity are the values of x that make the function equal to zero and the number of times they appear as a factor in the equation. In this case, the zeroes of multiplicity are:

-2 with a multiplicity of 1

1 with a multiplicity of 2

2/5 with a multiplicity of 1

A few midinterval points can be found by plugging in values of x between the x-intercepts and solving for the function value. For example, plugging in x=0.5 gives:

(1/2)(0.5+2)(0.5-1)^2(5(0.5)-2) = (1/2)(2.5)(-0.5)^2(-0.5) = -0.3125

So one midinterval point is (0.5, -0.3125).

Another midinterval point can be found by plugging in x=-1:

(1/2)(-1+2)(-1-1)^2(5(-1)-2) = (1/2)(1)(-2)^2(-7) = -7

So another midinterval point is (-1, -7).

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The product of the two given binomials can be expressed as the trinomial 2561104x³ + 684636x² + 87719x + 736, which is in its simplest form.

In this case, we will multiply the first two binomials (12x+1)(21x+1) and then multiply the second two binomials (65x+32)(56x+23). We will then multiply the two resulting expressions to get the final trinomial.

To multiply (12x+1)(21x+1), we can use the distributive property of multiplication, which states that a(b+c) = ab + ac. Therefore, we have:

(12x+1)(21x+1) = 12x(21x) + 12x(1) + 1(21x) + 1(1) = 252x² + 12x + 21x + 1 = 252x² + 33x + 1

Similarly, to multiply (65x+32)(56x+23), we have:

(65x+32)(56x+23) = 65x(56x) + 65x(23) + 32(56x) + 32(23) = 3640x² + 1495x + 1792x + 736 = 3640x² + 3287x + 736

Now, to find the product of the two expressions, we can multiply them using the distributive property again:

(252x² + 33x + 1)(3640x² + 3287x + 736) = 252x²(3640x²) + 252x²(3287x) + 252x²(736)

   • 33x(3640x²) + 33x(3287x) + 33x(736)

   • 1(3640x²) + 1(3287x) + 1(736)

Simplifying this expression by combining like terms, we get:

= 917280x⁴ + 1573824x³ + 684636x² + 87719x + 736

This final expression has four terms, but it can be simplified further to a trinomial by combining the first two terms using the associative property of addition. We have:

917280x⁴ + 1573824x³ + 684636x² + 87719x + 736 = (917280x⁴ + 1573824x³) + (684636x² + 87719x + 736) = 2561104x³ + 684636x² + 87719x + 736

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Complete Question:

Express the product of(12x+1)(21​x+1) and(65x+32)(56​x+23​) as a trinomial in simplest form

The common factors are \[(x+5)\], so the LCM is (x+5)²(x+6) of the given polynomials. The Least Common Multiple (LCM) of the two given polynomials can be found by factoring them and then finding the common factors:

\[ x²+10 x+25 = (x+5)(x+5) \]
\[ x²+11 x+30 = (x+5)(x+6) \]

To determine the LCM of the given polynomials, we need to factor each polynomial and then multiply the factors together, taking the highest power of each factor.

First, let's factor each polynomial:

\[ x²+10 x+25 = (x+5)(x+5) \]
\[ x²+11 x+30 = (x+5)(x+6) \]

Now, let's find the LCM by multiplying the highest power of each factor together:

LCM = (x+5)(x+5)(x+6) = (x+5)²(x+6)

So, the LCM of the given polynomials is (x+5)²(x+6) in factored form.

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The area of the trapezoid is 75 square units, and the lengths of the diagonals are 13 and 17 units.

An isosceles trapezoid is a type of trapezoid with two parallel sides that are equal in length, and two non-parallel sides that are also equal in length.  The two legs meet at an angle at the top of the trapezoid, and the bases are parallel to each other.

To find the area of the trapezoid, we use the formula:

Area = (b1 + b2) * h / 2

where b1 and b2 are the lengths of the bases, and h is the height.

In this case, b1 = 9, b2 = 21, and h is the distance between the bases. Since the trapezoid is isosceles, the height is also the length of the two diagonals minus the sum of the two bases, divided by 2:

h = (d1 + d2 - b1 - b2) / 2

we will use the Pythagorean theorem:

d1² = h² + (b2 - b1/2)²

d2² = h² + (b2 + b1/2)²

Plugging in the values we get:

h = (d1 + d2 - 9 - 21) / 2

h = (d1 + d2 - 30) / 2

d1² = h² + (21 - 9/2)²

d2² = h² + (21 + 9/2)²

Simplifying, we get:

h = (d1 + d2 - 30) / 2

d1² = h² + 225/4

d2² = h² + 529/4

Substituting the first equation into the other two, we get a system of two equations in two variables:

d1² = ((d1 + d2 - 30) / 2)² + 225/4

d2² = ((d1 + d2 - 30) / 2)² + 529/4

Simplifying and solving for d1 and d2, we get:

d1 = 13

d2 = 17

To find the area, we plug in the values of the bases and the height:

h = (d1 + d2 - 30) / 2 = (13 + 17 - 30) / 2 = 5

Area = (b1 + b2) * h / 2 = (9 + 21) * 5 / 2 = 75

Therefore, the area of the trapezoid is 75 square units, and the lengths of the diagonals are 13 and 17 units.

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Answer: +-root15/2

To find the x-intercepts, set the function equal to 0 and solve for x.

0.8x^2 - 3 = 0

0.8x^2 = 3

x^2 = 15/4

x = +- root15/2

Answer:

1st choice

Step-by-step explanation:

(r² -4r + 5 - r² -2r + 8) / (r - 4)

= (-6r + 13) / (r - 4)

The height of the person after 4 seconds is -48 meters. Below you will learn how to solve the problem.

The height of a person after 4 seconds can be found by plugging in the value of t into the given equation and solving for h.

Step 1: Plug in the value of t into the equation:
h = 2 * (4 - 5) ^ 2 - 50

Step 2: Simplify the equation:
h = 2 * (-1) ^ 2 - 50

Step 3: Simplify further:
h = 2 * 1 - 50

Step 4: Solve for h:
h = 2 - 50

Step 5: Simplify to get the final answer:
h = -48

Therefore, the height of the person after 4 seconds is -48 meters.

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Answer:

  x = 10.1

Step-by-step explanation:

You want the value of x in the given secant-tangent geometry.

The angle between the secant ON and the tangent MN is half the measure of arc ON. The measure of arc ON is the remainder of the circle after long arc ON = 283° is subtracted:

  arc ON = 360° -283° = 77°

  (5x -12)° = 1/2(77°) . . . . . relation of angle to arc

  10x -24 = 77 . . . . . . . . divide by °, multiply by 2

  10x = 101 . . . . . . . . . . add 24

  x = 10.1 . . . . . . . . . . divide by 10

Step-by-step explanation:

the area of the full larger circle minus the area of the smaller circle.

the area of a circle is

pi×r²

the radius of the smaller circle is 23.1 yd.

the radius or the larger circle is 23.1 + 7.8 = 30.9 yd.

the area of the larger circle is

pi×30.9² = 3.14 × 954.81 = 2,998.1034 yd²

the area of the smaller circle is

pi× 23.1² = 1,675.5354 yd²

the area of only the ring around the smaller circle is then

2,998.1034 - 1,675.5354 = 1,322.568 yd² ≈

≈ 1,322.57 yd²

or

pi×30.9² - pi×23.1² = pi(954.81 - 533.61) =

= 421.2pi = 421.2 × 3.14 =

= 1,322.568 ≈ 1,322.57 yd²

Answer:

$1.65

Step-by-step explanation:

9.7%×(11.73+5.27)

0.097×(11.73+5.27)

=1.649

to 2d.p

=1.65

Step-by-step explanation:

A + B = 437

A - B = 415 (for that sequence it is important to know that A is larger than B).

A = 415 + B

that we use now in the first equation :

415 + B + B = 437

2B = 22

B = 11

A = 415 + B = 415 + 11 = 426 tons

B = 11 tons

When the angle of elevation to the plateau's top is 20°, we are therefore 34.22 metres distant from the plateau's foot.

An angle, also known as the vertex of the angle, is the shared endpoint where two lines, line segments, or rays come together in geometry. Angles are commonly expressed as degrees or radians. A radian is the angle that the centre of a circle is subtended by an arc that is the same length as the circle's radius, while a degree is equal to 1/360th of a complete revolution. The relationships between lines and shapes are described using angles, which are essential to many mathematical ideas and applications in physics, engineering, and other disciplines.

given

Trigonometry can be used to resolve this issue. Let's designate the distance "x" from the plateau's base to where we are right now.

We must first determine the height we are at right now. Since we are aware of the slope angle, we can accomplish this using the tangent function:

tan(20°) Means adjacent/opposite

h is the height we are presently at, so tan(20°) = h/x.

To find h, we can change this equation as follows:

h Equals x * tan(20°)

x² + h² = 40^2

If you replace h = x * tan(20°):

x² + (x*tan(20°))

x² = 40²

Simplifying:

x² + 0.364x²= 1600

1.364x² = 1600

x² = 1171.61

x ≈ 34.22

When the angle of elevation to the plateau's top is 20°, we are therefore 34.22 metres distant from the plateau's foot.

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Answer:

9*5*7 = 315 week

9*5 = 40 day

Step-by-step explanation:

hope it helps

Answer:

9 songs/day × 5 days = 45 songs/day

45 songs/day × 7 days/week = 315 songs this week

The requried equation represents the volume of the gas in terms of temperature is V = 22 + 225T.

The equation model is defined as the representative of the given case in the form of an equation using variables and constants.

Here,
Let's denote the volume of the gas as V and temperature as T.

From the given information, we know that at 0°C temperature (i.e. T = 0), the volume of the gas is 22 liters.

For every 1°C increase in temperature, the volume of the gas increases by 225 liters.

Therefore, we can write the equation as:

V = 22 + 225T

This equation represents the volume of the gas in terms of temperature.

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