two trains leave towns 831 kilometers apart at the same time and travel toward each other. one train travels 15 km/h faster than the other. if they meet in 3 hours what is the rate of each train?

There will be 12 slices of pizza left over, which can be expressed as 3/2 or 1 1/2 slices in fraction form.

To find out how much pizza will be left over, we need to calculate the total number of slices available and subtract the number of slices consumed by the players.

Given that there are six pizzas and each pizza has eight slices, the total number of slices available is 6 pizzas * 8 slices/pizza = 48 slices.

Since there are 36 players on the team, and each player has one slice, the total number of slices consumed is 36 slices.

To determine the remaining slices, we subtract the consumed slices from the total available slices: 48 slices - 36 slices = 12 slices.

Therefore, there will be 12 slices of pizza left over.

To express this as a fraction, we can write it as 12/1, which simplifies to 12. This means there will be 12 whole slices of pizza left over.

If you would like to express it as a fraction in its simplest form, you can write it as 12/8. By dividing both the numerator and denominator by their greatest common divisor, which is 4, we get 3/2. So, in fraction form, there will be 3/2 or 1 1/2 slices of pizza left over.

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Answer:

15 minutes

Step-by-step explanation:

2 pages = 3 minutes

45 pages = 3x minutes

45 / 3 = 15

Given that the variables are complex numbers, the value of the complex expression \(\frac{\gamma}{\alpha} +\bar{\frac{\alpha}{\beta}}\) is -2

The given parameters are:

\(\alpha + \beta + \gamma = 0\)

\(\frac{1}{\alpha} + \frac{1}{\beta} + \frac{1}{\gamma} = 0\)

Rewrite the first equation as:

\(\alpha + \beta = - \gamma\)

Take LCM in the second equation

\(\frac{\alpha + \beta}{\alpha \beta} + \frac{1}{\gamma} = 0\)

So, we have:

\(\frac{ - \gamma}{\alpha \beta} + \frac{1}{\gamma} = 0\)

Rewrite as:

\(\frac{1}{\gamma} = \frac{\gamma}{\alpha \beta}\)

Multiply through by \(\alpha\)

\(\frac{\alpha}{\gamma} = \frac{\gamma}{\beta}\)

Inverse both sides

\(\frac{\gamma}{\alpha} = \frac{\beta}{\gamma}\)

Make \(\beta\) the subject in \(\alpha + \beta + \gamma = 0\)

\(\beta =-(\alpha + \gamma)\)

So, we have:

\(\frac{\gamma}{\alpha} = \frac{-(\alpha + \gamma)}{\gamma}\)

Expand

\(\frac{\gamma}{\alpha} = -\frac{\alpha}{\gamma}- 1\)

This gives

\(\frac{\gamma}{\alpha} +\frac{\alpha}{\gamma} = - 1\)

Make \(\gamma\) the subject in \(\alpha + \beta + \gamma = 0\)

\(\gamma = -(\beta + \alpha)\)

So, we have:

\(\frac{\gamma}{\alpha} +\frac{\alpha}{-(\beta + \alpha)} = - 1\)

Split

\(\frac{\gamma}{\alpha} +\bar{\frac{\alpha}{\beta}} + \frac{\alpha}{\alpha} = - 1\)

Evaluate the quotient

\(\frac{\gamma}{\alpha} +\bar{\frac{\alpha}{\beta}} + 1 = - 1\)

Subtract 1 from both sides

\(\frac{\gamma}{\alpha} +\bar{\frac{\alpha}{\beta}} = - 2\)

Hence, the value of \(\frac{\gamma}{\alpha} +\bar{\frac{\alpha}{\beta}}\) is -2

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The equation representing the relationship in the table is y = 2x - 3. The correct option is C.

The equation in mathematics is the relationship between the variables and the number and establishes the relationship between two or more variables.

Given data in the table:-

x              y

0              -3

1               -1

2              1

3              3

The equation satisfying the values of the table will be:-

y = 2x - 3

-3 = 2 x  0 - 3=-3

-1 = 2 x 1 - 3 =-1

1 = 2 x 2 - 3 = 1

3 = 2 x 3 - 3 = 3

Therefore, the equation representing the relationship in the table is y = 2x - 3. The correct option is C.

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To calculate the total volume of the solid we will divide it into n shell cyline thickness of \($\Delta y$.\)

The internal shell cylinder circumference C shall be\($2 \pi r_i$\)

where r is the in The shell cylinder internal area A shall be C.

where h is the height

The volume of the shell cylinder\($\Delta v$\) shall be\($A \cdot \Delta y$.\)

Then we will have:

\(\Delta v=A \cdot \Delta y=C \cdot h \cdot \Delta y=2 \pi r_i h \cdot \Delta y \Rightarrow d v=2 \pi r_i h \cdot d y$$\)

The total volume of the solid shall be the summation of all n shell cylinders

\(\int d v=\int 2 \pi r_i h d y \Rightarrow V=\int_a^b 2 \pi r_i h d y \Rightarrow V=2 \pi \int_a^b r_i h d y$$\)

\(\int d v=\int 2 \pi r_i h d y \Rightarrow V=\int_a^b 2 \pi r_i h d y \Rightarrow V=2 \pi \int_a^b r_i h d y\)

\(The value $a$ is the value of $y$ at the point where $x=0$ then:For $x=0 \Rightarrow y=0^3 \Rightarrow y=0$ then $a=0$.The value $b$ is the value of $y$ at the point where $x=1$ then:\)

\(For $x=1 \Rightarrow y=1^3 \Rightarrow y=1$ then $b=1$.Since the integration will be with variable $y$ we have to express the function $y=x^3$ in terms of $y$ :$$\)

y=x^3 \\(Rightarrow x=\sqrt[3]{y}\)

Substituting in V, we will have:

\(V= & 2 \pi \int_a^b r_i h d y=2 \pi \int_0^1(1-y)(1-\sqrt[3]{y}) d y=2 \pi\)\\(int_0^1(1-y)\left(1-y^{\frac{1}{3}}\right) d y \\\)

&\(1-y \\& \frac{1-y^{\frac{1}{3}}}{1-y} \\& \frac{-y^{\frac{1}{3}}+y^{\frac{1}{3}} \cdot y^{\frac{1}{1}}}{} \\\)

\(& 1-y-y^{\frac{1}{3}}+y^{\frac{1}{3}+\frac{1}{1}}= \\& =1-y-y^{\frac{1}{3}}+y^{\frac{1+3}{3}}= \\\)

\(& =1-y-y^{\frac{1}{3}}+y^{\frac{4}{3}}= \\& =y^{\frac{4}{3}}-y^{\frac{1}{3}}-y+1\)

Substituting in V:

\(V=2 \pi \int_0^1\left(y^{\frac{4}{3}}-y^{\frac{1}{3}}-y+1\right) d y=2\)\({1}{3}+1}}{\frac{1}{3}+1}-\frac{y^{1+1}}\){\(1+1}+y\right]_0^1=2\) \(\pi\left[\frac{y^{\frac{4+3}{3}}}{\frac{4+3}{3}}\)-\(\frac{y^{\frac{1+3}{3}}}{\frac{1+3}{3}}-\frac{y^2}{2}+y\right]_0^1$$\)

Calculating the definite integral:

By definition\(, $\int_a^b f(x) d x=\left.F(x)\right|_a ^b=F(b)-F(a)$\) then:

\(& V=\frac{\pi}{14}\left[\left(12 \cdot 1^{\frac{7}{3}}-21 \cdot 1^{\frac{4}{3}}-14\)\(\cdot 1^2+28 \cdot 1\right)-\left(12 \cdot 0^{\frac{7}{3}}-21 \cdot\) \(0^{\frac{4}{3}}-14 \cdot 0^2+28 \cdot 0\right)\right] \\\)

& V=\(\frac{\pi}{14}[(12 \cdot 1-21 \cdot 1-14 \cdot 1+28 \cdot 1)-\underbrace{(12 \cdot 0-21 \cdot 0-14 \cdot 0+28 \cdot 0)}_0]\)

\(& V=\frac{\pi}{14}(12-21-14+28)=\frac{\pi}{14}(12+28-21-14)=\frac{\pi}{14}(40-35)=\frac{5 \pi}{14} \approx \frac{5 \cdot 3,1416}{14} \approx \frac{15,708}{14} \\& V \approx 1,122\)

Answer:\($V \approx 1,122 u . v$. (units of volume)\)

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The parent function is  y = ∛x and the sequence of transformation is

From the question, we have the following parameters that can be used in our computation:

y = ^3√-8x_4 ​

Rewrite the above equation properly

So, we have the following representation

y = ∛-8x - 4

Start by shifting the function up by 4 units

So, we have the following representation

y = ∛-8x - 4 + 4

Evaluate the sum

y = ∛-8x

Reflect across the y-axis

So, we have

y = ∛8x

Horizontal stretch by 1/8

This is represented as

y = ∛1/8 * 8x

So, we have

y = ∛x

Hence, the parent function is  y = ∛x

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Answer:Rewrite the equation by factoring –8 from the radicand and taking the cube root to get –2 in front of the radical symbol.

The graph is reflected over the x-axis.

The graph is also reflected over the y-axis.

The graph is vertically stretched by a factor of 2.

The graph is translated ½ unit to the left.

Step-by-step explanation:

a. 759

b. 8769

c. 96699

d. 36754209

The trick is looking at the first numbers for either possible answer. Pick the one that is the greatest going backward. If you're stuck with the same numbers as in d, just continue going back until you see something like the 7 being greater than the 5.

Answer:

Option 3

(3xy³ + 5x²y⁴)  (3xy³ - 5x²y⁴)

Step-by-step explanation:

Factorize polynomials:

Use exponent law:

                   \(\boxed{\bf a^{m*n}=(a^m)^n} \ & \\\\\boxed{\bf a^m * b^m = (a*b)^m}\)

9x²y⁶ = 3²* x² * y³*² = 3² * x² * (y³)² = (3xy³)²

25x⁴y⁸ = 5² * x²*² * y⁴*² = 5² * (x²)² * (y⁴)² = (5x²y⁴)²

Now use the identity:  a² - b² = (a +b) (a -b)

Here, a = 3xy³ & b = 5x²y⁴

9x²y⁶ - 25x⁴y⁸ = 3²x²(y³)² - 5²(x²)² (y⁴)²

                       = (3xy³)² - (5x²y⁴)²

                      = (3xy³ + 5x²y⁴)  (3xy³ - 5x²y⁴)

Answer:

258.41 m

Step-by-step explanation:

Since there are three semi-circles in the length of the rectangle, we can divide 18 by 3 to get 6 as the diameter for each circle. The area of a semi-circle is (pi*r^2)/2, we can multiply that by 3 and add it with the area of the rectangle to get the total area.

(12*18) + (3(pi*3^2))/2 =

216 + 42.4115 =

258.41 m

Simplifying this equation, we get:

8 + 4k + 4k + 6 = 30

8k + 14 = 30

8k = 16

k = 2

Therefore, the value of k is 1.

In mathematics, a polynomial is an expression consisting of variables (usually represented by x), coefficients, and non-negative integer exponents, which are combined using the operations of addition, subtraction, and multiplication. For example,

\(3x^2 + 2x - 1\)

is a polynomial with three terms, or a "trinomial," where the variable x is raised to the powers of 2 and 1, and the coefficients are 3, 2, and -1.

The degree of a polynomial is the highest power of the variable in the expression. For example, the polynomial above has a degree of 2, since the highest power of x is 2.

Polynomials are used in many areas of mathematics, including algebra, calculus, and geometry, and are used to model many real-world phenomena.

We can use the remainder theorem, which states that if a polynomial f(x) is divided by (x - a), then the remainder is equal to f(a). In this case, we know that when the polynomial\(l x^3 + kx^2 + 2kx\) + 6 is divided by (x - 2), the remainder is 30. So, we can set up the following equation:

\(x^3 + kx^2 + 2kx + 6 = (x - 2)q(x) + 30\)

where q(x) is the quotient when. \(x^3 + kx^2 + 2kx + 6\) is divided by (x - 2). We don't need to know what q(x) is, since we're only interested in finding k.

Now, let's substitute x = 2 into the equation above:

\(2^3 + k(2^2) + 2k(2) + 6 = (2 - 2)q(2) + 30\)

Simplifying the left-hand side, we get:

\(8 + 4k + 4k + 6 = 30\)

\(16k = 16\)

\(k = 1\)

OR

8 + 4k + 4k + 6 = 30

8k + 14 = 30

8k = 16

k = 2

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Answer:

38.81 pounds

Step-by-step explanation:

Considering the definition of right rectangular prism and its volume,  the total weight of the contents is 38.81 pounds.

Right rectangular prism

A right rectangular prism (or cuboid) is a polyhedron whose surface is formed by two equal and parallel rectangles called bases and by four lateral faces that are also parallel rectangles and equal two to two.

Volume of right rectangular prism

To calculate the volume of the rectangular prism, it is necessary to find the product of its dimensions, or of the three edges that converge at a certain vertex.

That is, to calculate the volume of a rectangular prism, multiply its 3 dimensions: length×width×height.

Volume of the container

In this case, you know that:

the dimensions of the container built are 7.5 ft by 11.5 ft by 3 ft.

the container is entirely full and, on average, its contents weigh 0.15 pounds per cubic foot.

So, the volume of the container is calculated as:

7.5 ft× 11.5 ft× 3 ft= 258.75 ft³

Then, the total weight of the contents is calculated as:

258.75 ft³×  0.15 pounds per cubic foot= 38.8125 pounds≅ 38.81 pounds

Finally, the total weight of the contents is 38.81 pounds.

Answer:

224

Step-by-step explanation:

360.-136.

Answer:

y = -2x-8

Step-by-step explanation:

The equation for a slope is y=mx+b.

m = Slope (-2 in this case)

b = y-intercept (-8 in this case)

4. RSTU is a trapezoid because the opposite sides RS and UT are parallel.

5. RSTU is not an isosceles trapezoid because the diagonals are not congruent.

In order to verify that RSTU is a trapezoid, we would have to determine slope of the pair of opposite sides and check whether at least one pair of opposite sides are parallel;

RU ║ ST

Slope of side RU = Slope of side ST

Slope of RU = (y₂ - y₁)/(x₂ - x₁)

Slope of RU = (1 + 3)/(5 + 3)

Slope of RU = 4/8

Slope of RU = 0.5.

Slope of RS = (y₂ - y₁)/(x₂ - x₁)

Slope of RS = (-9 + 3)/(-4 + 3)

Slope of RS = -6/-1

Slope of RS = 6.

Slope of ST = (y₂ - y₁)/(x₂ - x₁)

Slope of ST = (-2 - 1)/(10 - 5)

Slope of ST = -3/5

Slope of ST = -0.6.

Slope of UT = (y₂ - y₁)/(x₂ - x₁)

Slope of UT = (-2 + 9)/(10 + 4)

Slope of UT = 7/14

Slope of UT = 0.5.

Therefore, RSTU is a trapezoid because the opposite sides RS and UT are parallel.

Question 5.

In order to determine whether RSTU is an isosceles trapezoid, we would have to determine length of the diagonals by using the distance formula and check whether they are congruent;

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Distance RT = √[(-2 + 3)² + (10 + 3)²]

Distance RT = √170 units.

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Distance US = √[(5 + 4)² + (1 + 9)²]

Distance US = √181 units.

Therefore, RSTU is not an isosceles trapezoid because the diagonals RT and US are not congruent.

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Answer:

D = L/k

Step-by-step explanation:

Since A represents the amount of litter present in grams per square meter as a function of time in years, the net rate of litter present is

dA/dt = in flow - out flow

Since litter falls at a constant rate of L  grams per square meter per year, in flow = L

Since litter decays at a constant proportional rate of k per year, the total amount of litter decay per square meter per year is A × k = Ak = out flow

So,

dA/dt = in flow - out flow

dA/dt = L - Ak

Separating the variables, we have

dA/(L - Ak) = dt

Integrating, we have

∫-kdA/-k(L - Ak) = ∫dt

1/k∫-kdA/(L - Ak) = ∫dt

1/k㏑(L - Ak) = t + C

㏑(L - Ak) = kt + kC

㏑(L - Ak) = kt + C'      (C' = kC)

taking exponents of both sides, we have

\(L - Ak = e^{kt + C'} \\L - Ak = e^{kt}e^{C'}\\L - Ak = C"e^{kt} (C" = e^{C'} )\\Ak = L - C"e^{kt}\\A = \frac{L}{k} - \frac{C"}{k} e^{kt}\)

When t = 0, A(0) = 0 (since the forest floor is initially clear)

\(A = \frac{L}{k} - \frac{C"}{k} e^{kt}\\0 = \frac{L}{k} - \frac{C"}{k} e^{k0}\\0 = \frac{L}{k} - \frac{C"}{k} e^{0}\\\frac{L}{k} = \frac{C"}{k} \\C" = L\)

\(A = \frac{L}{k} - \frac{L}{k} e^{kt}\)

So, D = R - A =

\(D = \frac{L}{k} - \frac{L}{k} - \frac{L}{k} e^{kt}\\D = \frac{L}{k} e^{kt}\)

when t = 0(at initial time), the initial value of D =

\(D = \frac{L}{k} e^{kt}\\D = \frac{L}{k} e^{k0}\\D = \frac{L}{k} e^{0}\\D = \frac{L}{k}\)

Answer:

Step-by-step explanation:

What is 3-3×6+2 please?

remember PEMDAS

3 - 3 × 6 + 2 =    (solve multiplication)

3 - 18 + 2 =         (solve addition)

3 - 16 =              (solve subtraction)

-13                     (result)

the answer is letter d)

if u arrange it correctly it will be -x +2y=2

-½x+y=1

then multiply -½ by the first equation and multiply -1 by the second equation..

then change the signs of the second equation

then cancel x .. then y =1

then substitute y with 1

..it won't be correct

The percent decrease in total principal and interest paid between a 30-year term mortgage and a 15-year mortgage with a principal balance of $484,500.00 and a 6.5% APR is 31.0%. (Option A)

To calculate the  percent decrease, we can use the following formula.

Percent decrease = ( (30-year factor -   15-year factor) / 30-year factor) x 100

Substituting the values from the chart.  

= (($ 6.65 - $8.71) / $6.65) x 100

= ( -$ 2.06 / $6.65) * 100

= -0.309 *  100

Percent decrease ≈ - 30.9 %

Since the question asks for the percent decrease as a positive value, we take the absolute value of the result which is

Percent decrease ≈ 31%

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The Answer:

Width = 6

Step-by-step explanation:

Let width be w

(3w + 8) x w = 156

3 \(w^{2}\) x 8n - 156 = 0

(w + 8 x 6) (w-6) = 0

w = 6

Total questions =10

Both part correct earns 5 points

One part correct earns 2 ponts

No parts correct earns - 1 points

P I-squared

Both = 4

One = 2

None = 4

Total points = (5×4) + (2×2) + (-1×4)

= 20 + 4 - 4

= 20

Euler circles

Both = 2

One = 6

None = 2

Total points = (5×2) + (2×6) + (-1×2)

= 10 + 12 - 2

= 20

Hope this will help....

Because the triangles are congruent, we will see that x = 2.5

Here we can see that we have two congruent triangles, RST and RTU. Because the triangles are congruent, all the correspondent sides must have equal measures.

This implies that:

RS = RU

Then, replacing the measures, we get:

8x = 6x + 5

Solving this for x we get:

8x - 6x = 5

2x = 5

x = 5/2 = 2.5

So we can conclude that x = 2.5

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The solution for b is: b = r * (f - h²).

the definition of an equation is a mathematical statement that demonstrates that two mathematical expressions are equal. For instance, the equation 3x + 5 = 14 consists of the two expressions 3x + 5 and 14, which are separated by the 'equal' symbol.

To solve for b, we need to isolate the variable b on one side of the equation. We can do that by multiplying both sides of the equation by (f - h²):

\($\frac{b}{(f - h^2)} = r * (f - h^2)\)

Now, we can isolate b by multiplying both sides by (f - h^2) again:

b = r * (f - h²)

Therefore, the solution for b is: b = r * (f - h²).

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Hey there!

(5 * 6) * 4

= 30 * 4

= 120

So you’re basically looking for something that’s equivalent to 120

CHOICE A.

5 * (5 * 6)

= 5 * 30

= 150

So, Choice A is probably NOT the answer you’re looking for!

CHOICE B.

4 * (5 * 6)

= 4 * 30

= 120

Choice B. is probably the answer you’re probably looking for.

So, I recommend you to color it apricot. :)

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

Answer:

Step-by-step explanation:

slope intercept: y = mx + b

where m is the slope and b is the y-intercept

Equation: y = -3x + 4

Since y-intercept is given, then we have the first point of the line as (0,4)

Let's find the value of x when y is 0

y = -3x + 4

0 = -3x + 4

3x = 4

x = 4/3

(4/3,0) ---second point

Since there are two points/coordinates already then we can now plot/graph.

Answer:

\(x = t\)

\(y = 1 - t\)

\(z = 2t\)

Step-by-step explanation:

Given

\(x=t\)

\(y=e^{-t}\)

\(z=2t-t^2\)

(0, 1, 0)

The vector equation is given as:

\(r(t) = (x,y,z)\)

Substitute values for x, y and z

\(r(t) = (t,\ e^{-t},\ 2t - t^2)\)

Differentiate:

\(r'(t) = (1,\ -e^{-t},\ 2 - 2t)\)

The parametric value that corresponds to (0, 1, 0) is:

\(t = 0\)

Substitute 0 for t in r'(t)

\(r'(t) = (1,\ -e^{-t},\ 2 - 2t)\)

\(r'(0) = (1,\ -e^{-0},\ 2 - 2*0)\)

\(r'(0) = (1,\ -1,\ 2 - 0)\)

\(r'(0) = (1,\ -1,\ 2)\)

The tangent line passes through (0, 1, 0) and the tangent line is parallel to r'(0)

It should be noted that:

The equation of a line through position vector a and parallel to vector v is given as:

\(r(t) = a + tv\)

Such that:

\(a = (0,1,0)\) and \(v = r'(0) = (1,-1,2)\)

The equation becomes:

\(r(t) = (0,1,0) + t(1,-1,2)\)

\(r(t) = (0,1,0) + (t,-t,2t)\)

\(r(t) = (0+t,1-t,0+2t)\)

\(r(t) = (t,1-t,2t)\)

By comparison:

\(r(t) = (x,y,z)\) and \(r(t) = (t,1-t,2t)\)

The parametric equations for the tangent line are:

\(x = t\)

\(y = 1 - t\)

\(z = 2t\)

Answer: The range of the tangent function is (-∞,∞). So the answer is A: All real numbers.

Step-by-step explanation:

It took Emily 33.4 minutes to make dinner.

A mixed number is a kind of fraction that also has a proper fraction and a whole number. The number of whole units is represented by the whole number, and the fraction of a unit is represented by the proper fraction.

To solve the problem, we have to convert the mixed number  \(9 \frac{1}{10}\)   to a decimal number:

⇒ \(9 \frac{1}{10} = 9 +\frac{1}{10} = \frac{(9*10)+1}{10}\)

⇒ \(\frac{91}{10}\)  =  9.1

This means that Emily finished making dinner 9.1 minutes sooner than the cake.

To find out how long it took Emily to make dinner, we can subtract 9.1 from the cake baking time:

⇒ 42.5 - 9.1 = 33.4 minutes

Therefore, it took Emily 33.4 minutes to make dinner.

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The value of 3¾ft in yards would be = 1 6/25 yard

A mixed number is the type of number that is made up of three parts such as the whole number, a numerator and a denominator.

To convert to yards;

1 ft = 0.33 yard

3¾ = X yards

make x yards the subject of formula;

X yards = 3¾ × 0.33

X yards = 3.75×0.33

X yards = 1.24 yards

X yards in mixed number= 124/100 = 31/25 = 1 6/25 yard.

Note that the final value which is 124/100 is reduce to the lower figure by dividing through with 4 to arrive at the mixed number 1⁶/25

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