Why are the expressions 3(y – 2) + 2(y – 2) and 5(y-2) equivalent?

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To calculate the molecular weight of a gas with a density of 1.524 g/l at STP, we can use the ideal gas law: PV = nRT. At STP, the pressure (P) is 1 atm, the volume (V) is 22.4 L/mol, and the temperature (T) is 273 K. The molecular weight of the gas with a density of 1.524 g/L at STP is approximately 32.0 g/mol.

Rearranging the equation, we get n = PV/RT.

Next, we can calculate the number of moles (n) of the gas using the given density of 1.524 g/l. We know that 1 mole of any gas at STP occupies 22.4 L, so the density can be converted to mass by multiplying by the molar mass (M) and dividing by the volume: density = (M*n)/V. Rearranging the equation, we get M = (density * V) / n.

Substituting the given values, we get n = (1 atm * 22.4 L/mol) / (0.0821 L*atm/mol*K * 273 K) = 1 mol. Then, M = (1.524 g/L * 22.4 L/mol) / 1 mol = 34.10 g/mol. Therefore, the molecular weight of the gas is 34.10 g/mol.

To calculate the molecular weight of a gas with a density of 1.524 g/L at STP, you can follow these steps:

1. Recall the ideal gas equation: PV = nRT

2. At STP (Standard Temperature and Pressure), the temperature (T) is 273.15 K and the pressure (P) is 1 atm (101.325 kPa).

3. Convert the density (given as 1.524 g/L) to mass per volume (m/V) by dividing it by the molar volume at STP (22.4 L/mol). This will give you the number of moles (n) per volume (V):

  n/V = (1.524 g/L) / (22.4 L/mol)

4. Calculate the molar mass (M) of the gas using the rearranged ideal gas equation, where R is the gas constant (8.314 J/mol K):

  M = (n/V) * (RT/P)

5. Substitute the values and solve for M:

  M = (1.524 g/L / 22.4 L/mol) * ((8.314 J/mol K * 273.15 K) / 101325 Pa)

6. Calculate the molecular weight of the gas:

  M ≈ 32.0 g/mol

Therefore, the molecular weight of the gas with a density of 1.524 g/L at STP is approximately 32.0 g/mol.

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To solve the trigonometric equation 2cos2x=cosx on the interval 0 to 2π, we can use some basic trigonometric identities and algebraic manipulations. The solutions to the trigonometric equation 2cos^2(x) = cos(x) on the interval 0 to 2π are x = π/2, 3π/2, π/3, and 5π/3

First, we can simplify the equation by moving all the terms to one side:
2cos2x - cosx = 0
Next, we can use the double angle formula for cosine to express cos2x in terms of cosx:
2cos^2x - cosx = 0
Then, we can factor out the common factor of cosx:
cosx(2cosx - 1) = 0
This equation is satisfied when either cosx = 0 or 2cosx - 1 = 0. Solving for cosx in the second equation, we get:
2cosx - 1 = 0
2cosx = 1
cosx = 1/2

Therefore, the solutions to the original equation 2cos2x = cosx on the interval 0 to 2π are the values of x for which either cosx = 0 or cosx = 1/2. Using the unit circle or a calculator, we can find the values of x that satisfy these conditions:
cosx = 0 when x = π/2 and x = 3π/2
cosx = 1/2 when x = π/3 and x = 5π/3
Thus, the solutions to the equation 2cos2x = cosx on the interval 0 to 2π are x = π/2, π/3, 3π/2, and 5π/3.
Hi! I'd be happy to help you find the solutions to the trigonometric equation 2cos^2(x) = cos(x) on the interval 0 to 2π.
Step 1: Rearrange the equation to create a quadratic equation.
Subtract cos(x) from both sides:
2cos^2(x) - cos(x) = 0
Step 2: Factor out cos(x).
cos(x)(2cos(x) - 1) = 0
Step 3: Solve for x.

Set each factor equal to zero:
a) cos(x) = 0
b) 2cos(x) - 1 = 0
Step 4: Find the solutions for each equation within the interval 0 to 2π.
a) cos(x) = 0
x = π/2, 3π/2
b) 2cos(x) - 1 = 0
cos(x) = 1/2
x = π/3, 5π/3
Step 5: Combine the solutions.
The solutions to the trigonometric equation 2cos^2(x) = cos(x) on the interval 0 to 2π are x = π/2, 3π/2, π/3, and 5π/3.

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Answer:

Step-by-step explanation:

14 x + 5y = 329

11x + 5y = 281(vans is x and busses are y)

cancel out 'y' by making the '5y' in 11x + 5y = 281 negative

-1 (11x + 5y = 281) =

-11x -5y = -281

insert second equation

-11x -5y = -281

14x + 5y = 320

3x = 48

x = 16

substitute vans in one equation

11(16) + 5y = 281

5y = 105

y = 21

Answer: height = 1.91 m

Step-by-step explanation: Using the formula

V=πr2h

Solving for h

h=V

πr2=37.5

π·2.52≈1.90986m

Given that x and y are two non-negative numbers such that x+y=2. The expression is \(x²y²/30\), which represents the area of a rectangle with dimensions x/√30 and y/√30.

To calculate its maximum and minimum values, we must analyze the limits of the function as x and y vary within their possible ranges. To do so, we must first examine the boundary conditions.

Boundary conditionsThe domain of the function is the square defined by the points (0,2), (2,0), (0,0), and (2,2).

By applying the constraints \(x≥0 and y≥0\), we see that this region is reduced to the triangle bounded by points (0,2), (2,0), and (0,0).

In this triangular region, the maximum and minimum values of x and y are limited to the endpoints of the line x+y=2.

The graph of the function is a paraboloid of revolution with its apex located at the origin of the coordinate system.

As a result, the maximum and minimum values of the function correspond to its points of intersection with the boundary of the triangular region.

The minimum value of the function is 0, which is attained at the origin of the coordinate system.

The maximum value of the function is 4/15, which is attained at the two points (2,0) and (0,2).

\(The difference between the maximum and minimum of the quantity x²y²/30,\) where x and y are two non-negative numbers such that\(x+y=2 is 4/15 - 0 = 4/15\)

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Answer:

2x - 10y = - 40

Step-by-step explanation:

x - 3y = -14

x - 7y = -26

2x - 10y = - 40

Answer:

B

Step-by-step explanation:

a fraction is equal to 0 when the numerator is 0

x - 4 = 0

x = 4

The correct answer is x=4.

Step-by-step explanation:

When the numerator is 0, a fraction is equal to 0.

x - 4 = 0

x = 4

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Answer:

Outlier, clusters, and gap in your value.

Step-by-step explanation:

An OUTLIER is a data point that falls away from the rest of the points in a scatter plot. It doesn't seem to fit with the rest of the points. DATA CLUSTERS are groups of points that are all graphed close together. A GAP IN VALUE occurs when there are points clustered at two different spots on a scatter plot.

Answer:

Step-by-step explanation:

Volume of the prism is the product of its base area and height

Find base area:

Area of the trapezoid:

Substitute given values and solve for h:

Find area of base

Now

Height of trapezoid base be x

Answer:

x = 18

Step-by-step explanation:

given y varies directly with x then the equation relating them is

y = kx ← k is the constant of variation

to find k use the condition y = 15 when x = 9 , then

15 = 9x ( divide both sides by 9 )

\(\frac{15}{9}\) = x , that is

x = \(\frac{5}{3}\)

y = \(\frac{5}{3}\) x ← equation of variation

when y = 30 , then

30 = \(\frac{5}{3}\) x ( multiply both sides by 3 to clear the fraction )

90 = 5x ( divide both sides by 5 )

18 = x

Answer:

DG = 48

Step-by-step explanation:

if line r bisects DG at point E, then point E is midpoint of DG

so DG = 2DE

5z - 7 = 2(2z + 2)

5z - 7 = 4z + 4

5z -  4z = 4 + 7

z = 11

DG = 5z - 7 = 5(11) - 7 = 55 - 7 = 48

Answer:

Step-by-step explanation:

The width of the hot tub given its volume, length and depth is 7 feet.

A rectangular prism is a three-dimensional object with six faces. Opposite faces are identical.

Volume of a rectangular prism = length x width x height

Width = volume / ( depth x length)

159 1/4 ÷ (7 x 3 1/4)

637/4 ÷  (91/4)

637/4 x 4/91 = 7 feet

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Answer:

c^6 d^18 x^3..........

Answer: 1 I’m pretty sure you divide 8 with 2 and then (2+2)  and then lastly do 4÷4 and then get 1.

If your doing PENDAS its right but if your not, it is 16.

Answer:

Hope it helps

Step-by-step explanation:

I think the answer to this question is 0

(0, 0), (1, -3), and (3, 0) for the vertices are answers of the reflected triangle D'E'F'.

When a triangle is reflected over the x-axis, the y-coordinate of each point is multiplied by -1. Therefore, the x-coordinate remains the same while the y-coordinate becomes its negative.

Starting with point D(0, 0), we reflect it over the x-axis to get D'(0, -0), which simplifies to D'(0, 0). Next, we reflect point E(1, 3) to get E'(1, -3). Finally, we reflect point F(3, 0) to get F'(3, -0), which simplifies to F'(3, 0).

Therefore, the vertices of the reflected triangle D'E'F' are (0, 0), (1, -3), and (3, 0). Option B represents these vertices, making it the correct answer.

In summary, reflecting a triangle over the x-axis involves multiplying the y-coordinate of each point by -1. By applying this rule to the given triangle DEF, we arrive at the correct answer of (0, 0), (1, -3), and (3, 0) for the vertices of the reflected triangle D'E'F'.

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Answer:

B

Step-by-step explanation:

(m^-2 n^-3)^-4

-2 x -4 = 8

-3 x -4 = 12

m^8n^12

The given expression (m − 2n − 3) − 4 is equivalent to →

(m - 2n - 7).

Given is the expression -

(m − 2n − 3) − 4

The given expression is -

(m − 2n − 3) − 4

m - 2n - 3 - 4

m - 2n - 7

Therefore, the given expression (m − 2n − 3) − 4 is equivalent to →

(m - 2n - 7).

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Answer:

Step-by-step explanation:

Hence the height of the building is 27.5 ft.

Given, Peter places a mirror between him and the wall. Peter is 2 feet 9 inches away from the mirror and the mirror is 11 feet away from the wall of the building. Peter knew his eye level was exactly 5 ft 6 inches off of the ground, so the height of peter is  5 ft 6 inches.

Yes he was able to calculate the height of the building.

We have the following formulae by similarity of triangles,

\(\frac{height of building}{peter's height } =\frac{13.75 ft}{2.75ft}\)

Now,\(\frac{height of building}{5.5ft} =\frac{13.75ft}{2.75ft}\)

\(\frac{height of building}{5.5ft}=5\)

\(height of building=5.5\times 5 ft\)

So,\(height of building = 27.5 ft\)

Hence the height of the building is 27.5 ft.

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Answer:

Answers

Step-by-step explanation:

1.) 4 weeks = 28 days

12 x 4 = 48 in

2.) 13.95 ÷ 4 = 4.65

3.) 9 ÷ 4 = $2.25 per pound

4.) yes, 4 x 4 = 16, 9 x 4 = 36

Can i get a brainiest if right? Have a good day! I hope this helps

It is unlikely that carrying more or fewer pencils in one's backpack would have a direct impact on GPA.

To determine if there is a relationship between a student's GPA and the number of pencils in their backpack, Jordynn and Angie would need to conduct the following steps:

If a correlation is found, then it suggests that there may be a relationship between the students' GPA and the number of pencils in their backpack. However, in this case, it is unlikely that carrying more or fewer pencils in one's backpack would have a direct impact on GPA.

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The correct option A. 1, is the value of the variable 's' for which the solution of the expression is greatest .

For the given question,

The expression is-

(s + 6) ÷ s

Use the options;

A : s = 1

= (s + 6) ÷ s

= (1 + 6) ÷ 1

= 7

B : s = 2

= (s + 6) ÷ s

= (2 + 6) ÷ 2

= 4

C : s = 3

= (s + 6) ÷ s

= (3 + 6) ÷ 3

= 3

D : s = 4

= (s + 6) ÷ 4

= (4 + 6) ÷ 4

= 2.5

Thus, the value of the variable 's' for which the solution of the expression is greatest is 1.

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Answer:

Yes

Step-by-step explanation:

I see no mathematical reason this could not happen. It has three sides which is what makes a triangle.

Answer:

volume of Figure B = 75 m³

Answer:

300-89 would equal your equasion which would be 211

Step-by-step explanation:

But there are 2 ways to think of it becaue=se if u used the people in the school to play on the stage there are still 300 seats left or your teacher would think of it as being 300-89=211 so this word problem has 2 answers!

In total 560 ways a committee of 3 professors and 2 instructors can be chosen from 6 professors and 8 instructors if the committee consists of at least one professor.

Combinations are used to calculate the total number of possible outcomes from a given set of items.

The total number of possibilities of selecting a committee of 3 professors and 2 instructors from 6 professors and 8 instructors is calculated using the combination formula:

Number of ways of selecting a committee=

{Number of ways of selecting 3 professors from 6 professors} X {Number of ways of selecting 2 instructors from 8 instructors}

=  (6C3) X (8C2)

= (6!/(3!*3!)) X (8!/(2!*6!))

= 20 X 28

= 560

Therefore, in total 560 ways a committee of 3 professors and 2 instructors can be chosen from 6 professors and 8 instructors if the committee consists of at least one professor.

From this sample space, 3 professors and 2 instructors are required to be selected for the committee. Therefore, the combination formula is used to calculate the total number of ways of selecting the committee in which the order of the members doesn't matter.

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Answer:

19x - 608

Step-by-step explanation:

Answer: 19x - 608

Step-by-step explanation: Basically 32 x 19 (not the way teachers would want, but it still works -v-

Hope I helped!

The equation of the circle graphed above is equal to (x - 1)² + (y - 6)² = 9.

In Mathematics, the standard form of the equation of a circle is represented by this mathematical expression;

(x - h)² + (y - k)² = r²

Where:

By critically observing the graph of this circle, we have the following parameters:

Radius, r = 3 units.

Center, (h, k) = (1, 6).

Substituting the given parameters into the equation of a circle formula, we have the following;

(x - h)² + (y - k)² = r²

(x - 1)² + (y - 6)² = 3²

(x - 1)² + (y - 6)² = 9.

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The pigeonhole principle shows that in any set of six classes, there must be at least two classes that meet on the same day because there are only five weekdays for each class to meet on.

This principle states that if there are more items than the number of spaces available to place them in, at least two items must occupy the same space. In this case, there are six classes and only five weekdays available for each class to meet on. Therefore, at least two classes must meet on the same day.

Correct answer: b. The pigeonhole principle shows that in any set of six classes, there must be at least two classes that meet on the same day because there are only five weekdays for each class to meet on.

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To represent the solution set of a linear equation parametrically, we introduce other parameters like s and t for the free variables.

Every linear equation has n - 1 free variables where n is the number of variables.

For x + y + z = 2, we have 3 variables and 3 - 1 = 2 free variables.

First, let y and z be the free variables, we first solve the linear equation for x to get:

x = 2 - y - z

Therefore , the parametric representation of the solution set is given by :

x = 2 - s -t

y = s

z = t

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