Simplfiy:
2x + 7 + 8x + 12
PLEASE HELPPP

At most, they can wash 96 cars and mow 96 lawns.

To determine the maximum number of cars they can wash and lawns they can mow, we need to consider the work rates of each person and the total number of hours they work.

Huey can wash 6 cars or mow 3 lawns in one hour, so in 8 hours, he can wash 6 \(\times\) 8 = 48 cars or mow 3 \(\times\) 8 = 24 lawns.

Dewey can wash 3 cars or mow 3 lawns in one hour, so in 8 hours, he can wash 3 \(\times\) 8 = 24 cars or mow 3 \(\times\) 8 = 24 lawns.

Louie can wash 3 cars or mow 6 lawns in one hour, so in 8 hours, he can wash 3 \(\times\) 8 = 24 cars or mow 6 \(\times\) 8 = 48 lawns.

Since two of them wash cars and one mows lawns, the maximum number of cars they can wash is the sum of the maximum cars each person can wash, which is 48 + 24 + 24 = 96 cars.

The maximum number of lawns they can mow is the sum of the maximum lawns each person can mow, which is 24 + 24 + 48 = 96 lawns.

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To find the magnitude and direction of a vector using trigonometry, you can follow these steps:

1. Identify the components of the vector: A vector can be represented by its horizontal (x) and vertical (y) components. For example, if we have a vector A with components Ax and Ay, we can express it as A = (Ax, Ay).

2. Calculate the magnitude of the vector: The magnitude of a vector is the length of the vector. To find the magnitude of a vector A, you can use the Pythagorean theorem. The formula is:
  magnitude(A) = √(Ax^2 + Ay^2)

3. Find the direction of the vector: The direction of a vector can be given in different forms, such as angles or degrees. Two common ways to express the direction of a vector are:
  a. Angle with the positive x-axis: This angle is measured counterclockwise from the positive x-axis to the vector. You can use trigonometric functions to find this angle. The formula is:
     angle = arctan(Ay / Ax)
  b. Angle with the positive y-axis: This angle is measured counterclockwise from the positive y-axis to the vector. To find this angle, you can subtract the angle obtained in step 3a from 90 degrees (or π/2 radians).

4. Convert the direction to degrees or radians, depending on the required format.

Let's consider an example to illustrate these steps:

Suppose we have a vector A with components Ax = 3 and Ay = 4.

1. Identify the components: A = (3, 4).

2. Calculate the magnitude:
  magnitude(A) = √(3^2 + 4^2) = √(9 + 16) = √25 = 5.

3. Find the direction:
  angle = arctan(4 / 3) ≈ 53.13 degrees.

4. Convert the direction:
  angle with positive y-axis = 90 degrees - 53.13 degrees ≈ 36.87 degrees.

So, the magnitude of vector A is 5, and its direction is approximately 36.87 degrees with a positive y-axis.

Remember, trigonometry can be used to find the magnitude and direction of a vector when you have its components.

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Answer:14/15 pounds of meat

Step-by-step explanation:

Answer:

25.8 cubic feet

Step-by-step explanation:

Volume = l · w · h

V = (3.2)(1.3)(6.2)

V = 25.792

Answer:

13+2=15+2=17+2=19+2=21

1+5=6+5=11+5=16+21

(The Pink Answer)

Answer:

24 cubic inches.

Step-by-step explanation:

\(2a \times a^{2} +a^{3} \\2a^{3} +a^{3}\)

\(3a^3\\3(2)^3\\3 \times 8\)

Answer:

(-6, 2)

Step-by-step explanation:

Multiply the second equation by 2

2x - 6y = -24

then add both equations together.

4x + 6y = -12

6x          = -36, divide both sides by 6

x = -6

then plug -6 back into either equation and solve for y

-6 - 3y = -12

-3y = -6

y = 2

The conditional statement "If a human being has 7 heads, then they have 11 arms" is false.

The statement is false because it is biologically impossible for a human to have 7 heads. The anatomy of a human being only allows for one head. Therefore, the statement is a contradiction and cannot be considered true.

Additionally, even if it were possible for a human to have 7 heads, it would not necessarily mean that they would have 11 arms. The statement makes an assumption that is not based on any scientific or logical evidence.

In conclusion, the statement "If a human being has 7 heads, then they have 11 arms" is false.

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To yield $26,000 in the future, compounded semiannually at an interest rate of 6%, a lump sum investment needs to be made today. The correct amount to invest can be calculated using the present value formula.

The present value formula can be used to calculate the amount that should be invested today to achieve a specific future value. The formula is given by:

PV = FV / (1 + r/n)^(n*t)

In this case, the future value (FV) is $26,000, the interest rate (r) is 6%, and the compounding is semiannually (n = 2). We need to solve for the present value (PV).

Using the formula and substituting the given values:

PV = 26,000 / \((1 + 0.06/2)^(2*1)\)

PV = 26,000 / \((1.03)^2\)

PV = 26,000 / 1.0609

PV ≈ $24,490.92

Therefore, the correct lump sum to invest today, at 6% compounded semiannually, to yield $26,000 in the future is approximately $24,490.92.

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Answer:

Degrees = Radians x 180/π

or

Degrees = 57.2958  x radians

Step-by-step explanation:

1 radian = 180/π degrees

1 radian = 57.2958 degrees

Multiply radians by this factor of 57.2958  to get the equivalent measure in degrees

π radians = 180°

2π radians = 360° which is the number of degrees in a circle

For anything greater than 2π radians you will have to subtract 360°

For example, 7 radians using the formula is 7 x (57.2958  ) ≈ 401.07°

But this still falls in the first quadrant, so relative to the x-axis it is
401.07 - 360 = 41.07°

First transformation: Reflection across the y-axis

Second transformation: Vertical translation down by 12 units.

A coordinate is a value that specifies the position of a point in a particular system or framework of reference. Coordinates are typically expressed as numerical values that describe the location of a point in relation to some predefined origin, axis, or set of reference points. The most common type of coordinate system is the Cartesian coordinate system, which uses two or three axes to describe points in a plane or in three-dimensional space, respectively. In this system, coordinates are typically expressed as ordered pairs (for two-dimensional points) or ordered triplets (for three-dimensional points), such as (x, y) or (x, y, z), where x, y, and z represent the distances along each axis from the origin. Other types of coordinate systems include polar coordinates, cylindrical coordinates, and spherical coordinates, which are used in various branches of mathematics and science to describe points in different contexts.

To find the two transformations, we can use the fact that applying multiple transformations to a figure is the same as applying a single transformation that is the composition of the individual transformations.

Let's start with the final vertices of the transformed figure: (-2,0), (2, 0), (2,-6), and (0,-2).

We can see that the first two vertices have the same x-coordinate and are located on the x-axis. This suggests a reflection across the y-axis, which would swap the x-coordinates of the vertices.

So, the first transformation is a reflection across the y-axis.

After this transformation, the transformed figure has vertices (-WXYZ).

Next, we need to find the second transformation that maps WXYZ to (-WXYZ) with the given final vertices.

We can see that the vertex (2,-6) has a lower y-coordinate than the other three vertices. This suggests a vertical translation that moves this vertex down to its final position.

To determine the amount of vertical translation, we can subtract the y-coordinate of the vertex in its initial position (6) from the y-coordinate of the vertex in its final position (-6), which gives a total downward movement of 12 units.

So, the second transformation is a vertical translation down by 12 units.

Therefore, the two transformations that Nelson applies to WXYZ are a reflection across the y-axis followed by a vertical translation down by 12 units.

First transformation: Reflection across the y-axis

Second transformation: Vertical translation down by 12 units.

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The location (x,0) that will minimize the amount of cable between the 3 towns is  x = 3.46

Consider that call L₁ total distance between Centerville and Springfield and L₂  total distance between Centerville and Shelbyville

Then, the total cable will be L₁ + L₂  

Noted that the length 12 - x  is common to the two distances.

Therefore, total distance  d = ( 12 - x ) + 2 √(x² ) + (6)²  

F(x) = 12 - x + 2*√ ( x² + 36 )

Taking derivatives on both sides of the equation;

F´(x) = -1 + 2 * 1/2 * 2*x/ √( x² + 36 )

F´(x) = - 1 + 2*x / √(x² + 36 )

F´(x) = 0

 -1 +  2*x/ √( x² + 36 ) = 0

Solving for x;

- √ ( x² +  36 ) + 2*x  = 0

- √ ( x² +  36 )  = - 2*x

 √ ( x² +  36 )  =  2*x

Taking squaring both sides;

x² + 36  = 4 x²

3*x² = 36

x² = 12

x =  3,46 m  

( 3,46 , 0 ) is the location for minimun length

Then total amount of cable is:

d  =  12 - 3,46 + 2 * √ (3,46)² + 36

d  = 8,54  + 2 * 6,92

d  = 22,38 m

Take the second derivative of F

F´´(x) = 0 + D/ dx (  2*x/ √( x² + 36 ) )

F´´(x) = [ 2*√( x² + 36 )  - 2*x [ x/√ ( x² + 36 ) ] / (x² + 36)

We can see that expression is an integer positive, since the second term is always smaller than the first one then we have a minimun for x = 3,46

The complete question is;

Centerville is located at (12,0) in the x -plane, Springfield is at (0,6) , and Shelbyville is at (0,−6) . The cable runs from Centerville to some point (x,0) on the x-axis where it splits into two branches going to Springfield and Shelbyville. Find the location (x,0) that will minimize the amount of cable between the 3 towns and compute the amount of cable needed.

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Answer:

The answer would be 3.6 degrees less than the starting temperature.

Step-by-step explanation:

1.2 * 3 = 3.6

4*3 = 12

3.6/12 hours

Answer:

Its the same because you add 12 to the first one, then you take back the 12. So its like you added nothing. And in the second one, you add zero

Step-by-step explanation:

Answer:

$45.

Step-by-step explanation:

When the TV is bought on hire purchase, you deposit $35 and pay $30 monthly. There are 12 payments. 12 * 30 = $360. 360 + 35 = $395.

Since cash would've cost $350, the amount of money saved by paying cash is 395 - 350 = $45.

Hope this helps!

Answer:

6

Step-by-step explanation:

The value of function, f(t) for L⁻¹ ( e−s /(s²+ 1)) is equals to sin( t - π ) u(t-π) .

The Laplace transform is the essential term of the given derivative function. Moreover, it comes with a real variable (t) for converting into complex function with variable (s). For ‘t’ ≥ 0, let ‘f(t)’ be given, the Laplace transform of ‘f(t)’, denoted by 'L{f(t)}' or ‘F(s)’ is definable with the equation:

\( L(f(t)) = F(s) = ₀∫^{ \infty } e⁻ˢᵗ f(t)dt\)

we have L⁻¹ ( e−s /(s²+ 1))

Now, L⁻¹ (1 /(s²+ 1)) = sin(t)

so, L⁻¹ ( e−s /(s²+ 1)) = sin( t - π ) u(t-π)

where u(t-π) is unit of step function.

so, required function f(t) is sin( t - π ) u(t-π).

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Complete question:

Find f(t) ℒ−1 (e−s /(s²+ 1))

f(t)=? + (?) (t - ?)

The number of unique 8-character passwords that can be formed using lowercase letters (a-z), uppercase letters (A-Z), and numbers (0-9) is 62 to the power of 8, which can be expressed in scientific notation as 2.1834 × 10^14.

To calculate the number of unique passwords, we need to determine the number of choices for each character position and multiply them together.

In this case, each character position can have one of 62 possibilities: 26 lowercase letters, 26 uppercase letters, and 10 numbers.

Since there are 8 character positions, the total number of unique passwords is calculated as 62 multiplied by itself 8 times: 62^8. This can be expressed using exponents as 62^8.

To convert this value into scientific notation, we divide the number by 10 raised to the power of its magnitude, while adjusting the coefficient accordingly. In this case, the number of unique passwords is approximately 2.1834 × 10^14. This means there are approximately 218,340,000,000,000 unique 8-character passwords that can be formed using the given character set.

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The expression will give you the equivalent amount of the car after 9 years at an annual interest rate of 6% compounded quarterly.

To calculate the equivalent amount of the car after 9 years at an annual interest rate of 6% compounded quarterly, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:
A = final amount
P = principal amount (initial amount)
r = annual interest rate (in decimal form)
n = number of times interest is compounded per year
t = number of years

Given that the car is to be paid P15,000 at a 9% interest rate, we need to find the equivalent amount after 9 years at a 6% annual interest rate compounded quarterly.

P = 15,000
r = 6% = 0.06
n = 4 (quarterly compounding)
t = 9

Plugging in these values into the formula:

A = 15,000(1 + 0.06/4)^(4*9)

Calculating this expression will give you the equivalent amount of the car after 9 years at an annual interest rate of 6% compounded quarterly.

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Answer:

48°

Step-by-step explanation:

33+ 99= 132

180 is the sum of all angles so u would subtract 132 from 180 giving you the answer

Answer:

If x is the last angle of a triangle, x=48. is its a just angles its, x=228.

Step-by-step explanation:

If it's a triangle its because triangle sum theorem states that all angles in a triangle add up to 180 degrees. So add the angles you know an subtract it from 180.

If it's just angels then you just need to again, add the angles you know but this time subtract it from 360 as that's he most degrees an angle can go.

The rule of inference used to arrive at the statements s(y) and c(y) from the statement s(y) ∧ c(y) is called Simplification. Simplification allows us to extract individual components of a conjunction by asserting each component separately.

The rule of inference used in this scenario is Simplification. Simplification states that if we have a conjunction (an "and" statement), we can extract each individual component by asserting them separately. In this case, the conjunction s(y) ∧ c(y) represents the statement "y is a movie produced by Sayles and y is a movie about coal miners."

By applying Simplification, we can separate the conjunction into its individual components: s(y) (y is a movie produced by Sayles) and c(y) (y is a movie about coal miners). This allows us to conclude that there is a movie produced by Sayles (s(y)) and there is a movie about coal miners (c(y)).

Using the Simplification rule of inference enables us to break down complex statements and work with their individual components. It allows us to extract information from conjunctions, making it a useful tool in logical reasoning and deduction.

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Answer:

both are equal is 0

Step-by-step explanation:

After substituting, the answer is 0 to both

59/150

How?

w= 59/150

59/150 and -2/3 have to have the same denominators.

So, what I did was, -2/3×50= -100/150.

(Process of a new equation)

59/150-(-100/150)

[The two - signs cross each other out, making it a + ]

59/150+100/150 <- New Equation

__________________________________

59/150+100/150= 159/150

159/150= 1 9/150

9÷150=0.06

1+0.06= 1.06

(PROOF ABOVE)

Answer

add 1.06 = 1 3/50  = 1 3/50 + (-2/3) =  59/150

Step-by-step explanation:

Option A is correct: z = -4.25.To calculate the z-score of a value, you need to use the formula z = (x - μ) / σ, where x is the value, μ is the mean, and σ is the standard deviation.

Here's how you can use this formula to find the z-score for the value 62, when the mean is 79 and the standard deviation is 4:z = (x - μ) / σ

Given that x = 62, μ = 79, and σ = 4,

we can substitute these values into the formula and simplify:z = (62 - 79) / 4z = -17 / 4z = -4.25..

Therefore, the z-score for the value 62, when the mean is 79 and the standard deviation is 4, is z = -4.25.Option A is correct: z = -4.25.

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27a³ + 189a²b + 441ab² + 343b³ = (3a + 7b)³

27a³ + 189a²b + 441ab² + 343b³

Therefore,

27a³  = (3a)³

189a²b  = 3(3a)²(7b)

441ab² = 3(3a)(7b)²

343b³ = (7b)³

(3a)³ + (7b)³ + 3(3a)²(7b) + 3(3a)(7b)²

a³ + b³ + 3a²b + 3ab²  = (a + b)³

Therefore,

27a³ + 189a²b + 441ab² + 343b³ = (3a + 7b)³

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Answer:

its 5 boxes

Step-by-step explanation:

Answer:

√22

√19

√21

√18

Step-by-step explanation

The answers are √22, √19, √21, √18.

Decimal numbers are 'in between' numbers. For example, 10.4 is in between the numbers 10 and 11. It is more than 10, but less than 11.

Given that, there are numbers, √22, √19, √21, √18, we need to determine they fall between which pairs of decimal numbers given,

√22 = 4.69

So, 4.69 will be in between 4.6 and 4.7

√19 = 4.35

So, 4.35 will be in between 4.3 and 4.4

√21 = 4.58

So, 4.58 will be in between 4.5 and 4.6

And,

√18 = 4.24

So, 4.24 will be in between 4.2 and 4.3

Hence, the answers are √22, √19, √21, √18.

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The statement that best proves that <XWY ≅ <ZYW is that two parallel lines are cut by a transversal, then the alternate interior angles are congruent

To determine the correct statement, we need to know the properties of a parallelogram.

These properties includes;

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