Jackets cost the retailer $75 a piece to purchase wholesale. If he has five to sell and
doesn't sell them until 30 days have gone by, how much money does he lose? Remember
a loss is shown with a negative rational number.
with Rational Numbers

The dimensions that maximize the area are 150ft × 300ft.

So, let y be the length of the side parallel to the river and x be the length of each of the two sides perpendicular to it.

The following provides the total fencing length:

The rectangular pen's surface area is:

We may determine the value of x required to maximize the area by determining the value of x for which the derivative of the area function is zero:

The value of y is: for x=150

Therefore, the dimensions that maximize the area are 150ft × 300ft.

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Answer:

$106.48

Step-by-step explanation:

use the compound interest formula at the top of the image

The length of the line segment is given by the distance equation

D = 7.2 units

The distance of a line between 2 points is always positive and given by the formula

Let the first point be A ( x₁ , y₁ ) and the second point be B ( x₂ , y₂ )

The distance between A and B is D , and the distance D is

Distance D = √ ( x₂ - x₁ )² + ( y₂ - y₁ )²

Given data ,

Let the distance of the line segment between two points be D

Now , the equation will be

Let the first point be represented as P ( 1 , 6 )

Let the second point be represented as Q ( 7 , 2 )

Now , distance between P and Q is D , and the distance D is

Distance D = √ ( x₂ - x₁ )² + ( y₂ - y₁ )²

D = √ ( 1 - 7 )² + ( 6 - 2 )²

On simplifying the equation , we get

D = √ ( -6 )² + ( 4 )²

D = √ ( 36 + 16 )

D = √ 52

D = 7.2 units

Hence , the distance is 7.2 units

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Answer:

166 square units

Step-by-step explanation:

Let’s find the area of the shapes that in the net.

First, we can see two of the triangles have a base of 2 and a height of 13. The formula for surface area of a triangle is bh÷2. (13x2)÷2=13. Since there are two triangles, we multiply 13 by 2 and get 26.

Second, we can see two of the triangles have a base of 10 and a height of 12. (10x12)÷2=60. Since there are two triangles, we multiply 60 by 2 and get 120.

Third, we can see a rectangle has a base of 10 and a height of 2. The formula for surface area of a rectangle is bh. 10x2=20.

Last, we add up all the areas:

20+120+26=166.

The mean should be used when the data is symmetric.

The integer variable bonus is assigned a value based on the value of the integer variable score

score > 100 implies bonus = 10 * score

score between 50 and 100 implies bonus = score

score < 50 implies bonus = 0

First, we need to analyze the conditions:

score > 100 implies bonus = 10 * score

score between 50 and 100 implies bonus = score

score < 50 implies bonus = 0

Writing the above as programming instructions, we have:

if(score > 100){//This represents the first condition

bonus = 2 * score;

}

else if(score >=50 && score<=100){//This represents the second

bonus = score;

}

else{//This represents the last condition

bonus = 0;

}

Hence, if score > 100 implies bonus = 10 * score

score between 50 and 100 implies bonus = score

score < 50 implies bonus = 0

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Answer:

  Q = 2850

Step-by-step explanation:

Given the demand function Q = 5700 -9.5P, you want the value of Q that maximizes revenue.

Revenue is the product of P and Q. Solving the given equation for P, we have ...

  Q = 5700 -9.5P

  Q -5700 = 9.5P

  (Q -5700)/9.5 = P

Then revenue is ...

  R = PQ = (Q -5700)Q/9.5

This is the factored form of an equation of a parabola that opens downward. It has zeros at Q=0 and Q=5700. The vertex of the parabola is on the line of symmetry halfway between these values:

  Q = (0 +5700)/2 . . . . . maximizes revenue

  Q = 2850

The value of Q that maximizes revenue is 2850.

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Answer:

Option 2 Step-by-step explanation: Option 1: $68.85 Option 2: $68.80 Option 3: $70.9 Option 4: $71.81  More

A triangle is obtained when a right rectangular pyramid is sliced by a plane that is perpendicular to the base of the pyramid.

A rectangular pyramid is a three-dimensional object with a rectangle base and a triangular face corresponding to each of the sides of the base.

Cross - sections perpendicular to the base and through the vertex will be triangles. A triangle is obtained as a right rectangular pyramid is sliced by a plane that is perpendicular to the base of the pyramid.

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Sides given by

Opposite sides must be equal

Let's check once

\(\\ \tt\hookrightarrow x+5=2x+3\implies x=2\)

Find sides now

One pair of opposite sides are equal but others not .

Answer:

Step-by-step explanation:

The opposite pairs are:

1)

2)

x + 5 with 2x - 3

It makes:

The sides are:

Correct answer choice is 1)

Answer:

b is the answer of the question because it is the only answer

Answer:

B. 7

Step-by-step explanation: 6/24= 1/4 so 7/24>1/4

The solution to the given differential equation is:

\(\[y(x)\ =\ a_0 + a_1x + \frac{1}{4}a_1x^4 + \sum_{n=2}^{\infty} \frac{2a_{n-2}}{(n-2)(n-1)}x^{n+3}\]\)

To solve the given differential equation

\(x^3y'''\ -\ 6y\ =\ 0,\)

we can use the method of power series. Let's assume a power series solution of the form

\(y(x)\ =\ \sum_{n=0}^{\infty} a_nx^n.\)

Differentiating y(x) with respect to x gives:

\(\[y'(x)\ =\ \sum_{n=0}^{\infty} n a_n x^{n-1}\ =\ \sum_{n=0}^{\infty} (n+1) a_{n+1} x^n\]\)

Differentiating again gives:

\(\[y''(x)\ =\ \sum_{n=0}^{\infty} (n+1)na_{n+1}x^{n-1}\ =\ \sum_{n=0}^{\infty} (n+2)(n+1)a_{n+2}x^n\]\)

Differentiating one more time gives:

\(\[y'''(x)\ =\ \sum_{n=0}^{\infty} (n+2)(n+1)na_{n+2}x^{n-1}\ =\ \sum_{n=0}^{\infty} (n+3)(n+2)(n+1)a_{n+3}x^n\]\)

Substituting these expressions into the differential equation, we have:

\(\[x^3 \sum_{n=0}^{\infty} (n+3)(n+2)(n+1)a_{n+3}x^n - 6 \sum_{n=0}^{\infty} a_n x^n\ =\ 0\]\)

Rearranging the terms and combining like powers of x, we get:

\(\[\sum_{n=0}^{\infty} (n+3)(n+2)(n+1)a_{n+3}x^{n+3} - 6 \sum_{n=0}^{\infty} a_n x^n\ =\ 0\]\)

Now, let's equate the coefficients of like powers of x to zero:

For n=0:

\(\[(3)(2)(1)a_3 - 6a_0 = 0 \implies 6a_3 - 6a_0 = 0 \implies a_3 = a_0\]\)

For n=1:

\(\[(4)(3)(2)a_4 - 6a_1 = 0 \implies 24a_4 - 6a_1 = 0 \implies a_4 = \frac{1}{4}a_1\]\)

\(For \: n\geq 2:

\[(n+3)(n+2)(n+1)a_{n+3} - 6a_n = 0 \implies a_{n+3} = \frac{6a_n}{(n+3)(n+2)(n+1)}\]

\)

Now we can write the solution as:

\(\[y(x)\ =\ a_0 + a_1x + \frac{1}{4}a_1x^4 + \sum_{n=2}^{\infty} \frac{6a_{n-2}}{n(n-1)(n-2)}x^{n+3}\]

\)

Simplifying the series, we get:

\(\[y(x)\ =\ a_0 + a_1x + \frac{1}{4}a_

1x^4 + \sum_{n=2}^{\infty} \frac{2a_{n-2}}{(n-2)(n-1)}x^{n+3}\]

\)

Therefore, the solution to the given differential equation is:

\(\[y(x)\ =\ a_0 + a_1x + \frac{1}{4}a_1x^4 + \sum_{n=2}^{\infty} \frac{2a_{n-2}}{(n-2)(n-1)}x^{n+3}\]\)

where a₀ and a₁ are arbitrary constants to be determined based on the initial conditions or boundary conditions given in the problem.

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The measure of the major arc JLK will be 206°. Then the correct option is B.

The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.

The measure of the minor arc JK will be 154°.

Then the sum of the major arc and minor arc in a circle is 360°.

Then the major arc JLK will be given as,

JLK + JK = 360°

JLK + 154° = 360°

JLK = 206°

The measure of the major arc JLK will be 206°. Then the correct option is B.

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Answer:

13.2 g

Step-by-step explanation:

let x = grams sugar in a 200 ml glass

16.5 g sugar / 250 ml = x g sugar / 200 ml

x(250) = (16.5)(200)

x =  (16.5)(200) / (250) = 3300 / 250 = 13.2

Answer:  there are 13.2 g sugar in a 200 ml glass of juice

Answer:

2.1 * 10 ^3

Step-by-step explanation:

5.67  * 10 ^7 ÷2.7 x 10^4

Divide the numbers

5.67 / 2.7 =2.1

Divide the exponents

10^7 / 10 ^4

Remember when dividing power, we subtract the exponents

10 ^(7-4) = 10^3

Put this back together

2.1 * 10 ^3

Verify that this is in scientific notation

Since this is in scientific notation, we are done

Answer:

2.1x10 to the power of three

Step-by-step explanation:

\frac{5.67\times 10^7}{2.7\times 10^4}

2.7×10

4

5.67×10

7

​

Divide them.

\frac{5.67}{2.7}\times \frac{10^7}{10^4}

2.7

5.67

​

×

10

4

10

7

​

Divide numbers and 10's separeately.

2.1\times 10^3

2.1×10

3

Subtract exponents.

Answer:

answer is 6

Step-by-step explanation:

Answer: 6

Step-by-step explanation:

Plug in 2 for t so the equation is p(2) = 2^3 - 2

This simplifies to 6

Answer:d

Step-by-step explanation:

The answer is d. None of the above is true.

To calculate velocity, we need to use the equation:

Velocity = M * P / Y

Given:

M = 1,000

P = 2.25

Y = 2,000

Plugging in the values:

Velocity = 1,000 * 2.25 / 2,000

Simplifying:

Velocity = 2.25 / 2

The result is:

Velocity = 1.125

Therefore, the correct answer is: d. None of the above is true.

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Step-by-step explanation:

10²+11²

=100+121

=221

=√221

=14.87

The correct option is A. The volume is 6.77 cubic units

The function and interval given are f(x) = (x - 1)^-1/4 and the x-axis on the interval (1, 6].

We want to find the volume of the solid of revolution when the region is rotated about the x-axis.

Let's consider the graph of the function: graph{(x-1)^(-1/4) [-10, 10, -5, 5]}

To set up the integral to find the volume of the solid of revolution, we can use the disk method.

We need to integrate the area of each disk perpendicular to the x-axis from x = 1 to x = 6.

The area of a disk is given by the formula: A = πr²

where r is the radius of the disk and is equal to f(x) in this case.

Therefore, the area of a disk is: A = πf(x)²

Let's substitute f(x) into this formula and integrate from x = 1 to x = 6 to get the volume of the solid.

We have The integral that should be used to find the volume of the solid is given as:

V = ∫₁⁶ πf(x)² dx

We substitute f(x) = (x - 1)^(-1/4) into this expression and integrate to get the volume.

We have: V = ∫₁⁶ π(x - 1)^(-1/2) dx

Let u = x - 1, so that du/dx = 1 and dx = du.

When x = 1, u = 0, and when x = 6, u = 5.

Therefore, we have: V = ∫₀⁵ πu^(-1/2) du= 2π[u^(1/2)]₀⁵= 2π(√5 - 1) ≈ 6.77 cubic units.

The volume of the solid of revolution when the region is rotated about the x-axis is approximately 6.77 cubic units.

Thus, the correct option is A. The volume is 6.77 cubic units.

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Each adult pays $9 and each child under 12 pays $4.50.

To find the cost of the buffet for each adult and child at a pizza restaurant, we can set up a system of equations using the given information. Let a be the cost for each adult and c be the cost for each child. Using the bills for Todd's family and Margot's family, we get the equations 2a + 3c = 40.5 and 3a + 4c = 57.5.

Solving this system of equations gives us a = $9 and c = $4.50. Therefore, each adult pays $9 and each child under 12 pays $4.50 for the buffet. It is important to set up and solve the system of equations correctly in order to find the cost for each category.

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Zorch would need to exert the opposing force for approximately 1.15 years to slow Earth's rotation to once per 35.0 hours.

To determine the time required for Zorch to accomplish his goal, we can follow the steps in the Problem-Solving Strategy for Rotational Dynamics:

Step 1: Identify what is given and what is asked for.

Given:

Force exerted by Zorch: 3.70×10^7 N

Desired period of Earth's rotation: 35.0 hours

Asked for:

Time Zorch must push with this force

Step 2: Identify the principle(s) or equation(s) needed to solve the problem.

The principle of rotational dynamics that we can use is:

Torque (τ) = Inertia (I) × Angular Acceleration (α)

Step 3: Set up the problem.

Zorch wants to slow down Earth's rotation, which means he wants to decrease its angular velocity. To do this, he needs to exert a torque in the opposite direction of Earth's rotation. The torque required can be calculated as:

τ = I × α

Step 4: Solve the problem.

The inertia (I) of Earth can be approximated as I = 0.330 × 10^38 kg·m² (a known value).

The angular acceleration (α) can be calculated using the equation:

α = Δω / Δt

Since Zorch wants to slow Earth's rotation to once per 35.0 hours, the change in angular velocity (Δω) is given by:

Δω = 2π / (35.0 hours)

Now, we can rearrange the equation τ = I × α to solve for time (Δt):

Δt = τ / (I × α)

Substituting the given values, we get:

Δt = (3.70×10^7 N) / (0.330 × 10^38 kg·m² × (2π / (35.0 hours)))

Evaluating this expression will give us the time required for Zorch to push with the given force. The result is approximately 1.15 years.

Therefore, Zorch must exert the opposing force for approximately 1.15 years to slow Earth's rotation to once per 35.0 hours.

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First, let's declare our variables

B = x+2

A = 3(x+2)

Now, let's create our expression.

A + B = 128

Plug in the values for A and B

x+2 + 3(x+2) = 128

We need to solve for x. Start off by simplifying the left side.

x+2 + 3x + 6 = 128

Combine like terms.

4x + 8 = 128

Subtract 8 from both sides.

4x = 120

Divide both sides by 4

x = 30

B = x+2 = 30 + 2 = 32 degrees

A = 3(x+2) = 3(30+2) = 3(32) = 96 degrees

one on right is 2,-2 and one on left is -1,1

The quotient is 3√110 over 15.

To evaluate the given expression, let's simplify each component step by step.

Simplify the numerator:

Numerator = √6√11

To simplify the product of two square roots, we can combine them under a single square root:

Numerator = √(6 * 11)

= √66

Simplify the denominator:

Denominator = √5√3

Similarly, we can combine the square roots:

Denominator = √(5 * 3)

= √15

Combine the numerator and denominator:

StartFraction (Numerator) / (Denominator) EndFraction = √66 / √15

To rationalize the denominator, we can multiply the numerator and denominator by √15 to eliminate the square root:

StartFraction √66 / √15 EndFraction = (√66 * √15) / (√15 * √15)

= √(66 * 15) / 15

= √990 / 15

Simplify the resulting square root:

√990 = √(9 * 110)

= √9 * √110

= 3√110

Therefore, the quotient is:

StartFraction √66 / √15 EndFraction = 3√110 / 15

To summarize, the quotient is 3√110 over 15.

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Answer:

x=147°

Step-by-step explanation:

BEING THE CORRESPONDING ANGLES ARE ALWAYS EQUAL.....

We will see that the system of equations has infinite solutions, each of the form:

y = (3/2)*(x + 1)

Here we have the system:

3x - 2y = -3

-9x + 6y = 9

Notice that if we add 3 times the first equation to the second one, we get zero.

3*(3x - 2y) + -9x + 6y  = 3*(-3) + 9

9x - 6y - 9x + 6y = -9 + 9

0 = 0

This actually means that both equations represent the same line, then, the "two" lines intersect in infinite points, meaning that the system of equations has infinite solutions, which are of the form:

3x - 2y = -3

2y = 3 + 3x

y = (3/2)*(x + 1)

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