clare is painting some doors that are all the same size. she used 2 liters of paint to cover doors. how many liters of paint are needed for 1 door? explain how you would represent the situation, then find the answer.

Therefore, the simplified cube root of 576,000 is 40∛9.

To simplify the cube root of 576,000, we need to find the largest perfect cube that is a factor of 576,000. In this case, the largest perfect cube that divides 576,000 is 1,000 (which is equal to 10^3).

So we can rewrite 576,000 as (1,000 x 576). Taking the cube root of both terms separately, we get:

∛(1,000 x 576) = ∛1,000 x ∛576

The cube root of 1,000 is 10 (∛1,000 = 10), and the cube root of 576 can be simplified further. We can rewrite 576 as (64 x 9), and taking the cube root of both terms separately:

∛(64 x 9) = ∛64 x ∛9 = 4 x ∛9

Now we can combine the results:

∛(1,000 x 576) = 10 x 4 x ∛9

Simplifying further:

10 x 4 x ∛9 = 40∛9

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The volume of first solid is obtained by rotating the region between y=x^6 and y=1 about y=5 is 120π/91 cubic units, The second solid is obtained by rotating the region bounded by x=0, y=1, and x=y^8 about y=1 is 2π/3 cubic units, The third solid is obtained by rotating the region between y=1/x^3, y=0, x=2, and x=6 about y=-3 is 737π/7 cubic units.

The region bounded by the curves y=x^6 and y=1 about the line y=5. To find the volume, we use the formula for the volume of a solid of revolution V = ∫(a,b) π(R(x)^2 - r(x)^2) dx,

where R(x) and r(x) are the outer and inner radii, respectively, and (a,b) is the interval of integration.

Since we are revolving about the line y=5, the outer radius is 5 - y and the inner radius is 5 - y(x^6) (notice that the curves are rotated "vertically" about a "horizontal" line). Thus,

V = ∫(0,1) π[(5-y)^2 - (5-y(x^6))^2] dx

= ∫(0,1) π[25 - 10y + y^2 - 25 + 10y(x^6) - y^2(x^6)^2] dx

= π ∫(0,1) (10x^6 - x^12) dx

= π [ (10/7)x^7 - (1/13)x^13 ] | from 0 to 1

= π [ 10/7 - 1/13 ]

= 120π/91

Therefore, the volume of the solid obtained by rotating the region bounded by y=x^6 and y=1 about the line y=5 is 120π/91 cubic units.

The region bounded by the curves x=0, y=1, and x=y^8 about the line y=1:

To find the volume, we again use the formula for the volume of a solid of revolution V = ∫(a,b) π(R(y)^2 - r(y)^2) dy,

where R(y) and r(y) are the outer and inner radii, respectively, and (a,b) is the interval of integration.

Since we are revolving about the line y=1, the outer radius is 1 and the inner radius is y. Thus,

V = ∫(0,1) π[(1)^2 - (y)^2] dy

= π ∫(0,1) (1 - y^2) dy

= π [ y - (1/3)y^3 ] | from 0 to 1

= 2π/3

Therefore, the volume of the solid obtained by rotating the region bounded by x=0, y=1, and x=y^8 about the line y=1 is 2π/3 cubic units.

The region bounded by the curves y=1/x^3, y=0, x=2, and x=6 about the line y=-3:

To find the volume, we again use the formula for the volume of a solid of revolution V = ∫(a,b) π(R(x)^2 - r(x)^2) dx,

where R(x) and r(x) are the outer and inner radii, respectively, and (a,b) is the interval of integration.

Since we are revolving about the line y=-3, the outer radius is 3 + y(x^3) and the inner radius is -y. Thus,

V = ∫(2,6) π[(3 + y(x^3))^2 - (-y)^2] dx

= π ∫(2,6) (9 + 6y(x^3) + y^2(x^6)) dx

(x^4) + (1/3)(x^3)(1/x^3) + (1/7)(1/x^3) ] | from 2 to 6

= π [ 42 + 54/2 + 1/7 ]

= 737π/7

Therefore, the volume of the solid obtained by rotating the region bounded by y=1/x^3, y=0, x=2, and x=6 about the line y=-3 is 737π/7 cubic units.

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Answer:

0.77

Step-by-step explanation:

According to the Question,

Let, We have 10000 patients & If the incidence rate is 10 out of 100, then 1000 people will have the disease.

        So, Out of the 9000 people who don't have the disease, 3%

       that is, 270 People, will get a false positive.

Thus, the probability that a person is chosen at random will both test positive and actually have the disease is \(\frac{950}{950+270}\) .

Answer:

Step-by-step explanation:

L = 2×π×r

9π cm = 2πr

9 cm = 2r

r = 4.5 cm

Answer:

-3/4, 1/2

Step-by-step explanation:

Because the axis are split into 4ths, we can assume that each line is worth 1/4 in coordinates. S is located 3/4ths in the negative x direction and 2/4, or 1/2 in the positive y direction.

Answer:

c

Step-by-step explanation:

No

Decision Variables and Objective:

The decision variables in this transportation model are the quantities to be shipped from each plant to each distribution center. Let's denote the quantity shipped from Marietta to Cleveland as X1, from Marietta to Baltimore as X2, and so on. Similarly, let's denote the quantity shipped from Minneapolis to each distribution center as Y1, Y2, and so forth.

The objective of the optimization model is to minimize the total transportation cost. The transportation cost is determined by multiplying the unit cost of shipping between each plant and distribution center by the corresponding quantity shipped and summing up these costs for all combinations.

To enforce the single sourcing constraint, we need to ensure that each distribution center is served from only one plant. This constraint can be represented by adding the following constraint for each distribution center:

X1 + X2 + X3 + X4 = Demand (for each distribution center)

Y1 + Y2 + Y3 + Y4 = Demand (for each distribution center)

These constraints ensure that the total quantity supplied from all plants to a particular distribution center is equal to the demand of that distribution center, effectively enforcing the single sourcing constraint.

Optimization Model and Interpretation of Results:

The optimization model can be formulated as a linear programming problem, where the objective is to minimize the total transportation cost while satisfying the capacity constraints and the single sourcing constraint.

The Excel Solver can be used to solve this model, providing the optimal solution for the decision variables and the corresponding minimum cost.

Interpreting the printouts, we can observe the values of the decision variables X1, X2, X3, X4, Y1, Y2, Y3, Y4, which represent the quantities shipped between each plant and distribution center. Additionally, we can see the total transportation cost, which is the objective value obtained by summing the costs of shipping for all combinations.

Pertinent results could include identifying the optimal shipping quantities that meet customer demand while minimizing costs. Interesting results might include identifying any significant differences in shipping costs between the plants and distribution centers. Unusual results could involve finding a scenario where the total transportation cost does not decrease proportionally with an increase in supply capacity or demand.

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Answer

60%

Step-by-step explanation:

Im not certain but i think its 60%,because the standard deviation is 6 and that as a percent is 60%

Statement Problem: Shane is a building engineer and is determining the length of an access ramp needed to reach a step 1.5 feet off the ground. He knows the length of the ramp, r, in feet, can be expressed with the equation below.

First, Shane finds that sin(4.5°) ≈ 0.08. Using his calculator, he then calculates the length of the ramp as shown below.

What could Shane do to make his calculation more accurate?

Solution:

The length of the ramp, r, in feet is expressed using the sine ratio;

Hence, Shane's calculation would be more accurate if he uses sin (4.5 degrees) in his calculator instead of 0.08

CORRECT OPTION: A

Answer:

Step-by-step explanation:

b

Answer:

A

Step-by-step explanation:

Using the rule of logarithms

logx - logy ⇔ log(\(\frac{x}{y}\) ) , so

log(\(\frac{12}{5}\) ) = log12 - log5 → A

Answer:

A. Iog (12) _ log(5)

Step-by-step explanation:

Answer:

The graph is compressed horizontally by a factor of 2, shifted left 3, reflected over the x-axis, and translated up 3.

Step-by-step explanation:

option third is correct answer

In parallelogram ,opposite sides are equal.

x+3=2x-6

solve the value you will get x=9

Answer:

its not loading

Step-by-step explanation:

Answer:

A.

C.

D.

B.

A.

A.

D.

B.

Step-by-step explanation:

Karmyn has 56 tablespoons of vinegar for a salad dressing recipe.

In mathematics, Multiplication operations perform Multiplying values on either side of the operator.

For example 4×2 = 8

Karmyn is making a salad dressing using vinegar. She has three and a half glasses of vinegar. She understands that one cup contains 16 tablespoons.

First, we need to convert the 3 1/2 cups of vinegar to tablespoons.

We know that there are 16 tablespoons in 1 cup, so we can multiply the number of cups by the number of tablespoons per cup to convert the measurement.

3 1/2 cups × 16 tablespoons/cup = 56 tablespoons.

Therefore, she has 56 tablespoons of vinegar.

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Answer:

see explaination

Step-by-step explanation:

area of rectangle =l×b

The group needs to build 44 feet of fence each day to finish on time.

To calculate the number of feet of fence the group needs to build each day, we first need to determine the total length of the fence in feet.

Since 1 mile equals 5,280 feet, the 2-mile fence is equal to 2 * 5,280 = 10,560 feet.

Next, we divide the total length of the fence by the number of days the group has to build it:

10,560 feet / 240 days = 44 feet per day.

So the group needs to build 44 feet of fence each day to finish on time.

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Answer:

-12

Step-by-step explanation:

x=6

g(6)=-2*6=-12. Answered by Gauthmath

The correct statements are:

Volume of a cone = 1/3(πr²h)

Volume of a cone = 1/3 x 2² x 11 x 3.14 = 46.05 inches cubed.

Base area = πr²

3.14 x 4 =  12.56 inches squared.

Price of one yellow candle = volume x price per cubic unit

46.05 x  $0.35 = $16.12

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Answer:

The volume of the yellow candle is about 46.05 inches cubed.

The radius of the yellow candle is 2 in.

The base area of the yellow candle is about 12.56 inches squared.

The price of one yellow candle is about $16.12.

Step-by-step explanation:

Answer:

78

Step-by-step explanation:

26 + 26 + 26 = 78

Answer:

please see the picture

Step-by-step explanation:

Answer: I think the first one is A. and the next one is B

Step-by-step explanation:

How do you write angle measurements?

Angles are measured in degrees (°) using a protractor. A protractor is a measuring device that is used to calculate or draw angles in terms of degrees. For example, in the image below, we see that using a protractor, the black arrow points to 100°, crossing 90°. Hence, the measure of the angle is 100°.

The idea of an angle

Degrees are the most widely used unit of measurement. A straight angle is 90° since a circle has 360 equal degrees.

degrees

Angles are measured in degrees (°) using a protractor. A protractor is a measuring device that is used to calculate or draw angles in terms of degrees. For example, in the image below, we see that using a protractor, the black arrow points to 100°, crossing 90°. Hence, the measure of the angle is 100°.

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Answer:

y-4=1/5(x-7)

Step-by-step explanation:

First, you need to find the slope of the line. From the point (2,3) to the point (7,4), the line rises 1 unit while moving sideways 5. Therefore, the slope of the line is 1/5. Hence, the equation of the line is y-4=1/5(x-7). Hope this helps!

Answer:

There is no gragh.

The tax multipliers from the MPC's and MPS's are

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

The MPC's and MPS's

The tax multipliers is calculated using

Tax multiplier = -MPC / (1 - MPC) or

Tax multiplier = - (1 - MPS) / MPS

Using the above as a guide, we have the following:

MPC = 0.90

Tax multiplier = -0.90/(1 - 0.90)

Tax multiplier = -9

MPS = 0.20

Tax multiplier = -(1 - 0.20)/0.20

Tax multiplier = -4

MPC = 0.75

Tax multiplier = -0.75/(1 - 0.75)

Tax multiplier = -3

MPS = 0.50

Tax multiplier = -(1 - 0.50)/0.50

Tax multiplier = -1

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The point of diminishing returns is (20.98, 21247.3).

The point of diminishing returns occurs when the marginal cost of producing an extra unit of output exceeds the marginal revenue generated from selling that unit. Mathematically, it is the point at which the derivative of the production function equals zero and the second derivative is negative.

Given the polynomial function N(x) of degree 3, we can find the point of diminishing returns by finding the critical points where the first derivative equals zero and evaluating the second derivative at those points.

The derivative of N(x) is N'(x) = -18x² + 360x + 2250. To find the critical points, we set N'(x) = 0:

0 = -18x² + 360x + 2250

Dividing by -18 simplifies the equation:

0 = x² - 20x - 125

Using the quadratic formula, we find the solutions to the equation:

x₁,₂ = (20 ± √(20² - 4(1)(-125))) / 2(1)

x₁,₂ = 10 ± 5√5

Thus, the two critical points of N(x) are at x = 10 - 5√5 and x = 10 + 5√5.

To determine the point of diminishing returns, we evaluate the second derivative N''(x) = -36x + 360 at these critical points:

N''(10 - 5√5) = -36(10 - 5√5) + 360 ≈ -264.8

N''(10 + 5√5) = -36(10 + 5√5) + 360 ≈ 144.8

From the evaluations, we find that N''(10 + 5√5) is negative while N''(10 - 5√5) is positive. Therefore, the point of diminishing returns corresponds to x = 10 + 5√5.

To find the corresponding y-coordinate (N(10 + 5√5)), we can substitute the value of x into the original function N(x).

Hence, the point of diminishing returns is approximately (20.98, 21247.3).

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Answer:

The answer is 3/8

Step-by-step explanation:

Set up a table to get one you divide 2 by 2 so then you have to divide 3/4 by 2 and that gets you 3/8

The equation of the line tangent to the curve is -

(y - 6) = 17(x - 1).

The equation of the tangent to the curve y = f(x), passing through the point (a, b) can be written as -

(y - b) = (dy/dx) (x - a)

Given is the curve y = f(x) = x⁴ + 6x² − x.

The given curve is -

y = x⁴ + 6x² − x

f'(x) = dy/dx = d(x⁴ + 6x² − x)/dx

f'(x) = dy/dx = 4x³ + 12x + 1

Now -

f'(x){1, 6} = (dy/dx){1, 6} = 4 x 1 x 1 x 1 + 12 x 1 + 1

f'(x){1, 6} = 17

We can write the equation as -

(y - 6) = 17(x - 1)

Therefore, the equation of the line tangent to the curve is -

(y - 6) = 17(x - 1).

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