A soap manufacturer advertises that it has increased the size of their bottle of dishwashing soap to 18.4 ounces, which is 5% more than the original size.

What is the original size of the bottle?
Round your answer to the nearest tenth.

Answer:

$430535434

Step-by-step explanation:

$430,934,932-$399,498 = 430535434

Answer:

C. The statement is false. Geometry is an axiomatic system where the accepted principles are the undefined terms point, line and plane.

Step-by-step explanation:

The 4 basic characteristics of axiomatic systems are:

The undefined terms or primitive terms of geometry are points, lines and planes that at some point meet or join together. This is called incidence, since geometry studies their relationship. E.g. 3 lines that form a triangle on a plane.

6

6/3

isthe simplestform pls markme as brainlist

Thus, 420 fish were ultimately caught, with 6x standing in for "6 times as much."

x + y = 420; y = 6x

Thus, 420 fish were ultimately caught, with 6x standing in for "6 times as much."

The smallest and largest fish range in size from 1 cm to 18 m. 18 m then equals 18 x 100 or 1800 cm. ∴ The length of large fish exceeds that of little fish by 1800 times.

The number of parrotfish Carlos purchased is represented by the variable y, whereas the number of angelfish Carlos purchased is represented by the variable x.

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Answer:

21

Step-by-step explanation:

Answer:

DC

Step-by-step explanation:

It is a straight line.

Answer:

C. D-C

Step-by-step explanation:

An arc that measures 180 degrees is a semicircle, and cd is a semicircle.

The volume of the solid obtained by rotating the region bounded by y = x^2 and y = 6 about the line x = -3 is approximately 481.39 cubic units.


To find the volume of the solid, we can use the method of cylindrical shells. The region bounded by y = x^2 and y = 6 in the first quadrant is a parabolic shape above the x-axis.
To set up the integral for the volume, we consider an infinitesimally small vertical strip of thickness Δx at a distance x from the line x = -3. The height of the strip is given by the difference between the two curves: h = 6 – x^2. The circumference of the cylindrical shell is given by the formula 2πr, where r is the distance between x and the line x = -3, which is r = x + 3.

The volume of the infinitesimal shell is then given by dV = 2π(x + 3)(6 – x^2)Δx. Integrating this expression from x = 0 to x = 3, we obtain the volume V = ∫[0,3] 2π(x + 3)(6 – x^2)dx. Evaluating this integral, we find V ≈ 481.39 cubic units.
In summary, the volume of the solid obtained by rotating the region bounded by y = x^2 and y = 6 about the line x = -3 is approximately 481.39 cubic units.

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Answer:

11

Step-by-step explanation:

Answer:

11 sandwich pieces

Step-by-step explanation:

The equation (1+00*1) + (1+00*1) (0+10*1) (0+10*1) is not equivalent to 0*1 (0+10*1)*. That is (1+001) + (1+001) (0+101) (0+101) ≠ 01 (0+101)*.

Let's simplify both sides of the equation and show that they are equal:

Left side: (1+00*1) + (1+00*1) (0+10*1) (0+10*1)

        = (1+0) + (1+0) (0+1) (0+1)      [since 0*1 = 0]

        = 1 + 1*1*1

        = 1 + 1

        = 2

Right side: 0*1 (0+10*1)*

         = 0 (0+1*1)*

         = 0 (0+1)*

         = 0*            [since 0+1 = 1 and 1* = 1]

         = 0

Since the left side simplifies to 2 and the right side simplifies to 0, we can see that they are not equal. Therefore, the statement (1+00*1) + (1+00*1) (0+10*1) (0+10*1) = 0*1 (0+10*1)* is not true.

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The depth of the water is changing at a rate of approximately 0.39 m/s when the radius of the top of the water is 10 meters.

To find the rate at which the depth of the water is changing, we can use related rates.

Given:
Height of the cone (h) = 8 meters
Base radius (r) = 26 meters
Rate of filling (dV/dt) = 12 m³/s
Radius of the top of the water (x) = 10 meters

First, we establish the relationship between the height and radius of the cone using similar triangles. The ratio of the height to the radius is constant, so we have h/r = 8/26.

Next, we differentiate both sides of the equation with respect to time (t) to find dh/dt in terms of dx/dt. This gives us (dh/dt)/(dr/dt) = 0.3077.

We can then substitute the given values into the equation: (dh/dt)/(dx/dt) = 0.3077. Rearranging the equation, we find that dx/dt = (dh/dt) / 0.3077.

To find the value of dh/dt, we can substitute the given rate of filling, dV/dt = 12 m³/s, into the equation. Solving for dh/dt, we get dh/dt = 3.693 m/s.

Finally, we substitute the values of dh/dt and 0.3077 into the equation to find dx/dt. This gives us dx/dt ≈ 0.39 m/s.

Therefore, the depth of the water is changing at a rate of approximately 0.39 m/s when the radius of the top of the water is 10 meters.

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Given the following information: Five years ago, someone used her $40,000 saving to make a down payment for a townhouse in RTP. The house is a three-bedroom townhouse and sold for $200,000 when she bought it. After paying down payment, she financed the house by borrowing a 30-year mortgage.

Mortgage interest rate is 4.25%. Right after closing, she rent out the house for $1,800 per month. In addition to mortgage payment and rent revenue, she listed the following information so as to figure out investment return: 1. HOA fee is $75 per month and due at end of each year 2. Property tax and insurance together are 3% of house value 3. She has to pay 10% of rent revenue for an agent who manages her renting regularly 4. Her personal income tax rate is 20%. While rent revenue is taxable, the mortgage interest is tax deductible. She has to make the mortgage amortization table to figure out how much interest she paid each year 5. In the last five years, the market value of the house has increased by 4.8% per year 6.

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The volume of the solid is  17124 cubic units. To find the volume of the solid, we need to integrate the area of each cross-section perpendicular to the base and parallel to the diameter.

Since these cross-sections are squares. We can find their area by squaring the side length.

Let's call the side length of each square "x". We know that the diameter of the semicircle is 32 (twice the radius of 16), so the side length of each square is also 32.

Now we need to express the volume of the solid as an integral. We can do this by summing the areas of all the infinitesimal squares as we slice the solid perpendicular to the base.

The infinitesimal thickness of each slice is dx. The width of each slice is also dx, since the squares are perpendicular to the base. The height of each slice is the length of the chord of the semicircle that corresponds to the x-coordinate of the slice.

We can use the Pythagorean theorem to find this height. The chord has length 2(sqrt(16^2 - x^2)), so the height is sqrt(16^2 - x^2).

Therefore, the volume of the solid is given by the integral:

V = ∫(0 to 16) of [x^2 * (2sqrt(16^2 - x^2))] dx

Evaluating this integral, we get:

V = (2/3)(16^3)(pi) - (2/3)(16^3)

So the volume of the solid is approximately 17124 cubic units.

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Answer:

2 over 3

Step-by-step explanation:

Answer:

#3

Step-by-step explanation:

there is a 2 to one ratio of string to precussion

By using the formula of curved surfaced area of cylinder, it can be calculated that-

Height of the cylinder = 3.18 cm

What is curved surface area of cylinder?

Curved surface area of cylinder is the space occupied by the curved surface of the cylinder.

If r is the radius of the cylinder and h is the height of the cylinder, then curved surface area of cylinder is calculated by the formula

Curved surface area of cylinder = 2\(\pi\)rh

Let the height of the cylinder be h cm

Radius = 5 cm

Curved surface area = 2\(\pi\)rh

                                  = \(2\times \frac{22}{7}\times 5 \times h\)

                                  = \(\frac{220}{7}h\)

By the problem,

\(\frac{220}{7}h = 100\)

\(h = \frac{100 \times 7}{220}\)

h = 3.18 cm

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19/403 of the people on the plane are crew

The given parameters are:

Population = 403

Passengers = 384

The number of crew is calculated using:

Crew = 403 - 384

Evaluate

Crew = 19

The fraction of crew is then calculated using:

Fraction = Crew/Population

This gives

Fraction = 19/403

Hence, 19/403 of the people on the plane are crew

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The derivative of a function f(x) at a point x = a is defined as the limit of the difference quotient as h approaches zero:

f'(a) = lim (h → 0) [f(a + h) - f(a)] / h

What is derivative?

The derivative of a function in calculus measures the function's sensitivity to changes in its input variable. Specifically, at a particular point, it represents the function's rate of change with respect to its input variable at that moment.

The derivative of a function f(x) at a point x = a is defined as the limit of the difference quotient as h approaches zero:

f'(a) = lim (h → 0) [f(a + h) - f(a)] / h

This limit represents the instantaneous rate of change or slope of the function at the point x = a. The difference quotient is the change in the function value divided by the change in the input variable (or the distance between two points on the graph of the function).

The derivative is a fundamental concept in calculus, and it has many applications in various fields of science, engineering, and economics. It allows us to calculate important quantities such as velocity, acceleration, and marginal cost, and it is used to optimize functions and solve many real-world problems.

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Answer: solve for x

x ∈ R, h = 0 and g = 0

Step-by-step explanation:

Each time the number of hours (on the x axis) goes up by 1, the cost (on the y axis) goes up by up by $2. So each hour costs $2.

You can pick two points on the graph, such as (1,2) and (2,4) to compute the slope using the slope formula below

m = (y2 - y1)/(x2 - x1)

m = (4-2)/(2-1)

m = 2/1

m = 2 we get a slope of 2

The slope is the rise/run

rise = change in cost = change in y

run = change in time = change in x

Answer:

x = 30

Step-by-step explanation:

To get the left side of the triangle, take the square root of the left squares area, 576, to get the two sides a nd b of 24 and 18. Use the Pythagorean theorem (a^2 + b^2 = c^2) to get x = 30

Good luck with your homework :)

Answer:

10x9+110x5+x4+1100x3

Step-by-step explanation:

calculator

The class boundaries of the third class can be determined based on the given frequency distribution. The boundaries are 21-30 and 31-40.

To determine the class boundaries of the third class, we need to examine the frequency distribution provided. The frequency distribution lists the frequency of occurrences for each class interval. In this case, there are six occurrences in the first class (1-10), three occurrences in the second class (11-20), two occurrences in the third class (21-30), four occurrences in the fourth class (31-40), six occurrences in the fifth class (41-50), and six occurrences in the sixth class (51-60).

Since the third class has two occurrences, its class boundaries can be determined by looking at the adjacent classes. The lower boundary of the third class is the upper boundary of the second class, which is 20. The upper boundary of the third class is the lower boundary of the fourth class, which is 31. Therefore, the class boundaries of the third class are 21-30.

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Answer:

f = 3

g = -1

h = 6

r = 18

Step-by-step explanation:

Box 1

f(x) = \(2x^{4}\)-\(12x^{3}\)+\(16x^{2}\)+4x+15 with x = 3

f(3) = \(2(3^{4)}\) - \(12(3^{3} )\) + \(16(3^{2})\)+ 4(3) + 15

Reorder

Evaluate

Multiply

3f = 2 x 81 - 12 + 27 +16 x 9 + 12 +15

3f = 162 - 324 + 144 + 12 + 15

3f =  9

3  ÷  3

f = 3

Box 1

g(x) = \(3x^{3}\) - \(16x^{2}\) - 7x - 36 with x = 6

g(6) = \(3(6^{3} )\) - \(16(6^{2})\) - 7(6) - 36

g6 = 3 x 216 - 576 - 42 - 36

g6 = -6

6   ÷ 6

g = -1

Box 2

h(x) = \(5x^{3}\) - \(2x^{2}\) - 3 with x = -1

h(-1) = \(5(-1^{3} )\) - \(2(-1^{2})\) -3

h-1 = -5 + 2 -3

h-1 = -6

-1    ÷  - 1

h = -6

Box 2

r(x) = \(4x^{4}\) - \(9x^{2}\) + 5x - 2 with x = 2

r(2) = \(4(2^{4} )\) - \(9(2^{2} )\) + 5(2) - 2

r2 = 64 - 36 + 10 - 2

r2 = 36

2   ÷  2

r = 18

Answer:

15

Step-by-step explanation:

I THINK THIS IS CORRECT

Answer:

15

Step-by-step explanation:

1x1=1

2x2=4

3x3=9

No 2 same numbers can be multiplied to give a result of 15.

5x5=25

6x6=36

7x7=49

Answer:7.3

Step-by-step explanation: a^2+b^2=c^2 then square root of a+b

Answer: 6.7

Step-by-step explanation:

Look closely

It could be slightly lower or higher, but we can be confident that it falls somewhere between 0.32 minutes and 1.47 minutes.

The most accurate interpretation of the given confidence interval is as follows:

We are 95% confident that the true difference in mean wait time between Facility A and Facility B falls within the range of 0.32 minutes to 1.47 minutes.

This means that if we were to repeat the study multiple times and calculate a new confidence interval each time, we would expect that approximately 95% of those intervals would contain the true difference in mean wait time between the two facilities.

Furthermore, based on the observed data and the calculated confidence interval, we can conclude that the difference in mean wait time between Facility A and Facility B is likely to be positive, with Facility B having a higher mean wait time than Facility A. However, we cannot say with certainty that the true difference is exactly within this specific range; it could be slightly lower or higher, but we can be confident that it falls somewhere between 0.32 minutes and 1.47 minutes.

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