A model rocket is launched from
the top of an observation tower
that is 75 feet high. The height
of the rocket, h(t), is
determined by the function
h(t)--16r2 + 48t +75 where t is
the number of seconds elapsed
since the rocket was launched.
When does the rocket land on
the ground? Round to the
nearest hundredth.

The correct statements of the given statements are -

Function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function

Expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators

Equation : A mathematical equation is used to equate two expressions.

Given is the distance of the elevator from the ground in floors.

Therefore, the correct statements of the given statements are -

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An inequality like the statement, x + 3 > 5, can be solved by finding the value of the variable, "x", which is x > 2.

Inequalities are used to express relationships between quantities or values that are not equal. They can be used to describe constraints or limitations on a solution to a problem, or to represent a range of possible values.

Inequality can also be used to describe relationships between variables in algebraic expressions or equations.

To solve an inequality, we need to isolate the variable in the given statement to determine the value of the variable.

For example, given the inequality, x + 3 > 5, in order to solve this inequality, we need to find the value of x by subtracting 3 from both sides:

x + 3 - 3 > 5 - 3

x > 2.

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120 m³ is cubic meters is the shed.

Given :

What in math is a cube?

The term "cube" refers to a solid three-dimensional shape in mathematics or geometry that has six square faces, eight vertices, and twelve edges. Also said to be a conventional hexahedron. Due to the fact that a cube is three dimensional, the space it occupies will also be three dimensional.

Six square faces surround a cube, hence combining the areas of all six square faces will yield the surface area. The cube formula's surface area is as a result. Cube surface area equals 6 (sides).

w = 6 m

l = 4 m

h = 5 m

a rectangular shed = 6 * 4 * 5

= 120 m³

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11.81 is the required mean of the given data set.

The mean (also known as the arithmetic mean, which varies from the geometric mean) of a dataset is calculated as the sum of all values divided by the total number of values.

This measure of central tendency is usually referred to as the "average".

Thus, the data set is as follows:

12, 20, 8, 15, 16, 14, 7, 5, 11, 8, 14

Mean formula: Sum of terms / Number of terms

The mean will now be determined as follows:

Mean: Sum of terms / Number of terms

Mean: 130/11

Mean: 11.81

Therefore, 11.81 is the required mean of the given data set.

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The roots of the given equation are real and distinct because the value of b2-4ac is greater than 0

where a, b, and c are the coefficients in the standard form of the quadratic equation ax²+bx+c=0

Given quadratic equation is 2x²-6x+3=0  on comparing with the standard form of the quadratic equation ax²+bx+c=0

We have a=2, b=(-6) ,c=3

Hence b²-4ac,

Here b²-4ac is also known as discriminant.

=(-6)²-(4×2×3)

=36-24

=12≥0

12 (Twelve) is obviously greater than zero (0)

here value of b²-4ac>0

Hence the nature of the roots of the given equation is real and distinct.

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Question

What is the nature of roots of 2x²- 6x+ 3= 0?

It is difficult to accurately estimate the values of fx and fy at point B without more information. In order to estimate the values of the partial derivatives at a point, you typically need to have a contour map or some other representation of the function in the neighborhood of that point.

A contour map is a graphical representation of a function that shows the values of the function at different points in the xy plane. The lines on the map, called contour lines, represent the values of the function, and the spacing between the lines indicates the rate of change of the function.

To estimate the values of the partial derivatives at a point using a contour map, you can:

For example, to estimate fx at point B, you could:

Without a contour map or other representation of the function in the neighborhood of point B, it is not possible to accurately estimate the values of fx and fy.

Since the question is incomplete and there is no similar one found, the answer is general.

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To find the x-intercept of a linear equation in two variables we set y intercept to 0.

When we are given with a two variable linear equation, we plug 0 in place of y and solve the equation to get the x-intercept of that linear equation.

For example, let us consider the linear equation 2x + 3y = 4

To get the x-intercept of the equation 2x + 3y = 4 we would plug y = 0.

Therefore, 2x + 3(0) = 0

⇒ 2x + 0 = 4

⇒ x = 4/2 = 2

Thus, the x-intercept of the linear equation 2x + 3y = 4 is 2.

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Answer: -1/34

Step-by-step explanation:

Answer:

f(134) = 9

Step-by-step explanation:

substitute x = 134 into f(x) and evaluate

f(x) = 10 - [tex]\frac{x}{134}[/tex] , then

f(134) = 10 - [tex]\frac{134}{134}[/tex] = 10 - 1 = 9

The volume of the pyramid is 1/3 of the volume of the prism.

The relationship between the volumes of pyramids and prisms is that when a prism and pyramid have the same base and height. The volume of the pyramid is 1/3 of the volume of the prism.

To see by the mathematically:

If a pyramid and a prism have the same base and height, their volumes are always in the ratio of

1:3.

As volume of prism is 108 cubic meters,

volume of pyramid is 1/3 × 108 = 36 cubic meters.

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answer: "approximately nine years

explanation : if an investment scheme promises an 8% annual compounded rate of return, it will take approximately nine years (72 / 8 = 9) to double the invested money.

hope this helps!!

Answer:4.1

Step-by-step explanation:

Important Formulas:

[tex]w=Fd[/tex]

[tex]p=\dfrac{w}{t}[/tex]

w = work (Measured in Joules)

F = Force (Measured in Newtons)

d = distance (Measured in meters)

p = power (Measured in watts)

t = time (measured in seconds)

______________________________

Given:

[tex]f=343.8N[/tex]

[tex]d=38.5m[/tex]

[tex]t=4.86s[/tex]

[tex]p=?[/tex]

______________________________

Finding Work:

[tex]w=Fd[/tex]

[tex]w=(343.8)(38.5)[/tex]

[tex]w=13236.3J[/tex]

______________________________

Finding Power:

[tex]p=\dfrac{w}{t}[/tex]

[tex]p=\dfrac{13236.3}{4.86}[/tex]

[tex]\fbox{p = 2723.52 watts}[/tex]

Mean mode formula  - Mean = {Sum of Observation} ÷ {Total numbers of Observations}

What does the mode mean?

By summing all the numbers in a data collection and dividing by the total number of values in the set, the mean (average) of the data set can be determined.

               A data collection is ordered from least to largest, and the median is the midpoint number. A data set's mode is the number that appears the most frequently.

What are the mean, median, and example?

The most frequent number, or the one that happens the most frequently, is known as the mode. Example: Since the number 2 appears three times, more than any other number, it is the mode of the numbers 4, 2, 4, 3, and 2.

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The nature of the roots of the quadratic equation 4x² - 5x + 3 is complex.

Polynomial is an equation written as the sum of terms of the form kx^n.

where k and n are positive integers.

We have,

4x² - 5x + 3

This is in the form of ax² + bx + c

a = 4

b = -5

c = 3

Now,

D = b² - 4ac

If D < 0 there will be complex roots.

Now,

D = (-5)² - 4 x 4 x 3 = 25 - 48 = -23

D < 0

This means,

The roots are complex.

Thus,

The equation has complex roots.

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After the pumping is complete, the volume of the empty space inside container [A] will be 1147.72 ft³.

        v{c} = πr²h = π(d/2)²h

Given are two containers designed to hold water are side by side, both in the shape of a cylinder. Container A has a diameter of 12 feet and a height of 19 feet. Container B has a diameter of 14 feet and a height of 13 feet. Container A is full of water and the water is pumped into Container B until Container B is completely full.

Volume of container [A] -

V{A} = (22/7) x (12/2)² x 19

V{A} = (22/7) x 6 x 6 x 19

V{A} = 3149.72 ft³

Volume of container [B] -

V{A} = (22/7) x (14/2)² x 13

V{A} = (22/7) x 7 x 7 x 13

V{B} = 2002 ft³

V{A} - V{B} → Empty space =  3149.72 ft³ -  2002 ft³ = 1147.72 ft³

Therefore, the free space inside the container A will be 1147.72 ft³.

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Set is the collection of objects with defined property and represented in curly brackets {} . Example: A = { 2, 4, 6 }.

Set is defined as:

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The formula for a prism is as follow,

The surface area of a prism = (2×Base Area) +Lateral Surface Area

The volume of a prism =Base Area× Height

A prism is a solid whose perimeter is defined by a number of congruent parallel plane polygons, two of which are known as the ends, and two of which are known as the side faces.

The polyhedron known as a prism has two parallel polygonal bases. A prism is a transparent optical device with flat, polished surfaces that refract light. The two polygonal bases are connected by their lateral faces. Longitudinally, the faces are primarily rectangular. It could even be a parallelogram occasionally.

The surface area of a prism is made up of the combined areas of the lateral faces and the two polygonal bases.

The total area that a prism takes up in three dimensions is known as its volume.

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Applying derivative on the formula of volume of cone and using the provided values, The answer is 0.059 feet per minute.

The rate at which a function changes in relation to a variable in mathematics.

A cone is a three-dimensional geometric structure with a smooth transition from a flat base often but not always circular to the point at the top, also known as the apex or vertex.

Formula for volume of cone is:

[tex]V= \pi r^{2}\frac{h}{3}[/tex]

derivate the formula for volume of cone , we get,

[tex]\frac{dV}{dt} = 2\pi r * \frac h3 * \frac {dr}{dt}[/tex]

dV / dt = 3

r=2

h=12

dr/dt = 0.059 feet per minute.

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Step-by-step explanation:

I am not what the answer My teacher

You can use calculus to find the maximum value of a parabola by these steps which are given in the solution part.

A parabola is a U-shaped curve this is drawn for a quadratic function,

To find the maximum value of a parabola using calculus, you can follow these steps:

1. Identify the equation of the parabola in the form "y = ax² + bx + c," where "a," "b," and "c" are constants.

2. Take the derivative of the equation with respect to x.

3. Set the derivative equal to 0 and solve for x. This will give you the value of x at the vertex of the parabola.

Substitute the value of x that you found in step 3 back into the original equation to find the corresponding y-value. This y-value is the maximum or minimum value of the parabola, depending on the value of a. If a is positive, the parabola opens upwards and the y-value is the maximum. If a is negative, the parabola opens downwards and the y-value is the minimum.

For example, suppose you want to find the maximum value of the parabola y = 2x² - 4x + 3. First, take the derivative of the equation: y' = 4x - 4. Set this equal to 0 and solve for x: 0 = 4x - 4, x = 1.

Substituting this value back into the original equation gives us y = 2(1)² - 4(1) + 3 = 2 - 4 + 3 = 1.

Therefore, the maximum value of the parabola is 1.

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If we answer yes, then 1, 2, 3, 4, and 5. No phrase is used more than once in this passage. Therefore, there is currently no most prevalent phrase. Thus, this data does not contain a mode.

The mode calculation is a rather simple process. Organize the numbers in a set in whatever order—from lowest to highest as well as highest to lowest—and then tally the frequency with which each number appears in the group. The mode is the one that shows up most frequently.

When the mean, as well as median, as well as median cannot be employed, the mode informs us of the most prevalent value in categorical data. The mode provides insight into the location of a dataset's "center".

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On solving the provided question, we can say that - the maximum value or maxima of the given function is 36.

Maximum describes a high point (plural maxima). The term "minimum" refers to a low point (plural minima). Extremum is the Latin term used to describe the greatest or minimum (plural extrema). When greater points are possible elsewhere but not close by, we say local maximum (or minimum). The greatest and smallest values of a function in either a specified range or throughout the whole domain are referred to as a function's maxima and minima, generally known as extrema, in mathematical analysis.

The vertex is used to determine that the function's maximum value is 36.

Function is provided by:

f(x) = [tex]16x^2 + 32x + 20[/tex]

coefficients  -

[tex]a = -16, b = 32 , c =20[/tex]

[tex]f_{max} = \frac{32^2 - 4(-16)(20)}{4(-16)}[/tex] = 36

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Answer:

To calculate the interest earned on a savings account, you first need to determine the interest rate per year and the time the money is invested. In this case, the interest rate is 4.5% and the time is 2 years.

The formula for simple interest is I=Prt, where I is the interest earned, P is the principal (the initial amount invested), r is the interest rate, and t is the time. Plugging in the values from the problem, we get I = 1250 * 0.045 * 2 = $112.50.

Therefore, Ethan will earn $112.50 in interest after 2 years if he does not add or withdraw any money from the account. Rounded to the nearest cent, this is $112.00.

Step-by-step explanation:

Here we can say that - A series of integers can be generated over time using the range() method.

Range: the discrepancy between the top and bottom numbers. To get the range, locate the greatest observed value of the variable and deduct the least observed value the minimum. The data points between the two extremes of the distribution are not taken into consideration by the range; just these two values are considered. Between the lowest and greatest numbers, there is a range. Values at the extremes make up the range. The data set 4, 6, 10, 15, 18, for instance, has a range of 18-4 = 14, a maximum of 18, a minimum of 4, and a minimum of 4.

given,

20, 25, 30, 45, 55, 90, 110,115,120

so range will be 120 - 20 = 100

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The numbers which are divisible by 3 are countless. We determine it by the divisibility rules.

A number is called divisible by others whenever it is divided properly and   obtain a whole number as an outcome. As example 125 can be divided by 5 and we get the whole number 25 so 125 is said divisible by 5.

On the other hand, 225 cannot be divided by 10 and we get a decimal number. So, 225 is not divisible by 10.

A number is said to be divisible by 3 if the sum of the digits is divided by 3. Suppose we are given two number 308 and 492.

At first, we will sum the digit of each number, 3+0+8 = 11

the sum of the digit of 492 = 4+9+2 = 15

we cannot divide 11 by 3 but 15 is divided by 3. Hence, 492 is divisible by 3.

So, there are countless number which are divisible by 3.

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A multiplicity example in mathematics is when a function has multiple solutions to a given equation.

For example, when solving the equation x2 + 4x + 3 = 0, there are two solutions, x = -3 and x = -1. This means that the equation has a multiplicity of two. This can be seen in the graph of the equation, which has two points of intersection on the x-axis.

The multiplicity is a measure of how many solutions a given equation has. It can be determined by using the discriminant, which is the difference between the square of the coefficient of the highest degree term, and four times the product of the coefficients of the lower degree terms, and the constant. In the example above, the discriminant is 16 - 12, which is 4. The multiplicity of the equation is determined by the sign of the discriminant: if it is positive, the equation has two solutions; if it is zero, the equation has one solution; and if it is negative, the equation has no solutions.

The multiplicity of an equation can also be used to determine the nature of the graph of the equation. If the equation has a multiplicity of two, the graph is a parabola, which is a curved line that has two points of intersection on the x-axis. If the equation has a multiplicity of one, the graph is a line, which has only one point of intersection on the x-axis. If the equation has a multiplicity of zero, the graph is a circle, which has no points of intersection on the x-axis.

The concept of multiplicity is important in mathematics, as it can be used to determine the number of solutions an equation may have, as well as the nature of the graph of the equation. Knowing the multiplicity of an equation can help to simplify the process of solving the equation.

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It will take 180 Hours to fill the pool if both hoses are used.

In our question, one data is missing. You require the pool's volume or some information that enables you to calculate it. The same statement given by you is part of a problem where you know a series of data that shows the time required to fill the pool at different flow rates:

flow rate           time

60 gal/h            300 h => 60 gal/h * 300 h = 18,000 gal

45 gal/h            400 h => 45 gal/h * 400 h = 18,000 gal

36 gal/h            500 h => 36 gal/h * 500 h = 18,000 gal

30 gal/h            600 h => 30 gal/h * 600 h = 18,000 gal

So for this pool to calculate (several times) that the volume is 18,000 gal.

You now possess two hoses, one of which has a flow rate of 40 gals per hour and the other of which has a flow rate of 60 gals per hour.

The total flow rate is the sum of the two flow rates"

total flow rate = 40 gal/h + 60 gal/h = 100 gal/h

And you just must divide the volume of the pool (18,000 gals) by the total flow rate (100 gal/h) to get the time to fill the pool:

time = volume / flow rate = 18,000 gal / 100 gal/h = 180 hours.

So, finally, our answer to fill the pool will be about 180 hours.

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flow rate           time

60 gal/h            300 h => 60 gal/h * 300 h = 18,000 gal

45 gal/h            400 h => 45 gal/h * 400 h = 18,000 gal

36 gal/h            500 h => 36 gal/h * 500 h = 18,000 gal

30 gal/h            600 h => 30 gal/h * 600 h = 18,000 gal

So for this pool to calculate (several times) that the volume is 18,000 gal.

You now possess two hoses, one of which has a flow rate of 40 gals per hour and the other of which has a flow rate of 60 gals per hour.

The total flow rate is the sum of the two flow rates"

total flow rate = 40 gal/h + 60 gal/h = 100 gal/h

And you just must divide the volume of the pool (18,000 gals) by the total flow rate (100 gal/h) to get the time to fill the pool:

time = volume / flow rate = 18,000 gal / 100 gal/h = 180 hours.

The amount of plastic needed for each batch of 50 coins is equal to the volume of 50 coins that is 80 cu.cm.

The diameter of the coin is 2.0 cm.

As radius is half of the diameter, so its radius will be 1.0 cm.

It is given that the coin is circular in shape, so the area of the circular surface will be πr² = 3.14 × 1² = 3.14 sq. cm.     (π = 3.14)

The thickness of the coin is 0.5 cm, which will be considered as the height of the coin.

So, the volume of each coin will be = 3.14 × 0.5 = 1.57 cu. cm.

Therefore, the plastic needed for the batch of 50 coins is,

1.57 × 50 = 78.5 cu.cm and in multiple of 10 it will be 80 cu.cm.

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The inverse of the function that is provided is calculated using the inverse function calculator. When a function, f(x), is given, its inverse, x=f(y), is calculated by switching the variables ( y ).

Given,

Inverse function;

An inverse in mathematics is a function that "undoes" another function. In other words, if f(x) produces y, then y entered into the inverse of f produces x. An invertible function is one that has an inverse, and the inverse is represented by the symbol f1.

Inverse function calculator;

The calculator for inverse functions determines the inverse of the supplied function. If a function, f(x), is supplied, then the inverse of the function, x=f(y), is determined by exchanging the variables ( y ).

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