A conical paper cup is 10 cm tall with a radius of 7 cm. The cup is being filled with water so that the water level rises at a rate of 3 cm/sec. At what rate is water being poured into the cup when the water level is 9 cm

When solving the following system of equations,  the x in the first equation would be the easiest to solve for.

Systems of equations can be solved using one of three techniques: graphing, substitution, or elimination. Simply plot the provided equations on a graph and locate the point(s) where they all cross to solve a problem by graphing. You may find the values of the variables you are working for by finding the location of this point.

The result of the first equation is

x + 6y = 25

we can easily solve for x by subtracting 6y from both sides we have  

x + 6y - 6y = 25 - 6y

x - 25 - 6y

So, the first equation's x term can be simply solved.

When solving the following system of equations,  the x in the first equation would be the easiest to solve for.

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Answer: B

Step-by-step explanation: These lines are parallel. If you count over then down from point to point, then the slope for both lines is negative since it is going down, the slop is -2/1

The value of F (- 3 2 where F x )= 4x2 3x 72 is:

F ( -3) = - 27 and F (2) = - 62

In mathematics, function is an expression that shows a relationship between an independent variable and a dependent variable. In other words, a function creates a relation between an input to an output.

As per the given function F(x), x is the independent variable and F (x) is the dependent variables.

generally, we write F(x) = y

given, F (x) = 4x² - 3x -72

F (x) is a function of x

for x = - 3, F ( -3) = 4(-3) ² - 3(-3) -72

F (- 3) = - 27

again, x = 2, we get F (2) = 4(2) ² - 3(2) - 72

F (2) = - 62

from the above calculation, we find (-3, 2) are domain of function F (x) and

(- 27, -62) are ranges of the above function.

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Answer: Ball A, B, C, F, E, D

Step-by-step explanation:

An object has the greatest amount of Gravitational Potential Energy when it is furthest from the ground.

This means that Ball A has the most gravitational potential energy. This is followed by Ball B and Ball C. Then, Ball F is farthest from the ground, followed by Ball E. Ball D has the least gravitational potential energy.

So, the order is as follows: Ball A, B, C, F, E, D

The first twenty digits after the decimal point of 7/11 when written as a decimal are: 6363636363636. The sum of these digits is 108.

Answer:

[tex] \sqrt{a {}^{2} + b {}^{2} }[/tex]

Answer:

Step-by-step explanation:

Let AB = 3 units , BC = 1 unit and AC = ? (TO BE CALCULATED)

By Pythagoras theorem:

(AC)²=(AB)²+(BC)²

therefore, (AC)²= 3²+1²

(AC)²=9+1

(AC)²=10

(AC) = √10 = 3.03 cm

Answer:

  y +8 = -1/9(x -9)

Step-by-step explanation:

You want the point-slope form of the equation of the line through point (9, -8) with slope -1/9.

The equation of the line through point (h, k) with slope m is ...

  y -k = m(x -h)

You have (h, k) = (9, -8), and m = -1/9. Using these values, the equation is ...

  y +8 = -1/9(x -9)

A simulation game attempts to copy various activities from real life in the form of a game for various purposes such as training, analysis, prediction, or entertainment.

The most suspicious set of outcomes for a simulated game of chess that is supposed to be biased in favor of player B winning 4 out of 5 times would be if player B won all 30 games. This outcome would be highly unlikely if the game was truly random and the bias towards player B was accurate. Other suspicious outcomes could include player B winning 29 out of 30 games or player B winning 28 out of 30 games with a high margin of victory in each game.

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For adults, there were 40 tickets sold, and for kids, there were 60 tickets sold.

There are several laws that regulate the sequence in which you should do the operations in math and algebra. The Commutative, Associative, and Distributive Laws are the three that are most frequently discussed.

Let x be the total number of adult tickets sold.

6.50 × x + 2.50 × (100 - x) = 410

6.50 × x + 250 - 2.50x = 410

4x = 410 - 250

x = 40

Hence,

a) 40 tickets were sold by adults, according to item

and

b) 100-40=60 tickets were sold to children.

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Answer: The answer is no, they are not proportional

Step-by-step explanation:

Let, third proportional is x 0.8 : 0.2 : : 0.2 : x = 0.8/0.2 = 0.2/x = x = 0.2 × 0.2/0.8 × 10 = 1/20 = 0.05 Hence, here third proportional is 0.05

Answer:

2[tex]\sqrt{2}[/tex]

Step-by-step explanation:

[tex]\sqrt{2x9}[/tex] - [tex]\sqrt{2}[/tex] = 3[tex]\sqrt{2}[/tex] - [tex]\sqrt{2}[/tex] = 2[tex]\sqrt{2}[/tex]

The 9 inches side must be the hypotenuse, and the other two sides must be 3 inches and 5 inches.

n a triangle, the longest side (the hypotenuse) is opposite the largest angle, and the other two sides are opposite the smaller angles. According to the Triangle Inequality Theorem, the sum of any two sides of a triangle must be greater than the length of the third side. So, if the longest side of Karen's triangle measures 8 inches, it means that the sum of a and b (the two shorter sides) must be greater than 8 inches. Therefore [tex]a+b > 8 inches[/tex].

For the second part of your question, only one triangle can be drawn with side lengths 3, 5, and 9. The three numbers 3, 5, and 9 form a Pythagorean triple, meaning they can be used as the lengths of the sides of a right triangle. Since the longest side (the hypotenuse) must be greater than the other two sides, the 9 inches side must be the hypotenuse, and the other two sides must be 3 inches and 5 inches.

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Answer:

12 possible outcomes

Step-by-step explanation:

The equation to find the possible outcomes is:

possible outcomes  x  total

We know she picks 1, so we have

1 x 12 = 12 possible outcomes

So, there are 12 possible outcomes

The first row of the SHORT BINGO card contains 5 numbers, one from each of the sets $1-10$, $11-20$, $21-30$, $31-40$, and $41-50$. Since the WILD square is in the middle of the card, it does not affect the possibilities for the first row.

A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

For the first column, there are 10 possibilities, as it can contain any number from the set $1-10$.

For the second column, there are 10 possibilities, as it can contain any number from the set $11-20$.

For the third column, there are 9 possibilities, as it can contain any number from the set $21-30$ except the one already used.

For the fourth column, there are 10 possibilities, as it can contain any number from the set $31-40$.

For the fifth column, there are 10 possibilities, as it can contain any number from the set $41-50$.

The total number of distinct possibilities for the values in the first row of a SHORT BINGO card is the product of the possibilities for each column, which is:

10 * 10 * 9 * 10 * 10 = 90000.

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The student population in the school can be modeled using an exponential function of the form:

P(t) = 2,035 * 1.03^t

where P(t) is the student population t years from now, and 1.03 is the factor by which the population increases each year.

To predict the number of students in the school after five years, we can substitute t = 5 into the function:

P(5) = 2,035 * 1.03^5

= 2,035 * 1.1895

= 2,408.76

Thus, there will be approximately 2,408.76 students in the school after five years.

Using the provided equations, Applying the addition method in the system of equations, The answer is x=-2 and y =-6.

An equation is a statement of equality between two expressions, usually containing one or more variables. Equations can be used to express mathematical relationships and can be solved to find the value of the variables. Equations can take many forms, such as linear equations, quadratic equations, and differential equations. They can also be represented graphically.

The addition method to solve a system of equations is a way to solve a system of two linear equations by adding them together. The goal is to eliminate one variable by adding or subtracting the equations. We can eliminate one variable by adding the equations together. To do this, we'll add the left-hand side of the first equation to the left-hand side of the second equation and add the right-hand side of the first equation to the right-hand side of the second equation. It is important to note that the addition method works only when the coefficients of the variable you want to eliminate are opposite in sign.

4x-5y=22

3x+2y=-18

multiplying first equation with 3 and second equation with 4 and subtracting them , we eliminate x and solve for y,

y=-6

put y=-6 in first equation , we get x,

x=-2

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Answer:

488 adults and 276 children

Step-by-step explanation:

So, we need two linear equations here to start, and we do have them.

Our first linear equation tells us how we get the number of forks:

2c + 5a = 2992

And the second tells us the number of people there:

c + a = 764

I will solve this using substitution. We start by minusing a from both sides in the second equation, giving us:

c = 764 - a

Then, we will substitute this into our first equation, giving us:

2(764 - a) + 5a = 2992

Then, we will open the parentheses, giving us:

1528 - 2a + 5a = 2992

Combining like terms and subtracting 1528 from both sides gives us:

3a = 1464

Dividing by 3:

a = 488

So there were 488 adults. Then, we take our original second equation and substitute 488 for a, giving us:

488 + c = 764

Minus 488 from both sides gives us:

c = 276

So, there were 276 children. In total, we had 488 adults and 276 children.

Hope this helped!

Answer:

Factor the numerator and denominator and then divide out any common factors.

Step-by-step explanation:

Answer:

well, you didnt give me any numbers or variables, so ill do it like  this. if the container is the size of a pint, and there are 8 runners, and a pint equals 16 fluid ounces, in turn it should end as that each runner gets 2 fluid ounces of energy drink

Step-by-step explanation:

By geometric formulas, the gray square has an area of 25 square units.

Squares are quadrilaterals with four right angles. In this question we find a geometric system formed by seven squares with distinct dimensions. By geometry, the area of a square (A), in square units, is equal to following formula:

A = l²

Where l is the length of the side of a square, in units.

All the required lengths are represented in the image attached below. First, determine the side length of the gray square:

7 + x = 12

x = 12 - 7

x = 5

The gray square has four sides with a length of 5 units.

Second, determine the area of the gray square by means of square formula:

A = x²

A = 5²

A = 25

According to area formula for squares, the area of the gray square is equal to 25 square units.

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To compute the sum of dollar amounts that are not whole numbers and to compute products of dollar amounts that are not whole numbers you can use the standard arithmetic operation and place decimal point correctly.

To compute the sum of dollar amounts that are not whole numbers, such as $5.89 and $1.45, you can use the standard arithmetic operations of addition, just like you would with whole numbers.

$5.89 + $1.45 = $7.34

When adding or subtracting decimal numbers, you align the decimal points and perform the operation column by column, just like you would with whole numbers.

To compute products of dollar amounts that are not whole numbers, such as 4 pounds of beef at $5.89 per pound, you can use the standard arithmetic operation of multiplication.

4 × $5.89 = $23.56

When multiplying decimal numbers, you multiply as you would with whole numbers and place the decimal point in the product to the right of the last digit in the product that corresponds to the number of decimal places in the original factors.

In both examples, it is important to pay attention to the placement of the decimal point and to use proper arithmetic operations. In general, it is important to consider the decimal places when working with decimal numbers and ensure that the final result is rounded to the appropriate number of decimal places, if necessary.

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A function is generally indicated by f.

A mathematical expression that indicates a relationship between an independent variable and a dependent variable.

In other word, a function shows a relation between a set of input values to a set of output values in where each input value is connected to only a particular output value.

A function is generally, expressed by letters such as f, g and h and so on.

It is said that f(x) is a function of x or g(x) and h(x) are a function of x when functions are denoted by g or h.

For an input value of an independent variable x, the output value is denoted by f(x) that is equal to a dependent variable such as y. We can write, y = f(x)

The set of x value are the domain of function, and the set of f(x) value are the ranges of a function.

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Complete question is: What is the value of f in a function?

Does there seem to be a pattern in the population estimates of the bugs on this tree is the query or the question .

Variation is the difference in an individual's genetic make-up that causes a population's members to have different physical characteristics. Variation can be shown in an individual's physical characteristics, fertility, metabolism, and method of reproduction. A variation is a relationship between a set of values for one variable and another set of values. direct change. If m is a nonzero constant and b = 0, the function y = mx (commonly written y = kx) that results from the equation y = mx + b is known as a direct variation.

given

the population of the bugs

b is the no. of bugs = 50 . [tex]3^{t}[/tex]

t is the no. of weeks they first counted

so this question explains

the range of population estimates

Is there a trend in the variation of estimates

Does there seem to be a pattern in the population estimates of the bugs on this tree is the query or the question .

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We can determine sin an in the above triangle using the available information without applying the Pythagorean theorem since the length of BC is required because it is the side opposite A.

We are told that we must calculate sin(a) without utilizing the Pythagorean theorem.

Now, we can see from the abbreviation SOHCAHTOA that if we wish to determine Sin a, it will be; sin a = opposite/adjacent

We must now locate a side opposing the angle A or the hypotenuse.

As a result, since the triangle is ABC, the required side is BC because it is the side opposite to A.

Finally, the length of BC is required because it is the side opposite A.

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The complete question should be like:

What additional information would be necessary to determine sin(A) without using the Pythagorean theorem? Explain.

On solving the provided question, we can say that by permutation 26 possible letters  x  10 possible digits  = 260 possible plates

The permutation of a set in mathematics is essentially the rearranging of its elements if the set is already ordered, or the arrangement of its members in a linear or sequential order. The act of altering the linear order of an ordered set is referred to as a "permutation" in this context. The mathematical calculation of the number of possible arrangements for a given set is known as permutation. Permutation, in its simplest form, refers to the variety of possible arrangements or orders. The placement of the elements matters with permutations. The placement of items in a specific order is known as a permutation. Here, the set's components are sorted in either chronological order or linear order. like in the case of

26 possible letters  x  10 possible digits  =

26 x 10   =

260 possible plates

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the answer would be -144

you would have to multiply 3 by square 2, then multiply them which would be 3*4=12 and then you would square that which is 144 and because it is negative it would be -144