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The rate at which air is being pumped in when the radius of the sphere is 10 cm and increasing at a rate of 2 cm/s is 400π/3 cm³/s.

The volume V of a sphere with radius r is given by V = (4/3)πr³. Taking the derivative of this expression with respect to time t, we get dV/dt = 4πr²(dr/dt). This equation relates the rate of change of volume to the rate of change of the radius. We are given that the radius is increasing at a rate of 2 cm/s, so dr/dt = 2 cm/s.

At the instant when the radius is 10 cm, we can find the rate at which air is being pumped in by substituting r = 10 cm and dr/dt = 2 cm/s into the equation for dV/dt. Thus, we have dV/dt = 4π(10)²(2) = 800π cm³/s.

Therefore, when the radius of the spherical balloon is 10 cm and is increasing at a rate of 2 cm/s, the rate at which air is being pumped in is 400π/3 cubic centimeters per second.

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Answer:

4x −7y=21

x+2y=99

Explanation

4x - 7y = 15

5x - 2y = 12

First equation times 2:

8x - 14y = 30

Second equation times 7:

35x - 14y = 84

Subtract,

27x = 54

x = 54/27 = 2

2y = 5x - 12 = 10 - 12 = -2

y = -1

Answer: x=2, y = -1

Check:

4(2)-7(-1)=8+7=15, good

5(2) -2(-1) = 10 + 2 = 12, good

ax + by = c    

dx + ey = f

has solutions

x = (ce-bf)/(ae-bd), y = (a f-cd)/(ae-bd)

4x - 7y = 15    

5x - 2y = 12

has solutions

denom = ae-bd = 4(-2) - (-7)(5) = 27

x = (15(-2) - (-7)(12))/27 = (-30 + 84)/27 = 2

y = (4(12)-15(5))/27 = (48-75)/27 = -27/27 = -1

Answer:

  (x, y) = (2, -1)

Step-by-step explanation:

You want to solve this system of equations using an algebraic method:

Writing these equations in general form and making an array of coefficients with the x-coefficient repeated, we get the equations and array ...

  [tex]\begin{array}{cccc}4&-7&-15&4\\5&-2&-12&5\end{array}[/tex]

Working from the left calculating determinants of pairs of columns, we have ...

  ∆ = 4(-2) -5(-7) = 27

  ∆x = -7(-12) -(-2)(-15) = 54

  ∆y = -15(5) -(-12)(4) = -27

The variable values are ...

  x = ∆x/∆ = 54/27 = 2

  y = ∆y/∆ = -27/27 = -1

The solution is (x, y) = (2, -1).

__

Additional comment

The graph confirms this solution.

The "cross multiplication method" is useful when the coefficients are such that elimination or substitution involves more arithmetic operations than the minimum. The amount of math involved in calculating the x- and y-values is on par with what would be required for "elimination." The method is substantially equivalent to "Cramer's Rule."

The area of the blue glass needed to fill each dot on the butterfly wing is 144π square inches.

The distance around each dot on the butterfly wing is given as 24π inches. This means that the circumference of each dot is 24π inches. The circumference of a circle is:

Circumference = 2πr

where "r" is the radius of the circle. So, we can write:

2πr = 24π

Simplifying this equation, we get:

r = 12

Therefore, the radius of each dot is 12 inches.

To find the area of the blue glass needed to fill each dot, we can use the formula for the area of a circle:

[tex]Area = \pi r^2[/tex]

Substituting the value of the radius, we get:

[tex]Area = \pi(12)^2[/tex]

Simplifying this equation, we get:

Area = 144π square inches

Therefore, the area of the blue glass needed to fill each dot on the butterfly wing is 144π square inches.

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The complete question is :

An artist is creating a large butterfly sculpture outside a museum. There is a circular dot on each wing made out of metal ring. The distance around each dot is 24π inches. The artist plans to fill the inside of each dot with blue colored glasses. What is the area of the blue glass will be needed to fill each butterfly dot?

Answer:

(4 + 3) x 2

Step-by-step explanation:

In one day, Vesi would snowboard 4+3 hours, so in two days, we would multiply this by two and get the expression (4+3) * 2.

About 195 students at Nikhil's middle school would have atleast one sibling.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

We can use proportion to estimate the number of students at Nikhil's middle school who have at least one sibling.

If 13 out of 20 students surveyed have at least one sibling, we can assume that the same proportion applies to the entire school.

So, we can set up a proportion as follows:

13/20 = x/300

where x is the number of students in the entire school who have at least one sibling.

Solving for x, we can cross-multiply and get:

13 * 300 = 20 * x

x = (13 * 300)/20

x = 195

Therefore, about 195 students at Nikhil's middle school would have at least one sibling.

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Value of angle ∠QUR in the given figure is 139°.

Vertically opposite angles are pairs of angles that are opposite to each other when two straight lines intersect. When two lines intersect, they form four angles, and the vertically opposite angles are the angles that are opposite to each other and share a common vertex.

In the given figure;

∠SUR=41°

∠TUS=90°

∠TUS=∠QUN  ( Vertically opposite angle)

∠TUN is a straight line, angle subtended over it makes 180°

∠TUS makes 90° so, ∠SUN will be 90°

∠SUN=∠SUR+∠RUN

90°=41°+∠RUN

∠RUN=90°-41°

∠RUN=49°

∠QUR=∠QUN+∠RUN

∠QUR=90°+49°

∠QUR=139°

Hence, Value of angle ∠QUR in the given figure is 139°

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Answer:

3. 75.4 and 4. 113.1

Step-by-step explanation:

Okay to find the volume of the cylinder the equation is πr⌃2h

3. so if H is 1.5 and r = 4 it would be π4⌃2(1.5) = 75.4 approx.

4. If h is 4 and r is 3 it would be π3⌃2(4) = 113.1 approx.

Answer:

3

start from -2 and count up 5

-2,-1, 1, 2, 3

The expression -(12 x - 6) + 18 is not equivalent to the other expressions.

Expression is a combination of words or symbols that communicate an idea, thought, opinion, or feeling. Expressions can be literal or figurative, and they often contain multiple layers of meaning. Expressions can be used to express emotions, opinions, beliefs, and values, and they are integral to communication and understanding.

This is because when all of the expressions are evaluated, the result of each expression is different. For example, when the expression -6(2 x - 4) is evaluated, the result is -24.

When the expression -4(3 x + 6) is evaluated, the result is -24. When the expression -3(4 x - 3) + 15 is evaluated, the result is -3. However, when the expression -(12 x - 6) + 18 is evaluated, the result is 12.

Therefore, the expression -(12 x - 6) + 18 is not equivalent to the other expressions.

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Complete questions as follows-
Which expression is not equivalent to the other expressions?
-6(2 x - 4)
-4(3 x + 6)
-(12 x - 6) + 18
-3(4 x - 3) + 15

The type of distribution which is utilized for the nominal data is option  b. Binomial distribution.

The appropriate distribution for nominal data is a binomial distribution.

The binomial distribution is used when the data consists of two possible outcomes.

The two outcomes such as success or failure, heads or tails, or pass or fail.

In nominal data, the categories do not have any inherent order.

And there is no numerical value associated with each category.

The binomial distribution gives the probability of obtaining a certain number of successes in a fixed number of independent trials.

The required probability of success is the same for each trial.

Therefore, option b.  binomial distribution is considered as more appropriate distribution for the nominal data.

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Answer:

d

Step-by-step explanation:

95,000÷100 then multiply by $0.83 since it's a wood home in the suburbs.

the garbage company in the city will collect approximately 5.72 pounds of garbage per person in one year.

To calculate how a lot garbage in step with man or woman the garbage enterprise collects in 12 months, we want to find out how many weeks are in a yr and then divide the overall amount of garbage collected in a 12 months by means of the population of the town.
wide variety of weeks in a year: 52 (assuming there aren't any bounce years)
overall amount of garbage collected in a 12 months: 14,three hundred kilos/week x fifty two weeks = 743,600 kilos/12 months
garbage in keeping with character in line with year: 743,six hundred kilos/12 months ÷ 1.three x 10^5 people = 5.72 kilos/person/yryr

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Answer:240 hours

Step-by-step explanation:100x20=2000

12/100=x/2000 multiply 12 and 100 by 20.

Answer:

y = x + 3

Step-by-step explanation:

The correct equation for x:y= 1:5 is (a) y = 5x.

In mathematics, an equation is a formula that connects two expressions with the equal sign = to indicate that they are equal. The equation consists of two sentences joined by an equal sign ("="). The expressions on both sides of the equation are called the "left" and "right" sides of the equation. Usually the right side of the equation is assumed to be zero. Assuming this doesn't reduce the width because it can be done by subtracting the right side from both sides.

Compare to a scale on which a weight is placed. When the same weight of something (like grain) is placed in two pans, the two weights balance the scales and are said to be equal.

According to the Question:

Given that:

x:y = 1:5

We can write the equation as:

   x/y = 1/5

⇒ y = 5x

Therefore x:y = 1:5 is y=5x

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By consulting these tables, you can quickly access important data and information that can help you better understand the Earth and its various processes.

Sure, I'm happy to help! Without seeing the actual table, I'm not sure what information you are looking for specifically. However, I can tell you that Earth Science reference tables often contain important information about the Earth's systems, including geology, meteorology, oceanography, and astronomy.

For example, these tables might include information on rock types, mineral identification, weather patterns, ocean currents, and celestial objects like planets and stars. They may also provide key equations and constants for various scientific calculations.

In general, Earth Science reference tables are a valuable resource for students, researchers, and professionals in the field.

If you have a specific question about the table you're looking at, feel free to let me know and I'll do my best to provide a helpful answer!

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The area of the shaded region in the given shapes is determined as 0.544 in².

The area of the shaded region is calculated by subtracting the area of the inscribed hexagon from the area of the circle.

Let's start by finding the side length of the regular hexagon inscribed in the circle.

The distance from the center of the circle to any vertex of the hexagon is equal to the radius of the circle, which is 1 inch.

In a regular hexagon, all sides are equal in length, so each side of the hexagon is also equal to 1 inch.

The area of the regular hexagon can be found using the formula:

Area of a regular hexagon = (3√3/2) x (side length)²

Substituting the side length of 1 inch, we get:

Area of regular hexagon = (3√3/2) x (1 inch)^2

= (3√3/2) square inches

= 2.598 in²

Now, to find the area of the circle, we can use the formula:

Area of a circle = π x (radius)²

Substituting the radius of 1 inch, we get:

Area of circle = π x (1 inch)²

= π square inches

= 3.142 in²

Area of the shaded region = area of circle - area of hexagon

= 3.142 in² - 2.598 in²

= 0.544 in²

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Therefore, the area of the pentagon is 928 square units.

Length is a measure of the size or extent of an object or a distance between two points. It refers to the longest dimension of an object or the distance between two points in space, typically measured in units such as inches, centimeters, meters, or miles. In mathematics, length is also used to describe the size of a line segment or a curve, which can be measured using various techniques such as Euclidean distance, arc length, or fractal dimension. Length is an important concept in many fields, including physics, engineering, geometry, and statistics.

Find the area.

Pentagon

apothem = 16 side = 23.2

Note: When necessary, enter your answer as a decimal If it is not a terminating decimal, round to the nearest hundredth

For the first question, we need more information to find the area of the triangle. Knowing the apothem and one side is not enough. We also need to know the number of sides of the triangle or the length of another side or the height.

For the second question, the formula to find the area of a regular pentagon is:

Area = (perimeter x apothem)/2

Since we are given the apothem and the side, we can find the perimeter of the pentagon as:

perimeter = 5 x side = 5 x 23.2 = 116

Substituting the values in the formula, we get:

Area = (116 x 16)/2 = 928

Therefore, the area of the pentagon is 928 square units.

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2 option is Correct for  sets of ordered pairs represents a function

The only set of ordered pairs that represents a function is (b), which can also be written as {(1.2, 2), (2, 1), (0.2, 0)}. To be a function, each input (x-value) must correspond to exactly one output (y-value). In set (a), the input value of 2 is associated with two different output values, so it is not a function. Set (c) has two input values that both correspond to the same output value, so it is not a function. Set (d) has two different input values that both correspond to different output values, so it is not a function.

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Answer:

[tex]-7^\circ C[/tex]

Step-by-step explanation:

Let

x -----> the height in meters

y ----> the temperature in Celsius degree

we know that

The linear equation in slope intercept form is equal to

[tex]y+mx+b[/tex]

where

m is the slope or unit rate

b is the y-intercept or initial value

In this problem we have

The slope or unit rate is equal to

[tex]m=-\dfrac{1}{100} \dfrac{^\circ C}{m}[/tex] ---> is negative because is a decreasing function

The y-intercept or initial value is equal to

[tex]b=4^\circ C[/tex] ----> value of y when the value of x is equal to zero (sea level)

substitute

[tex]y=-\dfrac{1}{100} x+4[/tex]

For x=1,100 m

substitute in the linear equation and solve for y

[tex]y=-\dfrac{1}{100} (1,100)+4[/tex]

[tex]x=-7^\circ C[/tex]

to evaluate (t x s)(4), we substitute x = 4 into the expression for (t x s)(x). This gives us (18x + 6)|x=4, which simplifies to 72 + 6 = 78.

(t-s)(x) = 6x - (3x+1) = 3x - 1

(t+s)(x) = 6x + (3x+1) = 9x + 1

(t x s)(4) = (6x)(3x+1)|x=4 = (18x + 6)|x=4 = 72 + 6 = 78

First, we need to define the functions s and t given by s(x)=3x+1 and t(x)=6x. We can then use these functions to calculate (t-s)(x) and (t+s)(x). To calculate (t-s)(x), we subtract s(x) from t(x). This gives us 3x - 1. To calculate (t+s)(x), we add s(x) and t(x). This gives us 9x + 1. Finally, to evaluate (t x s)(4), we substitute x = 4 into the expression for (t x s)(x). This gives us (18x + 6)|x=4, which simplifies to 72 + 6 = 78.

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Values of x for blanks 4 , 1 in inequality .

What in mathematics is an inequality number?

A relationship between two values in an algebraic statement that are not equal is shown by an inequality. One of the two variables on the two sides of the inequality can be represented by an inequality sign as greater than, greater than or equal to, less than, or equal to another value.

                              Despite the equals sign being substituted by an arrowhead, the formula 5x 4 > 2x + 3 resembles an equation. It serves as an illustration of inequity. This shows that the left half, 5x 4, is bigger than the right part, 2x + 3.

-3x/4 < 12/1

x < -16

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Government benefit programs have been established for a range of assistance over time.

What is context of above answer?

The answer given was "Government benefit programs have been established for a range of assistance." This sentence is referring to various programs created by the government to provide support or aid to those in need.

These programs may include financial assistance, food assistance, housing assistance, medical assistance, and more. The sentence suggests that the government recognizes the importance of providing help to individuals and families who may be struggling and has taken steps to create programs to address these needs.

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Complete Question:

What types of assistance have government benefit programs been established for?

The best graphical representation for the pediatrician's data would be a histogram. A histogram is a type of graph that shows the distribution of continuous data. In this case, the weights of the 14-year-olds would likely be continuous data. A histogram would allow the pediatrician to visualize the distribution of weights and identify any outliers or unusual patterns.

Answer:histogram

Step-by-step explanation:

The equation of the line shown in the graph, from (–2,2) to (–3,–1) is y = -5/4x – 7/4.

Equation is a mathematical statement that states the equality of two expressions. It contains an equal sign (=) and expresses the relationship between two values, expressions or functions. Equations are used to solve for unknown values, to describe relationships between variables, and to model and solve real-world problems.

To solve for the equation of the line, we can use the point-slope formula, y – y1 = m(x – x1), where m is the slope of the line and (x1, y1) is a point on the line. In this case, the point (x1, y1) is (–2,2) and the slope of the line is m = (–1 – 2)/(–3 – (–2)) = –3/–1 = 3. Therefore, the equation of the line is y – 2 = 3(x – (–2)).

Simplifying, we get y = 3x + 2. To put the equation in the slope-intercept form, y = mx + b, we can rewrite the equation as y = 3x + 2 = 3x + 2 – 2 = 3x – 2 + 2 = 3x – 2, which is the equation of the line, y = –5/4x – 7/4.

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The equation of the line shown in the graph is y = -3. This equation states that for every y-coordinate on the graph, the corresponding x-coordinate is -3.

Equation is a mathematical statement that states the equality of two expressions. It contains an equal sign (=) and expresses the relationship between two values, expressions or functions. Equations are used to solve for unknown values, to describe relationships between variables, and to model and solve real-world problems.

The equation of the line shown in the graph is y = -3. This equation states that for every y-coordinate on the graph, the corresponding x-coordinate is -3. This line is a horizontal line, which means that all points on the line have the same y-coordinate.

To verify this equation, we can use the two points given on the graph: (-2,-3) and (3,-3). Using the slope-intercept form of a line, we can plug in the points to determine the equation of the line.

The slope-intercept form is y = mx + b, where m is the slope, x is the x-coordinate, and b is the y-intercept. The slope is calculated by finding the change in y over the change in x. In this case, both points have the same y-coordinate, so the slope is 0. Therefore, the equation of the line is y = 0x + b.

Plugging in the coordinates of one of the points, (-2,-3), we get -3 = 0x + b. By solving for b, we get b = -3. Substituting b into the equation, we get y = 0x - 3. This is the equation of the line shown in the graph.

In conclusion, the equation of the line shown in the graph is y = -3. This equation states that for every y-coordinate on the graph, the corresponding x-coordinate is -3. This equation was verified by using the slope-intercept form of a line and plugging in the two points given on the graph.

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The area of the dilated triangle is 45 squared meters

Dilation is a geometric transformation that involves resizing a shape while maintaining its shape and proportions. The scale factor is the ratio of the size of the image to the size of the original shape.

In this problem, we are given a triangle with an area of 5 cm², and we are asked to find the area of the dilated triangle when it is scaled up by a factor of 3. To find the area of the dilated triangle, we need to use the formula for the area of a triangle, which is 1/2 * base * height.

When a triangle is dilated by a scale factor of k, both its base and height are multiplied by k. This means that the area of the dilated triangle is k^2 times the area of the original triangle. In this case, the scale factor is 3, so the area of the dilated triangle is 3^2 times the area of the original triangle.

Therefore, the area of the dilated triangle is 9 times the area of the original triangle, which is 9 * 5 cm² = 45 cm².

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To solve the system of equations:

5x + 2y = 24

2x + 5y = 24

We can use either elimination or substitution method.

Using elimination method:

Multiplying the first equation by 5 and the second equation by -2, we get:

25x + 10y = 120

-4x - 10y = -48

Adding the two equations together eliminates y:

21x = 72

Solving for x:

x = 72/21 = 8/3

Substituting x back into one of the original equations and solving for y:

5(8/3) + 2y = 24

2y = 24 - 40/3

2y = 12/3

y = 6/2 = 3

Therefore, the solution to the system of equations is:

x = 8/3

y = 3

In a statistical problem, a population consists of all items of interest in a statistical problem.The correct option in this case is option C - all items of interest in a statistical problem.

Population refers to the complete set of observations or items for which inferences are being made in statistical inference. It's the group that researchers are interested in studying, and it's the group to which they hope to extend their conclusions.

In statistics, the population is the entire collection of individuals, objects, or measurements that researchers are interested in studying. Researchers utilize statistical techniques to make inferences about population parameters based on data obtained from samples.

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