A cylinder shaped dispenser holds 5,652 cubic centimeters of liquid soap and is now full. the radius of the dispenser is 7.5 centimeters. what is the difference between the height of the soap in the full dispenser and the height when 4,239 cubic centimeters of soap remains in the dispenser? use 3.14 for pi. enter your answer in the box.

Using trigonometric ratios the approximate horizontal distance from the observatory to the island is option A: 322 feet.

What is trigonometric ratio?

Triangle side length ratios are known as trigonometric ratios. In trigonometry, these ratios show how the ratio of a right triangle's sides to each angle. Sine, cosine, and tangent ratios are the three fundamental trigonometric ratios.

We can use trigonometry to solve this problem.

Let's call the horizontal distance from the observatory to the island "x".

Since we know the opposite side (150 ft) and the angle of depression (25 degrees), we can use the tangent function -

tan(25) = opposite / adjacent

tan(25) = 150 / x

Solving for x, we get -

x = 150 / tan(25)

Using a calculator, we find that -

x ≈ 322 feet

Therefore, the horizontal distance value is 322 feet.

To learn more about trigonometric ratio from the given link

https://brainly.com/question/13276558

#SPJ1

Answer:

Step-by-step explanation:

Using trigonometric ratios the approximate horizontal distance from the observatory to the island is option A: 322 feet.

What is trigonometric ratio?

Triangle side length ratios are known as trigonometric ratios. In trigonometry, these ratios show how the ratio of a right triangle's sides to each angle. Sine, cosine, and tangent ratios are the three fundamental trigonometric ratios.

We can use trigonometry to solve this problem.

Let's call the horizontal distance from the observatory to the island "x".

Since we know the opposite side (150 ft) and the angle of depression (25 degrees), we can use the tangent function -

tan(25) = opposite / adjacent

tan(25) = 150 / x

Solving for x, we get -

x = 150 / tan(25)

Using a calculator, we find that -

x ≈ 322 feet

Therefore, the horizontal distance value is 322 feet.

To learn more about trigonometric ratio from the given link

brainly.com/question/13276558

#SPJ1

The cone’s radius r in terms of x is x + 7

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

Volume, V = 3πx^2 + 42πx + 147π

Height, h = 9

The volume of a cone is

V = 1/3πr^2h

Substitute the known values in the above equation, so, we have the following representation

1/3πr^2 * 9 = 3πx^2 + 42πx + 147π

So, we have

3πr^2 = 3πx^2 + 42πx + 147π

Divide by 3π

r^2 = x^2 + 14x + 49

So, we have

r = √(x² + 14x + 49)

Evaluate

r = x + 7

Read more about volume at

https://brainly.com/question/463363

#SPJ1

A pile of 6 boards is 2 timed the volume of a pile of 3 boards with the given dimensions. Option D is the correct answer.

The dimension of an item in mathematics is, approximately speaking, the quantity of degrees of freedom of a moving point on the object. To put it another way, a dimension is indeed the amount of distinct factors or coordinates required to define the location of a point that must be on an object. For instance, a point has a dimension of zero; a line has a size of one since a point can only move along a line in one direction (or its opposite); a plane has a dimension of two; etc.

The volume of the wooden board is given by the formula:

V = (l)(b)(h)

V = (2)(6)(14)

V = 168 cubic inches.

The volume of pile of 3 boards has dimensions:

l = 14

b = 6

h = 3(2)

V = 3(168) = 504 cubic inches.

Similarly, piling the boards and changing the height.

The volume of pile of four boards = 4(168).

The volume of pile of 5 boards = 5(168)

The volume of pile of 6 boards = 6(168) = 2(3(168))  = 2(Volume of pile of 3 boards)

Hence, a pile of 6 boards is 2 timed the volume of a pile of 3 boards with the given dimensions.

Learn more about volume here:

https://brainly.com/question/13338592

#SPJ1

Answer:

Step-by-step explanation:  15 feet of the ladder will be under the water because at first the ladder was 10 feet long then it  rises from under water

The coefficient of determination calculator is a tool that is used to calculate the proportion of the variation in the dependent variable that is explained by the independent variable

The coefficient of determination, also known as R-squared, is a statistical measure that ranges from 0 to 1, where 0 indicates that none of the variation in the dependent variable is explained by the independent variable, and 1 indicates that all of the variation in the dependent variable is explained by the independent variable.

To use the coefficient of determination calculator, follow these steps:

Input the data: You will need to enter the data for both the independent and dependent variables in the calculator. .

Run the calculation: Once you have input the data, the calculator will use it to calculate the coefficient of determination.

Interpret the result: The output of the calculator will be the coefficient of determination, expressed as a decimal.

It's important to note that the coefficient of determination is only meaningful for linear regression models, where the relationship between the variables is assumed to be linear.

Learn more about coefficient of determination here

brainly.com/question/28975079

#SPJ4

The chain rule is a formula used in calculus to find the derivative of a composition of functions. It is an important tool for solving problems in many areas of mathematics and science.

The chain rule formula can be stated as follows:

If y = f(g(x)), then the derivative of y with respect to x is given by:

dy/dx = (df/dg) * (dg/dx)

In other words, the derivative of y with respect to x is equal to the derivative of f with respect to g, multiplied by the derivative of g with respect to x.

Here, f and g are functions of x, and y is a function of g. The chain rule formula tells us how to find the derivative of y with respect to x, by taking into account the effect of both f and g on the function y.

The chain rule can be extended to more complex compositions of functions, by applying the formula repeatedly. For example, if y = f(g(h(x))), then the chain rule can be applied twice, as follows:

dy/dx = (df/dg) * (dg/dh) * (dh/dx)

This formula tells us how to find the derivative of y with respect to x, by taking into account the effects of all three functions f, g, and h on the function y.

For more questions on Calculus

https://brainly.com/question/29499469

#SPJ4

Answer:

Step-by-step explanation:

You want the graphical solution to the set of inequalities that describes the numbers of games (x) and songs (y) that Staci can buy with $20, if a game costs $2 and a song costs $1, and Staci wants to buy at least 12 items.

The inequalities that describe the numbers are ...

  2x +y ≤ 20 . . . . . Staci has at most $20 to spend

  x + y ≥ 12 . . . . . . Staci wants to buy at least 12 items

Each of these inequalities has a solid boundary line on its solution space graph. The shading is below the line for the first inequality, and above the line for the second one. The vertices of the triangular solution space are ...

  (0, 12), (0, 20), (8, 4)

Possible numbers are the coordinates of any grid point within the triangle or on its boundaries.

Answer:

410 is the outlier.

What is an outlier?

An outlier is an observation that lies an abnormal distance from other values in a random sample from a population. In a sense, this definition leaves it up to the analyst (or a consensus process) to decide what will be considered abnormal.

In simpler words, it is the number that is significantly bigger or smaller than the rest of the numbers, and 410 is it.

Step-by-step explanation:

Hope it helps! =D

Answer:

0.80*c = 20

Step-by-step explanation:

"80% of c is 20" can be written as:

  0.80*c = 20

80% of c is 0.80*c

"is" can be written as "="

Put these two together to obtain:

  0.80*c = 20

Answer:

The answer is 50, the median. The median is the value where 50% of the data lie above and below.

Answer:

6 US tablespoons

Step-by-step explanation:

Removing the electric car from the data set will reduce the standard deviation as the extreme value of 112 mpg is taken out, resulting in a decrease in the spread of the data. The interquartile range (IQR) will also be affected as the extreme outlier is taken out, will decrease the spread of the data in the boxplot.

The electric car with a rating equivalent to 112 miles per gallon is an extreme outlier, which means it is very far from the rest of the data. Therefore, removing this outlier from the data set will decrease the variability and, consequently, decrease the standard deviation. The extreme outlier with the rating equivalent to 112 miles per gallon is outside of the whiskers of the boxplot, which means it is beyond the range of the middle 50% of the data. Therefore, removing this outlier from the data set will decrease the spread of the data in the boxplot and, consequently, decrease the IQR.

To know more about standard deviation:

https://brainly.com/question/23907081

#SPJ4

52 cm is equivalent to nearly 20.47 inches, rounded to two decimal places.

The Imperial and US Customary measuring systems both utilise the inch as their unit of measurement.

It is the unit of length.

Furthermore, length is measured in centimeters,

Used in the International System of Units,

This is the metric system's present configuration.

52 centimetres equal 20.47 inches (centimeters).

To convert centimeters to inches,

We can use the following conversion:

1 inch = 2.54 cm

Therefore,

To convert 52 cm to inches,

You can divide 52 by 2.54:

52 cm / 2.54 = 20.47 inches

So, 52 cm is equivalent to nearly 20.47 inches,

rounded to two decimal places.

For similar questions on conversion on inches to cm,

https://brainly.com/question/29750822

#SPJ4

Answer:

Step-by-step explanation:

points

The y-intercept of the graph of this line is equal to 1.

Mathematically, the slope-intercept form of the equation of a straight line is given by this mathematical expression;

y = mx + c

Where:

In Mathematics, the y-intercept is sometimes referred to as an initial value and the y-intercept of any graph such as a linear function, generally occur at the point where the value of "x" is equal to zero (x = 0).

In this context, we can logically deduce that the y-intercept as shown in the image attached below is at point (0, 1).

Read more on y-intercept here: brainly.com/question/6240745

#SPJ1

Found that a short stanza contains 8 lines and a long stanza contains 9 lines.

What is linear equation ?

A linear equation is an equation that describes a straight line in a two-dimensional coordinate system. The general form of a linear equation is:

y = mx + b

Explanation:
Let's use "s" to represent the number of lines in a short stanza and "l" to represent the number of lines in a long stanza.

From the problem, we know that Megan wrote 10 short stanzas and 2 long stanzas, for a total of 98 lines. This can be written as the equation:

10s + 2l = 98

We also know that Sebastian wrote 3 short stanzas and 7 long stanzas, for a total of 87 lines. This can be written as the equation:

3s + 7l = 87

We want to find the values of s and l that satisfy both of these equations. We can use algebra to solve for s and l.

Multiplying the first equation by 3, we get:

30s + 6l = 294

Multiplying the second equation by 2, we get:

6s + 14l = 174

Now we can add the two equations together to eliminate the variable s:

30s + 6l + 6s + 14l = 468

Simplifying and rearranging, we get:

36s + 20l = 468

Dividing both sides by 4, we get:

9s + 5l = 117

Now we have a new equation that relates the values of s and l that satisfy both sets of stanzas. We can use this equation along with one of the original equations to solve for either s or l.

Let's use the first equation, 10s + 2l = 98. We can solve for s in terms of l:

10s + 2l = 98

10s = 98 - 2l

s = (98 - 2l)/10

Now we can substitute this expression for s into the equation 9s + 5l = 117:

9[(98 - 2l)/10] + 5l = 117

Simplifying and solving for l, we get:

l = 9

Now we can substitute this value of l back into either of the original equations to solve for s. Using the first equation:

10s + 2l = 98

10s + 2(9) = 98

10s = 80

s = 8

To know more about Linear equation visit:

https://brainly.com/question/30775719

#SPJ1

Answer: 18x+24

Step-by-step explanation:

The surface area of the given prism above would be = 606cm²

To calculate the surface area of the given prism is to add all the area of the faces.

The area of the two triangles = 2(1/2 base×height)

where base = 12 cm

height = 8cm

area = 1/2× 12×8

= 48 × 2 = 96cm²

Area of rectangle =3( l×w )= 3(17×10)

= 3×170 = 510cm²

Therefore the surface area of the prism = 96+510 = 606cm².

Learn more about multiplication here:

https://brainly.com/question/28768606

#SPJ1

As per multiplication, the value of 64 times π is 200.96

Multiplication is a fundamental arithmetic operation that involves repeated addition. In this case, we are tasked with finding the result of multiplying 64 and pi. Pi is a mathematical constant that represents the ratio of the circumference of a circle to its diameter and is commonly denoted by the Greek letter "π".

To find the product of 64 and pi, we simply need to multiply these two numbers. Multiplication is typically represented using the "×" symbol or the "dot" symbol ( · ). In this case, we can write:

64 × π

Since pi is a mathematical constant, we typically use an approximation of its value in calculations. The commonly used approximation is 3.14, which is accurate to two decimal places. Thus, we can substitute 3.14 for pi and obtain:

64 × 3.14

Using the distributive property of multiplication, we can break down 64 into smaller factors that are easier to multiply with 3.14. For example, we can write:

64 = 60 + 4

Then, we can use the associative property of multiplication to group the factors in a way that makes the calculation easier. For instance, we can write:

64 × 3.14 = (60 × 3.14) + (4 × 3.14)

Now, we can use our knowledge of multiplication tables to calculate the products on the right-hand side. We get:

60 × 3.14 = 188.4

4 × 3.14 = 12.56

Therefore, the final result is:

64 × π = 188.4 + 12.56 = 200.96

To know more about multiplication here.

https://brainly.com/question/5992872

#SPJ4

Answer:°

Based on the given information, we can see that the pair of parallel lines are intersected by a transversal, which creates corresponding angles on the two lines. Using this fact, we can set up the equation:

2x + 105 = 70^2

First, we simplify 70^2:

70^2 = 4900

Then, we solve for x:

2x + 105 = 4900

2x = 4900 - 105

2x = 4795

x = 2397.5

Therefore, x is equal to 2397.5.

The relationship between the angles is that they are corresponding angles, which means they are congruent. We can use this fact to find the measure of the other angle that is marked in the diagram.

From the diagram, we can see that the angle marked as (2x + 10^5)° is supplementary to the angle marked as 70^2°. This means that the sum of their measures is 180 degrees. We can use this fact to find the measure of the angle marked as (2x + 10^5)°:

(2x + 10^5) + 70^2 = 180

2x + 10^5 + 4900 = 180

2x + 10^5 = 175

2x = 175 - 10^5

2x = -99825

x = -49912.5

correct me if im wrong

Step-by-step explanation:

80 kilograms is equivalent to around 176.37 lbs.

Use the formula below to convert 80 kilograms' (kg) to pounds (lbs.):

1 kilograms = 2.20462 pounds

So, you may multiply 80 by 2.20462 to convert 80 kg to lbs:

80 kg x 2.20462 pounds/kg = 176.3696 lbs (rounded to four decimal places)

The term "lb" stands for pounds, a weight unit that is frequently employed in the United States and in other nations that use imperial units. The approximate weight of a pound in kilos is 0.4536. (kg).

The International System of Units' basic unit of mass, the kilogram, is denoted by the notation "kg" (SI). The standard unit for measuring mass or weight in the majority of nations is the kilogram. A kilogram is about equivalent to 2.20462 pounds (lbs).

For more such questions on kilogram

https://brainly.com/question/29022581

#SPJ4  

r

For more such questions on

#SPJ4  

The length of the arc that outlines the sector is 15π centimeters.

What is the area of sector?

The area of a sector is given by the formula:

[tex]A=\frac{\theta}{360^{\circ}} \times \pi r^2[/tex]

where A is the area of the sector, θ is the central angle of the sector (in degrees), and r is the radius of the circle.

To find the area of the shaded sector, we need to use the formula -

[tex]Area=\frac{central \angle}{360^{\circ}} \times \pi r^2[/tex]

In this case, the central angle is 270° and the radius is 10 cm. Plugging these values into the formula, we get:

Area of sector = [tex]\frac{270^{\circ}}{360^{\circ}} \times \pi (10)^2[/tex]

Area of sector = (3/4) x π x 100

Area of sector = 75π

So the area of the shaded sector is 75π centimeters.

To find the length of the arc that outlines the sector, we need to use the formula:

Length of arc = (central angle / 360°) x 2πr

Plugging in the values of the central angle and radius, we get:

Length of arc = (270/360°) x 2π x 10

Length of arc = (3/4) x 20π

Length of arc = 15π

Hence, the length of the arc that outlines the sector is 15π centimeters.

To learn more about area of sector, Visit

brainly.com/question/22972014

#SPJ1

I am to believe the answer is Yes because you add the exponents

The TI-84 calculator can be used to find the p-value associated with a hypothesis test, given the test statistic and the degrees of freedom (df).

Here are the steps to find the p-value on a TI-84 calculator:

Press the "2nd" button and then the "VARS" button (which is above the "STAT" button). This will open the DISTR menu.

Select "3: tcdf" from the menu by scrolling down with the arrow keys and pressing "ENTER".

Enter the test statistic and degrees of freedom. For a two-tailed test, enter the test statistic with the appropriate sign (positive or negative) and enter a very large number (such as 100 or 999) for the second argument.

For a one-tailed test, enter the test statistic and select "1" or "2" for the third argument, depending on the direction of the test.

Press "ENTER" to calculate the p-value.

The result displayed on the calculator screen will be the p-value associated with the hypothesis test, based on the test statistic and degrees of freedom entered.

Learn more about p-value at

https://brainly.com/question/30078820

#SPJ4

The question is -

How to find the p-value from the TI-84 calculator?

As a result, the probability that the next individual would buy more than one costume is 7/310, which can already be stated as a fraction in its most basic form.

A fraction is a way of representing a part of a whole or a ratio between two quantities. It is written as two numbers, one above the other, with a horizontal line separating them. The number above the line is called the numerator and the number below the line is called the denominator. For example, the fraction 3/4 represents three parts out of four equal parts, or the ratio of three to four. Fractions can be used to represent a wide range of values, including numbers between whole numbers (such as 1/2 or 3/5), ratios between quantities (such as 2/3 cups of flour to 1 cup of sugar), and percentages (such as 75/100, which is equivalent to 75%, or three-quarters). Fractions are an important concept in mathematics and are used in many different contexts, such as in cooking, measurement, and finance.

Here,

Out of the 93 visitors who did not purchase a costume, we do not have any information on how many of them might purchase more than one costume. So, we will ignore them for the purposes of this calculation.

Out of the 210 visitors who purchased exactly one costume, none of them purchased more than one costume.

Out of the 7 visitors who purchased more than one costume, we do not know how many costumes they actually purchased, but we do know that they purchased at least two.

So, out of a total of 93 + 210 + 7 = 310 visitors, we know that 7 purchased more than one costume, and we do not have any information on how many of the remaining 303 visitors might purchase more than one costume.

Therefore, the probability that the next person will purchase more than one costume is 7/310, which is already expressed as a fraction in simplest form.

To know more about fraction,

https://brainly.com/question/24638688

#SPJ1

Slope of relationship between length of icicle and time = −0.6; for every additional hour, the length of the icicle decreases by 0.6 inches .The correct option is D.

What is slope?

The slope of a line is defined as the change in vertical coordinate with respect to the change in horizontal coordinate of that line.

Given,

A student is measuring the length of an icicle, y, every hour, x

At present icicle is 9 inches long

melting at rate of 0.6 per hour

y = 9 - 0.6 x

Where y is the length of the icicle after x hours

comparing with slope intercept form of line: y = m x + c

slope m = -0.6

Hence, - 0.6 is the slope, represents that the length of the icicle decreases by 0.6 inches every hour.

Learn more about slope here:

brainly.com/question/3605446

#SPJ1

Therefore , the solution of the given problem of arithmetic comes out to be First sequence nth formula is  aⁿ = a(3)ⁿ and Second  sequence nth formula is  aⁿ = a + (n-1)5.

A list's values are added together to get the average values, also known as the group's mean, which is then multiplied by the maximum population of list items. Similar progression trends can be seen in math. The average of the actual numbers 5, 8, and Nine is 3, while a mean of the actual numbers 5, 7, & 9 is 4, and indeed the number 21 times three (there now multiple 3 numbers) equals seven. This is demonstrated by the following equation.

Here,

Given :

First sequence :

=> 7,21,63 ....

We can see it is a type of geometric progression:

As,

=> 21/7 = 3

=> 63/21 = 3

So, it's nth formula is :  aⁿ = a(3)ⁿ

And

Second sequence :

=> 3, 8, 13,....

it is a type of arithmetic progression:

As,

=> 8 -3 =5

=> 13 -8 = 5

So, it's nth formula is :  aⁿ = a + (n-1)5

Therefore , the solution of the given problem of arithmetic comes out to be First sequence nth formula is  aⁿ = a(3)ⁿ and Second  sequence nth formula is  aⁿ = a + (n-1)5.

To know more about arithmetic mean  , visit

brainly.com/question/13000783

#SPJ1

Answer:

3 times greater

Step-by-step explanation:

To find out how many times greater the population of Chicago is than Austin, we can divide the population of Chicago by the population of Austin:

Population of Chicago / Population of Austin = 2,720,546 / 900,000

Simplifying the expression by dividing both the numerator and denominator by 100,000, we get:

Population of Chicago / Population of Austin = 27.20546 / 9

Dividing these numbers, we get:

Population of Chicago / Population of Austin = 3.022838

Therefore, the population of Chicago is about 3 times greater than the population of Austin.