A thermos in the shape of a cylinder will be filled with hot chocolate. if the thermos has a radius of 4 inches and is 12 inches tall, which formula could be used to find the number of cubic inches of hot chocolate needed to completely fill this thermos?

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.

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Answer:

1 cake

Step-by-step explanation:

12 slices = 2 cakes

6 slices = 1 cake

The rate of the canoe in still water is 5 miles per hour, and the rate of the current is 1 mile per hour.

Let's use the letters "c" for the canoe's speed in still water and "r" for the current's speed. The formula is as follows:

Rate times distance

establishing two equations, one for the upstream trip and one for the downstream trip.

Trip downstream:

12 miles is the distance.

rate = c plus r. (since the current is helping them)

t = two hours

We thus have:

12 = (c + r) × 2

When we simplify this equation, we obtain:

6 = c + r

Trip upstream:

12 miles is the distance.

rate equals c-r (since they are now going against the current)

three hours.

We thus have:

12 = (c - r) × 3

When we simplify this equation, we obtain:

4 = c - r

There are now two equations:

6 = c + r

4 = c - r

By combining the two equations, we may find the value of one of the variables:

6 + 4 = 2c

If we simplify, we get:

10 = 2c

When you divide both sides by 2, you get:

c = 5

To solve for the other variable, we may now re-insert this value into one of the equations. Let's apply the formula:

6 = c + r

With c = 5, we obtain:

6 = 5 + r

5 is subtracted from both sides to yield:

r = 1

In still water, the canoe moves at a rate of 5 miles per hour, while the current moves at a rate of 1 mile per hour.

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Answer:(-2,-3)

Step-by-step explanation: We are using elimination to solve this system of equations. They've already done the balancing so let's use their given equation. It states

[tex]4y+3x=-6[/tex]  and  [tex]3y-3x=-15[/tex]

Combine the equations which will eliminate the x term and you get :

[tex]7y = -21[/tex]

which means

[tex]y=-3[/tex]

plug it back in to solve for x and you get the x-value to be -2.

The conversion of 1.70 meters to feet gives the value which is equal to 5.5774 feet ( approximately ) .

Meters to feet can be converted by the following relation ,

1 meter = 3.28084 feet

Now Substitute the given value to convert meters  into feet.

Here, convert 1.70 meters into feet we get,

⇒ 1.70 meters =  ( 1.70 ) × ( 3.28084 ) feet

⇒ 1.70 meters =  5.577428 feet

Rewrite upto four decimal places we get,

⇒ 1.70meters =  5.5774 feet ( approximately )

Therefore, after converting unit of 1.77 meters into feet it is equal to 5.5774 feet ( approximately ) .

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The method for determining the similar relationship between the parameters of two equations has been explained below.

The relationship between parameters in two equations depends on the specific equations and parameters involved. In general, parameters are constants or variables that are used to define or modify the behavior of a mathematical or physical system.

If two equations have the same parameters, then changes in those parameters will affect the behavior of both equations in the same way and if they have different parameters, then changes in those parameters may affect the behavior of the equations differently. In general, to determine the relationship between parameters in two equations, you would need to analyze the equations and their specific parameters to understand how they are related.

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Here is an explanation to understand step by step how to do this.

A volume can be determined for any three-dimensional object using formulas that are unique to that item's shape. For instance, the volume of a water bottle indicates how much water it can hold. Understanding an object's volume is crucial since it indicates how much stuff that shape can carry.

Any form or object's volume is directly inversely proportional to the volume of water it displaces when submerged in water because of its link to density. As a result, there are two ways to determine an object's volume: by mathematically calculating it using the formula unique to that shape, or by submerging it in water and measuring the volumetric displacement of the water.

Using distributive property, the expression 55x+5 can be written as 5(11x+1).

Algebraic equations with equivalent solutions or roots are called equivalent equations. An analogous equation is one that is created by adding or removing the identical quantity or expression from both sides of a given equation. An equation is equivalent if both sides are multiplied or divided by the same non-zero value.

Expression           Property         Equivalent expression

3(2+x)                 Distributive                  6+3x

2+(3+4)              Associative                  (2+3)+4

24x+18y             Distributive                 8(3x+y)

4x+5x                Commutative              5x+4x

5+2+3               Commutative               3+2+5

(5x.3y).2           Associative                  5x.(3y.2)

12-3x                Distributive                   3(4-x)

6+3                  Commutative                 3+6

(2x.3y).5z         Associative                  2x(3y.5z)

4(5-2y)             Distributive                   20-8y

y+0                  Identity                             y

a.b                  Commutative                   b.a

3x.1                  Identity                            3x

(a+b)+c           Associative                   a+(b+c)

55x+5            Distributive                   5(11x+1)

8(y-2)             Distributive                    8y-16

2x+5y             Commutative                5y+2x

Therefore, using distributive property, the expression 55x+5 can be written as 5(11x+1).

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Answer:

D.  (39.6) or 39.0

Step-by-step explanation:

See the attached worksheet.

Two right triangles are formed in the diagram.  Use the pythagorean theorem on both, starting with the lower triangle, since two of the sides are known and the third (d) may be calculated.  

1.  From the first (bottom) triangle, we find that d is 36.66.

2.  Using this value of d in the upper triangle provided a length for x of 39.6, closest to answer option D at 39.0

The value of the expression -13x-7y is -8.

What is the system of equations?

Simultaneous equations, or a system of equations, Two or more equations in algebra must be solved jointly. The number of equations must match the number of unknowns for a system to have a singular solution.

Given system of equations are

-9x + y = 2   .....(i)

-4x - 8y = -10 ....(ii)

Solve the equation by using system of equations.

Multiply equation (i) by 8 and add with equation (ii)

-72x + 8y = 16

-4x - 8y = -10

___________

-76x = 6

x = 6/-76

x = - (3/38)

Putting x = - (3/38) in equation (i):

-9[- (3/38)] + y = 2

27/38 + y = 2

y = 2 - 27/38

y = 49/38

Putting x = - (3/38) and y = 49/38 in -13x-7y:

-13(-3/38)-7(49/38)

= 39/38 - 343/38

= -304/38

= -8

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The table of values for y = -128x + 3840 is:

x y

0 3840

5 3200

8 2816

10 2560

30 0

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

Y= -128x + 3840

Then, we have

x = 0,5,8,10,30​

To find the values of y, we substitute each value of x into the equation and simplify:

This means that the above is the table of values for y = -128x + 3840 when x takes on the values 0, 5, 8, 10, and 30

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Answer:

210 students

Step-by-step explanation:

We want to find 75% of 280, which means we want to find 75 out of every 100 students who voted. We can do this by multiplying 280 by 75% (or 0.75).

280 x 0.75 = 210

So, 210 students voted for the Chiefs to win the Super Bowl.

I hope this helps! And if you could label my answer brainliest that would be awesome.

- Dante

Answer:

Step-by-step explanation:

75% = .75

280 x .75 =210

Answer = 210

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.

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Commutative property of addition is the property that we used to get the answer for 27+29+31 = 87.

The commutative property of addition says that changing the order of addends does not change the sum. As the first civilization to study fractions, the Egyptians used fractions to address a variety of mathematical problems, including the division of food and supplies and the absence of a bullion currency.

A fraction represents a part of a number or any number of equal parts. There is a fraction, containing numerator(upper value) and denominator(lower value).

In the properties used for this question use the properties of the Commutative property of addition

If counted then the final result

31 + 27 + 29

= (30 +1) + (30 - 3) + (30 - 1)

= 3(30) + 1 - 3 - 1

= 90 - 3

= 87

Hence, 27+29+31 = 87

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In linear equation,the number of customers who will pay by debit card will be 88.97.

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                    The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times. Known as a linear equation, this type of equation has a highest power of one for each variable.

Last week there were

87 + 24 + 7 = 118 customers.

That means that the fraction of the customers, who paid by debit card, was

7/118  

In situations like that, when we use historical data and try to predict future behaviour, we use that past experience and extrapolate to a predicted result.

we simply say that we expect the same fraction, 7/118 if customers use credit cards

for the absolute number of predicted debit  card customers we multiply the predicted number of customers by the expected fraction

1500  × 7 / 118 = 88.97

Therefore the number of customers who will pay by debit card will be 88.97.

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The spherical tanks of Eindhoven can hold a maximum of approximately 14,137 cubic meters of water.

The maximum amount of water that one of the spherical tanks of Eindhoven will hold can be found using the formula for the volume of a sphere:

V = (4/3) * π * [tex]r^3[/tex]

where V is the volume of the sphere, r is the radius of the sphere, and π is a constant equal to approximately 3.14159.

According to the Eindhoven website, the diameter of each spherical tank is 30 meters. The radius, therefore, is half of the diameter, which is:

r = 30/2 = 15 meters

Substituting this value into the formula for the volume of a sphere, we get:

V = (4/3) * π * [tex](15)^3[/tex]

V ≈ 14,137 cubic meters

When we round this to the closest integer, we obtain:

Maximum amount of water = 14,137 cubic meters

Therefore, one of the spherical tanks of Eindhoven can hold a maximum of approximately 14,137 cubic meters of water.

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the value of x will be 8√2 for the given right-angle triangle.

A triangle is said to be right-angled if one of its angles is exactly 90 degrees. The total of the other two angles is 90 degrees. Perpendicular and the triangle's base are the sides that make up the right angle. The longest of the three sides, the third side is known as the hypotenuse.

Given, Two right-angle triangles one with the height of "x" and a base angle of 45-degree.

Another with a base of 8 and a base angle of 60-degree.

From the cosine rule of trigonometry:

Cos θ = base/(hypotenuse)

Sin θ = height/(hypotenuse)

For the triangle with a base angle of 45-degree

sin 45 = height/(hypotenuse)

1/√2 = x/(hypotenuse)

hypotenuse = x *√2.....(1)

For the triangle with a base angle of 60-degree

cos 60 = base/(hypotenuse)

1/2 = 8/(hypotenuse)

hypotenuse = 16

substitute this value in equation 1

x = 8√2

therefore, the value of x will be 8√2 for the given right-angle triangle.

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Answer:

On a coordinate plane, an exponential function approaches y = 0 in quadrant 2 and increases in quadrant 1. It goes through (0, 1), (2, 4), and (3, 8).

Step-by-step explanation:

Answer:

graph 2

Step-by-step explanation:

I did the assignment

The value of x to 3 significant figures is approximately 18.9 cm.

Area of circle can be defined as the product of pi and square of radius of circle.

The area of a circle is given by the formula[tex]A = πr^2[/tex], where r is the radius of the circle.

Since the area of the circle is 56^2 cm, we can set up the equation:

[tex]πr^2 = 56^2[/tex]

Solving for r, we get:

[tex]r = √(56^2/π) ≈ 13.37 cm[/tex]

Since the square fits exactly inside the circle, its diagonal is equal to the diameter of the circle, which is 2r. Therefore:

x√2 = 2r

Substituting the value of r, we get:

[tex]x√2 = 2(√(56^2/π))[/tex]

x√2 ≈ 26.74

Dividing both sides by √2, we get:

x ≈ 18.94

Therefore, the value of x to 3 significant figures is approximately 18.9 cm.

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The magnitude of the vector is calculated by using the formula √((c-a)²+(d-b)²) where A(a,b) and B(c,d) are point on the plane.

A vector is any quantity that has a magnitude as well as directiom and that also follows the vector law of addition.

Let us say that there are any two points on the co-ordinate plane A(a,b) and B(c,d).

Now the magnitude of the vector AB can be found by using the formula,

AB = √((c-a)²+(d-b)²)

and the direction of this vector will be from A to B on the coordinate plane. If we want to find direction, then it is given by, tab A = (d-b)/(c-a)

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The line of best fit can be used to make predictions about the response variable based on the predictor variables. It can also be used to identify correlations between variables, as well as to estimate the strength of those correlations.

A. Line of Best Fit

A regression line is a statistical tool used to predict the value of a response variable based on the value of one or more predictor variables. It is also known as a line of best fit because it is used to show the best fit of a given data set. The line of best fit is a straight line that best represents the data by minimizing the sum of the squared distances between the observed data points and the line. The line of best fit can be used to make predictions about the response variable based on the predictor variables. It can also be used to identify correlations between variables, as well as to estimate the strength of those correlations.

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Using normal distribution we know that 7.78% of travelers reported spending less than $1,200 for a 12-day getaway.

Asymmetric probability distribution about the mean, known as the normal distribution or the Gaussian distribution, would indicate that data close to the mean occur more frequently than data far from the mean.

The "bell curve" is a visual representation of the normal distribution.

Currently, in response to the query:

The z-score can be calculated using the formula:

z = (x - μ)/σ

It averages $1,755:

μ = $1,755

$390 is the standard deviation:

σ = 390

The trip doesn't cost more than $1200:

x = $1200

Replace the values in the z-score formula:

z-score = (1200 - 1,755)/390 = -1.42

Use the z-negative table's normal distribution:

P(z < 1,200) = 0.07782

P(x < 1,200) = P(z < 1,200)

P(x < 1,200) = 0.07782

P(x < 1,200) = 7.78%

Therefore, using normal distribution we know that 7.78% of travelers reported spending less than $1,200 for a 12-day getaway.

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Correct question:

If the data are normally distributed with a standard deviation of $390, find the percentage of vacationers who spent less than $1,200 per 12-day vacation. round to the nearest hundredth of a percent.

The FRF method is a common technique for analyzing the dynamics of structures and systems, it is typically not used as a primary method for determining a system damping ratio by field measurements.

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The metric system is defined as the decimal system of units based on the meters, kilograms, and second as the units of length, mass, and time respectively. The imperial system is defined as the measurement system used in countries like the UK, Liberia, Myanmar, etc. that uses units like an inch, pound, ton etc.

The Metric and Imperial systems are both systems of measurement. That is, they are not just one unit of measure, but are correlated systems of many units of measure – measuring length and area, weight and mass, volume, force, temperature etc.

The imperial system of measurement is defined as a system that originated in Britain and came to formal use in the early 19th century with the Weights and Measures Act of 1824 and 1878. It uses some of the commonly used units there like an inch, ton, pound, gallon, pint, etc.

Most countries use the metric system which uses the measuring units such as meters and grams, and adds prefixes like kilo, milli, and centi to count orders of magnitude.

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Therefore, we would anticipate finding 150,000x golden fish throughout the entire lake based on the class average.

Volume is the measure of room within a particular 3D entity in mathematics. For illustration, a fish aquarium measures three feet long by one foot wide by two feet high. The capacity is calculated by multiplying the length, the breadth, and the height, or 3x1x2, that also equals six. The fish aquarium therefore has a 6 cubic foot capacity.

Let's say the class average is "x" yellow fish per liter of water.

If the sample contained 500 liters of water, we can estimate the number of yellow fish in the sample as:

500 * x = 500x

Now that we have an approximation, we can use it to determine the anticipated number of yellow fish in the 150,000,000-liter pool as a whole.

The expected number of yellow fish in the whole lake would be:

(500x / 500) * 150,000,000 = 150,000x

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Answer:

(4 × y) - 8 = <26

Step-by-step explanation:

The equation for this problem is:

(Let y = the unknown number)

Therefore, you can use (4 × y) - 8 = <26 as an inequality for this problem.

The required value of x and y in the given equation are ,

x= 1,

y = -1 .

The algebraic method to solving simultaneous linear equations is known as substitution method. This method, as the name suggests, involves substituting the value of one variable from one equation into the second equation. This makes it much easier to answer a pair of linear equations by combining them into a single linear equation with only one variable.

The given equations are

0.1x - 0.3y = 0.4                             ...(1)

0.3x − 0.2y=0.5                              ....(2)

Multiply both the equations by 10, we get

x - 3y = 4                                           ...(1)

3x − 2y = 5                                        ...(2)

Multiply (1) by 3

3x - 9y = 12

3x − 2y = 5

Subtracting both the equations

-7y = 7

y = -1

From (1):

x - 3(-1) = 4

x + 3 = 4

x = 4 - 3

x = 1

The required value for x and y is,

x= 1,

y = -1

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The domain of the given function in the graph will be x ≤ -1.

A relationship between a group of inputs and one output is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function. Typically, f(x), where x is the input, is used to represent a function.

Given, a function as we can see in the graph,

Since The domain of a graph is made up of all the input values displayed on the x-axis since the term "domain" refers to the set of potential input values.

The y-axis on a graph represents the possible output values or range.

thus, in the given graph the domain of the function will be All real values smaller than -1.

therefore, the domain of the given function in the graph will be x ≤-1.

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Answer:

x > -9.5

Step-by-step explanation:

2x - 6 > -25

2x > -19

x > -19/2

x > -9.5

Answer: x= 5/2, y= 11, z= 3/2

Step-by-step explanation:

Solve for the first variable in one of the equations, then substitute the result into the other equation.

Point form:

(5/2, 11, 3/2)