Matthew has 3.5 pounds of clay to make ceramic objects.
he needs 1/2 of a pond of clay to make one bowl.

A.how many bowls can Matthew make with his clay

B. Matthew can make two mugs with the same amount of clay he uses to make one ceramic bowl. How much clay does he need to make with all of his clay

Answer:

-77 + (-46)

=> -77 - 46 (When you add two negative integers, it is the same thing as subtracting a positive integer with a negative integer)

=> -123 (Because a negative + a negative = a negative)

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= -77 + ( - 46 )

= - 77 - 46 ( a positive integer and a negative integer makes a negative integer )

= -123 ( two negative signs resulted in the usage of addition )

Therefore , -77+ (-46) = -123

The required area of the sector of the circle with radius 5 yards and central angle 3.8 radians is approximately equals to  47.500 square yards (rounded to three decimal places).

Radius of the circle is equal to 5 yards

Central angle of the sector of the circle is equal to 3.8 radians.

Let us consider θ be the central angle in radians,

And r be the radius of the circle.

Let 'A' be the area of the sector of a circle.

The formula for the area of a sector of a circle is equal to,

A = (θ/2) r^2

Substitute the values in the formula of the area of the sector we have,

⇒ A = (3.8/2) × 5^2

⇒ A = 1.9 × 25

⇒A = 47.500 square yards (rounded to three decimal places)

Therefore,  the area of the sector of the circle is approximately equals to  47.500 square yards (rounded to three decimal places).

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Answer:

The table represents a nonlinear function because the rate is not constant.

Step-by-step explanation:

As shown in the picture below, the x side of the table has the same rate of change of +1. However, due to the fact that the y side does not have the same rate of change, +6 and +3, the table represents a non linear function. If the rate on the y side of the table were all the same, then this would be a Linear function.

Answer:

x = 4e² / (e² − 1)

x ≈ 4.626

Step-by-step explanation:

ln x = 2 + ln(x − 4)

e^(ln x) = e^(2 + ln(x − 4))

x = e^(2 + ln(x − 4))

x = e² e^(ln(x − 4))

x = e² (x − 4)

x = e² x − 4e²

4e² = e² x − x

4e² = x (e² − 1)

x = 4e² / (e² − 1)

x ≈ 4.626

Answer:

Step-by-step explanation:

Question: Determine the equation of the parabola that opens up, has vertex (7,7), and a focal diameter of 16 . This problem has been solved! You'll get a detailed solution from a subject matter expert that helps you learn core concepts.

Answer: ((x2)−14x+87)/16

Step-by-step explanation:

  focal diameter = 16,

  4a=16;

  a=4.

(h,v)=(7,7-a)

==> (h,v)=(7,3)

the equation of the parabola =  ((x-7)^2)=16(y-3)

                                                => y = ((x^2)-14x+87)/16.

9514 1404 393

Answer:

  17.5 mi/gal

Step-by-step explanation:

You can think of "per" as meaning "divided by." Then "miles per gallon" means "miles divided by gallons:"

  (166.25 mi)/(9.5 gal) = 17.5 mi/gal

John's car gets 17.5 miles per gallon.

x(x+1)=506

x^2+x-506=0

(x+23)(x-22)=0

x=22

Peter is 23 years old.

Answer:x(x+1)=506

x^2+x-506=0

(x+23)(x-22)=0

x=22

Peter is 23 years old

Step-by-step explanation:

The domain in interval notation:

[-5, 3]

The range in interval notation:

[-6, 5]

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the function are 3 and 5

The inputs of the function are 1 and 2.

We have,

From the graph we will consider:

Domain = x values.

Range = y values.

We see that,

The x values are from -5 to 3.

The y values are from -6 to 5.

Thus,

The domain in interval notation:

[-5, 3]

The range in interval notation:

[-6, 5]

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Answer: It is 18

Step-by-step explanation:

Answer:

18cm

Step-by-step explanation:

Answer:

x ≥ 6.

Step-by-step explanation:

Given : Kathy swims at least 6 laps every day.

To find: Write an inequality to show how long Kathy swims each day.

Solution : We have given that Kathy swims at least 6 laps every day.

We can see from given statement Kathy can swim 6 laps or greater then 6 laps in a day.

Then we use greater than or equal to sign  ( for at least)

Since x ≥ 6.

Therefore, x ≥ 6.

Each step of this theorem is proved below.

Given that,

S is finite,

Now enumerate all of its elements as x₁, x₂,..., x\(_{n}\).

According to the cancellation rule,

This product is independent of the order of the factors.

As a result, we can define the identity element e as this product.

It is simple to demonstrate that e meets the criteria of an identity element.

Now, let's show that every element of S has an inverse.

Let a be any element of S. Consider the set {a, a, a, ...}.

Since S is finite,

There exist positive integers m and n such that

am = an   for some m > n.

By the cancellation law,

We can cancel a power of a from both sides to get a\({(m-n)}\) = e.

This means that a has an inverse, and we can conclude that S is a group.

Consider the set of all positive integers under addition, except 1, as an example of an infinite semigroup in which the cancellation laws hold but which is not a group.

This set clearly meets the cancellation laws, but it does not have an inverse for every element, because the inverse of 2, for example, is not an integer.

As a result, this is not a group.

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Answer:

\(h = 162.0\ cm\)

Step-by-step explanation:

Given

\(BSA = \frac{\sqrt{w*h}}{60}\)

Required

Find h, when BSA = 1.5 and w = 50

We have:

\(BSA = \frac{\sqrt{w*h}}{60}\)

Substitute 1.5 for BSA and 50 for w

\(1.5 = \frac{\sqrt{50*h}}{60}\)

Multiply both sides by 60

\(60*1.5 = \frac{\sqrt{50*h}}{60}*60\)

\(60*1.5 = \sqrt{50*h\)

\(90 = \sqrt{50*h\)

Square both sides

\(90^2 = (\sqrt{50*h})^2\)

\(90^2 = 50*h\)

\(90^2 = 50h\)

\(8100 = 50h\)

Divide both sides by 50

\(\frac{8100}{50} = \frac{50h}{50}\)

\(\frac{8100}{50} = h\)

\(162 = h\)

\(h = 162\)

\(h = 162.0\ cm\)

Hence, the patient's height is 162.0cm

Step-by-step explanation:

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this is the link for explanation copy and paste it to see

Answer:

the ant would have traveled 2.045 miles

Answer:

V=a3=33=27

Step-by-step explanation:

sorry if its wrong

Answer:

Hello your answer should be A symmetric property

Step-by-step explanation:

hope this helps

Symmetric property of equality to show that 3a = 4b, then 4b = 3a?

The symmetric property of equality is a simple property that says we can interchange the sides of an equation without changing the truth-value of the equation. That is, if a = b, then b = a. Each side of the equation can be thought of as the mirror image of the other

We have the following information available from the question is:

We have to determine the which property can be used to show that if 3a = 4b, then 4b = 3a

Now, According to the question:

3a = 4b

4b = 3a (both are equal)

This property is used to simplify the equations, to reverse the equations, and also for proofs in numerical and non-numerical logic.

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The distance between the points Q and R is 7.211 units.

In geometry, an ellipse is a two-dimensional shape, that is defined along its axes. An ellipse is formed when a cone is intersected by a plane at an angle with respect to its base. It has two focal points.

Given an equation of ellipse x²/8+y²/18 =1, a line 2y = 3x intersect the ellipse at points Q and R,

x²/8+y²/18 =1........ (i)

2y = 3x....... (ii)

Use eq 2 in 1, we get

x²/8+(3x/2)²/18 = 1

On solving,  we get,

x²/4 = 1

x = ±2

And,

(2y/3)²/8+y²/18 = 1

On solving, we get,

y = ±3

Therefore, we got, y1 = 3, y2 = -3, x1 = 2 and x2 = -2

Using the distance formula, D = √(x1-x2)²+(y2-y1)²

QR = √(-2-2)²+(-3-3)² =  7.211

|QR| = 7.211

Hence, The distance between the points Q and R is 7.211 units.

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Answer:B is the answer for this question

The point (-√2,1) can also be represented as (√3, 5.18) in polar coordinates.

To find the polar coordinates of the rectangular coordinates (-√2,1), we can use the following formulas:

r = √(x² + y²)

θ = tan^⁻1(y/x)

Plugging in the given values of (-√2,1), we get:

r = √((-√2)² + 1²) = √(2 + 1) = √3

θ = tan^⁻1(1/(-√2)) ≈ 2.0344 radians

Note that since the point (-√2,1) is in the second quadrant, we need to add π to the value of θ obtained from the inverse tangent in order to obtain an angle in the interval [0,2π). Thus, we have:

θ ≈ 2.0344 + π ≈ 5.1779 radians

Rounding to 2 decimal places as needed, we get the polar coordinates of (-√2,1) as (r,θ) ≈ (√3, 5.18).

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1. Revised Net Operating Income = $66,760

2. Revised Net Operating Income  =$64,640

3. Revised Net Operating Income  =$52,

1. If the sales volume increases by 40 units:

So, New Sales = 8,700 units + 40 units = 8,740 units

and, New Contribution Margin =

= $14.00 x 8,740 units

= 122, 360

New Fixed Expenses remain the same at $55,600

Then, Revised Net Operating Income

= New Contribution Margin - New Fixed Expenses

= 122360 - 55600

= 66,760.

2. If the sales volume decreases by 40 units:

New Sales = 8,700 units - 40 units = 8,660 units

New Contribution Margin

= 14 x 8660

= 121,240

New Fixed Expenses remain the same at $55,600

Then, Revised Net Operating Income

= New Contribution Margin - New Fixed Expenses

= 65,640

3. If the sales volume is 7,700 units:

New Sales = 7,700 units

New Contribution Margin

= 14 x 7700

= 107,800

New Fixed Expenses remain the same at $55,600

Then, Revised Net Operating Income

= New Contribution Margin - New Fixed Expenses

= 52, 200

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Answer:

The scientific notation is a method of writing very large or very small numbers in a more compact and easy to read format. It is expressed in the form of a x 10^n, where "a" is a number between 1 and 10, and "n" is an integer.

To write 464000 in correct scientific notation, we need to move the decimal point to the left until we get a number between 1 and 10. We count the number of places we moved the decimal point, and that will be the exponent of 10.

So, we can write 464000 as:

4.64 x 10^5

Therefore, the correct scientific notation of 464000 is 4.64 x 10^5.

Step-by-step explanation:

Answer: the answer is (3,-2)

Step-by-step explanation: when you rotate a point about the origin 180 degrees clockwise, (x,y) turns into (-x,-y)

therefore

(-3,2) becomes (3,-2)

I'm pretty sure

Using simple interest, it is found that the principal loan amount was of $156,491.6.

The amount of money after t years in simple interest is modeled by:

\(A(t) = A(0)(1 + rt)\)

In which:

In this problem, she paid $984 monthly for 22 years, hence:

\(t = 22, A(t) = 984(22)(12) = 259776\)

Interest rate of 3%, hence \(r = 0.03\)

Then:

\(A(t) = A(0)(1 + rt)\)

\(259776 = A(0)[1 + 0.03(22)]\)

\(A(0) = \frac{259776}{1 + 0.03(22)}\)

\(A(0) = 156491.6\)

The principal loan amount was of $156,491.6.

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Matrices are a type of data structure that can be used to represent and manipulate data in a variety of ways.

One way to use matrices to represent data is to store the data in the form of a matrix. For example, a matrix could be used to represent a table of values, where each row represents a different data point and each column represents a different attribute or feature of the data.

Matrices can also be used to manipulate data by performing mathematical operations on the matrix elements. For example, matrices can be added, subtracted, and multiplied to perform operations such as matrix addition, matrix subtraction, and matrix multiplication. These operations can be used to perform various types of data manipulation, such as combining data from different sources, transforming data, or calculating statistics.

In addition to performing mathematical operations, matrices can also be used to store and manipulate data in other ways. For example, matrices can be used to represent and manipulate images and other types of data that have a two-dimensional structure. Matrices can also be used to represent and manipulate data in higher dimensions, such as data with a three-dimensional structure.

Overall, matrices are a powerful tool for representing and manipulating data in a variety of contexts, and they are widely used in a range of fields including mathematics, computer science, engineering, and data analysis.

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Matrices are a type of data structure that can be used in a variety of ways to represent and manipulate data.

One method for utilizing grids to address information is to store the information as a framework. A table of values, for instance, could be represented by a matrix, with each row representing a distinct data point and each column representing a distinct attribute or feature of the data.

The plural form of a matrix, a rectangular array or table in which numbers or elements are arranged in rows and columns, is referred to as a matrices. They can have as many columns and rows as you want. Matrix operations include addition, scalar multiplication, multiplication, transposition, and others.

When performing these matrix operations, certain rules must be followed. For example, they can only be multiplied if the first and second columns are exactly the same, and they can only be added or subtracted if they have the same number of rows and columns.

Matrices can also be used to manipulate data by performing mathematical operations on the matrix elements. For example, matrices can be added, subtracted, and multiplied to perform operations such as matrix addition, matrix subtraction, and matrix multiplication. These operations can be used to perform various types of data manipulation, such as combining data from different sources, transforming data, or calculating statistics.

In addition to performing mathematical operations, matrices can also be used to store and manipulate data in other ways. For example, matrices can be used to represent and manipulate images and other types of data that have a two-dimensional structure. Matrices can also be used to represent and manipulate data in higher dimensions, such as data with a three-dimensional structure.

In general, matrices are extensively utilized in a variety of fields, including mathematics, computer science, engineering, and data analysis. They are a powerful tool for representing and manipulating data in a variety of contexts.

Hence the matrices be used to represent and manipulate data.

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Answer:

FRACTION FORM:   x  =  33/2

MIXED NUMBER FORM:   x  =  16 and 1/2

DECIMAL FORM:   x  =  16.5

Step-by-step explanation:

(2x - 7) / 4      =      (x + 3) / 3

First, lets get rid of those fractions by multiplying both sides by 4 x 3...  (12)

6x - 21     =     4x + 12

Next, we have to get all x's on one side, and all regular numbers on the other.

 - Add 21 to both sides (to remove -21 from the left side)

6x - 21 + 21    =    4x + 12 + 21

   *simplify*.....

6x    =    4x + 33

 - Subtract 4x from both sides (to remove it from the right side)

6x - 4x    =    4x + 33 - 4x

    *simplify*.....

2x   =   33

 - Divide both sides by two (to get x by it's self)

FRACTION FORM:   x  =  33/2

MIXED NUMBER FORM:   x  =  16 and 1/2

DECIMAL FORM:   x  =  16.5

*Hope this helps!  If you have any questions, please feel free to ask.  Good luck!*

Answer:

Stefan originally paid $120 for the bicycle and helmet.

He made $72 by selling them to Jin.

Step-by-step explanation:

Given that:

Selling price of bicycle = $176

Selling price of helmet = $16

Total price = 176+16 = $192

This is 160% of what Stefan paid originally.

Let,

x be the original amount paid by Stefan.

160% of x = 192

\(\frac{160}{100}x=192\\1.6x=192\)

Dividing both sides by 1.6

\(\frac{1.6x}{1.6}=\frac{192}{1.6}\\x=120\)

Original amount paid by Stefan = $120

Profit = 192 - 120 = $72

Hence

Stefan originally paid $120 for the bicycle and helmet.

He made $72 by selling them to Jin.

Answer:

perimeter = 12

Step-by-step explanation:

In a right-angled triangle, a² + b² = c²

where c is the hypotenuse, and a and b are opposite and adjacent, either way.

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