Examine the statements below. Select each situation that would require the application of surface area.



Determining the amount of space inside a jewelry box.


Determining the amount of wrapping paper needed to wrap a birthday gift.


Determining the amount of wood needed to build a tree house.


Determining the amount of carpet needed to cover the floor of a room.


Determining the amount of water needed to fill a pool.


Determining the area of the shadow of a pine tree.

Answer:

Step-by-step explanation:

screen shot attached

Answer:

A

Each side must intersect exactly two others sides but only at their endpoints. The sides must be noncollinear and have a common endpoint.

Complete Question:

There are 8 rows and 8 columns, or 64 squares on a chessboard.

Suppose you place 1 penny on Row 1 Column A,

2 pennies on Row 1 Column B,

4 pennies on Row 1 Column C, and so on …

Determine the number of pennies in Row 1

Determine the number of pennies on the entire chessboard?

Answer:

255 in the first row

18,446,744,073,709,551,615 in the entire board

Step-by-step explanation:

Given

\(Rows = 8\)

\(Columns = 8\)

Solving (a): Number of pennies in first row

The question is an illustration of geometric sequence which follows

\(1,2,4....\)

Where

\(a =1\) --- The first term

Calculate the common ratio, r

\(r = \frac{T_2}{T_1} = \frac{4}{2} = 2\)

The number of pennies in the first row will be calculated using sum of n terms of a GP.

\(S_n = \frac{a(r^n - 1)}{n - 1}\)

Since, the first row has 8 columns, then

\(n = 8\)

Substitute 8 for n, 2 for r and 1 for a in \(S_n = \frac{a(r^n - 1)}{r - 1}\)

\(S_8 = \frac{1 * (2^8 - 1)}{2 - 1}\)

\(S_8 = \frac{1 * (256 - 1)}{1}\)

\(S_8 = \frac{1 * 255}{1}\)

\(S_8 = 255\)

Solving (b): The entire board has 64 cells.

So:

\(n = 64\)

Substitute 64 for n, 2 for r and 1 for a in \(S_n = \frac{a(r^n - 1)}{r - 1}\)

\(S_{64} = \frac{1 * (2^{64} - 1)}{2 -1}\)

\(S_{64} = \frac{(2^{64} - 1)}{1}\)

\(S_{64} = \frac{(18,446,744,073,709,551,616 - 1)}{1}\)

\(S_{64} = \frac{18,446,744,073,709,551,615}{1}\)

\(S_{64} = 18,446,744,073,709,551,615\)

Answer:

61 : 60

Step-by-step explanation:

Well to make a ratio, you just have to have David time : Mark time

So if you convert Mark's time into minutes, it is 60 minutes

61 : 60

That's the simplest form.

Answer:

ratio of David's time to Mark's time = 61/60 = 61:60 = 61 to 60

Step-by-step explanation:

A ratio is a way of comparing numbers by dividing one number by the other. In order to write a ratio, both numbers have to be in the same units.

David takes 61 minutes to do a task.

Mark 1 hour to do the same task. 1 hour = 60 minutes.

You are comparing David's time to Mark's time.

The ratio of David's time to Mark's time is 61 minutes to 60 minutes.

ratio of David's time to Mark's time = 61/60 = 61:60 = 61 to 60

Answer:

9

Step-by-step explanation:

Because each new term is obtained by adding 2 to the previous term, we identify this as an arithmetic sequence.  The first term. a(1). is 3 and the common difference (d) is 2.  

The general formula for an arithmetic sequence is a(n) = a(1) + d(n -1)

Here the specific formula is a(n) = 3 + 2(n - 1)

and the fourth term, a(4), is 3 + 2(4 - 1), or 3 + 6, or 9

The solution to the initial value problem is \(\(y(\theta) = \frac{3}{4} e^\theta + \frac{1}{4} e^{-\theta} + \frac{1}{2} e^{3\theta}\)\).

The complementary function is given by:

\(\[ y_c(\theta) = c_1 e^\theta + c_2 e^{-\theta} \]\)

The particular solution is:

\(\[ y_p(\theta) = \frac{1}{2} e^{3\theta} \]\)

Therefore, the general solution is:

\(\[ y(\theta) = y_c(\theta) + y_p(\theta) = c_1 e^\theta + c_2 e^{-\theta} + \frac{1}{2} e^{3\theta} \]\)

Applying the initial conditions \(\( y(0) = 1 \)\) and \(\( y'(0) = -1 \)\), we have the following system of equations:

\(\[\begin{align*}c_1 + c_2 + \frac{1}{2} &= 1 \\c_1 - c_2 + \frac{3}{2} &= -1 \\\end{align*}\]\)\(c_1 + c_2 + \frac{1}{2} &= 1 \\c_1 - c_2 + \frac{3}{2} &= -1 \\\)

Solving this system, we find \(\( c_1 = \frac{3}{4} \) and \( c_2 = \frac{1}{4} \)\).

Hence, the final solution to the initial value problem is:

\(\[ y(\theta) = \frac{3}{4} e^\theta + \frac{1}{4} e^{-\theta} + \frac{1}{2} e^{3\theta} \]\)

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Complete Question:

Find the solution to the initial value problem. \(y''(\theta)−y(\theta) = 4sin(\theta)-3e^{3\theta}, y(0)=1, y'(0)=-1\)

Answer:

I think the answer is 255cm squared

Step-by-step explanation:

If you look at the shape it has 2 shapes. A rectangle and a triangle.

17-10 to get the height of the triangle = 7

22-12 to get the base of the triangle = 10

The area to find a triangle is 1/2 * b * h

= (7 *10) / 2

= 35

To find the rectangle =

22 * 10

= 220

To find the area of the whole thing =

35 (triangle) + 220 (rectangle) = 255cm squared

Answer:

255 cm^

Step-by-step explanation:

If you cut your shape into a triangle and rectangle...or a trapezoid and a rectangle, then add the areas together.

Area of a rectangle is just length × width.



Area of a triangle is:

A = 1/2bh

Area of a trapezoid is:

A = 1/2(b1 + b2)

see image to see two different ways to cut the whole shape into two pieces. Then we calculate the total by adding the areas of the parts.

see image.

The Fibonacci series in which 0 does not consider is 1,2,3,5,8,13,21,34,…

A series of numbers known as the Fibonacci sequence is one in which each succeeding number is created by adding the two numbers that came before it. The Fibonacci sequence is named for the Italian mathematician who created it.

The standard Fibonacci series

0,1,1,2,3,5,8,13,21,34,…

When 0 is not considered as Fibonacci number, the series can be rewritten as,

1,2,3,5,8,13,21,34,…

The Fibonacci series where number 0 is excluded is 1,2,3,5,8,13,21,34,…

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Answer:

Two angles forming a linear pair are always supplementary. Linear pair of angles are formed when two lines intersect each other at a single point, and the sum of angles of a linear pair is always equal to 180°.

Step-by-step explanation:

Two angles forming a linear pair are always supplementary. Linear pair of angles are formed when two lines intersect each other at a single point, and the sum of angles of a linear pair is always equal to 180°.

Question :

Answer :

They are formed when two lines intersect each other at one point and the sum of angles is 180⁰ .

Using the given value numbers, we can represent the number as 203,167.

To represent the given number using the value numbers 3, 80, 7, 30, 200,000, 3,000, and 50, we need to understand the place value system. In this system, each digit's position determines its value relative to the other digits in the number.

Let's break down the given value numbers:

3 represents the digit 3.

80 represents the digit 8 in the tens place and 0 in the ones place.

7 represents the digit 7.

30 represents the digit 3 in the tens place and 0 in the ones place.

200,000 represents the digit 2 in the hundred thousands place and all other digits as zeros.

3,000 represents the digit 3 in the thousands place and all other digits as zeros.

50 represents the digit 5 in the tens place and 0 in the ones place.

Now let's combine these value numbers to form a single number:

(200,000) + (3,000) + (80) + (30) + (7) + (50)

To simplify this expression, we can add up each component:

200,000 + 3,000 + 80 + 30 + 7 + 50 = 203,167

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Inequality shows a relationship between two numbers or two expressions.

The solution for the inequality is x ≤ -2.

The graph is given below.

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal =

Greater than and equal=

Example:

2x > 4

We have,

x + 7 ≤ 5

Subtract 7 on both sides we get,

x + 7 - 7 ≤ 5 - 7

x ≤ -2

This inequality can be graphed as given below:

x is equal and less than -2.

Thus,

The solution for the inequality is x ≤ -2.

The graph is given below.

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There are 5 ways that the sum of the dice be equal to 6 if a pair of distinct dice are rolled one time

It is the ordered arrangement of members belonging to a set with no repeats.

Analyzing the possibilities for the sum of the dice be equal to 6, assuming that each die has six sides:

Red die = 6 sides

Blue die = 6 sides

The possibilists are:

(Bleu, red)

(1,5)

(2,4)

(3,3)

(4,2)

(5,1)

There are 5 ways to get at sum of 6 if a pair of distinct dice are rolled one time

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Answer:

3

Step-by-step explanation:

There are 4.5 diamonds, which represent 9 hours in total.

This corresponds to 9/3 = 3 circles.

Answer:

3 circles

Step-by-step explanation:

For the pig, it's 4.5 squares. Each square is two hours, and 4.5*2 is 9. Each circle is 3 hours, and 9 divided by 3 is 3. Therefore, the answer is 3 circles.

Answer:

x=27

Step-by-step explanation:

the attached photo might help you

Answer:

Step-by-step explanation:

You want to know the number of vases of each type of flower if there are 36 vases containing 125 flowers, with 3 daisies or 4 lilacs in a vase.

Let x and y represent daisy and lilac vases, respectively. The problem statement gives two relations:

  x +y = 36 . . . . . total number of vases

  3x +4y = 125 . . . total number of flowers

Substituting for x, we have ...

  x = 36 -y

  3(36 -y) +4y = 125

  108 +y = 125

  y = 13

  x = 36 -13 = 23

There are 23 vases of daisies and 13 vases of lilacs.

The expression that is equivalent to the expression d+d+d+d is option B) 4d.

In the given expression, we have the variable d added four times: d+d+d+d. To simplify this expression, we can combine the like terms. Adding d four times is the same as multiplying d by 4. Therefore, the simplified expression is 4d.

Option A) 4+d is not equivalent because it represents the addition of 4 and d, rather than multiplying d by 4.Option C) d² + d² represents the sum of two squared terms, which is not the same as the original expression.

Option D) d4 is not equivalent either, as it represents the product of d and 4, rather than adding d four times.The expression equivalent to d+d+d+d is option B) 4d, which simplifies the repeated addition of d into the product of 4 and d.

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The transformation on a line such that a line is obtained which is pependicular to previous line is possible only when it is reflected through y = x axis. This can be understood as,

When line is reflected about x-axis, the x coordinate remain same where as y-coordinate changes in opposite sign with same magnitude. So reflection of line x = 3 about x axis remain same.

Simillarly reflection of line x = 3 about x = 1 remain same as x = 3.

The reflection of line x = 3 about y-axis results n a parallel line passing through x = -3.

So answer is reflection across y = x.

Answer: 2 red balloons and 4 white balloons in each bunch

Step-by-step explanation:

divide 16/8 = 2 balloons in each bunch

divide 32/8 = 4 balloons in each bunch

Answer:

A closed cone has 0 verticals.. but 1 vertice

Step-by-step explanation:

Answer:

no

Step-by-step explanation:

Answer:

No, a parallelogram means that the opposite sides don't meet (are parallel), so a triangle isn't. A triangle has only three sides, and they all meet up.

Step-by-step explanation:

Answer:

J. (2, -3)​

Step-by-step explanation:

1. Substitute y = x - 5 in for y in the other equation:

5x + 2(x - 5) = 4

2. Simplify:

5x + 2x - 10 = 4 (distributed the 2)

7x - 10 = 4

3. Isolate for x:

7x - 10+10 = 4+10

7x = 14

7x/7 = 14/7

x = 2

4. Plug the new x value into an equation and solve for y:

y = 2 - 5

y = -3

hope this helps!

Answer:

If you multiply the numbers you will get

0.030634

By using Stoke's theorem ∬ S [ (∇ × v) ⋅ n ] dσ  is  6π. So, option e is the correct answer.

To apply Stoke's theorem and evaluate the surface integral, we need to calculate the curl of vector field v(x, y, z) and then find its dot product with the unit normal vector n.

Let's start by finding the curl of v(x, y, z):

∇ × v =

| i j k |

| ∂/∂x ∂/∂y ∂/∂z |

| 3z² 3x -4y³|

Applying the determinant expansion along the top row, we have:

∇ × v = (∂/∂y)(-4y³) - (∂/∂z)(3x) i

+ (∂/∂z)(3z²) - (∂/∂x)(-4y³) j

+ (∂/∂x)(3x) - (∂/∂y)(3z²) k

Simplifying, we get:

∇ × v = -12y² i + 3z² j + 3 k

Now, we need to find the dot product of ∇ × v with the unit normal vector n. Since the upper half of the unit sphere has positive z-component, the unit normal vector for this surface is n = (0, 0, 1).

Therefore, the dot product (∇ × v) ⋅ n simplifies to:

(-12y² i + 3z² j + 3 k) ⋅ (0, 0, 1)= 3

Now, we can evaluate the surface integral using Stoke's theorem:

∬ S [ (∇ × v) ⋅ n ] dσ = ∬ S (3) dσ

Since the surface S is the upper half of the unit sphere, the area element dσ can be written as dσ = r² sinθ dθ dφ, where r = 1 is the radius of the unit sphere, θ ranges from 0 to π/2, and φ ranges from 0 to 2π.

Therefore, the surface integral becomes:

∬ S (3) dσ = ∫∫ (3) r² sinθ dθ dφ

= 3 ∫[0 to 2π] ∫[0 to π/2] (1)² sinθ dθ dφ

= 3 ∫[0 to 2π] [-cosθ] [0 to π/2] dφ

= 3 ∫[0 to 2π] 1 dφ

= 3 (2π)

= 6π

Hence, the correct answer is e) 6π.

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Step-by-step explanation:

Put the what given of y in equation 2 to equation of 1

So you get

\( \frac{4}{5} x + \frac{2}{5} x - 7 = - 4 \\ \frac{6}{5} x = 3 \\ x = \frac{15}{6 } \\ x = \frac{5}{2} \)

Then put the value of x in second equation

You will get

\(y = - \frac{2}{5} \times \frac{5 }{2} + 7 \\ \\ y = 6\)

Based on the information, we can determine convergence or divergence of series.The given options do not provide a clear representation of potential outcomes.It is not possible to select correct option.

The given series is "nvž enn |||-) En=12 100 1-) Σπίο 3* 2"-1 ||-) En=2 n". In the series, we have the characters "nvž enn |||-)" which indicate the series notation. The characters "En=12 100 1-" suggest that there is a summation of terms starting from n = 12, with 100 as the first term and a common difference of 1. The characters "Σπίο 3* 2"-1 ||-) En=2 n" indicate another summation, starting from n = 2, with a pattern involving the operation of multiplying the previous term by 3 and subtracting 1.

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Answer:

1. $16 = $320

2. $23 = $460

Step-by-step explanation:

The population of Melonville follows a population growth, and the population of Melonville in 1993 is 201

Let the population in 1991 be x².

The 1992 population is

P₂ = y² + 1 = x² + 100

This means that:

x² + 100 = y² + 1

Rewrite as:

y² - x² = 100 - 1

y² - x² = 99

Express as difference of two squares

(y - x)(y + x) = 99

Express 99 as 9 * 11

(y - x)(y + x) = 9 * 11

Rewrite as:

(y - x)(y + x) = (10 - 1) * (10 + 1)

By comparison, we have:

y = 10 and x = 1

So, the populations are:

P₁ = x² --- 1991

P₂ = x² + 100 --- 1992

P₃ = x² +100 +100 --- 1993

Substitute 1 for x

P₃ = 1² +100 +100

Evaluate

P₃ = 201

Hence, the population of Melonville in 1993 is 201

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There are many ways that baseball players and basketball players can be selected from a group of athletes who play both sports.

One way is to use a selection process that allows for both players to be chosen based on their individual merits. For example, a team could use a combination of criteria such as previous performance, physical fitness, athleticism, and skill level to select the most suitable players for each sport. This could be done by assigning each player a score based on these criteria and then selecting the highest scoring players for each position.Another way to select players from a group of athletes playing both sports is to use a draft system. This system would allow teams to choose players based on the team's needs, rather than individual merits. This could be done by assigning each player an overall ranking and then allowing teams to select players in order of their ranking. A third way to select players from a group of athletes playing both sports is to have a tryout or combine where players can showcase their skills and abilities. This allows teams to evaluate players in a more comprehensive way and make sure they are selecting the best players for their team. Finally, teams can also use a combination of the above methods to select players. For example, they could use a combination of a draft system, individual merit selection, and a tryout/combine to get a better idea of which players are the best fit for their team. Overall, there are many different ways that teams can select baseball players and basketball players from a group of athletes playing both sports. The method chosen will depend on the team's individual needs and preferences.

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How many different combinations of baseball players and basketball players can be selected from a group of baseball players and basketball players?