Solutions to Systems of Linear Inequalities in Two Variables.

As per the given measurement , the area of the paper on the bottom of the cage 2736 square inches.

The formula to calculate the volume of the prism is written as

V = l x w x h

Where l refers the length , w refers the width and h refers the height.

Here we have know that the height of 24 inches and a volume of 6,480 cubic inches.

Now we have to apply the values on the formula in order to get the width of the cage,

=> 6480 = w x 24 x 12

=> w = 6480/288

=> W = 22.5

Therefore, the area of the bottom of the cage is calculated as,

=> A = 2[(24 x 22.5) + (24 x 12) + (22.5 x 24)]

When we simplify this one then we get the value of the area as,

=> A = 2736 square inches.

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Answer:

it is not an option for the rest of your life with a new one of the year old girl who is the best friend and I have a great day to be a great day to be a great day to be a great 6

Step-by-step explanation:

or false hope I can I get to be a great day to be

Elijah has a 41% debt-to-credit ratio. This means that for every $100 of available credit, he has used up $41. This ratio is calculated by dividing total debt by total credit limit.

Elijah's debt-to-credit ratio = Total Debt/Total Credit Limit

= $2,127.50/$5,750.00

= 0.37

= 37%

= 41% (rounded to the nearest whole percent)

Elijah's debt-to-credit ratio is a measure of how much of his available credit he has used. It is calculated by dividing his total debt by his total credit limit. In this case, Elijah currently owes a total of $2,127.50 on his revolving credit account, and his total credit limit is $5,750.00. When we divide his debit of $2,127.50 by his total credit limit of $5,750.00, we get a debt-to-credit ratio of 0.37. This is equivalent to 37%. When we round to the nearest whole percent, we get a debt-to-credit ratio of 41%. This means that for every $100 of available credit, Elijah has used up $41.

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Answer: Please use this method
Periods N = 8 years x 12 = 96 periods
The interest rate I = 4.5 % per year, compounding, divided by 12 = 0.375 % for each period.
Present value PV = minus $ 6,981.46
Future value FV = $ 10,000.20

Step-by-step explanation:

The situations that could be represented by a graph with an y-intercept of 10 is given as follows:

A. Sign up fee of $10.

B. Lilly starts with $10 in her savings account.

E. Tank begins with 10 gallons of water.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

Hence options A, B and E are the correct options as they have an initial amount of $10.

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The probability that the next chew Lamonte removes from the bag will be apple chew will be 38%

Probability simply means the chance that a particular thing or event will happen. It is the occurence of likely events. It is simply the area of mathematics that deals with the numerical estimates of the chance that an event will occur

In this case, Lamonte has a bag that contains apple chews, strawberry chews, and lime chews. He performs an experiment and then randomly removes a chew from the bag, records the result, and returns the chew to the bag.

Since Lamonte performs the experiment 34 times, the probability that the next chew Lamonte removes from the bag will be apple chew will be:

= 13 / 34

= 38%

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The number of ways of dealing a five-card hand from a regular 52-card deck, such that the hand contains at least one card in each suit is 2,593,812

What is the combination?

In simple words, combination involves the selection of objects or things out of a larger group where order doesn't matter. The formula for combination helps to find the number of possible combinations that can be obtained by taking a subset of items from a larger set.

In order to find the number of ways of dealing with a five-card hand from a regular 52-card deck, such that the hand contains at least one card in each suit, we can use the combination formula.

The combination formula is used to find the number of ways to select a certain number of items from a larger group without regard to order.

First, we need to find the total number of ways to select 5 cards from a 52-card deck.

This is given by the combination formula: nCr = n! / (r!(n-r)!)

Where n is the total number of items (52) and r is the number of items to be selected (5).

So, nCr = 52! / (5!47!) = 2, 598, 960

Now we need to subtract the number of ways to select a hand that doesn't contain at least one card of each suit.

We can select 4 cards from one suit and only one card from another suit in 4C1 * 48C4 ways = 448454239/24 = 5148.

Now we can subtract this number from the total number of ways to select 5 cards from a 52-card deck to find the number of ways to select a five-card hand that contains at least one card in each suit:

2598960 - 5148 = 2,593,812

Hence, the number of ways of dealing a five-card hand from a regular 52-card deck, such that the hand contains at least one card in each suit is 2,593,812

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Answer:

The area is 254.34 [tex]yds^{2}[/tex]

The circumference is 56.52 yards.

Step-by-step explanation:

a = [tex]\pi r^{2}[/tex]

a = (3.14) ([tex]9^{2}[/tex])

a = 3.14(81)

a = 254.34

The area is 254.34 [tex]yds^{2}[/tex]

c = 2[tex]\pi[/tex]r

c = 2(3.14)(9)

c = 56.52

The circumference is 56.52 yards.

The histogram shows that the majority of the students had between 0 and 5 absences. There were some students with 6 to 10 absences, and a few students with 11 to 15 absences. There were no students with more than 15 absences.

1. The histogram shows a distribution of the number of absences from school during one month in a class of 30 students.

2. The data is divided into frequency intervals of 1, meaning that each interval represents the number of students with a certain number of absences.

3. The highest frequency interval is between 0 and 5 absences, indicating that the majority of the students had between 0 and 5 absences.

4. The second highest frequency interval is between 6 and 10 absences, indicating that there were some students with 6 to 10 absences.

5. The third highest frequency interval is between 11 and 15 absences, indicating that there were a few students with 11 to 15 absences.

6. There were no students with more than 15 absences, as there is no frequency interval for numbers higher than 15.

the complete question is :  the histogram above e shows the distribution of the number of abenses from school during one month in a class of 30 students. The data is divided into frequency intervals of 1.

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All of the statements are true.

hope this helps.

The corresponding side in the other Hexagon will be 15.81.

What is Hexagon?

In geometry, a hexagon is a six-sided polygon. Each internal angle and the side length of a regular hexagon are both 120 degrees. The formula used to determine the area of a regular hexagon is:

Area = 3 [tex]\sqrt{3}[/tex]/2 * [tex]side^{2}[/tex]

Each internal angle in an irregular hexagon can be greater than or less than 120 degrees, and the sides are uneven in length.

In our question it is given that the ratio of the area of two similar hexagons is 5:2. This indicates that the sides' square ratio is 5: 2.

Let x represent the corresponding side in the opposite hexagon.

Then, [tex]25^{2}[/tex] : [tex]x^{2}[/tex] = 5:2

= 625/[tex]x^{2}[/tex] = 5/2

= [tex]x^{2}[/tex] = (625 *2)/5

= [tex]x^{2}[/tex] = 250

= x = [tex]\sqrt{250}[/tex]

= x = 15.81 approx

Therefore, the corresponding side in the other hexagon will be 15.81.

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The convergence set of the given power series is the set of all values of x in the interval (-|x-7|, |x-7|).

In order to determine the convergence set of the given power series, we can use the ratio test.

The ratio test states that if the limit as n goes to infinity of the absolute value of aₙ₊₁ / aₙ is less than 1, then the series converges for all x in the interval (-R, R) where R is the reciprocal of the limit.

The given power series is:

sigma n = 1 to infinity (17/ (n² + 5n))×(x - 7)ⁿ

We can apply the ratio test as follows:

aₙ₊₁ / aₙ = |(17/(n+1)² + 5(n+1))×(x - 7)⁽ⁿ⁺¹⁾ | / |(17/ (n² + 5n))×(x - 7)ⁿ|

aₙ₊₁ / aₙ = |(17/(n+1)² + 5(n+1))/(n² + 5n) × |(x - 7)|⁽ⁿ⁺¹⁾ | / |(x - 7)|ⁿ

As we can see the limit as n goes to infinity of the absolute value of

aₙ₊₁ / aₙ = |(x - 7)|

Let R = |x - 7|, therefore, the series converges for all x in the interval (-R, R)

So the series converges for all values of x in the interval (-|x-7|, |x-7|).

--The given question is incomplete, answering to the question below--

"Determine the convergence set of the given power series.

sigma n = 1 to infinity ( 17/ (n² + 5n))×(x - 7)ⁿ"

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10/√3 is the length of side x in simplest radical form with a rational denominator.

The fundamentals of radical form are simple. When a number or algebraic expression is under a radical, the term refers to that form of the expression. To improve that, we can manipulate a number or an algebraic expression in radical form to convert it to simplest radical form.

Simply put, simplifying a radical eliminate any need to find more square roots, cube roots & fourth roots, etc. when expressing it in its simplest radical form. Additionally, it entails eliminating any radicals from the denominator of a fraction.

The triangle is a right triangle, therefore we will apply trigonometry

To obtain the value of X which is the hypotenuse :

We know that

Cosθ = adjacent / hypotenuse

Cos 30 = 5 / X

√3/2 = 5 / X

√3 / 2 × X = 5

X = 5 ÷ √3 / 2

X = 5 × 2 / √3

X = 10/√3

Thus, 10/√3 is the length of side xx in simplest radical form with a rational denominator.

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The linear function that models the problem of telephones call service is

A linear function consists of functions where the variables has exponents of 1.

The graph of linear functions is a straight line graph and the relationship is expressed in the form.

y = mx + c

definition of variable to suit the problem

y = output variable

m = slope

x = input variable

c = y intercept

The problem is represented using linear function as follows

c = $5

m = $0.25 per minute

x = minutes of calls

y = $5 - $0.25x + $0.75

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The value of the x is option b. 9√3.

Right angled triangle are those triangle for which one of the angle is 90 degrees.

Given figure is a right angled triangle because it is marked in the figure.

For right angled triangle, we have the Pythagoras theorem,

Hypotenuse² = Base² +  Altitude²

Given,

Length of hypotenuse = 18

Length of base = 9

Substituting in the Pythagoras theorem,

18² = 9² + x²

x² = 18² - 9²

x² = 243

x² = 81 × 3

x = √(81 × 3)

x = 9√3

Hence the value of the unknown side is 9√3.

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sum all the following and divided it my 8

Answer:

0.28 = 28/100 = 14/50 = 7/25 and 0.8 = 8/10 = 4/5

Answer:

Step-by-step explanation:

TO the center

Answer:

area: 576 cm ^2

perimeter: (48 + 24π) cm

Step-by-step explanation:

the semicircle taken out of the square (the white area) is equal to the semicircle added to the left of it. thus, we just have the area of a square. we know this because both have the same diameter and are semicircles. thus, our area is 24^2 = 576 cm ^2

for perimeter:

top: 24 cm

bottom: 24 cm

right: this is equal to half the circumference of a circle. this is because we know it's a semicircle taken out. circumference = πd = 24 * π. divide this by 2 to get 12π.

left: this is also equal to half the circumference of a circle = 12π

sum = 48cm + 24π

The amount of Indian rupees that I would be able to receive when $13 is exchanged would be = 601.2

Indian rupees.

Local currency exchange is defined as the exchange of a money currency from its local form to another form which depends of its current exchange rate.

From the expression given;

= 62.4d -210

Where d = $13, substitute into the given equation.

= (62.4 ×13) - 210

= 811.2 -210

= 601.2

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Negative, positive, zero, and undefined are the 4 types of slopes from a graph.

Negative Slope: The line goes downward to the right as x increases, where m < 0.

Positive Slope: The line goes upward to the right as x increases, where m> 0

Zero Slope: A horizontal line has a slope of zero, m = 0

For any two points, the y values will be equal to the same real number. The equation will be y = some number. Ex:y=5

Undefined Slope: A vertical line has an undefined slope, m is undefined.

For any two points, the x values will be equal to the same real number. The equation will be x = some number. Ex=6

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Answer:

x= -9.17

Step-by-step explanation:

To solve for x, we can use the information provided about the rectangle to set up an equation. Since opposite sides of a rectangle are congruent (have the same length), we know that MO = NP.

Therefore, we can set up the equation:

-6x + 10 = 65

To solve for x, we can subtract 10 from both sides:

-6x = 55

And then divide both sides by -6:

x = -9.17

The width of the bookcase is 6 feet and height is 4 feet if the carpenter expects to use 28 feet of lumber to make it.

Let w = the width and h = the height of the bookcase. The width of the lumber you are using is not given.

Also, Let the height is x.

and, the width is 3x -14.

Since, we stated that this equals 28 feet and also that w = 3h - 14, we can insert this into the equation and use it to solve for h:

Now,

The total amount of lumber used to make the bookcase is:

L = 4w + 2h             -------------------------- (1)

Now Putting Width and height in the Equation (1):

⇒ 28 = 4(3h - 14) + 2h

⇒ 28 = 12h - 56 + 2h

⇒ 28 = 14h - 56

⇒ 84 = 14h

⇒ h = 84/14

      = 6 feet

Putting the value of height, h= 6 feet in

w = 3x -14

⇒ w = 3(6) - 14 = 4.

Therefore,

The width is 4 feet and the height is 6 feet.

Complete Question:

A bookcase is to have 4 shelves including the top as pictured below.

The width is to be 14 feet less than 3 times the height. Find the width and the height if the carpenter expects to use 28 feet of lumber to make it.

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A 5th degree polynomial have five complex roots. This means that the polynomial can be written as the product of five linear or quadratic polynomials.

The general formula to calculate the roots of a 5th degree polynomial is:

[tex]x^5 + ax^4 + bx^3 + cx^2 + dx + e = 0[/tex]

The roots of the polynomial can be found by solving the following equation:

[tex]x^4 + (a - x)x^3 + (b - a x + x^2)x^2 + (c - bx + ax^2 - x^3)x + (d - cx + bx^2 - ax^3 + x^4) = 0[/tex]

To calculate the roots of the polynomial, we need to solve the quartic equation, which can be done by using the quadratic formula. Then, we can use the solutions of the quartic equation to find the roots of the 5th degree polynomial.

For example, if we have the polynomial x^5 + 2x^4 + 3x^3 + 4x^2 + 5x + 6 = 0, then the roots can be calculated as follows:

x1 = -1.7177

x2 = -0.3181

x3 = 0.5813

x4 = 1.2520

x5 = 2.1771

These are the five complex roots of the polynomial.

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Step-by-step explanation:

that means we have to calculate the volume of that cylinder ?

as the decryption says : the volume is

base area × height

or

Bh

base area = 5.4 in²

height = 8 in

the volume is

5.4 × 8 = 43.2 in³

The probability of selecting a red tile is determined by the formula number of red tiles/total number of tiles.

Probability is used to determine the chances of events.

To calculate the probability of selecting a red tile, we start by:

Get the number of red tiles

The total number of tiles

Then we need to divide the number of red tiles by the total number of tiles.

According to the question, there are 15 red tiles in a total of 60 tiles, then the probability of selecting a red tile is:

P(red) = 15/60

Divide 15 by 60

P(red) = 0.25

Thus, the probability of selecting a red tile for the given values is 0.25.

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So the time taken to fill the pool by the slower pipe is 30 hours .

As mentioned about the time in the question stated below.

Let the slower pipe's  time be x and the quicker pipe's time be x/2.

By slower pipe in an hour = 1/x, quicker pipe in an hour = 2/x, and by both = 1/10.

2/x+1/x = 1/10

we have to take reciprocal of the time taken by each pipes.

(1+2)/x = 1/10

=> 3/x = 10

=> x= 30

The slower pipe requires 30 hours of times to completely fill the pipe.

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Complete question:

A single pipe can fill a pool twice as quickly as a second one. The pool will be filled in ten hours once both pipes are opened. If only the slower pipe is utilized, how long would it take to fill the pool?

Option C connects the motion of the trumpet with Newton's first law of motion.  The trumpet starts moving because a net force overcomes the trumpet's inertia.

According to Newton's first law of motion, a body won't begin to move unless and until an outside force acts on it. When anything starts moving, it won't stop or vary its speed unless another force acts on it. The law of inertia is another name for the first law of motion.

Given, The concert band's trumpet player is Andrew. Until it is time for him to play, he keeps the instrument still at his side. He positions the trumpet next to his mouth and begins to play afterward.

First of all, there are no movements, no acceleration, and no velocity for the trumpet. Newton's first law of motion, which states that an object at rest stays at rest and an object in motion stays in motion with the same speed and direction unless acted upon by an unbalanced force, explains why the trumpet is in this state. The trumpet continues to move at zero velocity since there is no net force exerted on it.

The trumpet is then moved by Andrew. It indicates that Andrew pushed the trumpet with vigor. It caused the body to transition from the resting condition to the moving state.

Finally, we can draw the conclusion that Trumpet will remain at rest unless Andrew applies a net force that is different from zero in accordance with Newton's first law of motion.

Hence, The trumpet starts moving because a net force overcomes the trumpet's inertia.

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The resulting reflection will be (4,-5) and will be followed by (-4,-5).

A coordinate system in geometry is a system that employs one or more integers, or coordinates, to define the position of points or other geometric components on a manifold such as Euclidean space. The ordinate is the distance of a point from the x-axis scaled with the y-axis. Coordinates are the abscissa and ordinate combined. A series of data indicating a precise position. On graphs, it is typically represented by a pair of numbers: the first number represents the distance along, while the second number represents the distance up or down. For instance, the point (12,5) is 12 units long and 5 units high.

Here,

given coordinates=(4,5)

Firstly, reflecting across x axis, point (x,y) turns to (x, -y).

=(4,-5)

Secondly, reflecting (x,-y) across y-axis, point (x,-y) turns to (-x,-y).

=(-4,-5)

The resultant reflection will lead (4,-5) followed by (-4,-5).

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Formula is an act or rule that uses mathematical symbols.

Equations, equalities, identities and inequalities are a few examples of formula.

An equation, also known as an equality, formula, or identity, is a mathematical phrase that states that two or more quantities are equal to one another.

A declaration of the mathematical equivalence of two quantities. The similarity A=B signifies that "A is equal to B."

A mathematical relationship that equalizes one quantity to another is known as an identity (which may initially appear to be different).

A proof in mathematics that one quantity is bigger or smaller than another A>b is used to indicate "A is bigger than B," whereas A<B is used to indicate "A is smaller than B." The symbols A<=B and A>=B stand for "A is less than or equal to" and "A is greater than or equal to B" respectively. The terms "A is much less than B" and "A is much more than B," respectively, are denoted by the symbols A<<B and A>>B.

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