Hudson is blocking off several rooms in a hotel for guests coming to his wedding. The
hotel can reserve small rooms that can hold 3 people, and large rooms that can hold 4
people. Hudson reserved twice as many large rooms as small rooms, which altogether
can accommodate 66 guests. Write a system of equations that could be used to
determine the number of small rooms reserved and the number of large rooms
reserved. Define the variables that you use to write the system.

Check picture for full question.

The line of best fit for the given points is as follows:

y = 1.21x + 1.57.

The equation for the line of fit is obtained inserting the points of the data-set into a linear regression calculator.

The points for the data-set in this problem are given as follows:

(1,2), (2,5), (3,7), (4,2), (5,10), (6,10) and (7,9).

Inserting these points into the linear regression calculator, the line of best fit for these points is defined as follows:

y = 1.21x + 1.57.

(rounding the coefficients to two decimal places).

More can be learned about linear regression at brainly.com/question/29613968

#SPJ1

The function h(x) represents the cost of the jeans if you first use the coupon and then apply the store discount.

The function h(x) can be computed using the composition of functions f(x) and g(x). The function j(x) represents the cost of the jeans if you first apply the store discount and then use the coupon.

The function g(x) can be computed using the composition of functions g(x) and f(x).

If you use the composition h(x), you will pay $27 for the jeans. If you use the composition j(x), you will pay $30 for the jeans.

Therefore, the composition h(x) will give you a better discount since it is cheaper.

Learn more about a function on https://brainly.com/question/12431044

#SPJ1

The function that represents how much you would pay if you use the store discount first and then mall coupon is:

j(x) = 0.75*x - 5

Wewant to write a function that represents how much you would pay if you use the store discount and then tha mall coupon.

We know that:

So if first we apply the discount, then we need to do the composition:

f(g(x)) = g(x) - 5

Replacing g(x) there we will get:

f(g(x)) = g(x) - 5 = 0.75*x - 5

j(x) = 0.75*x - 5

Learn more about composition of functions:

https://brainly.com/question/10687170

#SPJ1

Answer:

see below

Step-by-step explanation:

second one

fourth one

Answer:

2x+7

Step-by-step explanation:

this is because if you rearrange the bottom equation to be in y= format, this is the solution you will find

The mean of the data be 10.5, median is 10.5 and range be 5.

The numbers are sorted, added, and then divided to determine the mean.

8 + 9 + 10 + 10 + 10 + 11 + 11 + 11 + 12 + 13 = 105

Mean = 105 ÷ 10 = 10.5

Mean = 10.5

In essence, determining the median is locating the value in a data sample that lies physically between the other numbers.

The middle number, please. Your right finger should go on 8, and your left finger should go on 13. Your right finger should be at 11, while your left finger should be at 10.

10.5 is the median because it is the midpoint number.

Subtract the largest number from the smallest number to determine the range.

13 - 8 = 5

Therefore, 5 be the range of the data.

To learn more about range refer to:

https://brainly.com/question/29387957

#SPJ1

The mean of the data be 10.5, median is 10.5 and range be 5.

To learn more about mean and median refer to:

https://brainly.com/question/14532771

#SPJ1

one may determine how much fence is necessary for a playground with a 256 square yard area is P = 1024 / x.

What is quadrilateral?

Quadrilaterals are typically four-sided closed shapes, and there are numerous varieties of them. Square, rectangle, rhombus, kite, and trapezoid are the most typical shapes. Four closed sides make up a quadrilateral. Quadrilaterals are the following figures: a four-sided figure. The form features a single set of parallel sides and no right angles.

Having four equal sides, a square is a quadrilateral. There are numerous square-shaped objects in our immediate environment. Each square form may be recognized by its equal sides and 90° inner angles. A square is a closed form with four equal sides and interior angles that are both 90 degrees. Numerous different qualities can be found in a square.

P = 4x

Area = x²

Px = 4x²

x² = Px/4

Area = Px/4

The fencing will be equal to the perimeter, with an area 256 sq yd

256 = Px/4

P = 1024 / x

Thus, using a straightforward equation, one may determine how much fence is necessary for a playground with a 256 square yard area is P = 1024 / x.

Learn more about Quadrilaterals, by the following link.

brainly.com/question/23935806

#SPJ1

Answer:

No

20 inches

Step-by-step explanation:

Area of a triangle = 1/2 × breadth × height

Therefore,

[tex] \frac{1}{2} \times 5 \times 8[/tex]

[tex] = \frac{1}{2} \times 40[/tex]

That mean

[tex] = \frac{40}{2} = 20[/tex]

(1) By 1716 different ways can the offices be filled if each person can hold at most one office.

(2) By 132 number of ways Caden can be the chairperson.

(3) By 1320 of the 1716 total ways the offices can be filled,

(1) If each person can hold at most one office, there are 13 people to choose from for the first office, 12 people remaining to choose from for the second office, and 11 people remaining to choose from for the third office.

Therefore, the number of different ways the offices can be filled is:

13 * 12 * 11 = 1716 ways

(2) If Caden is the chairperson, there are 12 people to choose from for the second office and 11 people remaining to choose from for the third office.

Therefore, the number of ways Caden can be the chairperson is:

12 * 11 = 132 ways

(3) If Caden is an officer, there are 12 people to choose from for the first office, 11 people remaining to choose from for the second office, and 10 people remaining to choose from for the third office.

Therefore, the number of ways Caden can be an officer is:

12 * 11 * 10 = 1320 ways

So, in 1320 of the 1716 total ways the offices can be filled, Caden is one of the elected officers.

For more questions on Permutation and Combination

https://brainly.com/question/26852614

#SPJ4

Answer:

(a) 6

(b) 49

Step-by-step explanation:

(a) The largest integer which is a factor of 96 and 294 should be their HCF.

Therefore, 96 = 2 × 2 × 2 × 2 × 2 × 3

294 = 2 × 3 × 7 × 7

Therefore, HCF = 2 × 3 = 6

(b) 96n should be the LCM of 96 and 294.

We know, product of two numbers = HCF × LCM

or, LCM = (96 × 294)/6 = 4704

So, 96n = 4704

or n = 49

Hope it helps.

If you have any query, feel free to ask.

When converted from active voice to passive voice, the sentences read as follows:

Active Voice refers to a sentence construction where the subject is performing the action described by the verb. It emphasizes the doer of the action.

On the other hand, Passive Voice refers to a sentence construction where the action is performed on the subject, rather than the subject performing the action. It emphasizes the action or the object affected by the action.

Learn more about Passive Voice:
https://brainly.com/question/85850
#SPJ1

According to the growth factor, starting value and the number of years passed, the number of people who would have died is 12.94×10⁷.

The number of people who would have died from AIDS in 2005 will be calculated by the formula -

f(t) = a×[tex] {b}^{t} [/tex]. In this formula, f(t) is the number of cases that occured in the mentioned number of years and t is the number of years between the start and year in question. a is strating value and b is growth.

t = 2005 - 1990

Performing subtraction on Right Hand Side of the equation

t = 15 years

Keep the values in formula

f = 1900 × 2.1¹⁵

Calculating the power

f = 1900 × 68,122.32

Performing multiplication on Right Hand Side of the equation

f = 12.94 × 10⁷

Thus 12.94×10⁷ people would have died.

Learn more about growth factor -

https://brainly.com/question/27161222

#SPJ4

Answer: It would take a total of 11 hours

Step-by-step explanation: here I am using the universal equation of DST, depending on which elements we have we will use this equation.

if we have D, multiply S*T

If we have S Divide D/T

If we have T Divide D/S

If you have any other question let me know at my discord Acathia#0103

The transformation f(x)↦ 1/8f(x) will shrink the graph of f(x) by 8 times.

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 functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

f(x) → 1/8 f(x)

This means,

The function f(x) will shrink by 8 times.

Thus,

f(x) ↦ 1/8f(x) will shrink the graph of f(x) by 8 times.

Learn more about functions here:

https://brainly.com/question/28533782

#SPJ1

Answer:

rotation on x axis;

(x, y) 》(x, -y)

So,(-6,5) is the correct answer.

Answer:

(-6,5)

Step-by-step explanation:

(x,y) ------》 (x,-y) {reflection over x-axis}

The area of the rectangular piece of land owned by the rancher is:

13.5

The area of a rectangle is a measure of the size of the rectangular space it encloses.

It is calculated by multiplying the length and the width of the rectangle. In this case, the length of the rectangular piece of land owned by the rancher is 5.4 miles and the width is 2.5 miles. To find the area, we multiply these two values.

The formula for finding the area of a rectangle is:

Substituting the values of length and width into the formula:

So the area of the rectangular piece of land owned by the rancher is 13.5. This means that if we divide the land into unit squares of 1 square mile each, we would have 13.5 such unit squares.

The area of a rectangle is an important metric in geometry and is widely used in many fields, including construction, agriculture, and real estate.

To know more about area of a rectangle, click on the link below:

brainly.com/question/20693059

#SPJ4

8639 is the value of 75 U.S. dollars in Japanese yen.

The term "yen," which refers to Chinese round coins, dates back in time (yuan). The yen was first coined in 1869, following the Meiji Restoration, and was formally recognised as the fundamental unit in the 1871 monetary reform.

"Yen" is Japanese for "circle" or "round thing." With the "New Currency Act" of 1871, the Meiji government formally adopted this currency in an effort to stabilise the nation's monetary position at the time.

The difference between US and Japanese interest rates has been a major factor in the decline of the yen. In an effort to combat the growing cost of living, the US Federal Reserve has aggressively increased its key interest rate from 0.25% to 3.25% since March.

As we see from the table that,

1 U.S dollar = 115.19 Japanese Yen

$1 = 115.19 ¥

so, $75 = 115.19 × 75¥

$75 = 8639.25¥  ≈ 8639¥

To know more about Japanese yen refer to:

https://brainly.com/question/29115196

#SPJ1

Combinations and sequences are widely used in mathematics to explain and assess situations in which the order or selection of components might influence the final result.

A combination in mathematics is a selection of elements from a set with distinct members, where the order of selection is irrelevant. A combination is a mathematical approach for determining the number of potential arrangements in a set of objects when the order of the selection is irrelevant. You can choose the components in any order in combinations. A combination is a method of picking elements from a collection when the order of selection is irrelevant. Assume we have three integers P, Q, and R. Combination defines how many possibilities we may choose two numbers from each set.

Here,

A combination is a grouping of things from a bigger set in which the order of the components is irrelevant. A sequence is a collection of elements that are ordered in a precise order. Combinations and sequences are frequently used in mathematics to describe and evaluate situations where the order or selection of components might impact the final outcome, such as in combinatorics, probability, and statistics.

To know more about combination,

https://brainly.com/question/20211959

#SPJ4

Complete question:

A combination of values that, when arranged correctly, result in a final value. true/false

For the required value of the given complex numbers z₁z₂ = 32(cos 255° + isin 255°).

Complex numbers are those that expand on the idea of real numbers by incorporating an illogical element.

The formula for a complex number is "a + bi," where "a" and "b" are real numbers and "i" is the imaginary unit, which is equal to the square root of -1.

"A" stands for the complex number's real component, and "b" stands for the imaginary component.

We multiply the magnitudes of two complex numbers and add their arguments to determine their product.

Let's compute z₁z₂ with the supplied values.

Given:

z₁ = 8(cos 45° + isin 45°)

z₂ = 4(cos 210° + isin 210°)

We add the arguments and multiply the magnitudes to find z₁z₂:

Magnitude of z₁ = 8

Magnitude of z₂ = 4

Argument of z₁ = 45°

Argument of z₂ = 210°

Now, let's calculate z₁z₂:

Magnitude of z₁z₂ = (Magnitude of z₁) × (Magnitude of z₂) = 8 × 4 = 32

Argument of z₁z₂ = (Argument of z₁) + (Argument of z₂) = 45° + 210° = 255°

Therefore, z₁z₂ = 32(cos 255° + isin 255°).

Learn more about complex numbers click;

https://brainly.com/question/20566728

#SPJ6

The correct question =

Given z₁ = 8(cos 45° + isin 45°) and z₂ = 4(cos 210° + isin 210°), what is z₁z₂?

Yes, the vectors v1 = (0,0,-3), v2 = (0,-3, 9), and v3 = (4,-2,-6) do span ℝ3.  This is because any 3 vectors in ℝ3 will span the entire space, meaning that any vector in ℝ3 can be written as a linear combination of these 3 vectors.

To determine if a set of vectors spans a space, we can create a matrix with the vectors as columns and row reduce it to see if there are any free variables. If there are no free variables, the vectors span the space.

The matrix with v1, v2, and v3 as columns is:

| 0 0 4 |

| 0 -3 -2 |

| -3 9 -6 |

Row reducing this matrix gives us:

| 1 0 0 |

| 0 1 0 |

| 0 0 1 |

Since, there are no free variables, the vectors v1, v2, and v3 do span ℝ3.

know more about vectors here

brainly.com/question/29740341#

#SPJ12

The required maximum amount of money the salesperson earns for the entire year is given as $5400.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Here,
Let the total amount earned be x,
According to the question,
x = 2400 + 250×12
x = $5400

Thus, the required maximum amount of money the salesperson earns for the entire year is given as $5400.

Learn more about models here:
https://brainly.com/question/22591166
#SPJ1

The original number of CDs is between 1000 and 1500.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

Number of copies of a popular CD left to be sold in the store = 20

According to question, this is between 15 and 1.5% of the original number of copies of the CD in the store.

Let the original number of copies of the CD be 'x'.

Now, 20 is equal to 1% of the original number of copies of the CD,

1% of x = 20

1/100 of x= 20

x= 2000

Or if 15 is equal to 1.5% of the original number

1.25% of x= 20

1.25/100 x = 20

x = 1600

Hence, the CDs is between 1000 and 1500.

Learn more about Algebra here:

https://brainly.com/question/24875240

#SPJ1

The range of the new score distribution will be greater than the range of the original score distribution.

The range of a set of scores is the difference between the highest and the lowest scores in the set. Adding 5 bonus points to the 10 highest scores in the original set will increase the highest scores and therefore increase the range of the new score distribution.

The range of the original score distribution represents the spread of scores between the highest and lowest scores in the original set, and increasing the highest scores will increase the spread of scores between the highest and lowest scores in the new set, resulting in a greater range.

You can learn more about distribution at

https://brainly.com/question/27905732

#SPJ4

26x - 52y  is the equivalent expression.

2(13a - 5) is the equivalent expression.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

-13 (-2x + 4y)

= -13 x -2x+ -13 x 4y

= 26x - 52y

Now,

26a - 10

Taking out a common factor.

= 2 (13a - 5)

Thus,

26x - 52y and 2(13a - 5) are the equivalent expression.

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ1

The true statement about the functions is that that graphs are perpendicular lines

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

y = 3/4x + 7

y = -4/3x + 7

A linear equation is represented as

y = mx + c

Where

slope = m

This means that the slopes are

3/4 and -4/3

The above slopes are opposite reciprocal

i.e.

3/4 * -4/3 = -1

Hence, they are perpendicular lines

Read more about linear function at

https://brainly.com/question/15602982

#SPJ1

Answer: The slope between the points (0,-5) and (-2,3) is (-3 - (-5)) / (-2 - 0) = -8 / -2 = 4.

Step-by-step explanation:

The width of the enlargement would be 34.2857 cm.

The distance separating an object's ends is its length. The longest dimension is this one. The width of an object is the separation between its two sides. The shortest dimension is this one.

Initial dimension of shorter side = 10 cm

Initial dimension of longer side = 7 cm

Final dimension of shorter side = 24

Final dimension of longer side = x cm

The enlargement always ensure the aspect ratio = longer side / shorter side

10/7 = x/24

Solving for x, we get

[tex]$\frac{x}{24}=\frac{10}{7}$$[/tex]

simplifying the above equation, we get

[tex]$\frac{24 x}{24}=\frac{10 \cdot 24}{7}$$[/tex]

[tex]$x=\frac{240}{7} cm$$[/tex]

Therefore, the  value of x be 34.2857 cm.

To learn more about width refer to:

https://brainly.com/question/25292087

#SPJ1

The simplest form of the function is f(x) = x2. The graph is a parabola often called the basic parabola.

A parabola is an approximately U-shaped, mirror-symmetrical plane curve in mathematics. It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves. A parabola can be described using a point and a line.

Three different parabolas exist. Vertex form, standard form, and intercept form are the three forms. You can access a unique key feature for the graph on each form.

Any point on a parabola is at an equal distance from both the focus, a fixed point, and the directrix, a fixed straight line. A parabola is a U-shaped plane curve.

Solve f{x}=x-2?

f(x)=x-2    x∈R

x≤0

x-2≤2

Range of f(x)=[∞,2)

To learn more about parabola refers to:

https://brainly.com/question/29635857

#SPJ1

the area of the given figure will be 13.8 cm².

What is are of triangle?

The territory included by a triangle's sides is referred to as its area. Depending on the length of the sides and the internal angles, a triangle's area changes from one triangle to another. Square units like m2, cm2, and in2 are used to express the area of a triangle.

The area of triangle = 1/2 (hb)

The sum of all angle of triangle = 180

A triangle with side 6.9 cm extends to form a second right triangle with a height of 4cm.

So the area will be A = 1/2 *6.9 * 4

A = 13.8 cm²

Hence the area of the given figure will be 13.8 cm².

Learn more about triangle, by the following link

brainly.com/question/17335144

#SPJ1