To rent a certain meeting room, a college charges a reservation fee of $35 and an additional fee of $5.80 per hour. he history club wants to spend less than $69.80on renting the meeting room. What are the possible amounts of time for which they could rent the meeting room?

The total monthly cost of the phone bill is represented by y and the total number of minutes is represented by x. Then, a sample piece-wise function to describe their relationship is written as [tex]y(x)=\begin{cases} {{\$35\;&\mathrm{if}\;0\leq x \leq300} \\ {\$[35+(x-300)]\;&\mathrm{if}\;x > 300}} \end{cases}[/tex]

A function that is produced from bits of multiple functions over various periods is known as a piecewise function. By providing the input value, one can produce this function that operates differently.

Given the total cost of the phone bill is represented by y and the total number of minutes is represented by x. To write a piecewise function, let's consider an example of this.

For $35 per month, 300 minutes are included in a cell phone package. $0.25 will be charged for each additional minute. Then, the piecewise function for this is represented by,

[tex]y(x)=\begin{cases} {{\$35\;&\mathrm{if}\;0\leq x \leq300} \\ {\$[35+(x-300)]\;&\mathrm{if}\;x > 300}} \end{cases}[/tex]

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The graph of the piece-wise function f(x) is given by the image presented at the end of the answer.

A piece-wise function is a function that has different definitions, depending on the input of the function.

The extreme points of the function in this problem are given as follows:

Hence the graph of the function is composed by:

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The domain of the function is  x ≤ 1.

x ≤ 1 because your domain cannot have h(x) because that is your function and would be your range but in this case it is your domain and your domain, also known as the x coordinate, would have to be the number on the x axis that your line starts at, which would be your domain.

Your line starts on line 1 on the x axis, which would be your domain.

Consider the function y = f(x), which has the independent variable x and the dependent variable y. A value for x is said to be in the domain of a function f if it successfully allows the production of a single value y using another value for x.

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Answer:

13F

Step-by-step explanation:

-15+28

On rationalizing the expression 7/(2-√5) 7/(2-√5), the value is obtained as -7 (2 + √5).

What is rationalization?

In order to get rid of the irrational number in the denominator, the procedure of rationalisation is performed in elementary algebra. There are numerous rationalisation strategies that are used on the denominator.

The given expression is - 7/(2-√5).

Multiply the denominator and numerator by the (2 + √5).

= 7 × (2 + √5)/(2-√5) × (2 + √5)

= (14 + 7√5)/(2)² - (√5)²

Simplify it further -

= (14 + 7√5)/4 - 5

= (14 + 7√5)/-1

= -(14 + 7√5)

= -7 (2 + √5)

Therefore, the simplified expression is -7 (2 + √5).

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Answer:

X= k/2

Y= -k/2

Step-by-step explanation:

X= k/2

Y= -k/2

Answer:

it takes 8.8 years for the value of the account to reach $5,920.

Step-by-step explanation:

We can use the formula A = P(1+r/n)^(nt) to find the time it takes for Ella's investment to reach $5,920.

A is the future value of the investment, P is the present value (initial investment), r is the interest rate, n is the number of compounding periods per year and t is the time in years.

Plugging in the given values:

5920 = 4900(1 + 0.03/12)^(12t)

To solve for t, we need to take the natural logarithm of both sides of the equation and divide by the logarithm of (1+0.03/12)

t = ln(5920/4900)/(12*ln(1+0.03/12))

t = approximately 8.8 years (to the nearest tenth of a year)

So it takes 8.8 years for the value of the account to reach $5,920.

Answer:

yidyf

Step-by-step explanation:

jcyfifjfjhfueujevevve

The ball will drop 320 meters in the next 8 seconds, which can be calculated using the equation d = (t^2) * k, where d is the distance (in meters) dropped, t is the time (in seconds), and k is the constant.

In the next 8 seconds, the ball will drop 320 meters. This can be calculated by using the equation [tex]d = (t^2) * k[/tex], where d is the distance (in meters) dropped, t is the time (in seconds), and k is a constant. Since the ball dropped 80 meters in the first 4 seconds, we have d = (4^2) * k, or k = (d/16). Plugging this value of k into the equation, we get d = (t^2) * (d/16), which simplifies to d = (t^2) * (80/16). In the next 8 seconds, t = 8, so d = (8^2) * (80/16) = 320 meters.

The ball will drop 320 meters in the next 8 seconds, which can be calculated using the equation d = (t^2) * k, where d is the distance (in meters) dropped, t is the time (in seconds), and k is the constant.

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The expression for c and d in terms of a are c = a²+8  and d = 4a

An algebraic expression is an expression that is made up of variables and constants along with algebraic operations such as addition, subtraction, multiplication, exponent, etc.

(a+√8)²can be written in the form c+d√2 by expand the bracket. That is:

(a+√8)² = (a+√8)(a+√8)

(a+√8)² = a(a+√8) + √8(a+√8)

(a+√8)² = a² + a√8) + a√8 + 8

(a+√8)² = a² + 2a√8 + 8

(a+√8)² = a² + 4a√2 + 8

(a+√8)² = (a²+8) + 4a√2

Thus, c = a²+8  and d = 4a

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Note that the median in the data set given above is: 38.5.

The median is the value that separates the upper and lower halves of a data sample, population, or probability distribution in statistics and probability theory. It is sometimes referred to as "the middle" value in data collection.

Not that in the above case, the median is arrived at by finding adding the two central values (37 and 40) and dividing the result by 2. This is because the total number of data in the set is even. Where the total number of values is odd, then the central number, when the avalues are arranged in ascending order is the median.

Thus, median = 37 + 40

= 77/2

Median = 38.5

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According to the area the amount needed to cover the lawn with grass seed is £121.8075

In math the term called area is defined as the total space occupied by the object.

Here we have know that the Length is 100m and the Breadth is 45m :-

Then the area is calculated as,

=> A = 100 × 45 = 4500m²

Here we have to do the calculation for 3 circular pond, then it can be calculated as,

=> 1st pond = 20/2 = 10m

=> 2nd pond = 10/2 = 5m

=> 3rd pond = 5/2 = 2.5m

Then the Area of 3 circular pond is calculated as,

=> A =  (π × 10² + π × 5² + π × 2.5²)

Take the term π as common then we get,

=> A = π × ( 100 + 25 + 6.25)

Apply the value of π = 22/7, then we get,

=> A =  22/7 × (125 + 6.25)

When we simplify this one then we get

=> A = 22/7 × 131.25 = 2887.5/7

Therefore the area of the pond is  412.5m²

Now we need to do the calculation for required area for covering lawn, that can be written as

=> Required area = Area of lawn - Area of 3 circular ponds

Apply the value on it,

=> Required area = 4500 - 412.5 = 4087.5m²

As we know that packet of grass seed covers 50m, then it is simplified as,

=> Required Area = 4087.5/50 = 81.75m²

Now we need to do the calculation for cost of covering lawn is written as

=> Total cost = 81.75 × 1.49 = £121.8075

Therefore the cost of covering lawn with grass seed is £121.8075

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The measure of an exterior angle at the fifth vertex is 62°.

A pentagon has 5 straight sides. The shape must also be closed.

A convex pentagon has no angles pointing inwards, and no internal angles can be more than 180°.

When all angles are equal and all sides are equal it is regular, otherwise, it is irregular.

The sum of exterior angles is 360°.

To know the angle of the fifth vertex add the remaining four vertexes and subtract from the sum of exterior angles.

Given 4 vertexes of the pentagon are 83°, 83°, 26°, and 46°.

By adding these we get a total of 238°

Fifth vertex=360°-238°

Fifth vertex=62°

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The linear equation that represent the total cost over x GB is given as 10x + 20. The total cost when over 2 GB is $40

An equation is an expression that shows the relationship between numbers and variables.

The slope intercept form of linear equation is:

y = mx + b

Where m is the rate of change and b is the initial value of y

Let y represent the total cost over x GB of data.

y = mx + b

The data plan cost $20 per month and $10 per GB over 3 GB.

Hence:

m = 10, b = 20; y = 10x + 20

Total cost when over by 2 GB = 10(2) + 20 = $40

Total cost when over by x GB = 10x + 20

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1. One detail that establishes the story's regionalism is the setting, which takes place in a small mining town in the West called Poker Flat.

2. The author, Harte, conveys a culture about the West that emphasizes the harsh and unforgiving nature of the land and its people. The characters in the story struggle against the harshness of the environment and the moral ambiguity of the mining town.

3. If you were living in the East in the late 1800s, you would find interesting the story's depiction of the West as a land of opportunity and adventure, but also one of danger and hardship. The story would also provide a glimpse into the everyday lives of people living in the West, which would likely be quite different from what they were familiar with in the East.

4. The characters band together because they are all outcasts, each in their own way, and they find comfort in each other's company. They are all looking for a sense of community and belonging that they have been denied in Poker Flat.

5. The character that surprised me the most was Mother Shipton. I was surprised by her sudden change of character when she revealed her past and her true identity as a former prostitute, which was quite different from the religious and moral woman she had pretended to be. I think this was surprising because it shows how people can hide their past and their true selves in order to fit in and be accepted by society.

Another detail is the use of Western colloquialism and dialect in the dialogue of the characters.

Lastly, the story also includes a description of the harsh winter conditions and rugged terrain of the Sierra Nevada mountains, which is specific to that region.

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Answer: The best value for the cat food, milk and toys is Supermarket C. They are offering the 5 kg bag of cat food for $400 each/3 bags for $1,080, 1 litre of milk for $1100, and cat toys for $1799. Supermarket A is offering the 5 kg bag of cat food for $400 each/3 bags for $1,100, 1 litre of milk for $1,900, and cat toys for $1,900. Supermarket B is offering the 5 kg bag of cat food for $600 each/3 bags for $1,660, 1 litre of milk for $1,099, and cat toys for $2,300. Supermarket C has the lowest prices for all three items, so it is the best value.

Step-by-step explanation:

[tex]\cfrac{(2x^{-1} y^2)^{\frac{1}{4}}}{(12x^2 y^{-1})^{\frac{1}{2}}}\implies \cfrac{2^{\frac{1}{4}} x^{-\frac{1}{4}} y^{\frac{2}{4}}}{12^{\frac{1}{2}} x^{\frac{2}{2}} y^{-\frac{1}{2}}}\implies \cfrac{2^{\frac{1}{4}} x^{-\frac{1}{4}} y^{\frac{1}{2}}}{12^{\frac{1}{2}} x y^{-\frac{1}{2}}}\implies \cfrac{2^{\frac{1}{4}} y^{\frac{1}{2}}y^{\frac{1}{2}}}{12^{\frac{1}{2}} xx^{\frac{1}{4}} }[/tex]

[tex]\cfrac{2^{\frac{1}{4}} y^{\frac{1}{2}+\frac{1}{2}}}{12^{\frac{1}{2}} x^{1+\frac{1}{4}} }\implies \cfrac{2^{\frac{1}{4}} y}{12^{\frac{1}{2}} x^{\frac{5}{4}} }\implies \cfrac{2^{\frac{1}{4}} y}{12^{\frac{2}{4}} x^{\frac{5}{4}} }\implies \cfrac{2^{\frac{1}{4}}}{(12^2)^{\frac{1}{4}}}\cdot \cfrac{y}{x^{\frac{5}{4}}}[/tex]

[tex]\left( \cfrac{2}{12^2} \right)^{\frac{1}{4}}\cdot \cfrac{y}{x^{\frac{5}{4}}}\implies \left( \cfrac{1}{72} \right)^{\frac{1}{4}}\cdot \cfrac{y}{x^{\frac{5}{4}}}\implies {\Large \begin{array}{llll} \cfrac{y}{(72)^{\frac{1}{4}}x^{\frac{5}{4}}} \end{array}}[/tex]

For the problem , (a) The cost to park in a mall garage is $50 entry fee plus $10 per four ,  the function is y = 50 + 10x  , the domain is (0,∞)  and  range is also (0,∞)  .

and (b) A swimming pool in a hotel is draining at a rate of 3 feet per minute , the function is y = -3t  , domain is (0,∞) and range is (0,∞) .

Part(a) ;

The cost to park in a mall garage is $50 entry fee plus $10 per four ;

the the number of hours be = "x" ;

the fixed entry fees for the mall garage is = $50 ;

the per hour charge for the garage is = $10 ;

it can be represented as : y = 50 + 10x ;

the function is : y = 50 + 10x ;

The domain of this function is (0,∞) , as the input hours can't be negative and

the range of function is (0,∞) as the charge cannot be negative

since the parking hours will be non negative .

Part(b) ,

A swimming pool is draining at the rate of 3 feet per minute.

Rate of draining is represented as "y = -3t" where t is number of minutes  and

the negative sign in the function denotes the water is draining .

The domain and Range of this function is (0,∞) , as the input hours can't be negative .

The given question is incomplete , the complete question is

Find the Function , Domain and Range for the following problems :

(a) The cost to park in a mall garage is $50 entry fee plus $10 per four.

(b) A swimming pool in a hotel is draining at a rate of 3 feet per minute.

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The domain of the function is all real numbers while the range of the function is also all real numbers.

The domain of the function t(n) = 2x + 1 is all real numbers, since there are no restrictions on the input value of x. The range of the function is also all real numbers, since adding 1 to any real number will also result in a real number. So the domain is (-infinity, infinity) and the range is (-infinity, infinity)

We have to note that in the event that we have a function such as t(n) = 2x+1, x is free to take any of the values on the real number line and this would return a value for t(n).

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The formula for the area of ​​a triangle is (1/4)√(105a?)

By applying the triangle inequality theorem, we can verify that the given formula represents the length of the sides of a triangle. This theorem states that the sum of his two sides of a triangle must be greater than his third side.

Given the expressions 2a?, 6a + 5, and 10a?, applicable

2a? + 6a + 5 > 10a? (sum of first two pages greater than third)

2a?+10a?> 6a+5 (1st and his 3rd sides sum greater than 2nd)

6a + 5 + 10a? >2a? (sum of last 2 pages greater than first page)

Therefore, the given formula can express the length of the sides of a triangle.

According to Heron's formula, the area of ​​a triangle with side lengths a, b, and c is

Area = √(s(s-a)(s-b)(s-c))

where s is the semicircle of the triangle and is defined as

s = (a + b + c) / 2

Replacing the given formula with a, b, c, we get:

s = (2a? + 6a + 5 + 10a?) / 2

= 6a? + 3a + 5/2

Find the value of s to calculate the area of ​​the triangle.

Area = √((6a? + 3a + 5/2)((6a? + 3a + 5/2)-(2a? + 6a + 5))((6a? + 3a + 5/2)-(10a?)))

= √((6a? + 3a + 5/2)(2a? - 3a + 5/2)(-4a? + 3a + 5/2))

= √((15/4)(a?)(-5/4)(-a?)(-7/4)(a?))

= √(105a?/16)

= (1/4)√(105a?)

So the formula for the area of ​​a triangle is (1/4)√(105a?). 

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Answer:

$14390.75

Step-by-step explanation:

p=3650

i = 5.5% is this annual rate or monthly rate?  assuming annual rate

t=15 years compounding monthly = 15*12 = 300 periods

(1+5.5%/12)^300=3.94267155

multiply the principal 3650 *3.94267155 = $14390.75

The factor of the given quadratic equation is (4x + 3). Option C is correct.

One way to describe the polynomial as a product of its linear parts is to factor the quadratic equation. We may use this method to locate the roots of quadratic expressions, simplify them, and solve equations.

The formula for a quadratic polynomial usually takes the form ax² + bx + c, where a, b, and c are real values. We can obtain the zeros of the quadratic equation ax² + bx + c = 0 by factoring quadratics.

Given that:

4x² + 23x + 15 = 0

By applying the distributive property, we have:

4x² + 20x + 3x + 15 = 0

Factor out the greatest common factor for each group

(4x² + 3x) + 20x + 15

x(4x + 3) + 5(4x + 3)

Factor the polynomial by factoring out the greatest common factor. 4x + 3, then we have:

(4x + 3) (x + 5)

Therefore, we can conclude that one of the factors of the quadratic expression is (4x + 3).

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a. The number of disappointed customers is 157. b. Unsold dolls = 135. c. The dolls needed per week is 660. d. The price of $0.63 will make the supply of the doll tight. e. The price at which the demand and supply will be at equilibrium is $3.20.

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

a. The supply and the demand associated from the graphs are:

Supply: 95(2.50) - 60 = 178

Demand: -130(2.50) + 660 = 335

Subtracting the Demand and supply:

335 - 178 = 157

The number of disappointed customers is 157.

b. For unsold dolls set the equation for supply and demand:

Supply: 95(3.80) - 60 = 301

Demand: -130(3.80) + 660 = 166

Subtract the value of demand and supply:

301 - 166 = 135

Unsold dolls = 135

c. To give the dolls away, the cost of the doll is $0.

The demand equation thus becomes:

y = -130(0) + 660

y = 660

The dolls needed per week is 660.

d. Let the supply be 0.

y = 95x - 60

0 = 95x -60

x = $0.63

The price of $0.63 will make the supply of the doll tight.

e. The supply an demand will be in equilibrium when Demand = Supply, that is:

95x - 60 = -130x + 660

95x + 130x = 720

225x = 720

x = $3.20

The price at which the demand and supply will be at equilibrium is $3.20.

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The inverse of the function that indicates the amount Jake earns per hour at a local car wash is [tex]\mathbf{y =\dfrac{7.50}{x}}[/tex]

In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a map or transformation. Typically, these functions are identified by letters like f, g, and h. etc

A function is an operation or a relation that links each individual element of a non-empty set X, to at least one element of another non-empty set Y.  In mathematics, a relation f between two sets, X and Y, is referred to as the function's domain and co-domain and can be expressed for all values of x and y as:

f = {(x,y)| for all x ∈ X,  y ∈ Y}

The objective of this question is to write the inverse of the given function.

The function f(x) = 7.50x correlates Jake's pay to the number of hours he puts in the work.

The inverse of the function can be written as:

y = 7.50x

Interchange the variables

x = 7.5y

Divide both sides by 7.5

x/7.5 = 7.5y/7.5

Make y the subject of the formula:

[tex]\mathbf{y =\dfrac{7.50}{x}}[/tex]

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If the initial position s(0) = -5 and initial velocity v(0) = -2, the position function of the object is -8cost + t^3/3 - 2t + 3. So the option D is correct.

We have to determine the position function of the object.

An object moves along a straight line with acceleration a(t) = 8cost + 2t.

Initial position s(0) = -5

Initial velocity v(0) = -2

Integration of a(t) given us s(t)

[tex]\int a(t)dt = \int (8cost + 2t) dt[/tex]

v(t) = 8sint + 2t^2/2 + C

v(t) = 8sint + t^2 + C

At v(0) = -2

v(0) = 8sin(0) + (0)^2 + C

-2 = 8 × 0 + 0 + C

C = -2

v(t) = 8sint + t^2 - 2

The integration of v(t) gives us s(t)

[tex]\int v(t)dt = \int (8sint + t^2 - 2)dt[/tex]

s(t) = -8cost + t^3/3 - 2t + D

At s(0) = -5

s(0) = -8cos(0) + (0)^3/3 - 2(0) + D

-5 = -8 × 1 + 0 - 0 + D

-5 = -8 + D

Add 8 on both side, we get

D = 3

s(t) = -8cost + t^3/3 - 2t + 3

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Statement "B. the median is a negative number" will be correct among these options.

The sum of all values divided by the total number of values determines the mean (also known as the arithmetic mean, which differs from the geometric mean) of a dataset. The term "average" is frequently used to describe this measure of central tendency.

Given,  that A set of data contains 10 negative numbers and 4 positive numbers.

Since the value of data is not given it can be any positive or negative numbers

mode:

A mode is described as a value in a group of values that occurs most frequently. The value that appears the most frequently is this one.

Range:

When the sample maximum and minimum are subtracted, the range of a set of data in statistics is the difference between the greatest and lowest values.

Median:

The median is the value that's exactly in the middle of a dataset when it is ordered.

Thus, the Median will be negative.

Therefore, Statement "B. the median is a negative number" will be true among these options.

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Complete question:

A set of data contains 10 negative numbers and 4 positive numbers. Which one of these statements must be true?

A. The mean is a negative number.

B. The median is a negative number.

C. The mode is a negative number.

D. The range is a negative number.

In theory, this event could pay enough to cancel out Wanda's expenditures the job pay 16 trips.

Establish a variable.

Utilizing the variable, write an equation.

Make the equation work.

Let C be the total cost of each transaction.

T, the quantity of slides down the water slide,

Since the price is the same regardless of how much she rides, C = 89 for the first transaction.

For the second agreement, C = 16plus T.

Set the two costs equal to one another, then use T to determine when they are equal.

89 = 16 + T + T = 18 trips.

Given that the first contract can only have a cost of $90, the price must be $15.

90 = 15 + T + T = 16 trips.

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The range of values for how many fluid ounces of water will a 35 pound dog will drink in a day is given as follows:

27 oz < x < 32 oz.

The range of values is obtained applying the proportions in the context of this problem.

The conversion of milliliters to fluid ounces is given as follows:

1 ml = 0.0338 oz.

Hence the amounts of oz per kilogram are given as follows:

The conversion of pounds to kg is given as follows:

1 kg = 2.20462 pounds.

Hence the weight in kg of the dog is given as follows:

35/2.20462 = 15.87 kg.

The bounds of the interval are given as follows:

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