Iman ate 1/3 of a bag of popcorn.
His 4 friends ate equal shares of the remaining popcorn.

Which expression represents the popcorn that each friend ate?

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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Answer: 3

Step-by-step explanation: First you have to do 7 times 6 which is 42. Then you add 8 and get 50!

In version 1, if you choose to stay with the card you have initially chosen, your chances of winning are 1 in 8, since you have a 1 in 8 chance of having selected an ace initially.

If you choose to switch, your chances of winning are 7 in 8, since the card you are switching to is randomly selected from the remaining 7 cards, 4 of which are aces.  However, if the card you have initially chosen is an ace, you should stay with it since you have already won the prize. If it is not an ace, it may be beneficial to switch as you have a higher chance of getting an ace with the face-down card.  

In either case, the dealer has a 7-in-8 chance of winning since he has access to all the cards and can choose the card to be revealed at random. This means that he has a higher chance of winning than the player does.  Overall, the game is quite balanced in terms of the chances of winning for either the player or the dealer.

The dealer has an advantage due to knowing the cards and being able to select the card to be revealed, but the player still has a chance of winning depending on their decision to switch or stay with their initial selection.

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Answer:

1 fluid ounce

Step-by-step explanation:

if 10 drops is equal to 0.1 fl and we multiply 10 by 10 to get 100, we have to multiply 0.1 by 10 as well, which is 1 fluid ounce.

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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The required change in the water level per hour for Sally's swimming pool is  1074 gallons.

Rate of change is equal to (Change in completed assignments) / (Change in hours) Change in rate = (6-3) / (2-1) Change in rate = (3) / (1) The change rate is 3/1, or 3 assignments every hour. The rate of change is 3.0, or three assignments are completed every hour when time is measured in hours.

We have,

Her pool holds 9,774.5 gallons of water and will need to drain completely in 9.1 hours.

Number of gallons per hour are

gallons per hour = 9,774.5/9.1

gallons per hour = 1074 approx

Thus, required number of gallons per hours 1074.

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The 12th term in the sequence is (c) f(n) = 354294

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

The definition of the function is given as

-2, 6, -18, 54, ...

The above definitions imply that we simply multiply -3 to the previous term to get the current term

Using the above as a guide,

so, we have the following representation

f(n) = -2(-3)^n-1

Where

-2 is the first term and -3 is the common ratio

For the 12th term, we have

f(n) = -2(-3)^11

Evaluate

f(n) = 354294

Hence, the 12th term is (c) f(n) = 354294

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Answer:Given Prove

PSUR is a rectangle QS = RT

PQ = TU

Proof:

Since PSUR is a rectangle, we know that opposite sides are parallel.

Therefore, PQ and TU are parallel.

Also, PSUR is a rectangle, so the angles P and R are right angles.

Therefore, angles Q and S are also right angles.

Since PQ and TU are parallel, and angles Q and S are right angles, we know that QS and RT are corresponding angles.

Therefore, QS=RT

QED.

Step-by-step explanation:

Answer:

Aprende a leer expresiones algebraicas y comprende conceptos como variable, coeficiente u operador, entre otros.

Step-by-step explanation:

Ejemplo: la mitad de un número “x” si x= 8 x/2= 8/2= +4

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 correct option is -2. The range of function is found to be minimum is -2.

A function's global minimum is its lowest value across the entire function's range, whereas a localized minimum is its lowest value within a specific local area.

From the given graph of the function:

To get the lowest point of the range of the function, check the value where graph is turning.

This, shows the minima of the function which is -2 at x = 3.

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The complete question is attached-

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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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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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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Answer:

X= k/2

Y= -k/2

Step-by-step explanation:

X= k/2

Y= -k/2

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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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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Answer:

Step-by-step explanation:

ii) ratio = 60:12 = 5:1

iii) unit rate is 5

iv) 60 = 12M

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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It means Albin was 15 minutes late to a pickup.

a represents the Number of Minutes Late, (a=15 in this case)

Now, According to the question:

A daycare charges a base fee of 333 dollars plus 0. 500. 500, point, 50 dollars per minute for late (after closing time) pick-ups.

Albin had to pay 10. 5010. 5010, point, 50 dollars for a late pick-up.

Albin uses the equation,

10.50 = 0.50a+3

0.50a = 10.50-3

0.50a = 7.50

a = 7.50/0.5

a= 15

Hence, It means Albin was 15 minutes late to a pickup.

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Answer:

G < -7

Step-by-step explanation:

We can create an equation first with what the problem provides:

4 - 5G > 39

Now, since the question asks for the solution, we can solve for G:

-5G > 39-4

-5G > 35

-G > 7

Since G is still a negative, we need to switch the inequality around:

(-1)(-G) > (7)(-1) (To cancel out the negative)

G < -7

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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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

[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]

If we divide the candy according to numbers rather than type, I can give 4 pupils 6 identical chocolates and 6 identical gummy bears, ensuring that each student will get exactly 3 pieces of candy.

We have to find in how many ways I can distribute 6 identical gummy bears and 6 identical chocolates to 4 students, if each student must receive exactly 3 pieces of candy.

Gummy Bear = 6

Chocolates = 6

Total numbers of candy = Gummy bear + Chocolates

Total numbers of candy = 6 + 6

Total numbers of candy = 12

We have to distribute the tablet in between 4 students. So each student must receive exactly 3 pieces of candy if we distribute the candy by the numbers not their type.

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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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