Samantha stores all of her important paperwork in the file cabinet shown below.

A locker measurement at the bottom as 2 one by 6 ft 2, side as 1 and a half ft, and length as 2 2 by 3 ft.
*Picture not drawn to scale

What is the volume of the file cabinet?

The end behavior of the function f(x) = −x³ + 2x² +1 is:

as  x → ∞, f(x) → -∞

as  x → -∞, f(x) → ∞

Here we want to find the end behavior of the function below:

f(x) = −x³ + 2x² +1

Notice that the degree is odd, this means that the end behaviors are opposite in opposite values of x.

Because we have a negative sign on the term with the highest exponent, then as x tends to infinity, the function will tend to negative infinity.

And thus, because the degree is odd, the value of f(x) as x tends to negative infinity tends to positive infinity.

Thus we can write:

as  x → ∞, f(x) → -∞

as  x → -∞, f(x) → ∞

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The values of x from the given figures are 3 √29 and 24 respectively.

What is triangle ?

Triangle can be defined in which it has three sides , three angles and sum of three angles is always 180 degrees.

Given

In the figure,

The two given triangles are similar ,

So, in the first figure it is given that they are similar ,

√29 / 5  = x / 15

x  = √29 * 15  / 5

x =√29 * 3

x = 3 √29

And in the second figure , here also they gave they are similar

so we get,

12 / 13  =  x /  26

x = 12 * 26 / 13

x = 12 * 2

x = 24

Hence, The values of x from the given figures are 3 √29 and 24 respectively.

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As per the formula of compound interest the amount in his account after 6 year 3 months is $40,085.307

In math the term called compound interest is defined as when you earn interest on both the money you've saved and the interest you earn.

Here we know that Luke invests 34000 into an account that pays 3. 4% compound interest per annum for the first two years and 2. 3% thereafter.

Here we need to find the amount in his account after 6 years and 3 months.

Then it can be calculated as,

FV = PV(1 + i)ⁿ

Here we know that PV = 34000 and i = 3.4% for two years,

Then the FV is value is calculated as,

=> FV = 34000(1 + 3.4/100)²

=> FV = 34000 ( 1 + 0.034)²

=> FV = 36351.304

Similarly, the FV value of 4 years 3 months is calculated as,

=>  FV = 36351.304(1 + 2.3/100)⁴°³

=> FV = 36351.304(1 + 0.023)⁴°³

=> FV = 40085.307

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The graph and the points are added as an attachment

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

y = -x + 1 + 5

Evaluate the like terms

y = -x + 6

Set x = values from 0 to 3

So, we have

y = -0 + 6 = 6

y = -1 + 6 = 5

y = -2 + 6 = 4

y = -3 + 6 = 3

So, the points are (0, 6), (1, 5), (2, 4) and (3, 3)

Next, we plot the graph and the points

See attachment

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The HCF of the numbers 114, 138 and 234 is 6.

The term HCF in math is also know as the greatest common factor or highest common factor of a set of whole numbers is the largest positive integer that divides evenly into all numbers with zero remainder.

Here we have given the numbers 114, 138 and 234.

And we need to find the HCF of the numbers.

By using the prime factorization method, here we have identified the factors of the numbers, and it can be written as

The factors of 114 are: 1, 2, 3, 6, 19, 38, 57, 114

The factors of 138 are: 1, 2, 3, 6, 23, 46, 69, 138

The factors of 234 are: 1, 2, 3, 6, 9, 13, 18, 26, 39, 78, 117, 234

While we looking into the given number we have identified that the the greatest common factor is 6.

Complete Question:

Find the HCF of the numbers 114, 138, and 234 by using the prime factorization method.

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The amount of salt in the tank is decreasing exponentially with time.

At time t, the amount of salt in a tank containing oz of salt dissolved in gallons of water can be calculated using the following formula:

Salt in tank (oz) = 200 - 140e^(-t/25)

For example, at time t = 10 min, the amount of salt in the tank is 200 - 140e^(-10/25) = 200 - 140(0.7787) = 124.42 oz.

This calculation assumes that brine containing oz of salt per gallon of brine is allowed to enter the tank at a rate of gal/min and the mixed solution is drained from the tank at the same rate. Thus, the amount of salt in the tank is decreasing exponentially with time.

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I apologize for misunderstanding your question.

Regarding your new question, it depends on the specific expressions provided in column A and column B. Without knowing the exact expressions, I am unable to determine if they are equivalent or not. Additionally, if they are not equivalent, then to make them equivalent, you can use algebraic properties such as the commutative property, associative property, distributive property and simplification techniques to change one of the expressions so that it has the same value as the other expression for every input in their domain.

Please let me know the specific expressions you are working with and I will be happy to help you determine their equivalence and/or how to change one of the expressions to make them equivalent.

Answer:

SO bassically its is equivalent bc i seethat the dgene is really good

Step-by-step explanation:

1 + 1 =2w + 2x +2y = 3x and equiavelnt number

For the definition "An angle is 2 collinear rays with a common endpoint" , then

(a) the contradictory example is "When two rays are collinear having a  common end point; then the rays do not form an angle instead they form a line."

(b) the changed definition is , "An angle is formed at the intersection of two non-collinear rays that have the same endpoint " ;

(c) the example is "the Plane" .

The Angles are formed when the two straight lines or rays meet at a common endpoint.

Part(a) ;

An example which contradicts this definition of angles is "When two rays are collinear with a common endpoint; the rays do not form an angle ,instead  they form a line" because when all the points of two lines are collinear then all the points of the two lines will be overlapping .

Part(b) ;

The change that need to be made in the definition of angle is "An angle is formed at intersection of two non-collinear rays which have same endpoint ".

Part(c) ;

The Example of the undefined term is :

Undefined terms do not have a formal definition; an example of this is "the plane" . The plane pertains to the angles because the plane determines the parameter to be measured.

The given question is incomplete , the complete question is

An angle is two collinear rays with a common endpoint.

(a) Find an example that contradicts this definition.

(b) How would you change the definition to make it more accurate ?

(c) Give an example of an undefined term and how it pertains to angles .

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The object has both kinetic energy and potential energy.

The values of each type of energy the object has are KE = 67.5 J

GPE = 367.5 J

Energy is the ability to do work. It can take many forms, such as kinetic energy (energy of motion), potential energy (stored energy) etc.

If a 15-kg child is tossed up into the air by her parent and the child is 2.5 meters off the ground traveling 3 m/s.

Then boy has kinetic energy due to his motion and also has potential energy due to his height.

Thus, M = 15-kg, h = 2.5 meters and V = 3 m/s

KE = 1/2(M)(V)² = 1/2 × 15 × 3² = 67.5 J

GPE = mgh = 15 × 9.8 × 2.5 = 367.5 J

KE + PE = 67.5 + 367.5 = 435 J

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Answer: 10 I'm not sure ok

Step-by-step explanation: divide 50 and 5 you get 10

Let x be the cost price of an entertainment system.

The selling price is x+800

The number of systems sold is 60-((x+800-x)/20) = 60-((800)/20) = 60-40 = 20 systems

The revenue is the product of the number of systems sold and the selling price.

R = 20(x+800) = 20x+16000

To maximize the revenue, we need to differentiate the above equation with respect to x and set it to 0 and solve for x.

dR/dx = 20 = 0

20x = 0

x = 0

Therefore, the cost price of an entertainment system is 0 and the store should sell the system at x+800 = 800

This means that the store should sell the system at $800 more than the cost price to maximize the revenue.

An inequality which shows the constraint on the amount of apple John has to make pies and cobblers is: D. 4x + 2y ≤ 16.

In order to write an equation that model this situation, we would assign a variable to the number of pies John makes and the total number of cobblers John makes respectively, and then translate the word problem into algebraic equation as follows:

Since a pie uses 4 cups of apples and 3 cups of flour while a cobbler uses 2 cups of apples and 3 cups of flour, the constraint on the amount of flour is given by:

4x + 2y ≤ 16

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Answer: 12

Step-by-step explanation:

Say that your friends number is x

She says that when you divide the number by 4, add 6, and then multiply by -3, the result is -27, so:

(x/4 + 6) * -3 = -27

We can solve the equation by first dividing by -3 on both sides:

x/4 + 6 = 9

Multiply both sides by 4:

x + 24 = 36

Subtract 24 from both sides:

x = 12

Double checking...

(12/4 + 6) * -3

= (3+6) * -3

= 9 * -3

= -27

Correct :>

So your friend chose the number 12

The final resultant expressions are  3.9 - 0.8 x , 1.5 + t+0.66 x ,

77/5 k - 3m.

What is Algebraic expression ?

Algebraic expression can be defined as the combination of variables and constants.

Given expressions,

-2.5x+3.9 + 1.7x

3.9 + 1.7x-2.5x

3.9 - 0.8 x

1  1/2 + t + 2/3 s

= (2+1) / 2 + t+ 2/3  s

= 3/2 + t + 2/3 s

= 1.5 + t+0.66 x

15k+2/5 k -3m

k(15+2/5 ) - 3m

k (75 + 2 / 5 )  - 3m

77/5 k - 3m

Hence, The final resultant expressions 3.9 - 0.8 x , 1.5 + t+0.66 x ,

77/5 k - 3m

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To find out how many cans of white paint Emma will need to mix with 12 cans of pink paint, we can use the proportion of white paint to pink paint that she is currently using: 6 cans of white paint to every 4 cans of pink paint.

We can set up an equation using the proportion:

white paint/pink paint = 6/4 =3/2

We know that Emma wants to use 12 cans of pink paint, so we can use this information to solve for the number of cans of white paint she needs:

white paint/pink paint = 3/2

white paint = (3/2) * pink paint

white paint = (3/2) * 12 cans

white paint = 18 cans

So Emma will need 18 cans of white paint to mix with 12 cans of pink paint to get the desired color.

Answer: lol no it won't

Step-by-step explanation:

In order to determine if the circular tabletop with a diameter of 88 inches will fit through the door, we must compare the dimensions of the tabletop to the dimensions of the door.

The width of the door is 36 inches and the height of the door is 84 inches. The diameter of the tabletop is 88 inches. To fit through the door, the tabletop's diameter must be less than or equal to both the width and the height of the door.

88 inches > 36 inches and 88 inches > 84 inches

In this case, the tabletop will not fit through the door because its diameter is larger than both the width and the height of the door.

Pedro ate 3/2 of the cake that was left.

We know that the fraction is used to represent the portion or part of the whole thing.

The fraction has two parts: numerator and denominator.

The top part of fraction is numerator and the bottom part is denominator.

Consider a fraction 1/5.

Here, numerator is 1, denominator is 5

When certain thing is divided into 5 equal parts then each part of is represented by fraction 1/5

In this situation, there is 3/4 of a large cake left over from a party.

Pedro eats 1/2 of the cake that was left.

This means, Pedro eats half of the remaning cake.

We need to find the half of fraction 3/4

We divide fraction 3/4 by 2 in order to find the amount of cake he ate.

[tex]\frac{\frac{3}{4} }{2} \\\\=2\times \frac{3}{4} \\\\=\frac{3}{2}[/tex]

Thus he ate 3/2 of cake.

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Answer:

0

Step-by-step explanation:

First, you do 17 - 8, which is 9 and then you do 13 - 4, which is 9. Then, you subtract 9 from 9, which gives you 0.

84 inches times as long as a Thimble jellyfish is a Lion's Mane jellyfish.

Now, According to the question:

"Information available from the question"

A Thimble jellyfish is a Lion's Mane jellyfish.

Thimble jellyfish = 1 inch,

Lion's mane jellyfish = 7 feet

Convert feet into inches.

To calculate a value in feet to the corresponding value in inches, just multiply the quantity in feet by 12 (the conversion factor).

Here is the formula:

Value in inches = value in feet × 12

Formula: multiply the value in feet by the conversion factor '12'.

So, 7 feet = 7 × 12 = 84 inches.

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According to Isabella transactions, her present balance in bank statement is -$9.45

The term called transaction in math is defined as  a finalized agreement between a seller and a buyer for transferring goods, services, or financial assets in exchange for money

Here let us consider that Isabella's present balance be X.

According to the problem statements regarding her deposits, there is withdrawals, auto-payments, direct deposit and service charge are also done on the account.

Then those transaction values are calculated as,

=> (1/2)x - (1/3)x -(1/4)x +(1/10x) -$9.29 = x

Here by finding the LCM of common terms, then we get

=> (1/60)x - $9.29 = x

When we solve it for x, then we get the equation like the following,

=> 59x = -$9.29 × 60

=> 59x = -$557.4

Therefore the value of x is -$9.45.

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Correct answer is parallelogram and rhombus.

A parallelogram is a geometric object with sides that are parallel to one another in two dimensions. It is a form of polygon with four sides (sometimes known as a quadrilateral) in which each parallel pair of sides have the same length. A parallelogram has adjacent angles that add up to 180 degrees.

Rhombuses are a particular sort of quadrilateral in Euclidean geometry. It is a unique instance of a parallelogram in which the diagonals meet at a 90-degree angle and all sides are equal. This is a rhombus' fundamental characteristic. A rhombus has a diamond-shaped form. As a result, it is also known as a diamond.

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rectangle, rhombus

got it wrong on my test and was given the correct answers, so here they are.

The amount of paint needed is 176/36000 = 0.0049 gallons, which is equivalent to 4.9 milliliters, rounded to the nearest hundredth.

To calculate how much paint Mr.Todd needs to buy to cover the outside of the entire birdhouse, we must first know the dimensions of the birdhouse. Let's assume the birdhouse has the dimensions of 10 inches long, 8 inches wide and 6 inches tall, and each side requires 1 coat of paint. The total surface area of the birdhouse is then 10 x 8 + 10 x 6 + 8 x 6 = 176 inches squared. Next, we need to know the coverage of the paint, which we will assume is 250 square feet per gallon. Since 1 square foot is equal to 144 square inches, the coverage of the paint is 36000 square inches per gallon. To find out how many gallons of paint are needed to cover the birdhouse, we need to divide the total surface area of the birdhouse (176 square inches) by the coverage of the paint (36000 square inches per gallon). Therefore, the amount of paint needed is 176/36000 = 0.0049 gallons, which is equivalent to 4.9 milliliters, rounded to the nearest hundredth.

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The translation or the graph must be shifted upwards by 7 units .

Function, in mathematics, is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given here: The graph f(x)=9x

The required graph is given by g(x)=9x+7

A graph is translated k units vertically by moving each point on the graph k units vertically. g (x) = f (x) + k; can be sketched by shifting f (x) k units vertically.

Thus two transform the given graph into g(x) we have to translate the graph vertically or upwards by 7 units i.e f(x)=9x+7

where k=7

Hence, The translation or the graph must be shifted upwards by 7 units .

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Answer: 16

Step-by-step explanation:

8 * (6/3)

= 8 * 2

= 16

The ways they can fall are 4,8 and 36

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

The formula of probability is defined as the ratio of a number of favorable outcomes to the total number of outcomes.

P(E) = Number of favorable outcomes / total number of outcomes

Given;

Two coins, three coins and two dices are tossed

Probability of two coins;

=2x2=4

Probability of three coins;

=2x2x2=8

Probability of two dices;

=6x6=36

Therefore, the probability of coins and dice will be 4,8 and 36

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To represents JKLM is a parallelogram the required value of x is equal to 7.

In the parallelogram JKLM,

Let us consider the measure of each side in form of 'x' is represented by :

JK = 4x + 13

KL = 4x - 1

LM = 3x + 20

MJ = 5x - 8

Opposite side of the parallelogram JKLM are congruent to each other.

JK = LM

⇒ 4x + 13 = 3x + 20

⇒ 4x - 3x = 20 - 13

⇒ x = 7

When

KL = MJ

⇒ 4x - 1 = 5x - 8

⇒ 5x - 4x = 8 - 1

⇒ x = 7

JK = 4(7) + 13

    = 41

LM = 3(7) + 20

     = 41

KL = 4(7) -1

    = 27

MJ = 5(7) - 8

     = 27

Therefore, the value of x  which represents that JKLM is a parallelogram is equal to 7.

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The student has learned that GE4 is an introduction to mathematical proof and problem solving, including basic algebra, functions, sets, and the different approaches to problem solving.

Example of operation of function:

1. f(x) = x^2 + 3x - 2

When x = 3, f(3) = 3^2 + 3(3) - 2 = 14

2. g(x) = x^3 + 3

When x = 4, g(4) = 4^3 + 3 = 67

I have learned that GE4 is an introduction to mathematical proof and problem solving. We have gone through a variety of topics such as basic algebra, functions, and sets. We have also learned about the different approaches to problem solving, such as working backwards, proof by cases, and proof by PMI. I have also been introduced to the basics of logic and proof writing.

This answer explains the proof by PMI for the erie that if n is an odd number, then n^2 is an odd number. Two examples of operations of functions are also given. The student has learned that GE4 is an introduction to mathematical proof and problem solving, including basic algebra, functions, sets, and the different approaches to problem solving.

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The scientific notation of the given result is 8 x 10³

The number is written in the form  [tex]a \times 10^b[/tex] where we have  [tex]1 \leq a < 10[/tex]

The number b shows the order, which is the most important figure for which scientific notation is used. It tells us how much order large or small a value is in powers of 10. We can for a time, ignore the value of 'a' for two comparable quantities and only compare their orders(this type of comparison is useful when difference is too big, like size of human to size of a star etc sort of comparisons).

We are given that Maddie performed a calculation on her calculator and received a result of 8E3.

WE know that "E" means the power of ten

Therefore,

8E3 = 8 x 10³

This is the scientific notation.

For the standard form it should be 8,000.

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The ball travel horizontally 37 feet before it hits the ground.

What is Distance ?

Distance is the sum of an object's movements, regardless of direction. Distance can be defined as the amount of space an object has covered, regardless of its starting or ending position.

we have;

A(x) = -0.02x2 + 0.6x + 5

where

The horizontal distance, x, is given in feet.

The ball's height is indicated by the symbol A ---> in feet.

The fact that

The ball's altitude was zero when it landed on the earth.

so,

For A(x)=0

-0.02x^2 + 6x +5 = 0

'

the quadratic equation to be solved

The equation solving formula for a quadratic equation of the type;

ax^2 + bx + c = 0

this equation is equal to ;

[tex]x = \frac{-b\pm \sqrt{b^{2}- 4ac } }{2a}[/tex]

we have ;

-0.02x^2 + 0.6x +5 = 0

So,

a = -0.02

b = 0.6

c = 5

Subsititue this values in the formula;

[tex]x = \frac{-0.6\pm \sqrt{0.6^{2} -4 *(-0.02)(5) } }{2*(-0.02)}[/tex]

[tex]x = \frac{-0.6\pm \sqrt{0.76 } }{-0.04}[/tex]

[tex]x = \frac{-0.6\pm \ 0.87 }{-0.04}[/tex]

[tex]x = \frac{-0.6\ + \ 0.87 }{-0.04}= -6.75[/tex]

[tex]x = \frac{-0.6\ - \ 0.87 }{-0.04}= 36.75[/tex]

therefore

The ball travel horizontally 37 feet before it hits the ground.

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