A pet supply company makes a 5-gallon aquarium with a 10 inch by 10 inch base and a height of 14 inches. A museum wants to special-order a 135-gallon aquarium with the same shape. Find the new dimensions (length, width and height) of the new aquarium. Show or explain your work.​

The required sets of range of the corresponding functions are illustrated in the below solution part.

The range of a function is the set of all possible output values of the function.

To find the range of a function, we need to evaluate the function at every point in its domain and find the set of all possible output values.

For example, we are given the function f(x) = x² - 2x and the domain (-5, -1, 0, 5, 7). To find the range of this function, we need to evaluate it at every point in its domain, which gives us the following values:

f(-5) = (-5)² - 2 × (-5) = 25 + 10 = 35

f(-1) = (-1)² - 2 × (-1) = 1 + 2 = 3

f(0) = (0)² - 2 × (0) = 0

f(5) = (5)² - 2 × (5) = 25 - 10 = 15

f(7) = (7)² - 2 × (7) = 49 - 14 = 35

The range of the function is therefore the set of all possible output values, which are 3, 0, 15, and 35. Therefore, the range of this function is {3, 0, 15, 35}.

We can use the same method to find the range of the other functions in the questions. The ranges of the other functions are:

6) f(x)=x²-2x & Domain= (-5, -1, 0, 5, 7)

Range: {-1, 3, 0, 15, 35}

7) f(x) = -3x+12) & Domain= (-9, -4, 4, 8, 11)

Range: {0, 15, 36, 39, 48}

8) f(x)=x²-(x/2) & Domain = {4, 8, 12, 30)

Range: {2, 30, 102, 942}

9) f(x)= |x-2x & Domain= (-5, -4,-3, 3, 5)

Range: {-4, -3, 0, 3, 4}

10) f(x) = (x²/2) + 30 & Domain = {-4, -2, 6, 8)

Range: {26, 28, 54, 60}

Thus, the required sets of range of the corresponding functions are illustrated in the above solution part.

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the probability is 0.00539 for the household whose income is excess of $50000.

the ratio of favorable outcome to total possible outcome.

the ratio of the size of random sample to the actual size.

Given, sample proportion p∧ ≥0.22

size of random sample, p= 750

now, size of household, n = p/p∧ =750/0.22= 3409

number of households shown in census= 18.4%

now the probability = number of favorable outcome/ total possible outcome.

probability of gaining income excess of $50000 is 18.4/3409 = 0.00539

hence, 0.00539 is the proportion whose income is excess .

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The graph of a linear function is a straight line. One independent variable and one dependent variable make up a linear function.

Equations (functions or graphs) that create a straight line when graphically depicted are known as linear functions.

Typically, linear functions take the following form: y=mx+b or f(x)=a+bx.

X and Y are the two variables of a linear function.

Independent variable: x (Hori. axis)

dependent variable for y (Vert. axis)

Replace the problem's value with the value of f (x).

Distinguish the variable. In this instance, you transfer the constant term over by adding 1 to both sides to isolate the variable term.

Keep isolating the variable.

X serves as the independent variable while

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The number of people still living has a Binomial (n = 5, p = 2/3)

The probability of all five people still living is

P(X = 5) = (2/3)⁵ ≈ 0.1317

The probability of exactly two people living

P(X = 2) = 10 x (2/3)² (1/3)³ ≈ 0.16

The probability of at least three people still living

P(X ≥ 3) = P(X = 3) + P(X = 4) + P(X = 5)

≈ 0.3292 + 0.3292 + 0.1317

≈ 0.790

Probability is simply the probability that something will happen. Whenever  the outcome of an event is uncertain, we can talk about the probability of a particular outcome, i.e. its likelihood. The analysis of events driven by probability is called statistics.

Probabilities can be expressed numerically by the number of desired outcomes, divided by the total number of outcomes.

Properties:

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Answer:

a = 60

Step-by-step explanation:

a/5 - 8 = 4

a/5 = 12

a = 60

Answer:

a = 60

Step-by-step explanation:

a/5 - 8 = 4

a/5 = 4 + 8

a/5 = 12

a = 5*12

a = 60

Check:

60/5 - 8 = 4

12 - 8 = 4

The number of different groups of 7 people who can drive will be 31,824.

A permutation is an act of arranging items or elements in the correct order. Combinations are a way of selecting items or pieces from a group of objects or sets when the order of the components is immaterial.

You volunteer to help drive people home from an event. There are 18 people who need rides, but you can only fit 7 of them in your vehicle.

Then the number of different groups of 7 people can you drive will be

Different ways = ¹⁸C₇

Different ways = 18! / [(18 - 7)! x 7!]

Different ways = 18 x 17 x 16 x 15 x 14 x 13 x 12 x 11! / (11! x 7 x 6 x 5 x 4 x 3 x 2 x 1)

Different ways = 31824

The number of different groups of 7 people who can drive will be 31,824.

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Then the number of different groups of 7 people can you drive will be

Different ways = ¹⁸C₇

Different ways = 18! / [(18 - 7)! x 7!]

Different ways = 18 x 17 x 16 x 15 x 14 x 13 x 12 x 11! / (11! x 7 x 6 x 5 x 4 x 3 x 2 x 1)

Different ways = 31824

The number of different groups of 7 people who can drive will be 31,824.

The differential equation that could describe this relationship is → d²V/dt² - (3KV²)dV/dt = 0.

Given is that the rate of change of the volume {V} with respect to time {t} of water leaking from a tank is proportional to the cube of the volume.

We can write the proportional relationship as -

{dV/dt} [tex]$\alpha[/tex] {V}³

Replacing the proportional relationship as -

dV/dt = KV³               {K is constant}

d²V/dt² = K x d/dt (V³)

d²V/dt² = K x 3V² (dV/dt)

d²V/dt² = 3KV²(dV/dt)

d²V/dt² - (3KV²)dV/dt = 0

Therefore, the differential equation that could describe this relationship is → d²V/dt² - (3KV²)dV/dt = 0.

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The values are

Define Rounding Numbers

Rounding means replacing a number with an approximate value that has a shorter, simpler, or more explicit representation. For example, replacing $23.4476 with $23.45, the fraction 312/937 with 1/3.

Round Values to Nearest Tenth :

To round the decimal number to its nearest tenth, look at the hundredth number. If that number is greater than 5, add 1 to the tenth value. If it is less than 5, leave the tenth place value as it is, and remove all the numbers present after the tenth's place.

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Using line tangent, the approximation for f(2.1) is 3.95

Given,

The point (a, f(a)) is on the line tangent to the graph of y = f(x) at x = a, which has a slope of f'(a).

The equation be like;

y - f(a) / (x - a) = f'(a)

y = f'(a) (x - a) + f(a)

Using the provided data and a = 2, we can determine that the tangent line to the graph of y = f(x) at x = 2 has equation

y = f'(2) (x - 2) + f(2)

y = -1/2 (x - 2) + 4

To compute a "approximation of f(2.1) using the line tangent to the graph of f at x = 2," one must substitute x = 2.1 for f in the equation for the tangent line (2.1). You get 2.1 when you plug this in.

y = -1/2 (x - 2) + 4

y = -1/2 (2.1 - 2) + 4

y = -1/2 x 0.1 + 4

y = 3.95

That is,

The approximation for f(2.1) using line tangent is 3.95

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The proposed Exponential decay model for wolf population, w is given by  w(t) =w(1-r)∧t, where w is the function of time, t

w(t) =870(1-0.19)∧t

The model that estimates the number of populations decreases at a particular rate with the passage of time.

In the above question, rate of decay denoted by r = 19%

population size, w= 870 during the year 2009.

the population size w is the function of time, t

now, exponential decay model will be w(t) = w (1-r)∧t

Now using the given data, w(t) = 870(1-0.19)∧t

hence, exponential decay model is w(t) = 870(1-0.19)∧t

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The two different types of values for a parameter: Default and user given

The correct answer is an option (2)

In this question we need to select the two different types of values for a parameter.

We know that  a parameter is nothing but a special kind of variable which is used in a function to refer to input of the function.

If no argument value is passed during the function call, then  the function argument will take default value.

In PL/SQL, user given values for a parameter can be prompted to input a value using & character.

The ACCEPT command is used to obtain input from the user.

Therefore, default value and user given values are two different types of values for a parameter.

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The complete question is:

What are the two different types of values for a parameter?

1)    Default and System given

2)    Default and user given

3)    System given and user given

4)    Compile time and run time values

Answer:

10 packages

Step-by-step explanation:

153-63=90 since each package has 9, 90/9 is 10 packages

the algebraic version is

(153-63)/9=x

The ordered pair found in inverse of g is  ( 1 , 4 ) .

Given :

Relation :

A function is a relation which describes that there should be only one output for each input (or) we can say that a special kind of relation (a set of ordered pairs), which follows a rule .

Values for relation g are given in the table:

X  Y = g( X )

5  -3

4    1

3   -2

2    0

then the table for g inverse will be:

X      Y = g^-1 ( x )

-3       5

1       4

-2     3

0     2

Hence, the ordered pair found in inverse of g is ( 1 , 4 )

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Full question :

Values for relation g are given in the table. Which ordered pair would be found in the inverse of g?.

X  Y = g( X )

5  -3

4    1

3   -2

2    0

Answer:If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment. In addition to the Perpendicular Bisector Theorem, we also know that its converse is true.

Step-by-step explanation:

Points on a perpendicular bisector of a line segment are equidistant from the segment’s endpoints.

a. True

According to the given statement the width of the walkway (x) is 8 feet.

Four of the sides of a square's two-dimensional form are equal in length. In a square, all four internal angles were right angles, and the opposing sides are parallel to one another. Real-world examples of square-shaped things include floor tiles, tea towels, hexagonal tiles, cheddar cheese, and so on.

Area of a Square = (side)(side)

Total area of the pool and walkway = 506 sq. ft

Length of the pool and walkway = 7 + 2x

Width of the pool and walkway = 6 + 2x

Thus, we will have the equation of the total area as:

(7 + 2x)(6 + 2x) = 506

4x² + 12x + 14x + 42 = 506

4x² + 26x + 42 = 506

4x² + 26x + 42 - 506 = 0

4x² + 26x - 464 = 0

2x² + 13x - 232 = 0

[tex]x = - \frac{\sqrt{169 + 1856}}{4}- \frac{13}{4} ,\\\\\quad x = \frac{\sqrt{2025}}{4} - \frac{13}{4} \\\\\quad x = \frac{45}{4}- \frac{13}{4} \\\\[/tex]

x = 8

so, the width of the walkway (x) would be 8 feet.

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Answer:

let x = total cost

x = 5(18.5 + 3.25)

x = 5(21.75)

x = $108.75

108.75 = 5(18.5) + 5(3.25)

108.75 = 92.5 + 16.25

108.75 = 108.75

Therefore, the total cost will be $108.75.

Step-by-step explanation:

The Python range() method needs three arguments to work: start value, stop value, and step value. after increasing the values by the step value's stated amount.

For a specific data collection, the statistical range is the range of values between the highest and lowest values. The difference between the highest and lowest observation can also be used to illustrate the range. Subtracting the highest number from the lowest yields the sample interval. The sample range is a crucial indicator of variability for variables that are continuous.

here ,

The series of integers returned starts with this integer, startNumber (optional).

stopNumber: This number is the last in the series of integers returned by range().

the stepValue (optional): An integer value indicating how much each successive integer differs from the previous one.

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Transformations. Transform is the verb form of change. Therefore, to modify a geometric shape would entail to make certain changes to that shape.

Transforming something into another thing is referred to by the verbs transform, metamorphosis, transmute, convert, and transfigure. Transform suggests a significant shift in form, nature, or function. To completely and instantly modify something or someone so that they are considerably better or more beautiful is to transform them. When you move into a new home, quit your job, or become a parent, you are experiencing "change."

"Transition" refers to the process that takes place before to, during, and following the change event. We experience transition on a bodily, emotional, and psychological level, and we change as a result. Mathematicians define a transformation as a geometric shape or formula alteration that transfers the shape or formula from its pre-image, or original position, to its image, or after-transformation position.

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The complete and simplified answer to the question what is 7/9 of 45 is 35.

The number above the fraction line is called the numerator and the number below it is called the denominator. To work out the fraction of any number, we first need to convert that whole number into a fraction as well.

Any number can be converted to fraction if you use 1 as the denominator:

45 / 1

So now that we've converted 45 into a fraction, to work out the answer, we put the fraction 7/9 side by side with our new fraction, 45/1 so that we can multiply those two fractions.

All we need to do is convert the whole number to a fraction and then multiply the numerators and denominators.

7 × 45 / 9 × 1 = 315 / 9

In this case, our new fraction can actually be simplified down further. To do that, we need to find the greatest common factor of both numbers.

You can use our handy GCF calculator to work this out yourself if you want to. We already did that, and the GCF of 315 and 9 is 9.

We can now divide both the new numerator and the denominator by 9 to simplify this fraction down to its lowest terms.

315 / 9 = 35

9 / 9 = 1

When we put that together, we can see that our complete answer is:

35 / 1

The complete and simplified answer to the question what is 7/9 of 45 is:

35

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The factors are (3x + 2)(x + 5).

Factorization or factoring is the process of breaking down an entity—such as a number, matrix, or polynomial—into a product of another entity—or factors—that, when multiplied together, give the original number, matrix, or other entity.

Given  3x² + 17x + 10

factors of equation is

In order to factorize this expression, we can split the Middle Term.

If we want to factorize an expression like a x² + b x + c using this method, we need to think of two numbers that are like:

n₁.n₂ = a.c = 3.10 = 30

and n₁ + n₂ = b = 17

3x² + 2x + 15x + 10

= x(3x + 2) + 5(3x + 2)

= (3x + 2)(x + 5)

Hence, the factors are (3x + 2)(x + 5).

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The correct question is

Factorize 3x² + 17x + 10

A function is a relationship between a set of possible inputs and outputs, where each input is associated with exactly one output.

A non-function is a relation between a set of inputs and a set of possible outputs where there is at least one input with more than one output.

The vertical line test can be used to ascertain whether a relation is a function. If you can draw a vertical line through the graph of the relationship and it intersects the graph at more than one point, then the relation is a non-function. If the vertical line intersects the graph at only one point, then the relation is a function.

Another way to determine if a relation is a function is to look at the equation defining the relation. If the equation does not contain any x's in the denominator, then the relation is a function. If the equation contains x's in the denominator, then the relation is a non-function.

For example, consider the relation defined by the equation y = x^2. This relation is a function because there are no x's in the denominator.

On the other hand, consider the relation defined by the equation y = 1/x. This relation is a non-function because the equation contains an x in the denominator.

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Answer: y=14

Step-by-step explanation: y is directly proportional to x, meaning that multiplying x by a certain factor would also multiply y by that same factor. x=5 and y=7. If x changes to 10, it means that x is multiplied by a factor of (10/5) = 2. Therefore, y is multiplied by this same factor (2). As a result, 7*2=14

The expression 2x²y has in its entirety 1 term.

First let's define what algebraic expressions are.

An algebraic expression is a set of numbers and letters that make up an expression that has a meaning, the letters are variables and the numbers are coefficients or independent terms, algebraic expressions can be part of an equation and model mathematical processes.

The terms of an expression are identified by the fact that they are separated by means of an addition and subtraction operation:

Since 2x²y has neither addition nor subtraction operations, we can clearly state that it has only one term.

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To find the sale price of the item, we need to multiply the regular price by the discount percentage, then subtract the result from the regular price. In this case, the discount is 45% * $85 = $<<45*.01*85=38.25>>38.25. So the sale price of the item is $85 - $38.25 = $<<85-38.25=46.75>>46.75. Answer: \boxed{46.75}.

Answer:

$46.75

Step-by-step explanation:

Original price: $85

Markdown: 45%

Price: 0.55(85)=$46.75

Sale Price: $46.75

Answer:

8 years old and Laura is 32

Step-by-step explanation:t

Let the daughter be equal to "x".

Laura would be "4x".

In 16 years Laura will be twice as old can be expressed as this:

4x+16=2(x+16)

Solve:

4x+16=2x+32

2x=16

x=8

Therefore at present time, the daughter is 8 years old and Laura is 32.

The square root of k is 192 which is an integer.

Define Trigonometric functions

A right-angled triangle's angle can be related to side length ratios using real-world trigonometric functions.

Given expression is,

12 cos 30° + 2 tan 60°

We know,

cos 30° = √3/2

tan 60° = √3

Now, plug in the values

⇒12 * √3/2 + 2 * √3

⇒6√3 + 2√3

⇒8√3

We know, 8 * 8 = 64

The above value in square root form,

⇒√8*8*3

⇒√192

⇒√k  (where, k is 192 an integer)

Hence, the square root of k is 192 which is an integer.

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To solve a system of equations using substitution, you can start by solving one of the equations for one of the variables, such as x or y. For example, in this case, we can solve the first equation for x by subtracting y from both sides, like this:

[tex]-x - y = 1[/tex]
[tex]-x = 1 - y[/tex]

Now that we have an expression for x in terms of y, we can substitute that expression into the second equation to solve for y. When we do that, we get:

[tex]y = -(1 - y) + 4[/tex]
[tex]y = -1 + y + 4[/tex]

Now we can rearrange the terms on the right-hand side to make it easier to solve for y:

[tex]y = y + 4 - 1[/tex]

And when we combine the y terms on the left-hand side, we get:

[tex]2y = 3[/tex]

Finally, we can solve for y by dividing both sides by 2, like this:

[tex]y = 3 / 2[/tex]

Once we know the value of y, we can substitute it back into any of the original equations to solve for the other variable, x. In this case, if we substitute the value of y into the first equation, we get:

[tex]-x - y = 1[/tex]
[tex]-x - (3 / 2) = 1[/tex]

We can solve for x by rearranging the terms on the left-hand side and then dividing both sides by -1, like this:

[tex]-x = -1 + (3 / 2)[/tex]
[tex]x = (1 - 3) / 2[/tex]
Therefore, the solution to the system of equations is x = -1 and y = 3/2.

It's important to check your solution by substituting the values of x and y into the original equations to make sure they work. For example, if we substitute x = -1 and y = 3/2 into the first equation, we get:

[tex](-1) - (3 / 2) = 1[/tex]

And if we substitute the same values into the second equation, we get:

[tex](3 / 2) = (-1) + 4[/tex]

Both of these equations are true, which means our solution is correct.

Kelly's estimate cannot be said to be reasonable because it falls below the range of acceptable number of sunglasses from the given amount in each box.

We are told that Kelly bought 4 boxes.

Now, we are told that each box had either 20, 25, or 30 pairs of sunglasses in it.

Thus;

Minimum number of sunglasses = 20 * 4 = 80 sunglasses

Maximum number of sunglasses = 30 * 4 = 120 sunglasses

Now, we are told that Kelly estimates a reasonable number of sunglasses to be 70.

From our previous calculations, the minimum possible can only be 80 and as such her estimate falls lower and we conclude that it is unreasonable.

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Answer:

true

Step-by-step explanation:

click'thanks'on the question page

and follow

Answer: Zero point eighty four lbs

Step-by-step explanation: