arrange the following list of functions in increasing order of growth rate. that is, if function g(n) follows function f (n), then it should be the case that f (n) is o(g(n)) (the base of logarithms is 2). justify in simple words. (you do not have to show detailed calculations.)

The volume of the sphere = (4.0 / 3.0) π r^3.

What is the volume of the sphere?

The quantity of space occupied within a sphere is referred to as its volume. Every point on the surface of the sphere is equally spaced from its center, making it a three-dimensional round solid object. The fixed point and fixed distance are referred to as the sphere's center and radius, respectively.

Here, we have

The volume program in Python, where comments are used to explain each line is as follows

#This initializes pi to 3.142

pi= 3.142

#This gets input for the radius

sphere_radius = float(input("Radius: "))

#This calculates the sphere volume

sphere_volume = (4.0 / 3.0) * sphere_radius**3

#This prints the sphere volume

print(sphere_volume)
Hence, the volume of the sphere = (4.0 / 3.0) π r^3.

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Answer:

-1 ≤ y ≤ 6

[-1, 6]

Step-by-step explanation:

The y coordinates of all points on the graph are from -1 to 6, so the range is:

-1 ≤ y ≤ 6

[-1, 6]

By calculating, The value of given expression 8 · (2 + 3 )²- 4² is 184

What is Algebraic expression ?

Algebraic expressions are the concept of expressing numbers the use of letters or alphabets with out specifying their actual values. The fundamentals of algebra taught us a way to explicit an unknown price using letters along with x, y, z, etc. those letters are known as right here as variables.

An algebraic expression can be a combination of both variables and constants. Any cost this is positioned before and extended by using a variable is a coefficient.

Given expression ,

= 8 · (2 + 3 )²- 4²

= 8. (5)^2 - 4^2

=8.25 - 16

= 200 - 16

= 184

so, the value of expression is 184.

Therefore, The value go given expression 8 · (2 + 3 )²- 4² is 184

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If an open box is to be constructed from a square piece of sheet metal by removing a square of side 3 feet from each corner and turning up the edges. the dimensions of the sheet​ metal is 16 feet.

Let x represent the dimension of the sheet metal

So,

Volume =3×(x-2×3)×(x-2×3) = 300

Volume =3×(x-6)×(x-6) = 300

(x -6)² = 300/3 = 100

x-6 = √100 =10

x = 10 +6

x = 16 feet

Therefore the dimensions of the sheet​ metal is 16 feet

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The function that describes the height of the ball as a function of time t (in seconds) can be represented as:

h(t) = -16t^2 + 64t + 40

Where h(t) is the height of the ball in feet above the ground, t is the time in seconds, and the -16t^2 represents the acceleration due to gravity. The 64t represents the initial velocity of the ball, and 40 is the initial height of the ball above the ground.

Check the picture below.

92 Square inches is the area of the shaded region shown below

The area is the entire amount of space occupied by a flat (2-D) surface or an object's form. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a form on paper is the area that it occupies.

Given a rectangle, that has a length of 12 inches and 9-inch width

Since,

Area = length * width

Area of the given triangle = 12 * 9

Area of the given triangle = 108 square inch

There is also one square inside this rectangle of side 4 inch

Since the area of square = side * side

Thus in our case,

Area of square = 4 * 4 = 16 square inch

As we can see in the figure:

Area of shaded region  = complete area of rectangle - area of square

Area of shaded region  = 108 - 16

Area of shaded region  = 92 square inch

Therefore, The area of the shaded region is 92 Square inches.

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Complete question:

Answer:  (-5, -7)

Multiply the y coordinate by -1. Keep the x coordinate the same. The point (-5,7) reflects over the x axis to land on (-5,-7)

The reason why we multiply by -1 is because [tex]\text{y} = \text{h}(\text{x})[/tex], so [tex]-\text{y} = -\text{h}(\text{x})[/tex]

Answer:

(-5,-7)

................

Answer:  1⅗

Step-by-step explanation:  We can write 8 divided by 5 as 8/5.

As 8/5 is an improper fraction, when we divide 8 by 5, we get 1 as quotient and 3 as remainder.

To convert an improper fraction into a mixed fraction, we take quotient 1 as a whole part and in the fractional part remainder 1 as the numerator, and divisor 5 as the denominator.

The GCF of 5 and 1 is 1. So, divide both the numerator and denominator by the GCF to simplify and convert it to a mixed fraction.

Thus, 8 divided by 5 as a fraction in simplest form is 1⅗.

The faster car is traveling at 149 mph, and the slower car is traveling at 142 mph.

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Richard is incorrect, As if two angles are same then the 3rd angle must be same too using angle sum property and therefore ΔJFH ≅ ΔJGH with AAA congruency.

Two triangles are congruent if they have the same shape and size. Congruent triangles have all corresponding angles and sides congruent, meaning they are equal in measure.

A triangle can be shown to be congruent to another triangle by using one or more of the following criteria:

SSS (Side-Side-Side) Congruence: If three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent.

SAS (Side-Angle-Side) Congruence: If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

ASA (Angle-Side-Angle) Congruence: If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

HL (Hypotenuse-Leg) Congruence: If the hypotenuse and one leg of one right triangle are congruent to the hypotenuse and one leg of another right triangle, then the two triangles are congruent.

Richard is incorrect, As if two angles are same then the 3rd angle must be same too using angle sum of property and therefore ΔJFH ≅ ΔJGH

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Least-cost planning methodology (LCPM), sometimes known as "least-cost planning" (LCP), is a relatively new strategy used by economists to make logical decisions about investments in transportation and other urban infrastructure projects.

The complete question is,

What is a project's least cost?          

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Answer:

vendor sold 90 sodas and 45 hot dogs

Step-by-step explanation:

Let x = number of sodas sold

Let y = number of hot dogs sold

We have x = 2y (1)
( The number of sodas sold was two times the number of hot dogs sold)

We also have x + y = 135 (2)

( sold a combined total of 135 sodas and hot dogs.)

Substituting x = 2y we get

2y + y = 135

3y = 135

y = 135/3

y = 45

Therefore x = 135 - 45

x = 90

Therefore vendor sold 90 sodas and 45 hot dogs

Answer:

$18.85

Step-by-step explanation:

1. 127*18 = 2286 pages.

2. 2286/500 = 4.6 (approx.)

3. You need to buy 5 reams of paper 500 pages each.

     It will cost 5*$3.77 = $18.85

a. The profit function P(x) is 10x - 5000.

b. The break even point is at 500 units.

c. If 350 units were sold, the loss was Rs. 1500.

d. The graph of the functions are attached below.

The solutions are obtained using the profit function.

What is profit function?

A profit function is a mathematical relationship that represents the difference produced when the cost function is subtracted from the revenue function. The graph of a profit function shows the optimal combination of revenues and expenses to produce the maximum profit.

a. We are given cost of raw material as Rs. 15 and the fixed cost is Rs. 5000. The product is sold for Rs.25 per unit.

This means that R(x) = 25x

We know that TC= FC + VC(x)

So, TC = 5000 + 15x

Therefore, the profit function will be

⇒Profit = R(x) - TC

⇒Profit = 25x - 5000 - 15x

⇒Profit = 10x - 5000

b. For break even, the profit should be 0.

Therefore,

⇒10x - 5000 = 0

⇒10x = 5000

⇒x = 500

So, the break even will be at 500 units.

c. We are given x=350

Putting this value in profit function, we get

⇒Profit = 10(350) - 5000

⇒Profit = 3500 - 5000

⇒Profit = -1500

So, there is loss of Rs. 1500.

d. The red line represents the cost function and the blue line represents the revenue function.

The break even point is the point where the two lines are meeting.

The area below the break even is the loss area and above it is the profit area.

Hence, the solutions are obtained.

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Answer:

5 and 6

Step-by-step explanation:

sqrt of 32= 4sqrt2 = 5.656

To find the highest common factor (HCF) of two polynomials, we can use the Euclidean algorithm or the method of factoring the polynomials and comparing their common factors.

The first polynomial is x² - 2x - y² + 4y-3 and the second polynomial is x² + 2x - y² + 8y-15

x² - y² is common in both polynomials, let's factor it out.

x² - y² = (x-y)(x+y)

so the first polynomial can be written as (x-y)(x+y) - 2x + 4y - 3

and the second polynomial can be written as (x-y)(x+y) + 2x + 8y - 15

So the HCF of these two polynomials is (x-y)(x+y)

It is important to note that the HCF of polynomials is not unique, there can be more than one factorization.

The domain is discrete and the range is continuous, which can be an accurate statement regarding the two terms.

The range of values that we are permitted to enter into our function is known as the domain of a function.

The x values for a function like f make up this set (x).

A function's range is the collection of values it can take as input.

After we enter an x value, the function outputs this sequence of values.

So, the parameters are as follows, taken from the query:

Downloaded Amount = $2.50

Added amount to each player = $1.50

Use x to indicate how many players there are.

The following representations are what we have.

Total amount = Amount to download + Amount to add each player * Number of players

Now, we obtain:

y = 2.50 + 1.50 * x

y = 2.50 + 1.5x

The number of players serves as the input to the aforementioned linear function.

The domain is discrete as a result.

The amount, though, can have decimal points

The range is continuous as a result.

Therefore, the domain is discrete and the range is continuous, which can be an accurate statement regarding the two terms.

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I learned to save for the future and spend responsibly. In my adult life I will continue to save and be mindful of my spending habits. I will change my attitude towards money and become more frugal.

Saving money for the future requires discipline and dedication. One of the easiest ways to start saving is to create a budget and stick to it. Make sure to include a line item for savings in your budget and allocate a specific amount each month to save.

Additionally, set up automatic transfers from your checking account to your savings account to ensure money is put into savings each month. It's also important to find ways to minimize expenses. Cutting back on eating out, reducing your cell phone bill, and shopping for discounts are all great ways to save money.

Finally, look into investing your money in stocks, bonds, and other investments to help your savings grow. Saving money for the future takes time, but it is possible with the right strategies.

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Answer:

First choice: 5x²+21x-20

Step-by-step explanation:

This is easy to answer if you realize that there is only one way an x² term can appear in the result and that is by the multiplication of 5x and x which results in 5x².

The only choice which has 5x² as a term is the first:  5x²+21x-20

However, it is important to know the FOIL method to multiply two terms together

FOIL stands for First Outer Inner Last and is a technique for multiplying two terms of the form (a+b) and (c+d)

In (a + b) (c + d),

First terms are a and c so their product is ac

Outer terms are a and d so their product is ad

Inner terms are b and c with product bc

Last terms are b and d with product bd

The result is the sum of all these terms

Let's take (5x - 4)(x + 5)
F: 5x·x = 5x²

O: 5x · 5 = 25x

I: -4 ·x = -4x

L: -4·5 = -20

Adding up these individual terms we get

5x² +25x - 4x - 20 = 5x²+21x-20

So first choice is the correct answer

Least cost in the sales promotion is when (140, 70) i.e. Hats = 140 and pair of glasses = 70.

To determine if the data support the mixing of two potential sources or the fractionation of a single source, graphical approaches are frequently used.

To better interpret their data, researchers now employ a variety of graphical tools, including scatterplots, box plots, and histograms. Graphs are excellent for illustrating trends, patterns, and correlations between variables as well as for displaying and summarizing vast volumes of numerical data.

Value of cost at (140, 70) is 3 × 140+ 3 × 70

= $630

Consider any point on the feasible line, say (150, 60)

Cost = 3 × 150 + 3 × 60 =  $570

Cost is increasing towards the point (210, 0)

Thus, Least cost is when (140, 70) i.e. Hats = 140 and pair of glasses = 70.

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Answer:

12 inches

Step-by-step explanation:

3 inches / (1 / 4) = 12 inches

To find the median of the data set, we first need to arrange the data in numerical order. We can do this by grouping the digits in the stem & leaf diagram according to the key:

8016

92 35 67

100 124 34

113

123 8

Then we will arrange them in order as: 8016 92 35 67 100 124 34 113 123 8

To find the median we have to identify the middle value of the data set, considering that we have 12 data points. The middle value is the 7th value in the set which is 100, therefore the median is 100.

Answer:

No!

Step-by-step explanation:

(1 5/2)

is a mixed fraction so you will change it to proper fraction.

the solution is

=7/2 or 3.5

You will multiple two by one and add by five given 7/2.

Answer: 41,000

Step-by-step explanation:

If the hundreds column 5 or more than it rounds up if it is lower it rounds down

Answer:

----------------------------

Given expression:

Simplify it in steps below:

Answer:

[tex] \sf \: 98h - 56k [/tex]

Step-by-step explanation:

Given expression,

→ 9(7h - 4k) + 10k - 5(6k - 7h)

Let's simplify the expression,

→ 9(7h - 4k) + 10k - 5(6k - 7h)

→ 63h - 36k + 10k - 30k + 35h

→ (63h + 35h) + (-36k + 10k - 30k)

→ (98h) + (-56k)

→ 98h - 56k

Hence, answer is 98h - 56k.

The answer to the question is d) c and l; f and h.

The concept of opposite numbers on the number line can be expressed mathematically by the equation -x = y, where x is the original number and y is the opposite number. This equation can be used to calculate the opposite of any number. For example, if the number 5 is located at point a on the number line, the opposite of 5 is located at point k and can be calculated by substituting 5 for x in the equation and solving for y. -5 = y, therefore y = -5. The opposite of 5 is therefore -5. To calculate the opposite of any of the other numbers marked on the number line, the same equation can be used. The answer to the question is d) c and l; f and h.

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Answer: 1/24

Step-by-step explanation:

1st even = 3/6 (2,4,6)

2nd Prime = 3/6 (2,3,5)

3rd multiple of 5 = 1/6 (5)

3/6 x 3/6 x 1/6 = 9/216

9/216 = 1/24

The values of six trig functions are:

sinθ=− √5/5, cosθ=2√5/5, tanθ=-1/2, cot θ=−2, secθ=√5/2, cscθ=−√5

The relationship between the angles and sides of a triangle is given by these trig functions.

There are six functions of an angle commonly used in trigonometry. Their names and abbreviations are sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc).

The point's coordinates are:

x=2, y=−4

To calculate the functions we have to calculate the distance between the point and the origin:

r=√x²+y²=√2²+(−4)²=√16+4=√20

r=2√5

Now we can calculate the functions:

sinθ=y/r=−2/2√5=−√5/5

cosθ=x/r=4/2√5=2/√5=2√5/5

tanθ=y/x=−2/4=−1/2

cotθ=x/y=4/−2=−2

secθ=r/x=2√5/4=√5/2

cscθ=r/y=2/√5−2=−√5.

Hence, the values of trig functions are calculated.

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Answer:

-31

Step-by-step explanation:

Let's put this into an equation:

[tex]4-5 *7[/tex]

Note that 5 less than 4 means I take 5 AWAY from 4, not 5-4.

Most people would go about this straight across, doing 4-5, -1, and then times 7 which would be -7.
BUT if there are no parentheses around 4-5, we do 5 times 7 first.

Why? In PEMDAS or order of operations, you multiply before subtracting.

That means I do 5 times 7 first. That is 35.

Now I subtract 4-35. That is -31.

-12a is  a cubic function in exercises when Relative minimum (4,2).

What in mathematics is a relative maximum?

A point (x,y) on the graph of the function whose y-coordinate is larger than all other y-coordinates on the graph at locations "near to" is known as a relative maximum point (x,y). ( x , y ) .

  f'(x) = 3ax² + 2bx + c

(3,3) and (5,1 ) are print of  relative maximum

   so,    f'(3) = f'(5) = 0

  3a(3)² + 2b(3) + c = 0

or   27a + 6b + c = 0

and   3a(5)² + 2b(5) + c = 0

       75a + 10b + c = 0   ...................... 2

the  Inflection point occurs at point where f''(x) = 0

     d/dx ( 3ax² + 2bx + c ) ∫x = 4 = 0

       because (4,2) is point of  Inflection .

           6a(4) + 2b = 0

          24a + 2b = 0

          b = -12a

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