The exterior angle of a regular polygon is 30'. Find the number of sides, a) 3 b) 12 c) 9 d) 10 12) Suppose sin 8 > 0.

The required difference will be;

⇒ 6

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The difference between a two-digit number and the number obtained by interchanging the digits is 54.

And, The ratio between the digits of the number is 1 : 3.

Now,

Since, The number is greater than the number obtained in reversing the digits and the ten's digit is greater than the unit digit.

Let the unit and ten's place are x and 3x.

Hence, We get;

⇒ (10 × 3x + x) - (10x + 3x) = 54

⇒ 31x - 13x = 54

⇒ 18x = 54

⇒ x = 3

Thus, The required difference,

⇒ (3x + x) - (3x - x)

⇒ 4x - 2x

⇒ 2x

⇒ 2 × 3

⇒ 6

Therefore, The required difference will be;

⇒ 6

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A mathematical operation that is easily performed but highly unlikely to reverse in a reasonable amount of time is known as a "one-way function." One-way functions are fundamental to cryptography, particularly in areas like secure hashing and public-key encryption. These functions are designed to be simple and efficient to compute in one direction but extremely difficult and time-consuming to reverse.

A prime example of a one-way function is the multiplication of two large prime numbers. Multiplying them is a straightforward task, but attempting to factorize the product back into its original primes, known as the "prime factorization problem," is considered computationally infeasible for large numbers. This asymmetry in complexity is utilized in cryptographic systems, such as the RSA encryption algorithm, to ensure the security of sensitive information.

In summary, one-way functions are mathematical operations that can be easily performed but are highly challenging to reverse. Their properties make them invaluable in the realm of cryptography, where they provide the foundation for secure communication and data protection.

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Answer:

4.2 cubic inches

Step-by-step explanation:

Find the diagram attached

Volume of the rectangular pyramid = BH/3

B is the base area

H is the height of the pyramid

Given

Base area = 3.2in * 1.4in

Base area = 4.48sq. in

Height = 2.8in

Volume of the rectangular pyramid = 4.48*2.8/3

Volume of the rectangular pyramid = 12.544/3

Volume of the rectangular pyramid = 4.2 cubic inches

The system of equations that can be used to represent the cost of each type of ticket is  2a + 3c = 30.75   and 3a + 2c = 33   .

In the question ,

it is given that ,

a theater sells adult and child tickets for its play .

the cost for 2 adult ticket and 3 child ticket is = $30.75

and the cost for 3 adult tickets and 2 child tickets = $33.00

let the cost of 1 adult ticket = "a"   and

let the cost of 1 child ticket = "c"

So, According to the question ,

the equation to represent both the situation is

2a + 3c = 30.75   and

3a + 2c = 33

Therefore , The system of equations that can be used to represent the cost of each type of ticket is  2a + 3c = 30.75   and 3a + 2c = 33   .

The given question is incomplete , the complete question is

A theater sells adult and child tickets to its plays. 2 adult tickets and 3 child tickets cost $30.75. 3 adult tickets and 2 child tickets cost $33.00. let "a' represent the cost of 1 adult ticket, and "c" represent the cost of 1 child ticket . Write a system of equations can be used to determine the cost of each type of ticket ?

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The answers are a) The volume of the solid of revolution generated by rotating R around the x-axis is 64/3 cubic units. b) The volume of the solid of revolution generated by rotating R around the y-axis is 32π/3 cubic units. c) The solids in parts (a) and (b) do not have the same volume because revolving a curve around different axes results in different cross-sectional areas which means that they will have different volumes.

Given that R be the area bounded by the graph of y = 4 - x² and the x-axis over [0, 2].

We have to find the volume of the solid of revolution generated by rotating R around the x-axis and y-axis respectively.

a) Volume of the solid of revolution generated by rotating R around the x-axis

Using the disk method, the volume of the solid of revolution generated by rotating R around the x-axis is given by:

V = ∫[0, 2] πy² dx

Let us substitute y = 4 - x² in the above formula.

V = ∫[0, 2] π(4 - x²)² dx

V = π ∫[0, 2] (16 - 8x² + x^4) dx

V = π[16x - (8/3)x³ + (1/5)x⁵] [2, 0]

V = (32/15)π(2^5 - 0)

= 64/3 cubic units

Therefore, the volume of the solid of revolution generated by rotating R around the x-axis is 64/3 cubic units.

b) Volume of the solid of revolution generated by rotating R around the y-axis

Using the washer method, the volume of the solid of revolution generated by rotating R around the y-axis is given by:

V = ∫[0, 4] π(x² - 4)² dx

Let us substitute x² = 4 - y in the above formula.

V = ∫[0, 4] π(y - 4)² (1/2√y) dy

V = π ∫[0, 4] (1/2) y^2 - 4y + 16 (1/√y) dy

V = π [(1/6) y^(5/2) - 4(1/3) y^(3/2) + 16(2)√y] [4, 0]

V = (32π/3) cubic units

Therefore, the volume of the solid of revolution generated by rotating R around the y-axis is 32π/3 cubic units.

c) Explanation why the solids in parts (a) and (b) do not have the same volume

The solids in parts (a) and (b) do not have the same volume because revolving a curve around different axes results in different cross-sectional areas which means that they will have different volumes. Hence, option B is correct.

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A cone with a height of 9 in and a base diameter of 6 in has the volume 84.78 cubic inches.

The formula for the volume of a cone is:

V = (1/3)π\(r^{2}\)h, where r is the radius of the base and h is the height.

In the question it is given height = 9 in and a base diameter = 6 in.

Radius = diameter/2

r = d/2 = 6/2 = 3 inches

Substituting the values in the formula:

V = (1/3)π\((3\ in)^2\)(9 in)

Simplifying the expression:

V ≈ 84.78 \(in^3\)

Rounding to the nearest hundredth, we get:

V ≈ 84.78 \(in^3\)

Therefore, the approximate volume of the cone is 84.78 cubic inches.

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Answer:

48+23(6)½

Step-by-step explanation:

A = l × w

A =[(8-(6)^½) × (9+4(6)^½)]

A =8(9+4(6)^½) + [-(6)^½(9+4(6)^½]

A =(72 + 32(6)^½ - 9(6)^½ - 24)

A =(72 - 24 + 32(6)^½ - 9(6)^½)

A =(48 + 23(6)^½)

23$ is the total cost .

What is cost and example?

the total cost = 13$ + 10$= 23$ because he losses a hour in work .

13$ and additionally spending 10$ in carnival .

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In this the correct choice is: D. There are no relative maxima and no relative minima.

The given function is y = \(x^{3}\) - 12x + 3. To find the relative maxima and minima, we need to calculate the first and second derivatives of the function.

First, let's find the first derivative: y' = 3\(x^{2}\) - 12

Now, let's find the second derivative: y'' = 6x

To apply the second-derivative test, we need to determine the critical points by setting the first derivative equal to zero and solving for x:

3\(x^{2}\) - 12 = 0

\(x^{2}\)- 4 = 0

(x - 2)(x + 2) = 0

From this equation, we find that x = 2 and x = -2 are the critical points.

Now, let's evaluate the second derivative at these critical points:

y''(2) = 6(2) = 12

y''(-2) = 6(-2) = -12

Since the second derivative at x = 2 is positive (12 > 0) and the second derivative at x = -2 is negative (-12 < 0), the second-derivative test tells us that there are no relative maxima or minima. Therefore, the correct choice is D. There are no relative maxima and no relative minima for the given function.

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The complete question is:

Test for relative maxima and minima. Use the second-derivative test, if possible. y=x3 - 12x + 3 Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. O A. The relative maxima occur at x = 2. The relative minima occur at -2. (Type integers or simplified fractions. Use a comma to separate answers as needed.) The relative maxima occur at x=-2. There are no relative minima. (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) O C. The relative minima occur at x = 2 . There are no relative maxima. (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) OD. There are no relative maxima and no relative minima.

The average number of toys per person is 8 (option C).

let's calculate the average number of toys per person. We know that five people are working 8 hours a day for 5 days, so the total work hours for the week is 5 × 8 × 5 = 200 hours.

Since these five people can assemble 400 toys in that time, the average number of toys assembled per hour is 400 / 200 = 2 toys per hour.

Now, since each person works for 8 hours a day, the average number of toys assembled per person per day is 2 × 8 = 16 toys.

Since there are 5 working days in a week, the average number of toys assembled per person per week is 16 × 5 = 80 toys.

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Answer:

Your answer is dc

Step-by-step explanation:

The information provided indicates that it will take 78 minutes to load.

Time may be described in mathematics as a continuing and continuous series of events that take place one after another, from the past through the present, and into the future. The length of events or the gaps between them may be measured, compared, or even ordered using time.

If loading three and a half trucks takes 42 minutes, loading one truck will take 42 / 3.5 minutes, or 12 minutes. The time needed to load is calculated by multiplying the minutes per vehicle by 6.5. In this scenario, it would take 78 minutes to load 6 1/2 trucks (12 x 6.5). The time taken is calculated using the formula t = 12n, where n indicates the number of trucks and t is the time in minutes.

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Question:

You are running a fuel economy study. One of the cars you find is blue. It can travel \(44\frac{1}{2}\) miles on \(1\frac{1}{4}\) gallons of gasoline.

Another car is red. It can travel \(25\frac{3}{5}\) on \(\frac{4}{5}\) gallon of gasoline.

What is the unit rate for miles per gallon for each​ car?

Which car could travel the greater distance on 1 gallon of​ gasoline?

Answer:

(a)

\(Rate = 35\frac{3}{5}\ miles\ per\ gallon\)

\(Rate = 32\ miles\ per\ gallon\)

(b)

The blue car will travel faster

Step-by-step explanation:

Given

Blue Car:

\(Distance = 44\frac{1}{2}\ miles\)

\(Gasoline = 1\frac{1}{4}\ gallons\)

Red Car

\(Distance = 25\frac{3}{5}\ miles\)

\(Gasoline = \frac{4}{5}\ gallons\)

Solving (a):

This is solved by dividing the distance travelled by the amount of gasoline.

i.e.

\(Rate = Distance/Gasoline\)

Blue Car:

\(Rate = 44\frac{1}{2} / 1\frac{1}{4}\)

\(Rate = \frac{89}{2} / \frac{5}{4}\)

\(Rate = \frac{89}{2} * \frac{4}{5}\)

\(Rate = \frac{89}{1} * \frac{2}{5}\)

\(Rate = \frac{89 * 2}{1 * 5}\)

\(Rate = \frac{178}{5}\)

\(Rate = 35\frac{3}{5}\ miles\ per\ gallon\)

Red Car:

\(Rate = 25\frac{3}{5}/\frac{4}{5}\)

\(Rate = \frac{128}{5}/\frac{4}{5}\)

\(Rate = \frac{128}{5} * \frac{5}{4}\)

\(Rate = \frac{128 * 5}{5 * 4}\)

\(Rate = \frac{128}{4}\)

\(Rate = 32\ miles\ per\ gallon\)

(b)

In (a), we have:

\(Rate = 35\frac{3}{5}\ miles\ per\ gallon\) --- Blue Car

\(Rate = 32\ miles\ per\ gallon\) --- Red Car

By comparison:

The rate of the blue car is greater than that of the red

Hence, the blue car will travel faster

A grocer makes a display of cans in which there are 10 rows.

The top row has one can and each lower row has two more cans than the row above it.

We can write it as sequence:

1, 3, 5, 7, . . .

We can observe that it's an arithmetic sequence: 1, 3, 5, 7, . . . , 2n-1

We know that the formula for the sum of n-terms of arithmetic sequence:

S(n) = (n/2)(1 + 2n-1)

Here, Sn = 100

So, (n/2)[1 + 2n-1] = 100

n(1 + 2n + 1)

n(2n) = 200

2n^2 = 200

n^2 = 100

n = 10

Hence, the number of rows = 10

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Answer:

60

Step-by-step explanation:

nPr=n!/(n-r)!

5!/(5-3)!

(5*4*3*2*1)/(2*1)

120/2

60

Answer:

60

Step-by-step explanation:

A permutation is a rearrangement of its elements in any sequence or linear order.

We are asked to rearrange the word BEACH into three letter permutations.

We find that each letter represents the first letter 5 x 3 = 15

Then distributes 5 places, so that 15 x 5 = 60

Answer:

Step-by-step explanation:

First, distribute the 2 to the 3z and -6 within the parenthesis.

You know have 6z -12/5 + 6 = 10

Subtract 6 from both sides of the equation

6z -12/5 = 4

Multiply 5 on both sides of the equation

6z -12 = 20

Add 12 to both sides of the equation

6z = 32

Divide by 6 on both sides of the equation

z = 32/6

Simplify

z = 16/3

I hope that this helps! :)

Answer:

4.25(Divided) or 1,300,000,000(subtracted)

The root of the equation sinx = 2x-3 is 0.8401 (approx).

Given equation is sinx = 2x-3

We need to solve this equation using false position method.

False position method is also known as the regula falsi method.

It is an iterative method used to solve nonlinear equations.

The method is based on the intermediate value theorem.

False position method is a modified version of the bisection method.

The following steps are followed to solve the given equation using the false position method:

1. We will take the end points of the interval a and b in such a way that f(a) and f(b) have opposite signs.

Here, f(x) = sinx - 2x + 3.

2. Calculate the value of c using the following formula: c = [(a*f(b)) - (b*f(a))] / (f(b) - f(a))

3. Evaluate the function at point c and find the sign of f(c).

4. If f(c) is positive, then the root lies between a and c. So, we replace b with c. If f(c) is negative, then the root lies between c and b. So, we replace a with c.

5. Repeat the steps 2 to 4 until we obtain the required accuracy.

Let's solve the given equation using the false position method.

We will take a = 0 and b = 1 because f(0) = 3 and f(1) = -0.1585 have opposite signs.

So, the root lies between 0 and 1.

The calculation is shown in the attached image below.

Therefore, the root of the equation sinx = 2x-3 is 0.8401 (approx).

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Assuming all conditions for inference are met, a 95 per cent confidence interval for the slope of the least-squares regression line is defined as the range of values within which we are 95 per cent confident that the true population slope lies.

It is calculated as the point estimate (the slope of the least-squares regression line) plus or minus the margin of error, which is determined by multiplying the standard error of the slope by the critical value from the t-distribution with n-2 degrees of freedom (where n is the sample size). This critical value is chosen such that 95 per cent of the t-distribution falls within the interval. Therefore, a larger sample size or a smaller standard error will result in a narrower confidence interval, while a smaller sample size or a larger standard error will result in a wider confidence interval.

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Answer:

(1.2,-4.7)

Step-by-step explanation:

To write the dimensions of point C in the required ratio, we use the mathematical equation as follows;

({mx2 + nx1/(m+n)} , {my2 + ny1/(m+ n)})

In this particular question,

(m,n) = (5,8)

((x1,y1) = (7,-2)

(x2,y2) = (-8,-9)

Plugging these values into the equation written above, we have

[{5(-8) + 8(7)}/(5+8), {5(-9) + 8(-2)}/(5+8)]

= (-40+56)/13, (-45-16)/13)

= (16/13), (-61/13)

= (1.23, -4.69)

These rounded to the nearest tenth gives (1.2, -4.7)

Danielle earned a total of $1,058.25 last week.

A commission is a percentage of total sales as determined by the rate of commission. A commission is a profit paid due to making a sale.

commission=rate of commission⋅total sales.

To find the commission on a sale, multiply the rate of commission by the total sales.

commission = rate of commission⋅total sales.

commission = 7.75% x $4,300

commission = 0.0775 x $4,300

commission = $333.25

Danielle's earnings will be the addition of both her commission and base salary

Total = commission + base salary

Total = $333.25 + $725

Total = $1,058.25

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Answer:

The linear equation is y = 450 - 30 x, where y is the number of pages

Lourdes has left to read after x days

Step-by-step explanation:

Each day, Lourdes reads 30 pages of a 450-page book

- We need to write a linear equation to represent the number of pages

 Lourdes has left to read after x days

∵ Lourdes reads 30 pages each day

∵ Lourdes will read for x days

∴ The number of pages Lourdes will read in x day = 30 x

- The left pages will be the difference between the total pages of the

 book and the pages Lourdes read

∵ The book has 450 pages

∵ Loured will read 30 x in x days

∴ The number of pages left = 450 - 30 x

- Assume that y represents the number of pages Lourdes has left

 to read after x days

∴ y = 450 - 30 x

The linear equation is y = 450 - 30 x, where y is the number of

pages Lourdes has left to read after x days

Answer:

D

Step-by-step explanation:

Answer to this question:

I think the answer is 3

Hope this helps, have a nice day!!!

Answer:

y = 3/5 x + 2

Step-by-step explanation:

y = mx + b

From the graph, we see that b = 2.

y = mx + 2

From the graph, we see that the slope is

slope = m = rise/run = 3/5

y = 3/5 x + 2