Find the interior angles of a regular nonagon and a regular 100-gon
(I don’t understand this at all)

Answers

Answer 1

Answer:

nonagon: 140°

100-gon: 176.4°

Step-by-step explanation:

A regular polygon is one that has all sides the same length and all internal angles the same measure. A "nonagon" has nine (9) sides. An image of one is attached. There are some interesting relationships among the angles shown.

The figure can be divided into 9 congruent triangles. Each has a vertex at the center of the figure, and the other two vertices are each end of one side. The central angle (40°) is the supplement of the interior angle at each vertex of the nonagon (140°). Obviously, the central angles sum to 360° (one full circle), so each one has a measure that is 360° divided by the number of sides:

360°/9 = 40°

So, we can figure the interior angle (at the vertex) by subtracting from 180° the value of 360° divided by the number of sides.

For the 100-gon, with 100 sides, the interior angle will be ...

180° -360°/100 = 180° -3.6° = 176.4°

Find The Interior Angles Of A Regular Nonagon And A Regular 100-gon (I Dont Understand This At All)
Answer 2

Final answer:

The interior angle of a regular nonagon is 140°, and for a regular 100-gon, it's 176.4°.

Explanation:

To find the interior angles of a regular polygon, we use the formula: (n - 2) × 180°, where n is the number of sides of the polygon. This formula gives us the sum of all interior angles of the polygon.

To find the measure of one interior angle in a regular polygon (where all angles are equal), we divide this sum by the number of sides.

Interior Angle of a Regular Nonagon:

A nonagon has 9 sides. Using our formula:

Sum of interior angles = (9 - 2) × 180° = 7 × 180° = 1260°One interior angle = 1260° / 9 = 140°

Interior Angle of a Regular 100-gon:

A 100-gon has 100 sides. Following the same process:

Sum of interior angles = (100 - 2) × 180° = 98 × 180° = 17640°One interior angle = 17640° / 100 = 176.4°

Therefore, each interior angle of a regular nonagon is 140°, and each interior angle of a regular 100-gon is 176.4°.


Related Questions


The angles of elevation of a hot air balloon from the two points on level ground are 20° and 42° respectively. If the points are 4.8 miles apart and the balloon is between the points, approximate, to the nearest tenth of a mile, the height of the balloon above the ground.

Answers

Answer:

To the nearest tenth, the height of the balloon is 2.9 miles

Step-by-step explanation:

The nearer point takes the greater angle of elevation.

The diagram is shown in the attachment.

The height of the balloon above the ground is c unit.

From triangle ABD,

[tex]\tan 42\degree=\frac{c}{x}[/tex]

[tex]\implies x=\frac{c}{\tan 42\degree}[/tex]...eqn1

From triangle ABC,

[tex]\tan 20\degree=\frac{c}{x+4.8}[/tex]

[tex]\implies x+4.8=\frac{c}{\tan 20\degree}[/tex]

[tex]\implies x=\frac{c}{\tan 20\degree}-4.8[/tex]..eqn2

We equate both equations and solve for c.

[tex]\frac{c}{\tan 42\degree}=\frac{c}{\tan 20\degree}-4.8[/tex]

[tex]\frac{c}{\tan 42\degree}-\frac{c}{\tan 20\degree}=-4.8[/tex]

[tex]\implies (\frac{1}{\tan 42\degree}-\frac{1}{\tan 20\degree})c=-4.8[/tex]

[tex]\implies -1.636864905c=-4.8[/tex]

[tex]\implies c=\frac{-4.8}{-1.636864905}[/tex]

[tex]c=2.932435039[/tex]

To the nearest tenth, the height of the balloon is 2.9 miles

Answer:

on usatestprep its 1.2

Step-by-step explanation:

The recursive rule for a geometric sequence is given. a1=2; an=1/3a subscript (n−1) Enter the explicit rule for the sequence. an=

Answers

ANSWER

[tex]a_n=2{( \frac{1}{3}) }^{n-1}[/tex]

EXPLANATION

The recursive formula is given as:

[tex]a_n= \frac{1}{3} a_{n-1}[/tex]

where

[tex]a_1=2[/tex]

The explicit rule is given by:

[tex]a_n=a_1 {r}^{n-1}[/tex]

From the recursive rule , we have

[tex]r = \frac{1}{3} [/tex]

We substitute the known values into the formula to get;

[tex]a_n=2{( \frac{1}{3}) }^{n-1}[/tex]

Therefore, the explicit rule is:

[tex]a_n=2{( \frac{1}{3}) }^{n-1}[/tex]

Subtract.
(4x^2 + 8x - 2) - (2x^2 - 4x + 3)
Enter your answer, in standard form.​

Answers

Answer:

[tex]\large\boxed{(4x^2 + 8x - 2) - (2x^2 - 4x + 3)=2x^2+12x-5}[/tex]

Step-by-step explanation:

[tex](4x^2 + 8x - 2) - (2x^2 - 4x + 3)\\\\=4x^2 + 8x - 2 -2x^2 -(- 4x)- 3\\\\=4x^2+8x-2-2x^2+4x-3\qquad\text{combine like terms}\\\\=(4x^2-2x^2)+(8x+4x)+(-2-3)\\\\=2x^2+12x-5[/tex]

which expression represents the phrase "the cost of p pounds of rice at $1.97 per pound"?


WORTH 50 POINTS IF YOU HELP ME
PLZ HELP QUICKLY

Answers

That would be p times 1.97 or 1.97p (letter D) this is because each pound is worth 1.97 dollars more so if you bought 1 pound of rice you'd pay only $1.97 but if you bought 5 pounds of rice you'd pay $9.85 since 1.97 times 5 is 9.85

Hope this helped!

Let me know if this helped!

Jana is decorating 6 picture frames by gluing straws around the borders and adding wooden stars at the corners. Each picture frame measures 20 centimeters by 120 millimeters. How many straws does she need if she uses all of each straw? Each straw is 80 millimeters long. A. 21 straws B. 24 straws C. 48 straws D. 50 straws

Answers

Answer:

C: 48 straws

Step-by-step explanation:

First, find the perimeter of one picture frame: (2 x length) + (2 x width).  Convert 20 centimeters to millimeters so that you are working in the same units; there are 10 millimeters in 1 centimeter, so 20 centimeters = 200 millimeters.  

(2 x 200) + (2 x 120) = 400 + 240 = 640

Each picture frame has a perimeter of 640 millimeters.

Next, figure out how many straws are needed for one picture frame:

640/80 = 8

Jana uses 8 straws for each picture frame.  Since she is decorating 6 picture frames, solve 6 x 8 = 48.  

Jana needs 48 straws to complete her project.

There are 11 paintings at an art show. Three of them are chosen randomly to display in the gallery window. The order in which they are chosen does not matter. How many ways are there to choose the paintings?

Answers

Answer:

165 ways  to choose the paintings

Step-by-step explanation:

This is clearly a Combination problem since we are selecting a few items from a group of items and the order in which we chosen the items does not matter.

The number of possible ways to choose the paintings is;

11C3 = C(11,3) = 165

C denotes the combination function. The above can be read as 11 choose 3 . The above can simply be evaluated using any modern calculator.

Answer:

165 ways

Step-by-step explanation:

Total number of painting, n = 11

Now, three of them are chosen randomly to display in the gallery window.

Hence, r = 3

Since, order doesn't matter, hence we apply the combination.

Therefore, number of ways in which 3 paintings are chosen from 11 paintings is given by

[tex]^{11}C_3[/tex]

Formula for combination is [tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]

Using this formula, we have

[tex]^{11}C_3\\\\=\frac{11!}{3!8!}\\\\=\frac{8!\times9\times10\times11}{3!8!}\\\\=\frac{9\times10\times11}{6}\\\\=165[/tex]

Therefore, total number of ways = 165

Write these expressions in exponential form:
1. 10 * 10 * 10 * 10 *10
2. y * y * x * x * x * z * z * z * z *z
3. What is 14 to the zero power?

Answers

1. 10^5

2. z^5*x^3*y^2

3. 1

A mother who is 40 years old has a daughter and a son. The son is twice as old as the daugther. In 15 years the sum of all their ages will be 100 years. How old are the siblings now?

Answers

Answer:

The son's age is 10 and the daughter's age is 5 now

Step-by-step explanation:

Let

x-----> the son's age now

y----> the daughter's age now

we know that

x=2y ----> equation A

(x+15)+(y+15)+(40+15)=100

x+y+85=100

x+y=15 -----> equation B

Substitute equation A in equation B and solve for y

2y+y=15

3y=15

y=5 years

Find the value of x

x=2(5)=10 years

therefore

The son's age is 10.

The daughter's age is 5

Danny is a drummer who purchases his drumsticks online. When practicing with the newest pair, he notices they feel heavier than usual. When he weighs one of the sticks, he finds that it is 2.44 oz. The manufacturer's website states that the average weight of each stick is 2.00 oz with a standard deviation of 0.19 oz. Assume that the weight of the drumsticks is normally distributed. What is the probability of the sticks weight being 2.44 oz or greater?

Answers

Answer:

Probability of the sticks weight being 2.44 oz or greater is 0.01017 .

Step-by-step explanation:

We are given that the manufacturer's website states that the average weight of each stick is 2.00 oz with a standard deviation of 0.19 oz.

Also, it is given that the weight of the drumsticks is normally distributed.

Let X = weight of the drumsticks, so X ~ N([tex]\mu = 2,\sigma^{2} = 0.19^{2}[/tex])

The standard normal z distribution is given by;

               Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)

Now, probability of the sticks weight being 2.44 oz or greater = P(X >= 2.44)

P(X >= 2.44) = P( [tex]\frac{X-\mu}{\sigma}[/tex] >= [tex]\frac{2.44-2}{0.19}[/tex] ) = P(Z >= 2.32) = 1 - P(Z < 2.32)

                                                     = 1 - 0.98983 = 0.01017

Therefore, the probability of the sticks weight being 2.44 oz or greater is 0.01017 .

Final answer:

The probability of the sticks weighing 2.44 oz or more is approximately 0.01017.

Explanation:

Given that the manufacturer's website states that the average weight of each stick is 2.00 oz with a standard deviation of 0.19 oz, we know the weight of the drumsticks is normally distributed.

Let X represent the weight of the drumsticks, with X being normally distributed with a mean (μ) of 2 and a variance  [tex](\sigma^2) \ of \ 0.19^2[/tex]

To find the probability of the sticks weighing 2.44 oz or more, we need to calculate P(X ≥ 2.44).

We can standardize X using the formula Z = (X - μ) / σ, which results in a standard normal distribution with mean 0 and standard deviation 1.

So, to find P(X ≥ 2.44), we compute P((X - μ) / σ ≥ (2.44 - 2) / 0.19), which simplifies to P(Z ≥ 2.32).

From the standard normal distribution table or a calculator, we find that P(Z < 2.32) is approximately 0.98983.

Therefore, P(Z ≥ 2.32) = 1 - P(Z < 2.32) = 1 - 0.98983 = 0.01017.

Hence, the probability of the sticks weighing 2.44 oz or more is approximately 0.01017.

What is the value of x? Enter your answer in the box

Answers

Answer:

x = 20

Step-by-step explanation:

Formula

x1/x2 = x3/x4

Givens

x = 11

x2 = 11 + 121 = 132

x3 = 10

x4 = 10 + 5x + 10

Solution

11/132 = 10 / (5x + 10 + 10)        Combine

11/132 = 10/(5x + 20)                Cross multiply

11*(5x + 20) = 132 * 10              Combine on the right.

11(5x + 20 ) = 1320                   Divide by 11. (You could remove the brackets, but this is easier.

11(5x + 20)/11 = 1320/11            Do the division

5x + 20 = 120                          Subtract 20 from both sides

5x + 20-20 = 120 - 20             Combine

5x = 100                                   Divide by 5

5x/5 = 100/5

x = 20

Alice has a total of 12 dimes and nickels. She has 2 more nickels than dimes. Which equation represents the given problem situation?

A. c + (c + 2) = 12, where c is the number of dimes

B. c + 2c = 12, where c is the number of nickels

C. c + (c + 2) = 12, where c is the number of nickels

D. c + 2c = 12, where c is the number of dimes

Answers

Answer:  The correct option is

(A) [tex]c+(c+2)=12,[/tex] where c is the number of dimes.

Step-by-step explanation:  Given that Alice has a total of 12 dimes and nickels and she has 2 more nickels than dimes.

We are to select the correct equation that represents the given problem situation.

Let c represents the number of dimes. Then, the number of nickels will be (c + 2).

Since there are total 12 coins, so the required equation is given by

[tex]c+(c+2)=12.[/tex]

Thus, the required equation is

[tex]c+(c+2)=12,[/tex] where c is the number of dimes.

Option (A) is CORRECT.

The expression for the total number of dimes and nickels is  c+(c+2)=12. Option A is the correct answer.

How do you express the number of dimes and nickels?

Given that Alice has a total of 12 dimes and nickels.

Also given that she has 2 more nickels than dimes.

Let us consider that c is the number of dimes. Then the number of nickels is given as,

Number of nickels = c+2

The total sum of dimes and nickels is 12, then,

Number of dimes + Number of nickels = 12

c + (c+2) = 12

Hence the expression for the total number of dimes and nickels is  c+(c+2)=12. Option A is the correct answer.

To know more about the sum, follow the link given below.

https://brainly.com/question/24412452.

Corey bought 2 1/2 liters of paint for $60. What was the cost per liter of paint

Answers

Hello there!

Answer:

$24

Step-by-step explanation:

In order to find the answer to your problem, we're going to need to find out how much ONE liter of paint costs.

Lets gather the information of what we know:

2 1/2 liters of paint

↑ Cost $60.

With the information we know, we can solve to find the answer.

In order to get the answer, we would need to divide 60 by 2 1/2 (or 2.5). We would need to do this because when we divide it, it would allow us to get the cost for 1 liter.

Lets solve:

[tex]60 \div 2.5=24[/tex]

When you divide, you should get the answer of 24.

This means that one liter of paint cost $24.

$24 should be your FINAL answer.

Answer:

$24/liter

Step-by-step explanation:

Write the the dollar amount first and the paint volume second in this ratio:

 $60.00

--------------- = $24/liter

2.5 liters

     

Joan Arlington has twice as much money invested at 5% simple annual interest as
she does at 4%. If her yearly income from the two investments is $399, how much
does she have at each rate?
at each rate?


Please Help me ​

Answers

[tex]5 \div 100 \times 399 \times 1 = 19.95 \: and \: 4 \div 100 \times 399 \times 1 = 15.96[/tex]

How do you simplify this expression step by step using trigonometric identities?

Answers

[tex]\bf \textit{Pythagorean Identities}\\\\ 1+tan^2(\theta)=sec^2(\theta) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ sec^2(\theta )cos^2(\theta )+tan^2(\theta )\implies \cfrac{1}{\begin{matrix} cos^2(\theta ) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix} }\cdot \begin{matrix} cos^2(\theta ) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix} +tan^2(\theta ) \\\\\\ 1+tan^2(\theta )\implies sec^2(\theta )[/tex]

Consider the quadratic function f(x) = –2x2 + 4x – 2. Find the y-intercept and the equation of the axis of symmetry.

The y-intercept is 2.
The equation of the axis of symmetry is x = –1.

The y-intercept is 1.
The equation of the axis of symmetry is x = –2.


The y-intercept is –2.
The equation of the axis of symmetry is x = 1.

The y-intercept is –1.
The equation of the axis of symmetry is x = 2.

Answers

Answer:

The y-intercept is -2

The equation of the axis of symmetry is x = 1 ⇒ 3rd answer

Step-by-step explanation:

* Lets revise the general form of the quadratic function

- The general form of the quadratic function is f(x) = ax² + bx + c,

 where a, b , c are constant

# a is the coefficient of x²

# b is the coefficient of x

# c is the y-intercept

- The meaning of y-intercept is the graph of the function intersects

 the y-axis at point (0 , c)

- The axis of symmetry of the function is a vertical line

  (parallel to the y-axis) and passing through the vertex of the curve

- We can find the vertex (h , k) of the curve from a and b, where

 h is the x-coordinate of the vertex and k is the y-coordinate of it

# h = -b/a and k = f(h)

- The equation of any vertical line is x = constant

- The axis of symmetry of the quadratic function passing through

  the vertex then its equation is x = h

* Now lets solve the problem

∵ f(x) = -2x² + 4x - 2

∴ a = -2 , b = 4 , c = -2

∵ The y-intercept is c

∴ The y-intercept is -2

∵ h = -b/2a

∴ h = -4/2(-2) = -4/-4 = 1

∴ The equation of the axis of symmetry is x = 1

Given the system of equations:

2x – y = –2
x = 14 + 2y

Answer the following:
A) What is the value of the system determinant?
B) What is the value of the y−determinant?
C) What is the value of the x−determinant?
D) What is the solution to the system of equations?

My mind is blank when I look at this, any help will be appreciated.

Answers

Answer:

The determinant of A (the main matrix) is -3; the determinant of y is 30; the determinant of x is 18; the solution to the system is (-6, -10)

Step-by-step explanation:

Set up the matrix to find the determinant of the main matrix.  Find the determinant by multiplying the numbers on the major axis and subtract from that the multiplication of the numbers on the minor axis:

[tex]\left[\begin{array}{ccc}2&-1&\\1&-2\\\end{array}\right][/tex]

Find the determinant by multiplication:

(2×-2)-(1×-1)= -3

To find the determinant of y, replace the second column with the solutions to have a matrix that looks like this:

[tex]\left[\begin{array}{ccc}2&-2\\1&14\\\end{array}\right][/tex]

To find the determinant of that matrix by multiplication:

(2×14)- (1× -2) = 30

Lastly, find the determinant of x by replacing the first column with the solutions.  That matrix will look like this:

[tex]\left[\begin{array}{ccc}-2&-1\\14&-2\\\end{array}\right][/tex]

Find the determinant of x by multiplication:

(-2 × -2) - (14 × -1) = 18

Now we want Cramer's Rule that tells us if we divide the determinant of [tex]A_{x}[/tex]

by the determinant of A, we will find the value of x:

[tex]\frac{A_{x} }{A}=\frac{18}{-3}  =-6[/tex]

and the same for y:

[tex]\frac{A_{y} }{A}=\frac{30}{-3}=-10[/tex]

So the solution to the system is (-6, -10)

2x - y = -2

x = 14 + 2y

2x - y = -2

x - 2y = 14

The system determinant = -3

2 (-2) - 1 (-1)

-4 + 1

-3

The y-determinant = 30

(14) - 1 (-2)

28 + 2

30

The x-determinant = 18

-2 (-2) - 14 (-1)

4 + 14

18

The solution is x = -6 and y = -10 or (-6,-10)

x = 18/-3

x = -6

y = 30/-3

y = -10

HELP! (37PTS)
the graph of the of the quadratic function f is shown on the grid.Which of these best represents the domain of f ?
a. -3 ≤ х ≤ 2
b. all real numbers
c. y ≥ 5.5
d. All real numbers less than -3 or grater than 2

Domain:set of all possible x values,independent variable.
Range:Set of all possible y values, dependent variable.

Marissa reviews the graph and remembers
to look at how far the graph goes from the right to the left.She choses A for the correct domain

Error:

Solution:

Answers

Answer:

b. all real numbers

Step-by-step explanation:

The graphs of positive and negative x^2 parabolas will always have a domain of all real numbers.  Even though you only have a portion of the graph and see a "restriction" on your domain values, it is incorrect to assume that the domain is limited to what you can see.  As the branches of the parabola keep going up and up and up, the values of x keep getting bigger and bigger and bigger.  Again, this is true for all + or - parabolas.

Answer:

The error is C and the solution is B

Step-by-step explanation:

C is because she didn't look left to right to see that is goes on forever

B because you look left and right to see

help please

greatest common factor find the GCF of each

must show work

Answers

11) Factors of 55 are 1,5,11,55 Factors of 75 are 1,3,5,15,25,75

The greatest common factor is 5.

12) With algebraic expressions you just simplify and multiplier in the simplification is the greatest common factor.

66yx + 30x^2y --) 6yx( 11 + 5x ) so the greatest common factor is 6yx.

13) 60y + 56x^2 --) 4( 15y + 14x^2 ) so the greatest common factor is 4.

14) 36xy^3 + 24y^2 --) 12y^2( 3xy + 2 ) so the greatest common factor is 12y^2.

15) 18y^2 + 54y^2 --) 18y^2( 1 + 3 ) so the greatest common factor is 18y^2.

16) 80x^3 + 30yx^2 --) 10x^2( 8x + 3y ) so the greatest common factor is 10x^2.

17) 105x + 30yx + 75x --) 15x( 7 + 2y + 5 ) so the greatest common factor is 15x.

18) 140n + 140m^2 + 80m --) 20( 7n + 7m^2 + 4m ) so the greatest common factor is 20.

If you want a further explanation step by step just ask :)

If f (x) = – 4x3 + 2x2 – 1, find f (– 1)

Answers

Answer:

[tex]f(-1)=5[/tex]

Step-by-step explanation:

We know that the equation is

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

We can then plug -1 in for x

[tex]f(-1)=-4(-1)^3+2(-1)^2-1\\\\f(-1)=-4(-1)+2(1)-1\\\\f(-1)=4+2-1\\\\f(-1)=5[/tex]

ANSWER

[tex]f( - 1) = 5[/tex]

EXPLANATION

The given function is

[tex]f(x) = - 4 {x}^{3} + 2 {x}^{2} - 1[/tex]

We substitute x=-1 to obtain:

[tex]f( - 1) = - 4 {( - 1)}^{3} + 2 {( - 1)}^{2} - 1[/tex]

We simplify to obtain;

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

.

This evaluates to

[tex]f( - 1) = 5[/tex]

What are the solutions to the system of equations?
x = x^2 - 4x +3
y = -x +3

( , ) and ( , )

Answers

Answer:

(0,3) and (3,0)

Step-by-step explanation:

The first thing to do is graph the two equations to see where they intersect. Then you know what answer to look for. The graph is below. It was done on desmos.

I take it the first equation is a typo and should be y = x^2 - 4x + 3

Equate the two equations.

-x + 3 = x^2 -4x + 3    Subtract 3 from both sides

-x = x^2 - 4x + 3-3

-x = x^2 - 4x                Add x to both sides.

0 = x^2 - 4x + x

0 = x^2 - 3x                Factor

0 = x(x - 3)

So x can equal 0

or x can equal 3

In either case the right side will reduce to 0.

Case 1. x = 0

y= - x + 3

y = 0 + 3

y = 3

So the point is (0,3)

Case 2. x = 3

y = - x + 3

y = - 3 + 3

y = 0

So the point is (3,0)


What transformation has changed the parent function f(x) = log2x to its new appearance shown in the graph below?

logarithmic graph passing through point 2, negative 2.

−2 • f(x)
2 • f(x)
f(x) − 2
f(x) + 2

Answers

Answer: First Option

−2 • f(x)

Step-by-step explanation:

The function [tex]y=log_2(x)[/tex] passes through point (2,1) since the exponential function [tex]2 ^ x = 2[/tex] when [tex]x = 1[/tex].

Then, if the transformed function passes through the point (2, -2) then this means that f(x) was multiplied by a factor of -2. So if an ordered pair [tex](x_0, y_0)[/tex] belonged to f(x), then [tex](x_0, -2y_0)[/tex] belongs to the transformed function. Therefore, if [tex]f(x) = log_2 (x)[/tex] passed through point (2, 1) then the transformed function passes through point (2, -2)

The transformation that multiplies to f(x) by a factor of -2 is:

[tex]y = -2 * f (x)[/tex]

and the transformed function is:

[tex]y = -2log_2 (x)[/tex]

License plate numbers in a certain state consists of seven characters. The first character is a non-zero digit (1 through 9). The next four characters are capital letters (A through Z) and the last two characters are non-zero digits. Therefore, a license plate number in this state can be any string of the form:
Digit-Letter-Letter-Letter-Letter-Digit-Digit

(a) How many different liscence plate numbers are possible?
(b) How man licence plate numbers are possible if no digit appears more than once?
(c) How man licence plate numbers are possible if no digit or letter appears more than once?

Answers

Answer:

a)  333,135,504 different plates

b) 230,315,904 different plates

c) 180,835,200 different plates

Step-by-step explanation:

Pattern: Digit(1-9)-Letter-Letter-Letter-Letter-Digit(1-9)-Digit (1-9)

We will calculate the number of possibilities for the digits part, then for the letters part, then we'll multiply them together.

For the digits, we have 3 numbers, first and last 2 positions. We can consider this is a single 3-digit number, where n = 9 (since they are non-zero digits) and r = 3.  

For the letters part, it's basically a 4-letter word, where n = 26 (A through Z) and r = 4.

(a) How many different license plate numbers are possible?

No limitation on repeats for this question:

For the digits, we have 9 * 9 * 9 = 729 (since repetition is allowed, and we can pick any digit from 0 to 9 for each position)

For the letters we have: 26 * 26 * 26 * 26 = 456,976

Because the digits and letters arrangements are independent from each other, we multiply the two numbers of possibilities to have the global number of possibilities:

P = 729 * 456976 = 333,135,504 different plates, when there's no repeat limitation.

(b) How man license plate numbers are possible if no digit appears more than once?

Repeats limitation on digits:

For the digits, we have 9 * 8 * 7 = 504 (since repetition is NOT allowed, we can pick any of 9 digits for first position, then any 8 remaining and finally any 7 remaining at the end)

For the letters we still have: 26 * 26 * 26 * 26 = 456,976

Because the digits and letters arrangements are independent from each other, we multiply the two numbers of possibilities to have the global number of possibilities:

P = 504 * 456976 = 230,315,904 different plates, when there's no repeat on the digits.

(c) How man license plate numbers are possible if no digit or letter appears more than once?

Repeats limitation on both digits and letters:

For the digits, we have 9 * 8 * 7 = 504 (

For the letters we still have: 26 * 25 * 24 * 23 = 358,800

Because the digits and letters arrangements are independent from each other, we multiply the two numbers of possibilities to have the global number of possibilities:

P = 504 * 358800 = 180,835,200 different plates, when there's no repeat on the digits AND on the letters.

8) Factor each sum or difference of cubes completely.
a. 8x3 + 27

Answers

Answer:

[tex]\large\boxed{(2x+3)(4x^2-6x+9)}[/tex]

Step-by-step explanation:

[tex]8=2^3\\\\8x^3=2^3x^3=(2x)^3\\\\27=3^3\\\\8x^3+27=(2x)^3+3^3\qquad\text{use}\ a^3+b^3=(a+b)(a^2-ab+b^2)\\\\=(2x+3)\bigg((2x)^2-(2x)(3)+3^2\bigg)=(2x+3)(4x^2-6x+9)[/tex]

Can you please help me find the volume? The answer must also be rounded to the nearest tenth

Answers

Answer:

67.0 cm^3

Step-by-step explanation:

The volume of the cylinder is given by the formula ...

V = πr^2·h

The volume of the hemisphere is given by the formula ...

V = (2/3)πr^3

The volume of the two figures together will be ...

V = πr^2·h + (2/3)πr^3 = πr^2(h +2/3r)

V = π(2 cm)^2·(4 cm + 2/3·2 cm) = 64π/3 cm^3

V ≈ 67.0 cm^3

Which could be the area of one face of the rectangular prism?Check all that apply

Answers

the area of the rectangle=length x width area=11x6=66

Answer:

24 cm², 44 cm², and 66 cm²

Step-by-step explanation:

The rectangular prism has six faces.  The opposite faces have the same area, so we can say there are three faces with unique areas.

The face on the bottom of the rectangular prism has an area of:

A = 11 cm * 4 cm = 44 cm²

The face on the side of the rectangular prism has an area of:

A = 4 cm * 6 cm = 24 cm²

And the face on the front of the rectangular prism has an area of:

A = 11 cm * 6 cm = 66 cm²

So 24 cm², 44 cm², and 66 cm² are all answers that apply.

how much string is left when 1 and 3/4 in are cut from a piece measuring 3 and 1 /6 inches​

Answers

Answer:

1 5/12 inches.

Step-by-step explanation:

That is 3 1/6 - 1 3/4

= 19/6 - 7/4

The lowest common denominator of 4 and 6 is 12, so we have:

38/12 - 21/12

= 17 /12

= 1 5/12 inches (answer).

The remaining string length after cutting [tex]\(1 \frac{3}{4}\)[/tex] inches is [tex](1 \frac{5}{16}\)[/tex]inches.

The correct option is (a).

find out how much string is left when [tex]\(1 \frac{3}{4}\)[/tex] inches are cut from a piece initially measuring[tex]\(3 \frac{1}{16}\)[/tex]inches.

1. Convert the mixed numbers to improper fractions:

[tex]- \(1 \frac{3}{4}\) inches = \(\frac{7}{4}\) inches[/tex]

[tex]- \(3 \frac{1}{16}\) inches = \(\frac{49}{16}\) inches[/tex]

2. Make the denominators equal:

  - Multiply the numerator and denominator of [tex]\(\frac{7}{4}\)[/tex]by 16 to make the denominators equal:

[tex]\(\frac{7}{4} = \frac{112}{64}\)[/tex]

  - Now we have:

    - Initial length = [tex]\(\frac{49}{16}\)[/tex] inches

    - Cut length = [tex]\(\frac{112}{64}\)[/tex] inches

3. Subtract the two fractions:

  - Subtract the cut length from the initial length:

[tex]\(\frac{49}{16} - \frac{112}{64}\)[/tex]

  - To subtract, we need a common denominator. The least common multiple (LCM) of 16 and 64 is 64.

 - Convert both fractions to have a denominator of 64:

[tex]\(\frac{49}{16} = \frac{196}{64}\)[/tex]

[tex]\(\frac{112}{64}\) remains the same.[/tex]

- Subtract the numerators:

   [tex]\(\frac{196}{64} - \frac{112}{64} = \frac{84}{64}\)[/tex]

4. Simplify the result:

  - Divide both the numerator and denominator by their greatest common factor (GCF), which is 4:

[tex]\(\frac{84}{64} = \frac{21}{16}\)[/tex]

5. Convert back to a mixed number:

  - Divide the numerator by the denominator:

[tex]\(\frac{21}{16} = 1 \frac{5}{16}\)[/tex]

Therefore, the remaining string length after cutting [tex]\(1 \frac{3}{4}\)[/tex] inches is [tex](1 \frac{5}{16}\)[/tex]inches.

1. In a game, if you roll a 6 on a 6-sided number cube, you lose a turn. (a) What is the probability that you roll a 6? Explain your reasoning. (b) What is the probability that you don’t roll a 6? Explain your reasoning. (c) What is the probability that you either roll a 6 or do not roll a 6? Explain your reasoning. (d) Suppose you rolled the 6-sided number cube 120 times, how many times would you expect to roll a 6? Explain and show all of your work.

Answers

Try this options:

a. total - 6 digits, '6' - 1 digit, then probability of rolling a '6' is 1/6;

b. total - 6 digits, '6' - 1 digit, then probability of rolling 1,2,3,4,5 is 5/6;

c. if probability of rolling a '6' is p and not rolling a '6' is q, then p+q=1;

d. if expected probability of one rolling a '6' is 1/6, then numbers of times of rolling a '6' during 120 times is 120/6=20 times.

What is the value of x?

Answers

Answer:

Step-by-step explanation:

When an angle is bisected the opposite sides and the sides of the bisected angle are in a set ratio.

That translates into

(x + 8)/10 = (2x - 5)/14            Cross multiply

14* (x + 8) = 10* (2x - 5)          Remove the brackets on both sides.

14x + 112 = 20x - 50               Subtract 14x from both sides.

112 = 20x - 14x - 50                Combine

112 = 6x - 50                           Add 50 to both sides.

112+50 = 6x - 50 + 50             Combine

162 = 6x                                   Switch

6x = 162                                   Divide by 6

x = 27

please help and thank you. ​

Answers

Answer:

Step-by-step explanation:

This is a negative x^2 quadratic.  I'm not sure if there's anything else you need.

Solve the equation of exponential decay. The population of a city is expected to be 440,000 in 2020. This is a decline of 12% from 2010 to 2020. Assuming this continued what would the population of the city be in 2040? Round to the nearest ten thousand

Answers

Answer:

about 340,000

Step-by-step explanation:

In 10 years, the population dropped to 0.88 of what it was in 2010. At the same rate, in 20 more years, it will drop to 0.88² of what it was in 2020:

2040 population = 440,000·0.88² ≈ 340,000

Answer:

about 340,000

Step-by-step explanation:

In 10 years, the population dropped to 0.88 of what it was in 2010. At the same rate, in 20 more years, it will drop to 0.88² of what it was in 2020:

2040 population = 440,000·0.88² ≈ 340,000

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