Find the area of a regular 12-gon inscribed in a unit circle.
Shown below is a regular octagon. Each of the four red regions has area 12. What is the area of the blue region?
Isosceles triangle OPQ has legs OP=OQ, base PQ=2, and angle POQ=45 degrees. Find the distance from O to PQ.
ABCDEF is a regular hexagon with area 1. The intersection of triangle ACE and triangle BDF is a smaller hexagon. What is the area of the smaller hexagon?
A, B, C, D, and E are points on a circle of radius 2 in counterclockwise order. We know AB=BC=DE=2 and CD=EA. Find [ABCDE].

She bought 7 first class tickets and 5 coach tickets. The solution has been obtained by using the linear equation.

What is a linear equation?

It is a linear equation that has the highest degree of one. This demonstrates that there aren't any variables in linear equations with exponents higher than one. A straight line is produced on the graph by such an equation.

Let the number of first class tickets be 'x' and coach tickets be 'y'.

We are given that total of 12 people took the trip.

So,

x + y = 12   ....(1)

Also, we are given that she was able to purchase coach tickets for $340 and first class tickets for $1220 and the total fare came out to be $8480.

So,

340x + 1220y = 8480   ....(2)

From (1), we get

x = 12-y

Substituting this in (2), we get

⇒340(12-y) + 1220y = 8480

⇒4080 - 340y + 1220y = 8480

⇒4080 + 880y = 8480

⇒880y = 4400

⇒y = 5

Therefore, x = 12-5 = 7

Hence, she bought 7 first class tickets and 5 coach tickets.

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The complete statements are:

A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.

Given:

Mean= 32 minutes

Standard deviation = 2.1 minutes

So, [tex]\mu[/tex]- 3[tex]\sigma[/tex] = 38 - 3x 4= 26

[tex]\mu[/tex]- 2[tex]\sigma[/tex] = 38 - 2x 4 = 30

[tex]\mu[/tex]- [tex]\sigma[/tex] = 38 -4 =34

[tex]\mu[/tex]=38

[tex]\mu[/tex]+ [tex]\sigma[/tex] = 38+ 4= 42

[tex]\mu[/tex]+ 2[tex]\sigma[/tex]= 46

[tex]\mu[/tex]+ 3[tex]\sigma[/tex]=50

Thus, 68% of the data between 34 and 42 minutes.

95% of the data between 30 and 46 minutes.

99.7% of the data between 26 and 50 minutes.

50% of the data between 38 minutes.

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Answer: b= 5

Step-by-step explanation:

y + 3 = -2(x-4)

y = -2x + 8 -3

y = -2x + 5

b = 5

Answer:

no solution

Step-by-step explanation:

2x+2x+2=4x+2

4x+2=4x+2

4x-4x=2-2

0=0

Answer:

x=8

Step-by-step explanation:

34=34, always true

Answer:

$23.13

Step-by-step explanation:

The subtotal of the books before the discount is $25. To calculate the value, you multiply $25 by 12% (0.12), which equals $3. So the total cost of the books after the discount is $25 - $3 = $22.

Next, to calculate the cost of the books, including the state sales tax, you would multiply $22 by 7.5% (0.075), which equals $1.65.

Therefore, the total cost of the books, including the state sales tax is $22 + $1.65 = $23.65

the answer to this question is 4,5,6

If he purchased only 2 pair of shoes, the amount he has to pay based on average price would be $34.62.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

The total bill for four pairs of shoes came to $69.24

Number of pairs of shoes = 2

We need to find the average price for each pair of shoes .

69.24=2x

x=34.62

Hence, the average price is $34.62.

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Answer:

20%

Step-by-step explanation:

To answer this question we have to 5% of 400, this will give us the number of managers!

1) 5% of 400

This gives us the answer!

Have a lovely day :)

Answer:

below

Step-by-step explanation:

1/15 = 1 divided by 15 =  .06      (underlined part repeats)

The dimensions of the rectangle are width = 3.5 feet and length = 18 feet.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

Area of the rectangle is 63 ft².

The length of a rectangle is 11 ft more than double the width.

let the width be x.

So, the length is 2x + 11.

So, Area of rectangle = 63 ft².

l x  w = 63

(2x+ 11) x = 63

2x² + 11x = 63

2x² + 11x - 63 =0

On solving the above Quadratic equation we get

x = 7/2 and -9.

So, the width is 3.5 feet and length = 2(3.5) +11 = 18 feet

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Answer:

  (x, y, z) = (-2, 5, 3)

Step-by-step explanation:

You want an algebraic solution to the system of equations ...

The second equation suggests an expression for x:

  x = 2y -5z +3

Substituting this into the first and third equations, we have ...

  2(2y -5z +3) +3y -4z = -1   ⇒   7y -14z = -7   ⇒   y -2z = -1

  -4(2y -5z +3) +y +z = 16   ⇒   -7y +21z = 28   ⇒   y -3z = -4

These equations are reduced to standard form by dividing by the leading coefficient.

Subtracting the second of these equations from the first, we have ...

  (y -2z) -(y -3z) = (-1) -(-4)

  z = 3 . . . . . . . simplify

The first of these reduced equations tells us ...

  y = 2z -1 = 2(3) -1 = 5

And our original substitution equation says ...

  x = 2y -5z +3 = 2(5) -5(3) +3 = -2

The solution is (x, y, z) = (-2, 5, 3).

__

Additional comment

A calculator confirms this solution. The "work" is entering the correct coefficients into the appropriate calculator function, then interpreting the result.

The series of transformations of the figure will be rotation, reflection, and translation shown in the figure.

A point, line, or mathematical figure can be converted in one of four ways, and each has an effect on the object's structure and/or position.

Rotation does not change the shape and size of the geometry. But changes the orientation of the geometry.

The translation does not change the shape and size of the geometry. But changes the location.

The reflection does not change the shape and size of the geometry. But flipped the image.

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The solution of the expression ( 7⁻²  x  7⁵ x  7⁻³ ) is equal to 1.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the expression is ( 7⁻²  x  7⁵ x  7⁻³ ). The expression will be solved as below,

E = ( 7⁻²  x  7⁵ x  7⁻³ )

E = 7⁽ ⁻²⁺⁵⁻³⁾

E = 7⁽⁻⁵⁺⁵⁾

E = 7⁰

E =1

Hence, the solution of the expression ( 7⁻²  x  7⁵ x  7⁻³ ) is equal to 1.

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The total bill is  $36.87, which you can pay using one $20 bill, one $10 bill, one $5 bill, one $1 bill, and 0.87 in pennies to avoid getting any pennies back.

Let's calculate and add the 6% (sales tax)

[tex]34.78 x 0.06 = 2.08\\\\34.78 + 2.08 = 36.86[/tex]

This can be rounded to $36.87.

Considering the available bills, the best option to pay without getting pennies is :

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Answer:

x = 4y/5 + 9/5

y = 5x/4 - 9/4

Step-by-step explanation:

5x - 4y = 9  ==> solve for x

5x = 4y + 9  ==> add 4y on both sides to isolate x

x = (4y + 9) / 5  ==> divide both sides by 5 to isolate x

x = 4y/5 + 9/5  ==> distribution property

5x - 4y = 9  ==> solve for y

5x = 4y + 9  ==> add 4y on both sides to make y positive

5x - 9 = 4y  ==> subtract 9 on both sides to isolate y

y = (5x - 9) / 4  ==> divide both sides by 4 to isolate y

y = 5x/4 - 9/4  ==> distribution property

The f(8) of the exponential function is 131072

The general form of the exponential function is f(x) = abˣ

First, derive the function using the table. That is:

From the table, when x = 0, f(x) = 2. Substitute the values into the function:

f(x) = abˣ

2 = ab⁰             (Note: b⁰ = 1)

2 = a(1)

2 = a

a = 2

Also, from the table, when x = 3, f(x) = 128. Substitute the values into the function:

128 = 2 × b³

128 = 2b³

64 = b³

b³ = 64

b = ∛64

b = 4

We can now write the exponential function for the data:

f(x) = abˣ

f(x) = 2(4)ˣ

Thus, f(8) = 2(4)⁸ = 131072

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Answer: Without more information about the outstanding balance on your mortgage and the exact terms of the new mortgage, it is not possible to determine the answer to your question. The amount of the monthly payments and the total amount of interest paid over the life of the loan will depend on these factors. But here a way you can do it.

Step-by-step explanation:

First, determine the outstanding balance on the original mortgage by calculating the total payments made over the past five years and subtracting them from the original loan amount. To do this, multiply the monthly payment amount by the number of months in five years (60) to find the total payments made.

Next, calculate the new monthly payment amount on the refinance mortgage by using a mortgage calculator or the formula: M = P[r(1+r)^n]/[(1+r)^n-1], where M is the monthly payment, P is the outstanding balance from step 1, r is the interest rate (0.06625), and n is the number of payments (360 for a 30-year mortgage).

Compare the new monthly payment amount to the original monthly payment amount to see how much you will save or pay more each month.

Consider any fees or closing costs associated with refinancing and factor those into the decision to refinance.

If the savings from the lower interest rate outweigh the costs of refinancing, it may be a good decision to move forward with the refinance.

The dozens of muffins that garnet can make with the flour she has is;

1²/₅

Let us begin by saying that one dozen is 12 and not a bakers dozen (13).

Thus, our solution will be arrived as by first seeing how many times 2¹/₂ can go into 3¹/₂ by dividing the two.

Let us first convert the mixed fractions to improper fractions  to get;

2¹/₂  = 5/2

3¹/₂  = 7/2

Thus, the final step is;

7/2 ÷ 5/2

= 7/5

= 1²/₅

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The difference between two events that are 300s apart on clock A will also be 300s apart on clock B and clock C when clock A reads 380s. The time difference between events is independent of the reading on any individual clock.

The time on any of these clocks is a straight-line function of that on another, with slopes 1 and y-intercepts. Use the equation of the straight line to calculate the above quantities.

If two figures are similar, then the ratio of its corresponding sides is equal to the scale factor.

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The length of DC is 24.

Pythagoras theorem states that for a right angled triangle, the square of the hypotenuse is the sum of the squares of base and altitude.

Given is a figure of a quadrilateral.

Given that EC = 13.

Then AE = 13, since the diagonals bisect each other.

AC = 13 + 13 = 26

AD = 10

Using Pythagoras Theorem,

(AC)² = (AD)² + (DC)²

26² = 10² + (DC)²

(DC)² = 26² - 10²

         = 576

DC = √576 = 24

Hence the length of the side DC is 24,.

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E ∪ F and E' ∩ F' are not mutually exclusive events.

If two things can't happen at the same moment, they are mutually exclusive. Disjoint is another word that denotes mutual exclusion. When two occurrences are unrelated, there is no chance that both will happen at the same moment.

Given:

S= {1, 2, 3}

and E= {1}, F= {2, 3}

We know that the union contain all elements of sets.

E ∪ F = {1, 2, 3} = S

and. E' = S - E

            = {2, 3}

and, F'= S - F

          = {1}

Now, intersection contain the common elements of both sets

Then, E' ∩ F' = {1, 2, 3}

As, E ∪ F = E' ∩ F' are not mutually exclusive events.

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For P - value = 0.18, there is not sufficient evidence that more than 50% of city residents supports the tax increase. So, the right answer of this problem is option ( c ).

Hypothesis testing is a statistical method utilized to make a decision about a population, with results from a set of sampled data from said population. We consider the assumptions as the null hypothesis, or H and alternative hypothesis, that is, the hypothesis we wish to examine whether it was true or not. Using the sampled data, we can calculate the test statistic, and obtained what is known as the P-value. The P-value is used to draw a convenient vasis conclusions in hypothesis-testing and is often referred to as the observed significance level of the test. We have, survey as a random sample of 300 city residents and use the results to test the following hypotheses:

H₀ : p = 0.50

Hₐ : p>0.50

where p is proportion of all city residents who support a 1% increase in the sales tax to fund road repairs and p-hat ( sample proportion) = 158/300 = 0.52 , P - value = 0.18. Now, we check the options and try to draw the conclusion. P-value is the probability where the population proportion (p) is more extreme than sample proportion ( p-hat). but p-hat > p , i.e, P value is large, we fail to reject null hypothesis. So, There is not sufficient evidence to support null hypothesis. The option (c) is correct.

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The last term of the missing pattern is 57.

A sequence is a list of items where repetitions are allowed and hierarchy is crucial. The same as a set, it has members. The number of items determines how long the sequence is.

Given:

Sequence: 7,11,2,18,-7

As, the difference between the first two-term is 4,

while in the next two-term is 16(4²),

So, in the next two-term the difference will be equal to 64(4³).

Then, the last term is

x- (-7)= 64

x+ 7= 64

x= 57

Hence, the last term is 54.

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The slope of the line described in the table is m=-1/2

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

The points from the table are (-4, 3) and (-2, 2)

slope=2-3/-2+4

=-1/2

Hence,  the slope of the line described in the table is m=-1/2

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Answer:

  304 in²

Step-by-step explanation:

You want the surface area of a rectangular prism with dimensions 4 in, 8 in, and 10 in.

The area of a rectangular prism is given by the formula ...

  A = 2(LW +H(L +W))

Using the given dimensions, the area is ...

  A = 2(4·8 +10(4+8)) = 2(32 +120) = 304 . . . . square inches

The area of the box is 304 square inches.

The value of B on the table is given as follows:

D. 90.

A proportional relationship is defined as follows:

y = kx.

In which k is the constant of proportionality.

From the table, the constant is obtained as follows:

k = 20/14 = 40/28 = 10/7.

Hence the relationship is given as follows:

y = 10x/7.

The value of B is the value of y when x = 63, hence:

y = 10 x 63/7

y = 10 x 9

y = 90.

Meaning that the correct option is given by option D.

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The correct option is option(a) as only one letter is required to name a point.

What is a point?

A point in traditional Euclidean geometry is a simple concept that represents an exact place in space and has no length, breadth, or thickness. A point in modern mathematics is more broadly referred to as a component of a set known as a space. A point is an area that is depicted by a dot. A point just has a position; it lacks any dimensions such as length, width, shape, or size.

Usually, a geometrical figure is named by assigning one letter to each vertex of the figure.

So for a rectangle, it is 4 letters.

Hexagon is named using 6 letters since it has 6 vertices.

For a point, as mentioned there are no dimensions. It is just a dot.

Therefore a point is named using only one letter.

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Answer:

sinB= 3.8(sin16/2.4) or ~0.45162

[Note: ~ means about]

Step-by-step explanation:

To solve this problem, we need to use the Law of Sines. The Law Of Sines states that sinA/a = sinB/b. Since we know the value of A,a, and b, we can plug our known values in to find our unknown value, sinB.

sinA/a = sinB/b   [Plug in known values]

sin16/2.4 = sinB/3.8

Now, we want to just find the value of sinB. To do this, we will need to multiply both sides by 3.8, so the right side just reads sinB.

sin16/2.4 = sinB/3.8   [Multiply by 3.8]

3.8(sin16/2.4) = sinB

Now, if we want the exact answer, we can leave it as is. If you are looking for a decimal answer, let's continue to see what we would get:

3.8(sin16/2.4) = sinB

3.8(0.27563/2.4) ~ sinB

3.8(0.11484) ~ sinB

0.43642 ~ sinB

B ~ 0.45162

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