Luna's dining room is 19 feet wide and 22 feet long. Luna wants to install wooden trim
around the top of the room. The trim costs $0.06 per foot. How much will it cost Luna to buy
enough trim?

The attached picture is of a similar problem. But different radii.

Notice how you can form 2 equilateral triangles, and that there are 4 semi circles (at AC, AD, BC, BD).

This is because points C and D lie on the circumference of the circles. So distance from centres( A and b) to C and D are the radius

To get the area of your shaded section, you would just need to add up the areas of the 4 semi circles and 2 equi. triangles.

To get the area of a semi circle, work out the area of one of the sectors, i.e sector ABC, then subtract area of an equilateral triangle.

(Note, due to symmetry all semi circles have same area)

________________________________________________________

For example, for the picture below:

Area of equi triangle = absinC = 1*1*sin60 = √(3)   --> (C is angle)

Area of sector = (angle/360) * πr² = (60/360) * π * (1)² = π/6

So area of 1 semi circle = Area of Sector - Area of equi triangle

                                       = π/6 - √(3)

Now you would just add the areas of 4 semi circles, and 2 equi triangles, and compare coefficients to get a, b, c.
______________________________________

Now you would do the same for your question, except radius is now 6cm instead of 1cm.

Answer:

here,

simple interest (S)=12.50$

Principal(p)=30.00$

time(t)=0.5 year

Now,

S=PTR/100

or,12.50=30×0.5×R/100

or,1250=15R

or,1250/15=R

:.R=83.33% per annum

Answer:

Step-by-step explanation:

You want the solutions to the following inequalities by any convenient method:

We choose to rewrite these inequalities to be comparisons to zero. This is because our graphing calculator easily identifies the x-intercepts of a graph. We can look a the graph to tell where the function is above or below the x-axis.

The attached graph shows the solutions to be ...

The values obtained for the first equation will be  x ≤ 3/5 and x ≤ -5/2 and the values obtained for the second equation will be x < 1/2 and x < -3/4.

Inequalities are mathematical expressions where neither side is equal. In inequality, as opposed to equations, we compare the two values. Less than (or less than and equal to), larger than (or greater or equal to), or not similar to signs are used in place of the equal sign in between.

As per the given inequalities in the question,

1.

x(10x + 19) ≤ 15

Firstly, simplify it to the simpler form,

10x² + 19x - 15 ≤ 0

Solve the quadratic equation,

D = b² - 4ac

= 19² - 4(10)(-15).

D = 961

Now, use the formula,

(-b±√D)/2a

√D = √961 = 31

(-19 ± 31)/2(10)

So, the roots are:

1.

(-19 + 31)/20 = 12/20 = 3/5

Or, x ≤ 3/5

2.

(-19 - 31)/20 = -50/20 = -5/2

Or, x ≤ -5/2

2.

(x + 2)² > (3x + 1)²

Simplify the equation first.

x² + 4x + 4 > 9x² + 6x + 1

x² - 9x² + 4x - 6x + 4 - 1 > 0

-8x² - 2x + 3 >

8x² + 2x - 3 < 0

Now, find the roots for the equation,

D = b² - 4ac

D = 4 + 96

D = 100

Now, use the formula,

(-b ± √D)/2a

(-2 ± 10)/16

So, the roots are:

1. (-2 + 10)/16 = 1/2

Or, x < 1/2

2. (-2 - 10)/16 = -12/16 = -3/4

Or, x < -3/4

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Answer:  The following that could represent the side lengths of a triangle are A, C, D.

Step-by-step explanation:

The sum of the first two numbers of the triangle must be greater than the third.

A. 6+10= 16>14             -----------a triangle

B. 12+15= 27<29           -----------not a triangle

C. 8+8= 16>11                -----------a triangle

D. 19+24= 43>40          ------------a triangle

E. 9+17= 26=26            -------------not a triangle

Answer:Value of x are 16 and -2

Step-by-step explanation:

Solve for x in the equation:

Subtract 63 from both sides we have;

To factor this equation as:

⇒

Take (x-16) common we have;

⇒

By zero product property we have;

x-16 = 0 or x+2 = 0

⇒x = 16 or x = -2

Therefore, the value of x are: 16 and -2

The value of x in the equation are x = -2 or x = 16.

Quadratic equations are polynomial equations of second degree.

The general form of a quadratic equation is ax² + b x + c = 0.

Given is a quadratic equation,

x² - 14x + 31 = 63

We have to find the value of x.

x² - 14x + 31 - 63 = 0

x² - 14x - 32 = 0

Using the quadratic formula,

x = [14 ± [tex]\sqrt{(-14)^2-(4*1*-32)}[/tex]] / 2

  = (14 ± √324) / 2

  = (14 ± 18) / 2

x = 14 + 18 / 2 or x = 14 - 18 / 2

x = 16 or x = -2

Hence the value of x are x = 16 or x = -2.

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The number of goals scored in a hockey game is a discrete random variable.

A discrete random variable has a countable number of different possible values, such as 0,1,2,3,4, etc. Usually, but not always, discrete random variables are counted. If a random variable has a limited range of possible values, it is discrete.

The number of children in a household, the Friday night movie attendance, the number of patients at a doctor's office, and the number of faulty light bulbs in a box of ten are a few examples of discrete random variables. A discrete random variable's probability distribution is a table of the probabilities connected to each of its potential values.

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The angles m∠CEA and m∠AED are supplementary .hence the value of x will be 10 has been proved.

An angle is a geometry in plane geometry that is created by 2 rays or lines that have an identical terminus.

The identical endpoint of the two rays known as the vertex—is referenced as an angle's sides.

We are Given that m∠CEA and m∠AED are only two angles on a straight line thus they will be supplementary.

Therefore, we have

m∠CEA + m∠AED = 180°

8x + 10 + 6x + 30 = 180

14x + 40 = 180

14x = 140

x = 10

Hence "The value of x will be 10 that proved the angles m∠CEA and m∠AEDare complementary".

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Answer:

RS, SQ, QR

Step-by-step explanation:

The three angles in a triangle add up to 180° Two angles are given, so we can find the third angle.

11 + 40 + S = 180

51 + S = 180

subtract 51

S = 129°

S is the biggest angle, so the biggest side will be opposite from S. QR is the biggest side.

AngleQ is 11°, the smallest angle. The smallest side will be opposite from the smallest angle. The smallest side is RS.

The 40° angle, AngleR is in the middle. The medium length side is opposite from the medium size angle. SQ is the medium length side.

From small to big:

RS, SQ, QR

Answer:

The 4th answer down

RS, SQ, RQ

Step-by-step explanation:

There is a relationship between the angle measurement and the length of the side opposite of the angle.  The side opposite of the largest angle measurement has the longest side opposite to that angle, the same is true for the middle angle and the smallest angle.

Answer:

$5,851.88

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{7 cm}\underline{Simple Interest Formula}\\\\$ A = P(1 + rt)$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}[/tex]

Given values:

Substitute the given values into the formula and solve for P:

[tex]\implies 6000=P\left(1+0.02375 \times \dfrac{389}{365}\right)[/tex]

[tex]\implies P=\dfrac{6000}{1+0.02375 \times \dfrac{389}{365}}[/tex]

[tex]\implies P=\dfrac{6000}{1+0.0253116438...}[/tex]

[tex]\implies P=\dfrac{6000}{1.0253116438...}[/tex]

[tex]\implies P=5851.87931....[/tex]

Therefore, you would need to deposit $5,851.88 in your account now.

The shape of the graph of a function is the shape assumed by the graph of the function after the dataset generated by using the function is plotted on the coordinate plane. The shape in the graph of the question is a triangular shape.

A function is a direction used to map the values of an input variable of the function to the output variables.

The points in the attaches graph which are connected by lines are;

(0, 1.5), and (4.5, 0)

The joining of the above points in the attached graph, and the origin forms a triangular shape.

Details about the shape of the graph of a function

The graph of a function such as f(x) = -x² + 2·x + 3, is obtained by finding the values of the output values of the function, f(x) for each input value of the function, x as follows;

x     [tex]{}[/tex]             f(x)

0     [tex]{}[/tex]              3

1     [tex]{}[/tex]               4

2     [tex]{}[/tex]              3

3     [tex]{}[/tex]              0

4     [tex]{}[/tex]              -5

5     [tex]{}[/tex]              -12

6     [tex]{}[/tex]              -21

7     [tex]{}[/tex]              -32

8     [tex]{}[/tex]              -45

Please find attached the graph of the sample function created with MS Excel

The graph of the function f(x) = -x² + 2·x + 3 has the shape of a parabola, which is the shape of a quadratic function.

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Answer:

11/20

Step-by-step explanation:

4/5 - 1/4

find greatets common denominator aka 20 cuz 5 and 4 can go into 20

multiply that many tiems it goes into 20 for the numerator

you now have 16/20 - 5/20
the answer is 11/20

The volume, in milliliters, of hbrhbr solution required to neutralize 28.0 mlml of a 0.210 mm liohlioh solution is 1.176 ml.

Volume is a degree of the quantity of area that be counted occupies. Matter is described as a bodily substance that occupies area and has a mass. In bodily sciences like chemistry, the usual unit of extent is cubic metres (m3). From this, different gadgets are derived inclusive of litre (L) and millilitre (mL).

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Geometric mean will be a line segment with length x such that x² = a × c.

Geometric mean of two line segments p and q is a line x such that it satisfies the formula x² = a × b or x/a = b/x.

To construct geometric mean, first simply draw a line segment and mark a point P anywhere on this line.

Mark the length of the line segment 'a' from the point P and mark the endpoint of 'a' as A. Now, in the same line, from the point P, mark the length of the given line 'c' and mark its endpoint as C.

Now, draw a perpendicular bisector of the resulting line PC. Then we get the midpoint of PC. Let this point be O.

Draw a semicircle with center O and the endpoints P and C.

Now draw a vertical perpendicular line from the point A until it cuts the semicircle. Let N be the point where this line touches the semicircle.

Now join P with N.

The line PN will be the geometric mean x such that a × c = x².

Hence the line segment PN is the geometric mean with length x.

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The first possible date on which she will complete 25 hours of exercise for the year is on March 1.

In general, dates can refer to a specific day on the calendar, such as January 1 or December 31. Dates can also refer to a specific point in time, such as a specific hour, minute, or second. In some cases, dates can also refer to a specific period of time, such as a year, month, or week.

Since Nora plans to do a 45-minute workout four times a week,

she will exercise for a total of 4 * 45 minutes = 180 minutes per week.

This means that each week, she will exercise for a total of 180 / 60 = 3 hours.

To complete 25 hours of exercise for the year,

Nora will need to exercise for a total of 25 / 3 = 8.3 weeks.

The first possible date on which she will complete 25 hours of exercise is therefore 8.3 weeks after Jan 1,

Which is approximately 8.3 * 7 = 58 days after Jan 1.

Therefore, the first possible date on which Nora will complete 25 hours of exercise is 58 days after Jan 1, which is on March 1.

Overall, if Nora sticks to her New Year's resolution to exercise four times a week, the first possible date on which she will complete 25 hours of exercise for the year is on March 1.

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Answer: 113% = 9153

100% = ?

100/113 X 9153 = 915300/113 = Rs 8100 = sale price

90 % = 8100

100% = ?

100/90 X 8100 = Rs 9000 = marked price

108% = 8100

100% = ?

100/108 X 8100 = Rs7500 = cost

Difference = 9000 -7500 = Rs 1500

1500/7500 X 100 = 20%

ANSWER Marked price is 20% above cost price

Step-by-step explanation:

Answer:

AB - [tex]\frac{2}{1}[/tex]

BC - [tex]\frac{4}{2}[/tex]

AC - [tex]\frac{6}{3}[/tex]

Slope = 2

Step-by-step explanation:

For AB the rise (counting upwards) is 2 and the run (counting to the right) is 1. If you simplify it, it would be 2. The reason why it's not a negative is that the slope is going upwards not downwards.

The fraction in the question is 9 / 14

Fractions are represented as a numerical value, which defines a part of a whole. A fraction can be a portion or section of any quantity out of a whole, where the whole can be any number, a specific value, or a thing.

To solve this problem, we have to write an algebraic equation and solve for the unknown.

Assuming x represents the unknown value

Original fraction = x - 5 / x

When 1 is added to both numerator and denominator;

x - 5 + 1 / x + 1 = 2/3

x - 4 / x + 1 = 2/3

Cross multiplying both sides

2(x + 1) = 3(x - 4)

2x + 2 = 3x - 12

Collect like terms and solve for x

2 + 12 = 3x - 2x

x = 14

The fraction is 14 - 5 / 14 = 9 /14

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Answer:

  B.  216 in²

Step-by-step explanation:

You want to know the area of a triangle with a base of 36 inches and a height of 12 inches.

The area of a triangle is given by ...

  A = 1/2bh

where b is the base of the triangle (one side), and h is the height to the opposite vertex, measured perpendicular to the base.

The figure shows a base of 36 inches and a height of 12 inches. Using these values in the formula, we have ...

  A = 1/2(36 in)(12 in) = 216 in²

The area of the triangle is 216 in².

Answer: 216

Step-by-step explanation: I got it right sorry for the late comment

Yes, the deviation is greater than it was in tossing them 40 times.

A standard deviation (or σ) is a measure of how widely distributed the data is in reference to the mean. A low standard deviation suggests that data is grouped around the mean, whereas a large standard deviation shows that data is more spread out.

Given:

n= 400 trials

Tossing 2 coins 400 times gives 800 trials

so, [tex]\sigma_1[/tex]² = np(1- p)

        = 800 x 1/2 x 1/2

      [tex]\sigma_1[/tex]  = √200

      [tex]\sigma_1[/tex] = 10√2

Now, n=40

and,  [tex]\sigma_2[/tex]² = np(1- p)

        = 80 x 1/2 x 1/2

      [tex]\sigma_2[/tex]  = √20

      [tex]\sigma_2[/tex] = 2√5

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The mean and standard deviation of X are 0.9 and 1.68 points.

Since Nikola gets 3 points for each ringer which he scores, then total points he gets from ringers could be determined by multiplying the number of ringers by 3.

So, X = R * 3 = 3R

Where:

R = numbers of ringers

X = total points Nikola gets from ringers

Given:

Mean : μR = 0.3

Standard deviation : σR = 0.56

Thus, multiplying by 3 will effects the mean as follows:

μX = 3 (μR)

= 3 (0.3)

= 0.9

And, multiplying by 3 also will effects the standard deviation as follows:

σX = 3 (σR)

≈ 3 (0.56)

≈ 1.68

Hence, the mean of X is 0.9 and and the standard deviation of X is 1.68.

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Answer:

-4

Step-by-step explanation:

[tex]-3*2 + 2=-4[/tex]

If during the year, Salaries Payable decreased by $12,000. Using the direct method of reporting cash flows from operating activities, if Salaries Expense amounted to $450,000 for the year, the cash paid to employees is $462,000.

Cash paid can be defined can be defined as the amount that is payable to an employee by an employer.

Using this formula to find the cash paid to employees

Cash paid to employees = Salaries payable decreased + Salaries Expense

Where:

Salaries payable decreased = $12,000

Salaries expense = $450,000

Let plug in the formula

Cash paid to employees = $450,000 + $12,000

Cash paid to employees = $462,000

Therefore the Cash paid to employees  is the amount of $462,000.

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Answer:

36647.36

Step-by-step explanation:

Lease payment =$1000

interest rate= 6%, compounded monthly

Time = 4 years

We have to calculate the present value

PV = 10000 + 10000/(1+ 0.06/12)^12 + 10000/(1+0.06/12)^24+ 10000(1+0.06/12)^36 = 36647.36

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Answer:

70 degrees

Step-by-step explanation:

Triangle XBC is an isosceles triangle.

From the question given, you already know that angle XBC = 55 degrees. This means that angle XCB = 55 degrees. This is because the two sides XB and XC are of equal length, which means that the angles are also equal to each other.

Using this info, we can calculate angle BXC:

The sum of a triangle adds up to 180, so call the unknown angle x:

55 + 55 + x = 180

110 + x = 180

x = 180 - 110 = 70 degrees

Given average speed=340 miles per hour

                         speed= distance/time (formula)

                         speed= 340/60

                         speed=5.6 miles/min

now,we have to calculate time,

                             time=distance/speed

                             time=1190/5.6

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Value of x is 30 and y is 30, if angle A is (2x), angle B is (y+x), and angle C is (y-x).

The names of fundamental angles include acute, obtuse, right, straight, reflex, and full rotation. A geometrical shape called an angle is created by connecting two rays at their termini. In most cases, an angle is expressed in degrees. In geometry, there are several different kinds of angles. a geometric shape made up of two lines that meet at the same point or two planes that meet at the same line. the distance in degrees between such lines or planes.

Given

Angle A = 2x

Angle B = y + x

60 =  y + x

y = 60 - x

Angle C = y - x

60 = y - x

60 + x = y

As we know, sum of triangle is 180

2x + 60 - x + 60 + x = 180

2x - x + x = 180 - 120

2x = 60

x - 30

For value of y, equating value of x in y = 60 - x

y = 60 - 30

y = 30

Value of x is 30 and y is 30, if angle A is (2x), angle B is (y+x), and angle C is (y-x).

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Answer:

The answer is $14.224.

Step-by-step explanation:

Answer:

25%

Step-by-step explanation:

we know that you have to do amount of error/ correct amount

so the amount of error is 10 and the correct amount is 40, so its 10/40.

10 divided by 40 is 0.25.  They want the answer as a percent, so in order to turn 0.25 to a percent, you have to move the decimal 2 times over. It then turns into 25%

The ways to assign for different people is 126 ways

From the question, we have

Total number of questions, n = 9

Numbers to people, r = 4

The number of ways of selection could be drawn is calculated using the following combination formula

Total = ⁿCᵣ

Where

n = 9 and r = 4

Substitute the known values in the above equation

Total = 9C4

Apply the combination formula

ⁿCᵣ = n!/(n - r)!r!

So, we have

Total = 9!/5!4!

Evaluate

Total = 126

Hence, the number of ways is 126

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