Find the area of a regular decagon with an apothem of 6. 2 units. Round your answer to the nearest hundredth.

Sylvia can fit 9 large cubic boxes and 240 small rectangular boxes into her car trunk.

We first need to convert all measurements to the same unit. Since the large cubic boxes are given in inches, we need to convert the dimensions of the trunk to inches as well.

The trunk measures 51 inches wide (4.25 ft x 12 in/ft), 48 inches deep (4 ft x 12 in/ft), and 53.33 inches high (4*1/3 ft x 12 in/ft).

Next, we need to determine how many large boxes can fit in the trunk. Since each large box is 16 inches wide,

we can fit 3 boxes across the width of the trunk:

(51 inches ÷ 16 inches = 3.19)

Similarly, we can fit 3 boxes deep and 3 boxes high.

Therefore, the maximum number of large boxes Sylvia can fit in her trunk is:

27 (3 x 3 x 3 = 27)

After fitting as many large boxes as possible, we can calculate the remaining volume of the trunk and use this to determine how many small boxes can fit.

The remaining volume is approximately 59,712 cubic inches (51 in x 48 in x 20 in).

Dividing this by the volume of each small box:

(3 in x 6 in x 4 in = 72 cubic inches)

We can fit 829 small boxes in the remaining space.

Therefore, Sylvia can fit a total of 27 large boxes and 829 small boxes in her trunk.

Learn more about measurements

brainly.com/question/2107310

#SPJ11

The required equation for the length of the candle is L = 9-0.75t.

Given that a 9-inch candle burns at the rate of 0.75 in per hour we need to determine the equation for the length L of the candle when it burns for t hours,

So, if the candle is burning at the rate of 0.75 in per hour so after burning for t hour the length decreases by 0.75t, from the original length i.e 9 in

So, we can write the equation as =

L = 9-0.75t

Hence the required equation for the length of the candle is L = 9-0.75t.

Learn more about equations click;

https://brainly.com/question/29657983

#SPJ1

The critical value needed to test for independence between the type of restoration and sensory disorders is 6. 635.

To evaluate the correlation between sensory impairments and restoration type, a chi-square test of independence can be used. To determine the critical value for this statistical test, consult the chi-square distribution table at a 0.01 significance level.

The degrees of freedom for a chi-square test of independence :

Degrees of Freedom ( df ) = ( Number of Rows - 1 ) x ( Number of Columns - 1 )

The number of rows from the table = 2

Number of columns is also = 2

The df is therefore:

df = (2 - 1) x (2 - 1) = 1 x 1 = 1

The critical value for χ² with 1 degree of freedom at a 0. 01 significance level can be founding using the Chi - Square table to be approximately 6.635.

Find out more on critical value at https://brainly.com/question/14040224

#SPJ4

Full question is:

In recent years, concerns have been expressed about adverse health effects from amalgam dental restorations, which contain mercury. The table shows results from a study in which some patients were treated with amalgam restorations and others were treated with composite restorations that do not contain mercury. Use a 0. 01 significance level to find the critical value needed to test for independence between the type of restoration and sensory disorders.

Answer:

1.5 for both

Step-by-step explanation:

Taking each number and multiplying it by 1.5 will get you the dilated coordinates

Answer:

Step-by-step explanation:

The value of x is 19 if the lines l and m are parallel.

The lines l and m are parallel

The corresponding angles are equal

We have to find the value of x

6x-9 = 5x+10

Let us take all the variable terms on one side

6x-5x=10+9

x=19

Hence, the value of x is 19 if the lines l and m are parallel.

To learn more on Coordinate Geometry click:

brainly.com/question/27326241

#SPJ1

1) Bona can drive 108 miles if she drove for 3 hour at the same speed as Claire.

2) Janet would take 1.5 hour to complete the journey and Andrew spend half hour more driving than Janet.

1) Bona speed is 44mph

Time taken by Bona is 3 hour

distance travelled by Claire is 144 miles

Time taken by Claire is 4 hour

Claire's speed = distance / time

Claire's speed = 144/4

Claire's speed = 36 mph

Distance travelled by Bona = speed × time

Distance travelled by Bona = 36 × 3

Distance travelled by Bona = 108 miles

2) Janet distance = 60 miles

Janet speed = 40 mph

Time taken by Janet = distance / speed

Time taken by Janet = 60/40

Time taken by Janet = 1.5 hour

Janet would take 1.5 hour to complete the journey

Andrew distance = 80 miles

Andrew speed = 40 mph

Time taken by Andrew = distance / speed

Time taken by Andrew = 80/40

Time taken by Andrew= 2 hour

Andrew spend half hour more driving than Janet.

To know more about speed click here :

https://brainly.com/question/28224010

#SPJ4

Each car on Mabel's train is a little less than half a foot long i.e., 3/8 feet long, or 0.375 feet long. This is solved by using simple mathematical operations.

To find the length of each car on Mabel's train, we can use the formula:

Total length of train = length of one car × number of cars

We are given that Mabel's train has 8 cars and is 3 feet long, so we can substitute those values into the formula and solve for the length of one car:

3 = x × 8

where x is the length of one car.

To solve for x, we can divide both sides by 8:

3/8 = x

Therefore, each car on Mabel's train is 3/8 feet long, or 0.375 feet long.

In other words, each car is a little less than half a foot long.

To help visualize this, imagine dividing the 3-foot length of the train into 8 equal parts. Each part would be 3/8 feet long, which is the length of one car. So when Mabel puts all 8 cars together, they form a train that is 3 feet long.

To know more about mathematical operations, refer to the link below:

https://brainly.com/question/29708824#

#SPJ11

a) Parametrization for the curve of intersection of 9y2 + z2 = 1 and xyz = 1 is:
x = 1/(z(sqrt((1 - z^2)/9)))
y = ±sqrt((1 - z^2)/9)
z = t

b)Parametrization for the curve of intersection of  x=y_and x2 - y2 =z is

x = t
y = t
z = 0
c)Parametrization for the curve of intersection of  x2 + y2 + z = is

x = r cos(t)
y = r sin(t)
z = 1 - r

a) To find the curve of intersection of the two surfaces [tex]9y^2 + z^2 = 1[/tex] and xyz = 1:

We can solve for one variable in terms of the others.

For example, we can solve for y in terms of z and x using the first equation:
[tex]9y^2 + z^2 = 1[/tex]
[tex]9y^2 = 1 - z^2[/tex]
[tex]y^2 = (1 - z^2)/9[/tex]
y = ±sqrt([tex](1 - z^2)/9)[/tex]
Substituting this into the second equation, we get:
x(sqrt((1 - [tex]z^2)/9))z = 1[/tex]
x = 1/(z(sqrt((1 - [tex]z^2)/9)))[/tex]
So, a parametrization for the curve of intersection is:
x = 1/(z(sqrt((1 - [tex]z^2)/9)))[/tex]
y = ±sqrt((1 - z^2)/9)
z = t
This is defined for all t except at z = ±1.
b) To find the curve of intersection of the two surfaces x = y and [tex]x^2 - y^2 = z:[/tex]

We can substitute x = y into the second equation:
[tex]x^2 - y^2 = z[/tex]
[tex]y^2 - y^2 = z[/tex]
z = 0
So the curve of intersection is just the x = y line.

A parametrization for this line is:
x = t
y = t
z = 0
c) To find a parametrization for the surface [tex]x^2 + y^2 + z = 1:[/tex]

We can use cylindrical coordinates:
x = r cos(t)
y = r sin(t)
z = 1 - r
where 0 ≤ r ≤ 1 and 0 ≤ t < 2π.

This parameterization covers the surface of a unit cylinder with its top and bottom caps removed.

To know more about Parameterization:

https://brainly.com/question/15585522

#SPJ11

The ranking from worst to best is Portfolio 3, Portfolio 2, and Portfolio 1. So, correct option is B.

To calculate the weighted mean of the RORs for each portfolio, we need to first multiply each ROR by the corresponding portfolio value and then sum the products for each portfolio. We then divide the total by the sum of the portfolio values.

The weighted mean for Portfolio 1 = [(10.4% x $700) + (-29.7% x $12,000) + (37.2% x $600) + (7.5% x $4,400) + (6.3% x $250)] / ($700 + $12,000 + $600 + $4,400 + $250) = -16.8%

Similarly, the weighted mean for Portfolio 2 = 3.8% and for Portfolio 3 = 11.2%.

Based on the results, the list that shows a comparison of the overall performance of the portfolios from worst to best is option b) Portfolio 3, Portfolio 2, Portfolio 1. Portfolio 3 has the highest weighted mean return of 11.2%, followed by Portfolio 2 with a return of 3.8%, and Portfolio 1 has the lowest weighted mean return of -16.8%.

Therefore, correct option is B.

To learn more about weighted mean click on,

https://brainly.com/question/30168285

#SPJ1

Complete question is:

ROR     Portfolio 1     Portfolio 2     Portfolio 3

10.4%        $700              $6,000         $3,500

-29.7%    $12,000           $9,000         $5,500

37.2%        $600              $4,500         $5,750

7.5%          $4,400            $2,000        $1,500

6.3%          $250                $1,100          $4,500

Calculate the weighted mean of the RORs for each portfolio. Based on the results, which list shows a comparison of the overall performance of the portfolios, from worst to best?

a) Portfolio 3, Portfolio 1, Portfolio 2

b) Portfolio 3, Portfolio 2, Portfolio 1

c) Portfolio 1, Portfolio 2, Portfolio 3

d) Portfolio 1, Portfolio 3, Portfolio 2

This is a statistical question because it involves collecting data. Most employees work around 40 hours each week.

a. This is a statistical question because it involves collecting data on the number of hours worked by employees each week and analyzing the distribution or pattern of the data.

b. Here's a dot plot of the data provided:

   37: •
   38: ••
   39: ••
   40: ••••••••
   41: •••
   42: ••
   43: •
   47: •

The distribution of the data in the dot plot shows that the majority of employees worked around 40 hours each week, as this is where the data is most heavily clustered. Most of the data are clustered around 40 hours, with a peak at 40 hours. There is a gap between 43 and 47 hours.

c. Based on the distribution of the data, most employees work about 40 hours each week.

More on statistics: https://brainly.com/question/13312813

#SPJ11

If 3 quarts is greater than 4prints, then the measure is not equivalent.

Equivalent units can be used to convert different units to the same unit for comparison. Equivalent means equal. For example , 1 kilogram is equal to 1,000 grams.

For example,

3 teaspoons = 1 tablespoon.

4 tablespoons = 1/4 cup.

5 tablespoons + 1 teaspoon = 1/3 cup.

8 tablespoons = 1/2 cup.

1 quart = 2pints

therefore 3 quarts = 2×3 = 6pints

therefore the statement that 3 quarter is greater than 4 prints is true and not an equivalent measure.

learn more about equivalent measure from

https://brainly.com/question/30609996

#SPJ1

Declan swims faster than Madison, with a speed of 7/2 miles per hour compared to Madison's speed of 2/5 miles per hour.

Declan swims faster than Madison. While Madison swims 2/5 mile in an hour, which means her speed is 2/5 miles per hour, Declan swims 7/10 mile in 1/5 hour, which means his speed is 7/2 miles per hour. This indicates that Declan's speed is greater than Madison's speed.

In fact, we can see that Declan's speed is almost 4 times faster than Madison's speed. This means that Declan can cover a greater distance in the same amount of time compared to Madison.

Therefore, based on the given information, we can confidently say that Declan swims faster than Madison.

Learn more about swims

brainly.com/question/29211856

#SPJ11

If there were four girls and four boys to choose from, the new sample size is one that will be a total of 16 possible combinations.

When making selections for the student council's representatives, the sample size belongs to the whole of the feasible options.

To know the sample size, we must reason every conceivable permutation involving a single female and a single male.

So, if there were four girls and four boys to choose from, the new sample size would be:

There are:

4 choices for girls

4 choices for boys.

So, for each girl's choice, there would be 4 corresponding choices for boys.

Hence it will be:

4 x  4 = 16

Learn more about sample  from

https://brainly.com/question/24466382

#SPJ4

Answer: Therefore, the tip of the pendulum rotated through an angle of approximately 0.31 radians.

Step-by-step explanation:

The length of the arc traveled by the tip of the pendulum is 8 centimeters, and the radius of the pendulum is 26 centimeters. We can use the formula for the length of an arc of a circle to find the radian angle rotated through:

Length of arc = radius * angle in radians

Solving for the angle in radians, we get:

Angle in radians = Length of arc / radius

Plugging in the given values, we get:

Angle in radians = 8 / 26

Simplifying this expression, we get:

Angle in radians = 0.30769...

Rounding this value to the nearest hundredth, we get:

Angle in radians = 0.31

Therefore, the tip of the pendulum rotated through an angle of approximately 0.31 radians.

To Know more about pendulum refer here

https://brainly.com/question/14759840#

#SPJ11

At least 95% of the observed values are expected to lie between mu minus 2 sigma and mu plus 2 sigma.

This is because of the empirical rule, also known as the 68-95-99.7 rule, which states that in a normal distribution, approximately 68% of the observations will fall within one standard deviation of the mean, about 95% of the observations will fall within two standard deviations of the mean, and around 99.7% of the observations will fall within three standard deviations of the mean.

In this case, we are given that x has mean mu and standard deviation sigma. Therefore, about 95% of the values of x are expected to lie between mu minus 2 sigma and mu plus 2 sigma, as this interval covers two standard deviations on either side of the mean.

Mathematically, we can express this as:

P(mu - 2sigma < x < mu + 2sigma) ≈ 0.95

where P is the probability that x falls within the interval mu - 2sigma to mu + 2sigma.

To learn more about sigma follow the link:

https://brainly.com/question/30592021

#SPJ1

2)By using Comparison Test,the series 23-1 5k-1 k=1,is divergent.

3)By using Integral Test the series Ink k k=1 is divergent.

2) To determine the convergence or divergence of the series 23-1 5k - 1 k=1:

For the first series, 23-1 5k-1 k=1, we can use the Limit Comparison Test.

Let's compare it to the series 5k-1 k=1.

We take the limit as k approaches infinity of the ratio of the two series:
lim(k->∞) [(23-1 5k-1) / (5k-1)] = lim(k->∞) [23 / 5] = 23/5
Since this limit is finite and positive, and the series 5k-1 diverges (as it is a p-series with p=1),

we can conclude that the given series also diverges.

3)To determine the convergence or divergence of the series Ink k k=1:
For the second series, Ink k=1, we can use the Integral Test.

We need to check if the following improper integral converges or diverges:
∫(1 to ∞) ln(x) dx
Integrating by parts, we get:
∫(1 to ∞) ln(x) dx = [xln(x) - x]1∞ + ∫(1 to ∞) dx/x
The first term evaluates to -∞, and the second term is the divergent harmonic series.

Therefore, the improper integral and the series both diverge.

To know more about Comparison Test and Integral Test:

https://brainly.com/question/30026152

#SPJ11

Answer:

ben earns $9 per hour and $6 for each delivery he makes

Step-by-step explanation:

Answer:

Step-by-step explanation:

The arc length formula is

[tex]L=\frac{\theta}{360}*2\pi r[/tex]

Theta is the angle that intersects arc HJ. That measure is 180-122 which is 58 degrees. We put that into the formula along with the radius measure of 10 to get:

[tex]L=\frac{58}{360}*2\pi (10)[/tex] which gives us, rounded to the nearest hundredth,

L = 10.12 units

To approximate the change in z = f(x, y) as x changes from −1 to −0.93 and y changes from 2 to 1.94, we can use the differential dz.

First, we need to find the partial derivatives of f with respect to x and y:

∂f/∂x = -10/x³(y²)
∂f/∂y = -10(x²)/y³

Then, we can use the following formula:

dz ≈ ∂f/∂x * Δx + ∂f/∂y * Δy

where Δx and Δy are the changes in x and y, respectively.

Substituting in the given values, we have:

Δx = -0.93 - (-1) = 0.07
Δy = 1.94 - 2 = -0.06

Using the partial derivatives we calculated earlier, we get:

dz ≈ (-10/-1.037³(2²)) * 0.07 + (-10((-1)²)/1.94³) * (-0.06)
dz ≈ -0.031

Therefore, the approximate change observed in z as x changes from −1 to −0.93 and y changes from 2 to 1.94 is -0.031.
To approximate the change in z using the differential dz, we first need to find the partial derivatives of z with respect to x and y. Given z = f(x, y) = 5/(x² + y²):

∂z/∂x = -10x/(x² + y²)²
∂z/∂y = -10y/(x² + y²)²

Now, we need to find the differential dz:

dz = (∂z/∂x)dx + (∂z/∂y)dy

Since x changes from -1 to -0.93, dx = -0.93 - (-1) = 0.07. Similarly, y changes from 2 to 1.94, so dy = 1.94 - 2 = -0.06.

Now, plug in the initial values of x and y (-1, 2):

∂z/∂x = -10(-1)/((-1)² + 2²)² = -10/25
∂z/∂y = -10(2)/((-1)² + 2²)² = -40/25

Now, plug in dx and dy into the dz equation:

dz = (-10/25)(0.07) + (-40/25)(-0.06) = 0.28 - 0.096 = 0.184

So, the approximate change in z when x changes from -1 to -0.93 and y changes from 2 to 1.94 is 0.184.

Visit here to learn more about differential brainly.com/question/31239084

#SPJ11

Answer:

Step-by-step explanation:

eeeeee

Answer:

64

Step-by-step explanation:

Answer:

64...i think

Step-by-step explanation:

125 - 88=37

88-64=24

PLS MARK BRAINLIEST

As per the given information in the question, we can compute that the correct option is C) 11.

According to the question:

[tex]f(x)=x^{2} -6x-4[/tex]

[tex]g(x)=5x+3[/tex]

Therefore,

[tex](f+g)(x)= f(x)+g(x) \\

          =x^{2} -6x-4+5x+3 \\

          =x^2-x-1[/tex]

Now, to find (f+g)(-3):

substituting x=-3 in the above equation

we get,

[tex](f+g)(-3)= (-3)^2-(-3)-1 \\

                         = 9+3-1 \\

                         =11[/tex]

Hence  (f+g)(-3)=11

To know about questions on function:

brainly.com/question/16976467

#SPJ4

The value of the angle of the arc FE⏜ is calculated as: 20°

The angle of an arc is identified by its two endpoints. The measure of an arc angle is found by dividing the arc length by the circle's circumference, then multiplying by 360 degrees. Formulas for calculating arcs and angles vary based on where they are in reference to the circle.

Now, from the given image, we see that:

FGC⏜ = 220°

∠B = 30°

∠OEC = ∠OCE = 30°

CDE⏜ = 220°

Thus:

FE⏜ = 360° - 220° - 120°

FE⏜ = 20°

Read more about Angle at Arc at: https://brainly.com/question/2005046

#SPJ1

The statement "limit as x goes to infinity of the quotient of f of x and g of x equals 5" means that as x gets larger and larger, the ratio of f(x) to g(x) approaches 5.

If f(x) grows faster than g(x) as x goes to infinity, then the ratio of f(x) to g(x) would approach infinity, not 5.

If f(x) and g(x) grow at the same rate as x goes to infinity, then the ratio of f(x) to g(x) would approach a constant value, not necessarily 5.

Therefore, the statement "limit as x goes to infinity of the quotient of f of x and g of x equals 5" shows that g(x) grows faster than f(x) as x goes to infinity. L'Hôpital's Rule is not necessary to determine this conclusion.

To learn more about limit, refer below:

https://brainly.com/question/8533149

#SPJ11

The probability of the mouse finding its way out before reaching a dead end or going out in the opening can be estimated by dividing the number of successful outcomes by the total number of trials in the sample.

To create a simulation to determine the probability that the mouse will find its way out before coming to a dead end or going out in the opening, we can follow these steps:

The probability of the mouse finding its way out before reaching a dead end or going out in the opening can be estimated by dividing the number of successful outcomes by the total number of trials in the sample. This simulation approach can help us understand the probability of success in a random maze environment, and also explore the impact of various factors such as maze complexity, size and starting position of the mouse on the outcome.

To know more about simulation, refer to the link below:

https://brainly.com/question/28564990#

#SPJ11

The coordinates of the resulting point, R′ are R' = (-9, -2)

From the question, we have the following parameters that can be used in our computation:

The point R(-2, 9) is rotated 90° clockwise around the origin.

This means thar

R = (-2, 9)

Rotation rule = 90° clockwise around the origin.

The rotation rule of 90° clockwise around the origin is

(x,y) becomes (y,-x)

So, we have

R' = (y, -x)

Substitute the known values in the above equation, so, we have the following representation

R' = (-9, -2)

Hence, the coordinates of the resulting point, R′ are R' = (-9, -2)

Read more about transformation at

https://brainly.com/question/27224272

#SPJ1

the price per foot of the copper wire is $1.62.

What is the arithmetic operation?

The basic mathematical operations are addition, subtraction, multiplication, and division, which involve manipulating two or more quantities. They are essential to the study of numbers, including the order of operations, and are fundamental to other mathematical areas such as algebra, data management, and geometry. Understanding the rules of arithmetic operations is crucial for solving problems that involve these operations.

There are 3 feet in one yard, so 2 yards of copper wire is equal to 6 feet.

To find the price per foot, we need to divide the total price by the number of feet:

Price per foot = Total price ÷ Number of feet

Price per foot = $9.72 ÷ 6

Price per foot = $1.62

Therefore, the price per foot of the copper wire is $1.62.

Learn more about arithmetic, by the following link.

https://brainly.com/question/13181427

#SPJ4

If we are drawing without replacement, the probability is approximately 27.7%, which is closest to option B: 27%.

The probability of drawing a yellow marble on the next draw depends on whether we are drawing with or without replacement.

If we are drawing without replacement, then the probability of drawing a yellow marble is 13 out of the remaining 47 marbles, since we have already drawn 35 white marbles and 13 yellow marbles out of the 48 total marbles.

If we are drawing with replacement, then the probability of drawing a yellow marble on the next draw is still 1/3, or approximately 33.3%.

Learn more about probability at: https://brainly.com/question/24756209

#SPJ1

The size of the student body is approximately 1440 students.

To determine the size of the student body, we'll use the given information that 936 students represent 65% of the total number of students. We can set up a proportion to solve for the unknown total (let's call it "x"):

(65% of x) = 936

To express the percentage as a decimal, divide 65 by 100, which equals 0.65:

0.65 * x = 936

Next, to find the value of x, divide both sides of the equation by 0.65:

x = 936 / 0.65

x ≈ 1440

So, the size of the student body is approximately 1440 students. In this problem, we used the concept of percentage to find out the total number of students in the student body, knowing that 936 students (65%) attended the football game.

Learn more about percentage here: https://brainly.com/question/24339661

#SPJ11

To find the center of the circle, we need to find the midpoint of the diameter segment CD.

Using the midpoint formula, we can find the coordinates of the midpoint M:

Midpoint formula:

M = ( (x1 + x2)/2 , (y1 + y2)/2 )

Plugging in the coordinates of C (-3,5) and D (6,-2):

M = ( (-3 + 6)/2 , (5 - 2)/2 )

M = (1.5, 1.5)

Therefore, the center of the circle is at point M with coordinates (1.5, 1.5).

Learn more about center of the circle: https://brainly.com/question/25938130

#SPJ11