Dara drove from home to the airport to pick up her
friend and then came back home on the same route.
Her average speed on the way to the airport was
55 miles
per
hour (mph), and her average speed on
the way back home was 45 mph. If the total driving
time was 1 hour and 20 minutes, how far, in miles, is
the airport from Dara's home?

The area of the domain enclosed by the curve with parametric equations x = tsin t, y = cost, t ∈ [0, 2π] is 2π + 2.

The parametric equations given are:

x = t sin t
y = cos t

To find the area of the domain enclosed by the curve, we can use the formula for the area of a region bounded by a curve given in parametric form:

A = ∫[a,b] y dx

where a and b are the limits of the parameter t that describe the domain of the curve.

In this case, we have:

a = 0
b = 2π

So, we need to compute:

A = ∫[0,2π] cos(t) (t sin(t)) dt

Using integration by parts with u = t and dv = sin(t) dt, we get:

A = [t cos(t)]|[0,2π] - ∫[0,2π] cos(t) dt + ∫[0,2π] sin(t) dt

The first integral evaluates to:

[t cos(t)]|[0,2π] = 2π

The second integral evaluates to:

∫[0,2π] cos(t) dt = [sin(t)]|[0,2π] = 0

The third integral evaluates to:

∫[0,2π] sin(t) dt = [-cos(t)]|[0,2π] = 2

Therefore, the area of the domain enclosed by the curve is:

A = 2π - 0 + 2 = 2π + 2

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Answer:

Answer:

Weight of each large box: 18.25kg

Weight of each small box: 13.25kg

Step-by-step explanation:

For this question, we have two unknowns, but we can solve them as we are given two equations.

If we use the variables 'L' for Large and 'S' for small, we  an write out the information given to us as equations:

3L + 5S = 121

6L + 2S = 136

Now we can solve these simultaneous equations by multiplying one of them by a constant so that one of the variable co-efficients are the same so we can cancel them. We can see here that we can easily double the first equation which would result in both having 6L:

2(3L + 5S) = 2(121)

=> 6L+10S=242

Now that we have one term which is the same, we can subtract one equation from the other:

  6L+ 10S = 242

- (6L + 2S = 136)

------------------------

=>0L + 8S = 106

Now we can solve for S:

8S/8 = 106/8

S = 13.25

And use this value of S to solve for L:

3L + 5(13.25) = 121

3L + 66.25 = 121

3L + 66.25 - 66.25 = 121 - 66.25

3L = 54.75

3L/3 = 54.75/3

L = 18.25

Hope this helped!

In the context of statistics, a statistic refers to a numerical value that is calculated from a sample of data, while a parameter refers to a numerical value that describes a population.

In the given scenario, the number of birds in different regions can be considered as either a statistic or a parameter depending on the context in which it is used.

If the number of birds is obtained by counting the birds in a specific region and then calculating summary measures such as the mean, median, or standard deviation based on that sample, then it would be considered a statistic. This is because the data is collected from a subset (sample) of the entire population of birds.

On the other hand, if the number of birds represents the total count or an average count across all regions without any sampling involved, then it would be considered a parameter. In this case, the value represents a characteristic of the entire population of birds in different regions.

It is important to note that whether the number of birds is considered a statistic or a parameter depends on how the data is collected and analyzed.

If multiple samples are taken from different regions and statistical inference techniques are used to make inferences about the entire population, then it would be appropriate to consider it as a statistic. However, if the data represents a complete count or an average across all regions without any sampling involved, then it would be considered a parameter.

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Answer:

149.49° (nearest hundredth)

Step-by-step explanation:

To calculate the direction of the plane's resultant vector, we can draw a vector diagram (see attachment).

Since the two vectors form a right angle, we can use the tangent trigonometric ratio.

\(\boxed{\begin{minipage}{7 cm}\underline{Tangent trigonometric ratio} \\\\$ \tan x=\dfrac{O}{A}$\\\\where:\\ \phantom{ww}$\bullet$ $x$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle.\\\end{minipage}}\)

The resultant vector is in quadrant II, since the plane is travelling north (positive y-direction) and then west (negative x-direction).

As the direction of a resultant vector is measured in an anticlockwise direction from the positive x-axis, we need to add 90° to the angle found using the tan ratio.

The angle between the y-axis and the resultant vector can be found using tan x = 767 / 452. Therefore, the expression for the direction of the resultant vector θ is:

\(\theta=90^{\circ}+\arctan \left(\dfrac{767}{452}\right)\)

\(\theta=90^{\circ}+59.4887724...^{\circ}\)

\(\theta=149.49^{\circ}\; \sf (nearest\;hundredth)\)

Therefore, the direction of the plane's resultant vector is approximately 149.49° (measured anticlockwise from the positive x-axis).

This can also be expressed as N 59.49° W.

Answer: 11

Explanation: You did everything right in terms of the steps you took. It looks like you accidentally wrote "1" instead of "-4" as the answer to "2(-2)".

Answer:

-16x + 14 4/5

Step-by-step explanation:

Perform the indicated multiplication.  We get:

2x + 14 - 18x + 4/5

Next, combine like terms:  We get:

-16x + 14 4/5

The equation of the circle centered at (-6, 2) with a diameter of 16 can be written as (x + 6)² + (y - 2)² = 64.

To determine the equation of a circle, we need the coordinates of the center and either the radius or the diameter. In this case, the center of the circle is given as (-6, 2), and the diameter is 16.

The radius of the circle can be calculated as half of the diameter, which is 16/2 = 8. Using the coordinates of the center and the radius, we can construct the equation of the circle.

The general equation of a circle centered at (h, k) with radius r is (x - h)² + (y - k)² = r². Substituting the given values, we have (x + 6)² + (y - 2)² = 8².

Simplifying further, we have (x + 6)² + (y - 2)² = 64.

Therefore, the equation of the circle centered at (-6, 2) with a diameter of 16 is (x + 6)² + (y - 2)² = 64.

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Answer:

36 ounces

Step-by-step explanation:

9 x 4 = 36

Using the z-distribution, as we have the standard deviation for the population, it is found that the 99% confidence interval for the population mean is given by:

\(\overline{x} \pm 2.58\frac{s}{\sqrt{n}}\)

The confidence interval is:

\(\overline{x} \pm z\frac{s}{\sqrt{n}}\)

In which:

99% confidence level, hence\(\alpha = 0.99\), z is the value of Z that has a p-value of \(\frac{1+0.99}{2} = 0.995\), so \(z = 2.58\).

The other parameters are symbolic, hence the interval is given by:

\(\overline{x} \pm 2.58\frac{s}{\sqrt{n}}\)

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In this case we must apply the properties of supplementary angles and opposite angles.

1 .

opposite angles

∠ 1 = 120 °

supplementary angles

∠ 1 + ∠ 2 = 180

120 + ∠ 2 = 180

∠ 2 = 180 - 120

∠ 2 = 60 °

The same properties can be applied in the other exercises to solve them.

The solution is:

∠ 1 = 120 °

∠ 2 = 60 °

Using proportions, it is found that Sylvia needs to order 324 square feet.

The rule of three is:

1 square yard - 9 square feet

36 square yards - x square feet

Applying cross multiplication:

\(x = 9 \times 36 = 324\)

Sylvia needs to order 324 square feet.

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Answer:

$181.25

Step-by-step explanation:

Given data

Amount=  $7250

The amount the parent will pay

=70/100*7250

=0.7*7250

= $5075

Hence the balance left for her to pay is

=7250 -5075

=$2175

Hence the least monthly amount is

=2175/12

=$181.25

Answer:

It will take 43.37 mins for the cake to cook off to 90

Step-by-step explanation:

From Newton's law of cooling

\(T_{(t)} = T_{s} + (T_{o} - T_{s})e^{kt}\)

Where

\(t =\) time

\(T_{(t)}\) = Temperature of the given body at time \((t)\)

\(T_{s}\) = Surrounding temperature

\(T_{o}\) = Initial temperature of the body

and \(k\) = constant

From the question,

\(T_{o}\) = 357

\(T_{s}\) = 72

\(T_{o} - T_{s}\) = 357 - 72 = 285

∴ \(T_{(t)} = 72 + 285e^{kt}\)

From the question, the cake cools to 130 after 25 min. Then, we can write that

\(T_{(25)} = 72 + 285e^{k(25)}\)

∴ \(130 = 72 + 285e^{25k}\)

Then,

\(130 - 72 = 285e^{25k}\)

\(58 = 285e^{25k}\)

\(\frac{58}{285} = e^{25k}\)

Take the natural log (ln) of both sides

\(ln^{\frac{58}{285} } =ln^{ e^{25k}}\)

\(-1.5920 = 25k\)

∴ \(k =\frac{-1.5920}{25}\)

\(k = -0.06368\)

Now, to determine how long it take for the cake to cook off to 90

That is,

\(T_{(t)} = 72 + 285e^{kt}\)

\(90 = 72 + 285e^{-0.06368t}\)

\(90 - 72= 285e^{-0.06368t}\)

\(18 = 285e^{-0.06368t}\)

\(\frac{18}{285} = e^{-0.06368t}\)

\(\frac{6}{95} =e^{-0.06368t}\)

Take the natural log (ln) of both sides

\(ln^{\frac{6}{95} } = ln^{e^{-0.06368t}}\)

\(-2.7621 = -0.06368t\\\)

∴ \(t = \frac{-2.7621}{-0.06368}\)

\(t = 43.37 mins\)

Hence, it will take 43.37 mins for the cake to cook off to 90.

Answer: T

=

$

36

Step-by-step explanation: Hmm...

Let's organize this problem.

Since he saved

$

30

, he as

$

30

Now, that is five-sixths of the total cost of the game.

Let's name the total cost

T

.

If we have a fraction of something, say, half of four, we multiply the fraction by the whole.

half of four

1

2

⋅

4

Similarly, two-thirds of the total can be represented as:

5

6

⋅

T

Now, the problem is telling us that

$

30

is equal to the expression above.

Therefore,

2/3

T

=

30

=>

6

5

⋅

5

6

⋅

T

=

6

5

⋅

30

1

=>

1

⋅

T

=

6

5

⋅

30

1

=>

T

=

$

36

Answer:

radius can't be found of a number. radius is used for geometry. If it is the area of circle, soln is below

Step-by-step explanation:

πr²= 484

r² = 484×7/22

r²=22×7

r = √154

r= 12.409 ans

The Lewis dot symbol for each element is as follows:Carbon: Carbon has 4 valence electrons. The symbol for the Lewis dot structure of carbon is as shown below: Nitrogen: Nitrogen has 5 valence electrons.

The symbol for the Lewis dot structure of nitrogen is as shown below: Oxygen: Oxygen has 6 valence electrons. The symbol for the Lewis dot structure of oxygen is as shown below: Sulfur: Sulfur has 6 valence electrons. The symbol for the Lewis dot structure of sulfur is as shown below Chlorine: Chlorine has 7 valence electrons. The symbol for the Lewis dot structure of chlorine is as shown below.

Paired electrons and unpaired electrons for the given elements are as follows:Carbon: All the electrons in carbon are paired electrons.Nitrogen: There are 3 unpaired electrons in nitrogen.Oxygen: There are 2 unpaired electrons in oxygen.Sulfur: There are 2 unpaired electrons in sulfur.Chlorine: There is 1 unpaired electron in chlorine.

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The volume of the solid is 64/3 cubic units.

To compute the volume of the solid, we integrate the area of the cross sections over the interval [0, 2] along the x-axis. The area of each cross section is given by the product of the height f(x) = 8x² and the width dx. Hence, we have:

V = ∫[0,2] f(x) dx

= ∫[0,2] 8x² dx

= [8(x³/3)] [0,2]

= 8(2³/3 - 0³/3)

= 8(8/3)

= 64/3

Therefore, the volume of the solid is 64/3 cubic units.

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Answer:

Its 26

Step-by-step explanation:

286 divided by 11 is 26

Let the unknown number of plantains be x.

It is given that one plantain costs $0.49. It is required to find the number of plantains that can be bought at $7.84.

Since one plantain can be bought for $0.49, it follows that x plantains will be bought for:

Equate this expression to the given price:

Solve the equation for x:

Hence, the required number of plantains that can be bought for $7.84 is 16.

The correct answer is 16 plantains.

Answer:

16

Step-by-step explanation:

1 plantain costs = $.49

how much can be bought from $7.84

7.84/.49 = 16 plantains

Answer:

18

Step-by-step explanation:

Given

x - 1 = 2 ( add 1 to both sides )

x = 3

Then

2x² = 2(3)² = 2 × 9 = 18

Answer:

If \(17x-1=2\\\), then \(2(x)^2\\\) will equal \(\frac{18}{289}\)

If \(x-1=2\), then \(2(x)^2\\\) will equal \(2\\\)

Step-by-step explanation:

For the step-by-step solution, please see the attachment. Part A, \(17x-1=2\\\) and \(x-1=2\), is executed in black ink while Part B, \(2(x)^2\\\), is executed in blue ink. Detailed justification of each step in green. The given function is provided in red ink.

~~~

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The length of the bridge is 12.12 feet.

The length the dog swam is 32.36 feet.

The situation forms a right angle triangle.

A right angle triangle has one of its angles as 90 degrees. Therefore, the sides and angle can be found using trigonometric ratios.

The length of the bridge is the opposite side of the triangle and the length the dog swim is the hypotenuse side of the triangle.

Therefore,

Let's find the length of the bridge as follows:

tan 68° = opposite / adjacent

tan 68° = 30 / l

cross multiply

l = 30 / tan 68

l = 12.1212121212

length of the bridge = 12.12 ft

The length the dog swim is as follows:

sin 68°= opposite / hypotenuse

sin 68° = 30 / h

h = 30 / sin 68

h = 32.3561767942

The distance the dog swimmed = 32.36 ft

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Answer:

Step-by-step explanation:

The poster will lie flat in the box because the length of the poster is less than the length of the cube shaped box.

She has a​ square-framed poster with an area of 4 square feet.

She wants to put the poster in the cube shaped box. The  cube-shaped box has a volume of 11 cubic feet.

Therefore,

volume of a cube = l³

where

Hence,

volume of a cube = l³

11 = l³

l = ∛11

l = 2.239 ft

The area of the square framed poster = l²

where

Therefore,

The area of the square framed poster = l²

4 = l²

l = √4

l = 2 ft

Hence, the poster will lie flat in the box because the length of the poster is less than the length of the cube shaped box.

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Answer:

Angle DHG

Step-by-step explanation:

From the total of 300 workers in the factory :

a. Number of men = 200 and Women = 100

b. Number of workers works in the morning = 225

c. Number of workers unionized are 150.

d. Number of workers trustworthy are 50.

Total number of workers in the factory are 300.

a. Fraction of men in the factory are ( 2/3)

= 2/3 of 300

= 200

Women

= 300 -200

= 100

b. Number of workers in the morning shift are

= 3/4 of 300

= 225

c. Total number of workers unionized

= 1/ 2 of 300

= 150

d. Number of trustworthy workers

= 1/6 of 300

= 50

Therefore, out of 300 workers in the factory answer of the following questions are:

a. Number of men and women work in the factory are 200 and 100 respectively.

b. Number of workers works in the morning is 225.

c. Unionized workers = 150

d. Trustworthy workers = 50.

The above question is incomplete , the complete question is :

The Factory has 300 workers of which 2/3 are men, 3/4 work in the morning, 1/2 are unionized and 1/6 are trusted personnel.

a. How many men work in the factory and how many women?

b. How many workers work in the morning?

c. How many are unionized?

d. How many are trustworthy?

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Answer:

dat it

116cm times 7=812

128cm times 8=1024

1024-812=212cm

Answer:

I hope you get your answer soon I've tried and couldn't get it, fingers crossed for you.