Unit 11 Volume And Surface Area Homework 1 Area Of Plane Figures (2024)

Answer:

225 cars

Step-by-step explanation:

he can wash 120 in 8 hours.

that's 120/8 = 15 cars per hour.

so he can was 15 X 15 = 225 cars

The correct equation to find the total number of penguins living in the building is option (b): (4.6) + (3.6) + (3.6) = p

Let's break down the equation: (4.6) represents the number of penguins per home on the first floor, multiplied by the total number of homes on the first floor (6 homes per floor). (3.6) represents the number of penguins per home on the second floor, multiplied by the total number of homes on the second floor (6 homes per floor).

(3.6) represents the number of penguins per home on the third floor, multiplied by the total number of homes on the third floor (6 homes per floor). By adding these three terms together, we get the total number of penguins, represented by p.

Therefore, option (b) is the correct equation to find the total number of penguins living in the building.

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At the end of three years, Ava's account will have $750 more than Zoe's account.

To calculate the difference in the final amounts, we need to consider the interest earned on the initial deposits over the three-year period. Assuming both accounts earn the same annual interest rate, we can use the formula A = P(1 + r)^n, where A is the final amount, P is the principal (initial deposit), r is the interest rate, and n is the number of years.

For Ava's account, with an initial deposit of $5000, we have A_Ava = 5000(1 + r)^3.

For Zoe's account, with an initial deposit of $4000, we have A_Zoe = 4000(1 + r)^3.

Since no additional money is deposited or withdrawn, the difference in the final amounts will be A_Ava - A_Zoe.

Substituting the values into the equation, we get the difference as $5000(1 + r)^3 - $4000(1 + r)^3.

By simplifying the expression, we find that at the end of three years, Ava's account will have $750 more than Zoe's account.

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The relative frequency of selecting a blue marble is 33%

A jar contained 18 red marbles, 14 green marbles, and 20 blue marbles.

Let's event A: selecting a blue marble

⇒ n(A) = 20

Here, the number of trials (t) = 60

So, the relative frequency of selecting a blue marble would be,

⇒ f(A) = n(A)/t

⇒ f(A) = 20/60

⇒ f(A) = 1/3

The relative frequency to the nearest percent would be,

⇒ f(A) = (1/3 × 100)%

⇒ f(A) = 33.33%

⇒ f(A) ≈ 33%

Therefore, the relative frequency of selecting a blue marble is 33%

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Complete question:

In a circle formed by twelve synchronized swimmers, the locations of three specific swimmers can be described using their positions in relation to the other swimmers.

To describe the locations of three swimmers in a circle formed by twelve synchronized swimmers, we need additional information or specifications about their positions.

In a circle, each swimmer is equidistant from the neighboring swimmers, forming a regular pattern. However, without knowing any specific positions or reference points, it is not possible to pinpoint the exact locations of the three swimmers.

To describe the locations, we can refer to their positions relative to other swimmers, such as "swimmer A is three positions to the left of swimmer B," or "swimmer C is opposite swimmer D." By using such descriptions in relation to other swimmers, we can provide some information about the positions of the three swimmers.

However, without any specific instructions or positions given, it is not possible to provide accurate or definitive information about the locations of the three swimmers within the circle formed by twelve synchronized swimmers.

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When ordering the given numbers on the number line from left to right, the correct order is:

-4, -(-4) or 4, |3.5| or 3.5, -3, |-2.5| or 2.5, and |5| or 5.

Starting with x = -4, which is already given, we move to -(-4) or 4, which is the positive value of -4. Next, we have |3.5|, which represents the absolute value of 3.5, resulting in 3.5. Moving to -3, we have a negative number. Then, |-2.5| is the absolute value of -2.5, which is 2.5. Finally, |5| is the absolute value of 5, which remains as 5.

Therefore, the numbers on the number line, from left to right, would be -4, 4, 3.5, -3, 2.5, and 5.

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The probability of getting two numbers that have a sum of 5 on the spinner is 1/9.

What is the likelihood of obtaining two numbers with a sum of 5 on the spinner?

In probability theory, the probability of an event happening is defined as the number of favorable outcomes divided by the total number of possible outcomes. In this case, we need to determine the number of favorable outcomes where the sum of two numbers on the spinner is 5. There are two such favorable outcomes: (2, 3) and (3, 2). Since the spinner has three equal sections, the total number of possible outcomes is 3 * 3 = 9.

Therefore, the probability is calculated as 2 favorable outcomes divided by 9 total outcomes, resulting in 2/9 or approximately 0.2222.

Probability theory and calculating probabilities by considering favorable and total outcomes in different scenarios.

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The standard error of the sampling distribution is approximately 0.052 when rounded to three decimal places.

The formula for the standard error of the sampling distribution, denoted as SE, can be calculated using the formula:

SE = √[(p * (1 - p)) / n]

where p is the sample proportion and n is the sample size.

Given:

Sample size (n) = 90

Sample proportion (p) = 0.5

Substituting these values into the formula, we have:

SE = √[(0.5 * (1 - 0.5)) / 90]

= √[(0.25) / 90]

= √0.002777777777777778

≈ 0.052

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In the recent art project, the teacher purchased 94 pieces of red construction paper and 80 pieces of blue construction paper. To determine the exact ratio of red construction paper to blue construction paper, we divide the number of red construction paper pieces by the number of blue construction paper pieces.

The ratio of red construction paper to blue construction paper can be expressed as:94:80

However, we can simplify this ratio by dividing both numbers by their greatest common divisor. In this case, the greatest common divisor of 94 and 80 is 2.

Dividing 94 by 2 gives us 47, and dividing 80 by 2 gives us 40.

Therefore, the exact simplified ratio of red construction paper to blue construction paper is: 47:40

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For an integer n greater than 1, if [tex]b^{n}[/tex] = a, then b is the nth root of a.

How to complete the sentence

In the sentence, we are told about an integer greater than 1. An integer is a whole number that can either be positive or negative or even 0. Now we can assign the number n the integer, 2, and b the number 4

[tex]4^{2} = 16[/tex]

The result a for this expression is 16. This means that the value 4 is the 2nd root of 16. We can express this thus:

[tex]\sqrt[2]{16} = 4[/tex]

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An expression equivalent to 2 4/8 is 5/2.

What is expression?

Mathematical statements are called expressions if they have at least two terms that are related by an operator and contain either numbers, variables, or both.

To simplify the expression 2 4/8, we can convert the mixed number into an improper fraction and then simplify further if needed.

2 4/8 can be rewritten as 2 + 4/8.

First, let's convert the mixed number into an improper fraction:

2 + 4/8 = (2 * 8 + 4)/8 = 16/8 + 4/8 = 20/8

Now, let's simplify the fraction:

20/8 = 10/4 = 5/2

Therefore, an expression equivalent to 2 4/8 is 5/2.

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The Probability that the third student will draw a red or blue marble is 20/44, which simplifies to 5/11 or approximately 0.45.

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According to the question we have the volume of 1.35 moles of chlorine gas at RTP is 31.1 L.

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Answer:

11 years

Step-by-step explanation:

N = A (1 + increase) ^n

Where N is future amount, A is initial amount, increase is percentage increase/decrease, n is number of mins/hours/days/months/years.

479.56 = 1200(1-0.08)^n

479.56 = 1200 (0.92)^n

0.92^n = (479.56/1200)

takes logs for both sides:

log 0.92^n = log (479.56/1200)

simplify:

n log 0.92 = log (479.56/1200)

n = log (479.56/1200) ÷ log 0.92

= 11.

it will take 11 years for the value to be $479.56

The two numbers that multiply to 30 and add to 13 are 10 and 3, or 3 and 10.

To find two numbers that multiply to 30 and add to 13, we can use algebraic equations.

Let's assume the two numbers are x and y. According to the given conditions, we have two equations:

Equation 1: x× y = 30

Equation 2: x + y = 13

We can solve this system of equations by substitution or elimination.

Let's solve it using substitution:

From Equation 2, we can express one variable in terms of the other:

x = 13 - y

Substituting this value of x into Equation 1:

(13 - y) × y = 30

Expanding the equation:

13y - y² = 30

Rearranging the equation:

y² - 13y + 30 = 0

Now we can factorize this quadratic equation:

(y - 3)(y - 10) = 0

Setting each factor equal to zero and solving for y:

y - 3 = 0 or y - 10 = 0

Solving these equations:

y = 3 or y = 10

If y = 3, substituting it back into Equation 2:

x + 3 = 13

x = 13 - 3

x = 10

If y = 10, substituting it back into Equation 2:

x + 10 = 13

x = 13 - 10

x = 3

Therefore, the two sets of numbers that satisfy the conditions are:

x = 10, y = 3

x = 3, y = 10

So, the two numbers that multiply to 30 and add to 13 are 10 and 3, or 3 and 10.

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The narrator describes the house in this way to convey a sense of decay and deterioration. It is not to show that it has a nice design, remind him of something rotting, indicate the number of people inside, or suggest that the owner had a lot of parties.

The line from "Fall of the House of Usher" describes the house using imagery of old wood-work that has rotted in a neglected vault. This description serves to create a mood of decay and deterioration. The phrase "specious totality of old wood-work" suggests that the once-grand and impressive architecture of the house has fallen into disrepair. By comparing it to something rotting in a neglected vault, the narrator conveys a sense of neglect and isolation. The description emphasizes the dilapidated state of the house, setting the tone for the eerie and decaying atmosphere that permeates the story.

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The acceleration of the object can be calculated by determining the change in velocity over the given time interval. In this case, the object decreases its velocity from 60 mph to 30 mph in 5 seconds.

The acceleration can be determined using the formula: acceleration = (final velocity - initial velocity) / time.

Using the given values, we can calculate the acceleration as follows:

Acceleration = (30 mph - 60 mph) / 5 seconds

Acceleration = -30 mph / 5 seconds

Acceleration = -6 mph/s

The negative sign indicates that the object is decelerating or slowing down. The acceleration value of -6 mph/s means that the object's velocity is decreasing by 6 miles per hour every second.

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The length of segment AB is 1 unit, which is equal to the radius of the circle centered at O.

Since line AC is perpendicular to the circle centered at O, it means that line AC intersects the circle at point A. Given that the length of line AC is 1.5 units, and considering that point A lies on the circle, we can conclude that the distance from point A to the center O is equal to the radius of the circle, which is 1 unit.

Therefore, segment AB represents the distance from the center O to the point of intersection A, which is the radius of the circle. Consequently, the length of segment AB is 1 unit, matching the radius of the circle centered at O.

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The biased sample is option (h) where every fifth shopper at the mall is asked if they voted.

A biased sample is one that does not accurately represent the entire population due to a systematic bias in the sampling method. In this case, option (h) is biased because it only selects every fifth shopper at the mall and asks if they voted. This method may introduce a bias because it assumes that the opinions of every fifth shopper are representative of the entire population of mall shoppers. However, this may not be the case as there could be certain factors or characteristics that distinguish the fifth shoppers from the rest. To obtain a more representative sample, a random sampling method should be used where each individual has an equal chance of being selected, as in option (j) where a random sample of people is asked to name their favourite vehicle.

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Graph C is the graph of the exponential function [tex]F(x) = 3(0.5)^x[/tex] in this problem.

How to define an exponential function?

An exponential function has the definition presented according to the equation as follows:

[tex]y = ab^x[/tex]

In which the parameters are given as follows:

a is the value of y when x = 0.b is the rate of change.

The function for this problem is given as follows:

[tex]F(x) = 3(0.5)^x[/tex]

Hence the parameters are given as follows:

a = 3 -> y-intercept of y = 3.b = 0.5 -> decreasing exponential function.

Hence graph C is the correct graph for this problem.

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New England should be proud of the town hall meeting form of government because it promotes civic engagement and ensures direct participation in decision-making processes.

What are the reasons behind New England's pride in the town hall meeting form of government?

The town hall meeting form of government is deeply rooted in the history and culture of New England. Christopher Collier, an esteemed historian, believes that this form of government holds significant value and should be a source of pride for the region.

At its core, the town hall meeting allows community members to come together in a direct and democratic setting to discuss and decide on local matters. It fosters civic engagement by providing a platform for individuals to voice their opinions, concerns, and ideas. The participatory nature of these meetings ensures that every citizen has the opportunity to actively contribute to the decision-making process.

Furthermore, the town hall meeting form of government promotes transparency and accountability. By gathering in a public forum, citizens can witness firsthand how decisions are made and hold their elected officials accountable for their actions. This open and inclusive process strengthens the bond between the government and the governed, creating a sense of shared responsibility and trust.

In addition, town hall meetings cultivate a strong sense of community and civic pride. These gatherings provide a space for residents to connect with one another, exchange information, and collaborate on local initiatives. By coming together as a community, New Englanders can collectively address challenges, celebrate achievements, and shape the future of their towns.

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The inequality that represents the number of hours anna needs to work, h, to have enough money to buy a bike is 12h > 168

To create an inequality representing the number of hours Anna needs to work, h, to have enough money to buy a bike, we can use the given information.

Let's break down the information provided:

Anna has $30 in her account.

She earns $12 per hour at her job.

She needs more than $168 to buy a bike.

We can create the inequality as follows:

Total earnings > Cost of the bike

Since Anna earns $12 per hour and needs more than $168 to buy a bike, we can multiply her hourly earnings by the number of hours she needs to work to have enough money:

12h > 168

This inequality states that the total earnings, which is 12 times the number of hours Anna needs to work (h), must be greater than $168.

Therefore, the inequality representing the number of hours Anna needs to work, h, to have enough money to buy a bike is:

12h > 168

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The variance measures the spread or dispersion of the weights in the random sample. To calculate the variance, we square the standard deviation. Given that the standard deviation is 8.9105 kg, we square this value to obtain the variance.

The variance of the weights for the random sample of 10 subjects is approximately 79.36 kg^2, rounded to two decimal places. This means that, on average, the weights in the sample deviate from the mean weight by approximately 79.36 kg^2.

It's important to note that the variance is expressed in square units, representing the squared units of the original data (weights). It quantifies the variability or spread of the weights within the sample, providing insight into the dispersion of the data points.

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The survey question that could have been asked to produce this data display is "How many bags of dog food do you buy each month?"

The data display provided suggests that the information being analyzed relates to the frequency of dog food purchases. The question "How many bags of dog food do you buy each month?" would directly elicit the specific data required to create such a display. By asking dog owners about the number of bags they purchase monthly, the survey collects quantitative data that can be organized and displayed graphically or numerically. This information can be used to identify patterns, trends, or variations in dog food consumption, providing insights for retailers, manufacturers, and pet owners. It allows for comparisons between different demographic groups or regions and can help inform marketing strategies or product development related to dog food. Overall, this survey question provides a clear and focused inquiry into the purchasing habits of dog owners, generating data that can be visually represented and analyzed for various purposes.

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A single parachute canopy will require roughly 88.48 [tex]ft^2[/tex] of each colour (red, white, and blue).

Approximately how much fabric of each color will be needed to make a single parachute canopy?

The canopy of the parachute is a semicircle with a radius of 13 feet. The area of a semicircle is given by the formula:

[tex]A = (\pi * r^2) / 2[/tex]

where A represents the area and r represents the radius.

Calculate the area of the semicircle canopy:

[tex]A = (\pi * 13^2) / 2 = (\pi * 169) / 2 = 265.45 ft^2[/tex] (rounded to two decimal places).

Since the company wants each parachute to be made from equal parts of red, white, and blue fabric, divide the total area by 3 to determine the amount of fabric needed for each color.Calculate the amount of fabric needed for each color:

[tex]265.45 ft^2 / 3 = 88.48 ft^2[/tex] (rounded to two decimal places).

Therefore, approximately 88.48 ft² of each color (red, white, and blue) will be needed to make a single parachute canopy.

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The reference to "Lincoln" in this context is most likely about Abraham Lincoln's famous speech, the Gettysburg Address. In the Gettysburg Address, Lincoln asks his listeners to commit themselves to four specific ideas at the end of the speech. The ideas are as follows:

1. "That from these honored dead we take increased devotion to that cause for which they gave the last full measure of devotion." Lincoln urges the listeners to honor and remember the sacrifice of those who died in the Civil War and to be even more dedicated to the cause for which they fought.

2. "That we here highly resolve that these dead shall not have died in vain." Lincoln emphasizes the importance of ensuring that the deaths of those who fought in the war were not in vain. He encourages the listeners to work towards preserving the principles and ideals for which they fought.

3. "That this nation, under God, shall have a new birth of freedom." Lincoln expresses his hope for a renewed sense of freedom and unity in the nation, emphasizing that the war and its aftermath should lead to a stronger and more inclusive nation.

4. "And that government of the people, by the people, for the people, shall not perish from the earth." Lincoln underscores the importance of a democratic government that is founded on the principles of the people, by the people, and for the people. He asserts that such a government should endure and continue to exist.

These four ideas encapsulate the core messages and calls to action in Lincoln's Gettysburg Address.

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Outer space lacks friction, which allows spaceships to fly.

Friction is a force that opposes motion between two surfaces in contact, and in the vacuum of space, there is no air or other matter to create friction. This absence of friction allows spaceships to move freely without the need to overcome the resistance that friction would normally provide. However, it is important to note that spaceships still experience other forces, such as gravity and inertia, which need to be considered and accounted for in space exploration and spacecraft navigation.

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To make a wave with a greater frequency, the student's hand motion would need to become faster. The frequency of a wave is determined by the number of waves that pass a given point in a unit of time.

So, by increasing the speed of the hand motion, the waves created would pass the same point more frequently, resulting in a higher frequency. Alternatively, the amplitude (height) of the waves could be decreased, as the frequency of a wave is inversely proportional to its wavelength (the distance between two consecutive peaks or troughs of a wave). By reducing the wavelength through decreasing the amplitude, the frequency would increase.
To make a wave with a greater frequency, the student's hand motion should be changed as follows:
1. Increase the speed of hand motion: Move the hand back and forth more quickly. This will create more waves in the same amount of time, resulting in a higher frequency.
2. Decrease the wavelength: By moving the hand in smaller, more rapid motions, the distance between each wave crest will decrease, leading to an increase in frequency.
By making these changes to the hand motion, the student will create a wave with a greater frequency.

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