The edge of a cube-shaped box is 1 yard long. Three students each made an observation about the box. • Janae said that the area of each face of the box is 9 square feet. • Archie said that the perimeter of each face of the box is 3 feet. • Gail said that the volume of the box is 1 cubic yard. Whose observations about the box are correct?​

There may be a difference on speed based on various factors

Though it would be reasonable to conclude that if it takes less time for a car to move 50 centimeters than 150 centimeters, they must be traveling faster; we do not know exactly when they did this and whether their speed changed accordingly.

Furthermore, it could have taken the same time covering both distances; thus leaving unanswered questions regarding their relative speeds.

Due to variables affecting car speed such as changes in terrain or obstacles in its path, we cannot accurately predict its speed without more information regarding these two runs.

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Answer:

Ф  Exponential.                                

Step-by-step explanation:

The most appropriate for tehe data shown is:

Ф  Exponential.                                          

...

The scale of the map can be written as:

1cm to 20km

We want to find the distance that 1 cm in the map representes in the real world.

We know the relation:

3cm = 60km

We want to get a 1 in the left side, then we can divide both sides by 3 to get:

1cm = 60km/3

1cm = 20km

Then the scale of the map is 1cm to 20km

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The confidence level for length of the thorax of 49 fruit fly males is  (0.7820 mm, 0.8188 mm).

Here the sample size (n=49), the sample mean (a=0.8004 mm), and the sample standard deviation (s=0.0782 mm), we can calculate the confidence interval as follows:

1. Determine the critical value (z-score) for a 90% confidence level. You can use a z-table or calculator to find the z-score, which is approximately 1.645.

2. Calculate the margin of error using the z-score, sample standard deviation, and sample size:
Margin of Error = z-score * (s / √n)
Margin of Error = 1.645 * (0.0782 / √49)
Margin of Error ≈ 0.0184 mm

3. Add and subtract the margin of error from the sample mean to obtain the confidence interval:
Lower Limit = a - Margin of Error = 0.8004 - 0.0184 ≈ 0.7820 mm
Upper Limit = a + Margin of Error = 0.8004 + 0.0184 ≈ 0.8188 mm

So, the 90% confidence interval for the true mean thorax length of a male fruit fly is approximately (0.7820 mm, 0.8188 mm). This means that we are 90% confident that the true mean thorax length of a male fruit fly falls within this range.

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The percentage of the data values that are greater than 16, as shown in the box plot is: 75%.

A box plot shows how the data points of a data set are distributed, in such a way that, 25% of the data points lie below the lower quartile, % lie below the median, and 75% lie below the upper quartile.

In the box plot given, the values that are greater than 16 lie above the upper quartile, which equals about 75% of the data values.

Therefore, the percentage of the data values that are greater than 65, as shown in the box plot is: 75%.

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The prize wheel's area is approximately 12.56 square yards.

The area of a circle can be calculated using the formula A = πr², where A represents the area, r represents the radius, and π is approximately 3.14. In Lucy's case, the big prize wheel has a radius of 2 yards.

To find the area of the prize wheel, we can plug the radius value into the formula:

A = π(2 yards)²

Squaring the radius (2 yards) gives us:

A = π(4 square yards)

Now, we can multiply by the given value of π (3.14):

A = 3.14 × 4 square yards

Finally, multiplying these values together, we get:

A = 12.56 square yards

Therefore, the area of the prize wheel is approximately 12.56 square yards. This calculation helps us understand the size of the prize wheel, which can be useful for various purposes such as determining the space required for the game show set or designing the prize sections on the wheel.

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The measurement closest to the number of meters Chelsea sprinted is F) 109.1 yd.

To determine the number of meters Chelsea sprinted, we need to convert the distance she sprinted from yards to meters.

Given:

Chelsea sprinted 120 yards.

Conversion:

1 meter is approximately equal to 1.1 yards.

To convert yards to meters, we divide the distance in yards by the conversion factor:

120 yards / 1.1 yards/meter ≈ 109.1 meters.

Therefore, the measurement closest to the number of meters Chelsea sprinted is F) 109.1 yd.

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Answer:

shape a is 20 cm squared

Step-by-step explanation:

shape a is a parallogram, A =b×h. 5x4=20

shape b is a trapezoid. The picture is cut off but here are the steps for you to solve. A=0.5h(base1+base2) count the number of squares on the top and bottom of the shape. I can see the top is 2, you will need to tfind the length of the bottom base.then count the height, how far to get from the bottom to top, here it is 4.

area=0.5*4(2+bottom base) simply and that's your answer! Don't forget your units

The fraction value of 0.64 is 16/25 using the greatest common factor method to represent. There are no repeating digits in value.

The given decimal value = 0.64

There are no repeating numbers in the given decimal number 0.64.

To convert the given number into a fraction, we need to multiply the value with 10 on both sides to move the decimal point two places to the right.

0.64 × 100/100 = 64/100

Now simply this value by dividing both the numerator and denominator with the greatest common factor of both values. The greatest common factor is 4.

64/100 = 16/25

Therefore, we can represent the fraction value of 0.64 as 16/25.

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The trigonometric function equivalent to sec(-270) is -1.

The secant function is defined as the reciprocal of the cosine function, i.e., sec(x) = 1/cos(x). To find the value of sec(-270), we need to first find the cosine of -270 degrees. The cosine function has a period of 360 degrees, which means that cos(-270) is the same as cos(-270 + 360) = cos(90) = 0. Therefore, we have sec(-270) = 1/0, which is undefined.

However, we can determine the sign of sec(-270) by examining the quadrant in which the angle -270 degrees lies. Since -270 degrees is in the fourth quadrant, the cosine function is negative in that quadrant. Therefore, we can write sec(-270) = -1/0-, which is equivalent to -1. Hence, the trigonometric function equivalent to sec(-270) is -1.

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The total amount of the principal, interest, down payment, and fees described for Brooke's condominium is $1,154,091.59

The first step is to calculate the mortgage amount, which is the purchase price minus the down payment:

Mortgage amount = $413,600 - 9% of $413,600 = $376,576

Next, we need to calculate the total cost of the fees and charges:

Discount points = 1% of $376,576 = $3,766

Origination fee = 0.75% of $376,576 = $2,823.42

Documentary stamp tax on deed = $0.70 per $100 or portion thereof, so for $413,600 it would be:

$0.70 * ($413,600 / $100) = $2,895.20

Documentary stamp tax on mortgage = $0.35 per $100 or portion thereof, so for $376,576 it would be:

$0.35 * ($376,576 / $100) = $1,318.02

Brokerage fee = $175 + 5% of $376,576 = $19411.8

Intangible tax = 0.2% of $376,576 = $753.15

Now we can calculate the total cost of the principal and interest payments over the life of the mortgage. We'll use a mortgage calculator to do this, based on the mortgage amount, interest rate, and term:

Total mortgage payments = $2,244 * 12 months * 25 years = $673,200

Finally, we can add up all of these amounts to get the total cost of the principal, interest, down payment, and fees:

Total cost = Purchase price + Down payment + Mortgage payments + Discount points + Origination fee + Documentary stamp tax on deed + Documentary stamp tax on mortgage + Brokerage fee + Intangible tax

Total cost = $413,600 + $37,224 + $673,200 + $3,766 + $2,823.42 + $2,895.20 + $1,318.02 + $19,411.80 + $753.15

Total cost = $1,154,091.59

Therefore, we got a total cost of $1,154,091.59

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Answer:

there both symmetrical

Answer:

Congruent

Step-by-step explanation:

When visualizing how two angles are related, try squashing the two parallel lines into each other. When you do that with these angles, they go from appearing like =\= to appearing like -\-, with x and y being catty-corner from each other.

Because the parallel lines are straight, x and y are both half of a pair that adds up to 180. However, x and y aren't sharing a straight line, so they cannot add up to 180 with each other. That leaves only one possibility, that x and y have the same angle measure.

Answer:

39.27 square units

Step-by-step explanation:

In circle E with m∠DEF = 70∘ and DE=8, we want to find the area of sector DEF. To do this, we can use the formula for the area of a sector:

A_sector=1/2 r^2⋅

α

where r is the radius of the circle and α is the central angle in radians. In our case, r=8 and α=70 ∘ ⋅ π/180∘ = 7π/18 radians

Now, we can plug these values into the formula:

A_sector = 1/2(8^2) ⋅ 7π/18 = 32 ⋅ 7π/18 ≈ 39.27

So, the area of sector DEF is approximately 39.27 square units, rounded to the nearest hundredth.

The area of sector DEF in circle E is approximately 6.10 square units, rounded to the nearest hundredth.

To find the area of sector DEF in circle E, we need to use the formula for the area of a sector:

Area of sector = (Central angle / 360°) * π * r^2

where "Central angle" is the measure of angle DEF in degrees, "r" is the radius of the circle (DE in this case).

Given that m/DEF = 70° and DE = 8, we can calculate the area of sector DEF as follows:

Area of sector = (70° / 360°) * π * 8^2

Now, perform the calculations step by step:

Area of sector = (70/360) * π * 64

Area of sector = (7/36) * π * 64

Area of sector ≈ 3.14 * (7/36) * 64

Area of sector ≈ 3.14 * 1.9444

Area of sector ≈ 6.10 (rounded to two decimal places)

Therefore, the area of sector DEF in circle E is approximately 6.10 square units, rounded to the nearest hundredth.

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The value of x in the similar figures is 2.33

When two figures have the same shape but their sizes are different, then such figures are called similar figures

The two polygons are similar

We have to find the value of x

Let us form a proportional equation

4590/21=510/x

4590x=21×510

4590x=10710

Divide both sides by 4540

x=10710/4590

x=2.33

Hence, the value of x in the similar figures is 2.33

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The two true statements are:

A "When the time starts, there are 13.5 gallons of water in the pool."

C "The water is draining at a rate of 1.25 gallons per minute."

Here we have the linaer equation y = –1.25x + 13.5 that represents the gallons of water y left in an inflatable pool after x minutes.

And we want to see which of the given statements are true.

We can see that the slope is -1.25, this means that the volume of water is reducing (due to the negative sign) then the statement C is true.

We also can see that the y-intercept is 13.5, that would be the initial volume of water in the pool, then the statement A "When the time starts, there are 13.5 gallons of water in the pool." is also true.

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Cos(165) in terms of sine and cosine of an acute angle is -1 + 2sin^2(7.5).

We can use the trigonometric identity cos(180 - x) = -cos(x) to find cos(165) in terms of cosine of an acute angle.

Since 165 = 180 - 15, we have:

cos(165) = cos(180 - 15) = -cos(15)

To express cos(15) in terms of sine and cosine of an acute angle, we can use the following trigonometric identities:

sin(2x) = 2sin(x)cos(x) and cos(2x) = cos^2(x) - sin^2(x)

Let's take x = 7.5, which is half of 15 (the acute angle):

sin(15) = 2sin(7.5)cos(7.5)

cos(15) = cos^2(7.5) - sin^2(7.5)

Now, we can solve for cos(15):

cos(15) = cos^2(7.5) - sin^2(7.5)

= (1 - sin^2(7.5)) - sin^2(7.5)

= 1 - 2sin^2(7.5)

Therefore, we have:

cos(165) = -cos(15)

= -[1 - 2sin^2(7.5)]

= -1 + 2sin^2(7.5)

So, cos(165) in terms of sine and cosine of an acute angle is -1 + 2sin^2(7.5).

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To determine the range and sample standard deviation of tornadoes that touched down during each month of one year, we need to use the data in the table.

However, the table is not provided in the question.

Please provide the table with the number of tornadoes that touched down during each month of one year so I can help you with your question.
To determine the range and sample standard deviation of the number of tornadoes that touched down each month, you'll first need to provide the data in a table format.

Once you provide the data, I can help you calculate the range and sample standard deviation.

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Correct question:

Each​ year, tornadoes that touch down are recorded. The following table gives the number of tornadoes that touched down during each month of one year. Determine the range and sample standard deviation.

3 2 41 115 197 95

70 85 68 64 110 91

Range?

Sample Standard Deviation?

There were 19 teachers sitting in the school auditorium.

The question provides us with the total number of people present in the auditorium, which is 81. It also tells us that 19 of them were teachers. Therefore, the number of students present in the auditorium can be found by subtracting the number of teachers from the total number of people, which is 81 - 19 = 62.

Since the question only asks about the number of teachers present in the auditorium, the answer is simply 19. This is because the question already provides us with the information that there were 19 teachers present.

Alternatively, we can use algebra to solve the problem. Let x be the number of students present in the auditorium. Then, we can write an equation based on the total number of people in the auditorium: x + 19 = 81. Solving for x, we get x = 81 - 19 = 62. Therefore, the number of teachers present in the auditorium is 19.

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A theater can make at least $675 from ticket sales by selling at least 100 adult tickets and up to 50 child tickets.

To solve this problem, we can use a system of equations. Let's define:

- x as the number of adult tickets sold
- y as the number of child tickets sold

We know that:

- x + y ≤ 150 (due to the limit on seating)
- 12x + 7.5y ≥ 675 (they want to make at least $675)

We can solve this system of equations using substitution or elimination. Let's use elimination:

- Multiply the second equation by 2 to get rid of the decimals: 24x + 15y ≥ 1350
- Multiply the first equation by 15: 15x + 15y ≤ 2250
- Subtract the second equation from the first: 9x ≥ 900
- Divide both sides by 9: x ≥ 100

So they need to sell at least 100 adult tickets to make at least $675. Let's see if that's possible:

- If they sell 100 adult tickets, that leaves 50 tickets for children
- 100 adult tickets * $12 = $1200
- 50 child tickets * $7.50 = $375
- Total ticket sales = $1575 (more than $675)

So they can make at least $675 from ticket sales by selling at least 100 adult tickets and up to 50 child tickets.

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The density of deer for 400 square miles is around 1:4 based on stated number of deers.

The density of deer will be given by the formula -

Population density of deer = number of deer/ area

Population density is the amount or number of individuals of a population on land per unit area.

Keep the value in formula to find the population density

Population density = 100/400

Cancelling zero as common in both numerator and denominator

Population density = 1:4

Thus, there is 1 deer for every 4 square mile.

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Cloud storage is the storage option that has the ability to update itself regularly.

Unlike internal hard drives and flash drives, which require manual updates and data transfers, cloud storage services automatically synchronize and update your files across multiple devices. This feature ensures that you always have access to the most recent version of your data, without needing to perform manual updates.

Cloud storage services operate on remote servers managed by service providers, allowing users to store, share, and access their data from any device with internet access. This not only provides convenience but also offers enhanced data security and protection against data loss due to hardware failure or damage.

On the other hand, internal hard drives and flash drives are physical storage devices that store data locally. While they offer a certain level of convenience and portability, they lack the ability to automatically update or sync across multiple devices, making them less versatile compared to cloud storage.

In summary, cloud storage is the storage option with the ability to update itself regularly, providing users with convenience, enhanced security, and the ability to access their data from multiple devices. Meanwhile, internal hard drives and flash drives require manual updates and are limited in their capacity to sync data across devices.

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Herbert will earn $63,417 for his tenth year of work which is calculated using compound interest formula.

After graduating from college, Herbert decided to join a new company. He agreed to a salary which will increase by 4.5% each year. This means that every year, Herbert's salary will increase by 4.5% of his previous year's salary. For example, if his salary in the first year is $50,000, his salary in the second year will be $52,250, and so on.

To find out Herbert's salary for his tenth year of work, we need to use compound interest formula. The formula is:

A = P(1 + r)ⁿ

Where:
A = Final amount (salary in the tenth year)
P = Initial amount (salary in the first year)
r = Annual interest rate (4.5%)
n = Number of years (10)

Substituting the values in the formula, we get:

A = $50,000(1 + 0.045)¹⁰
A = $63,417

Therefore, Herbert will earn $63,417 for his tenth year of work. It is important to note that the increase in salary is a result of compound interest, which means that the salary growth rate accelerates over time. This is a good incentive for Herbert to stay with the company and work hard.

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Answer:

Not enough info

Step-by-step explanation:

Volume of cone formula is: V = 1/3 π r²h

You did not give the radius so it is not possible to find the solution

If radius is given, isolate h by dividing the V by 1/3 π r²

Then simplify the left side of the equation and that is what h is

Answer:

13 units

Step-by-step explanation:

To find the distance between the two points, use the distance formula.

[tex]\sqrt{(x-x)^{2}+(y-y)^{2} }[/tex]

Plug in the point values.

[tex]\sqrt{(-8--3)^{2}+(-6-6)^{2} }[/tex]

Simplify the parenthesis.

[tex]\sqrt{(5)^2+(-12)^2}[/tex]

Get rid of the parenthesis.

[tex]\sqrt{25+144}[/tex]

Simplify.

[tex]\sqrt{169}[/tex]

Solve.

13 units

Discovering commonalities and variations among objects or people encountered daily is beneficial in several ways:

Decision-Making: Recognizing similarities and variations is key to making smart choices, such as selecting products or services based on their features, benefits, and drawbacks.

Problem Solve: Recognizing patterns and distinguishing features can assist with problem-solving by helping you pinpoint the causes of issues and create custom solutions.

Understanding commonalities and differences among people can enhance communication and relationships, enabling you to empathize with them, appreciate diverse viewpoints, and adjust your communication style appropriately.

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It would cost $735 to buy a cover for the pool at $0.30 per square foot

From the complete question (see attachment), we have the following parameters that can be used in our computation:

Unit rate = $0.30 per square foot

Dimensions = 10 inches by 20 inches

Scale = 2 inches : 7 feet

Using the above as a guide, we have the following:

Total cost = Unit rate * Area of pool

Where

Area of the pool = 10 inches * 20 inches

Using the scale, we have

Area of the pool = (10 * 7/2)* (20 * 7/2) square feet

Area of the pool = 2450 square feet

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

Total cost = $0.30 per square feet * 2450 square feet

This gives

Total cost = $735

Hence, it would cost $735 to buy a cover for the pool

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Complete question

The blueprint of a pool has a scale of 2 inches equals 7 feet. The scale drawing is shown below (see attachment)

How much would it cost to buy a cover for the pool that cost $0.30 per square foot

Answer:

y = 10

Step-by-step explanation:

If y varies directly with x, and y=20 when x=-2, the best way to find y when x=-1 is to divide 20/-2, which equals -10.

Now cancel out -1 by dividing it by 1, and do the same with -10 by dividing it by 1 also. This equals 10, and that's your answer. Check the table I made below representing the problem. It should make it easier understand.

The percentage of plastic beads on clearance is 98.99%.

To calculate the percentage of plastic beads on clearance, you need to divide the number of plastic beads by the total number of beads and then multiply by 100 to get the percentage.

In this case, the total number of beads on clearance is the sum of plastic beads and metal beads:

In this question, you are given the number of plastic beads and metal beads on clearance, and you are asked to find the percentage of plastic beads.

To do this, you need to calculate the total number of beads on clearance by adding the number of plastic beads and the number of metal beads.

Once you have the total number of beads, you can find the percentage of plastic beads by dividing the number of plastic beads by the total number of beads.

And then multiplying by 100 to convert the answer into a percentage. This formula can be expressed as:

Percentage of plastic beads = (Number of plastic beads / Total number of beads) x 100%

Plugging in the given values, we get:

Total number of beads = 882 + 18 = 900

Percentage of plastic beads = (882 / 900) x 100% = 98.99%

So, the answer is that 98.99% of the beads on clearance are plastic.

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The total number of possible lock combination using the 40 possible numbers for making lock of 3 numbers is equal to 64,000.

Possible number used for lock combination are 40.

Range is 0 - 39.

Total number chosen for lock combination is equal to 3.

Since there are 40 possible numbers to choose from for each of the three positions on the combination lock.

The total number of possible combinations is equal to ,

40 x 40 x 40

= 40^3

= 64,000

Therefore, there are 64,000 possible lock combinations when choosing 3 numbers out of 40 possible numbers, assuming repeated numbers are allowed.

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We can expect  4 giant swallowtails to visit Ellie's garden.

In total, there were 96 butterfly visits (32 monarchs + 56 gulf fritillaries + 8 giant swallowtails).

Now, we can calculate the probability of a giant swallowtail visit:
Probability

= (number of giant swallowtails) / (total butterfly visits)

= 8/96

= 1/12

Given that 48 butterflies visit her garden, we can expect the number of giant swallowtails to be:
Expected giant swallowtails

= (total butterflies) × (probability of giant swallowtails)

= 48 × (1/12)

= 4

So, we can expect approximately 4 giant swallowtails to visit Ellie's garden out of the 48 butterflies.

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