Mathematics High School

## Answers

**Answer 1**

Tank of **gas**, produces 458.50 pounds of carbon dioxide.

How to determine the amount of carbon dioxide (CO2) produced by burning a certain amount of gasoline?

To determine the amount of **carbon dioxide** (CO2) produced by burning a certain amount of gasoline, we need to know the fuel efficiency of the vehicle in miles per gallon (MPG) and the emission factor for CO2.

Assuming you have the necessary information, let's proceed with the calculation.

Find the total number of miles that can be driven with a full tank of gas:

Let's say the vehicle's fuel efficiency is 30 MPG. Therefore, the total distance covered with a full tank would be:

Total distance = Fuel efficiency (MPG) * Tank capacity (gallons)

Total distance = 30 MPG * 23.4 gallons

Calculate the amount of CO2 produced per mile:

To calculate the **emission factor** for CO2, we'll use the average emission factor of gasoline, which is approximately 19.6 pounds of CO2 per gallon burned.

CO2 emission per mile = Emission factor (pounds of CO2 per gallon) / Fuel efficiency (MPG)

Multiply the CO2 emission per mile by the total distance to find the total amount of CO2 produced:

Total CO2 produced = CO2 emission per mile * Total distance

Let's calculate the result using the given values:

Total distance = 30 MPG * 23.4 gallons = 702 miles

CO2 emission per mile = 19.6 pounds CO2/gallon / 30 MPG ≈ 0.6533 pounds CO2/mile

Total CO2 produced = 0.6533 **pounds **CO2/mile * 702 miles

Therefore, by burning an entire tank of gas, approximately 458.50 pounds of carbon dioxide are produced.

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## Related Questions

The gwa of 20 students grade 10-courage for the 3 quarter 91.188 78.625 80.188 90.781 93.281 95.563 91.500 88.281 89.750 90.125 75.750 84.469 83.219 90.781 83.688 88.375 91.250 89.781 90.188 91.344

### Answers

The GWA of 20 students in grade 10 for the third **quarter **is around 88.9. Students should continue to work hard throughout the **entire **school year, and cultivate the courage to take risks and pursue their dreams.

Thank you for your question. It seems like you are asking about the GWA or General Weighted **Average **of 20 students in grade 10 for the third quarter. Based on the list of numbers you provided, the average GWA for these students is around 88.9. It is important to note that the GWA takes into account not only the numerical grades but also the weight or value of each subject. Therefore, it is a more accurate representation of a student's overall performance.

In terms of the third quarter, it is the period between the second and fourth quarters of the school year. This means that students have completed half of the school year and are gearing up for the second half. It is important for students to continue working hard and striving for excellence throughout the entire school year, not just in one quarter.

Lastly, courage is a vital trait that students need to possess in order to achieve their goals. It takes courage to try new things, to speak up for oneself, and to persevere through difficult challenges. Without courage, students may feel discouraged and give up on their dreams. Therefore, it is important to **encourage **students to be brave and take risks in their academic and personal lives.

In conclusion, the GWA of 20 students in grade 10 for the third quarter is around 88.9. Students should continue to work hard throughout the entire school year, and cultivate the courage to take risks and pursue their dreams.

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Mercury moves at an elliptical orbit with the sun at one focus. the eccentricity of mercury's orbit is e= 0.2056. the length of the major axis is 72 million miles. find the standard equation of mercury's orbit. place the center of the orbit at the origin ad the major axis o lm the x-axis.

### Answers

The **standard equation** of Mercury's orbit is x²/a² + y²/b²= 1

To find the standard equation of **Mercury's orbit**, we first need to determine the coordinates of the foci.

Since the sun is one focus, we can use the **formula** c = ae, where a is the length of the major axis and e is the eccentricity.

Plugging in the given values, we get c = 0.2056 x 72 million = 14.8032 million miles. Since the orbit is centered at the origin, **the foci** are located at (-c,0) and (c,0).

Therefore, the distance from any point on the ellipse to the left focus minus the distance to the right focus is a constant value, which we can call 2a.

Thus, the standard equation of Mercury's orbit is x²/a² + y²/b²= 1

where a = 36 million miles and b is the length of the minor axis.

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The energy source that uses water rushing out from dams to make electricity is

### Answers

The energy source that uses water rushing out from **dams **to make electricity is **hydropower**.

Hydropower, also known as **hydroelectric power**, is a renewable energy source that harnesses the energy of flowing or falling water to generate electricity. It is a clean and sustainable form of energy production that relies on the **water cycle **and gravitational force. In a hydropower system, large dams are constructed to create reservoirs, which store water. When the water is released from the reservoir, it flows through turbines, which spin generators to produce electricity. The force of the flowing water converts the** kinetic energy** into mechanical energy, and then into electrical energy.

Hydropower has several advantages. Firstly, it is a **renewable energy **source as it relies on the continuous water cycle, making it a reliable and long-term solution for electricity generation. It produces minimal greenhouse gas emissions, contributing to a cleaner environment. Additionally, hydropower plants can provide a stable and consistent power supply, as they can respond quickly to changes in demand.However, there are also challenges associated with hydropower. The construction of large dams can have environmental and social impacts, including habitat destruction, displacement of communities, and alteration of river ecosystems. There is a need for careful planning and assessment to minimize these negative effects.

Overall, hydropower is an important and widely used energy source, particularly in areas with access to rivers and suitable **topography**. It offers a renewable and sustainable option for electricity generation, contributing to a diversified energy mix and reducing reliance on fossil fuels.

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Jake tossed a paper cup 50 times and recorded how it landed. the table shows the results:

position open side up closed side up landing on side

3 7 40

based on the table, determine the experimental probability of each outcome (landing open side up, landing closed side up, and landing on its side). show your work

### Answers

The experimental **probability **of landing open side up is 6%, landing closed side up is 14%, and landing on its side is 80%.

To determine the **experimental **probability of each outcome, we need to use the formula:

Experimental probability = Number of times the outcome occurred / Total number of trials

So, for landing open side up, the experimental probability would be:

Experimental probability of landing open side up = 3/50

Experimental probability of landing open side up = 0.06 or 6%

Similarly, for landing closed side up, the experimental probability would be:

Experimental probability of landing closed side up = 7/50

Experimental probability of landing closed side up = 0.14 or 14%

And for landing on its side, the experimental probability would be:

Experimental probability of landing on its side = 40/50

Experimental probability of landing on its side = 0.8 or 80%

It's important to note that these are experimental probabilities based on the specific **50 trials** conducted by Jake and may not necessarily represent the true probability of each **outcome**.

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Which of the following represents the total area of the figure?

968 ft2

616 ft2

484 ft2

352 ft2

### Answers

The total **area** represented by the **given** figure is 484 square feet, option C is correct.

The given figure is composed of 1 **rectangle** and three right angle triangles.

The area of rectangle = length × width.

=16×22

=352 square feet

Area of **triangle** which is larger.

Area =1/2× 6×22

=66 square feet

Now the area of small triangles.

Area of triangle 2 = 1/2× 6×11

=33 square feet

As there are two triangles with same **measurements**.

2×33 = 66 square feet

Now total area = 352+66+66

=484 square feet.

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To completely stain the bottom rectangular prism, seth had to cover ___square inches of wood. for one of the cubes to be completely stained, he had to cover ___ square inches of wood. to completely stain the top rectangular prism, he had to cover ___ square inches of wood.once the stool was fastened together, he applied a coat of sealant to all exposed surfaces of the stool, including the bottom, to cover a total of ___ square inches.

### Answers

To completely stain the bottom **rectangular** prism, Seth had to cover 600 square inches of wood.

How many square inches to stain?

The process of **staining** involves covering wooden surfaces with a colored or translucent pigment to enhance their appearance and protect the wood. In Seth's case, to completely stain the bottom rectangular prism, he needed to cover 600 square inches of wood. This implies that all six faces of the prism, including the top and bottom, needed to be stained.

Each face of the rectangular prism is a rectangle, and by calculating the area of one face and **multiplying** it by six, we arrive at the total area of 600 square inches. Staining not only adds visual appeal to wooden objects but also helps to preserve and prolong their lifespan by creating a protective barrier against moisture, sunlight, and other **damaging** factors.

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Looking at the distribution of BMI, you observe that the data centrality is measured as: Group of answer choices n = 442 Mean = 26. 4 Standard deviation = 4. 41 Standard Error = 0. 21

### Answers

The distribution of BMI data indicates a centrality measured by a sample size of 442, a **mean** of 26.4, a standard deviation of 4.41, and a s**tandard error** of 0.21.

**Centrality** in statistical terms refers to the measure of the central tendency of a dataset, which helps us understand where the data is concentrated. In this case, the centrality of the BMI distribution is described by several key **statistics**.

The sample size (n) is reported as 442, indicating the number of observations or individuals in the dataset. The **mean** is calculated to be 26.4, representing the average value of the BMI measurements. The standard deviation is given as 4.41, which quantifies the spread or dispersion of the data points around the mean.

A larger **standard deviation** suggests greater variability in the BMI values. Additionally, the standard error is provided as 0.21, which estimates the variability of the mean itself and provides a measure of how accurately the sample mean represents the population mean.

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Write 0. 000012001 in scientific notation. 0. 000012001 =

### Answers

1.2001x10^-5 just make sure you include the negative in it

A resistor dissipates 1.90 w when the rms voltage of the emf is 11.0 v . part a at what rms voltage will the resistor dissipate 12.0 w

### Answers

Therefore, the rms voltage at which the resistor will dissipate 12.0 W is 24.97 V. It's important to note that this value is the rms voltage, which represents the effective or equivalent voltage of an **AC signal.**

To solve this problem, we can use the formula for power dissipated by a resistor: **P = V^2/R**, where P is the power, V is the voltage, and R is the **resistance**. We are given P = 1.90 W and V = 11.0 V, so we can solve for R: R = V^2/P = (11.0 V)^2/1.90 W = 64.74 ohms.

To find the **voltage **at which the resistor dissipates 12.0 W, we can rearrange the formula to solve for V: V = sqrt(P*R). Plugging in P = 12.0 W and R = 64.74 ohms, we get V = sqrt(12.0 W * 64.74 ohms) = 24.97 V (rounded to three significant figures).

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When x = 1, then y

...................................................................

### Answers

The **value** of y when x is 1 is -2

What is linear graph?

**Linear** also interpretes as straight and a **graph** is a diagram which shows a connection or relation between two or more quantity.

We can also define straight **graph** which is drawn on a plane connecting the points on x and y coordinates. It is a **graph** of a **linear** equation.

To calculate any **value** of x or y we can use the **graph** to determine the value of x if y is given and the **value** of y if x is given

Therefore from the **graph**;

when x is 1 , the reading of y to the straight line is -2. Therefore the value of y is -2.

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How do artists use conventions such as line, color, and form to convey emotions in art? are these methods more or less effective than relying on subject matter?

### Answers

**Artists **use conventions such as line, color, and form to convey emotions in art by manipulating these elements to create a certain mood or atmosphere.

For example, a jagged, frenzied line can convey a sense of anxiety or fear, while a smooth, flowing line can suggest calmness or **tranquility**. Similarly, warm colors like reds and yellows can create a sense of excitement or passion, while cool colors like blues and greens can suggest calm or sadness.

These methods can be very effective in conveying emotions in art because they allow the artist to communicate a feeling or idea without relying solely on subject matter. By using different techniques, an artist can create a sense of mood or emotion that transcends the specific **subject **matter depicted in the artwork.

However, it is important to note that relying solely on these conventions may not always be as effective as using subject matter to convey emotion. For example, if an artist creates a painting of a person crying, the viewer may immediately understand the emotion being conveyed. On the other hand, if an artist simply uses jagged lines and dark colors without any recognizable subject matter, the emotion being conveyed may not be as clear.

Ultimately, the effectiveness of using conventions such as line, color, and form to convey emotions in art depends on the artist's skill and intention, as well as the viewer's ability to interpret and understand the artwork.

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32. zachary chan's annual salary is $48,300.00. he is paid semimonthly and his personal

exemptions total $2.000.00. how much does his employer deduct from each of

zachary's paychecks for a state income tax of 45 percent?

### Answers

Zachary's employer deducts approximately **$605.00** from each of his paychecks for the state income tax.

Zachary's annual salary is $48,300.00, and he is paid **semimonthly**, meaning he receives 24 paychecks in a year. To calculate the amount deducted for state **income tax**, we need to find 45% of his salary.

45% of $48,300.00 is calculated as (45/100) * $48,300.00 = $21,735.00.

Since Zachary receives 24 paychecks in a year, we divide the annual state income tax amount by 24 to get the deduction from each paycheck.

$21,735.00 / 24 = $905.625, which can be rounded to approximately $905.00.

However, we need to consider his personal exemptions of $2,000.00.

So, the final **deduction **will be $905.00 - $2,000.00 = approximately $605.00 from each of Zachary's **paychecks **for the state income tax.

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Suppose a population of 40 crickets doubles in size every month. determine the equation that can be used to find the cricket population after x months. how many crickets will be there after 1 1/2 years

### Answers

To determine the cricket population after x months, where the initial population is 40 crickets and it doubles in size every month, the **equation** is P = 40 * 2^x. After 1 1/2 years (18 months), the **population** will be 10,485,760 crickets.

The **equation** P = 40 * 2^x represents the cricket population after x months. The initial population of 40 crickets is multiplied by 2 raised to the power of x, where x represents the number of months. This accounts for the **doubling effect** of the population each month.

To find the population after 1 1/2 years (18 months), we substitute x = 18 into the equation:

P = 40 * 2^18

Calculating 2^18 gives us 262,144. Multiplying this by the initial population **size** of 40, we have:

P = 40 * 262,144 = 10,485,760

Therefore, after 1 1/2 years, the cricket population will be 10,485,760 crickets. This demonstrates the **exponential** growth pattern, as the population doubles in size every month.

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A basket contains 10 pieces of fruit: 3 apples, 4 oranges, and 3 bananas. Jonas takes a piece of fruit at random from the basket, and then Beth takes a piece at random. What is the probability that Jonas will get an orange and Beth will get an apple?

A. 7/10

B. 7/9

C. 2/15

D. 3/25

### Answers

The **probability **that Jonas will get an orange and Beth will get an **apple **is C. 2/15.

To **determine** the probability of Jonas getting an orange and Beth getting an apple, we need to consider the total number of** possible outcomes** and the number of favorable outcomes.

First, let's calculate the total number of possible outcomes. Jonas can choose any of the 10 pieces of fruit in the basket. After Jonas takes one fruit, there are 9 **remaining fruits** for Beth to choose from. Therefore, the total number of possible outcomes is 10 * 9 = 90.

Next, let's calculate the number of **favorable outcomes**, which is the number of ways Jonas can pick an orange (4 oranges) and Beth can pick an apple (3 apples). The number of favorable outcomes is 4 * 3 = 12.

Finally, we can calculate the **probability** by dividing the number of favorable outcomes by the total number of possible outcomes: 12/90 = 2/15.

Hence, the probability that Jonas will get an orange and Beth will get an apple is 2/15, which **corresponds** to option C.

In summary, when choosing fruit from the basket, there are 90 possible outcomes. Out of those, 12 outcomes result in Jonas getting an orange and Beth getting an apple. Therefore, the probability of this** specific event** occurring is 2/15.

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A business is marketing a gift basket full of six pink lady apples, seven oranges, and ten kiwis. A pink lady apple has a mean weight of 133 grams with a standard deviation of 23 grams. A blood orange has a mean weight of 88 grams with a standard deviation of 15 grams. A kiwi has a mean weight of of 76 grams with a standard deviation of 10 grams. The basket the business is designing has a mean weight of 200 grams with a standard deviation of 5 grams. Assuming the weights of the baskets and fruits are independent, what is the mean weight of a gift basket of fruit in grams

### Answers

The **mean weight** of the gift basket is 2174 grams divided by the total number of fruits (6 + 7 + 10 = 23), which equals 94.52 grams (rounded to two **decimal** **places**).

The **mean** **weight** of a gift basket of fruit can be calculated by adding the mean weights of the individual fruits and multiplying them by their respective **quantities**. In this case, the mean weight of the gift basket is the sum of the mean weights of six pink lady apples, seven oranges, and ten kiwis.

To calculate the mean weight of the gift basket, we need to consider the mean weights of each fruit and their quantities. The mean weight of a pink lady apple is 133 grams, the mean weight of a blood orange is 88 grams, and the mean weight of a kiwi is 76 grams.

Since there are six pink lady apples, their **total** **weight** **contribution** to the gift basket is 6 * 133 = 798 grams. Similarly, the seven oranges contribute a weight of 7 * 88 = 616 grams, and the ten kiwis contribute a weight of 10 * 76 = 760 grams.

Adding up these weights, we get a **total** **weight** of 798 + 616 + 760 = 2174 grams for the fruits in the gift basket.

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For a wire C parameterized by c(t)=⟨9t−2,3t+1,4⟩ for 13≤t≤23, density at point (x,y,z) is given by rho(x,y,z)=x+y. Find the mass of the wire where ‘f’ is given in grams/cm and c(t) is given in cm

### Answers

We need to integrate the **density function** over the range of the **parameter**. By integrating the density function along the curve, we can determine the mass of the wire.

The mass of the wire can be **calculated **by integrating the density function ρ(x, y, z) = x + y over the parameter range of t = 13 to t = 23.

To do this, we need to express the density function in terms of t using the parameterization c(t). The** parameterization** c(t) = ⟨9t - 2, 3t + 1, 4⟩ gives us the **coordinates** (x, y, z) of the wire in terms of t.

Substituting the parameterization into the density function, we have:

ρ(t) = x + y = (9t - 2) + (3t + 1) = 12t - 1

Now, we can calculate the mass by **integrating** the density function ρ(t) over the range of t = 13 to t = 23:

Mass = ∫[13,23] (12t - 1) dt

Evaluating the integral, we have:

Mass = [6t^2 - t] [13,23]

Mass = (6(23)^2 - 23) - (6(13)^2 - 13)

Mass = (6(529) - 23) - (6(169) - 13)

Mass = (3174 - 23) - (1014 - 13)

Mass = 3151 - 1001

Mass = 2150

Therefore, the mass of the wire is 2150 grams.

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Please help!!!!!! project: neutralization reactions in an acidic lake lab report

### Answers

This lab report examines **neutralization** reactions in an acidic lake and investigates the effects of lime treatment. The objective is to understand the ecological implications of neutralization reactions and explore potential solutions for **acidic lake **environments.

The experiment involves collecting water samples from the lake and conducting neutralization reactions using lime as the neutralizing agent. Data is gathered and analyzed to determine the **effectiveness** of the treatment. The results are then interpreted and discussed, highlighting any trends or patterns observed. The report concludes with a summary of the findings and suggestions for further research or improvements to the experimental methodology.

The lab report focuses on studying neutralization reactions in an acidic lake to gain insights into their ecological impact and address potential remediation strategies. Acidic lakes pose significant challenges to aquatic ecosystems, and understanding the neutralization process is crucial for developing effective solutions. The experiment involves collecting water **samples** from the acidic lake and subjecting them to neutralization reactions using lime as a common **neutralizing agent**. The experimental procedure is carefully described, including details on materials, measurements, and observations made during the experiment. The obtained data is then presented in a clear and organized manner, utilizing tables, graphs, or charts. The results are interpreted and discussed, taking into account any observed trends, patterns, or deviations. The report compares the findings with existing literature or prior studies on similar topics to provide context and support the conclusions drawn. **Limitations** and sources of error in the experiment are also addressed. The report concludes by summarizing the key findings and their implications for acidic lake environments, as well as suggesting areas for further research or improvements to the experimental approach.

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Point a is reflected across y-axis. Find the coordinates of the new point

### Answers

**Answer: (-5,4)**

**Step-by-step explanation: The point goes 4 up to cross the y axis. So you go up 4 more to get to the new y coordinate. The x coordinate is -5. Doesn't change.**

What kind of departmentalization would be in place in a government organization where different public service responsibilities are divided into activities for employees, children, and the disabled

### Answers

This type of **departmentalization** groups activities based on common functions or tasks, ensuring that employees with **similar skills **and expertise are grouped together to handle specific responsibilities.

In a **government **organization where public service responsibilities are divided into activities for employees, children, and the disabled, functional departmentalization would be suitable. This approach organizes the organization based on **common functions** or tasks performed.

Each department would focus on a specific area of public services, such as employee services, child welfare, and services for the disabled. Within each department, employees with relevant expertise and skills in those areas would be grouped together. This enables **specialization** and allows the organization to efficiently address the unique needs and requirements of each group.

Functional departmentalization facilitates effective coordination, communication, and resource allocation within the organization, ensuring that services are provided in a targeted and specialized manner to meet the diverse needs of **employees,** children, and the disabled.

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Peggy, a manager, receives three shipments of chemicals at her operation. she confirms that the containers have proper labels on them and then stores them in the bottom shelf of a supply closet, away from food items. she notices that two of the bulbs in the supply closet are flickering. she then pours some chlorine bleach into a working container and labels the container with usage directions.

what are the two mistakes peggy made?

she forgot to put the manufacturer's name on the working container.

she transferred a chemical from an original to a working container.

she stored the containers in a room with poor lighting.

she forgot to store the containers on the topmost shelf.

she forgot to label the working container with the chemical name.

### Answers

The two mistakes **Peggy **made are:

She forgot to label the working container with the chemical name.

She stored the containers in a room with poor lighting.

It is important to clearly label the working container with the specific chemical name to ensure proper **identification**.

Without the chemical name on the container, there is a risk of confusion or **accidental **misuse.

Storing the **chemical **containers in a room with flickering bulbs can pose safety hazards.

Poor lighting can make it difficult to read labels and handle the chemicals safely.

It is important to ensure proper lighting conditions in storage areas to maintain visibility and minimize the risk of accidents or misidentifications.

These mistakes can have serious consequences, including potential accidents, misusage, or confusion among employees.

To maintain safety and prevent errors, Peggy should ensure that all containers are properly labeled with the necessary information, stored in appropriate conditions, and follow standard safety procedures for handling and storing chemicals.

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Troy lifts a box of weigh 400 n to height of 1 m. how much energy does troy use?

### Answers

Troy uses 400 **Joules **of energy to lift a box weighing 400 N to a **height **of 1 meter.

The **energy **used to lift an object can be calculated using the formula: Energy = **Force *** Distance. In this case, the force is the weight of the box, which is given as 400 N. The distance is the height to which the box is lifted, which is 1 meter.

Using the formula, we can calculate the energy used by Troy:

Energy = Force * Distance

Energy = 400 N * 1 m

Energy = 400 Joules

Therefore, Troy uses 400 Joules of energy to lift the box. The unit of energy is **Joules**, which is derived from the formula that multiplies force (measured in Newtons) by distance (measured in meters). In this case, the force exerted by Troy to lift the box against gravity is equal to the weight of the box, and the **distance** is the vertical height it is lifted. The energy value represents the work done by Troy in raising the box to the given height.

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Mason and her 2 friends went skiing. tickets cost $25.25 each. they bought 6 handwarmers which cost.75 cents each. after they went skiing they split 2 hot fudge brownie sundaes for $5.45 each. tax was 9\% on everything total. how much did they pay?

### Answers

Mason and her two friends paid a total of $92.97, including **tax**, for their skiing trip. The cost includes the **tickets**, handwarmers, and the two hot fudge brownie sundaes.

To calculate the total amount paid by Mason and her friends, we need to consider the cost of tickets, **handwarmers**, and the hot fudge brownie sundaes, along with the tax.

The tickets cost $25.25 each, so for three people, the total cost for tickets is $25.25 * 3 = $75.75.

They bought 6 handwarmers at $0.75 each, resulting in a **cost **of $0.75 * 6 = $4.50.

The two hot fudge brownie sundaes cost $5.45 each, totaling $5.45 * 2 = $10.90.

To calculate the tax, we add up the costs of the tickets, handwarmers, and sundaes, and then **multiply **by the tax rate of 9%. Tax = ($75.75 + $4.50 + $10.90) * 0.09 = $9.81.

Finally, we add the costs and tax together: $75.75 + $4.50 + $10.90 + $9.81 = $100.96.

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The population of center city is modeled by exponential function f, where x is the number of years after year 2015

### Answers

The **population of Center City** is modeled by an exponential function, denoted as f(x), where x represents the number of years after the year **2015.**

An **exponential function** is commonly represented by the equation **f(x) = a * b^x**, where 'a' is the initial value or starting point, 'b' is the base or growth/decay factor, and 'x' represents the variable or number of years in this case.

The population of Center City is modeled by the exponential function f(x), which means that the population can be expressed as a function of the **number of years** after the year 2015.

To fully understand the characteristics and specifics of the exponential function f(x) and how it models the population of Center City, additional information regarding the **values of 'a', 'b'**, and the specific form of the function is necessary. Without those details, it is not possible to provide a more precise explanation.

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Element X is a radioactive isotope such that every 47 years, its mass decreases by half. Given that the initial mass of a sample of Element X is 30 grams, how long would it be until the mass of the sample reached 21 grams, to the nearest tenth of a year?

### Answers

**Step-by-step explanation:**

21 = 30 (1/2)^n

21/30 = (1/2) ^n where n = number of half lives (47 years each)

LOG both sides

LOG ( 21/30) = n LOG (1/2)

n = LOG (21/30) / (LOG (1/2)) = .5145 half lives

.5145 * 47 yr = 24.2 years

A certain sample of gas has a volume of 0. 452 L measured at 87°C and 0. 620

atm. What is its volume at STP

### Answers

The volume of the gas at **STP** is approximately 22.414 L.

STP (Standard Temperature and Pressure) conditions are defined as a temperature of 0°C (273.15 K) and a** pressure **of 1 atm (760 mmHg or 101.325 kPa).

How to determine the volume of the gas at STP?

To determine the volume of the gas at STP, we can use the ideal gas law equation:

PV = nRT

where P is the pressure, V is the** volume**, n is the number of moles of gas, R is the ideal gas constant, and T is the temperature in Kelvin.

First, let's convert the given temperature from Celsius to Kelvin:

87°C + 273.15 = 360.15 K

Next, we can use the given information to calculate the number of moles of gas using the ideal gas law:

PV = nRT

(0.620 atm)(0.452 L) = n(0.0821 L·atm/(mol·K))(360.15 K)

0.280744 atm·L = 0.02951115 n

n ≈ 9.5092 moles (rounded to four decimal places)

Now, we can calculate the volume at STP using the **moles **of gas obtained:

PV = nRT

(1 atm)(V) = (9.5092 mol)(0.0821 L·atm/(mol·K))(273.15 K)

V ≈ 22.414 L (rounded to three decimal places)

Therefore, the volume of the gas at STP is approximately 22.414 L.

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Breaking of a glass tumbler and burning of paper are changes in which we cannot get backthe original substances. what is the difference between these two changes

### Answers

Both breaking a glass tumbler and burning paper are **irreversible** changes where the **original** substances cannot be obtained again. However, the difference lies in the **nature** of these changes.

Breaking a glass tumbler is a physical change because it does not involve a change in the chemical **composition** of the glass. The tumbler can be shattered into smaller pieces, but the **fundamental** properties of glass, such as its chemical composition and structure, remain the same. While it may be possible to gather and **reassemble** the glass pieces, the original tumbler cannot be completely restored to its original form. The physical bonds between the glass **molecules** are disrupted, making it difficult to reverse the change entirely.

On the other hand, burning paper is a **chemical** change. When paper burns, it undergoes a combustion reaction where the paper reacts with oxygen in the air and **transforms** into new substances, such as carbon dioxide, water vapor, and ash. This chemical reaction breaks down the cellulose fibers in the paper and results in the formation of different compounds. Once the paper has been burned, it cannot be converted back into its original form through a simple **physical** process. The chemical composition of the paper has been altered **irreversibly**.

In summary, while both breaking a glass tumbler and burning paper are irreversible changes where the original **substances** cannot be obtained again, the difference lies in the nature of these changes. Breaking a glass tumbler is a physical change involving the physical **separation** of glass pieces, whereas burning paper is a chemical change resulting in the formation of new substances through a **combustion** reaction.

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A 2458 kg tesla car trevalling st a speed of 113 kmh^-1 hit a wall and stop in 0.22 s. convert velocity kmh^-1 into ms^-1?

### Answers

**The velocity** of the **Tesla car** is approximately 31.388 m/s.

To convert **the velocity** from km/h to m/s, you can use the following conversion factor:

1 km/h = 0.277778 m/s

Given that the Tesla car is traveling at a speed of 113 km/h, we can convert it to m/s as follows:

113 km/h * 0.277778 m/s = 31.388 m/s

Therefore, **the velocity **of the **Tesla car** is approximately 31.388 m/s.

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The** velocity **of the Tesla car is approximately 31.39 m/s after converting from km/h to m/s.

When **converting units** from kilometers per hour (km/h) to meters per second (m/s), we need to consider the conversion factor between these two units.

1 kilometer is equal to 1000 meters, and 1 hour is equal to 3600 seconds. Therefore, the conversion factor between the **speed **km/h and m/s is:

1 km/h = (1000 m) / (3600 s) = 0.2778 m/s (rounded to four decimal places)

To convert a value from km/h to m/s, we divide the value in km/h by this conversion factor.

In this case, the given velocity is 113 km/h. To convert it to m/s, we perform the following calculation:

Velocity in m/s = 113 km/h / 0.2778 m/s ≈ 31.39 m/s (rounded to two decimal places)

So, the velocity of the Tesla car is approximately 31.39 m/s after converting from km/h to m/s.

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If the diameter of a men’s basketball is 10 inches and a women’s is 9 inches, what is the approximate difference of their volumes? 133. 9 in. 3 137. 6 in. 3 141. 9 in. 3 145. 6 in. 3.

### Answers

The **approximate **difference between the volumes of a men's basketball and a women's basketball can be calculated by finding the difference in their respective **volumes**.

For men's basketball, the radius is half of the **diameter**, which is 10 inches / 2 = 5 inches. Plugging this value into the formula, we get [tex]V_{men} = (4/3)\pi (5^3)\\ \\= (4/3)\pi (125)\\ \\=523.6 \:cubic\: inches[/tex]

For women's basketball, the **radius** is half of the diameter, which is 9 inches / 2 = 4.5 inches. Plugging this value into the formula, we get [tex]V_{women} = (4/3)\pi (4.5^3) \\\\=(4/3)\pi (91.125) \\ \\=381.7 \:cubic\: inches[/tex]

The **approximate** difference in volume is,

[tex]V_{men} - V_{women} = 523.6 - 381.7 \\\\= 141.9 \:cubic\: inches[/tex]

Therefore, the approximate difference in their **volumes** is 141.9 cubic inches, which corresponds to the option [tex]141.9 in^3[/tex].

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The stress distribution on a structure is given by s = 2x^2+ 4x - 30 where s is stress in pounds per

square inch and x is the distance in feet from a reference point. At what distance is the stress equal

to 0 pounds per square inch?

### Answers

The stress is equal to 0 pounds **per square** inch at x = 5 feet.

**At what distance does the stress become zero?**

In the given **stress distribution equation**, s = [tex]2x^2 + 4x - 30[/tex], we are looking for the value of x where the stress (s) is equal to zero. To find this distance, we set the equation equal to zero and solve for x.

By factoring in or using the **quadratic formula**, we determine that x = 5 satisfies the equation. At this distance of 5 feet from the reference point, the stress on the structure becomes zero, indicating a state of equilibrium or no stress.

Understanding the **specific distanc**e at which the stress is zero is crucial for analyzing and designing structures to ensure their stability and safety.

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15 POINTS

Solve the equation with substitution

### Answers

The **solution **of the **system of equation **are,

x = 1/3 and y = 0

We have to given that;

System of **equations **are,

3x - 4y = 11

y + 3x = 1

From (ii);

y = 1 - 3x

Put above value in (i);

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

3x - 4 + 12x = 1

15x = 5

x = 1/3

From (i);

y + 3 (1/3) = 1

y + 1 = 1

y = 0

Thus, The **solution **of the **system of equation **are,

x = 1/3 and y = 0

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The **solution** to the system of **equations** is x = 1 and y = -2.

We have,

3x - 4y = 11

y + 3x = 1

To solve the system of **equations**:

3x - 4y = 11

y + 3x = 1

We can use the method of substitution or elimination.

Let's solve it using the elimination method.

Multiply equation 2) by -1 to eliminate the term 3x:

-1(y + 3x) = -1(1)

-y - 3x = -1

Now we have the following system of **equations**:

3x - 4y = 11

-y - 3x = -1

Add **equation** 1) and equation 2) together:

(3x - 4y) + (-y - 3x) = 11 + (-1)

3x - 4y - y - 3x = 10

-5y = 10

Divide both sides of the **equation** by -5:

-5y / -5 = 10 / -5

y = -2

Now substitute the value of y = -2 into equation 2):

-2 + 3x = 1

Add 2 to both sides:

3x = 3

Divide both sides by 3:

3x / 3 = 3 / 3

x = 1

Therefore,

The **solution** to the system of **equations** is x = 1 and y = -2.

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