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Jim and Pam bought x quarts of ice cream...

Jim and Pam bought x quarts of ice cream for a party. If 10 people attended the party, including Jim and Pam, ate all the ice cream, and each person ate the same account of ice cream, which of the following represents the account of ice cream, in quarts, eaten by each person at the party?

A

`10x`

B

`5x`

C

`(x)/(5)`

D

`(x)/(10)`

Text Solution

AI Generated Solution

The correct Answer is:
To find the amount of ice cream eaten by each person at the party, we can follow these steps: 1. **Identify the total amount of ice cream**: Jim and Pam bought a total of \( x \) quarts of ice cream. 2. **Determine the total number of people at the party**: There were 10 people at the party, including Jim and Pam. 3. **Calculate the amount of ice cream eaten by each person**: Since all the ice cream was consumed and it was equally distributed among the 10 people, we need to divide the total amount of ice cream \( x \) by the number of people (10). \[ \text{Amount of ice cream eaten by each person} = \frac{x}{10} \] Thus, the amount of ice cream eaten by each person at the party is \( \frac{x}{10} \) quarts.
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Arun bought 1/(4) kg of ice cream. After his children had eaten some, there was 1/(10) kg left. How much did his children eat?

The given figure shows the cross-section of an ice cream cone consisting of a cone surmounted by a hemisphere. The radius of the hemisphere is 3.5 cm and the height of the cone is 10-5 cm. The outer shell ABCDEF is shaded and is not filled with ice-cream. AF = DC = 0.5 cm, AB // FE and BC // ED. Calculate : (i) the volume of the ice-cream in the cone (the internal volume of the cone including the hemisphere) in cm ^(3), (ii) the volume of the outer shell (the shaded portion) in cm ^(3). In each case, give your answer correct to the nearest cm ^(3).

Knowledge Check

  • The table above shows the flavors of ice cream and the toppings chosen by the people at a party. Each person chose one flavor of ice cream and one topping. Of the people who chose vanilla ice cream, what fraction chose hot fudge as a topping?

    A
    `8/25`
    B
    `5/13`
    C
    `13/25`
    D
    `8/13`

  • Read each sentence with its instructions. Choose the correct answer from the options provided beneath each: It was a hot day. Everyone bought ice-cream. (use: being)

    A
    As everyone bought ice cream, it was a hot day.
    B
    It being a hot day everyone bought ice-cream
    C
    Being a day that was cold, everyone bought ice-cream.
    D
    none of these

  • Passage 1 Follow the money and you will end up in space. That’s the message from a first-of-its-kind forum on mining beyond Earth. Convened in Sydney by the Australian Centre for 5 Space Engineering Research, the event brought together mining companies, robotics e5 xperts, lunar scientists, and government agencies that are all working to make space mining a reality. he forum comes hot on the heels of the 10 2012 unveiling of two private asteroid-mining firms. Planetary Resources of Washington says it will launch its first prospecting telescopes in two years, while Deep Space Industries of Virginia hopes to be harvesting metals from asteroids by 2020. Another 15 commercial venture that sprung up in 2012, Golden Spike of Colorado, will be offering trips to the moon, including to potential lunar miners. Within a few decades, these firms may be meeting earthly demands for precious metals, such as 20 platinum and gold, and the rare earth elements vital for personal electronics, such as yttrium and lanthanum. But like the gold rush pioneers who transformed the western United States, the first space miners won’t just enrich themselves. They also hope 25 to build an off-planet economy free of any bonds with Earth, in which the materials extracted and processed from the moon and asteroids are delivered for space-based projects. In this scenario, water mined from other 30 worlds could become the most desired commodity. “In the desert, what’s worth more: a kilogram of gold or a kilogram of water?” asks Kris Zacny of HoneyBee Robotics in New York. “Gold is useless .Water will let you live.” 35 Water ice from the moon’s poles could be sent to astronauts on the International Space Station for drinking or as a radiation shield. Splitting water into oxygen and hydrogen makes spacecraft fuel, so ice-rich asteroids could become interplanetary 40 refuelling stations. Companies are eyeing the iron, silicon, and aluminium in lunar soil and asteroids, which could be used in 3D printers to make spare parts or machinery. Others want to turn space dirt into 45 concrete for landing pads, shelters, nd roads. Passage 2 The motivation for deep-space travel is shifting from discovery to economics. The past year has seen a flurry of proposals aimed at bringing celestial riches down to Earth. No doubt this will make a few 50 billionaires even wealthier, but we all stand to gain: the mineral bounty and spin-off technologies could enrich us all. But before the miners start firing up their rockets, we should pause for thought. At first glance, space 55 mining seems to sidestep most environmental concerns: there is (probably!) no life on asteroids, and thus no habitats to trash. But its consequences —both here on Earth and in space—merit careful consideration. 60 Part of this is about principles. Some will argue that space’s “magnificent desolation” is not ours to despoil, just as they argue that our own planet’s poles should remain pristine. Others will suggest that glutting ourselves on space’s riches is not an 65 acceptable alternative to developing more sustainable ways of earthly life. History suggests that those will be hard lines to hold, and it may be difficult to persuade the public that such barren environments are worth preserving. 70 After all, they exist in vast abundance, and even fewer people will experience them than have walked through Antarctica’s icy landscapes. There’s also the emerging off-world economy to consider. The resources that are valuable in orbit and 75 beyond may be very different to those we prize on Earth. Questions of their stewardship have barely been broached—and the relevant legal and regulatory framework is fragmentary, to put it mildly. Space miners, like their earthly counterparts, are 80 often reluctant to engage with such questions. One speaker at last week’s space-mining forum in Sydney, Australia, concluded with a plea that regulation should be avoided. But miners have much to gain from a broad agreement on the for-profit 85 exploitation of space. Without consensus, claims will be disputed, investments risky, and the gains made insecure. It is in all of our long-term interests to seek one out 42. In lines 9-17, the author of Passage 1 mentions several companies primarily to

    A
    note the technological advances that make space mining possible.
    B
    provide evidence of the growing interest in space mining.
    C
    emphasize the large profits to be made from space mining.
    D
    highlight the diverse ways to carry out space mining operations.

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    Passage 1 Follow the money and you will end up in space. That’s the message from a first-of-its-kind forum on mining beyond Earth. Convened in Sydney by the Australian Centre for 5 Space Engineering Research, the event brought together mining companies, robotics e5 xperts, lunar scientists, and government agencies that are all working to make space mining a reality. he forum comes hot on the heels of the 10 2012 unveiling of two private asteroid-mining firms. Planetary Resources of Washington says it will launch its first prospecting telescopes in two years, while Deep Space Industries of Virginia hopes to be harvesting metals from asteroids by 2020. Another 15 commercial venture that sprung up in 2012, Golden Spike of Colorado, will be offering trips to the moon, including to potential lunar miners. Within a few decades, these firms may be meeting earthly demands for precious metals, such as 20 platinum and gold, and the rare earth elements vital for personal electronics, such as yttrium and lanthanum. But like the gold rush pioneers who transformed the western United States, the first space miners won’t just enrich themselves. They also hope 25 to build an off-planet economy free of any bonds with Earth, in which the materials extracted and processed from the moon and asteroids are delivered for space-based projects. In this scenario, water mined from other 30 worlds could become the most desired commodity. “In the desert, what’s worth more: a kilogram of gold or a kilogram of water?” asks Kris Zacny of HoneyBee Robotics in New York. “Gold is useless .Water will let you live.” 35 Water ice from the moon’s poles could be sent to astronauts on the International Space Station for drinking or as a radiation shield. Splitting water into oxygen and hydrogen makes spacecraft fuel, so ice-rich asteroids could become interplanetary 40 refuelling stations. Companies are eyeing the iron, silicon, and aluminium in lunar soil and asteroids, which could be used in 3D printers to make spare parts or machinery. Others want to turn space dirt into 45 concrete for landing pads, shelters, nd roads. Passage 2 The motivation for deep-space travel is shifting from discovery to economics. The past year has seen a flurry of proposals aimed at bringing celestial riches down to Earth. No doubt this will make a few 50 billionaires even wealthier, but we all stand to gain: the mineral bounty and spin-off technologies could enrich us all. But before the miners start firing up their rockets, we should pause for thought. At first glance, space 55 mining seems to sidestep most environmental concerns: there is (probably!) no life on asteroids, and thus no habitats to trash. But its consequences —both here on Earth and in space—merit careful consideration. 60 Part of this is about principles. Some will argue that space’s “magnificent desolation” is not ours to despoil, just as they argue that our own planet’s poles should remain pristine. Others will suggest that glutting ourselves on space’s riches is not an 65 acceptable alternative to developing more sustainable ways of earthly life. History suggests that those will be hard lines to hold, and it may be difficult to persuade the public that such barren environments are worth preserving. 70 After all, they exist in vast abundance, and even fewer people will experience them than have walked through Antarctica’s icy landscapes. There’s also the emerging off-world economy to consider. The resources that are valuable in orbit and 75 beyond may be very different to those we prize on Earth. Questions of their stewardship have barely been broached—and the relevant legal and regulatory framework is fragmentary, to put it mildly. Space miners, like their earthly counterparts, are 80 often reluctant to engage with such questions. One speaker at last week’s space-mining forum in Sydney, Australia, concluded with a plea that regulation should be avoided. But miners have much to gain from a broad agreement on the for-profit 85 exploitation of space. Without consensus, claims will be disputed, investments risky, and the gains made insecure. It is in all of our long-term interests to seek one out 46. What function does the discussion of water in lines 35-40 serve in Passage 1?

    Passage 1 Follow the money and you will end up in space. That’s the message from a first-of-its-kind forum on mining beyond Earth. Convened in Sydney by the Australian Centre for 5 Space Engineering Research, the event brought together mining companies, robotics e5 xperts, lunar scientists, and government agencies that are all working to make space mining a reality. he forum comes hot on the heels of the 10 2012 unveiling of two private asteroid-mining firms. Planetary Resources of Washington says it will launch its first prospecting telescopes in two years, while Deep Space Industries of Virginia hopes to be harvesting metals from asteroids by 2020. Another 15 commercial venture that sprung up in 2012, Golden Spike of Colorado, will be offering trips to the moon, including to potential lunar miners. Within a few decades, these firms may be meeting earthly demands for precious metals, such as 20 platinum and gold, and the rare earth elements vital for personal electronics, such as yttrium and lanthanum. But like the gold rush pioneers who transformed the western United States, the first space miners won’t just enrich themselves. They also hope 25 to build an off-planet economy free of any bonds with Earth, in which the materials extracted and processed from the moon and asteroids are delivered for space-based projects. In this scenario, water mined from other 30 worlds could become the most desired commodity. “In the desert, what’s worth more: a kilogram of gold or a kilogram of water?” asks Kris Zacny of HoneyBee Robotics in New York. “Gold is useless .Water will let you live.” 35 Water ice from the moon’s poles could be sent to astronauts on the International Space Station for drinking or as a radiation shield. Splitting water into oxygen and hydrogen makes spacecraft fuel, so ice-rich asteroids could become interplanetary 40 refuelling stations. Companies are eyeing the iron, silicon, and aluminium in lunar soil and asteroids, which could be used in 3D printers to make spare parts or machinery. Others want to turn space dirt into 45 concrete for landing pads, shelters, nd roads. Passage 2 The motivation for deep-space travel is shifting from discovery to economics. The past year has seen a flurry of proposals aimed at bringing celestial riches down to Earth. No doubt this will make a few 50 billionaires even wealthier, but we all stand to gain: the mineral bounty and spin-off technologies could enrich us all. But before the miners start firing up their rockets, we should pause for thought. At first glance, space 55 mining seems to sidestep most environmental concerns: there is (probably!) no life on asteroids, and thus no habitats to trash. But its consequences —both here on Earth and in space—merit careful consideration. 60 Part of this is about principles. Some will argue that space’s “magnificent desolation” is not ours to despoil, just as they argue that our own planet’s poles should remain pristine. Others will suggest that glutting ourselves on space’s riches is not an 65 acceptable alternative to developing more sustainable ways of earthly life. History suggests that those will be hard lines to hold, and it may be difficult to persuade the public that such barren environments are worth preserving. 70 After all, they exist in vast abundance, and even fewer people will experience them than have walked through Antarctica’s icy landscapes. There’s also the emerging off-world economy to consider. The resources that are valuable in orbit and 75 beyond may be very different to those we prize on Earth. Questions of their stewardship have barely been broached—and the relevant legal and regulatory framework is fragmentary, to put it mildly. Space miners, like their earthly counterparts, are 80 often reluctant to engage with such questions. One speaker at last week’s space-mining forum in Sydney, Australia, concluded with a plea that regulation should be avoided. But miners have much to gain from a broad agreement on the for-profit 85 exploitation of space. Without consensus, claims will be disputed, investments risky, and the gains made insecure. It is in all of our long-term interests to seek one out 49. Which statement best describes the relationship between the passages?

    Passage 1 Follow the money and you will end up in space. That’s the message from a first-of-its-kind forum on mining beyond Earth. Convened in Sydney by the Australian Centre for 5 Space Engineering Research, the event brought together mining companies, robotics e5 xperts, lunar scientists, and government agencies that are all working to make space mining a reality. he forum comes hot on the heels of the 10 2012 unveiling of two private asteroid-mining firms. Planetary Resources of Washington says it will launch its first prospecting telescopes in two years, while Deep Space Industries of Virginia hopes to be harvesting metals from asteroids by 2020. Another 15 commercial venture that sprung up in 2012, Golden Spike of Colorado, will be offering trips to the moon, including to potential lunar miners. Within a few decades, these firms may be meeting earthly demands for precious metals, such as 20 platinum and gold, and the rare earth elements vital for personal electronics, such as yttrium and lanthanum. But like the gold rush pioneers who transformed the western United States, the first space miners won’t just enrich themselves. They also hope 25 to build an off-planet economy free of any bonds with Earth, in which the materials extracted and processed from the moon and asteroids are delivered for space-based projects. In this scenario, water mined from other 30 worlds could become the most desired commodity. “In the desert, what’s worth more: a kilogram of gold or a kilogram of water?” asks Kris Zacny of HoneyBee Robotics in New York. “Gold is useless .Water will let you live.” 35 Water ice from the moon’s poles could be sent to astronauts on the International Space Station for drinking or as a radiation shield. Splitting water into oxygen and hydrogen makes spacecraft fuel, so ice-rich asteroids could become interplanetary 40 refuelling stations. Companies are eyeing the iron, silicon, and aluminium in lunar soil and asteroids, which could be used in 3D printers to make spare parts or machinery. Others want to turn space dirt into 45 concrete for landing pads, shelters, nd roads. Passage 2 The motivation for deep-space travel is shifting from discovery to economics. The past year has seen a flurry of proposals aimed at bringing celestial riches down to Earth. No doubt this will make a few 50 billionaires even wealthier, but we all stand to gain: the mineral bounty and spin-off technologies could enrich us all. But before the miners start firing up their rockets, we should pause for thought. At first glance, space 55 mining seems to sidestep most environmental concerns: there is (probably!) no life on asteroids, and thus no habitats to trash. But its consequences —both here on Earth and in space—merit careful consideration. 60 Part of this is about principles. Some will argue that space’s “magnificent desolation” is not ours to despoil, just as they argue that our own planet’s poles should remain pristine. Others will suggest that glutting ourselves on space’s riches is not an 65 acceptable alternative to developing more sustainable ways of earthly life. History suggests that those will be hard lines to hold, and it may be difficult to persuade the public that such barren environments are worth preserving. 70 After all, they exist in vast abundance, and even fewer people will experience them than have walked through Antarctica’s icy landscapes. There’s also the emerging off-world economy to consider. The resources that are valuable in orbit and 75 beyond may be very different to those we prize on Earth. Questions of their stewardship have barely been broached—and the relevant legal and regulatory framework is fragmentary, to put it mildly. Space miners, like their earthly counterparts, are 80 often reluctant to engage with such questions. One speaker at last week’s space-mining forum in Sydney, Australia, concluded with a plea that regulation should be avoided. But miners have much to gain from a broad agreement on the for-profit 85 exploitation of space. Without consensus, claims will be disputed, investments risky, and the gains made insecure. It is in all of our long-term interests to seek one out 51. Which choice provides the best evidence for the answer to the previous question?

    Passage 1 Follow the money and you will end up in space. That’s the message from a first-of-its-kind forum on mining beyond Earth. Convened in Sydney by the Australian Centre for 5 Space Engineering Research, the event brought together mining companies, robotics e5 xperts, lunar scientists, and government agencies that are all working to make space mining a reality. he forum comes hot on the heels of the 10 2012 unveiling of two private asteroid-mining firms. Planetary Resources of Washington says it will launch its first prospecting telescopes in two years, while Deep Space Industries of Virginia hopes to be harvesting metals from asteroids by 2020. Another 15 commercial venture that sprung up in 2012, Golden Spike of Colorado, will be offering trips to the moon, including to potential lunar miners. Within a few decades, these firms may be meeting earthly demands for precious metals, such as 20 platinum and gold, and the rare earth elements vital for personal electronics, such as yttrium and lanthanum. But like the gold rush pioneers who transformed the western United States, the first space miners won’t just enrich themselves. They also hope 25 to build an off-planet economy free of any bonds with Earth, in which the materials extracted and processed from the moon and asteroids are delivered for space-based projects. In this scenario, water mined from other 30 worlds could become the most desired commodity. “In the desert, what’s worth more: a kilogram of gold or a kilogram of water?” asks Kris Zacny of HoneyBee Robotics in New York. “Gold is useless .Water will let you live.” 35 Water ice from the moon’s poles could be sent to astronauts on the International Space Station for drinking or as a radiation shield. Splitting water into oxygen and hydrogen makes spacecraft fuel, so ice-rich asteroids could become interplanetary 40 refuelling stations. Companies are eyeing the iron, silicon, and aluminium in lunar soil and asteroids, which could be used in 3D printers to make spare parts or machinery. Others want to turn space dirt into 45 concrete for landing pads, shelters, nd roads. Passage 2 The motivation for deep-space travel is shifting from discovery to economics. The past year has seen a flurry of proposals aimed at bringing celestial riches down to Earth. No doubt this will make a few 50 billionaires even wealthier, but we all stand to gain: the mineral bounty and spin-off technologies could enrich us all. But before the miners start firing up their rockets, we should pause for thought. At first glance, space 55 mining seems to sidestep most environmental concerns: there is (probably!) no life on asteroids, and thus no habitats to trash. But its consequences —both here on Earth and in space—merit careful consideration. 60 Part of this is about principles. Some will argue that space’s “magnificent desolation” is not ours to despoil, just as they argue that our own planet’s poles should remain pristine. Others will suggest that glutting ourselves on space’s riches is not an 65 acceptable alternative to developing more sustainable ways of earthly life. History suggests that those will be hard lines to hold, and it may be difficult to persuade the public that such barren environments are worth preserving. 70 After all, they exist in vast abundance, and even fewer people will experience them than have walked through Antarctica’s icy landscapes. There’s also the emerging off-world economy to consider. The resources that are valuable in orbit and 75 beyond may be very different to those we prize on Earth. Questions of their stewardship have barely been broached—and the relevant legal and regulatory framework is fragmentary, to put it mildly. Space miners, like their earthly counterparts, are 80 often reluctant to engage with such questions. One speaker at last week’s space-mining forum in Sydney, Australia, concluded with a plea that regulation should be avoided. But miners have much to gain from a broad agreement on the for-profit 85 exploitation of space. Without consensus, claims will be disputed, investments risky, and the gains made insecure. It is in all of our long-term interests to seek one out 50. The author of Passage 2 would most likely respond to the discussion of the future of space mining in lines 18-28, Passage 1, by claiming that such a future

    Passage 1 Follow the money and you will end up in space. That’s the message from a first-of-its-kind forum on mining beyond Earth. Convened in Sydney by the Australian Centre for 5 Space Engineering Research, the event brought together mining companies, robotics e5 xperts, lunar scientists, and government agencies that are all working to make space mining a reality. he forum comes hot on the heels of the 10 2012 unveiling of two private asteroid-mining firms. Planetary Resources of Washington says it will launch its first prospecting telescopes in two years, while Deep Space Industries of Virginia hopes to be harvesting metals from asteroids by 2020. Another 15 commercial venture that sprung up in 2012, Golden Spike of Colorado, will be offering trips to the moon, including to potential lunar miners. Within a few decades, these firms may be meeting earthly demands for precious metals, such as 20 platinum and gold, and the rare earth elements vital for personal electronics, such as yttrium and lanthanum. But like the gold rush pioneers who transformed the western United States, the first space miners won’t just enrich themselves. They also hope 25 to build an off-planet economy free of any bonds with Earth, in which the materials extracted and processed from the moon and asteroids are delivered for space-based projects. In this scenario, water mined from other 30 worlds could become the most desired commodity. “In the desert, what’s worth more: a kilogram of gold or a kilogram of water?” asks Kris Zacny of HoneyBee Robotics in New York. “Gold is useless .Water will let you live.” 35 Water ice from the moon’s poles could be sent to astronauts on the International Space Station for drinking or as a radiation shield. Splitting water into oxygen and hydrogen makes spacecraft fuel, so ice-rich asteroids could become interplanetary 40 refuelling stations. Companies are eyeing the iron, silicon, and aluminium in lunar soil and asteroids, which could be used in 3D printers to make spare parts or machinery. Others want to turn space dirt into 45 concrete for landing pads, shelters, nd roads. Passage 2 The motivation for deep-space travel is shifting from discovery to economics. The past year has seen a flurry of proposals aimed at bringing celestial riches down to Earth. No doubt this will make a few 50 billionaires even wealthier, but we all stand to gain: the mineral bounty and spin-off technologies could enrich us all. But before the miners start firing up their rockets, we should pause for thought. At first glance, space 55 mining seems to sidestep most environmental concerns: there is (probably!) no life on asteroids, and thus no habitats to trash. But its consequences —both here on Earth and in space—merit careful consideration. 60 Part of this is about principles. Some will argue that space’s “magnificent desolation” is not ours to despoil, just as they argue that our own planet’s poles should remain pristine. Others will suggest that glutting ourselves on space’s riches is not an 65 acceptable alternative to developing more sustainable ways of earthly life. History suggests that those will be hard lines to hold, and it may be difficult to persuade the public that such barren environments are worth preserving. 70 After all, they exist in vast abundance, and even fewer people will experience them than have walked through Antarctica’s icy landscapes. There’s also the emerging off-world economy to consider. The resources that are valuable in orbit and 75 beyond may be very different to those we prize on Earth. Questions of their stewardship have barely been broached—and the relevant legal and regulatory framework is fragmentary, to put it mildly. Space miners, like their earthly counterparts, are 80 often reluctant to engage with such questions. One speaker at last week’s space-mining forum in Sydney, Australia, concluded with a plea that regulation should be avoided. But miners have much to gain from a broad agreement on the for-profit 85 exploitation of space. Without consensus, claims will be disputed, investments risky, and the gains made insecure. It is in all of our long-term interests to seek one out 44. Which choice provides the best evidence for the answer to the previous question?

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