Bloom

The conditional (A > B) says that: *

A is sufficient for B

A is necessary for B

B is necessary for A

Both options 1 and 3 are correct

Both options 1 and 2 are correct

Assume that you and a friend are both capable of traveling a straight-line path from Earth to Jupiter. You take a spacecraft that is capable of traveling an average speed of 70,811 km/hr (44,000 mi/hr) to the actual planet, while your friend drives a vehicle at an average speed of 112.7 km/hr (70 mi/hr) along the red line of the scaled solar system. Which answer below is correct?

Choose one:

 4.9 hr (car) vs. 369.9 days (spacecraft)

 7.9 hr (car) vs. 595.2 days (spacecraft)

 6.1 hr (car) vs. 457.9 days (spacecraft)

 4.9 hr (car) vs. 515.3 days (spacecraft)

Say that the present-day diameter of Manicouagan Crater is 75 km and the present-day diameter of Meteor Crater is 1.2 km. Assume that a 40-m-diameter meteorite created Meteor Crater. Although clearly an oversimplification, use a simple ratio between meteorite size and crater diameter to estimate the size of the meteorite that might have created Manicouagan Crater (use the crater diameters I provided).

Choose one:

 ~40 m

 ~170 m

 ~2,500 m

 ~3,500 m

When you look at Neptune in a telescope, you are actually looking into the past, as the light has to travel from Neptune to your eyes. If the speed of light is ~300,000 km/s, how far back into the past are you looking (or put another way, how long does it take light to travel from Neptune to your eyes on Earth)?

Choose one:

 ~14,501 hr

 ~4 hr

 ~242 hr

 ~1,233 hr

 Assume that you and a friend are both capable of traveling a straight-line path from Earth to Jupiter. You take a spacecraft that is capable of traveling an average speed of 70,811 km/hr (44,000 mi/hr) to the actual planet, while your friend drives a vehicle at an average speed of 112.7 km/hr (70 mi/hr) along the red line of the scaled solar system. Which answer below is correct?

Choose one:

 4.9 hr (car) vs. 369.9 days (spacecraft)

 7.9 hr (car) vs. 595.2 days (spacecraft)

 6.1 hr (car) vs. 457.9 days (spacecraft)

 4.9 hr (car) vs. 515.3 days (spacecraft)

Say that the present-day diameter of Manicouagan Crater is 75 km and the present-day diameter of Meteor Crater is 1.2 km. Assume that a 40-m-diameter meteorite created Meteor Crater. Although clearly an oversimplification, use a simple ratio between meteorite size and crater diameter to estimate the size of the meteorite that might have created Manicouagan Crater (use the crater diameters I provided).

Nebular Supernova – Crab Nebula. Some red giant stars undergo a violent supernova explosion, as opposed to forming planetary nebulas. Which type of star will form a supernova?

Choose one: high-mass star (greater than 8x the mass of our Sun) intermediate- to low-mass stars (between 0.8x to 8x the mass of our Sun)

Planetary Nebula/White Dwarf Stars – Little Ghost Nebula. Some red giant stars develop into planetary nebulas as their cores continue to contract, to increase in temperature, and to burn and vent the remaining gases into interstellar space. Eventually, the core collapses to the point where it is hot enough to ionize the vented gases, forming a relatively short-lived (~10,000-20,000 years) planetary nebula. The remaining core collapses into a white dwarf star. The vented materials from the planetary nebula play an important role in enriching the universe in elements with atomic weights less than 26 (forming the basis for carbon-based life like ourselves!). Which type of star will form a planetary nebula?

Choose one:

 high-mass star (greater than 8x the mass of our Sun)

 intermediate- to low-mass stars (between 0.8x to 8x the mass of our Sun)

Red Giant Stars – Aldebaran. Eventually, the majority of hydrogen in the core of the main sequence stars is consumed, and the core collapses due to gravity. Very low-mass stars form white dwarf stars, whereas most other stars collapse and heat up until helium fusion begins. This fusion causes the star to expand outward several times larger than before, forming a red giant star (making the star cooler...Aldebaran is an example). When this happens to our Sun (in about 4.5 billion to 5 billion years), what will happen to Earth?

Choose one:

 Earth will be pushed by the expanding Sun to maintain its orbital distance from the Sun, allowing Earth to retain the same environmental conditions that it has now.

 Earth will experience increased temperatures but will retain its atmosphere and water.

 Earth will lose its atmosphere and water and may/may not be completely vaporized by the Sun as it expands close to Earth’s current orbit.

Stellar Nursery – Pillars of Creation, Eagle Nebula. The Pillars of Creation are large, dense masses of dust and interstellar gas (mostly molecular hydrogen) that rise from the stellar nursery of the Eagle Nebula (M16). Here, dense pockets of dust and gas collapse in on themselves to form young stars. The Pillars of Creation are located about 6,500 light-years from Earth, and the left-most pillar has a current length of approximately 4 light-years (a light-year is the distance light travels in one year...about 9.5 trillion km). What is the length of the left-most pillar (in km)?

Choose one:

 ~13.5 trillion km

 ~38 trillion km

 ~9.5 trillion km

 ~2.375 trillion km

An apple contains 170 calories and 2 g of fiber. A banana contains 130 calories and 5 g of fiber. Set up a system of equations that could be solved to determine the number of apples (x

x

) and bananas (y

y

) that should be eaten to obtain 6560 calories and 157 g of fiber.

Equation 1:

Equation 2:

Solve the system to find the required:

Number of apples:

Number of bananas :

[1 1 2 5 ]

[2 3 −6 6 ]

[−4 −8 2 6 ]

First: −2R1+R2→R2

Second: 4R1+R3→R3

Third: 4R2+R3→R3

Perform each row operation in the order specified. What would be the final result?

Compute the following matrix

[3 -3] [-1 -2]  [12] 

[1 2] [3 -1] +  [34] 

[1 -3]             [56] 

first matrix: 2 7 1

-2 -1 4

-5 -1 10

Second matrix: -10 0 0

0 -60

0 0 2

In a city, 54 % are conservatives, 16 % are liberals and 30 % are independents. Records show that, in a particular election, 77 % of conservatives voted, 68 % of liberals voted and 84 % of independents voted. For each of the following questions, express any probability value as a fraction or a decimal with 10 places. 

If a person from such a city is selected at random and it is learned that he/she voted, what is the probability that he/she is independent? 

In a city, 54 % are conservatives, 16 % are liberals and 30 % are independents. Records show that, in a particular election, 77 % of conservatives voted, 68 % of liberals voted and 84 % of independents voted. For each of the following questions, express any probability value as a fraction or a decimal with 10 places. 

If a person from such a city is selected at random and it is learned that he/she voted, what is the probability that he/she is liberal?