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N]o man [should] be compelled to make or yield any Gift, Loan, Benevolence, Tax, or such like Charge, without Common Consent by Act of Parliament. –English Petition of Right 1628 What is the key idea stated in this quote...
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Which ancient principles can be found in American government today? In a paragraph, provide at least three examples of government structures and principles that are based on ancient ideas.
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Marco has a bag of red, blue, and green tiles. Which set of events would be considered independent? A tile is drawn and replaced, and then a second tile is drawn. A tile is drawn and removed, and then a second tile is dr...
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Two events, A and B, are independent of each other. P(A)= and P(A and B)=. What is P(B) written as a decimal? Round to the nearest hundredth, if necessary. 0.02 0.04 0.29 0.75
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A box contains different-colored marbles. If P(blue) = , P(green) = , and P(blue and green) = , which statement is true? The events are independent because P(blue) P(green) = P(blue and green). The events are independent...
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For an in-class demonstration, a teacher flips a fair coin 5 times, and each of the 5 times it lands on heads. A student argues that it is more likely to land on tails on the next, or 6th, flip. Is the student correct? E...
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Consider a situation in which P(A) = , P(C) = , and P(A and B) = . What is P(B and C)?
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A bag contains a variety of different-colored marbles. If P(red) = , P(green) = , and P(red and green) = , which statement is true? The events are independent because P(red) • P(green) = P(red and green). The events are...
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Andrea rolls a number cube twice. She determines P(even, then odd) = . Which statements are accurate? Check all that apply. Andrea’s solution is incorrect. The total number of possible outcomes is 12. The probability of...
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A spinner contains 3 equal sections: one red, one yellow, and one blue. The possible results of two spins are shown in the tree diagram below. What is P(red, then yellow)?
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Two events, A and B, are independent. If P(A) = 0.3 and P(B) = 0.2, what is P(A and B)?
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Which events are independent? Check all that apply. rolling two number cubes at the same time choosing a card, and then flipping a coin choosing a first, second, and third place winner drawing a name from a hat, keeping...
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Which statement correctly describes dependent events? Two events are dependent if they have no outcomes in common and cannot occur at the same time. Two events are dependent if they have outcomes in common and can occur...
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Given the following probabilities for choosing 2 marbles from a bag of 10 marbles, determine if the events are dependent or independent. P(blue) = , P(green) = , and P(blue and green) = dependent, because the product of...
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Consider a situation where P(A) = and P(A and B) =. If the events are independent, then what is P(B)?
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Three coins are flipped. The possible results are shown in the tree diagram below. What is P(2 heads, 1 tails)?
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Which are dependent events? Check all that apply. choosing 2 socks from a drawer, without replacement flipping a coin 4 times picking 4 cards from a deck, one after the other rolling a number cube twice spinning a spinne...
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Each letter of the alphabet is written on a piece of paper and put in a hat. If a piece of paper is chosen at random, what is the probability that it will be a vowel? The number of favorable outcomes is . The number of p...
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Kalina is choosing a sandwich and a drink for lunch. She can choose between turkey, ham, and vegetarian sandwiches. She chooses her drink from a selection of water, orange juice, milk, or lemonade. How many possible ways...
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The two right triangular prisms are similar solids. The scale factor of the larger prism to the smaller prism is . How do the volumes compare? The volume changes by . The volume changes by , or . The volume changes by ,...
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A cone has a radius of 5 cm and a slant height of 10 cm. The area of the base of the cone is π cm2. The lateral area of the cone is π cm2. The surface area of the cone is π cm
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In the derivation of the formula for the volume of a cone, the volume of the cone is calculated to be StartFraction pi Over 4 EndFraction times the volume of the pyramid that it fits inside. A cone is inside of a pyramid...
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Suppose the height of a cylinder is equal to its radius. The cylinder can fit inside a square prism, as shown below. The cross-sectional areas are still the same and the ratio of the area of the circle to the area of the...
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Three oblique pyramids have the same regular square base. Which one has a volume of 15 cubic units if the area of the bases are all 15 square units? An oblique triangular pyramid is shown. The slant height is 5, the vert...
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On a coordinate plane, kite W X Y Z has points (1, 1), (3, 4), (5, 1), (3, negative 3). Kite WXYZ is graphed on a coordinate plane. What is the approximate perimeter of the kite? Round to the nearest tenth. 10.6 units 11...
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