The remaining weight of the empty bottle is 0.5 because each third of the bottle weighs 2.5 pounds and of the remaining juice and the bottle was 3 pounds 2.5 subtracted from 3 is 0.5
Answer:
see below for drawings and description
Step-by-step explanation:
For geometry problems involving translation, rotation, and reflection—transformations that change location, but not size ("rigid" transformations)—it might be helpful for you to trace the image onto tracing paper or clear plastic so that you can manipulate it in the desired way. Eventually, you'll be able to do this mentally, without the aid of a physical object to play with.
For the images attached here, I copied the triangle onto a piece of clear plastic so I could move it to the desired positions. The result was photographed for your pleasure.
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a. Translation means the image is moved without changing its orientation or dimensions. You are asked to copy the triangle so that the upper left vertex is moved to what is now point E. See the first attachment.
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b. Reflection means the points are copied to the same distance on the other side of the point or line of reflection. Just as an object held to a mirror has its reflection also at the mirror, any points on the line of reflection do not move. Reflection flips the image over. See the second attachment.
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c. Rotation about point D means point D stays where it is. The angle of rotation is the same as the angle at D, so the line DE gets rotated until it aligns with the line DF. The rest of the triangle maintains its shape. See the third attachment.
Answer:
Step-by-step explanation:
At a Baseball Match.
35% of spectators are New York Yankees fan
The rest are Boston Red Sox fan = 100 - 35% = 65%
30% of fans in both teams are females.
30% of 35% of spectators are New York Yankees fan = 0.105 females
30% of 65% of spectators are Boston Red Sox fan = 0.195 females
The number of males in New York Yankees fan = 1 - 0.105 females
= 0.895 males
The number of males in Boston Red Sox fan = 1 - 0.195 females
= 0.805 males
The dog with the weight of 110lbs is the outlier in the equation--since the other dogs only range from 20 to 35 lbs.
Answer:
c)The proof writer mentally assumed the conclusion. He wrote "suppose n is an arbitrary integer", but was really thinking "suppose n is an arbitrary integer, and suppose that for this n, there exists an integer k that satisfies n < k < n+2." Under those assumptions, it follows indeed that k must be n + 1, which justifies the word "therefore": but of course assuming the conclusion destroyed the validity of the proof.
Step-by-step explanation:
when we claim something as a hypothesis we can only conclude with therefore at the end of the proof. so assuming the conclusion nulify the proof from the beginning