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A half-life is the amount of time that it takes for a radioactive substance to decay to one half of its original quantity. Suppose radioactive decay causes 300 grams of a substance to decrease to `300 xx 2^(–3)` grams after 3 half-lives. Evaluate `300 xx 2^(–3)` to determine how many grams of the substance are left. Explain why the expression `300 xx 2^(–n)` can be used to find the amount of the substance that remains after n

asked Jan 17, 2022 in 8th-maths by sumit (1.6k points)

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Consider a quantity of a radioactive substance. The fraction of this quantity that remains after t half-lives can be found by using the expression `3^(–t)`. (a) What fraction of substance remains after 7 half-lives? (b) After how many half-lives will the fraction be `1/243` of the

asked Jan 17, 2022 in 8th-maths by Arun (1.7k points)

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One Fermi is equal to `10^(–15)` metre. The radius of a proton is 1.3 Fermis. Write the radius of a proton in metres in standard

asked Jan 17, 2022 in 8th-maths by Arun (1.7k points)

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The paper clip below has the indicated length. What is the length in standard form.

asked Jan 17, 2022 in 8th-maths by nishit (1.8k points)

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Use the properties of exponents to verify that each statement is true. (a) `1/4(2^n) = 2^(n-2)` (b) `4(n-1) = 1/4(4)^n` (c) `25(5^(n–2)) =

asked Jan 17, 2022 in 8th-maths by nishit (1.8k points)

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Fill in the blanks

asked Jan 17, 2022 in 8th-maths by Simran (1.8k points)

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There are 864,00 seconds in a day. How many days long is a second? Express your answer in scientific

asked Jan 17, 2022 in 8th-maths by Simran (1.8k points)

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The given table shows the crop production of a State in the year 2008 and 2009. Observe the table given below and answer the given questions. Crop 2008 Harvest (Hectare) Increase/Decrease (Hectare) in 2009 Bajra `1.4 × 10^3` – 100 Jowar `1.7 × 10^6` -440,000 Rice `3.7 × 10^3` – 100 Wheat `5.1 × 10^5` + 190,000 (a) For which crop(s) did the production decrease? (b) Write the production of all the crops in 2009 in their standard form. (c) Assuming the same

asked Jan 17, 2022 in 8th-maths by nishit (1.8k points)

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Stretching Machine Suppose you have a stretching machine which could stretch almost anything. For example, if you put a 5 metre stick into a `(xx 4)` stretching machine (as shown below), you get a 20 metre stick. Now if you put 10 cm carrot into a `(xx 4)` machine, how long will it be when it comes out?

asked Jan 17, 2022 in 8th-maths by nishit (1.8k points)

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Two machines can be hooked together. When something is sent through this hook up, the output from the first machine becomes the input for the second. (a) Which two machines hooked together do the same work a `( xx 10^2)` machine does? Is there more than one arrangement of two machines that will work? (b) Which stretching machine does the same work as two `(xx 2)` machines hooked together?

asked Jan 17, 2022 in 8th-maths by nikhil (1.8k points)

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Repeater Machine Similarly, repeater machine is a hypothetical machine which automatically enlarges items several times. For example, sending a piece of wire through a `(xx 2^4)` machine is the same as putting it through a (xx 2) machine four times. So, if you send a 3 cm piece of wire through a `(xx 2^4)` machine, its length becomes `3 xx 2 xx 2 xx 2 xx 2 = 48` cm. It can also be written that a base (2) machine is being applied 4 times. What will be the new length of a 4 cm strip inserted in

asked Jan 17, 2022 in 8th-maths by nikhil (1.8k points)

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For the following repeater machines, how many times the base machine is applied and how much the total stretch is?

asked Jan 17, 2022 in 8th-maths by yogita (1.8k points)

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Find three repeater machines that will do the same work as a `(xx64)` machine. Draw them, or describe them using

asked Jan 17, 2022 in 8th-maths by yogita (1.8k points)

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What will the following machine do to a 2 cm long piece of chalk?

asked Jan 17, 2022 in 8th-maths by krutika (1.7k points)

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In a repeater machine with 0 as an exponent, the base machine is applied 0 times. (a) What do these machines do to a piece of chalk? (b) What do you think the value of 60

asked Jan 17, 2022 in 8th-maths by Arun (1.7k points)

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Shrinking Machine In a shrinking machine, a piece of stick is compressed to reduce its length. If 9 cm long sandwich is put into the shrinking machine below, how many cm long will it be when it emerges?

asked Jan 17, 2022 in 8th-maths by purvi (1.8k points)

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What happens when 1 cm worms are sent through these hook-ups?

asked Jan 17, 2022 in 8th-maths by Simran (1.8k points)

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Sanchay put a 1cm stick of gum through a `(1 xx 3^(–2))` machine. How long was the stick when it came

asked Jan 17, 2022 in 8th-maths by Simran (1.8k points)

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Ajay had a 1cm piece of gum. He put it through repeater machine given below and it came out `1/100,000 cm` long. What is the missing value?

asked Jan 17, 2022 in 8th-maths by Arun (1.7k points)

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Find a single machine that will do the same job as the given hook-up. (a) a`(xx 2^3)` machine followed by `(xx 2^(–2))` machine. (b) a`(xx 2^4)` machine followed by `(xx(1/2)^2)` machine (c) a`(xx 5^99)` machine followed by a `(5^(–100))`

asked Jan 17, 2022 in 8th-maths by purvi (1.8k points)

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