Answer: i think (4n+1)^2(4n-1)^2 isnt a multiple of 8 for all integers of n because:
(4n + 1)²(4n - 1)²
= [(4n + 1)(4n - 1)]²
= (16n² - 1)²
= 16².n².n² - 2.16.n² + 1
= 8n²(32n² - 4) + 1
can see 8n²(32n² - 4) is a multiple of 8 but 1 isnt a multiple of 8
=> (4n + 1)²(4n - 1)² isnt a multiple of 8 for all integers of n.
Step-by-step explanation:
The volume of the sphere is expressed in the formula V = 4/3 pi r^3. The rate of change of volume is determined by differentiating the formula: dV/dt = 4pi r^2 dr/dt. When we substitute 500 cm3/min as dV/dt and 30 cm as r. Then dr/dt is equal to 0.0442 cm/min
The probability that a three shows on at least one of the dice is 11/36.
<h3>How to calculate the probability?</h3>
It should be noted that of probability means the likelihood of the occurence of an event.
The probability that a three shows on at least one of the dice will be:
= 11/36
This can be seen from the table that is attached.
The probability that the total is less than 8 will be:
= 21/36
= 7/12
Here, there are 21 places where the total is less than 8.
Learn more about probability on:
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Answer:
X- axis is the line at the bottom of the graph and y-axis is the line on the side
The range is all real numbers.
The function given simplifies to just f(x) = 4x.
This is just a straight line that is increasing from left to right. If we reflect the line over the x-axis, it is still a line that goes on forever in each direction.
Therefore, the range will be all real numbers.
