Hi there!
Question 1:
For this, we are taking away 1/4 yards of spring from 7/8 yards. This is essentially just subtracting 1/4 from 7/8. This then gives us the equation:
Now, to subtract these, we want to make it so the denominators are the same, or the numbers on the lower half are the same. (One way to explain why this is true is: 
). Now, to make it so the denominators are the same, we can multiply the second fraction, 1/4, by 2/2 as 2/2 is essentially 1, and multiplying by 1 will get the same result, just with a denominator switched in this case. Doing this, we get:
Now, subtracting the numerators, we get:
yards of string will remain.
Question 2:
For this, we are combining these two thicknesses, and thus we add 1/4 to 7/12. This gives us the equation:
Now, we again want to make it so the denominators are the same. (Here's a similar proof but for addition this time: 
). Now, to make the denominators the same, we can multiply the first fraction, 1/4, by 3/3 (also equivalent to 1). Doing this, we get:
, which is equivalent to (dividing both the top and the bottom by 2) 
inches.
Hope this helps!
Answer:-47/40
Step-by-step explanation:
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Answer is 0</h3>
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Explanation:
Logarithms are used to solve exponential equations. Specifically if you have a variable in the exponent, then you use a log to isolate the variable.
If we set the given log expression to x, then we can rewrite it into 8^x = 1. The only value of x that works is x = 0.
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Or put another way,
8^x = 1
8^x = 8^0 ... replace the 1 with 8^0
x = 0 ... the bases are equal (to 8) so the exponents must be equal
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You can use the change of base formula to directly calculate this log
Step-by-step explanation:
The exact question is as follows :
Given - The student who traveled to 3 states visited 6 new states during a vacation.
To find - Does increasing the 3 to 6 change the median? If so, how?
Proof -
Yes,
If we increase the 3 states to 6 states, it changes the median
Because
The median of the first 3 states is the middle state.
For example -
If we have 3 states X, Y, Z
Then the median is the state Y
Now,
The median of 6 states is the average of the 2 middle states.
For example -
If we have 6 states
X, Y, Z, U, V, W
Then
The median is not explicit.
Median is the average of the two middle states, Z and U.
And
Average of Z and U = half of the sum of Z and U.
i.e. (Z + U)/2.
And we can see that,
Median of 3 States is not equal to Median of 6 states
i.e. Y is not equal to (Z + U)/2.
So,
We can say that,
Increasing the state 3 to 6 changes the median.
Answer:
2:4
or in simplest form, 1:2
Step-by-step explanation:
