Answer:
what problem?
Step-by-step explanation:
1000= 10^3 -- ten to the third power
assuming you mean whole numbers,
graba calculator, figure out what
1^3, 2^3 3^3 ... 9^3 are
or
1x1x1
2x2x2
3x3x3
...
9x9x9
6 times a number n is 6n.
In algebra, when number multiply with variables, you don't need a multiplication sign (x). You just put them together like 6n (instead of 6 x n).
Happy to Help!
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The median number of minutes for Jake and Sarah are equal, but the mean numbers are different.
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For this, you never said the choices, but I’ve done this before, so I’m going to use the answer choices I had, and hopefully they are right.
Our choices are -
• The median number of minutes for Jake is higher than the median number of minutes for Sarah.
• The mean number of minutes for Sarah is higher than the mean number of minutes for Jake.
• The mean number of minutes for Jake and Sarah are equal, but the median number of minutes are different.
• The median number of minutes for Jake and Sarah are equal, but the mean number of minutes are different.
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So to answer the question, we neee to find the median and mean for each data set, so -
Jack = [90 median] [89.6 mean]
Sarah = [90 median] [89.5 mean]
We can clearly see the median for both is 90, so we can eliminate all the choices that say they are unequal.
We can also see that Jack has a higher mean (89.6) compared to Sarah (89.5).
We can eliminate all the choices that don’t imply that too.
That leaves us with -
• The median number of minutes for Jake and Sarah are equal, but the mean number of minutes are different.
The given equation
x/2 = y/3 = z/4
can be broken into three separate equations which I'll call equations (A), (B) and (C)
- x/2 = y/3 ..... equation (A)
- y/3 = z/4 .... equation (B)
- x/2 = z/4 .... equation (C)
We'll start off solving for z in equation (C)
x/2 = z/4
4x = 2z ... cross multiply
2z = 4x
z = 4x/2 ... divide both sides by 2
z = 2x
Now let's solve for y in equation (A)
x/2 = y/3
3x = 2y
2y = 3x
y = 3x/2
y = (3/2)x
y = 1.5x
The results of z = 2x and y = 1.5x both have the right hand sides in terms of x. This will allow us to replace the variables y and z with something in terms of x, which means we'll have some overall expression with x only. The idea is that expression should simplify to 3 if we played our cards right.
We won't be using equation (B) at all.
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The key takeaway from the last section is that
Let's plug those items into the expression (2x-y+5z)/(3y-x) to get the following:
(2x-y+5z)/(3y-x)
(2x-y+5(2x))/(3y-x) ..... plug in z = 2x
(2x-y+10x)/(3y-x)
(12x-y)/(3y-x)
(12x-1.5x)/(3(1.5x)-x) .... plug in y = 1.5x
(12x-1.5x)/(4.5x-x)
(10.5x)/(3.5x)
(10.5)/(3.5)
3
We've shown that plugging z = 2x and y = 1.5x into the expression above simplifies to 3. Therefore, the equation (2x-y+5z)/(3y-x) = 3 is true when x/2 = y/3 = z/4. This concludes the proof.
