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Answer:
The definition of a z-score is:
z = (X - μ)/σ where X is our given score (33), μ is the distribution's mean (40) and σ is the distribution's standard deviation (9).
To calculate the z-score for 33, plug the numbers in:
z = (33 - 40)/9 = -7/9 = -.78
Hope this helps!
Step-by-step explanation:
Answer:
Step-by-step explanation:
Biking is x and bussing is y. We know that the total distance is 325. Thus, the first equation in this system is
x + y = 325 (which says that the km traveled by bike plus the km traveled by bus totaled 325 km).
We also know that the pair biked 75 km more than they rode, giving us the second equation in our system:
x = y + 75. Now we use simple substitution and plug y + 75 in for x in the first equation:
(y + 75) + y = 325 and
2y + 75 = 325 and
2y = 250 so
y = 125 km. They rode the bus for 125 km and biked for 325 - 125 which is 200. And the difference is 75 km, as it should be!
Start by writing out the information you know mathematically (I used S for cost of senior ticket, and C for cost of child ticket. You could use X and Y, or any other combination of letters as variables)
3s + 1c=38
3s + 2c=52
Now, you'll want to eliminate one of the variables by subtracting it out. Remember - Same sign, subtract (and therefore different sign, add).
In this case, 3s exists in the first and second equation, so it's very easy to get rid of. They're both positive, so they have the same sign (+). Same sign, subtract.
3s + 1c=38
-(3s + 2c=52)
__________
0 -1c= -14
-c=-14
C=14
Now, plug c=14 into either of the original equations.
3s + C= 38
3s + 14=38
3s=24
S=8.
So, a child ticket costs $14 and a senior ticket costs $8.
Common factor is such a term which can be taken out common from each term of the expression.
If you observe the given expression, 2x can be taken out common leaving the expression which cannot be factored any further.
14x² - 12x
= 2x (7x - 6)
So 2x is the common factor. The answer to this question is option C
