Answer:
x = 21 / 228
Step-by-step explanation:
4x - 10y = - 3 -----> equation 1
112x + 5y = 12 -----> equation 2
Multiply 2 on both sides in the equation 2,
2 ( 112x + 5y = 12 )
224x + 10y = 24 -----> equation 3
Add equations 1 & 3,
4x - 10y = - 3
224x + 10y = 24
_____________
228x + 0 = 21
228x = 21
x = 21 / 228
Answer:
the probability that a sample of the 35 exams will have a mean score of 518 or more is <em> 0.934 </em>or<em> 93.4%</em>.
Step-by-step explanation:
This is s z-test because we have been given a sample that is large (greater than 30) and also a standard deviation. The z-test compares sample results and normal distributions. Therefore, the z-statistic is:
(520 - 518) / (180/√35)
= 0.0657
Therefore, the probability is:
P(X ≥ 0.0657) = 1 - P(X < 0.0657)
where
- X is the value to be standardised
Thus,
P(X ≥ 0.0657) = 1 - (520 - 518) / (180/√35)
= 1 - 0.0657
= 0.934
Therefore, the probability that a sample of the 35 exams will have a mean score of 518 or more is <em>0.934 or 93.4%</em>.
Answer:
(1, 14)
Step-by-step explanation:
To find the vertex, complete the square.
First, factor out the leading coefficient from the first two terms:
y = -2 (x² − 2x) + 12
Now take half of the second coefficient, square it, and add and subtract the result:
(-2/2)² = 1
y = -2 (x² − 2x + 1 − 1) + 12
Factor the perfect square:
y = -2 ((x − 1)² − 1) + 12
Distribute:
y = -2 (x − 1)² + 2 + 12
y = -2 (x − 1)² + 14
So the vertex is (1, 14).
X+12 +5x =6x+12 =90
-12 from 90
=78
/6
X=13
