Answer:
x = 11
Step-by-step explanation:
Properties of a square,
1). Diagonal of a square bisect the opposite angles.
2). All interior angles of a square measure 90°.
From these properties,
m∠PQR = 90°
Since, diagonal QS bisects angle PQR,
m∠PQS = m∠RQS = 45°
(6x - 21)° = 45°
6x = 45 + 21
6x = 66
x = 11
Answer:
57% of the class failed the test.
Step-by-step explanation:
28 - 12 = 16
16/28 = 0.57142857142 ≈ 0.57
Thus, 57% of the class failed the test.
Answer:
18.0167≤x≤21.9833
Step-by-step explanation:
Given the following
sample size n = 10
standard deviation s = 3.2
Sample mean = 20
z-score at 95% = 1.96
Confidence Interval = x ± z×s/√n
Confidence Interval = 20 ± 1.96×3.2/√10
Confidence Interval = 20 ± (1.96×3.2/3.16)
Confidence Interval = 20 ± (1.96×1.0119)
Confidence Interval = 20 ± 1.9833
CI = {20-1.9833, 20+1.9833}
CI = {18.0167, 21.9833}
Hence the required confidence interval is 18.0167≤x≤21.9833
Answer:
Function is decreasing on (-8,infinity)
Step-by-step explanation:
The given function is 
The first derivative is given by
For the function to be decreasing, we have
Divide both sides by -2. Since, we are dividing by a negative number hence, the inequality sign will change.
Subtract 8 to both sides
Therefore, the function is decreasing on (-8,infinity)
First option is correct.
Answer:
3x²+8xy+4y²
Step-by-step explanation:
Opening brackets,
3x²+6xy+2xy+4y²
=3x²+8xy+4y²
