Answer:
a) 0.108
b) 1.00
c) 0.170
d) 0.0109
e) 0.0121
f) 0.999
Step-by-step explanation:
Success: p = 0.15
Failure: q = 1 - p = 0.85
a) q²p = 0.85² × 0.15
= 0.108375 = 0.108 (3 sf)
b) 1 - P(all hits)
= 1 - p⁷ = 1 - 0.15⁷
= 0.9999982914= 1.00 (3 sf)
c) q³p + q⁴p = 0.1704196875
= 0.170 (3 sf)
d) 7C4×p⁴×q³ = 35 × 0.15⁴ × 0.85³
= 0.01088152734 = 0.0109 (3 sf)
e) P(4,5,6 or 7)
= 7C4×p⁴×q³ + 7C5×p⁵×q² +
7C6×p⁶×q + 7C7×p⁷×q⁰
= 0.01210317188 = 0.0121 (3 sf)
f) 1 - P(more than 4)
= 1-(0.01210317188-0.01088152734)
= 1 - 0.001221644531
= 0.9987783555 = 0.999 (3 sf)
Answer:
To convert a quadratic from y = ax2 + bx + c form to vertex form, y = a(x - h)2+ k, you use the process of completing the square.
Step-by-step explanation:
Answer:
x = 37°
Step-by-step explanation:
Given the triangle with two given exterior angles, m ∠107° and m ∠110°:
We can use the <u>exterior angle theorem</u> where it states that the measure of each exterior angle of a triangle is equal to the sum of the measures of the opposite and remote interior angles.
Start by finding the supplement of m ∠110°, that will serve as the other remote interior angle.
The supplement of ∠110° is:
∠110° + y = 180°
Where y = represents the other unknown interior angle.
Subtract ∠110° from both sides:
∠110° - ∠110° + y = 180° - ∠110°
y = 70°
Therefore, the other remote interior angle is y = 70°. Now, we can determine the value of x by establishing the following equation:
107° = x° + 70°
Subtract 70 from both sides:
107° - 70° = x° + 70°- 70°
x = 37°
