Answer:
x = 180 - (37 + 53)
Step-by-step explanation:
x + 37 + 53 = 180
x = 180 - (37 + 53)
All of the angles have to equal 180 due to the supplementary angles thm
Answer:
The second option shows the correct translation of 3 units to the right and 1 unit down.
Answer:
A)0.86
B)0.99
C)6.047E-13
Step-by-step explanation:
Since p = 0.01 and q= 0.99
Number of event n = 15
Using binomial expansion
A) Probability (No samples are mutated) = 15C0 (p)^0 * (q)^15
= 1*(0.01)^0*(0.99)^15 = 0.86
B)Probability (At most one sample is mutated) = 15C0 * p^0 *q^15 + 15C1 * p^1 * q^14 = 1*(0.01)^0*(0.99)^15 + 15C1 * 0.01 * 0.99^14 = 0.86 + 15*0.01*0.8687 = 0.86 + 0.13 = 0.99
C) Probability (More than half the samples are mutated) = 15C8* 0.01^8 * 0.99^7 + 15C9* 0.01^9 * 0.99^6 +15C10* 0.01^10 *0.99^5 + 15C11 * 0.01^11 * 0.99^4 + 15C12 * 0.01^12 * 0.99^3 + 15C13 * 0.01^13 * 0.99^ 2 + 15C14 * 0.01^14 * 0.99^1 + 15C15 * 0.01^15 * 0.99^0
Probability (More than half the samples are mutated) = 6E-13 + 4.71E-15 + 2.86E-17 + 1.31E-19 + 4.41E-22 + 1.03E-24 + 1.49E-27 + 1E-30 = 6.047E-13
Answer:
1/3 of 45 = 15 cubic feet
Step-by-step explanation:
volume of rectangular prism = (B)(h)
volume of rectangular pyramid = 1/3(B)(h)
2x + 3y = -21
2x = -21 - 3y
x = -10.5 - 3/2y
-10x + 2y = 20
-10(-10.5 - 3/2y) + 2y = 20
105 + 15y + 2y = 20
105 + 17y = 20
17y = -85
y = -5
2x + 3y = -21
2x + 3(-5) = -21
2x - 15 = -21
2x = -6
x = -3
Therefore, the coordinates are (-3, -5).
