Answer:
a. 0.0368
b. 0.99992131
c. 0.2039
d. 0.0048
e. 0.6533
Step-by-step explanation:
Let the probability of obtaining a head be p = 65% = 13/20 = 0.65. The probability of not obtaining a head is q = 1 - p = 1 -13/20 = 7/20 = 0.35
Since this is a binomial probability, we use a binomial probability.
a. The probability of obtaining 11 heads is ¹²C₁₁p¹¹q¹ = 12 × (0.65)¹¹(0.35) = 0.0368
b. Probability of 2 or more heads P(x ≥ 2) is
P(x ≥ 2) = 1 - P(x ≤ 1)
Now P(x ≤ 1) = P(0) + P(1)
= ¹²C₀p⁰q¹² + ¹²C₁p¹q¹¹
= (0.65)⁰(0.35)¹² + 12(0.65)¹(0.35)¹¹
= 0.000003379 + 0.00007531
= 0.0007869
P(x ≥ 2) = 1 - P(x ≤ 1)
= 1 - 0.00007869
= 0.99992131
c. The probability of obtaining 7 heads is ¹²C₇p⁷q⁵ = 792(0.65)⁷(0.35)⁵ = 0.2039
d. The probability of obtaining 7 heads is ¹²C₉q⁹p³ = 220(0.65)³(0.35)⁹ = 0.0048
e. Probability of 8 heads or less P(x ≤ 8) = ¹²C₀p⁰q¹² + ¹²C₁p¹q¹¹ + ¹²C₂p²q¹⁰ + ¹²C₃p³q⁹ + ¹²C₄p⁴q⁸ + ¹²C₅p⁵q⁷ + ¹²C₆p⁶q⁶ + ¹²C₇p⁷q⁵ + ¹²C₈p⁸q⁴
= = ¹²C₀(0.65)⁰(0.35)¹² + ¹²C₁(0.65)¹(0.35)¹¹ + ¹²C₂(0.65)²(0.35)¹⁰ + ¹²C₃(0.65)³(0.35)⁹ + ¹²C₄(0.65)⁴(0.35)⁸ + ¹²C₅(0.65)⁵(0.35)⁷ + ¹²C₆(0.65)⁶(0.35)⁶ + ¹²C₇(0.65)⁷(0.35)⁵ + ¹²C₈(0.65)⁸(0.35)⁴
= 0.000003379 + 0.00007531 + 0.0007692 + 0.004762 + 0.01990 + 0.05912 + 0.1281 + 0.2039 + 0.2367
= 0.6533
Answer: 
Explanation:
Multiplying by 1/2 is the same as dividing by 2.
For example, if you have 10 slices of cake and 2 friends, then each friend gets 10/2 = 5 slices. We could also say 
The fraction 1/2 converts to the decimal form 0.5, which means 
Yes, because you can multiply $3 by 3 to get $9 and 6 muffins by 3 to get 9 muffins.
Answer: 30°, 67° e 83°.
Step-by-step explanation: The angles are (2x + 16)/5 , x e x + 16°
Adding all the angles, comes:
(2x + 16)/5 + x + x + 16° = 180° ;
2x + 16° + 5x + 5x + 80° = 900° ;
12x = 900° - 16° - 80° ;
12x = 804°° ;
x = 804°/12 ;
x = 67°
So, the first angle is (2,67 + 16)/5 = 30°, the second is 67° and the third is 83°.
Answer:
Step-by-step explanation:
4 g.
c=42
a=b=d
a+b+42=180
a+a=180-42
2a=138
a=138/2=69
a=69
b=69
c=42
d=69
5a.
a=30
angle O=180-(a+30)=180-(30+30)=180-60=120°
d=80
angle O=180-(d+80))=180-(80+80)=180-160=20°
central angle O of middle triangle=180-(120+20)=180-140=40°
b=c
b+c+40=180
b+b=180-40
2b=140
b=140/2=70
b=70°
c=70°
