Answer: F
Step-by-step explanation:
- This does not have infinitely many solutions (adding the equations, we get a fixed value of x)
- This has no solutions (the left hand sides are the same but the right hand sides have different values)
- This has one solution (the first equation givess a fixed value for x)
- This has no solutions (same reason as 2)
- This has one solution (same reason as 3, just the second equation instead of the first)
- This has infinitely many solutions (multiplying both sides of the top equation by -2 gives the bottom equation).
<span>The correct answer is: 800
Explanation:
If the threatre holds 1200 people, it means that there are total 1200 seats in the theatre.
2/3 of the total seats are sold; mathematically we can write it as:
(Total-number-of-seats) * (Fraction-of-seats-sold)
1200 * 2/3 = 800
Hence there are 800 tickets are sold.</span>
Answer:
D. 280°
Step-by-step explanation:
The question lacks the required diagram. Find the diagram attached below.
From the diagram,
arc EAC = arc EAB + arc BC ... (1)
Note that arc EAB is the angle on the straight line EB and since sum of angle on a straight line is 180°, arc EAB = 180°
Next is to get the arc BC. It can be seen from the diagram that arc BC + arc CD + arc DE = 180°
Given arc CD = 25°, arc DE = arc AB = 55° (since the diameter AD and BE are the same). On substituting this values we will have:
arc BC + 25°+55° = 180°
arc BC = 180° - 80°
arc BC = 100°
Remember from initial equation 1 that arc EAC = arc EAB + arc BC
arc EAC = 180°+100°
arc EAC = 280°
The measure of EAC is therefore 280°
Answer:
see below
Step-by-step explanation:
total - no nuts = nuts 186 - 104 = 82
total - o raisin = chip = 82 - 40 =42
2/3 of the cookies are c chip 2/3 * 186 = 124
124- 42 = 82 no nuts
104 - 82 = 22
40 +22 = 62
c chip o raisin total
nuts 42 40 82
no nuts 82 22 104
total 124 62 186
P ( nuts) = number of nuts / total in the total column 82 / 186 =41/93
P (nuts | oatmeal) = nuts / total in the oatmeal column =40/ 62 =20/31
They are not independent
They need to have the same probability to be independent
Answer:640
Step-by-step explanation:
Since 15 out of every 75 fish are more than 30 cm long, the probability of finding a fish more than 30 cm is P(x > 30) = 15/75 = 1/5.
The probability of finding a fish 30 cm or less is P(x ≤ 30) = 1 - P(x > 30)
= 1 - 1/5
= (5 - 1)/5
= 4/5
Since we have 800 fish and the probability of finding a fish 30 cm or less is P(x ≤ 30) = 4/5, then the number of fish in the population that are 30 cm or less in length are 800 × P(x ≤ 30) = 800 × 4/5
= 160 × 4
= 640
So, 640 fish in the population are 30 cm or less in length
