Answer:
63.6mm
Step-by-step explanation:
According to cosine rule;
AB² = BC²+AC²-2(BC)(AC)cos m<C
Substitute the given values
AB² = 70²+40²-2(70)(40)cos 64
AB² = 4900+1600-5600cos64
AB² = 6500-5600(0.4384)
AB² = 6500-2,454.87
AB² = 4,045.12
AB = √4,045.12
AB = 63.6mm
Hence the length of AB is 63.6mm
Answer:

Step-by-step explanation:
Factor each half of the expression separately:

Since both 4k² and 7 are being multiplied by (7k-6), we can combine them to get:

Answer: 12
Step-by-step explanation: because each pack is 50cents so multiply .50 by 24 so the answer is 12
All these cases represent experiments whose outcomes are all equaly likely. What we mean is that the cards have all the same probability of being dealt (1/52), and all the spaces of the spinner have the same probability of being landed into (1/5).
These probabilities are computed as 1 over all the possible outcomes.
(a) If you want a heart card and a five, you want the 5 of hearts. So, only one card would satisfy your request, and thus you have probability 1/52 of dealing the 5 of hearts.

(b) There are four 10s and four Jacks in the deck, so 8 cards satisfy your request. With probability 8/52, you'll be dealt a Jack or a 10.

(c) You have two "good" outcomes out of 5, so your probability is 2/5.
