Answer:
60, 75
150 165
240 255
330 345
Step-by-step explanation:
csc 4 theta = -2 sqrt(3)/3
Write in terms of sin
1/ sin (4 theta) = -2 sqrt(3)/3
Using cross products
-2 sqrt(3) = 3 sin (4 theta)
Divide each side by 3
-2 sqrt(3)/3 = sin (4 theta)
Take the inverse sin on each side
sin ^ -1(-2 sqrt(3)/3) = sin ^ -1 (sin (4 theta))
240 +360n = 4 theta
and 300 +360n = 4 theta where n is an integer
Dividing each side by 4
240/4 +360n/4 = 4/4 theta and 300/4 +360n/4 = 4/4 theta
60 + 90n = theta and 75 +90n = theta
We want all the values between 0 and 360
Let n=0
60, 75
n=1
60+90=150 and 75+90 =165
n=2
60+180= 240 75+180=255
n=3
60+270 = 330 75+ 270 =345
Answer:
Approximately 11 inches
Step-by-step explanation:
Y + 1 = 5(x - 7)
y + 1 = 5x - 35
y = 5x - 36
A standard deck of 52 cards has 4 suits (spades, clubs, hearts, and diamonds) with 13 different cards (ace, 2, 3, 4, 5, 6, 7, 8,
Inessa [10]
Answer:
P(a pair with matching cards in different suits) = 1/52
Step-by-step explanation:
We are told that there are 4 suites and each suit has 13 different cards. This is a total of 52 cards.
Thus;
Probability of selecting one card of a particular suit = 13/52 = 1/4
If we now want to select a matching card of another suit without replacing the first one, then, we now have; 52 - 13 = 39 cards. Now, there are only 3 matching cards of the 3 remaining suits that is same as the first card drawn.
Thus; probability = 3/39 = 1/13
Thus;
P(a pair with matching cards in different suits) = 1/4 × 1/13
P(a pair with matching cards in different suits) = 1/52
