Two six-sided dice are rolled (one red and one green). Some possibilities are (Red=1,Green=5) or (Red=2,Green=2) etc.

1 answer:

6 0

A.) There are going to be 72 total possibilities.
Because if you have 6 times 6 is 36 times 2 is 72.
B.) The probability that the sum on the dice come out to be 11 is 2:72
Because you can only have (6,5) and (5,6)
C.) The probability that the sum on the two dice comes out to be 7 is 6:72
Because you have (6,1) (1,6) (5,2) (2,5) (4,3) (3,4)
D.) The probability that the numbers on the two dice are equal is 6:72
Because you have (6,6) (5,5) (4,4) (3,3) (2,2,) (1,1)

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If sin theta= - 5/7, which of the following are possible?

Sphinxa [80]

Answer:

$\large\boxed{\sec\theta=\dfrac{7}{\sqrt{24}},\ and\ \tan\theta=-\dfrac{5}{\sqrt{24}}}\\\boxed{\cos\theta=\dfrac{\sqrt{24}}{7},\ and\ \tan\theta=\dfrac{5}{\sqrt{24}}}$

Step-by-step explanation:

$\text{Use:}\\\\\sin^2\theta+\cos^2\theta=1\to\cos\theta=\pm\sqrt{1-\sin^2\theta}\\\\\tan\theta=\dfrac{\sin\theta}{\cos\theta}\\\\\sec\theta=\dfrac{1}{\cos\theta}\\\\==========================\\\\\sin\theta=-\dfrac{5}{7}\\\\\cos\theta=\pm\sqrt{1-\left(-\frac{5}{7}\right)^2}=\pm\sqrt{1-\frac{25}{49}}=\pm\sqrt{\frac{24}{49}}=\pm\dfrac{\sqrt{24}}{\sqrt{49}}=\pm\dfrac{\sqrt{24}}{7}\\\\\sec\theta=\pm\dfrac{1}{\frac{\sqrt{24}}{7}}=\pm\dfrac{7}{\sqrt{24}}$

$\tan\theta=\pm\dfrac{-\frac{5}{7}}{\frac{\sqrt{24}}{7}}=\mp\dfrac{5}{7\!\!\!\!\diagup_1}\cdot\dfrac{7\!\!\!\!\diagup^1}{\sqrt{24}}=\mp\dfrac{5}{\sqrt{24}}$