The answer for the first blank would be 1/2 because it had been dilated down to half it's original size. I hope this helps!
Answer:
-4 sqrt(7)/7
Step-by-step explanation:
csc theta = -4/3
csc theta = hypotenuse / opposite side
hypotenuse = 4
opposite = 3
Using the pythagorean theorem
a^2 + b^2 = c^2
3^2 + b^2 = 4^2
9+b^2 = 16
b^2 = 16-9
b^2 = 7
Taking the square root
sqrt(b^2) = sqrt(7)
b = sqrt(7)
We are in the third quadrant so only tan and cot are positive
that means the x and y values are "negative" so a = -3 and b = - sqrt(7)
sec theta = hypotenuse / adjacent
= 4/ - sqrt(7)
rationalizing
-4 sqrt(7)/ sqrt(7)* sqrt(7)
= -4 sqrt(7)/7
The required probability is
a) both are cups is 0.05
b) At least one cup is 0.19
c) One is a cup and the other is a sword is 0.06
<h3 /><h3>What is probability?</h3>
Probability can be defined as the ratio of favorable outcomes to the total number of events.
a) for both are cups
P= 12*11/48*47
p = 0.05
b) for At least one cup
p = 12*36/48*47
p = 0.19
c) for One is a cup and the other is a sword
p = 12*12/48*47
p = 0.06
Thus, the required probability is 0.05, 0.19, 0.06
Learn more about probability here:
brainly.com/question/14290572
<h3>#SPJ1</h3><h3 />
2/3x -14/3 = -2 -foiled
2/3x = -6/3 +14/3 -common denominator
2/3x = 8/3
x = 8/3 * 3/2
x = 24/6
x= 4
