Answer:
Step-by-step explanation:
At the point where two line cut across, the vertically opposite angles formed are equal. This means that
2x degrees = 78 degrees
Dividing the left hand side and the right hand side of the equation by 2, it becomes
2x/2 = 78/2
x = 39
Checking,
The sum of the angles on a straight line is 180 degrees.
180 - 78 = 102 degrees
2x + 102 = 180
2x = 180 - 102 = 78
x = 78/2 = 39
Answer:

Step-by-step explanation:
Given that:

for 
That means, angle
is in the 3rd quadrant.
To find:
Value of cot(t)
Solution:
First of all, let us recall what trigonometric ratios are positive and what trigonometric ratios are negative in 3rd quadrant.
In 3rd quadrant, tangent and cotangent are positive.
All other trigonometric ratios are negative.
Let us have a look at the following identity:

here, 
So, 

But, angle
is in 3rd quadrant, so value of

Answer:
95% Confidence interval: (0.361,0.539)
Step-by-step explanation:
We are given the following in the question:
Sample size, n = 120
Number of farmers who reusable cloth bags, x = 54
95% Confidence interval:
Putting the values, we get:
is the required 95% confidence interval for the proportion of adults who have purchased reusable cloth bags.
Answer:
measure of two unknown angles are 35.7° and 75.4°
measure of one unknown side is 16.6 inches
Step-by-step explanation:
i used law of sines to find the angle opposite 10 inch side
sin 68.9/16 = sinФ/10
Ф = 35.7°
then is added 35.7 and 68.9 and subtracted the sum from 180° to get the measure of the third angle, 75.4°
i used law of sines again to find the measure of the third side
sin 68.9/16 = sin 75.4/x
x = 16.59