I'm not sure if an equation is needed. Since you put the marble back into the bag the odds are still 50/50 that you will draw either color.
If you would have left it out then it would be dependent because the ratio would change.
Answer:
∠ 1 = 123°
Step-by-step explanation:
One way
The external angle of a triangle is equal to the sum of the 2 opposite interior angles.
∠ 1 is an external angle of the triangle, thus
∠ 1 = 90° + 33° = 123°
Second way
The sum of the 3 angles in a triangle = 180°
Subtract the sum of the 2 given angles from 180 for third angle in Δ
third angle = 180° - (90 + 33)° = 180° - 123° = 57°
The third angle and ∠ 1 form a straight angle and are supplementary, thus
∠ 1 = 180° - 57° = 123°
Answer:
The t value for 99% CI for 21 df is 2.831.
The critical value that should be used in constructing the confidence interval is (64.593, 86.407).
Step-by-step explanation:
Now the sample size is less than 30 and also population standard deviation is not known.
Then we will use t distribution to find CI
t value for 99% CI for 21 df is TINV(0.01,21)=2.831
The margin of error is 
Hence CI is
Idk,
Tips with decimals....
Our decimal system gives us the flexibility to write numbers as large or
small as we like. The key to the decimal system is the decimal point. Anything
on the left of the decimal point represents a whole number, anything on the
right of the decimal represents less than one (similar to a fraction). Going
from left to right, the value of each place on the right of the decimal point is
1/10 the value of the place on the left. Good luck!
Answer:
<em>Proof below</em>
Step-by-step explanation:
<u>Right Triangles</u>
In any right triangle, i.e., where one of its internal angles is 90°, some interesting relations stand. One of the most-used is Pythagora's Theorem.
In a right triangle with shorter sides a and b, and longest side c, called the hypotenuse, the following equation is satisfied:

The image provided in the question shows a line passing through points A(0,4) and B(3,0) that forms a right triangle with both axes.
The origin is marked as C(0,0) and the point M is the midpoint of the segment AB. We have to prove.

First, find the coordinates of the midpoint M(xm,ym):


Thus, the midpoint is M( 1.5 , 2 )
Calculate the distance CM:


CM=2.5
Now find the distance AB:

AB=5
AB/2=2.5
It's proven CM is half of AB