Answer:
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Step-by-step explanation:
Answer:
<u>y = w and ΔABC ~ ΔCDE</u>
Step-by-step explanation:
Given sin(y°) = cos(x°)
So, ∠y + ∠x = 90° ⇒(1)
And as shown at the graph:
ΔABC is aright triangle at B
So, ∠y + ∠z = 90° ⇒(2)
From (1) and (2)
<u>∴ ∠x = ∠z </u>
ΔCDE is aright triangle at D
So, ∠x + ∠w = 90° ⇒(3)
From (1) and (3)
<u>∴ ∠y = ∠w</u>
So, for the triangles ΔABC and ΔCDE
- ∠A = ∠C ⇒ proved by ∠y = ∠w
- ∠B = ∠D ⇒ Given ∠B and ∠D are right angles.
- ∠C = ∠E ⇒ proved by ∠x = ∠z
So, from the previous ΔABC ~ ΔCDE by AAA postulate.
So, the answer is <u>y = w and ΔABC ~ ΔCDE</u>
Answer:
Approximately 3 grams left.
Step-by-step explanation:
We will utilize the standard form of an exponential function, given by:
In the case of half-life, our rate <em>r</em> will be 1/2. This is because 1/2 or 50% will be left after <em>t </em>half-lives.
Our initial amount <em>a </em>is 185 grams.
So, by substitution, we have:
Where <em>f(t)</em> denotes the amount of grams left after <em>t</em> half-lives.
We want to find the amount left after 6 half-lives. Therefore, <em>t </em>= 6. Then using our function, we acquire:
Evaluate:
So, after six half-lives, there will be approximately 3 grams left.
Answer:
0.0025 = 0.25%
Step-by-step explanation:
First we need to find how many people don't have flue shots.
28% of 50 is equal to 0.28 * 50 = 14 people.
If 14 people have flue shots, we have 50 - 14 = 36 people that don't have flue shots.
Now, to solve this problem, the probability will be the cases where we have a group of people that don't have flue shots (that is, a combination of 36 choose 15) over the total cases (combination of 50 choose 15):
C(36,15) / C(50,15) = (36!/15!*21!) / (50!/15!*35!) = 0.0025 = 0.25%
