Answer:
-1.99, 1.99
Step-by-step explanation:
Use a table to find the z-scores.
For the first z-score:
P(x < z) = 0.0233
z = -1.99
For the second z-score:
P(x > z) = 0.0233
P(x < z) = 1 − 0.0233 = 0.9767
z = 1.99
Picture a right triangle whose hypotenuse is of unknown length. Let's call that length L. The triangle side opposite the 70 degree angle is then 20 feet. I'd suggest you actually draw this triangle.
Then, using the definition of the sine function,
sin 70 deg = opp / hyp = (20 ft) / L. Transforming this equation, L sin 70 deg = 20 ft. Solving for L:
L = (20 ft) / (sin 70 deg) = 21.28 ft
The ladder length must be 21.28 ft.
<h3>
Answer: 163,185</h3>
This is one single number. The number is slightly larger than 163 thousand.
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Explanation:
Consider four slots labeled A,B,C,D
We have....
- 46 choices for slot A
- 45 choices for slot B
- 44 choices for slot C
- 43 choices for slot D
There's a countdown going on (46,45,44,43) when filling up the slots. This countdown is because we cannot reselect any specific person for multiple slots at the same time.
If order mattered, then we'd have 46*45*44*43 = 3,916,440 permutations possible.
However, order doesn't matter. For any group of 4 people, there are 4! = 4*3*2*1 = 24 ways to arrange them. So we must divide the previous result over 24 to get (3,916,440)/24 = 163,185
This means there are 163,185 different combinations and this is the number of possible samples of size 4 from a population of 46 people. The order of any sample doesn't matter.
