Answer:
Option D.
Step-by-step explanation:
- First, the you need ti understand that the triangle is an isosceles right angled triangle. In other words, the base and height are equal in length. The third side is the slide. This is the longest side.
- Next, we know that the formula for calculating the area of a right angled triangle is given by:
A = 1/2 (base × perpendicular height)
- The perpendicular height is equal to the base. Let's say the base is <em>x</em>. It means that the height is also x, since height = base.
- Therefore, the formula will be:
A = 1/2 (x.x)
=1/2 (x²)
32 = 1/2 (x²)
Multiplying both sides by 2 gives:
32×2 = x²
64 = x²
8 = x
To find the third side, we use the Pythagoras theorem:
C² = A² + B²
= 8² + 8²
= 128
C = √128
= 8√2
However, the answer will not be exact, so we multiply the length of the base and height by 2. This gives x = 16 (Length of base = length of height)
Repeating the steps above gives C = √ (16)² + (16)²
= √256
This corresponds to option D.
Answer: 0.03855
Step-by-step explanation:
Given :A population of skiers has a distribution of weights with mean 190 pounds and standard deviation 40 pounds.
Its maximum safe load is 10000 pounds.
Let X denotes the weight of 50 people.
As per given ,
Population mean weight of 50 people = 
Standard deviation of 50 people 
Then , the probability its maximum safe load will be exceeded =
![P(X>10000)=P(\dfrac{X-\mu}{\sigma}>\dfrac{10000-9500}{282.84})\\\\=P(z>1.7671-8)\\\\=1-P(z\leq1.7678)\ \ \ \ [\because\ P(Z>z)=P(Z\leq z)]\\\\=1-0.96145\ \ \ [\text{ By p-value of table}]\\\\=0.03855](https://tex.z-dn.net/?f=P%28X%3E10000%29%3DP%28%5Cdfrac%7BX-%5Cmu%7D%7B%5Csigma%7D%3E%5Cdfrac%7B10000-9500%7D%7B282.84%7D%29%5C%5C%5C%5C%3DP%28z%3E1.7671-8%29%5C%5C%5C%5C%3D1-P%28z%5Cleq1.7678%29%5C%20%5C%20%5C%20%5C%20%5B%5Cbecause%5C%20P%28Z%3Ez%29%3DP%28Z%5Cleq%20z%29%5D%5C%5C%5C%5C%3D1-0.96145%5C%20%5C%20%5C%20%5B%5Ctext%7B%20By%20p-value%20of%20table%7D%5D%5C%5C%5C%5C%3D0.03855)
Thus , the probability its maximum safe load will be exceeded = 0.03855
Answer:
8
Step-by-step explanation:
1. 3b - 2 (1 - b) / a - 2
2. 3(2) - 2 (1 - 2) / 3 - 2
3. 6 - 2 (-1) / 1
4. 6 + 2 / 1
5. 8 / 1
6. 8
