Answer: a = 40, b = 50, c = 115
Solution:
a = 40 (the vertical angles are equal)
b = 180 - 40 - a = 50 (the sum of interior angles of triangle is 180)
c = 180 - 65 = 115 (the linear theorem)
The probability that it rains at most 2 days is 0.00005995233 and the variance is 0.516
<h3>The probability that it rains at most 2 days</h3>
The given parameters are:
- Number of days, n = 7
- Probability that it rains, p = 95%
- Number of days it rains, x = 2 (at most)
The probability that it rains at most 2 days is represented as:
P(x ≤ 2) = P(0) + P(1) + P(2)
Each probability is calculated as:

So, we have:



So, we have:
P(x ≤ 2) =0.00000002097 + 0.00000168821 + 0.00005824315
P(x ≤ 2) = 0.00005995233
Hence, the probability that it rains at most 2 days is 0.00005995233
<h3>The mean</h3>
This is calculated as:
Mean = np
So, we have:
Mean = 7 * 92%
Evaluate
Mean = 6.44
Hence, the mean is 6.44
<h3>The standard deviation</h3>
This is calculated as:
σ = √np(1 - p)
So, we have:
σ = √7 * 92%(1 - 92%)
Evaluate
σ = 0.718
Hence, the standard deviation is 0.718
<h3>The variance</h3>
We have:
σ = 0.718
Square both sides
σ² = 0.718²
Evaluate
σ² = 0.516
This represents the variance
Hence, the variance is 0.516
Read more about normal distribution at:
brainly.com/question/4079902
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Standard form for equations is ax + by = c. So all we have to do is transfer this equation into standard form. But, in standard form, there can also be no denominators, so our first step is to multiply each side of the equation by 5 to get rid of all denominators. The equation becomes 5y = 3x + 20. Now we need to get 20 on one side, which we can do by subtracting 3x from each side. The equation becomes -3x + 5y = 20, giving us our final answer of -3x + 5y = 20.
Answer:
Amount borrowed from friend = 4000
From Bank = 8000
From insurance = 3200
Step-by-step explanation:
Given that:
Amount borrowed = $15200
Let amount borrowed from friend = x
x at 5% = 0.05x
From Bank = 2x at 8% = 0.08*2x = 0.16x
From insurance = 15200 - (x + 2x) at 4%
From insurance = 15200 - 3x at 4% ; (15200 - 3x)* 0.04 = 608 - 0.12x
Interest paid in first year = $968
Simple interest = principal * rate * time
968 =
968 = (0.05x + 0.16x + 608 - 0.12x)
968 - 608 = 0.05x + 0.16x - 0.12x
360 = 0.09x
x = 360 / 0.09
x = 4000
Hence,
Amount borrowed from friend = 4000
From Bank = 2x = 4000 * 2 = 8000
From insurance = 15200 - (4000 + 8000) = 3200