(7)
if r perpendicular to s then angles 1,2,3,4=90 deg.
if t perpendicular to s then angles 5,6,7,8=90 deg.
If two different lines intersect a third line at the same angle then they must be parallel.
r and t intersect s at the angle 2=90 deg and 6 = 90 deg, therefore r and t are parallel.
(6) use sum of angles in a triange =180 deg property.
first, the complement to 105 is an angle of 75 deg. then x=180-(24+75)=81 deg
x=81 deg
(5)
(4) sum of angles = 180 deg
62 +45 + k = 180
k = 180 -107 = 73
k = 73
- The contribution of the friend's company is of: $60.
- The account's balance after 20 years will be of: $130,694.36.
- The total deposits after 20 years are given as follows: $28,800 by the friend and $14,400 by the company.
- The interest earned during this entire period was of: $87,494.36.
<h3>How to obtain the balance?</h3>
The balance is obtained using the future value formula, which is presented as follows:
The meaning of each parameter is explained as follows:
- P is the total month deposit.
- n is the number of coupoundings per period, that is, compoundings per year.
- t is the number of years.
The deposits will be of:
- Company: $60, as it is half of the friend.
Then the parameter P is of:
P = 120 + 60 = 180.
The remaining parameters to obtain the balance after 20 years are given as follows:
r = 0.03, n = 12, t = 20.
Then the balance after 20 years is obtained as follows:
B = $130,694.36.
The total deposits will be of:
- Friend: 120 x 20 x 12 = $28,800.
- Company: half of friend -> $14,400.
The interest accrued is the balance subtracted by the total deposits, hence:
130694.36 - (28800 + 14400) = $87,494.36.
A similar problem, also featuring the future value formula, is presented at brainly.com/question/24703884
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Answer:
Therefore, the mean and the standard deviation for the number of electrical outages (respectively) are 0.26 and 0.5765 respectively.
Step-by-step explanation:
Given the probability distribution table below:
(a)Mean
Expected Value, 
=(0*0.8)+(1*0.15)+(2*0.04)+(3*0.01)
=0+0.15+0.08+0.03
Mean=0.26
(b)Standard Deviation
Standard Deviation 
Therefore, the mean and the standard deviation for the number of electrical outages (respectively) are 0.26 and 0.5765 respectively.
