Answer:
x = 32, y = 51
Step-by-step explanation:
Since the triangles are congruent then corresponding sides and angles are congruent, that is
∠ U = ∠ N
∠ N = 180° - (142 + 24)° = 180° - 166° = 14° , then
2x - 50 = 14 ( add 50 to both sides )
2x = 64 ( divide both sides by 2 )
x = 32
and
NP = US
2x - y = 13
2(32) - y = 13
64 - y = 13 ( subtract 64 from both sides )
- y = - 51 ( multiply both sides by - 1 )
y = 51
Answer: the amount by which her lunch account would have been impacted is $45
Step-by-step explanation:
Each day Valerie charges her lunch account for her lunch. If the cost of lunch is $3 then, it means that Valerie charges the lunch account with $3 daily. It means that in x days, she would have charged her lunch account with 3×x = $3x
If she charged her account for a period of 15 days, it means that x = 15. Therefore, the amount by which her lunch account would have been impacted is 3×15 = $45
We're going to be using combination since this question is asking how many different combinations of 10 people can be selected from a set of 23.
We would only use permutation if the order of the people in the committee mattered, which it seems it doesn't.
Formula for combination:

Where
represents the number of objects/people in the set and
represents the number of objects/people being chosen from the set
There are 23 people in the set and 10 people being chosen from the set


Usually I would prefer solving such fractions by hand instead of a calculator, but factorials can result in large numbers and there is too much multiplication. Using a calculator, we get

Thus, there are 1,144,066 different 10 person committees that can be selected from a pool of 23 people. Let me know if you need any clarifications, thanks!
~ Padoru
Answer:
By using the rule that the interior angles of any triangle equal 180 we see that:
m<ABC+m<CAB+m<ACB=180°
Therefore,
(2x+15)+(x+10)+(3x+5) = 180°
Now we have an equation and can solve for x:
Combine like terms:
(2x+15)+(x+10)+(3x+5) = 180°
6x+30=180°
6x+30-30=180-30
6x=150
x=25
To check our work just plug in 25 for x in each equation and the sum of those answers should add up to 180:
2x+15
2(25)+15
65
x+10
25+10
35
3x+5
3(25)+5
75+5
80
65+35+80=180
x=25 is valid
Step-by-step explanation:
Answer:
The probability is 
Step-by-step explanation:
From the question we are told that
The capacity of an Airliner is k = 300 passengers
The sample size n = 320 passengers
The probability the a randomly selected passenger shows up on to the airport

Generally the mean is mathematically represented as
=>
=>
Generally the standard deviation is

=> 
=> 
Applying Normal approximation of binomial distribution
Generally the probability that there will not be enough seats to accommodate all passengers is mathematically represented as

Here 
=>
Now applying continuity correction we have
=> ![P(X >300 ) = P(Z > \frac{[300.5] - 307.2}{3.50} )](https://tex.z-dn.net/?f=P%28X%20%20%3E300%20%29%20%3D%20%20P%28Z%20%3E%20%20%5Cfrac%7B%5B300.5%5D%20-%20307.2%7D%7B3.50%7D%20%29)
=> 
From the z-table

So
