Answer:
the exact answer is 314.159265359
Step-by-step explanation:
but it simplifies to 314.16
The probabilities in each of the given categories are; A) 51.33%; B) 51.33% C) 30.33% D) 30.33%
<h3>How to find the Probability of Selection?</h3>
The number of ways to select 2 out of 25 is; 25C2 = 25! / (23! * 2!)
= 25*24/2
= 300
(A) Probability of selecting 1 male and 1 female:
[(11C1) * (14C1)]/300 = [11!/(10! * 1!)] * [(14!/(12! * 2!))
= 51.33%
(B) Probability of selecting 1 female and 1 male:
[(14C1) * (11C1)]/300 = 51.33%
(C) Probability that 2 females are selected is;
(14C2)/300 = 30.33%
D) Probability that no males are selected is;
P(no males) = (11C0 * 14C2 )/300 = 30.33%
Read more about probability of Selection at; brainly.com/question/251701
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Answer:
UT = 104
∠R = 126°
Step-by-step explanation:
Part 1: Finding UT
The symbols on the triangles indicate that the triangles have the same side lengths.
That means 2x + 84 = 14x - 36
We can find the length of UT by solving for x
2x+84=14x−36
<u>Step 1: Subtract 14x from both sides.</u>
2x + 84 − 14x = 14x − 36 − 14x
−12x + 84 = −36
<u>Step 2: Subtract 84 from both sides.</u>
−12x + 84 − 84 = −36 − 84
−12x = −120
<u>Step 3: Divide both sides by -12.</u>
-12x / -12 = -120 / -12
x = 10
Now we know x=10, we can substitute 10 for x to get UT
UT = 2x + 84
UT = 2(10) + 84
UT = 20 + 84
UT = 104
So the length of UT is 104
Part 2: Finding ∠R
Since we know angle R is equal to angle U, we know
10y - 14 = 5y + 56
We can solve for y to find R
<u>Step 1: Subtract 5y from both sides.</u>
10y − 14 − 5y = 5y + 56 − 5y
5y − 14 = 56
<u>Step 2: Add 14 to both sides.</u>
5y−14+14=56+14
5y=70
<u>Step 3: Divide both sides by 5.</u>
5y/5 = 70/5
y=14
Now that we know y=14, we can substitute that value to find ∠R
∠R = 10y - 14
∠R = 10(14) - 14
∠R = 140 - 14
∠R = 126°
9514 1404 393
Answer:
(b) (6, 0)
Step-by-step explanation:
You are given the value of x. Substitute that in the other equation and find the value of y.
-3x +14y = -18
We know x=6 from the second given equation, so ...
-3(6) +14y = -18
Add 18 to both sides
14y = 0
Divide by 14
y = 0
Then the solution is ...
(x, y) = (6, 0)
