Answer:
Step-by-step explanation:
∑⁴ₙ₌₁ -144 (½)ⁿ⁻¹
This is a finite geometric series with n = 4, a₁ = -144, and r = ½.
S = a₁ (1 − rⁿ) / (1 − r)
S = -144 (1 − (½)⁴) / (1 − ½)
S = -270
If you wanted to find the infinite sum (n = ∞):
S = a₁ / (1 − r)
S = -144 / (1 − ½)
S = -288
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Answer:
d. ∠2 and ∠6
Step-by-step explanation:
Definition : Alternate Exterior Angles are a pair of angles on the outer side of each of those two parallel lines but on opposite sides of the transversal.
Option a. ∠3 and∠4
These angles are interior angles.
Option b . ∠1 and∠2
These angles are linear pair.
Option c . ∠1 and ∠6
These angles are outer angles
Option d . ∠2 and ∠6
According to the definition of alternate evterior angles . ∠2 and ∠6 are alternate exterior angles
Hence Option d is pair of alternate exterior angles.
Answer:x=4 y=3
Step-by-step explanation:
Let's solve your system by substitution.
2x−1=y+4;3y+1=3x−2
Step: Solve2x−1=y+4for y:
2x−1=y+4
2x−1+−y=y+4+−y(Add -y to both sides)
2x−y−1=4
2x−y−1+−2x=4+−2x(Add -2x to both sides)
−y−1=−2x+4
−y−1+1=−2x+4+1(Add 1 to both sides)
−y=−2x+5
−y
−1
=
−2x+5
−1
(Divide both sides by -1)
y=2x−5
Step: Substitute2x−5foryin3y+1=3x−2:
3y+1=3x−2
3(2x−5)+1=3x−2
6x−14=3x−2(Simplify both sides of the equation)
6x−14+−3x=3x−2+−3x(Add -3x to both sides)
3x−14=−2
3x−14+14=−2+14(Add 14 to both sides)
3x=12
3x
3
=
12
3
(Divide both sides by 3)
x=4
Step: Substitute4forxiny=2x−5:
y=2x−5
y=(2)(4)−5
y=3(Simplify both sides of the equation)
Answer:
P = 1 / 6
Step-by-step explanation:
Given:-
- A deck has 500 cards
- Numbered from 1-500
Find:-
you are asked to pick three cards, one at a time, what's the probability of each subsequent card being larger than the previous drawn card
Solution:-
- Suppose we draw three cards. We don't care what they actually are, irrespective of number.
- Let the three numbers be a, b, c: Such that:
a < b < c.
- The total possible combinations with 3 numbered cards will be:
a b c
b a c
a c b
b a c
b c a
c a b
- We have 6 possibilities for 3 numbered cards. So the probability of of each subsequent card being larger than the previous drawn card would be:
P = 1 / possible combinations
P = 1 / 6
Answer:
6
Step-by-step explanation:
what you have to do to find that out is add them all togeather the divide that whole by the amount of numbers you were adding so in this case it would be 3 so you would add 8,7, and 3 to get 18 then divide that by 3 to get 6.
hope this helps
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