Answer:
Answer is 0.696
Step-by-step explanation:
The sum number of sets possible for no two students to have the same birthday in a class of 30 is:
=30 * (30-1)/2
= 435.
Now, there are 365 days in a year. Therefore, the probability of students having a birthday on a different date would be 364/365. Now there are a number of combination, to be exact 870 combinations.
So, the probability that no two students having the same birthday is:
(364/365)^435 = 0.303.
Now, the probability that two students would have their birthdays on the same equal date would be:
1-0.303 = 0.696 or 70%
Answer:
f is increasing on interval (-infty, 13/4)
Inequality notation: x<13/4
In words: f is increasing on the interval of x that is less than 13/4.
Step-by-step explanation:
f is increasing on interval of x if f' of such interval is positive.
f=-2x^2+13x-8
Differentiate both sides
(f)'=(-2x^2+13x-8)'
Sum and difference rule:
f'=(-2x^2)'+(13x)'-(8)'
Constant multiple rule:
f'=-2(x^2)'+13(x)'-(8)'
Power rule (recall x=x^1):
f'=-2(2x^1)+13(1x^0)-(8)'
Constant rule:
f'=-2(2x^1)+13(1x^0)-(0)
Recall again x^1=x:
f'=-2(2x)+13(1x^0)-(0)
Recall x^0=1:
f'=-2(2x)+13(1×1)-(0)
Associative property of multiplication:
f'=-(2×2)x+13(1×1)-(0)
Performed grouped multiplication:
f'=-(4)x+13(1)-(0)
f'=-4x+13-(0)
Additive identity:
f'=-4x+13
f' is positive when -4x+13>0.
Subtract 13 on both sides:
-4x>-13
Divide both sides by -4:
x<-13/-4
x<13/4
f is increasing on interval (-infty, 13/4)
Answer:
D) x=-3, y=-7
Step-by-step explanation:
9x - 7y = 22
x + 3y= -24
9x - 7y = 22
x= -24-3y
9(-24-3y)-7y=22
x= -24-3y
-216-27y-7y=22
x= -24-3y
-34y=22+216
x= -24-3y
-34y=238
x= -24-3y
y=238/(-34)
x=-24-3y
y=-7
x=-24-3*(-7)
y=-7
x=-24+21
y=-7
x=-3
(x,y)=(-3,-7)
Answer:on which interval is the function increasing
Answer:(4, infinity
Step-by-step explanation:
