Answer:
133/143
Step-by-step explanation:
Let S be the sample space
Let E be the event of selecting three committee partners with at least one junior partner.
Partners in the law firm include:
Senior partners = 6
Junior partners = 7
Total partners = 13
n(S) = number of ways of selecting 3 partners from 13 = 13C3
n(S) = 13C3 = 13!/(10!3!) = (13x12x11)/(3x2x1) = 286
To get n(E) i.e least 1 junior partner in the selected committee, we may have:
(2 senior and 1 junior) or ( 1 senior and 2 junior) or (3 junior).
Therefore, the required number of way is given below:
= (6C2 x 7C1) + (6C1 x 7C2) + 7C3
= [(6x5)/2 x 7] + [6 x (7x6)/2] + [(7x6x5)/(3x2)]
= 105 + 126 + 35
n(E) = 266
Therefore, the probability P(E) that at least one of the junior partners is on the committee is given below:
P(E) = n(E) /n(S)
P(E) = 266/286
P(E) = 133/143
Answer:
461 adults and 864 students
Step-by-step explanation:
We can set-up a system of equations to find the number of adults. We know students and adults attended. We will let s be the number of students and a be the number of adults. Since 1,325 tickets were purchased, then s+a=1325.
We also know that a total of $3,169 was collected and adult tickets cost $5 each and students cost $1 each. We can write 1s+5a=3169.
We will solve by substituting one equation into the other. We first solve the first equation for s which is s=1325-a. Substitute s=1325-a into 1s+5a=3169. Simplify and isolate the variable a.
1(1325-a)+5a=3169
1325-a+5a=3169
1325+4a=3169
1325-1325+4a=3169-1325
4a=1844
a=461
This means that 461 adults attended and 864 students attended since 864+461=1325.
Answer:
consecutive = x+x+2
x+x+2 = 4x-20
2x+2=4x-20
2=2x-20
22=2x
x=11
Numbers are 11,13.
Hope this helps plz hit the crown :D
Answer:
<u>The smaller angle measures 44° and the larger measures 136°</u>
Step-by-step explanation:
Let'e recall that supplementary angles are two angles whose sum is 180° degrees.
Smaller angle = x
Larger angle = 3x + 4
Therefore, we have:
x + 3x + 4 = 180
4x = 180 - 4
4x = 176
x = 176/4
x = 44 ⇒ 3x + 4 = 136
<u>The smaller angle measures 44° and the larger measures 136°</u>
Answer:
$15
Step-by-step explanation:
Given that :
Aunt's distance = 120 miles
Miles per gallon of Olivia's car = 24 miles per gallon
Cost of gasoline = 3 per gallon
Cost of gasoline for the trip :
(Aunt's distance / miles per gallon) * cost of gasoline per gallon
(120 miles / 24 miles per gallon) * 3
5 * 3 = $15
Cost of gasoline for the trip = $15
