C = 2πr Divide both sides by 2r
= π Switch the sides to make it easier to read
π = <span>
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Answer: D)3.5h+4
Step-by-step explanation:
Let h denotes the number of hours that the ice skates are rented.
Since, The cost of renting ice skates is $4 plus $3.50 for each hour that the ice skates are rented.
So , the total cost for ice-skating = $4 + $3.50 x (number of hours that the ice skates are rented.)
= 4+3.50 x ( h) [as expression]
Hence, the expression can be used to find the cost in dollars of renting ice skates for h hours :-
5 children so you have 2^5=32 possibilities to "assign" genders
P(3 girls):
how many possibilities are there to "assign" the 3 girl-genders to the 5 children? the first girl has 5 possibilities then the next 4, 3 -> 5*4*3=60
but these possibilities include orders of assigned genders, while children 1-5 might differ the gender "girl" is always the same so we have the remove the orderings of the 3 girl-gender assignments which is 3*2*1=6
if we divide 60/6 we get 10 possibilities to have 3 girls, so what is the resulting chance? the 10 possibilities divided by the total 32 possibilities: 10/32=5/16=P(3 girls)=P(2 boys)
this is a bit of lengthy way of saying "use the binomial coefficient" equation/explaining it a bit which is (n!)/(k!(n-k)!) with n=5, k=3:
5*4*3*2*1/((3*2*1)*(2*1))=
5*4*3*2/(3*2*2)=
5*4*3*2/(3*4)=
5*2=
10 possibilities again
P(girls>=4)=P(boys<=1)=P(boys=1)+P(boys=0)
(or P(girls=4)+P(girls=5))
P(boys=0) is the easy case: simply multiply the chance of getting a girl 5 times: (1/2)^5=1/32
P(boys=1)= again the binomial coefficient with n=5 and k=1:
5*4*3*2*1/((1)*(4*3*2*1))=
5*4*3*2/(4*3*2)=
5 possibilities
so the P(boys=0)=1 possibility + P(boys=1)=5 possibilities totals to 6 possibilities
again the chance is the 6 possibilities divided by all 32 possibilities: 6/32=3/16
P(alternate gender starting with boy): when thinking about the possibilities then there is only a single way to build that order: bgbgb, so one possibility
knowing there is only one way we already know P(alternate...)=1/32 by again dividing by the total amount of possibilities
the alternative way would be to multiply P(boy)*P(girl)*P(boy)*P(girl)*P(boy)=(1/2)^5= 1/32 again
Answer:
The first mechanic $90/hour and the second charged $70/hour
Step-by-step explanation:
Lets start off by letting x be the first mechanics rate and y being the second mechanics rate. We know that the first mechanic worked 5 hours and that the second mechanic worked 10 hours and together they charged 1150. An equation to express this would be:
5x+10y = 1150
We also know that together they charged 160/per hour. An equation to express this would be:
x+y = 160
Now we can solve the second equation for x or the first mechanics rate.
x+y = 160
x = 160 - y
Now that we have an expression for x we can plug that back into the first equation and solve for y or how much the second mechanic charged.
5x+10y=1150 plug in x =160-y
5(160-y)+10y=1150 Distribute
800 -5y+10y = 1150 Combine like terms
800 +5y = 1150 Subtract 800 from both sides
5y = 350 divide by 5
y = 70
So we know that the second mechanic charged $70/hour. We also know that(from our work before) that the first mechanic charges $160 - the rate the second mechanic charged. We know that's $70/hour so we can plug in and solve for the first rate.
x = 160-y
x = 160-70
x = 90
So we know that the first mechanic charged $90/hour and the second mechanic charged $70/hour.
