Answer:
These are similar. The scale factor is 1.5 going from ABC to DEF.
Step-by-step explanation:
What I did was divide the side lengths of DEF by the corresponding side on ABC.
12/8 = 1.5
9/6 = 1.5
15/10 = 1.5
Since the scale factor is the same on all three sides, these two figures are similar.
ANSWER
1.2 hours
EXPLANATION
Let x represent the number of hours it takes to complete the paint job.
The fraction of a job done per hour with both of them working is 1/x.
Lyle does 1/3 of the painting in one hour
(For example, if it took 3 hours to paint the room, then in one hour, only 1/3 of the room will be painted. In two hours, 1/3 + 1/3 = 2/3 of the room will be painted. In three hours, 1/3+1/3+1/3=3/3=1 of the room will be painted---completed)
Selena does 1/2 of the painting in one hour.
Therefore, for one hour, the fraction of the Job that Lyle does added with the fraction of the Job that Selena does is equal to 1/x, which is the fraction of the job done with both of them working
1/3 + 1/2 = 1/x
Multiply both sides of the equation by x
x/3 + x/2 = 1
Factor out x from the left side
x(1/3 + 1/2) = 1
Combine fractions. Get a common denominator for 1/3 and 1/2.
LCD of 1/3 and 1/2 is 6. 1/3 is equivalent to 2/6 and 1/2 is equivalent to 3/6.
x(2/6 + 3/6) = 1
x (5/6) = 1
x = 1 * 6/5
x = 6/5
x = 1.2 hours
ALTERNATIVE EXPLANTION:
job = rate · time ⇔ rate = job/time ⇔ time = job/rate
Lyle can do 1 paintjob of the room in 3 hours. Therefore, Lyle's rate is 1/3 paintjob per hour.
Selena can do 1 paintjob of the room in 2 hours. Therefore, Selena's rate is 1/2 paintjob per hour.
Their rate when working together is combined:
rate = 1/3 + 1/2 = 2/6 + 3/6 = 5/6
Since time = job/rate and we are interested in 1 paintjob, then job = 1 and
time = 1 / (5/6) = 6/5 = 1.2 hours
Answer:
a) 32
b) 67.613
Step-by-step explanation:
<em><u> In Game 3, Emerson struck out 42 times in 140 times at-bat.</u></em>
<em><u>Part A</u></em>
<em><u>Drag numbers to complete the proportion to represent the percent of strikeouts per at-bats.</u></em>
<em><u>Numbers may be used once or not at all.</u></em>
<em><u /></em>
<em><u>Part B</u></em>
<em><u>What percentage of times at bat did Emerson actually hit the ball?</u></em>
Part A
Total number of strikeouts= 30+40+42= 112
Total number of at bats = 90+120+140= 350
strikeouts : times
112: 350
p:100
Using cross product rule
p/100= 112/350
p * 350= 112*100
or p= 11200/350= 32
It means that there were 32 strikeouts if 100 times were bat at hits.
Part B:
Total number of strikeouts= 30+40+42= 112
Total number of at bats = 90+120+140= 350
But we need the percentage of times at bat hit
Therefore
Hits= times - strikeouts= 350-112= 238
Percentage = 238/352*100= 67.613
Check
The above answers are correct because
100-32 = 68
68 ≅ 67.613
Put this into a scientific calculator
1/3 x pi x 18 squared x 16
First of all, don't let "b" confuse you. Know that b = 5/6k = -10, so all you really have to solve for this problem is 
.
Before anything else, you have to isolate k. Do this my multiplying both sides by the reciprocal of 5/6.
The 6/5 and 5/6 cancel each other out, so we are left with 
--> 
---> 
So k = -12.
Hope this helped. Good luck.
