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murzikaleks [220]
4 years ago
9

On the last day of a Shakespeare class, an English teacher asked her students which play they liked most. Out of the 18 students

who have submitted responses so far, 6 liked Much Ado About Nothing best. What is the experimental probability that the next student to respond likes Much Ado About Nothing best?
Write your answer as a fraction or whole number.
Mathematics
1 answer:
Vika [28.1K]4 years ago
7 0

Answer:

1/3

Step-by-step explanation:

There were 18 students and six liked Much Ado About Nothing. So, you could write this as 6/18 which simplifies to 1/3.

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likoan [24]

It's easy to show that 7\tan(4x) is strictly increasing on x\in\left[0,\frac\pi8\right]. This means

M = \max \left\{7\tan(4x) \mid \dfrac\pi{16} \le x \le \dfrac\pi{12}\right\} = 7\tan(4x) \bigg|_{x=\pi/12} = 7\sqrt3

and

m = \min \left\{7\tan(4x) \mid \dfrac\pi{16} \le x \le \dfrac\pi{12}\right\} = 7\tan(4x) \bigg|_{x=\pi/16} = 7

Then the integral is bounded by

\displaystyle 7\left(\frac\pi{12} - \frac\pi{16}\right) \le \int_{\pi/16}^{\pi/12} 7\tan(4x) \, dx \le 7\sqrt3 \left(\frac\pi{12} - \frac\pi{16}\right)

\implies \displaystyle \boxed{\frac{7\pi}{48}} \le \int_{\pi/16}^{\pi/12} 7\tan(4x) \, dx \le \boxed{\frac{7\sqrt3\,\pi}{48}}

7 0
2 years ago
Randy wants to join a gym to lose his winter weight. Gym A has a membership fee of $39 and charges $30 per month. Gym B has a me
siniylev [52]

Answer:

5 months

Step-by-step explanation:

Value m= months

Gym A Money needed to pay= 30m+ 39

Gym B Money needed to pay= 20m+ 89

30m+ 39= 20m+ 89

Now isolate m

(30m-20m) + (39-39)= (20m-20m) + (89-39)

10m = 50

10m/10= 50/10

m=5; You can plug this number in to check my answer.

8 0
3 years ago
You charge $2 per evening plus $5 per hour to babysit and you only charge for whole hours. You have a goal to earn at least $121
KATRIN_1 [288]

Answer:

8 hours

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
Hucks bowling average over 5 games was 100. He scored 118 on the next game. What was his new average?
NikAS [45]
average=\frac{\ sum\ of\ numbers}{amount\ of\ numbers}\\\\
x-\ sum\ of\ point\ during\ 5\ games\\100=\frac{x}{5}\ \ |*5\\
500=x\\
new\ average=\frac{500+118}{6}=\frac{618}{6}=103\\\\
\textbf{His\ new\ average\ is\ 103.}
7 0
3 years ago
Read 2 more answers
Joe has read 20% of a book. He has 16 more pages to finish. How many pages are there in the book?
andrey2020 [161]

Answer:

20

Step-by-step explanation:

16 is 80% of 20

8 0
3 years ago
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