1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
aleksandr82 [10.1K]
3 years ago
8

You always need some time to get up after the alarm has rung. You get up from 10 to 20 minutes later, with any time in that inte

rval being equally likely. a. What is the probability that you need less than 5 minutes to get up?b. What is the expected amount of minutes that you will need to get up? Interpret this in the context of the problem in a sentence or two. c. What is the probability that you will need between 8 and 13 minutes? You have 9:30am classes three times a week and 9am classes two times a week, with each class being independent from the other. d. You will be late to your 9:30am class if you need more than 14 minutes to get up. What is the probability that you will be late to each of the 9:30am classes next week? e. You will be late to your 9am class if you need more than 9 and a half minutes to get up. What is the probability that you are late to at least one 9am class next week?
Mathematics
1 answer:
Mama L [17]3 years ago
3 0

Answer:

a) P(x<5)=0.

b) E(X)=15.

c) P(8<x<13)=0.3.

d) P=0.216.

e) P=1.

Step-by-step explanation:

We have the function:

f(x)=\left \{ {{\frac{1}{10},\, \, \, 10\leq x\leq 20 } \atop {0, \, \, \, \, \, \,  otherwise }} \right.

a)  We calculate  the probability that you need less than 5 minutes to get up:

P(x

Therefore, the probability is P(x<5)=0.

b) It takes us between 10 and 20 minutes to get up. The expected value is to get up in 15 minutes.

E(X)=15.

c) We calculate  the probability that you will need between 8 and 13 minutes:

P(8\leq x\leq 13)=P(10\leqx\leq 13)\\\\P(8\leq x\leq 13)=\int_{10}^{13} f(x)\, dx\\\\P(8\leq x\leq 13)=\int_{10}^{13} \frac{1}{10} \, dx\\\\P(8\leq x\leq 13)=\frac{1}{10} \cdot [x]_{10}^{13}\\\\P(8\leq x\leq 13)=\frac{1}{10} \cdot (13-10)\\\\P(8\leq x\leq 13)=\frac{3}{10}\\\\P(8\leq x\leq 13)=0.3

Therefore, the probability is P(8<x<13)=0.3.

d)  We calculate the probability that you will be late to each of the 9:30am classes next week:

P(x>14)=\int_{14}^{20} f(x)\, dx\\\\P(x>14)=\int_{14}^{20} \frac{1}{10} \, dx\\\\P(x>14)=\frac{1}{10} [x]_{14}^{20}\\\\P(x>14)=\frac{6}{10}\\\\P(x>14)=0.6

You have 9:30am classes three times a week.  So, we get:

P=0.6^3=0.216

Therefore, the probability is P=0.216.

e)  We calculate the probability that you are late to at least one 9am class next week:

P(x>9.5)=\int_{10}^{20} f(x)\, dx\\\\P(x>9.5)=\int_{10}^{20} \frac{1}{10} \, dx\\\\P(x>9.5)=\frac{1}{10} [x]_{10}^{20}\\\\P(x>9.5)=1

Therefore, the probability is P=1.

You might be interested in
What is the answer to 15 - 5x??​
anzhelika [568]

Answer:

x=3

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
44 × 20 × 10 = 440 × 2. but is it true or false ?
Vinil7 [7]
If you would like to know if 44 * 20 * 10 equals to 440 * 2, you can check it like this:

44 * 20 * 10 = 440 * 20 = 8800
and
440 * 2 = 880

So, the correct result is False, because 8800 is not equal to 880.
6 0
2 years ago
Read 2 more answers
Find the exact value by using a half-angle identity.<br><br> tan seven pi divided by eight
murzikaleks [220]

9514 1404 393

Answer:

  1 -√2

Step-by-step explanation:

  \tan(x/2)=\dfrac{1-\cos(x)}{\sin(x)}\\\\\tan\left(\dfrac{1}{2}\cdot\dfrac{7\pi}{4}\right)=\dfrac{1-\cos\dfrac{7\pi}{4}}{\sin\dfrac{7\pi}{4}}=\dfrac{1-\dfrac{1}{\sqrt{2}}}{-\dfrac{1}{\sqrt{2}}}=\boxed{1-\sqrt{2}}

tan(7π/8) = 1 -√2

7 0
3 years ago
What is the answer to this
skad [1K]
The answer is 10 because 5 and 5 is 10
8 0
3 years ago
What is the cross section perpendicular to the base of a cylinder?
melamori03 [73]

Answer:

circle

Step-by-step explanation:

circle

4 0
3 years ago
Other questions:
  • how to change the following indicated sums to indicated products as in the preceding model: 5 • 20 + 5 • 3
    15·1 answer
  • Plz help ok so confused
    5·1 answer
  • The table shows values for functions f(x) and g(x) . x f(x)=3x g(x)=2x+1 −2 19 −3 −1 13 −1 0 1 1 1 3 3 2 9 5 What is the solutio
    5·1 answer
  • What is 5(10 + 3/8 x 16 + (3+4)? Please help I keep getting 63
    13·2 answers
  • Kenny plans to paint the mailbox below. If it costs $3.50 per quart of paint and one quart will cover 10 square feet, how many q
    5·1 answer
  • What is the function? 4th grade math
    12·2 answers
  • Represent Real-World Problems Writea real-world situation that can berepresented by 15C 17.50. Thensolve the equation and descri
    7·1 answer
  • Side lengths in screens that have a ratio of 16:9.
    14·2 answers
  • A parachutist's rate during a free fall reaches kilometers per hour. What is this rate in meters per second? At this rate, how m
    14·1 answer
  • The table shows how much Noah earns each day. About how much money did Noah earn altogether? Use the table and rounding to choos
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!