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Grace [21]
3 years ago
14

A train arrives at a station and waits 2 min before departing. Another train arrives at the station 18 minutes later, repeating

the cycle. Identify the probability that a train will be at the station when you arrive.

Mathematics
2 answers:
svetlana [45]3 years ago
5 0

Answer:

1/10.

Step-by-step explanation:

The length of each cycle is 2 + 18 = 20 minutes.

During this time  the train in stationary for 2 minutes.

So the probability of the train being at the station when you arrive is 2/20 = 1/10.

nadya68 [22]3 years ago
4 0

|\Omega|=20\\|A|=2\\\\P(A)=\dfrac{2}{20}=\dfrac{1}{10}=10\%

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(PLEASE HELP)An elevator car in a skyscraper can hold at most 15 people. For safety reasons, each car can carry a
natali 33 [55]

Answer:

70x + 25y + 4x + 4y \leqslant 1500

where x = number of adults

y = number of children

and the extra weights of 4kg of each person.

8 0
2 years ago
A 150 cm pendulum swings through an arc which measured 100pi cm. In exact radians, through what angle does it swing?
choli [55]

Answer:

Pendulum will swing by an angle 0.666π

Step-by-step explanation:

We have given arc = 100\pi cm

And length of the pendulum l = 150 cm

Length of the pendulum will be equal to radius of the pendulum so r = 150 cm

Arc is given by arc=radius\times angle

So 100\pi =150\times\times  \Theta

\Theta =0.666\pi

So pendulum will swing by an angle 0.666π

5 0
3 years ago
A ball is thrown into the air from a height of 4 feet at time t = 0. The function that models this situation is h(t) = -16t2 + 6
katrin2010 [14]

Answer:

Part a) The height of the ball after 3 seconds is 49\ ft

Part b) The maximum height is 66 ft

Part c) The ball hit the ground for t=4 sec

Part d) The domain of the function that makes sense is the interval

[0,4]

Step-by-step explanation:

we have

h(t)=-16t^{2} +63t+4

Part a) What is the height of the ball after 3 seconds?

For t=3 sec

Substitute in the function and solve for h

h(3)=-16(3)^{2} +63(3)+4=49\ ft

Part b) What is the maximum height of the ball? Round to the nearest foot.

we know that

The maximum height of the ball is the vertex of the quadratic equation

so

Convert the function into a vertex form

h(t)=-16t^{2} +63t+4

Group terms that contain the same variable, and move the constant to the opposite side of the equation

h(t)-4=-16t^{2} +63t

Factor the leading coefficient

h(t)-4=-16(t^{2} -(63/16)t)

Complete the square. Remember to balance the equation by adding the same constants to each side

h(t)-4-16(63/32)^{2}=-16(t^{2} -(63/16)t+(63/32)^{2})

h(t)-(67,600/1,024)=-16(t^{2} -(63/16)t+(63/32)^{2})

Rewrite as perfect squares

h(t)-(67,600/1,024)=-16(t-(63/32))^{2}

h(t)=-16(t-(63/32))^{2}+(67,600/1,024)

the vertex is the point (1.97,66.02)

therefore

The maximum height is 66 ft

Part c) When will the ball hit the ground?

we know that

The ball hit the ground when h(t)=0 (the x-intercepts of the function)

so

h(t)=-16t^{2} +63t+4

For h(t)=0

0=-16t^{2} +63t+4

using a graphing tool

The solution is t=4 sec

see the attached figure

Part d) What domain makes sense for the function?

The domain of the function that makes sense is the interval

[0,4]

All real numbers greater than or equal to 0 seconds and less than or equal to 4 seconds

Remember that the time can not be a negative number

6 0
3 years ago
Which of the following is true about the expression 3 Squared times 12 squared
ololo11 [35]

Answer:

?

Step-by-step explanation:

the expression would look like this:  3^2 x 12^2

3 squared is 9 (3 x 3)

12 squared is 144 (12 x 12)

3 0
3 years ago
Which account has the lowest minimum balance requirement? Bank Account Terms and Conditions Bank A has a $500 minimum balance, b
Genrish500 [490]

Answer:

The correct option is Account D

Step-by-step explanation:

Bank requires that $500 minimum balance,this is the highest minimum balance out of all the four banks.

Bank B's minimum required balance is $250 which is the third highest minimum balance.

Bank C requires account holder to have as minimum balance $300 which is second highest minimum balance.

Bank D only requires $100 that is the minimum among all the four banks

6 0
3 years ago
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