Which choice is equivalent to the product below?

It takes a train 60 seconds to completely drive through a bridge of 1260 m, and 90 seconds to completely drive through a tunnel

Olegator [25]

The length of train is 120 meters

The speed of train is 25 meter per second

Solution:

The speed is given by formula:

$speed = \frac{distance}{time}$

Given that,

It takes a train 60 seconds to completely drive through a bridge of 1260 m

And 90 seconds to completely drive through a tunnel of 2010 m

Let the length of the train be "x"

The total distance travelled by the train across the bridge is given by:

total distance = x + 1260 + x = 2x + 1260

[ here we use x + x to represent that train completely drives through bridge ]

The time taken is given as 60 seconds

Therefore, the speed is given as:

$speed = \frac{2x+ 1260}{60}$

The total distance travelled by the train through the tunnel is given by:

total distance = x + 2010 + x = 2x + 2010

The time taken is given as 90 seconds

Therefore, the speed is given as:

$speed = \frac{2x+ 2010}{90}$

The speed of the train was the same in both cases.

Equate both speeds

$\frac{2x+ 1260}{60} = \frac{2x+ 2010}{90}$

$\frac{x+630}{30} = \frac{x+1005}{45}$

$45(x+630) = 30(x+1005)\\\\45x + 28350 = 30x + 30150\\\\45x - 30x = 30150 - 28350\\\\15x = 1800\\\\x = 120$

Thus length of train is 120 meters

Find the speed of train:

$speed = \frac{2x+ 1260}{60}\\\\speed = \frac{2(120) + 1260)}{60}\\\\speed = 25$

Thus speed of train is 25 meter per second

5 0

3 years ago

Poker. 26 red, 26 black. Take one every time, you can choose to guess whether it’s red. You have only one chance. If you are rig

xenn [34]

Answer: 339/8788= 0.039

Step-by-step explanation:

Let black card be represented with B and the red card be represented with r. Therefore, P(B,r) is the expected value.

Hence, we say, (b,r) is not equal to (0,0) for the first state, we then, have a probability of B/r+B(the probability of drawing out a black card and loosing a point.

Also, (B-1,r) state with the probability of r/r+B(which is the probability of drawing out a red card and gaining a point).

The expected value is therefore;

B/r+B(-1+(B-1,r) + r/r+B(1+P(B,r-1))

Therefore, if we have negative, then;

P(B,r)=0,B/r+B(-1,r)) + r/r+B(1+P(B,r-1))...

P(0,0)=0; P(26,26) = 339/8788

=.039

Note: we say that the expectation at the start if we draw red,gaining +1 and if we draw black and then draw two reds you end +1. That is; 1/26 × 2/26 × 1/26 = 1+ 338/8788

= 339/8788.

5 0

3 years ago

Solution for x+4 is equal to 10

Mars2501 [29]

The answer is x=6. This is because 6+4 equals 10

8 0

3 years ago

Read 2 more answers

A person earns 23,000 one year and gets a 5% raise in salary. Calculate the new yearly salary using a percent greater than 100

Kazeer [188]

Answer:

24,150

Step-by-step explanation:

Given that :

Salary earned this year = 23,000

Percentage Raise in salary for the new year = 5%

The new yearly salary can be obtained thus ;

(100% + percentage raise in salary) * salary earned this year

(100% + 5%) * 23,000

105% * 23000

1.05 * 23000

24,150

4 0

3 years ago

What is the constant of the expression? 5x−2y+2.4

Leno4ka [110]

The correct answer is the 2.4

The constant in an equation is the number(s) that don't have variables.

This is because variables can change the number they are attached to, making them not constant.

Hope this helps!

6 0

2 years ago

Read 2 more answers