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3 years ago

Hi can anyone tell me the answer

Mathematics

1 answer:

AnnyKZ [126]3 years ago

3 0

Answer:

$\frac{4}{5}$

Step-by-step explanation:

Total no. of outcomes = 20

No. of green counters = 16

Therefore, Probability of getting green counter

$= \frac{16}{20} = \frac{4}{5}$

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A car is being driven at a rate of 40 ft/sec when the brakes are applied. The car decelerates at a constant rate of 10 ft/sec2.

IRISSAK [1]

Answer:

80 feet

Step-by-step explanation:

Given:

Initial speed of the car ( $v_0$ ) = 40 ft/sec

Deceleration of the car ( $\frac{dv}{dt}$ ) = -10 ft/sec²

Final speed of the car ( $v_x$ ) = 0 ft/sec

Let the distance traveled by the car be 'x' at any time 't'. Let 'v' be the velocity at any time 't'.

Now, deceleration means rate of decrease of velocity.

So, $\frac{dv}{dt}=-10\ ft/sec^2$

Negative sign means the velocity is decreasing with time.

Now, $\frac{dv}{dt}=\frac{dv}{dx}(\frac{dx}{dt})$ using chain rule of differentiation. Therefore,

$\frac{dv}{dx}\cdot\frac{dx}{dt}= -10\\\\But\ \frac{dx}{dt}=v.\ So,\\\\v\frac{dv}{dx}=-10\\\\vdv=-10dx$

Integrating both sides under the limit 40 to 0 for 'v' and 0 to 'x' for 'x'. This gives,

$\int\limits^0_{40} {v} \, dv=\int\limits^x_0 {-10} \, dx\\\\\left [ \frac{v^2}{2} \right ]_{40}^{0}=-10x\\\\-10x=\frac{0}{2}-\frac{1600}{2}\\\\10x=800\\\\x=\frac{800}{10}=80\ ft$

Therefore, the car travels a distance of 80 feet before stopping.

4 0

3 years ago

Ship A receives a distress signal from the southwest, and ship B receives a distress from the same vessel from the north. At wha

Fiesta28 [93]

I've attached an image showing the coordinates of Ship A and Ship B.

Answer:

distressed vessel is located at (1, 1.5)

Step-by-step explanation:

From the image attached, we can see that;

Coordinate of ship A is (3, 4)

Coordinate of ship B is (1, 1)

Now, we are told that Ship A receives a distress signal from the southwest, and ship B receives a distress from the same vessel from the north.

This means that the distressed ship is somewhere in between ship A & B.

To solve this, we will extend the arrow line from Ship A in that same SW direction and we will do the same for ship B in the same North direction. Their point of intersection is where the distressed ship is located.

Now, if we do that, we will see that they will intersect at the point; (1, 1.5)

Thus,distressed vessel is located at (1, 1.5)

5 0

3 years ago

(3 points) Blades of grass Suppose that the heights of blades of grass are Normally distributed and independent, with each heigh

NemiM [27]

The final answer is:

a) P( Y < 42.5 ) = 0.8541

b) P( 39.5 < Y < 40.5 ) = 0.1670.

What is the normal distribution?

A continuous probability distribution for a real-valued random variable in statistics is known as a normal distribution or Gaussian distribution.

If x follows a normal distribution with mean μ and standard deviation σ then the distribution of

$\sum_{i =1}^{n}x_{i}$ follows an approximately normal distribution with a mean $n\mu$ and standard deviation $\sqrt{n }\sigma$