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Bond [772]
3 years ago
14

La altura de una portería de futbol reglamentaria es de 2.4m y la distancia desde el punto de penalti hasta la raya de gol es de

10.8m. ¿Qué distancia recorre un balón que se lanza desde el punto de penalti y se estrella en el punto central del larguero?
Mathematics
1 answer:
mihalych1998 [28]3 years ago
3 0

Answer:

11.06 meters

Step-by-step explanation:

Given that

The height of a regulation soccer goal is 2.4 meters

And, the distance is 10.8 meters

We need to find out the hypothesis

Here we applied the pythagoreans theorem

So,

= √ (2.4m) ^2 + (10.8 m) ^2

= √5.76 m^2 + 116.64m^2

h = 11.06 m

Hence, the hypothesis is 11.05 meters

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The lifetime of a certain type of battery is normally distributed with mean value 15 hours and standard deviation 1 hour. There
KIM [24]

Answer:

If the lifetime of batteries in the packet is 40.83 hours or more then, it exceeds for 5% of all packages.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 15

Standard Deviation, σ = 1

Sample size = 4

Total lifetime of 4 batteries = 40 hours

We are given that the distribution of lifetime is a bell shaped distribution that is a normal distribution.

Formula:

z_{score} = \displaystyle\frac{x-\mu}{\sigma}

Standard error due to sampling:

\displaystyle\frac{\sigma}{\sqrt{n}} = \frac{1}{\sqrt4} = 0.5

We have to find the value of x such that the probability is 0.05

P(X > x)  = 0.05

P( X > x) = P( z > \displaystyle\frac{x - 40}{0.5})=0.05  

= 1 -P( z \leq \displaystyle\frac{x - 40}{0.5})=0.05  

=P( z \leq \displaystyle\frac{x - 40}{0.5})=0.95  

Calculation the value from standard normal z table, we have,  

\displaystyle\frac{x - 40}{0.5} = 1.64\\x = 40.825 \approx 40.83  

Hence, if the lifetime of batteries in the packet is 40.83 hours or more then, it exceeds for 5% of all packages.

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