Find the area of the circle. Use 3.14 or 22/7 for pi. Round your answer to the nearest hundredth, if necessary.

The time for this event for boys in secondary school is known to possess a normal distribution with a mean of 460 seconds and a

AlekseyPX

Answer:

The time that the boys need to beat in order to earn a certificate of recognition from the fitness association is 511.264 seconds.

Step-by-step explanation:

We are given that the time for this event for boys in secondary school is known to possess a normal distribution with a mean of 460 seconds and a standard deviation of 40 seconds.

The fitness association wants to recognize the fastest 10% of the boys with certificates of recognition.

Let X = time for this event for boys in secondary school

SO, X ~ Normal( $\mu=460,\sigma^{2} =40^{2}$ )

The z-score probability distribution for normal distribution is given by;

Z = $\frac{X-\mu}{\sigma}$ ~ N(0,1)

where, $\mu$ = mean time = 460 seconds

$\sigma$ = standard deviation = 40 seconds

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.

Now, it is given that the fitness association wants to recognize the fastest 10% of the boys with certificates of recognition, which means;

P(X > x) = 0.10 {where x is the required time which boy need to beat}

P( $\frac{X-\mu}{\sigma}$ > $\frac{x-460}{40}$ ) = 0.10

P(Z > $\frac{x-460}{40}$ ) = 0.10

So, the critical value of x in the z table which represents the top 10% of the area is given as 1.2816, that is;

$\frac{x-460}{40} =1.2816$

${x-460}{} =1.2816\times 40$

$x$ = 460 + 51.264 = 511.264 seconds

Hence, the time that the boys need to beat in order to earn a certificate of recognition from the fitness association is 511.264 seconds.

8 0

3 years ago

I need help with this equation 5x (2x-2)

Doss [256]

Answer: 10x^2-10x

Explanation: You would distribute the 5x into the parenthesis making it 10x(to the second power) -10x

8 0

3 years ago

Michael can type 4 pages of his term paper in 30 minutes. How long will it take him to type the paper if it has 14 pages?

Stella [2.4K]

Answer:

105 minutes

Step-by-step explanation:

we know that

Michael can type 4 pages of his term paper in 30 minutes

so

using proportion

Find out how long will it take him to type the paper if it has 14 pages

$\frac{30}{4}\frac{min}{pages}=\frac{x}{14}\frac{min}{pages}\\\\x=30*14/4\\ \\x=105\ min$

8 0

3 years ago

I really need help with 15 and 16 please

Mandarinka [93]

Answer:

15. 50 kg

16a. 5 kg

16b. 3.75 kg

Step-by-step explanation:

The formula relating force, mass, and acceleration can be solved for mass. This formula will apply to both problems. We'll use m for both "mass" and "meters". We presume you can avoid getting mixed up by understanding that meters is used in the context of acceleration: m/s².

F = ma

m = F/a . . . . . divide by a

__

15. m = (250 N)/(5 m/s²) = 50 kg

__

16a. m = (15 N)/(3 m/s²) = 5 kg

16b. m = (15 N)/(4 m/s²) = 3.75 kg

_____

Comment on units

Especially for physics problems, I like to keep the units with the numbers. It is helpful to remember that Newtons are equivalent to kg·m/s². So, dividing Newtons by acceleration in m/s² will give mass in kg. Since you're familiar with F=ma, it's not too hard to remember that the units of force (N) are the product of the units of mass (kg) and acceleration (m/s²).

6 0

3 years ago

A company lost an average of $30,000 per month. Find the total loss of the company in 1 year.

Art [367]

Answer:

$360,000

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers