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2 years ago

Solve this.....................

Mathematics

2 answers:

Masja [62]2 years ago

8 0

Answer:

10 + 3π cm

Step-by-step explanation:

In the given figure,

Radius of arc/circle = 6 cm
Length + width of rectangle = 8 cm

Here, we are asked to find the perimeter of the shaded figure, i.e, SA + AC + CT + Arc SBT.

The perimeter of arc SBT can be found using the formula 2πr/4 [Given ⟶ arc SBT = quarter (¼) of a circle].

So,

2πr/4

= 2π(6)/4

= 12π/4

= 3π cm

Now, from the figure..

SA + AC + CT

= (SR - AR) + AC + (RT - RC)

By, rearranging the terms...

= SR + AC + RT - (AR + RC) ---------> (1)

Again, from the figure, we can see that,

SR = RT = 6 cm (radii of the same circle)
AC = RB = 6 cm (radii of the same circle)
AR + RC = 8 cm (length + width of rectangle)

So, by substituting these values in (1)

SR + AC + RT - (AR + RC)

= 6 + 6 + 6 - (8)

= 18 - 8

= 10 cm

And, the perimeter of the shade figure is,

SA + AC + CT + Arc SBT.

$= \boxed{\tt\:10 + 3\pi \: cm}$

_________

Hope it helps!

$\mathfrak{Lucazz}$

scoray [572]2 years ago

5 0

Answer:

10 + 3π units

Step-by-step explanation:

Take into account that:

AC = RB as diagonals of rectangle ABCR

Since R is the center and B is on the circle we have:

AC = r = 6 units

The arc SBT is the quarter of the length of circle:

SBT = 1/4*2πr = 1/2*6π = 3π units

Find the sum of SA and CT:

SA + AR = 6 ⇒ SA = 6 - AR
CT + RC = 6 ⇒ CT = 6 - RC
SA + CT = 6 - AR + 6 - RC = 12 - (AR + RC) = 12 - 8 = 4 units

So the perimeter of shaded zone is:

P = 6 + 3π + 4 = 10 + 3π units

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The time a randomly selected individual waits for an elevator in an office building has a uniform distribution with a mean of 0.

Amiraneli [1.4K]

Answer:

The mean of the sampling distribution of means for SRS of size 50 is $\mu = 0.5$ and the standard deviation is $s = 0.0409$

By the Central Limit Theorem, since we have of sample of 50, which is larger than 30, it does not matter that the underlying population distribution is not normal.

0% probability a sample of 50 people will wait longer than 45 seconds for an elevator.

Step-by-step explanation:

To solve this problem, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value 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. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central limit theorem:

The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$ , a large sample size, of at least 30, can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$

In this problem, we have that:

$\mu = 0.5, \sigma = 0.289$

What are the mean and standard deviation of the sampling distribution of means for SRS of size 50?

By the Central Limit Theorem

$\mu = 0.5, s = \frac{0.289}{\sqrt{50}} = 0.0409$

The mean of the sampling distribution of means for SRS of size 50 is $\mu = 0.5$ and the standard deviation is $s = 0.0409$

Does it matter that the underlying population distribution is not normal?

By the Central Limit Theorem, since we have of sample of 50, which is larger than 30, it does not matter that the underlying population distribution is not normal.

What is the probability a sample of 50 people will wait longer than 45 seconds for an elevator?

We have to use 45 seconds as minutes, since the mean and the standard deviation are in minutes.

Each minute has 60 seconds.

So 45 seconds is 45/60 = 0.75 min.

This probability is 1 subtracted by the pvalue of Z when X = 0.75. So

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$