Which of the following equations correctly represents the law of sines?

A certain type of thread is manufactured with a mean tensile strength of 78.3 kilograms and a standard deviation of 5.6 kilogram

azamat

Answer:

(a) The variance decreases.

(b) The variance increases.

Step-by-step explanation:

According to the Central Limit Theorem if we have a population with mean μ and standard deviation σ and we take appropriately huge random samples (n ≥ 30) from the population with replacement, then the distribution of the sample mean will be approximately normally distributed.

Then, the mean of the sample mean is given by,

$\mu_{\bar x}=\mu$

And the standard deviation of the sample mean is given by,

$\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}$

The standard deviation of sample mean is inversely proportional to the sample size, n.

So, if n increases then the standard deviation will decrease and vice-versa.

(a)

The sample size is increased from 64 to 196.

As mentioned above, if the sample size is increased then the standard deviation will decrease.

So, on increasing the value of n from 64 to 196, the standard deviation of the sample mean will decrease.

The standard deviation of the sample mean for n = 64 is:

$\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}=\frac{5.6}{\sqrt{64}}=0.7$

The standard deviation of the sample mean for n = 196 is:

$\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}=\frac{5.6}{\sqrt{196}}=0.4$

The standard deviation of the sample mean decreased from 0.7 to 0.4 when n is increased from 64 to 196.

Hence, the variance also decreases.

(b)

If the sample size is decreased then the standard deviation will increase.

So, on decreasing the value of n from 784 to 49, the standard deviation of the sample mean will increase.

The standard deviation of the sample mean for n = 784 is:

$\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}=\frac{5.6}{\sqrt{784}}=0.2$

The standard deviation of the sample mean for n = 49 is:

$\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}=\frac{5.6}{\sqrt{49}}=0.8$

The standard deviation of the sample mean increased from 0.2 to 0.8 when n is decreased from 784 to 49.

Hence, the variance also increases.

6 0

2 years ago

I WILL AWARD BRAINLIEST!! PLEASE HELP!!! The figure below shows the movement of a pedestrian from point B to point E. Using the

MissTica

A) The speed of the pedestrian BC is 5 km/h

The speed of the pedestrian CD is 0 km/h

The speed of the pedestrian DE is 5 km/h

B) He arrived E since the stop after 6 hours

C) The formula for section BC is d(t) = 40 - 5t

The formula for section CD is d(t) = 20

The formula for section DE is d(t) = 50 - 5t

Step-by-step explanation:

A)

In the time-distance graph the speed is the rate of change of distance

and that mean speed = Δd/Δt ⇒ (slope of the line)

In line BC:

1. Δd = 40 - 20 = 20 km

2. Δt = 4 - 0 = 4 hours

3. The speed = 20 ÷ 4 = 5 km/h

The speed of the pedestrian BC is 5 km/h

In line CD:

1. Δd = 20 - 20 = 0 km

2. Δt = 6 - 4 = 2 hours

3. The speed = 0 ÷ 2 = 0 km/h

The speed of the pedestrian CD is 0 km/h

In line DE:

1. Δd = 20 - 0 = 20 km

2. Δt = 10 - 6 = 4 hours

3. The speed = 20 ÷ 4 = 5 km/h

The speed of the pedestrian DE is 5 km/h

B)

∵ He stop at t = 4 hours

∵ He arrived at point E at t = 10 hours

∵ 10 - 4 = 6 hours

He arrived E since the stop after 6 hours

C)

The speeds are represented by lines

The form of the equation of a line is f(x) = mx + c, where m represents

the slope of the line and c is the y-intercept (y when x = 0)

1. f(x) is d(t)

2. m is the speed

3. x is t

4. You can find c by substitute d and t by any point on the line

Line BC

Line BC has negative slope because d decreases when t increases

∵ m = -5 and c = 40

∴ d(t) = 40 - 5t

The formula for section BC is d(t) = 40 - 5t

Line CD

Line CD is a horizontal line (equation any horizontal line is y = c)

∴ m = 0 and c = 20

∴ d(t) = 20

The formula for section CD is d(t) = 20

Line DE

Line DE has negative slope because d decreases when t increases

∵ m = -5

∴ d(t) = -5t + c

To find c substitute the coordinates of point D in the equation

∵ The coordinates of point D are (6 , 20)

∴ 20 = -5(6) + c

∴ 20 = -30 + c

Add 30 to both sides

∴ c = 50

∴ d(t) = 50 - 5t

The formula for section DE is d(t) = 50 - 5t

Learn more:

You can learn more about the distance, speed, and time in

brainly.com/question/5102020

#LearnwithBrainly

3 0

2 years ago

HELP!!!!

Nonamiya [84]

Your answer is E. $25.

First let under 12 = u, over 12 = o, and adults = a.
We can now write the equations:

2u + 3a + 3o = 174
4u + 2a = 122
a + o = 46

Because we know that a + o = 46, and 3a + 3o is in the first equation, we can multiply 46 by 3 to get what 3a + 3o equals. This makes 138.
Now we can substitute 138 into the first equation to get 2u + 138 = 174
2u = 36
u = 18

Now that we know what u equals, we can substitute it in to the second equation to get:
4(18) + 2a = 122
72 + 2a = 122
2a = 50
a = $25

I hope this helps! Let me know if you have any questions :)

8 0

2 years ago

Please solve this equation

Darya [45]

Answer: if you simplify the equation, your answer should be 16

Step-by-step explanation: Simplify 2+22+22+2 to 444.

8÷2×48\div 2\times 48÷2×4

2

Simplify 8÷28\div 28÷2 to 444.

4×44\times 44×4

3

Simplify.

16

4 0

2 years ago

Read 2 more answers

What is the average rate of change of y=cos(2x) on the interval 0 pi/2?

Snezhnost [94]

Jesus is the answer to this

7 0

2 years ago

Read 2 more answers