The product of a number, x, and six is four more than the product of the number and three-eighths.

During a rock concert, the noise level (in decibels) in front row seats has a mean of 92 dB with a standard deviation of 9 dg_ W

rodikova [14]

Answer:

The minimum percentage of noise level readings within 8 standard deviations of the mean is 98.44%.

Step-by-step explanation:

When we do not know the shape of the distribution, we use the Chebyshev's Theorem to find the minimum percentage of a measure within k standard deviations of the mean.

This percentage is:

$p = 1 - \frac{1}{k^{2}}$

Within 8 standard deviations of the mean

This means that $k = 8$ . So

$p = 1 - \frac{1}{8^{2}} = 1 - \frac{1}{64} = \frac{64 - 1}{64} = \frac{63}{64} = 0.9844$

The minimum percentage of noise level readings within 8 standard deviations of the mean is 98.44%.

6 0

3 years ago

Find the obtuse angle between the following pair of straight lines.

ioda

Given:

$y=-2$

$y=\sqrt{3}x-1$

To find:

The obtuse angle between the given pair of straight lines.

Solution:

The slope intercept form of a line is

$y=mx+b$ ...(i)

where, m is slope and b is y-intercept.

The given equations are

$y=0x-2$

$y=\sqrt{3}x-1$

On comparing these equations with (i), we get

$m_1=0$

$m_2=\sqrt{3}$

Angle between two lines whose slopes are $m_1\text{ and }m_2$ is

$\tan \theta=\left|\dfrac{m_2-m_1}{1+m_1m_2}\right|$

Putting $m_1=0$ and $m_2=\sqrt{3}$ , we get

$\tan \theta=\left|\dfrac{\sqrt{3}-0}{1+(0)(\sqrt{3})}\right|$

$\tan \theta=\left|\dfrac{\sqrt{3}}{1+0}\right|$

$\tan \theta=\pm \sqrt{3}$

Now,

$\tan \theta= \sqrt{3}$ and $\tan \theta=-\sqrt{3}$

$\tan \theta= \tan 60^\circ$ and $\tan \theta=\tan (180^\circ-60^\circ)$

$\theta= 60^\circ$ and $\theta=120^\circ$

$120>90$ , so it is an obtuse angle and $60$ , so it is an acute angle.

Therefore, the obtuse angle between the given pair of straight lines is 120°.

6 0

2 years ago

Which of the following equations has no solution?

Ronch [10]

Answer:

B and D

Step-by-step explanation:

Equations with the same x- term on both sides will have no solution

A

4x - 13 = 5(x + 4) = 5x + 20

4x ≠ 5x

This equation has a solution

B

5(3 + 2x) = 10x + 4

15 + 10x = 10x + 4

10x on both sides ⇒ no solution

C

2(3 - 5x) = 8(x + 1)

6 - 10x = 8x + 8

- 10x ≠ 8x

This equation has a solution

D

9x - 6 = 3(3x - 2) = 9x - 6

9x on both sides ⇒ no solution

8 0

2 years ago

Select which form to use when you know the slope of the line and one of the points on the line. a. horizontal line c. slope-inte

Cloud [144]

The form which should be used when you know the slope of a line and one of the points on the line is: d. point-slope form.

<h3>What is the point-slope form?</h3>

The point-slope form can be defined as an equation which is used when the slope of a line and one of the points on this line is known.

Mathematically, the point-slope form of a line is given by:

y - y₁ = m(x - x₁)

<u>Where:</u>

m is the slope.

x and y are the points.

In conclusion, you should use the point-slope form when you know the slope of a line and one of the points on the line is given.

Read more on point-slope form here: brainly.com/question/24907633

#SPJ1

6 0

1 year ago

Explain how to find the slope and y-intercept by just looking at the equation

Margaret [11]

Y = x - 2. Then graph the equation and verify your answers.

4 0

2 years ago