All categories

3 years ago

Solve the compound inequality.

Mathematics

2 answers:

oksano4ka [1.4K]3 years ago

7 0

5x - 11 < -11
5x < 0
x < 0

4x + 2 > 14
4x > 12
x > 3

x<0 or x > 3

Alenkinab [10]3 years ago

6 0

Answer:

x<0 or x> 3

First option is correct.

Step-by-step explanation:

The given inequality is

5x – 11 < –11 or 4x + 2 > 14

Add 11 to both sides in first inequality and subtract 2 to both sides in second inequality

5x < –11+11 or 4x > 14-2

5x < 0 or 4x > 12

Divide both sides by 5 in first inequality and divide both sides by 4 in second inequality

x<0 or x> 3

First option is correct.

You might be interested in

Graph the following and state the domain, range, and end behavior y=2x-4

jasenka [17]

Answer:

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

What is the SURFACE AREA of the pyramid?

Tamiku [17]

Answer:

85in²

Step-by-step explanation:

s = side

triangle: ((b x h) ÷ 2) x 4

((5 x 6) ÷ 2) x 4 = 60in

square: s2(squared not 2)

5² = 25

total sa: 25 + 60 = 85in²

5 0

3 years ago

Teacher raises A school system employs teachers at

Cerrena [4.2K]

By adding a constant value to every salary amount, the measures of

central tendency are increased by the amount, while the measures of

dispersion, remains the same

The correct responses are;

(a) The shape of the data remains the same

(b) The mean and median are increased by $1,000

Reasons:

The given parameters are;

Present teachers salary = Between $38,000 and $70,000

Amount of raise given to every teacher = $1,000

Required:

Effect of the raise on the following characteristics of the data

(a) Effect on the shape of distribution

The outline shape of the distribution will the same but higher by $1,000

(b) The mean of the data is given as follows;

$\overline x = \dfrac{\sum (f_i \cdot x_i)}{\sum f_i}$

Therefore, following an increase of $1,000, we have;

$\overline x_{New} = \dfrac{\sum (f_i \cdot (x_i + 1000))}{\sum f_i} = \dfrac{\sum (f_i \cdot x_i + f_i \cdot 1000))}{\sum f_i} = \dfrac{\sum (f_i \cdot x_i)}{\sum f_i} + \dfrac{\sum (f_i \cdot 1000)}{\sum f_i}$

$\overline x_{New} = \dfrac{\sum (f_i \cdot x_i)}{\sum f_i} + \dfrac{\sum (f_i \cdot 1000)}{\sum f_i} = \dfrac{\sum (f_i \cdot x_i)}{\sum f_i} + 1000 = \overline x + 1000$

Therefore, the new mean, is equal to the initial mean increased by 1,000

Median;

Given that all salaries, $x_i$ , are increased by $1,000, the median salary, $x_{med}$ , is also increased by $1,000

Therefore;

The correct response is that the median is increased by $1,000

Where;

n = The number of teaches;

Given that, we have both a salary, $x_i$ , and the mean, $\overline x$ , increased by $1,000, we can write;

$\sigma_{new} =\sqrt{\dfrac{\sum \left ((x_i + 1000) -(\overline x + 1000)\right )^{2} }{n}} = \sqrt{\dfrac{\sum \left (x_i + 1000 -\overline x - 1000\right )^{2} }{n}}$

$\sigma_{new} = \sqrt{\dfrac{\sum \left (x_i + 1000 -\overline x - 1000\right )^{2} }{n}} = \sqrt{\dfrac{\sum \left (x_i + 1000 - 1000 - \overline x\right )^{2} }{n}}$

$\sigma_{new} = \sqrt{\dfrac{\sum \left (x_i + 1000 - 1000 - \overline x\right )^{2} }{n}} =\sqrt{\dfrac{\sum \left (x_i-\overline x \right )^{2} }{n}} = \sigma$

Therefore;

$\sigma_{new} = \sigma$ ; The standard deviation stays the same

Interquartile range;

The interquartile range, IQR = Q₃ - Q₁

New interquartile range, IQR $_{new}$ = (Q₃ + 1000) - (Q₁ + 1000) = Q₃ - Q₁ = IQR

Therefore;

The interquartile range stays the same

Learn more here:

brainly.com/question/9995782

6 0

3 years ago

I need help with another set of math questions.

Anit [1.1K]

For question 11, you essentially need to find when h(t) = 0, since that is when the height of the ball reaches 0 (ie touches the ground).

For question 12, it is asking for a maximum height, so you need to find when dh/dt = 0 and taking the second derivative to prove that there is maximum at t. That will find you the time at which the ball will hit a maximum height.

Rinse and repeat question 12 for question 13

7 0

3 years ago

% of 50 = 12.5 Please help.

andrezito [222]

Answer:

25 percent

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers