Simplify- 28 x*5 y*-3 z w

Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options.

avanturin [10]

The correct simplified inequality is - 6x + 15 < 10 - 5x and the number line representation is "an open circle is at 5 and a bold line starts at 5 and is pointing to the right".

The given inequality is -3(2x - 5) < 5(2 - x)

We need to simplify the inequality.

<h3>What is inequality?</h3>

In mathematics, inequality is a statement of an order relationship greater than, greater than or equal to, less than, or less than or equal to between two numbers or algebraic expressions.

Consider LHS and simplify -3(2x - 5) = -3(2x)-5(-3)

⇒ -3(2x - 5) = - 6x + 15 [∵(-)(-) = (+)]

Consider RHS and simplify 5(2 - x) = 5(2) + 5(-x)

⇒5(2 - x) = 10 - 5x [∵(+)(-) = (-)]

Now, - 6x + 15 < 10 - 5x

By subtracting 15 from both sides, we get

- 6x < -5 - 5x

By adding 5x to both sides, we get - x < - 5

The coefficient of x is -1. So, divide both sides by -1

Then we get x > 5

Hence, the correct simplified inequality is - 6x + 15 < 10 - 5x and the number line representation is "an open circle is at 5 and a bold line starts at 5 and is pointing to the right".

To learn more about inequalities visit:

brainly.com/question/20383699.

#SPJ1

5 0

1 year ago

Soft drink consumption in New Zealand. A survey commissioned by the Southern Cross Healthcare Group reported that 16% of New Zea

lidiya [134]

<h2>Answer with explanation:</h2>

Given : The proportion of New Zealanders consume five or more servings of soft drinks per week : $\hat{p}= 0.16$

a) The number of survey respondents reported that they consume five or more servings of soft drinks per week = 2006

b) Confidence interval for population proportion (p) :

$\hat{p}\pm z^*\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}$

, where $\hat{p}$ = Sample proportion.

n= Sample size.

z* = Critical value.

For n= 2006 , $\hat{p}= 0.16$ and critical value for 95% confidence interval : z* = 1.96

Then , the required confidence interval will be :

$0.16\pm (1.96)\sqrt{\dfrac{ 0.16(1- 0.16)}{2006}}$

$0.16\pm (1.96)\sqrt{ 0.000066999002991}$

$0.16\pm (1.96)(0.00818529186963)$

$0.16\pm 0.0160431720645$

$(0.16-0.0160431720645,\ 0.16+0.0160431720645)$

$(0.143956827935,\ 0.176043172064)\approx(0.144,\ 0.176)$

i.e. A 95% confidence interval for the proportion of New Zealanders who report that they consume five or more servings of soft drinks per week. = $(0.144,\ 0.176)$