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Mumz [18]
3 years ago
6

Solve for x: −3x + 3 < 6 (2 points)

Mathematics
2 answers:
dimaraw [331]3 years ago
4 0

Answer:

x > −1

Step-by-step explanation:

−3x + 3 < 6

Subtract 3 from each side

-3x+3-3 <6-3

-3x <3

Divide by -3.  Remember that when you multiply or divide by a negative, you flip the inequality.

-3x/-3 > 3/-3

x >-1

In-s [12.5K]3 years ago
3 0

-3x + 3 < 6                <em>subtract 3 from both sides</em>

-3x < 3      <em>change the signs</em>

3x > -3      <em>divide both sides by 3</em>

<h2>x > -1</h2>
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Match the justifications for each step in order to prove the Alternate Interior Angles Theorem. Note that lines p and q are para
Alex_Xolod [135]

Answer:

Option (3)

Step-by-step explanation:

There are two parallel lines 'p' and 'q' and a transversal line is intersecting these lines at two distinct points.

Each pair of angles formed on the inner side of the parallel lines but opposite sides of the transversal line are the alternate interior angles.

Pair of angles (∠2 and ∠6) and (∠3 and ∠7) are the alternate interior angles.

Since, alternate interior angles are equal in measure,

∠2 ≅ ∠6

∠3 ≅ ∠7

Option (3) will be the answer.

6 0
3 years ago
3. Using the sample size of 800 and the proportion 0.47, calculate the margin of error associated with the estimate of the propo
salantis [7]

Answer:

ME=1.96\sqrt{\frac{0.47 (1-0.47)}{800}}=0.0346  

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

The population proportion have the following distribution

p \sim N(p,\sqrt{\frac{p(1-p)}{n}})

Solution to the problem

We assume for this case a confidence level of 95%. In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by \alpha=1-0.95=0.05 and \alpha/2 =0.025. And the critical value would be given by:

z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96

The confidence interval for the mean is given by the following formula:  

\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}

The margin of error for the proportion interval is given by this formula:  

ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}    (a)  

And if we replace the values obtained we got this:

ME=1.96\sqrt{\frac{0.47 (1-0.47)}{800}}=0.0346  

6 0
3 years ago
Which of the following could be the system of nonlinear inequalities graphed below?
Ivan

Answer:

Option A.

Step-by-step explanation:

step 1

we know that

The equation of the solid line is

y=5

The solution is the shaded area above the solid line

so

The equation of the first inequality is

y\geq 5

step 2

The equation of the dashed line is

y=x^{2} -5x+6

The solution is the shaded area above the dashed line

so

The equation of the second inequality is

y>x^{2} -5x+6

therefore

The system of inequalities could be

y\geq 5

y>x^{2} -5x+6

4 0
4 years ago
How to write 8÷2×(5+5) in words​
Ivenika [448]

Eight divided by two times (5 plus 5)

6 0
3 years ago
Read 2 more answers
What is the value of n? -10= n/-0.2
Nata [24]

n/0.2=-10

Goal: Make n by itself!

Solution: We can do this by multiplying each side by -0.2

-10 * -0.2=2

I hope this helps! If you have anymore questions, please feel free to contact me!

6 0
3 years ago
Read 2 more answers
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