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4 years ago

Write the smaller solution first and larger solution second. (X-2)(3x+3)

Mathematics

1 answer:

saw5 [17]4 years ago

4 0

If this is an equation then write:
x-2=0
x=2

3x+3=0
x=-1

so smaller solution is x= -1 and larger is x=2

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Insurance companies are interested in knowing the population percent of drivers who always buckle up before riding in a car. Whe

kherson [118]

Answer:

$n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}$

$n=\frac{0.5(1-0.5)}{(\frac{0.03}{1.96})^2}=1067.11$

And rounded up we have that n=1068

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

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 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 on this case we have that $ME =\pm 0.03$ and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}$ (b)

We don't have a prior estimation for the proportion $\hat p$ so we can use 0.5 as an approximation for this case

And replacing into equation (b) the values from part a we got:

$n=\frac{0.5(1-0.5)}{(\frac{0.03}{1.96})^2}=1067.11$

And rounded up we have that n=1068

5 0

3 years ago

Which point could be removed in order to make the relation a function? (4 points)

dolphi86 [110]

0,-2 or 0,8. As long as the x variable does not repeat in a relation, it is a function.

4 0

3 years ago

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Which expression is equivalent to -4 - 9?<br> A. 4 + 9<br> B. 4 - 9<br> C. -4 + (-9)<br> D. -4 + 9

musickatia [10]

Answer: C. -4 + (-9)

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3 years ago

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If the length of a rectangle is increased by 120%, and its width is decreased by 20%, what is the percentage change in the area

velikii [3]

Answer:

The area of the rectangle is increased in 76 percent.

Step-by-step explanation:

The area of a rectangle ( $A$ ) is represented by the following formula:

$A = w\cdot l$

Where:

$w$ - Width.

$l$ - Length.

If length is increased by 120 %and width is decreased by 20 %, the percentage change in the area of the rectangle is: ( $l = 2.2\cdot l_{o}$ , $w = 0.8\cdot w_{o}$ )