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3 years ago

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There is a value of a such that subtracting a-4 from 4a+16 gives an answer of -25. What is that value of a? (We suggest that you

check your answer)
Any help is to be valued highly and much appreciated! Thank you!

1 answer:

kodGreya [7K]3 years ago

3 0

$\bf (4a+16)-(a-4)=-25\implies 4a+16-a+4=-25
\\\\\\
3a=-25-16-4\implies 3a=-45\implies a=\cfrac{-45}{3}\implies \boxed{a=-15}$

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$n=\frac{0.5(1-0.5)}{(\frac{0.05}{1.96})^2}=384.16$

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Step-by-step explanation:

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 $ME =\pm 0.05$ 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)

The estimated proportion for this case is $\hat p=0.5$ . And replacing into equation (b) the values from part a we got:

$n=\frac{0.5(1-0.5)}{(\frac{0.05}{1.96})^2}=384.16$

And rounded up we have that n=385

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Step-by-step explanation:

Given

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Now we will solve the equation by putting all the 6 pairs so we get the following

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The above all are Quadratic equations inn general form $ax^{2} +bx+c=0$

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So for a real Solution we must have

$Disciminant , b^{2} -4\timesa\timesc \geq 0$

for $a = -3 , c=-5$ we have

$Discriminant =-24$ which is less than 0 ∴ not a real solution.

for $a = -4 , c=5$ we have

$Discriminant = 116$ which is greater than 0 ∴ a real solution.

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$Discriminant =12$ which is greater than 0 ∴ a real solution.

for $a = 2 , c=3$ we have

$Discriminant =12$ which is greater than 0 ∴ a real solution.

for $a = 3 , c=3$ we have

$Discriminant =0$ which is equal to 0 ∴ a real solution.

for $a = 5 , c=4$ we have

$Discriminant =-44$ which is less than 0 ∴ not a real solution.

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