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2 years ago

The sum of 5.5 and twice a number is -10

Mathematics

2 answers:

elena-s [515]2 years ago

3 0

The answer is n= 7.75.

elena-s [515]2 years ago

3 0

Answer:

n=-7.75

Step-by-step explanation:

Based on the given conditions, formulate: 5.5+2×X=-10

Rearrange unknown terms to the left side of the equation:2x=-10-5.5

Calculate the sum or difference:2x=-15.5

Divide both sides of the equation by the coefficient of variable:x=-15.5/2

Multiply both the numerator and denominator with the same integer:-155/20

Cross out the common factor:-31/4

get the result: -7.75

Answer: -7.75

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riadik2000 [5.3K]

Answer:

a) $4.85-2.33\frac{0.75}{\sqrt{20}}=4.46$

$4.85+2.33\frac{0.75}{\sqrt{20}}=5.24$

b) $4.56-2.33\frac{0.75}{\sqrt{16}}=4.12$

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Step-by-step explanation:

Part a

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

$\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (1)

The Confidence is 0.98 or 98%, the value of $\alpha=0.02$ and $\alpha/2 =0.01$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.01,0,1)".And we see that $z_{\alpha/2}=2.33$

Now we have everything in order to replace into formula (1):

$4.85-2.33\frac{0.75}{\sqrt{20}}=4.46$

$4.85+2.33\frac{0.75}{\sqrt{20}}=5.24$

Part b

$4.56-2.33\frac{0.75}{\sqrt{16}}=4.12$

$4.56+2.33\frac{0.75}{\sqrt{16}}=4.99$

Part c

The margin of error is given by this formula:

$ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (a)

And on this case we have that ME =0.4/2 =0.2 we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=(\frac{z_{\alpha/2} \sigma}{ME})^2$ (b)

The critical value for 95% of confidence interval now can be founded using the normal distribution. And in excel we can use this formla to find it:"=-NORM.INV(0.025;0;1)", and we got $z_{\alpha/2}=1.960$ , replacing into formula (b) we got:

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