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Mathematics

2 answers:

Wewaii [24]3 years ago

6 0

what do you need help with exactly

LenKa [72]3 years ago

5 0

Repost this it is glitched and the picture is broken .

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Find constants A and B such that (x + 7)/(x^2 - x - 2) = A/(x - 2) + B/(x + 1) for all x such that x≠ -1 and x≠ 2 Give your answ

Yanka [14]

For this case we have the following expression:
(x + 7) / (x ^ 2 - x - 2) = A / (x - 2) + B / (x + 1)
Rewriting we have:
(x + 7) / ((x-2) (x + 1)) = A / (x - 2) + B / (x + 1)
We multiply the equality by (x-2) (x + 1):
x + 7 = A (x + 1) + B (x - 2)
Rewriting we have the following system of equations:
A + B = 1
A - 2B = 7
Solving the system we have:
A = 3
B = -2
Answer:
constants A and B are:
A = 3
B = -2

6 0

3 years ago

You are trying to estimate the average amount a family spends on food during a year. In the past the standard deviation of the a

PolarNik [594]

The number of the families that need to be surveyed will be 2663.

<h3>What is the margin of error?</h3>

Your results will deviate from the actual population value by how many percentage points, as indicated by the margin of error.

We have the following info:

ME = 50 margins of error desired

$\sigma$ = 1000 the standard deviation for this case

The margin of error is given by this formula:

(a) $ME=Z_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}$

And on this case, we have that ME =50 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

(b) $n =(\dfrac{Z_{a\2}\sigma}{ME})^2$

The critical value for the 99% of confidence interval now can be founded using the normal distribution. The significance is $\alpha$ = 0.01. And for this case would be $Z_{\alpha / 2}$ = 2.58, replacing into formula (b) we got: