Help me substitution method define variables

Mathematics

1 answer:

Rina8888 [55]3 years ago

7 0

$\left \{ {{S=14+L} (I) \atop {S+L=124}(II)} \right.$

Substitute (I) into (II), we have:
 $S+L=124$
$(14+L)+L=124$
$14 + 2L = 124$
$2L = 124 - 14$
$2L = 110$
$L = \frac{110}{2}$
$\boxed{L = 55}$

Replace (II) in (I), we have:
 $S=14+L$
$S = 14+ 55$
$\boxed{S = 69}$

Answer:
each student sell:
Lori = 55 pizzas
Steve = 69 pizzas

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Find the 90% confidence interval for the population standard deviation given the following.

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Answer:

b. 2.01 < σ < 2.81

Step-by-step explanation:

The 90% confidence interval for the population standard deviation is calculated as:

$\sqrt{\frac{(n-1)*s^{2} }{X^2_{\alpha/2 } } }$ < σ < $\sqrt{\frac{(n-1)*s^{2} }{X^2_{1-\alpha/2 } } }$

Where n is equal to 51, s is equal to 2.34, $\alpha$ is 10%, $X^{2} _{\alpha /2}$ is the value for the Chi squared distribution with n-1 degrees of freedom that has a probability of $\alpha /2$ in the right tail and $X^{2} _{1-\alpha /2}$ is the value for the Chi squared distribution with n-1 degrees of freedom that has a probability of $1-\alpha /2$ in the right tail.

So, replacing n by 51, s by 2.34, $X^{2} _{\alpha /2}$ by 67.50 and $X^{2} _{1-\alpha /2}$ by 34.76, we get that the The 90% confidence interval is equal to:

$\sqrt{\frac{(51-1)*2.34^{2} }{67.50} } }$ < σ < $\sqrt{\frac{(51-1)*2.34^{2} }{34.76} } }$