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4 years ago

What is log3 ( x+5)=2?

Mathematics

1 answer:

Naddik [55]4 years ago

4 0

(3) is the base of the new equation

(x + 5) is the answer of the new equation

(2) is the exponent on base (3)

;The new equation after simplifying is...,

; 3^2 = x + 5

; 9 = x + 5

; x = 9 - 5

;Hence...x = 4

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Arturiano [62]

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4 years ago

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3 years ago

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3 years ago

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Guest ages at a ski mountain resort typically have a right-skewed distribution. Assume the standard deviation (σ) of age is 14.5

ValentinkaMS [17]

Answer: (30.49 years, 42.31 years)

Step-by-step explanation:

The formula to find the confidence interval is given by :-

$\overline{x}\pm z^*\dfrac{\sigma}{\sqrt{n}}.$

, where $\overline{x}$ = Sample mean

z* = Critical value.

$\sigma$ = Population standard deviation.

n= Sample size.

As per given , we have

$\overline{x}=36.4$

$\sigma=14.5$

n= 40

We know that the critical value for 99% confidence interval : z* = 2.576 (By z-table)

A 99 percent confidence interval for µ, the true mean age of guests will be :

$36.4\pm (2.576)\dfrac{14.5}{\sqrt{40}}\\\\ 36.4\pm (2.576)2.29265130362\\\\=36.4\pm5.90586975813\\\\\approx36.4\pm5.91\\\\=(36.4-5.91,\ 36.4+5.91)\\\\=(30.49,\ 42.31)$

∴ a 99 percent confidence interval for µ, the true mean age of guests = (30.49 years, 42.31 years)

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3 years ago