3 years ago

Rewrite the logarithm as an exponential equation: In(X)= 7

Mathematics

1 answer:

Leto [7]3 years ago

4 0

Answer:

$e^7=x$

Step-by-step explanation:

Given the logarithm function

$In\left(x\right)=\:7$

For logarithmic equations, $\log _b\left(x\right)=y$ is equivalent to $b^y=x$ such that

$x>0\:,\:b>0$ and $b\ne 1$

In current case:

$b=e\:$

$\:x=x$

$\:y=7$

Substituting the values of $b\:,\:x\:$ and $y$ into the equation $b^y=x$

$e^7=x$

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assume that women's heights are normally distributed with a mean of 63.6 inches and a standard deviation of 2.5 inches. find the

drek231 [11]

Answer:

65.3658 inches

Step-by-step explanation:

Let X be the height of a woman randomly choosen. We know tha X have a mean of 63.6 inches and a standard deviation of 2.5 inches. For an x value, the related z-score is given by z = (x-63.6)/2.5. We are looking for a value $x_{0}$ such that $P(X < x_{0}) = 0.76$ , but, $0.76 = P(X < x_{0}) = P((X-63.6)/2.5 < (x_{0}-63.6)/2.5) = P(Z < (x_{0}-63.6)/2.5)$ , i.e., $(x_{0}-63.6)/2.5$ is the 76th percentile of the standard normal distribution. So, $(x_{0}-63.6)/2.5 = 0.7063$ , $x_{0} =63.6+(2.5)(0.7063) = 65.3658$ . Therefore, the height of a woman who is at the 76th percentile is 65.3658 inches.