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sertanlavr [38]
3 years ago
8

Which of the following equations is equivalent to log(y)= 3.994 ?

Mathematics
1 answer:
horrorfan [7]3 years ago
3 0

Answer:

The correct answer is option D: y = 10^{3.994}

Step-by-step explanation:

Given:  

log(y)= 3.994

Solution:

A logarithm base b of a positive number x satisfies the following definition:

y =log_b(x) => b^y =x

For x > 0, b >0, b \neq 1

Also if no base  b  is indicated, the base of the logarithm is assumed to be  10 .

Thus, in log(y)= 3.994 base b is not indicated. so its base is assumed to be 10

now

log_{10}(y)= 3.994

Then

y = 10^{3.994}

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There is not enough evidence to support the administrator’s claim and the true mean is not significantly greater than 280.

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A hypothesis to test the given parameters requires that we determine if the mean score of the eighth graders is more than 283, thus:

The null hypothesis:

\mathbf{H_o \leq 283}

The alternative hypothesis:

\mathbf{H_i > 283}

From the population deviation, the Z test for the true mean can be computed as:

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\mathbf{Z = \dfrac{283 -280}{\dfrac{37}{\sqrt{87}}}}

Z = 0.756

Note that, since we are carrying out a right-tailed test, the p-value for the test statistics is expressed as follows:

P(z > 0.756)

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Since the P-value is greater than the significance level at α = 0.14, we can conclude that there is not enough evidence to support the administrator’s claim and the true mean is not significantly greater than 280.

Learn more about hypothesis testing here:
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We want to find the values of a, b, c, and d such that the given matrix product is equal to a 2x2 identity matrix. We will solve a system of equations to find:

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<h3>Presenting the equation:</h3>

Basically, we want to solve:

\left[\begin{array}{cc}-1&2\\a&1\end{array}\right]*\left[\begin{array}{cc}b&c\\1&d\end{array}\right] = \left[\begin{array}{cc}1&0\\0&1\end{array}\right]

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