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3 years ago

in a Pythagorean theorem, how would you reverse the radical form if your trying to find a side of the right trianle

1 answer:

8 0

It would be best to keep it the same. So if I knew the hypotenuse was 9 and that one side was 4 and I was looking for the other one I would right it like this:

4^2 + B^2 = 9^2
Then simplify
16 + B^2 =81
Then subtract
B^2 = 65
And then take the square root of both sides
B = 8.0622577483 (since I came up with random numbers it ended up so uneven :P)

Does that make sense to you? I hope that helped you to understand! Feel free to let me know if you have any questions!

- mathwizzard3

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A phone manufacturer wants to compete in the touch screen phone market. He understands that the lead product has a battery life

Tasya [4]

Answer:

(a) H₀: μ ≤ 10. vs. Hₐ: μ > 10.

(b) The test statistic value is 1.86.

(d) The battery life of the new touch screen phone is not more than 10 hours.

Step-by-step explanation:

In this case we need to determine the significance of the claim made by the phone manufacturer, that the battery life of the new touch screen phone is more than twice as long as that of the leading product.

The information provided is:

$\bar x=10.5\\s=1.8\\n=45$

(a)

The hypothesis can be defined as follows:

H₀: The battery life of the new touch screen phone is not more than 10 hours, i.e. μ ≤ 10.

Hₐ: The battery life of the new touch screen phone is more than 10 hours, i.e. μ > 10.

(b)

As the population standard deviation is not provided, we will use a t-test for single mean.

Compute the test statistic value as follows:

$t=\frac{\bar x-\mu}{s/\sqrt{n}}=\frac{10.5-10}{1.8/\sqrt{45}}=1.86$

The test statistic value is 1.86.

(c)

The significance level of the test is, α = 0.10.

The degrees of freedom will be:

$df=n-1=45-1=44$

Compute the critical value as follows:

$t_{0.10, 44}=1.301$

*Use a t-table for the value.

Thus, the critical value to test the phone manufacturer's claim is 1.301.

(d)

Decision rule:

If the test statistic value is less than the critical value then the null hypothesis will be rejected and vice-versa.

t = 1.86 > t₀.₁₀, ₄₄ = 1.30

The calculated t-value of the test is more than the critical value.

The null hypothesis will not be rejected.

Thus, it can be concluded that the battery life of the new touch screen phone is not more than 10 hours.

6 0

3 years ago

medical tests. Task Compute the requested probabilities using the contingency table. A group of 7500 individuals take part in a

uysha [10]

Probabilities are used to determine the chances of an event

The probability that a person is sick is: 0.008
The probability that a test is positive, given that the person is sick is 0.9833
The probability that a test is negative, given that the person is not sick is: 0.9899
The probability that a person is sick, given that the test is positive is: 0.4403
The probability that a person is not sick, given that the test is negative is: 0.9998
A 99% accurate test is a correct test

(a) Probability that a person is sick

From the table, we have:

$\mathbf{Sick = 59+1 = 60}$

So, the probability that a person is sick is:

$\mathbf{Pr = \frac{Sick}{Total}}$

This gives

$\mathbf{Pr = \frac{60}{7500}}$

$\mathbf{Pr = 0.008}$

The probability that a person is sick is: 0.008

(b) Probability that a test is positive, given that the person is sick

From the table, we have:

$\mathbf{Positive\ and\ Sick=59}$

So, the probability that a test is positive, given that the person is sick is:

$\mathbf{Pr = \frac{Positive\ and\ Sick}{Sick}}$

This gives

$\mathbf{Pr = \frac{59}{60}}$

$\mathbf{Pr = 0.9833}$

The probability that a test is positive, given that the person is sick is 0.9833

(c) Probability that a test is negative, given that the person is not sick

From the table, we have:

$\mathbf{Negative\ and\ Not\ Sick=7365}$

$\mathbf{Not\ Sick = 75 + 7365 = 7440}$

So, the probability that a test is negative, given that the person is not sick is:

$\mathbf{Pr = \frac{Negative\ and\ Not\ Sick}{Not\ Sick}}$

This gives

$\mathbf{Pr = \frac{7365}{7440}}$

$\mathbf{Pr = 0.9899}$

The probability that a test is negative, given that the person is not sick is: 0.9899

(d) Probability that a person is sick, given that the test is positive

From the table, we have:

$\mathbf{Positive\ and\ Sick=59}$

$\mathbf{Positive=59 + 75 = 134}$

So, the probability that a person is sick, given that the test is positive is:

$\mathbf{Pr = \frac{Positive\ and\ Sick}{Positive}}$

This gives

$\mathbf{Pr = \frac{59}{134}}$

$\mathbf{Pr = 0.4403}$

The probability that a person is sick, given that the test is positive is: 0.4403

(e) Probability that a person is not sick, given that the test is negative

From the table, we have:

$\mathbf{Negative\ and\ Not\ Sick=7365}$

$\mathbf{Negative = 1+ 7365 = 7366}$

So, the probability that a person is not sick, given that the test is negative is:

$\mathbf{Pr = \frac{Negative\ and\ Not\ Sick}{Negative}}$

This gives

$\mathbf{Pr = \frac{7365}{7366}}$

$\mathbf{Pr = 0.9998}$

The probability that a person is not sick, given that the test is negative is: 0.9998

(f) When a test is 99% accurate

The accuracy of test is the measure of its sensitivity, prevalence and specificity.

So, when a test is said to be 99% accurate, it means that the test is correct, and the result is usable; irrespective of whether the result is positive or negative.