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3 years ago

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Aaron saw it was 86° Fahrenheit, F, in Australia in January. Aaron used the formula C=5/9(F−32) to find the temperature in degre

es Celsius, C. What temperature, in degrees Celsius, did Aaron find?

1 answer:

gogolik [260]3 years ago

6 0

Answer:

$30^{\circ}\text{C}$

Step-by-step explanation:

The temperature that Aaron saw was $86^{\circ}\text{F}$

The formula to convert Fahrenheit to Celsius is

$C=\dfrac{5]{9}(F-32)$

$\Rightarrow C=\dfrac{5}{9}\times (86-32)$

$\Rightarrow C=30^{\circ}\text{C}$

The given temperature in Celsius that Aaron found would be $30^{\circ}\text{C}$ .

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Answer:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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2 years ago

Help! I really need to pass!

Dmitriy789 [7]

Answer:

$\huge{ \boxed{ \bold{ \sf{y = - 2x + 6}}}}$

☥ $\tt{Question} :$

Write the equation of a line in slope - intercept form that has a slope of -2 and passes through the point ( - 1 , 8 ).

☥ $\tt{Step - \: by \: - \: step \: explanation}$

☪ $\underline{ \underline{ \text{Given : }}}$

Slope ( m ) = -2
Given point = ( - 1 , 8 )

☪ $\underline {\underline{ \text{To \: find}}} :$

Equation of a line in slope - intercept form ( i.e y = mx + c )

Let the point ( -1 , 8 ) be ( x₁ , y₁ )

☪ $\underline{ \underline{ \text{Solution}}} :$

$\underline{ \sf{y - y1 = m(x - x1)}}$

plug the known values :

↦ $\text{y - 8 = - 2 \{ x - ( - 1) \} }$

↦ $\text{y - 8 = - 2(x + 1)}$

Distribute -2 through the parentheses :

↦ $\text{y - 8 = - 2x - 2}$

Transpose 8 to right hand side and change it's sign

↦ $\text{y = - 2x - 2 + 8}$

↦ $\boxed{ \text{y = - 2x + 6}}$

And we're done !

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♡ Have a wonderful day / night ツ

~TheAnimeGirl ♪

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Answer:

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Step-by-step explanation:

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A quality control expert at LIFE batteries wants to test their new batteries. The design engineer claims they have a variance of

iris [78.8K]

Answer:

The probability that the mean battery life would be greater than 533.2 minutes (in a sample of 75 batteries) is $\\ P(z>0.48) = P(x>533.2) = 0.3156$

Step-by-step explanation:

The main thing we have to take into account in this question is that we are about to find the probability of a <em>sample mean</em>. The distribution for <em>sample means</em> follows a <em>normal distribution</em> with mean $\\ \mu$ and standard deviation $\\ \frac{\sigma}{\sqrt{n}}$ . Mathematically

$\\ \overline{x} \sim N(\mu, \frac{\sigma}{\sqrt{n}})$

For values of the sample $\\ n \ge 30$ , no matter the distribution the data come from.

And the variable <em>z</em> follows a <em>standard normal distribution</em>, and, as we can remember, this distribution has a mean = 0 and a standard deviation = 1. Mathematically

$\\ z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}$ [1]

That is

$\\ z \sim N(0, 1)$

We have a variance of 3364. That is, a <em>standard deviation</em> of

$\\ \sigma^2 = 3364; \sigma = \sqrt{3364} = 58$

The population mean is

$\\ \mu = 530$

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The sample mean is $\\ \overline{x} = 533.2$

With all this information, we can solve the question

The probability that the mean battery life would be greater than 533.2 minutes

Using equation [1]

$\\ z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}$

$\\ z = \frac{533.2 - 530}{\frac{58}{\sqrt{75}}}$

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$\\ z = \frac{3.2}{6.69726}$

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With this value of z we can consult a <em>cumulative standard normal table</em> (or use some statistic program) to find the cumulative probability for <em>z</em> (and remember that this variable follows a standard normal distribution).

Most standard normal tables have values for z for only two decimals, so we can round the previous value for z as z = 0.48.

Then

$\\ P(z$

However, in the question we are asked for $\\ P(z>0.48) = P(x>533.2)$ . As well as all normal distributions, the standard normal distribution is symmetrical around the mean, and we have

$\\ P(z>0.48) = 1 - P(z$

Thus

$\\ P(z>0.48) = 1 - 0.68439$

$\\ P(z>0.48) = 0.31561$

Rounding to four decimal places, we have

$\\ P(z>0.48) = 0.3156$

So, the probability that the mean battery life would be greater than 533.2 minutes is (in a sample of 75 batteries) $\\ P(z>0.48) = P(x>533.2) = 0.3156$ .

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