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zlopas [31]
2 years ago
14

Reabilwe is conducting an experiment in which the temperature is measured carefully. The temperature was 106°C at the end of the

first minute, and then it falls by 6°C every minute after that.
Determine a formula to calculate the temperature (T) after m minutes.
Mathematics
1 answer:
frosja888 [35]2 years ago
5 0

The formula to calculate the temperature (T) after m minutes is -

T = 106 - 6m

We have Reabilwe who is conducting an experiment in which the temperature is measured carefully. The temperature was 106°C at the end of the first minute, and then it falls by 6°C every minute after that.

We have to tp determine a formula to calculate the temperature (T) after m minutes.

<h3 /><h3>Starting from x, if the bacteria count rises by 5 every second, then determine the formula to calculate the bacteria count after 30 seconds.</h3>

Initial count = x

Count increasing per second = 5

Assume that the bacteria count after t seconds is y. Then -

y = x + 5t

for t = 30 ↔ y = 150 + x

According to question, we have -

Initial Temperature = 106 degrees Celsius

Temperature increase per minute = 6 degrees Celsius

Assume that the Temperature fall after m minutes is T. Then -

T = 106 - 6m

Hence, formula to calculate the temperature (T) after m minutes is -

T = 106 - 6m

To solve more questions on Equation Modelling, visit the link below -

brainly.com/question/20876878

#SPJ1

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Find the area of a triangle with a base of 7.5 m and a height of 4*
oksian1 [2.3K]

Answer:

15 units²

Step-by-step explanation:

Hi there!

A=\displaystyle\frac{1}{2} bh where <em>b</em> is the base and <em>h</em> is the height

Plug in the base (7.5) and height (4):

A=\displaystyle\frac{1}{2} (7.5)(4)\\\\A=\displaystyle\frac{1}{2} (30)\\\\A=15

Therefore, the area of the triangle is 15 units².

I hope this helps!

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HHHH HHHT HTHH HHTT HHTH HTHT HTTH HTTT TTTT TTTH THTT TTHH TTHT THTH THHT THHH What is the probability that at least three coin
faust18 [17]

Answer:

5/16

Step-by-step explanation:

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6 0
2 years ago
The CPA Practice Advisor reports that the mean preparation fee for 2017 federal income tax returns was $273. Use this price as t
skad [1K]

Answer:

a) 0.6212 = 62.12% probability that the mean price for a sample of 30 federal income tax returns is within $16 of the population mean.

b) 0.7416 = 74.16% probability that the mean price for a sample of 50 federal income tax returns is within $16 of the population mean.

c) 0.8804 = 88.04% probability that the mean price for a sample of 100 federal income tax returns is within $16 of the population mean.

d) None of them ensure, that one which comes closer is a sample size of 100 in option c), to guarantee, we need to keep increasing the sample size.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

The CPA Practice Advisor reports that the mean preparation fee for 2017 federal income tax returns was $273. Use this price as the population mean and assume the population standard deviation of preparation fees is $100.

This means that \mu = 273, \sigma = 100

A) What is the probability that the mean price for a sample of 30 federal income tax returns is within $16 of the population mean?

Sample of 30 means that n = 30, s = \frac{100}{\sqrt{30}}

The probability is the p-value of Z when X = 273 + 16 = 289 subtracted by the p-value of Z when X = 273 - 16 = 257. So

X = 289

Z = \frac{X - \mu}{\sigma}

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

Z = \frac{289 - 273}{\frac{100}{\sqrt{30}}}

Z = 0.88

Z = 0.88 has a p-value of 0.8106

X = 257

Z = \frac{X - \mu}{s}

Z = \frac{257 - 273}{\frac{100}{\sqrt{30}}}

Z = -0.88

Z = -0.88 has a p-value of 0.1894

0.8106 - 0.1894 = 0.6212

0.6212 = 62.12% probability that the mean price for a sample of 30 federal income tax returns is within $16 of the population mean.

B) What is the probability that the mean price for a sample of 50 federal income tax returns is within $16 of the population mean?

Sample of 30 means that n = 50, s = \frac{100}{\sqrt{50}}

X = 289

Z = \frac{X - \mu}{\sigma}

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

Z = \frac{289 - 273}{\frac{100}{\sqrt{50}}}

Z = 1.13

Z = 1.13 has a p-value of 0.8708

X = 257

Z = \frac{X - \mu}{s}

Z = \frac{257 - 273}{\frac{100}{\sqrt{50}}}

Z = -1.13

Z = -1.13 has a p-value of 0.1292

0.8708 - 0.1292 = 0.7416

0.7416 = 74.16% probability that the mean price for a sample of 50 federal income tax returns is within $16 of the population mean.

C) What is the probability that the mean price for a sample of 100 federal income tax returns is within $16 of the population mean?

Sample of 30 means that n = 100, s = \frac{100}{\sqrt{100}}

X = 289

Z = \frac{X - \mu}{\sigma}

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

Z = \frac{289 - 273}{\frac{100}{\sqrt{100}}}

Z = 1.6

Z = 1.6 has a p-value of 0.9452

X = 257

Z = \frac{X - \mu}{s}

Z = \frac{257 - 273}{\frac{100}{\sqrt{100}}}

Z = -1.6

Z = -1.6 has a p-value of 0.0648

0.9452 - 0.0648 =

0.8804 = 88.04% probability that the mean price for a sample of 100 federal income tax returns is within $16 of the population mean.

D) Which, if any of the sample sizes in part (a), (b), and (c) would you recommend to ensure at least a .95 probability that the same mean is withing $16 of the population mean?

None of them ensure, that one which comes closer is a sample size of 100 in option c), to guarantee, we need to keep increasing the sample size.

6 0
2 years ago
What does 23/2 reduce down to in its simplest form?
Lunna [17]

To simplify this improper fraction we can turn it into a mixed number. The fact that the denominator is 2 and the numerator isn't divisible by 2 shows that it can't simplified any further as a improper fraction.

23/2 = 11 1/2

Best of Luck!

5 0
3 years ago
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