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3 years ago

What is a scientific theory?

2 answers:

5 0

a method of procedure that has characterized natural science since the 17th century, consisting in systematic observation, measurement, and experiment, and the formulation, testing, and modification of hypotheses.

ch4aika [34]3 years ago

5 0

Answer:

Step-by-step explanation:

A scientific theory is an explanation of an aspect of the natural world that can be repeatedly tested, in accordance with the scientific method, using a predefined protocol of observation and experiment.

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3 years ago

The local high school is hosting an ice cream social for new students. They

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3 years ago

Write an expression in factored form for the polynomial of least possible degree graphed below.

dexar [7]

Answer:

- 1/64 (x+4)² (x-3) (x-4) = 0

Step-by-step explanation:

f(x) = a (x+4)²(x-3)(x-4) ... curve touch (-4,0) and not cross x axis

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3 years ago

How many hours is 3200 seconds 3200 s =_____hrs

dezoksy [38]

Dividing by 3,600

Determine the number of seconds you have. This information should be given, or it should be a figure you calculated yourself.

For example, you might be converting 2,400 seconds into hours.

ivide the number of seconds by 3,600. Note that there are 3,600 seconds in one hour.[1] So, if you have more than 3,600 seconds, your conversion will be greater than hour. If you have less than 3,600 seconds, your conversion will be a fraction of an hour.

Convert your decimal to minutes. This step is helpful if you are working with a number of seconds equal to less than an hour, so that you can gauge how long a certain decimal is. To convert the decimal to minutes, multiply it by 60.[2]

3200 seconds = 0.88888889 Hours

(rounded to 8 digits)

6 0

2 years ago

Read 2 more answers

"A manufacturer of automobile batteries claims that the average length of life for its grade A battery is 55 months. Suppose the

STALIN [3.7K]

Answer:

$\\ P(z>-2) = 0.97725$ or P(x>49) is about 97.725% (or being less precise 97.5% using the empirical rule).

Step-by-step explanation:

We solve this question using the following information:

We are dealing here with normally distributed data, that is "the frequency distribution of the life length data is known to be mound-shaped".
The normal distribution is defined by two parameters: the population mean ( $\\ \mu$ ) and the population standard deviation ( $\\ \sigma$ ). In this case, we have that $\\ \mu = 55$ months, and $\\ \sigma = 3$ months.
To find the probabilities, we have to use the standard normal distribution, which has $\\ \mu = 0$ and $\\ \sigma = 1$ . The probabilities for this distribution are collected in the standard normal table, available in Statistics books or on the Internet. We can also use statistics programs to find these probabilities.
For most cases, we need to use the cumulative standard normal table, and for this we have to previously "transform" a raw score (x) into a z-score using the next formula: $\\ z = \frac{x - \mu}{\sigma}$ [1]. A z-score tells us the distance from the mean that a raw score is from it in standard deviations units. If this value is negative, the raw score is below the mean. Conversely, a positive value indicates that it is above the mean.
The cumulative standard normal table is made for positive values of z. Since the normal distribution is symmetrical around the mean, we can find the negative values of z using this formula: $\\ P(z$ [2].

Having all this information, we can solve the question.

<h3>The percentage of the manufacturer's grade A batteries that will last more than 49 months</h3>

First Step: Use formula [1] to find the z-score of the raw score x = 49 months.

$\\ z = \frac{49 - 55}{3}$

$\\ z = \frac{-6}{3}$

$\\ z = -2$

This means that the raw score is represented by a z-score of $\\ z = -2$ , which tells us that it is two standard deviations below the population mean.

Second Step: Consult this value in the cumulative standard normal table for z = 2 and apply the formula [2] to find the corresponding probability.

For a z = 2, the probability is 0.97725.

Then

$\\ P(z$

$\\ P(z2)$

But we are not asked for P(z<-2) but for P(z>-2) = P(x>49). This probability is the complement of the previous result, that is

$\\ P(z>-2) = 1 - P(z$

$\\ P(z>-2) = 1 - 0.02275$

$\\ P(z>-2) = 0.97725$

That is, the "percentage of the manufacturer's grade A batteries will last more than 49 months" is

$\\ P(z>-2) = 0.97725$ or about 97.725%

A graph below shows this result.

Notice that if we had used the 68-95-99.7 rule (also known as the empirical rule), that is, in a normal distribution, the interval between one standard deviation below and above the mean contains, approximately, 68% of the observations; the interval between two standard deviations below and above the mean contains, approximately, 95% of the observations; and the interval between three standard deviations below and above the mean contains, approximately, 99.7% of the observations, we could have concluded that 2.5 % of the manufacturer's grade A batteries will last less than 49 months, and, as a result, 1 - 0.025 = 0.975 or 97.5% will last more than 49 months.

We can conclude that with a less precise answer (but faster) because of the symmetry of the normal distribution, that is, 1 - 0.95 = 0.05. At both extremes we have 0.05/2 = 0.025 or 2.5% and we were asked for P(x>49) = P(z>-2) (see the graph below).

6 0

3 years ago