Write down a pair of integers whose sum is –3

Mathematics

2 answers:

inysia [295]3 years ago

7 0

The pair is any numbers, 1 positive and one negative, that add up to -3.
Here is a sample;
(-5, 2)

Vadim26 [7]3 years ago

3 0

Answer:

The pair of two integers such that their sum is -3 are : 6 and -9

Step-by-step explanation:

Integers : This includes the set of all counting numbers and their additive inverses . This set is denoted by Z

Now, we need to find the pair of integers such that their sum is -3

Let x be any integer and the second integer by y

Let x = 6

Now, x + y = -3

⇒ 6 + y = -3

⇒ y = -9

So, The required pair of integers is : 6 and -9

Hence, The pair of two integers such that their sum is -3 are : 6 and -9

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The Ohio Department of Agriculture tested 203 fuel samples across the state

Rus_ich [418]

Answer:

$\hat p = \frac{14}{105}= 0.133$

And that represent the proportion of failures.

The confidence interval for the mean is given by the following formula:

$\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$

If we replace the values obtained we got:

$0.133 - 2.58\sqrt{\frac{0.133(1-0.133)}{105}}=0.0475$

$0.133 + 2.58\sqrt{\frac{0.133(1-0.133)}{105}}=0.2185$

The 99% confidence interval would be given by (0.0475;0.2185)

Step-by-step explanation:

Previous concept

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

Solution to the problem

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 99% of confidence, our significance level would be given by $\alpha=1-0.99=0.01$ and $\alpha/2 =0.005$ . And the critical value would be given by: