If the p-value is smaller than the level of significance, then it indicates strong evidence against the null hypothesis, as there is less than a 5% probability the null hypothesis is correct.
In this question,
A p-value is a probability, calculated after running a statistical test on data and it lies between 0 and 1. The p-value only tells you how likely the data you have observed is occurred under the null hypothesis.
One of the most commonly used p-value is 0.05. If the value is greater than 0.05, the null hypothesis is considered to be true. If the calculated p-value turns out to be less than 0.05, the null hypothesis is considered to be false, or nullified (hence the name null hypothesis).
A small p-value (< 0.05 in general) means that the observed results are unusual, assuming that they were due to chance only. Now, the smaller the p-value, the stronger the evidence that should reject the null hypothesis.
Hence we can conclude that if the p-value is smaller than the level of significance, then it indicates strong evidence against the null hypothesis, as there is less than a 5% probability the null hypothesis is correct.
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2. So for this question, you do the distributive property, which is multiplying the term outside of the parenthesis by the terms in the parenthesis. In this case, the outside term is 1/2. 8x * 1/2 = 4x and 1/2 * -16 is -8. That brings us to 4x - 8, which is our answer. Therefore, the correct answer choice is B.
3. Okay. In this problem, we are talking about the sum of 12 and a number. That's 12 + n, because sum means the answer to the addition problem D is out, because we don't do distributive property in this case. The sum of 12 + n is 4n. The expression is 12 + n = 4n. The answer is B.
About 450 books and articles Euler completed after he lost his sight entirely.
<h3>Who was Leonhard Euler?</h3>
Leonhard Euler was a mathematician from Switzerland. He introduced the fundamentals of graph theory and topology.
His main field of work includes number theory, mechanics, fluid mechanics, and many more.
The life span of Euler was between 1707 and 1783. In the last few years of his life, he lost the eye sight. But the eye sight loss doesn't affect him from doing his work. In his lifespan, he published around 886 books and articles on various fields or science, mathematics and engineering.
After the total blindness, he published more than 450 books and articles.
For more details about Euler, refer to the link:
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Answer:
The brown house has the longer driveway
Step-by-step explanation:
So we would need to convert both of these units of measurements to feet in order to compare them.
- There are <u>3 feet in 1 yard</u>
Converting yards to feet, wee need to multiply the number of yards by 3
Since the red house has a driveway of 7 yards and 9 feet, we can rewrite this to 21 feet + 9 feet, which is equivalent to 30 feet
Now comparing the two driveways, the 35 ft-long brown driveway is 5 feet longer than the 30 ft-long red driveway.
The brown house has the longer driveway