A quadratic equation is shown:x2 - 14x + 41 = 0 Which of the following is the first correct step to write the above equation in the form (x - p)2 = 9, where p and q are integers? x2 - 14x + 41 + 8 = 0 + 8 x2 - 14x + 41 + 9 = 0 + 9 x2 - 14x + 41 - 8 = 0 - 8 x2 – 14x + 41 - 9 = 0 - 9
The correct answer is the first option
The standard form of a quadratic equation is
Sometimes we need to change the expression of the same equation to the form
To accomplish that change, we usually modify the left-hand expression to make it look like the square of a binomial.
The given quadratic equation is
Recall the square of a binomial is
The first term is already present. The second term gives us the value of p:
Now we need to produce the third term . We only have 41, thus we need to add 8 to both sides of the equation:
The lengths of two sides of a triangle are 9 and 15. What can be said about the length of the third side? A. It must be greater than or equal to 6 and less than 24. B. It must be greater than or equal to 6 and at most 24. C. It must be greater than 6 and less than 24. D. It must be greater than 6 and at most 24.
Your answer is B As the sum of any 2 lengths of a triangle is always greater than the third length
Hope it helps ♥
Answer: Its C
Step-by-step explanation: Just took unit test
The Food and Drug Administration (FDA) is a U.S. government agency that regulates (you guessed it) food and drugs for consumer safety. One thing the FDA regulates is the allowable insect parts in various foods. You may be surprised to know that much of the processed food we eat contains insect parts. An example is flour. When wheat is ground into flour, insects that were in the wheat are ground up as well. The mean number of insect parts allowed in 100 grams (about 3 ounces) of wheat flour is 75. If the FDA finds more than this number, they conduct further tests to determine if the flour is too contaminated by insect parts to be fit for human consumption. The null hypothesis is that the mean number of insect parts per 100 grams is 75. The alternative hypothesis is that the mean number of insect parts per 100 grams is greater than 75. Is the following a Type I error or a Type II error or neither? The test fails to show that the mean number of insect parts is greater than 75 per 100 grams when it is. Group of answer choices Type I error Type II error
Type II error
Let's remember the definition of Type I error and Type II error:
A type I error is the rejection of a true null hypothesis, this means that we would get a "false positive" with this error.
A type II error is the non rejection of a not true null hypothesis, this error would give us a "false negative".
In this problem the mean number of insect parts per 100 grams is 75. However, the test fails to show that this number is greater than 75 when it is, this means that the test is not detecting these insect parts and therefore is giving a "false negative"
Thus, this is a Type II error.
This situation is an example of a Type II error. This occurs when the test fails to reject the null hypothesis when it should be rejected. In this context, it means the test was unable to detect the actual average content of insect parts is higher than the allowable limit.
The situation presented constitutes a Type II error in the field of hypothesis testing in statistics. A Type II error occurs when the tester fails to reject the null hypothesis when it should be rejected. In this context, it means the test failed to show that the mean number of insect parts per 100 grams is greater than 75, when in fact, it is. This can potentially mean allowing more contaminated flour into the market because the test did not pick up on the true mean being higher than 75 insect parts per 100 grams.