MATHEMATICS COLLEGE

What is the domain of the function f (x) = StartFraction x + 1 Over x squared minus 6 x + 8 EndFraction?

Answers

Answer 1

Answer:

Answer:

D Edg

Step-by-step explanation:

all real numbers except 2 and 4

Answer 2

Answer:

Answer: (-∞, 2)∪(2, 3]∪(4, ∞)

Step-by-step explanation:

Domain is the allowed x values in the function. The numerator, x + 1 will be defined for all numbers. But that fraction wont be, the minute that fractions denominator is equal to zero, your entire function becomes undefined.

So lets figure out what number will make this undefined. Then we'll know the functions domain is everywhere but that x value.

Make x^2 - 6x + 8 = 0

What two numbers multiply to equal +8 but add to equal -6? Thats -4 and -2.

(x - 4)(x - 2) = 0 This means the function is undefined when x equals 4 and 2

(-∞, 2)∪(2, 3]∪(4, ∞)

Related Questions

Please help a homie out
Help me please! It’s number 45.
Plz help with all the questions
Rewrite the expression without using a negative exponent.12x^−4 Simplify your answer as much as possible.
Body temperature (in degrees Fahrenheit) of randomly selected normal and healthy adults are shown below. Compute the mean, median, and mode of the data set.98.198.698.798.598.098.298.099.098.098.8The mean is °F.(Round to the nearest hundredth as needed.)

You are the operations manager for an airline and you are considering a higher fare level for passengers in aisle seats. How many randomly selected air passengers must you survey? Assume that you want to be 99% confident that the sample percentage is within 5.5 percentage points of the true population percentage. Complete parts (a) and (b) below. a. Assume that nothing is known about the percentage of passengers who prefer aisle seats. nequals 549 (Round up to the nearest integer.) b. Assume that a prior survey suggests that about 34% of air passengers prefer an aisle seat. nequals nothing (Round up to the nearest integer.)

Answers

Answer:

a) $n=(0.5(1-0.5))/(((0.055)/(2.58))^2)=550.116$

And rounded up we have that n=551

b) $n=(0.34(1-0.34))/(((0.055)/(2.58))^2)=493.78$

And rounded up we have that n=494

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

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

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 $\alpha/2 =0.05$ . And the critical value would be given by:

$z_(\alpha/2)=-2.58, t_(1-\alpha/2)=2.58$

Part a

The margin of error for the proportion interval is given by this formula:

$ME=z_(\alpha/2)\sqrt{(\hat p (1-\hat p))/(n)}$ (a)

And on this case we have that $ME =\pm 0.05$ and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=(\hat p (1-\hat p))/(((ME)/(z))^2)$ (b)

We can assume that $\hat p =0.5$ since we don't know prior info. And replacing into equation (b) the values from part a we got:

$n=(0.5(1-0.5))/(((0.055)/(2.58))^2)=550.116$

And rounded up we have that n=551

Part b

$n=(0.34(1-0.34))/(((0.055)/(2.58))^2)=493.78$

And rounded up we have that n=494

Final answer:

To determine the required sample size for the survey, we can use a sample size formula based on the desired confidence level and margin of error. If nothing is known about the passenger preferences, a sample size of 549 would be needed. If a prior survey suggests a certain proportion, the sample size can be calculated using the known proportion.

Explanation:

In order to determine the number of randomly selected air passengers that must be surveyed, we need to calculate the required sample size for a desired confidence level and margin of error.

a. If nothing is known about the percentage of passengers who prefer aisle seats, we can use a sample size formula given by n = (Z^2 * p * q) / E^2, where Z is the z-score corresponding to the desired confidence level, p and q are the estimated proportions for aisle seat preference and non-aisle seat preference respectively, and E is the desired margin of error. Since a confidence level of 99% and a margin of error of 5.5% are specified, we can round up the sample size to 549.

b. If a prior survey suggests that about 34% of air passengers prefer an aisle seat, we can use the same sample size formula but with the known proportion p = 0.34. We do not have information about the non-aisle seat preference, so we cannot determine the required sample size.

Learn more about Sample size calculation here:

brainly.com/question/34288377

#SPJ11

What are the zeroes of f(x) = y2 - 2x - 3?

Answers

Answer:

Step-by-step explanation:

Product = -3

Sum = -2

Factors = -3 , 1

y² - 2y - 3 = y² + y - 3y - 3

= y( y + 1) - 3(y + 1)

= (y +1) (y - 3)

Answer:

x=y^2/2 - 3/2

Step-by-step explanation:

Identify the roots of gx= x2+3x-4 x^2-4x+29

Answers

Answer:

x1=1

x2= -4

x3= (2 + 5i)

x4= (2 - 5i)

Step-by-step explanation:

STEP 1-

Find the roots of the first term.

(x^2 + 3x -4)=0

Then group the terms that contain the same variable, and move the constant to the opposite side of the equation.

(x^2 + 3x)=4

Complete the square. Remember to balance the equation by adding the same constants to each side.

(x^2 + 3x + 1.5^2)=4 + 1.5^2

(x^2 + 3x + 1.5^2)=6.25

Rewrite as perfect squares

(x + 1.5)^2=6.25

Square root both sides.

(x + 1.5) = (+/-)2.5

x= -1.5(+/-)2.5

x= -1.5 + 2.5 = 1

x= -1.5 + 2.5= -4

so the factored form of the first term.

(x^2 + 3x + 4) = (x - 1) (x + 4)

STEP 2-

Find the roots of the second term

(x^2 - 4x + 29)= 0

Group terms that contain the same variable, and move the constant to the opposite side of the equation

(x^2 - 4x)= -29

Complete the square. Remember to balance the equation by adding the same constants to each side

(x^2 - 4x + 4) = - 29 + 4

(x^2 -4x + 4) = -25

Rewrite as perfect squares

(x - 2)^2 = -25

Remember that

i = square root of -1

Square root both sides

(x - 2) = (+/-)5i

x= 2 (+/-)5i

x= 2 + 5i

x= 2 - 5i

so the factored form of the second term is

(x^2 - 4x + 29) = (x - (2 + 5i))(x - (2 - 5i))

STEP 3-

Substitute the factored form of the first and second term in g(x)

g(x) = (x-1)(x + 4)(x- (2+ 5i))(x- ( 2-5i)

there for you have your answers

Part A Each time you press F9 on your keyboard, you see an alternate life for Jacob, with his status for each age range shown as either alive or dead. If the dead were first to appear for the age range of 75 to 76, for example, this would mean that Jacob died between the ages of 75 and 76, or that he lived to be 75 years old. Press F9 on your keyboard five times and see how long Jacob lives in each of his alternate lives. How long did Jacob live each time? Part B The rest of the potential clients are similar to Jacob, but since they’ve already lived parts of their lives, their status will always be alive for the age ranges that they’ve already lived. For example, Carol is 44 years old, so no matter how many times you press F9 on your keyboard, Carol’s status will always be alive for all the age ranges up to 43–44. Starting with the age range of 44–45, however, there is the possibility that Carol’s status will be dead. Press F9 on your keyboard five more times and see how long Carol lives in each of her alternate lives. Remember that she will always live to be at least 44 years old, since she is already 44 years old. How long did Carol live each time? Part C Now you will find the percent survival of each of your eight clients to the end of his or her policy using the simulation in the spreadsheet. For each potential client, you will see whether he or she would be alive at the end of his or her policy. The cells in the spreadsheet that you should look at to determine this are highlighted in yellow. Next, go to the worksheet labeled Task 2b and record either alive or dead for the first trial. Once you do this, the All column will say yes if all the clients were alive at the end of their policies or no if all the clients were not alive at the end of their policies. Were all the clients alive at the end of their policies in the first trial? Part D Next, go back to the Task 2a worksheet, press F9, and repeat this process until you have recorded 20 trials in the Task 2b worksheet. In the Percent Survived row at the bottom of the table on the Task 2b worksheet, it will show the percentage of times each client survived to the end of his or her policy, and it will also show the percentage of times that all of the clients survived to the end of their respective policies. Check to see whether these percentages are in line with the probabilities that you calculated in questions 1 through 9 in Task 1. Now save your spreadsheet and submit it to your teacher using the drop box. Are your probabilities from the simulation close to the probabilities you originally calculated?

Answers

Answer:

Jacob:

Alive 69-70

alive 79-80

alive 62-63

alive 73-74

alive 78-Died 79

Carol:

alive 88-89

alive 67-68

alive 99-100

alive 73-74

alive 94- Died 95

Step-by-step explanation:

Bill and Ben each have three cards numbered 4,5,6 they each take one of their own cards then they add the two numbers on the cards what is the probability that their answer is an odd number. What is the probability that their answer is a number less than 11.