What math sites do you guys use? :/<br>or apps?<br><br>for me I use "Khan Academy"

What is the domain of the function f(x)= x + 1 / x^2 - 6x + 8?

VARVARA [1.3K]

Answer:
all real numbers except 4 and 2

Explanation:
The given function is:
f(x) = $\frac{x+1}{x^2-6x+8}$

Domain of the function is defined as the values of x that can be used to substitute in the function.

We know that any fraction cannot have a zero in its denominator. Because if this happens, then the fraction would be undefined.

This means that in the given function, we cannot substitute with any value for x that makes the denominator a zero.

Now, we will get the zeroes of the denominator as follows:
x² - 6x + 8 = 0
(x-4)(x-2) = 0
either x-4 = 0 ...........> x = 4
or x-2 = 0 .............> x = 2

Based on the above, we can substitute with any value for x excluding 4 and 2.

This means that the domain of the function is any real real number except 4 and 2

Hope this helps :)

7 0

3 years ago

Most individuals are aware of the fact that the average annual repair cost for an automobile depends on the age of the automobil

o-na [289]

The question is incomplete! Complete question along with answer and step by step explanation is provided below.

Question:

Most individuals are aware of the fact that the average annual repair cost for an automobile depends on the age of the automobile. A researcher is interested in finding out whether the variance of the annual repair costs also increases with the age of the automobile. A sample of 26 automobiles 4 years old showed a sample standard deviation for annual repair costs of $120 and a sample of 23 automobiles 2 years old showed a sample standard deviation for annual repair costs of $100. Let 4 year old automobiles be represented by population 1.

State the null and alternative versions of the research hypothesis that the variance in annual repair costs is larger for the older automobiles.

At a 0.01 level of significance, what is your conclusion? What is the p-value?

Answer:

Null hypotheses = H₀ = σ₁² ≤ σ₂²

Alternative hypotheses = Ha = σ₁² > σ₂²

Test statistic = 1.44

p-value = 0.1954

0.1954 > 0.01

Since the p-value is greater than the given significance level therefore, we cannot reject the null hypothesis.

We can conclude that there is no sufficient evidence to support the claim that the variance in annual repair costs is larger for older automobiles.

Step-by-step explanation:

Let σ₁² denotes the variance of 4 years old automobiles

Let σ₂² denotes the variance of 2 years old automobiles

State the null and alternative hypotheses:

The null hypothesis assumes that the variance in annual repair costs is smaller for older automobiles.

Null hypotheses = H₀ = σ₁² ≤ σ₂²

The alternate hypothesis assumes that the variance in annual repair costs is larger for older automobiles.

Alternative hypotheses = Ha = σ₁² > σ₂²

Test statistic:

The test statistic is given by

Test statistic = σ₁²/σ₂²

Test statistic = 120²/100²

Test statistic = 1.44

p-value:

The degree of freedom corresponding to 4 years old automobiles is given by

df₁ = n - 1

df₁ = 26 - 1

df₁ = 25

The degree of freedom corresponding to 2 years old automobiles is given by

df₂ = n - 1

df₂ = 23 - 1

df₂ = 22

Using Excel to find out the p-value,

p-value = FDIST(F-value, df₁, df₂)

p-value = FDIST(1.44, 25, 22)

p-value = 0.1954

Conclusion:

When the p-value is less than the significance level then we reject the Null hypotheses

p-value < α (reject H₀)

But for the given case,

p-value > α

0.1954 > 0.01

Since the p-value is greater than the given significance level therefore, we cannot reject the null hypothesis.

We can conclude that there is no sufficient evidence to support the claim that the variance in annual repair costs is larger for older automobiles.

8 0

3 years ago

Chas build a circular pattern for his dog The radius of the pen is 9 feet how much fencing did Chaz use for the pen

kicyunya [14]

Answer:

The fencing Chaz used for the pen is 56.67 feet

Step-by-step explanation:

Fencing interprets to circumference

If the radius of the pen is 9 ft

circumference = $2\pi r$

= 2*(22/7)*9

= 396/7

= 56.67 ft

3 0

2 years ago

.

Vika [28.1K]

Answer:

the answer would be 4/10 but the simplified version would be 2/5.

Step-by-step explanation:

add up how many bows you have, that will be the denominator. Then, the numerator is the number of purple bows. and if your going to simplify it divide the numerator and denominator by 2.

5 0

3 years ago

Read 2 more answers

Jon has 6 kites he and his friends will each fly one kite how many people in all will fly a kit

True [87]

Answer:

6

Step-by-step explanation:

One person will fly a kite for each of the 6 kites Jon has.

6 people in all will fly a kite.

6 0

2 years ago

What math sites do you guys use? :/or apps?for me I use "Khan Academy"​

What math sites do you guys use? :/or apps?for me I use "Khan Academy"