Given $f(x) = \frac{\sqrt{2x-6}}{x-3}$, what is the smallest possible integer value for $x$ such that $f(x)$ has a real number value? please show steps. Thank you!

Answers

Answer 1

Given:

The function is:

[tex]f(x)=\dfrac{\sqrt{2x-6}}{x-3}[/tex]

To find:

The smallest possible integer value for $x$ such that $f(x)$ has a real number value.

Solution:

We have,

[tex]f(x)=\dfrac{\sqrt{2x-6}}{x-3}[/tex]

This function is defined if the radicand is greater than or equal to 0, i.e., [tex]2x-6\geq 0[/tex] and the denominator is non-zero, i.e., [tex]x-3\neq 0[/tex].

[tex]2x-6\geq 0[/tex]

[tex]2x\geq 6[/tex]

[tex]\dfrac{2x}{2}\geq \dfrac{6}{2}[/tex]

[tex]x\geq 3[/tex]             ...(i)

And,

[tex]x-3\neq 0[/tex]

Adding 3 on both sides, we get

[tex]x-3+3\neq 0+3[/tex]

[tex]x\neq 3[/tex]             ...(ii)

Using (i) and (ii), it is clear that the function is defined for all real values which are greater than 3 but not 3.

Therefore, the smallest possible integer value for x is 4.


Related Questions

See above. okokokoookkokokokokkkkokokkokokkok

Answers

Answer:

B

Step-by-step explanation:

B is the correct answer

i spend 3 hours a day out of a 8 hour shift, what percentage is that

Answers

Answer:

0.375 = 38%

Step-by-step explanation:

Just divide 3 from 8 and that will give you 0.375

Then you round that to the nearest  one which is 38 and

that will get your percentage

Answer: 37.5%

Step-by-step explanation: I just divided 3 by 8 then once I got my answer I moved the decimal point over to the right by 2.

Which of the following pairs of functions are inverses of each other?
O A. f(x) = 8x? - 10 and g(x) = x +10
8
B. f(x) = {+8 and g(x) = 2x - 8
O C. f(x) = 18 - 9 and g(x) =
O D. f(x) = 3x2 +16 and g(x) = -
18
X+9
16

Answers

Answer:

A is the answer I guess so...

The functions f(x) = 18/x -9 and g(x) = 18/x+9 are inverse to each other.

What is a function?

A relation is a function if it has only One y-value for each x-value.

The  given function f(x)= 18/x - 9

Let us replace f(x) by y

y=18/x - 9

Now  x=18/y-9

Add 9 on both sides

x+9=18/y

Apply cross multiplication

y(x+9)=18

Divide both sides by x+9

y=18/(x+9)

f⁻¹(x)=18/(x+9)

Hence, the functions f(x) = 18/x -9 and g(x) = 18/x+9 are inverse to each other.

To learn more on Functions click:

https://brainly.com/question/30721594

#SPJ7

Suppose the daily customer volume at a call center has a normal distribution with mean 5,500 and standard deviation 1,000. What is the probability that the call center will get between 4,800 and 5,000 calls in a day

Answers

Answer:

0.0665 = 6.65% probability that the call center will get between 4,800 and 5,000 calls in a day.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean 5,500 and standard deviation 1,000.

This means that [tex]\mu = 5500, \sigma = 1000[/tex]

What is the probability that the call center will get between 4,800 and 5,000 calls in a day?

This is the p-value of Z when X = 5000 subtracted by the p-value of Z when X = 4800. So

X = 5000

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{5000 - 5500}{1000}[/tex]

[tex]Z = -0.5[/tex]

[tex]Z = -0.5[/tex] has a p-value of 0.3085.

X = 4800

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{4800 - 5500}{1000}[/tex]

[tex]Z = -0.7[/tex]

[tex]Z = -0.7[/tex] has a p-value of 0.2420.

0.3085 - 0.2420 = 0.0665

0.0665 = 6.65% probability that the call center will get between 4,800 and 5,000 calls in a day.

Consumer products are required by law to contain at least as much as the amount printed on the package. For example, a bag of potato chips that is labeled as 10 ounces should contain at least 10 ounces.Assume that the standard deviation of the packaging equipment yields a bag weight standard deviation of 0.2 ounces. Assume the bag weight distribution is bell-shaped. Determine what average bag weight must be used to achieve at least 99 percent of the bags having 10 or more ounces in the bag.

Answers

Answer:

The average bag weight must be used to achieve at least 99 percent of the bags having 10 or more ounces in the bag=9.802

Step-by-step explanation:

We are given that

Standard deviation, [tex]\sigma=0.2[/tex]ounces

We have to find the average bag weight must be used to achieve at least 99 percent of the bags having 10 or more ounces in the bag.

[tex]P(x\geq 10)=0.99[/tex]

Assume the bag weight distribution is bell-shaped

Therefore,

[tex]P(\frac{x-\mu}{\sigma}\geq 10)=0.99[/tex]

We know that

[tex]z=\frac{x-\mu}{\sigma}[/tex]

Using the value of z

Now,

[tex]\frac{10-\mu}{0.2}=0.99[/tex]

[tex]10-\mu=0.99\times 0.2[/tex]

[tex]\mu=10-0.99\times 0.2[/tex]

[tex]\mu=9.802[/tex]

Hence, the average bag weight must be used to achieve at least 99 percent of the bags having 10 or more ounces in the bag=9.802

Which explains whether or not the graph represents a direct variation?

Answers

Answer:

The slope is 3 and equation of the line is y=3x. I think the answer is the 1st option

Step-by-step explanation:

Given:

y=3x

Direct variation equations have the form:

y=kx,

where

k is the constant of proportionality

so k=3

Given C(4, 3) and D(-4, -3) are two points on a circle, centered at the origin. Given
that CD is a diameter of the circle,
a) Find the radius of the circle.

b) State the equation of the circle

Answers

Answer:000

Step-by-step explanation:000

Construct the confidence interval for the population standard deviation for the given values. Round your answers to one decimal place. n=21 , s=3.3, and c=0.9

Answers

Answer:

The correct answer is "[tex]2.633< \sigma < 4.480[/tex]".

Step-by-step explanation:

Given:

n = 21

s = 3.3

c = 0.9

now,

[tex]df = n-1[/tex]

    [tex]=20[/tex]

⇒ [tex]x^2_{\frac{\alpha}{2}, n-1 }[/tex] = [tex]x^2_{\frac{0.9}{2}, 21-1 }[/tex]

                  = [tex]31.410[/tex]

⇒ [tex]x^2_{1-\frac{\alpha}{2}, n-1 }[/tex] = [tex]10.851[/tex]

hence,

The 90% Confidence interval will be:

= [tex]\sqrt{\frac{(n-1)s^2}{x^2_{\frac{\alpha}{2}, n-1 }} } < \sigma < \sqrt{\frac{(n-1)s^2}{x^2_{1-\frac{\alpha}{2}, n-1 }}[/tex]

= [tex]\sqrt{\frac{(21-1)3.3^2}{31.410} } < \sigma < \sqrt{\frac{(21.1)3.3^2}{10.851} }[/tex]

= [tex]\sqrt{\frac{20\times 3.3^2}{31.410} } < \sigma < \sqrt{\frac{20\times 3.3^2}{10.851} }[/tex]

= [tex]2.633< \sigma < 4.480[/tex]

i need the answer no explanation

Answers

Answer:

the answer is option D because it cant be division or multiplication and minus does not work

Answer:

log 1/9 * log k

Step-by-step explanation:

[tex]\frac{1}{9} /k[/tex] = 1/9 * k/1 = 1/9 * k

1289 +(-1236) + (2434) =
0 -1431
O 2345
O 2487
0 -1956

Answers

Answer:

This answer is 2487

which will be the third one

Hope this help

How
many solutions are there to the equation below?
4(x - 5) = 3x + 7
A. One solution
B. No solution
O C. Infinitely many solutions
SUB

Answers

Answer:

A one solution

Step-by-step explanation:

4(x - 5) = 3x + 7

Distribute

4x - 20 = 3x+7

Subtract 3x from each side

4x-3x-20 = 3x+7-3x

x -20 = 7

Add 20 to each side

x -20+20 = 7+20

x = 27

There is one solution

Answer:

Step-by-step explanation:

Let's simplify that before we make the decision, shall we? We'll get rid of the parenthesis by distribution and then combine like terms.

4x - 20 = 3x + 7 and combining like terms and getting everything on one side of the equals sign:

1x - 27 = 0. Since that x has a power of 1 on it (linear), that means we have only 1 solution. If that was an x², we would have 2 solutions; if that was an x³, we would have 3 solutions, etc.

To make concrete, the ratio of cement to sand is 1 : 3. If cement and sand are sold in bags of equal mass, how many bags of cement are required to make concrete using 15 bags of sand?

Answers

Answer:

5 bags of cement are required.

Step-by-step explanation:

Since to make concrete, the ratio of cement to sand is 1: 3, if cement and sand are sold in bags of equal mass, to determine how many bags of cement are required to make concrete using 15 bags of sand the following calculation must be done:

Cement = 1

Sand = 3

3 = 15

1 = X

15/3 = X

5 = X

Therefore, 5 bags of cement are required.

Evaluate the expression when a=-7 and y=3 3y-a

Answers

Answer:

3y-a

3.3-7

9-7

2

Step-by-step explanation:

first we have to do multiply by replacing the value of y and the subtract by using the value of a.

Hope this will be helpful for you

Find x and explain how you found x

Answers

Answer:

x=60

Step-by-step explanation:

There are different ways to find x but this is what I found easiest.

To solve first note that AOD and CFB are vertical angles; this means that they are congruent. AOD consists of two angles with the measurements of 90 and x. CFB consists of two angles with the measurements of 30 and 2x. So, to find x set add the adjacent angles and set them equal to the other pair of angles. The equation would be [tex]90+x=30+2x[/tex]. First, subtract x from both sides; this makes the equation [tex]90=30+x[/tex]. Then, subtract 30 from both sides. This gives the final answer, x=60.

what is the quotient 3/8 ÷5/12

Answers

Answer:

9/10

Step-by-step explanation:

3/8 ÷5/12

Copy dot flip

3/8 * 12/5

Rewriting

3/5 * 12/8

3/5 * 3/2

9/10

answer this question

Answers

Answer:

(-2, 13) (-1,8) (0, 5) (1, 4) (2, 5) (3, 8)

(2.4 , 6) or (-0.4, 6)

Step-by-step explanation:

Graph y = 6 on top of y = [tex]x^{2}[/tex] -2x + 5 and use the points where the two lines meet.

Brendan has $65 worth of balloons and flowers delivered to his mother. He pays the bill plus an 8.5% sales tax and an 18% tip on the total cost including tax. He also pays a $10 delivery fee that is charged after the tax and tip. How much change does he receive if he pays with two $50 bills? Round to the nearest cent.

Answers

Answer:

its 6.78 i believe

Step-by-step explanation:

What type of object is pictured below?
O A. Point
O B. Ray
C. Segment
D. Line

Answers

Answer:

It is a ray because there are two points with a line passing through them which is extenging on one side but not on the other.

It would be b, a ray

Help Please ASAP!!! Not sure how to solve this problem. Can someone help me please? Thank you for your help!

Answers

Answer:

This question is formatted incorrectly

Step-by-step explanation:

uhhh I think something is wrong here

7/18 - 1/3 , 1/2 - 1/5 - 1/10 and 3 1/2 - 2 5/9 please help thank you ​

Answers

Answer:

Step-by-step explanation:

7/18=7/18

it cant be divided agian

1/3=1/3

it cant be divded agian

1/5=1/5

it cant be divded agian

1/10=1/10

it cant be divded agian

3 1/2=3/2

2 5/9 =10/9

i am not sure if this is what you wanted ...

Is this true or false ??

Answers

Answer:  True

=============================================================

Explanation:

We'll use these two properties of integrals [tex]\displaystyle \text{If f(x) is an even function, then } \int_{-a}^{a}f(x)dx = 2\int_{0}^{a}f(x)dx[/tex]

[tex]\displaystyle \text{If f(x) is an odd function, then } \int_{-a}^{a}f(x)dx = 0[/tex]

These properties are valid simply because of the function's symmetry. For even functions, we have vertical axis symmetry about x = 0; while odd functions have symmetry about the origin.

------------------------

Here's how the steps could look

[tex]\displaystyle \int_{-7}^{7}(ax^8+bx+c)dx=\int_{-7}^{7}((ax^8+c)+bx)dx\\\\\\\displaystyle \int_{-7}^{7}(ax^8+bx+c)dx=\int_{-7}^{7}(ax^8+c)dx+\int_{-7}^{7}(bx)dx\\\\\\\displaystyle \int_{-7}^{7}(ax^8+bx+c)dx=\left(2\int_{0}^{7}(ax^8+c)dx\right)+(0)\\\\\\\displaystyle \int_{-7}^{7}(ax^8+bx+c)dx=2\int_{0}^{7}(ax^8+c)dx\\\\\\[/tex]

Therefore, the given statement is true. The values of a,b,c don't matter. You could replace those '7's with any real number you want and still end up with a true statement.

We can see that ax^8+c is always even, while bx is always odd.

------------------------

Side note:

For the second step, I used the idea that [tex]\int(f(x)+g(x))dx=\int f(x)dx+\int g(x)dx\\\\[/tex]

which allows us to break up a sum into smaller integrals.

True
Good job and hope you have a good day

1/4 + 4/10 what is the answer plz give correct

Answers

Answer:

0.65 is the correct answer

Step-by-step explanation:

hopes it helps

Hi there!  

»»————- ★ ————-««

I believe your answer is:  

[tex]\boxed{\frac{13}{20}}[/tex]

»»————- ★ ————-««  

Here’s why:  

⸻⸻⸻⸻

[tex]\boxed{\text{Calculating the answer...}}\\\\\frac{1}{4} +\frac{4}{10}\\------------\\LCM(4,10) = 20\\\\\rightarrow \frac{1}{4}=\frac{1*5}{4*5} = \frac{5}{20}\\\\\rightarrow \frac{4}{10}=\frac{4*2}{10*2}=\frac{8}{20}\\\\\\\rightarrow\frac{5}{20}+ \frac{8}{20} = \boxed{\frac{13}{20}}\\\\\\\text{The answer is in it's simplest form.}[/tex]

⸻⸻⸻⸻

»»————- ★ ————-««  

Hope this helps you. I apologize if it’s incorrect.    

Use the distributive property to remove the parentheses.
-5(6u - 4w-2)

Answers

Answer:

-30u + 20w + 10

Step-by-step explanation:

Answer:

-30u+20w+10

Step-by-step explanation:

multiple each term inside the parenthesis by -5. remember negative times negative = positive

plzz help with this question

Answers

Answer: 51 liters of fuel are required

Step by step: start by seeing how many times 476 can go into 1428

(1428/476=3)

Then take your sum of that and multiply it by 17 since that’s the number that correlates with 476

(17x3=51) therefore your answer is 51 liters

which relation is a function?

Answers

Answer:

Choice A.

Step-by-step explanation:

Every other choice has multiple of the same x-values that have different corresponding y-values.

Point P is plotted on the coordinate grid. If point S is 12 units to the left of point P, what are the coordinates of point S? On a coordinate grid from negative 12 to positive 12 in increments of 2, a point P is plotted at the ordered pair 6, negative 4. (6, −16) (−6, −16) (−6, −4) (6, 4)

Answers

9514 1404 393

Answer:

  (−6, −4)

Step-by-step explanation:

Translating a point 12 units left subtracts 12 from its x-coordinate.

  P(6, -4) +(-12, 0) = S(-6, -4)

A company manufactures televisions. The average weight of the televisions is 5 pounds with a standard deviation of 0.1 pound. Assuming that the weights are normally distributed, what is the weight that separates the bottom 10% of weights from the top 90%?​

Answers

Answer:

[tex]0.2564\text{ pounds}[/tex]

Step-by-step explanation:

The 90th percentile of a normally distributed curve occurs at 1.282 standard deviations. Similarly, the 10th percentile of a normally distributed curve occurs at -1.282 standard deviations.

To find the [tex]X[/tex] percentile for the television weights, use the formula:

[tex]X=\mu +k\sigma[/tex], where [tex]\mu[/tex] is the average of the set, [tex]k[/tex] is some constant relevant to the percentile you're finding, and [tex]\sigma[/tex] is one standard deviation.

As I mentioned previously, 90th percentile occurs at 1.282 standard deviations. The average of the set and one standard deviation is already given. Substitute [tex]\mu=5[/tex], [tex]k=1.282[/tex], and [tex]\sigma=0.1[/tex]:

[tex]X=5+(1.282)(0.1)=5.1282[/tex]

Therefore, the 90th percentile weight is 5.1282 pounds.

Repeat the process for calculating the 10th percentile weight:

[tex]X=5+(-1.282)(0.1)=4.8718[/tex]

The difference between these two weights is [tex]5.1282-4.8718=\boxed{0.2564\text{ pounds}}[/tex].

Answer:

0.2564

Step-by-step explanation:

90th percentile, we use the formula X=μ + Zσ,

Where u = mean and  sigma = standard deviation and Z = 1.282

The mean is 5 and sigma = .1

X = 5+1.282(.1)

X = 5.1282

10th percentile, we use the formula X=μ + Zσ,

Where u = mean and  sigma = standard deviation and Z = -1.282

The mean is 5 and sigma = .1

X = 5-1.282(.1)

X = 4.8718

The difference is

5.1282 - 4.8718

0.2564

A​ half-century ago, the mean height of women in a particular country in their 20s was inches. Assume that the heights of​ today's women in their 20s are approximately normally distributed with a standard deviation of inches. If the mean height today is the same as that of a​ half-century ago, what percentage of all samples of of​ today's women in their 20s have mean heights of at least ​inches?

Answers

Answer:

0.26684

Step-by-step explanation:

Given that :

Mean, μ = 62.5

Standard deviation, σ = 1.96

P(Z ≥ 63.72)

The Zscore = (x - μ) / σ

P(Z ≥ (x - μ) / σ)

P(Z ≥ (63.72 - 62.5) / 1. 96) = P(Z ≥ 0.6224)

P(Z ≥ 0.6224) = 1 - P(Z < 0.6224)

1 - P(Z < 0.6224) = 1 - 0.73316 = 0.26684

The firm has bonds with par value of 10,000,000 VND, coupon rate of 11%, annual interest payment, and the remaining maturity period is 07 years. If the bond's interest rate and current risk level have a return rate of 12%, what price should company C sell the bond in the present?

a.
10,000,000

b.
14,152,000

c.
12,053,000

d.
11,150,000

Answers

It should be letter b

Which of the following is the most accurate statement about statistics?

a) We can absolutely be 100% certain in accurately generalizing the characteristics of entire population based on the sample data

b) By analyzing data, we may be able to identify connections and relationships in our data

c) We can explore in the midst of variation to better understand our data

d) limited data or experience likely generates less confidence

e) Non of the above

Answers

Answer:

b) By analyzing data, we may be able to identify connections and relationships in our data.

Step-by-step explanation:

In statistics decisions are based on probability sampling distributions. As statics is collection and analysis of data along with its interpretation and presentation.
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