What is the answer
5 10 25 100 × ÷ ÷

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Explanation:

The given function is

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

which is the same as writing f(x) = ( sqrt(2x-6) )/(x-3)

The key for now is the square root term. Specifically, the stuff underneath. This stuff is called the radicand.

Recall that the radicand cannot be negative, or else the square root stuff will result in a complex number. Eg: [tex]\sqrt{-4} = 0+2i[/tex]

The question is basically asking: what is the smallest x such that [tex]\sqrt{2x-6}[/tex] is a real number?

Well if we made 2x-6 as small as possible, ie set it equal to 0, then we can find the answer

[tex]2x-6 = 0\\\\2x = 6\\\\x = 6/2\\\\x = 3\\\\[/tex]

I set the radicand equal to 0 because that's as small as the radicand can get (otherwise, we're dipping into negative territory).

So 2x-6 set equal to 0 leads to x = 3.

This means x = 3 produces the smallest radicand (zero) and therefore, it is the smallest allowed x value for that square root term.

But wait, if we tried x = 3 in f(x), then we get...

[tex]f(x) = \frac{\sqrt{2x-6}}{x-3}\\\\f(3) = \frac{\sqrt{2*3-6}}{3-3}\\\\f(3) = \frac{\sqrt{0}}{0}\\\\[/tex]

which isn't good. We cannot have 0 in the denominator. Dividing by zero is not allowed. The result is undefined. It doesn't even lead to a complex number. So we'll need to bump x = 3 up to x = 4. You should find that x = 4 doesn't make the denominator 0.

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In short, we found that x = 3 makes the square root as small as possible while staying a real number, but it causes a division by zero error with f(x) overall. So we bump up to x = 4 instead.

Answer:

breathing, jk buddy

Step-by-step explanation:

Answer:

630 and 90 respectively

Step-by-step explanation:

Let the speed of wind be x and the plane speed be y

ATQ, (y+x)*3=2160 and (y-x)*4=2160. Solving it, we will get x=90 and y=630

The speed of the plane in still air is 630 miles per hour and the speed of the wind is 90 miles per hour.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

An airplane takes 3 hours to travel a distance of 2160 miles with the wind. The return trip takes 4 hours against the wind.

Let 'x' be the speed of the plane and 'y' be the speed of the wind. Then the equations are given as,

x + y = (2160 / 3)

x + y = 720                  ...1

x - y = (2160 / 4)

x - y = 540                  ...2

Add equations 1 and 2, then we have

2x = 720 + 540

x = 1260 / 2

x = 630 miles per hour

Then the value of 'y' is calculated as,

630 + y = 720

y = 90 miles per hour

The speed of the plane in still air is 630 miles per hour and the speed of the wind is 90 miles per hour.

More about the solution of the equation link is given below.

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Answer:

B. 24.

Step-by-step explanation:

3

4 = 2*2

6 = 2*3

8 = 2*2*2

LCM = 2*2*2*3 = 24

Answer:

37.68

Step-by-step explanation:

Formula for finding the circumference of a circle is C = 2πr

If you substitute the numbers in you should get 37.68.

Answer:

36 intervals will capture the value of the unknown parameter p, and 4 will miss it.

Step-by-step explanation:

x% confidence interval:

A confidence interval is built from a sample, has bounds a and b, and has a confidence level of x%. It means that we are x% confident that the population mean is between a and b. x% of confidence intervals capture the unknown parameter.

About how many of the 40 intervals will capture the value of the unknown parameter p?

90% of them will capture, so:

0.9*40 = 36

0.1*40 = 4

36 intervals will capture the value of the unknown parameter p, and 4 will miss it.

Answer:

It is 10√2

Step-by-step explanation:

[tex] = \sqrt{200} \\ = \sqrt{2 \times 100} \\ = ( \sqrt{2} ) \times ( \sqrt{100} ) \\ = \sqrt{2} \times 10 \\ = 10 \sqrt{2} [/tex]

Answer:

B Trevor isn't correct because -2i must also be a root

Step-by-step explanation:

A Trevor is correct.

B Trevor is not correct because –2i must also be a root.

C Trevor is not correct there cannot be an odd number of roots.

D Trevor is not correct because there cannot be both rational and complex roots.

statements^^^^^^

The statement that f(x) must be a polynomial with degree 3 is not necessarily true based on the given roots.

A function has an input and an output.

A function can be one-to-one or onto one.

It simply indicated the relationships between the input and the output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

Since one of the roots is complex (2i), it follows that the coefficients of f(x) must be complex as well, and therefore f(x) must be a polynomial with complex coefficients.

However, it is possible for f(x) to have a higher degree than 3.

For example,

The polynomial (x + 7)(x - 2i)(x + 2i)(x - 7) has degree 4 and has the given roots of -7, 2i, and 7. Therefore, f(x) could be a polynomial with degree 4 or higher.

Thus,

The statement that f(x) must be a polynomial with degree 3 is not necessarily true based on the given roots.

Learn more about functions here:

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Answer:b. (8,-1) is a solution to one equation but not the other, so it is a solution to the system

Step-by-step explanation:

27. Which statement is true about the system

x+3y=11

y=r-7

a. (8,-1) is a solution to both equations, so it is a solution to the system

b. (8,-1) is a solution to one equation but not the other, so it is a solution to the system

C. (8,-1) is a solution to one equation but not the other so it is not the solution to the system

d. (8,-1) is not a solution to either equation, so it is not a solution to the system​

Answer

3y(5x+1)

Step-by-step explanation:

9*(5x+1)/3y

3(5x+1)y

Answer:

Step-by-step explanation:

sum: 5x + 1

factor: 3 which divides into 9 evenly

quotient: the answer to division: 9(5x + 1)/(3y) = 3(5x +1)/y

coefficent: this depends on what you have been told. In my day, there were two kinds of coefficents

numerical: 5 and 3

literal: x and y

Answer:

1.

An extraneous solution is a root of a transformed equation that is not a root of the original equation as it was excluded from the domain of the original equation.

It emerges from the process of solving the problem as a equation.

2.I begin like:

The vertical asymptotes will occur at those values of x for which the denominator is equal to zero:

for example:

x² − 4=0

x²= 4

doing square root on both side

x = ±2

Thus, the graph will have vertical asymptotes at x = 2 and x = −2.

To find the horizontal asymptote, the degree of the numerator is one and the degree of the denominator is two.

9514 1404 393

Answer:

  25

Step-by-step explanation:

To make this expression into a perfect square trinomial, we must add the square of half the coefficient of the linear term.

  v^2 -10v +(-10/2)^2 = v^2 -10v +25

The missing constant is 25.

Answer:

x=-1/4+i*sqrt(47)/4 and x=x=-1/4-i*sqrt(47)/4

Step-by-step explanation:

Using quadratic formula, x=(-1±sqrt(1-48))/4.

x=-1/4+i*sqrt(47)/4 and x=x=-1/4-i*sqrt(47)/4

Answer:

If you do not understand any steps, please feel free to comment down below.

Answer:

1)( y= 0.12 * x )             y(dependent) , x(independent)                                                                     2)  x=150 : y=18  /  x=300 : y=36  / x=450 : y=54  /  x=600 :   y=72  /  x=750 : y=90 / x=900 : y=108                                                                                                  3) 300+750+1050=2100 pound

 2100*0.12=252 pound food they need to eat in each day

252*7=1764 pound in each month

9514 1404 393

Answer:

  5√13 m

Step-by-step explanation:

The length of the space diagonal is the "Pythagorean sum" of the lengths of the edges of the cuboid.

  AC = √(8² +6² +15²) = √325 = √(13·25)

  AC = 5√13 . . . meters

__

AB is the hypotenuse of the right triangle with legs 6 and 8, so is 10 units. AC is the hypotenuse of right triangle ABC, so is ...

  AC = √(AB² +BC²) = √(10² +15²)

Answer:

x = -5

Step-by-step explanation:

-(5x-2) = 27

Distribute the minus sign

-5x +2 = 27

Subtract 2 from each side

-5x +2-2 = 27-2

-5x = 25

Divide by -5

-5x/-5 = 25/-5

x = -5

Answer:

X=-5

Step-by-step explanation:

-(5x-2)=27

-5x+2=27

-5x=27-2

-5x=25

x=25/-5

=-5

9514 1404 393

Answer:

  (b)  √6 mi

Step-by-step explanation:

Putting the given heights into the formula, we find the difference in distances to be ...

  Adam' horizon distance = √((3/2)(400)) = 10√6 . . . miles

  Pam's horizon distance = √((3/2)(324)) = 9√6 . . . . miles

Then the difference Adam can see is farther than the distance Pam can see by ...

  10√6 -9√6 = √6 . . . miles

Answer:

The appropriate answer is "256".

Step-by-step explanation:

Given:

Standard error,

SE = 128.13

Standard deviation,

[tex]\sigma[/tex] = $2050

As we know,

⇒ [tex]SE = \frac{\sigma}{\sqrt{n} }[/tex]

or,

⇒ [tex]\sqrt{n}= \frac{\sigma}{SE}[/tex]

By substituting the values, we get

         [tex]=\frac{2050}{128.13}[/tex]

         [tex]=\frac{205000}{12813}[/tex]

     [tex]n = (\frac{205000}{12813} )^2[/tex]

         [tex]=255.98[/tex]

or,

         [tex]=256[/tex]

Answer:

0.0015 = 0.15% probability that if the motel books 150 guests, not enough seats will be available.

Step-by-step explanation:

Binomial probability distribution

Probability of exactly x successes on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

Normal probability distribution

Problems of normally distributed 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.

When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex], if [tex]np \geq 10[/tex] and [tex]n(1-p) \geq 10[/tex].

150 guests booked:

This means that [tex]n = 150[/tex]

85% of booked guests show up for their room.

This means that [tex]p = 0.85[/tex]

Is the normal approximation suitable:

[tex]np = 150(0.85) = 127.5[/tex]

[tex]n(1-p) = 150(0.15) = 22.5[/tex]

Both greater than 10, so yes.

Mean and standard deviation:

[tex]\mu = E(X) = np = 150*0.85 = 127.5[/tex]

[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{150*0.85*0.15} = 4.3732[/tex]

Find the probability that if the motel books 150 guests, not enough seats will be available.

More than 140 show up, which, using continuity correction, is [tex]P(X > 140 + 0.5) = P(X > 140.5)[/tex], which is 1 subtracted by the p-value of Z when X = 140.5. So

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

[tex]Z = \frac{140.5 - 127.5}{4.3732}[/tex]

[tex]Z = 2.97[/tex]

[tex]Z = 2.97[/tex] has a p-value of 0.9985.

1 - 0.9985 = 0.0015.

0.0015 = 0.15% probability that if the motel books 150 guests, not enough seats will be available.

Answer:

The answer is "2.4049"

Step-by-step explanation:

Calculating the test of Hypothesis: [tex]H_{0}: 23\% \ \text{off all adults which reconize the compony's logo}\\\\H_{1}: \text{more than 23\% of adult recornise the compony's logo}\\\\[/tex]

that is

[tex]H_{0}: p=0.23\ against \ H_{1}:p>0.01\\\\Z=\frac{P-p}{\sqrt{\frac{p(1-p)}{n}}}\sim N(0,1)\\\\[/tex]

Given:

[tex]p= 0.23\\\\ \therefore \\\\1-p=0.77\\\\n=1200\\\\ P=\frac{311}{1200}=0.2591\\\\\therefore\\\\Z= \frac{0.2591-0.23}{\sqrt{((0.23)\times \frac{(1-0.23))}{1200}}}=2.4049[/tex]

Z=2.576 tabled value. Because Z is 2.4049, that's less than Z stated, there is no indication that a null hypothesis is rejectable, which means that 23% of all adults record the logo of the Company.

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Answer:

  9 square inches

Step-by-step explanation:

The area is proportional to the square of the linear scale factor. We can use this to write the proportion ...

  A/(144 m²) = ((2 in)/(8 m))²

  A = (144·4/64) in² = 9 in²

The area representing 144 square meters is 9 square inches.

Answer:

The answer varies depending if your teacher wants the answer in cents only, or in dollars only.

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Explanation:

Based on that, we know,

and ultimately

p+5n+50p = 51p+5n

represents the total value of all the coins, and this value is in cents. We would divide by 100 to convert from cents to dollars. So we can say that 51p+5n cents = (51p+5n)/100 dollars

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As an example, let's say

So we have

This would mean we have

Overall we have p+5n+25q = 4+25+200 = 229 cents which converts to 229/100 = $2.29

We can also say 51p+5n = 51*4+5*5 = 204+25 = 229 which is a slight shortcut to get the same result (that result being in cents).

Answer:

It's option C. only 3

Step-by-step explanation:

A line of symmetry is a line which will cut any shape in exactly half. In your given picture, only line 3 is symmetrical because if you were to fold the shape after you cut it in half, both halves would match and be equal.

Answer:

2nd option, rectangle B

Step-by-step explanation:

After reflexion, the figure will be at the left side of x=-5

Answer:

Step-by-step explanation:

Part (a)

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Explanation:

L = 2.4 = length

W = unknown width

The perimeter of any rectangle is P = 2(L+W)

We replace L with 2.4, and replace P with 14.2 to get 14.2 = 2(2.4+w) which is equivalent to 2(2.4+w) = 14.2

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Part (b)

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Explanation:

We'll solve the equation we set up in part (a)

2(2.4+w) = 14.2

2(2.4)+2(w) = 14.2

4.8+2w = 14.2

2w = 14.2-4.8

2w = 9.4

w = 9.4/2

w = 4.7

The width must be 4.7 cm.

Answer:

no entiendo inglés........,

Hi,

Answer:

Tachycardia is a fast heart rate

Answer:

1006

Step-by-step explanation:

Take proportion, p = 62%

n = (Z² * pq) / M.E²

Margin error = 0.03

p = 62% = 0.62

q = 1 - p = 1 - 0.62 = 0.38

Zcritical at 95% = 1.96

n = (1.96² * (0.62*0.38)) / 0.03²

n = 0.90508096 / 0.0009

n = 1005.6455

n = 1006

Sample size = 1006

Answer:

Onetta can salect a sandwich and a salad in 78 different ways.

Step-by-step explanation:

Since Onetta goes to the food court to get a salad and sandwich for lunch, and the Daily Deli has 8 varieties of sandwiches and 3 salads, while Better Bites has 2 varieties of sandwiches and 7 salads, and the Lunch Spot has 5 varieties of sandwiches and 8 salads, to determine the number of ways Onetta can select a sandwich and a salad, the following calculation must be performed:

8 x 3 + 2 x 7 + 5 x 8 = X

24 + 14 + 40 = X

78 = X

Therefore, Onetta can salect a sandwich and a salad in 78 different ways.