For the functions f(x) = 3x - 4 and g(x) = x - 41, find the value of ƒ(4) - 2g(3)

The true statement about the function is that (c) the domain of f(x) consists of all values of x such that g(x) does not equal 0 and h(x) does not equal 0.

The complete question is added at the end of this solution

From the complete question, we have the following equation

f(x) = g(x)/h(x)

The above equation means that

The function f(x) is the quotient of the functions g(x) and h(x)

For the function f(x) to have real values, the function h(x) must not equal 0

i.e. h(x) ≠ 0

This is so because

A number or an expression divided by 0 is not a real number

Hence, the true statement is that the domain of f(x) consists of all values of x where h(x) does not equal 0.

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Complete question

which of the following statements is true about a rational function of the form where g and h are polynomial functions?

A. If the rational function has a removable discontinuity, then it cannot have a vertical asymptote. g(x)

B. The rational function f(x) h(x) will have a removable discontinuity at x = a if g(a) = 0. g(x)

C. The domain of f(x) consists of all values of x such that g(x) does not equal 0 and h(x) does not equal 0.

D. If the rational function has a removable discontinuity, then it cannot have a horizontal asymptote.

Answer: The volume of the sculpture is approximately 14 894 m3

Explanation v=lwh

v=(29)(33)(15)

v=14366

formula for the volume of a right cylinder.

The radius

r=1/2(7m)

r=3.5m

v=3.14(r)^2h

v=3.14*(3.5)^2(14)

v=538

The volume of the sculpture is:

14355+538

which is eq to 14893        

q 2 .....

The surface area of the sculpture is approximately 4082 m2

The equation of the line in Slope-Intercept Form is y = 1/3x - 6

Given,

A line passes through the points (−6,−8) and (−3,−7).

To find the equation of the line in Slope-Intercept Form

Now, According to the question:

Write the slope formula :

[tex]m = \frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]

Substitute x1 = -6 , x2 = -3 and y1 = -8 , y2 = -7 into above slope formula:

Calculate;

[tex]m = \frac{-7-(-8)}{-3-(-6)}[/tex]

Determine the sign :

m = (-7+8)/ (-3+6)

m = 1/3

Substitute m = 1/3 , x = -6 and y = -8 into y = mx + b

Calculate:

-8 = 1/3 x (-6) + b

Reduce the expression:

-8 = -2 + b

-b = 6

b = -6

Again , Substitute

y = 1/3x - 6

m = 1/3  into y = mx +b:

y = 1/3x - 6

Hence, The equation of the line in Slope-Intercept Form is y = 1/3x - 6

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Answer:

2 in 5 or 40%

Step-by-step explanation:

The value of the sinθ is -3/5.

What is the Pythagorean identity?

The Pythagorean trigonometric identity, also known as the Pythagorean identity, is a trigonometric identity that expresses the Pythagorean theorem. It is one of the fundamental relationships between the sine and cosine functions, along with the sum-of-angles formulae.

We have,

cosθ = 4/5

sin θ = ?

We'll use the definition of cos to find the known sides of the unit circle right triangle. The quadrant determines the sign on each of the values.

[tex]cos\theta = \frac{Adjacent}{hypotenuse} = \frac{4}{5}[/tex]

We know the hypotenuse and adjacent sides and we'll use the Pythagorean theorem to find the remaining side(opposite side).

opposite = √hypotenuse² − Adjacent²

opposite = √(5)² − (4)²

opposite = √25 - 16

opposite = √9

opposite = 3

[tex]sin\theta = \frac{opposite}{hypotenuse}[/tex]

sin θ = 3/5

In the fourth quadrant, the sine and tangent ratios are negative and the cosine ratio is positive.

Hence, the value of the sinθ is -3/5.

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Answer:

y=1/4x+4

Step-by-step explanation:

because the slope is 1/4

so k=1/4

y=1/4x+b

put the point into the equation

so

6=1/4*8+b

so

b=4

60 percent of the sandwiches were not pastrami with work showing.

What do you mean by percentage?

percentage, a comparative figure denoting one-hundredth of any quantity. One percent (symbolized as 1%), being the hundredth component, is represented as 100 percent, while 200 percent signifies twice the amount specified, percentage.

The total number of sandwiches sold by the deli owner is 90

total number of pastrami is 36.

total number of pastrami is 54.

so, the percentage of sandwiches sold that were NOT pastrami is,(54/90)×100

Hence, 60 percent pastrami with work showing.

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The ounces of milk chocolate that the shop sells is 1/27 ounces.

A fraction is a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.

In this case, the chocolate shop sold 1/6 ounces of white chocolate and it sold 2/9 times as much milk chocolate as white chocolate.

The milk chocolate sold will be:

= 1/6 × 2/9

= 2/54.

= 1/27

The ounces is 1/27 ounces.

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The vertex of your parabola lies at those two coordinates .The axis of symmetry, x is 1, was already discovered.

To locate a parabola's vertex, you must first determine x (or y, if your parabola is sideways) using the axis of symmetry formula. The quadratic equation will then be used to solve for y (or x, if your parabola opens to the side) using that value. The vertex of your parabola lies at those two coordinates.

The axis of symmetry is shown as a line, hence x=1. Since it is the highest or lowest point of the parabola, the vertex of a quadratic equation also serves as its maximum and minimum. We need to do a few things in order to locate the vertex: The axis of symmetry, x=1, was already discovered.

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The 90% confidence interval is  (5.09% , 5.41%)  and the 99% confidence interval is (52.24% , 52.76%)  .

In the question ,

it is given that ,

number of sample of loans taken = 28

the average of the sample is = 5.25%

the standard deviation of the normally distributed population is 0.5 %

The formula to find the Confidence Interval (CI) for the population mean is written as

[tex]\bar{x}[/tex] ±[tex]t_{n-1} , _{\alpha /2} \frac{\sigma}{\sqrt{n} }[/tex]

it is given that the 30 year fixed mortgage rates are normally distributed .

the sample size (n) = 28

Since sample size is less than 30 , the t - test is applied .

Sample mean ( [tex]\bar{x}[/tex] ) = 0.0525

the standard deviation (σ) = 0.005

the significance level : α = 1 - 0.90 = 0.1

critical value = [tex]t_{n-1} , _{\alpha}[/tex] = [tex]t_{27} , _{0.05}[/tex] = 1.703

So , 90% confidence interval will be :

= 0.525 ± (1.703)×(0.005/√28)

≈ 0.0525 ± 0.0016

= (0.0525 - 0.0016 , 0.0525 + 0.0016)

= (0.0509 , 0.0541)

= (5.09% , 5.41%)

For the 99% confidence interval ,

the significance level : α = 1 - 0.99 = 0.01

critical value = [tex]t_{n-1} , _{\alpha}[/tex] = [tex]t_{27} , _{0.005}[/tex] = 0.2771

So , 99% confidence interval will be :

= 0.525 ± (0.2771)×(0.005/√28)

≈ 0.0525 ± 0.00026

= (0.0525 - 0.00026 , 0.0525 + 0.00026)

= (0.05224 , 0.05276)

≈ (52.24% , 52.76%)

Therefore , The 90% confidence interval is  (5.09% , 5.41%)  and the 99% confidence interval is (52.24% , 52.76%)  .

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Answer: y=1/2x+1

Step-by-step explanation:

Use the equation y=mx+b

Insert the points and slope: 3=1/2(4)+b

Simplify: 3=2+b

Simplify: 1=b

Final equation: y=1/2x+1

Answer:

Domain: all real numbers >= 4

Range: all real numbers >= 3

The function in the values menu would you use to summarize the data is SUM

Because

I would use the SUM function to figure out how much box office revenue each genre earned. In the pivot table, the SUM function would add the total revenue separately for each genre.

This function, as clear from the name, is used to add all the values provided as arguments and to display the result in the cell-containing function. Argument Type All Numbers Return Type Number. Syntax = SUM(number 1 , number2, ).

The SUM function will sum hardcoded values and numbers that result from formulas. If you need to sum a range and ignore existing subtotals, see the SUBTOTAL function.

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As per the law of sine, the value of ∠ABC is 13°

Law of sine:

In math, the law of sine refers the relationship between the sides and angles of non-right (oblique) triangles.

Given,

Triangle ABC is drawn with AB = 3.6 units. BC = 4.2 units, and BCA = 28°. Here we need to find the measure of ∠ABC.

According to the law of sine, the given measures of the given triangle  are written as,

=> sin 28°/4.2 = sin x°/3.6

Apply the value of sin 28° = 0.27, then we get,

=> 0.27/4.2 = sin x/3.6

=> 0.972/4.2 = sin x

=> sin x = 0.2314

=> x = sin⁻¹(0.2314)

=> x = 13°

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Answer: 3x-3

Step-by-step explanation:

Equation of the line 'm' is 5x - 6y - 30 = 0.

According to graph,

A(6,0) and B(0,-5) lies on the line m.

Slope-intercept form -> y = mx + c

Putting B(0,-5) in slope-intercept form,

-5 = m(0) + c

 c = -5

Putting A(6,0) in slope-intercept form,

  0 = m(6) - 5

6m = 5

 m = 5/6

Putting the values of m and c in slope-intercept form,

 y = (5/6)x - 5

6y = 5x - 30

5x - 6y - 30 = 0

Hence, equation of the line is 5x - 6y - 30 = 0.

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Answer:

Step-by-step explanation:

A formula that is used to find the time period of a cyclic phenomena based on the frequency as follows

T=1/f

f is frequency

We need to solve the formula for f in terms of T. Cross multiplying the above formula such that :

Therefore, this is the required explanation.

The statement 'the expected value of a random variable must equal one of the values that the random variable can have.' is False

In this question, we have been given a statement.

We need to state whether given statement is true or false.

Given statement : the expected value of a random variable must equal one of the values that the random variable can have.

We know that the expected value of a random variable is the mean of all possible values of the variable.

It is denoted by E(x).

E(x) can not be one of the values that the random variable have, because it is a average of all values of random variable.

Therefore, the statement 'the expected value of a random variable must equal one of the values that the random variable can have.' is False

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Answer:

1,105

Step-by-step explanation:

since the first digit is 1/5 them the last digit it can only be 1 because if it was 2 then the last digit will be 10 which isn’t possible

So we know the last digit is 5 so we multiply by 2 to get the second and third digit of 10

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Answer:

a: 147.7 in thousands

b: 467.8 in thousands

Step-by-step explanation:

y=123.1(1.069)^x, after 1998 1 year per each.

a. solve for the number of students in 2001.

okay, so there is already the equation given, so we just have to put the right number in the x.

it says x represents the number of years after 1998;

then it means we should add the number we added in years to zero for x

(if I didn't get it wrong).

so if x is 1 in 1999, in 2001 it is 3.

let's put 3 in the equation: y=123.1(1.069)^3 -> y=123.1*1.2 -> y=147.7

answer for a: the number of students in 2001 is 147.7 in thousands.

b. solve for the number of students in 2018.

add the number you added in years to zero in order to solve x.

1998+20=2018,

0+20=20;

y=123.1(1.069)^20 -> y=123.1*3.8 -> y=467.8

answer for b: the number of students in 2018 is 467.8 in thousands.

For the given rectangle, the area for given rectangle is 257 1/4 in. and length of a rectangle is 10 1/2 in. then its width is given by 24 1/2 in.

As given in the question,

For the given rectangle,

Area of a given rectangle is equal to 257 1/4 in.

length of a given rectangle is 10 1/2 in.

Let w be the width of a rectangle we have,

Area of a rectangle = length × width

257 1/4 = 10 1/2 × w

Convert mixed fraction into proper fraction we get,

(1029 /4) = (21/2) × w

⇒ w = (1029 ×2) / (21 × 4)

⇒ w = 49 /2

⇒ w = 24 1/2 in.

Therefore, for the given rectangle, the area for given rectangle is 257 1/4 in. and length of a rectangle is 10 1/2 in. then its width is given by 24 1/2 in.

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The total number of ways can these dice be rolled so the numbers on the faces sum to a total of 20 is 300

The number of ways of partitioning 20 into exactly 10 distinct parts with  the 6 numbers {1,2,3,4,5,6} we have:

30 partitions of 20 into ten distinct parts.

The 30 distinct partitions with the sum 20 are:

  1.) {2,2,2,2,2,2,2,2,2,2}

  2.) {1,2,2,2,2,2,2,2,2,3}

  3.) {1,1,2,2,2,2,2,2,3,3}

  4.) {1,1,2,2,2,2,2,2,2,4}

  5.) {1,1,1,2,2,2,2,3,3,3}

  6.) {1,1,1,2,2,2,2,2,3,4}

  7.) {1,1,1,2,2,2,2,2,2,5}

  8.) {1,1,1,1,2,2,3,3,3,3}

  9.) {1,1,1,1,2,2,2,3,3,4}

 10.) {1,1,1,1,2,2,2,2,4,4}

 11.) {1,1,1,1,2,2,2,2,3,5}

 12.) {1,1,1,1,2,2,2,2,2,6}

 13.) {1,1,1,1,1,3,3,3,3,3}

 14.) {1,1,1,1,1,2,3,3,3,4}

 15.) {1,1,1,1,1,2,2,3,4,4}

 16.) {1,1,1,1,1,2,2,3,3,5}

 17.) {1,1,1,1,1,2,2,2,4,5}

 18.) {1,1,1,1,1,2,2,2,3,6}

 19.) {1,1,1,1,1,1,3,3,4,4}

 20.) {1,1,1,1,1,1,3,3,3,5}

 21.) {1,1,1,1,1,1,2,4,4,4}

 22.) {1,1,1,1,1,1,2,3,4,5}

 23.) {1,1,1,1,1,1,2,3,3,6}

 24.) {1,1,1,1,1,1,2,2,5,5}

 25.) {1,1,1,1,1,1,2,2,4,6}

 26.) {1,1,1,1,1,1,1,4,4,5}

 27.) {1,1,1,1,1,1,1,3,5,5}

 28.) {1,1,1,1,1,1,1,3,4,6}

 29.) {1,1,1,1,1,1,1,2,5,6}

 30.) {1,1,1,1,1,1,1,1,6,6}

These pairs can be arranged each in 10 ways.

Therefore, 10× 30

= 300

Hence the number of partitions is 300.

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Taking into account the definition of a system of linear equations, the amount generated by person​ A's tour is ​$171 ​million, and the amount generated by person​ B's tour is ​$143 million.

A system of linear equations is a set of linear equations that have more than one unknown, related by the aforementioned equations and whose objective is to find out their values.

Then, solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied.

In this case, a system of linear equations must be proposed taking into account that:

You know:

The system of equations to be solved is

A + B= 314 million

B= A - 28 million

From the several methods to solve a system of equations, it is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.

In this case, substituting the second equation in the first one you get:

A + A - 28 million= 314 million

Solving:

A + A= 314 million + 28 million

2A= 342 million

A= 342 million÷ 2

A= 171 million

Substituting this value in the second equation:

B= A - 28 million

B= 171 million - 28 million

B= 143 million

Finally, the amount generated by person​ A's tour and B's tour is $171 million and $143 million respectively.

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Answer: 44800000

Step-by-step explanation:56000 x 800=44800000

44800000÷56000=800

The average rate of change of the function g(n) = 10(1.02)ⁿ is 0.25   inches/day.

The Average Rate of Change function is defined as the average rate at which one quantity is changing with respect to something else changing.

To calculate the average rate of change of the function g(n), we use the formula below.

Formula:

Where:

From the question,

Given:

Therefore,

Substitute these values into equation 1

Hence, the average rate of change is 0.25 inches/day.

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Based on given details  i would say a reasonable expectation would be about 6 children .

Probability turned into added into arithmetic to are expecting the possibility of an occasion occurring. Probability essentially approach how in all likelihood it's miles that some thing will happen. This is the fundamental principle of possibility and is likewise utilized in possibility distributions to examine feasible consequences of random experiments.

For the question above, we will use probability.

after 4 children, there is 37.5% chance you have 2 boys/2 girls

after 5 children, there is 62.5% chance you have at least 2boys/2 girls

after 6 children, there is 78% chance you have at least 2boys/2 girls

after 8 children, there is 93% chance you have at least 2boys/2 girls ...

based on this i would say a reasonable expectation would be about 6 children

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The unit rate at which Darrell walks is 1.5 meters per second, so the options with 1.5 meters per second is correct.

Given:

Darrell is walking for a distance of 90 meters in time 60 seconds.

To find out the unit rate we must divide the distance traveled by Darrell by the time taken to travel that distance.

Unit rate = Distance traveled / Time taken

= 90 meters / 60 seconds.

= 1.5 meters per second.

Therefore , The unit rate at which Darrell walks is 1.5 meters per second, so the options with 1.5 meters per second is correct.

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