What is the range of F?

The domain restrictions on the rational function [tex]\frac{50}{4x - 12} + \frac{x- 4}{x^2 + x - 12} = \frac{x}{2}[/tex] are (b) x = 3 or and (d) x = -4

The function as expressed in the correct format is:

[tex]\frac{50}{4x - 12} + \frac{x- 4}{x^2 + x - 12} = \frac{x}{2}[/tex]

Factorize the denominators of the fractions

[tex]\frac{50}{4(x - 3)} + \frac{x- 4}{x^2 + 4x- 3x - 12} = \frac{x}{2}[/tex]

Factor out x and -3

[tex]\frac{50}{4(x - 3)} + \frac{x- 4}{x(x + 4)- 3(x + 4)} = \frac{x}{2}[/tex]

Factor out x + 4

[tex]\frac{50}{4(x - 3)} + \frac{x- 4}{(x- 3)(x + 4)} = \frac{x}{2}[/tex]

Set the denominators to 0

4(x - 3) = 0

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

Solve for x:

4(x - 3) = 0 ⇒ x = 3

(x - 3)(x + 4) = 0 ⇒ x = 3 or x = -4

This means that the domain restrictions on the rational function are (b) x = 3 or and (d) x = -4

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Answer:

120% are sixth graders

But, If you meant to say 18 basketball players and 15 6th graders, the percentage would be around 83.3%

Answer:

FOR THE AREA:

Count how many full squares are in the middle, then count how many halves there are on the outer edge. the divide the amount of halves by 2 then add to the amount of full squares.

Answer:

The right one is ........

Step-by-step explanation:

do you mean "base area" ?

and this is relative, friend how the object is placed on the ground.

the way it is depicted, the base is a triangle.

and the area of a triangle is

baseline × height / 2

in our case

11 × 4.3 / 2 = 23.65 cm²

Answer:

A parameter is a numerical description of a population characteristic

Step-by-step explanation:

A parameter is a numerical description of a population characteristic

Answer:

total surface area = 324 m²

lateral surface are = 132 m²

top surface area = 96 m²

bottom surface area = 96 m²

[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]

Let's solve ~

[tex]\qquad \sf  \dashrightarrow \: log_{5}(2x) = 4[/tex]

[tex]\qquad \sf  \dashrightarrow \: 2x= {5}^{4} [/tex]

[tex]\qquad \sf  \dashrightarrow \: 2x= 625[/tex]

[tex]\qquad \sf  \dashrightarrow \: x= 625 \div 2[/tex]

[tex]\qquad \sf  \dashrightarrow \:x = 312.5[/tex]

I Hope you understood the procedure ~

The sales they might anticipate if they raise the price to $40 a bottle is $1,500.

Using this formula

Anticipated sales=(Current selling price÷Increase in price)×Number of bottle sold

Let plug in the formula

Anticipated sales=($30÷$40)×2,000

Anticipated sales=$0.75×2,000

Anticipated sales=$1,500

Therefore the sales they might anticipate if they raise the price to $40 a bottle is $1,500.

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For dark line

Slope

Equation in point slope form

Put (0,0)

As line is dark sign is ≤

The inequality

For dashed line

Equation in intercept form

Put (0,0)

Symbol is >

Inequality is

[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ (\stackrel{x_1}{11}~,~\stackrel{y_1}{-3})\qquad (\stackrel{x_2}{x}~,~\stackrel{y_2}{y}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ x +11}{2}~~~ ,~~~ \cfrac{ y -3}{2} \right)~~ = ~~\stackrel{\stackrel{midpoint}{\downarrow }}{(7~~,~~-2}) \\\\[-0.35em] ~\dotfill[/tex]

[tex]\cfrac{ x +11}{2}~~ = ~~7\implies x+11=14\implies \boxed{x=3} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ y -3}{2}~~ = ~~-2\implies y-3=-4\implies y=-1\implies y=-1i\implies \boxed{y=-i}[/tex]

Answer:

Step-by-step explanation:

Formula

P = 5 + 1.50n

P is the total Cost

n is the number of Km travelled.

Solution

Substitute n = 25 into the formula

P = 5 + 1.5 * 25

P = 5 + 37.5

P = 42.50

Answer

42.50 dollars for 25 km.

The option u1 =/ u2 =/ u3 is correct if the researcher randomly assigns 60 people to 1 of the 3 treatment conditions.

The null and alternative hypotheses are two generalizations about a population that are strictly contradictory. The null hypothesis can be denoted by H₀ and the alternative hypothesis can be denoted by H₁.

We have:

A group of researchers wants to determine whether the type of psychotherapy has an effect on the number of PTSD symptoms in refugees.

As we can see in the problem, there are three treatment conditions are given.

Alternative hypothesis H₁: Not all means are equal

[tex]\rm H_0: \mu_1\neq \mu_2\neq \mu_3[/tex]

Thus, the option u1 =/ u2 =/ u3 is correct if the researcher randomly assigns 60 people to 1 of the 3 treatment conditions.

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The statement is correct about the radionuclide the atomic number is 31, the mass number is 67, and its symbol is superscript 67 subscript 31 baseline upper g a.

To answert the question, we need to know what an atom is.

An atom is the smallest indivisible part of a substance. It is represented by letters.

So, since the atom of this radionuclide contains 31 protons and 36 neutrons.

So, its atomic number is 31. Its mass number is number of protons + number of neutrons = 31 + 36 = 67. Its symbol is superscript 67 and subscript 31.

So, the statement is correct about the radionuclide the atomic number is 31, the mass number is 67, and its symbol is superscript 67 subscript 31 baseline upper g a.

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Answer:

60

Step-by-step explanation:

[tex]\begin{aligned}f(x) & =x^2-4\\\implies f(8) & =(8)^2-4\\& =64-4\\& =60\end{aligned}[/tex]

Answer:

15.9

Step-by-step explanation:

Answer:

There is a total of 200 dollars profit

The mean is the ratio of the actual number of observations to the sum of the observations. Then the mean will be 2.5.

The average of a group of numbers is simply defined as the mean. In statistics, the mean is regarded as one of the indicators of central tendency. Arithmetic mean is a term used to describe the average.

The graph below represents data that was collected by students on the number of social media posts they made the previous day.

Then the mean will be

The sum of the observation will be

Observation sum = 4 + 2 + 2 + 3 + 3 + 2 + 1 +3

Observation sum = 20

Then the mean will be

Mean = 20/8

Mean = 2.5

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The factor of the polynomial 18x³ + 6x²y - 9x² - 3xy will be 3x(6x² - 2xy - 3x - y). Then the correct option is C.

It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.

The polynomial is given below.

⇒ 18x³ + 6x²y - 9x² - 3xy

Then the factor of the polynomial will be

⇒ 18x³ + 6x²y - 9x² - 3xy

⇒ 3x(6x² - 2xy - 3x - y)

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Answer:

3

Step-by-step explanation:

Coefficient in the number behind the variable.

In 3x + 7,

x is the variable.

3 is the coefficient.

Answer:

A

Step-by-step explanation:

If you read the sentences aloud, A is the only answer that makes grammatical sense, since colons are short pauses in sentences, much like commas. Colons are also commonly used for the beginning of a list, as shown here.

Hope this helped!

Answer: Answer below

Step-by-step explanation:

just draw 2 rectangles and draw 3 lines in each one to make 4 equal sections

Answer:

  7/80 lb

Step-by-step explanation:

We are given that 1/10 of the 7/8 pound package is raisins.

__

The weight of raisins is ...

  (1/10)(7/8 lb) = 7/80 lb

Answer:

Week 8

Step-by-step explanation:

week 1 8

week 2 11

week 3 14

week 4 17

week 5 20

week 6 23

week 7 26

week 8 29

Answer:If im correct the answer is C

Step-by-step explanation:

Answer:4 PCs and 8 Macs

Step-by-step explanation:

They consists of equations and unknown variables. There are 4 PCs and 8 Mac in the room

They consists of equations and unknown variables

Let the number of PCs be x

Let the number of Mac be y

If Mke has 12 computers, then;

x + y = 12

If there are two Macs for every PC in his classroom, then;

y = 2x

Substitute

x + 2x = 12

3x = 12

x = 4

Recall y = 2x

y = 2(4)

y = 8

There are 4 PCs and 8 Mac in the room

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Answer:

See below ~

Step-by-step explanation:

Subpart (e) :

⇒ New volume = 2 x 3 x 2 x 4 x 2 x 5

⇒ New volume = 8 x 60

⇒ New volume = 480 in³

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

Subpart (f) :

⇒ New volume : Original volume

⇒ 480 : 60

⇒ 1 : 8

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

Subpart (g) :

Step 1

⇒ SA = 2(6 × 9 + 9 × 11 + 6 × 11)

⇒ SA = 2(54 + 99 + 66)

⇒ SA = 2(219)

⇒ SA = 438 in²

Step 2

⇒ V = 6 × 9 × 11

⇒ V = 54 × 11

⇒ V = 594 in³

Step 3

⇒ New SA = 2 x 438

⇒ New SA = 876 in²

Step 4

⇒ New : Original

⇒ 876 : 438

⇒ 2 : 1

Step 5

⇒ New V = 2³ x 594

⇒ New V = 8 × 594

⇒ New V = 4752 in³

Step 6

⇒ New : Original

⇒ 4752 : 594

⇒ 8 : 1

Answer:

Min max median and q3 is correct, q2 should be 8.5