A teacher has 15 students in his class, 8 girls and 7 boys. He wants to seat them in three rows of five, but knows that if any row has two girls or two boys sitting next to each other, they will talk and won't pay attention. How many seating arrangements can he make that avoid this

Answer:

B

Step-by-step explanation:

Using the rules of logarithms

log x + log y = log (xy)

[tex]log_{b}[/tex] x = n , then x = [tex]b^{n}[/tex]

Given

[tex]log_{4}[/tex] (x + 3) + [tex]log_{4}[/tex] x = 1 , then

[tex]log_{4}[/tex] x(x + 3) = 1

x(x + 3) = [tex]4^{1}[/tex] = 4

x² + 3x = 4 ( subtract 4 from both sides )

x² + 3x - 4 = 0 ← in standard form

(x + 4)(x - 1) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 4 = 0 ⇒ x = - 4

x - 1 = 0 ⇒ x = 1

However, x > 0 , thus x = 1

Answer:

0.008 or 1/125

Step-by-step explanation:

Answer:

[tex]5^{-3}[/tex] in scientific notation would be [tex]8*10^{-3}[/tex].

Step-by-step explanation:

An integer to the power of a negative number is equivalent to one over that base to the power of the positive exponent. In this case, [tex]5^{-3}[/tex] would be [tex]\frac{1}{5^{3}}[/tex] or [tex]\frac{1}{125}[/tex], which equals 0.008. Scientific notation is a way to express a number in the form of [tex]a * 10^{b}[/tex] where [tex]a[/tex] is greater than or equal to 1 but less than 10. We know that 8 would be the value of [tex]a[/tex], so all you need to know is the value of [tex]b[/tex]. Because [tex]10^{-3}[/tex] is equivalent to 0.001, and multiplied by 8 is equivalent to 0.008, that means [tex]5^{-3}[/tex] in scientific notation would be [tex]8*10^{-3}[/tex].

Answer:

semoga jawapan ini dapat membantu

Answer:

867 plz make me brien list

Answer:

should be 0

Step-by-step explanation:

Find the equation of the line passes through ( -3, 4) and parallel to the line 2y-4x + 2 = 0

Answer:

[tex]y = x + 1[/tex]

Step-by-step explanation:

We want to determine the equation of the line that passes through the point (3, 4) and is parallel to the line containing the points (3, 5) and (0, 2).

Recall that parallel lines have equivalent slopes.

Hence, first find the slope of the line containing the points (3, 5) and (0, 2):

[tex]\displaystyle m = \frac{\Delta y }{\Delta x} = \frac{(2)-(5)}{(0)-(3)} = \frac{-3}{-3} = 1[/tex]

Therefore, the slope of our new line must also be 1.

We are given that it passes through the point (3, 4). Since we are given a slope and a point, we can consider using point-slope form:

[tex]\displaystyle y - y_1 = m(x - x_1)[/tex]

Substitute:

[tex]\displaystyle y - (4) = (1)(x - (3))[/tex]

Simplify:

[tex]y - 4 = x - 3[/tex]

And add. Hence, our equation in slope-intercept form is:

[tex]y = x + 1[/tex]

In conclusion, the line that passes through the point (3, 4) and is parallel to the line containing the two points (3, 5) and (0, 2) is:

[tex]y = x + 1[/tex]

Answer:

7087.8m or 7.09km

Step-by-step explanation:

formula used:

distance = speed * time

total distance = distance1 + distance2

let d1 be distance1, d2 be distance2, s1 be speed1, s2 be speed2, t1 be time1, and t2 e time2:

s1 = 5.8m/s, t1 = 12.9 min or 774 sec, s2 = 6.10m/s, t1 = 7.1 min or 426 second

d1 = s1 * t1

   = 5.8 m/s * 774 s

   = 4489.2 m

d2 = s2 * t2

   = 6.10 m/s * 426 s

   = 2598.6 m

total distance = d1 + d2

                       = 4489.2m + 2598.6m

                       = 7087.8 meter or 7.09 kilometer

Answer:

1. x minus twenty

2. five n plus two

3. a raised to the third power / a cubed

4. n raised to the fourth power then minus one

Step-by-step explanation:

Ight I got u. Im a AP calc bc student so trust xd

Answer:

a₈ = [tex]\frac{1}{78125}[/tex]

Step-by-step explanation:

The nth term of a geometric sequence is

[tex]a_{n}[/tex] = a₁[tex](r)^{n-1}[/tex]

Here a₁ = 1 and r = [tex]\frac{1}{5}[/tex] , then

a₈ = 1 × [tex](\frac{1}{5}) ^{7}[/tex] = 1 × [tex]\frac{1}{78125}[/tex] = [tex]\frac{1}{78125}[/tex]

Step-by-step explanation:

total area is 18 × 20 = 360

but by excluding window it will be less than 360

here U have not given lenght of windows so i can not find answer

Answer:

4. ☐ A [tex]\displaystyle \frac{1}{3}[/tex]

☐ B [tex]\displaystyle 2[/tex]

☑ C [tex]\displaystyle 3[/tex]

3. ☐ A [tex]\displaystyle \frac{\pi}{3}[/tex]

☐ B [tex]\displaystyle \pi[/tex]

☑ C [tex]\displaystyle 6\pi[/tex]

Step-by-step explanation:

[tex]\displaystyle y = -2sin\:(\frac{1}{3}x + \frac{\pi}{2}) \\ y = -2cos\:\frac{1}{3}x[/tex]

[tex]\displaystyle y = Asin(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{-1\frac{1}{2}\pi} \hookrightarrow \frac{-\frac{\pi}{2}}{\frac{1}{3}} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{6\pi} \hookrightarrow \frac{2}{\frac{1}{3}}\pi \\ Amplitude \hookrightarrow 2[/tex]

OR

[tex]\displaystyle y = Acos(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{6\pi} \hookrightarrow \frac{2}{\frac{1}{3}}\pi \\ Amplitude \hookrightarrow 2[/tex]

The above information can help you interpret the graph much better. First off, JUST IN CASE you needed to know the trigonometric equation(s) of this graph, keep in mind that although this looks EXACTLY like the cosine graph, if you plan on writing your equation as a function of sine, then there WILL be a horisontal shift, meaning that a C-term will be involved. As you can see, the photograph on the right displays the trigonometric graph of [tex]\displaystyle y = -2sin\:\frac{1}{3}x,[/tex] in which you need to replase "cosine" with "sine", then figure out the appropriate C-term that will make the graph horisontally shift and map onto the cosine graph [photograph on the left], accourding to the horisontal shift formula above. Also keep in mind that the −C gives you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so you must be careful with your calculations. So, between the two photographs, we can tell that the sine graph [photograph on the right] is shifted [tex]\displaystyle 1\frac{1}{2}\pi\:unit[/tex] to the right, which means that in order to match the cosine graph [photograph on the left], we need to shift the graph BACK [tex]\displaystyle 1\frac{1}{2}\pi\:unit,[/tex] which means the C-term will be negative, and perfourming your calculations, you will arrive at [tex]\displaystyle \boxed{-1\frac{1}{2}\pi} = \frac{-\frac{\pi}{2}}{\frac{1}{3}}.[/tex] So, the sine graph of the cosine graph, accourding to the horisontal shift, is [tex]\displaystyle y = -2sin\:(\frac{1}{3}x + \frac{\pi}{2}).[/tex] Now, with all that being said, in this case, sinse you ONLY have a graph to wourk with, you MUST figure the period out by using wavelengths. So, looking at where the graph hits [tex]\displaystyle [0, -2],[/tex] from there to [tex]\displaystyle [-6\pi, -2],[/tex] they are obviously [tex]\displaystyle 6\pi\:units[/tex] apart, telling you that the period of the graph is [tex]\displaystyle 6\pi.[/tex] Now, the amplitude is obvious to figure out because it is the A-term, but of cource, if you want to be certain it is the amplitude, look at the graph to see how low and high each crest extends beyond the midline. The midline is the centre of your graph, also known as the vertical shift, which in this case the centre is at [tex]\displaystyle y = 0,[/tex] in which each crest is extended two units beyond the midline, hence, your amplitude. So, no matter how far the graph shifts vertically, the midline will ALWAYS follow. Now, in this case, you were probably wondering why the negative was inserted in front of the amplitude in the equation(s). Well, here is why:

[tex]\displaystyle y = sin\:x \\ y = cos\:x[/tex]

Knowing your parent functions, sine commenses upright from the origin, while cosine commenses one unit above the origin [tex]\displaystyle [0, 1].[/tex] This should tell you that inserting a negative in front of the amplitude will REFLECT each crest over the midline. Well, there you have it.

I am delighted to assist you at any time.

9514 1404 393

Answer:

Step-by-step explanation:

1) (fg)(x) = f(x)·g(x) = (5x -2)·(1 -2x)

  = (5x)(1) -(2)(1) +(5x)(-2x) +(-2)(-2x)

  = 5x -2 -10x^2 +4x

  = 9x -10x^2 -2 . . . . matches A

__

2) (f+g)(-2) = f(-2) +g(-2) = (-5(-2) +1) +(-6(-2) +2)

  = 10+1 +12 +2 = 25 . . . . matches C

Answer:

I think the first one is the best answer but you might be expected to say variable. I cannot choose one answer. It all depends what you have been told or what your teacher has said about it.

Myself, I would pick A.

Step-by-step explanation:

Symbols (like letters) that are used to represent numbers which are unspecified.

The problem is that variable is also a possible answer. The problem is that a variable is usually a letter. Symbols do are not used for variables in anything but counting systems.

When you look up the word variable it is defined as a symbol. But that is too confining.

N = 4.2m

Sorry for my bad writing but this is the explanation and answer.

Answer:

The one on the middle left.

Explanation:

x goes infinitely in the positive direction.

y does not show any sign of not going infinitely positively or negatively.

Answer:

Step-by-step explanation:

Answer:

Company C

Step-by-step explanation:

$60+4($20)=$140, lowest total price

Answer:

8+the square root of 50 is greater.

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

I think you just rotate the triangle...

But since angle P and angle Z are the same, they fix the position the rays will go and since ZY=PQ=6cm and ZX=RP=4cm, they are the same triangle so QR=XY.

Pairs of matching angles would be angle R= angle X and angle Q = angle Y

Answer:

Yes,By CPCT

Step-by-step explanation:

SEE the image for solution.

HOPE it helps

Have a great day

Answer:

[tex]6faces \\ thank \: you[/tex]

Answer:

no

Step-by-step explanation:

-5.5=-55/10=-11/2

-11/2 is not an integer because it is not a whole number. even if it is negative, as long as it is in fraction form it is not an integer. therefore rachel is not correct

Answer:

j = 144

Step-by-step explanation:

-j / 18 = -8

[multiply both sides by 18 to cancel out the denominator of 18

Answer:

The answer is $1,300

Step-by-step explanation:

Problem 1

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

Explanation:

The tickmarks say that TU and UV are the same length. Both are 23 units each. They combine to TU+UV = 23+23 = 46, which is the length of TV

TV = 5x+6

TV = 46

5x+6 = 46

5x = 46-6

5x = 40

x = 40/5

x = 8

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

Problem 2

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

Explanation:

We use the same idea as the previous problem.

PQ = 6x-1 is the same length as QR

PQ+QR = (6x-1)+(6x-1) = 12x-2 = PR

Since PR = 15x-29, we can then say,

PR = 12x-2

15x-29 = 12x-2

15x-12x = -2+29

3x = 27

x = 27/3

x = 9

From there,

This shows that PQ+QR = PR is true and it helps confirm the answer.

Answer:

c. b= 4/11

d. b= -4/11

Step-by-step explanation:

b^2 = 16/121

Take the square root of each side

sqrt(b^2) =± sqrt(16/121)

b = ±4/11

b² = -16/121

16 is 4² and 121 is 11²

b² = -4²/11²

b² = -(4/11)²

When exponents are common they are eliminated. Here, 2 is common

b = ±4/11

OPTION c and d IS CORRECT

Answer:

54+456/79*78=5689

Step-by-step explanation:

maaf kalo salah

[tex]45 \times 456[/tex]

Answer: 14-degree decrease

Step-by-step explanation:

because it is getting colder and we know this because anytime temperature goes from positive to negative it becomes mad cold.

Anyways subtracting 14 from our initial temp at 8 degrees celsius brings us to a brisk -6 celsius

Answer:

-10 [tex]^\circ C[/tex]

Step-by-step explanation:

Subtract 7 from -3.   -3 - 7 = 0=-10

The temperature that is 7°C below -3°C is equal to -10°C.

To find the temperature that is 7°C below -3°C, we need to subtract 7 from -3. When subtracting a positive number from a negative number, the result becomes more negative.

Starting with -3°C, we subtract 7°C:

-3°C - 7°C = -10°C

A negative temperature indicates a temperature below zero on the Celsius scale. In this case, -10°C means that the temperature is 10 degrees below freezing point.

The Celsius scale is based on the freezing and boiling points of water, with 0°C representing the freezing point and 100°C representing the boiling point at standard atmospheric pressure.

Since we are subtracting 7°C, we are moving further below the freezing point. So, -10°C indicates a colder temperature than -3°C.

To learn more about temperature click on,

https://brainly.com/question/28827315

#SPJ2

Complete question is:

Write down the temperature that is 7 °C below -3°C?