384 divided by 24000long division

[tex]\left( x+\frac{1}{x}\right)^{8} =\sum _{k=0}^{8}\binom{8}{k} \cdotp x^{8-k} \cdotp \left(\frac{1}{x}\right)^{k}\\\\\\ \begin{array}{l}\text{We\ wish\ to\ find\ } x^{0} :\\\\x^{8-k} \cdotp \left(\frac{1}{x}\right)^{k} =x^{0}\\\\\Longrightarrow x^{8-k} \cdotp x^{-k} =x^{0}\\\\\Longrightarrow \cancel{x}^{8-2k} =\cancel{x}^{0}\\\\\Longrightarrow 2k=8\\\\\Longrightarrow k=4\end{array}\\\\\therefore \binom{8}{4} \cdotp x^{4} \cdotp \left(\frac{1}{x}\right)^{4} =\frac{8!}{( 8-4) !\cdotp 4!}[/tex]

[tex]\binom{8}{4} \cdotp x^{4} \cdotp \left(\frac{1}{x}\right)^{4} =\frac{8\cdotp 7\cdotp 6\cdotp 5\cdotp \cancel{4!}}{\cancel{4!} \cdotp 4\cdotp 3\cdotp 2\cdotp 1}\\\\\binom{8}{4} \cdotp x^{4} \cdotp \left(\frac{1}{x}\right)^{4}=70\\\\\therefore \boxed{\boxed{\text{The\ constant\ term\ is\ } 70}}[/tex]

Work Shown:

9 trains headed north

5+4+9 = 18 trains total

P(north) = (# of north)/(# total) = 9/18 = 1/2

Answer:

g(f(x)) = x² - 3

Step-by-step explanation:

g(f(x))=g(x²)

= x² - 3

Step-by-step explanation:

[tex]f(x) = {x}^{2} \\ g(x) = x - 3 \\ g(f(x)) = g( {x}^{2} ) = {x}^{2} - 3 \\ thank \: you[/tex]

Answer:

Step-by-step explanation:

P{2 of 4 tagged}=(52)(152)(204)  

=0.2167

Answer:

General equation of a line:

[tex]y = mx + b[/tex]

then express in that form:

[tex] \frac{x}{2} - y + 6 = 0 \\ \\ - y = - \frac{x}{2} - 6 \\ \\ { \boxed{ \boxed{y = \frac{1}{2} x + 6}}}[/tex]

Answer:

47

Step-by-step explanation:

According to the number system 7 lines and 12 dots, a line is 5 and a dot is 1

you do 5*7+12 which is equal to 47

So the answer is 47,

Hope this helps!

First look at the chart and then convert each symbols to their respective numbers

[tex]\\ \tt\longmapsto 6+14+13+4+0+10[/tex]

[tex]\\ \tt\longmapsto 20+17+10[/tex]

[tex]\\ \tt\longmapsto 37+10[/tex]

[tex]\\ \tt\longmapsto 47[/tex]

Answer:

See Below.

Step-by-step explanation:

By definition, if two functions, f and g, are inverses, then:

[tex]\displaystyle f(g(x)) = g(f(x)) = x[/tex]

We are given the two functions:

[tex]\displaystyle g(x) = \sqrt{x + 8} -4 \text{ and } f(x) = x^2 + 8x + 8[/tex]

Find f(g(x)) and g(f(x)):

[tex]\displaystyle \begin{aligned} f(g(x)) &= (\sqrt{x + 8} -4)^2 + 8(\sqrt{ x+ 8}-4) + 8 \\ \\ &= ((x+8) -8\sqrt{x + 8} +16) + 8\sqrt{x + 8} - 32 + 8 \\ \\ &= x + (-8\sqrt{x+8} + 8\sqrt{x + 8}) +(16 - 32 + 8 + 8) \\ \\ &= x \stackrel{\checkmark}{=} x\end{aligned}[/tex]

And:

[tex]\displaystyle \begin{aligned}g(f(x)) &= \sqrt{(x^2 + 8x + 8) + 8} - 4 \\ \\ &= \sqrt{x^2 + 8x+16 } - 4 \\ \\ &=\sqrt{(x+ 4)^2} - 4 \\ \\ &= (x +4) - 4 \\ \\ &= x \stackrel{\checkmark}{=} x \end{aligned}[/tex]

Hence, f and g are indeed inverses of each other.

Answer:

part b is B

Step-by-step explanation:

not sure about the first part i dont want you to get it wrong i kind of forgot about it

Answer:

it's either an ant, small beetle, black termite, or something

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

-2 + 12 = 10

Answer:

simplifed   -10/27

Step-by-step explanation:

Answer:

hii

Step-by-step explanation:

which question do you want

The amount of money used for scholarship and the fraction of the estate gotten by Miss Maple are :

The entire fraction of the estate = 1/1

Fraction given to children = 2/3

Fraction left = Total - fraction given to children

Fraction left = 1/1 - 2/3 = 1/3

For scholarship :

1/5 of fraction left :

1/5 of 1/3 = 1/5 × 1/3 = 1 /15

Fraction Given to grand children :

1/5 - 1/15 = 2/15

Amount of money used for scholarship :

1/15 × 8424000 = $561,600

B.)

Since There are four grand children and it was equally shared among them:

Miss Maple is one of the grand children:

Fraction each grandchild gets is :

2/15 ÷ 4

2/15 ÷ 4/1

2/15 × 1/4 = 2/60 = 1/30

Hence, miss Maple will get 1/30

Learn more : https://brainly.com/question/18109354

Answer: 4 /15

Step-by-step explanation:

[tex]0.2\overline{6}\\\\=0.2+\dfrac{1}{10} *\dfrac{6}{9} \\\\=\dfrac{1}{5} +\dfrac{1}{15} \\\\\\\boxed{0.2\overline{6}=\dfrac{4}{15} }\\[/tex]

Answer:

7 1/12

Step-by-step explanation:

i just know

Answer:

its -4 1/3

Step-by-step explanation:

Step-by-step explanation:

-3x + 6y = 18

-3x = 6y+14

a) the slope of the 1st equation = -(-3)/6 = ½

b) the slope of the 1st equation = -3/6 = -½

c) they are niether parallel nor perpendicular

#1

slope=1/2

#2

slope=-1/2

#3

Neither

Answer:

a: 2 1/2 cups of flour

b: 1 1/2 cups of milk

Answer:

Step-by-step explanation:

______

0.7857142

note the first 7 is not included in the bar

The slope is -2. In context to this problem, the candle will burn away 2cm of its length every hour.

The slope of the equation, -2, means that the height of the candle reduces at a rate of 2 cm per hour.

Given the linear equation of the height of a candle that has been burning as: [tex]h = 28 - 2t[/tex].

This implies that:

28 in the equation represents the initial height of the candle = 28 cm.

-2 in the equation is slope, which is the rate of change at which the candle burns, meaning the height of the candle reduces by 2 cm every hour.

Therefore, the slope of the equation can be interpreted in the context of the problem as:

for every hour that passes, the height of the candle reduces by 2 cm.

Learn more about linear equation here:

https://brainly.com/question/19408983

Answer:

X-7y+391

Step-by-step explanation:

First multiply

8x47=376

Now group those that are the same together

X-3y -4y+376 +15

X-7y+391

Answer:

x - 7y + 391

Step-by-step explanation:

[tex]x - 3y + 8 \times 47 + 15 - 4y[/tex]

[tex]x - 3y + 376 + 15 - 4y[/tex]

[tex] - 3y - 4y = (- 3 - 4)y = - 7y[/tex]

[tex]x - 7y + 376 + 15[/tex]

[tex] = x - 7y + 391[/tex]

Answer:

7.5

Step-by-step explanation:

168.75 divided by 22.5 = 7.5

$7.50 dollars an hour.

7.50 x 22.5 = 168.75

The Answer is:

an = -15 + 9(n - 1)

Answer:

rational numbers equalslf 26×1=26the value of x =26ans

Answer:

C. [tex] \frac{5}{4} [/tex]

D. [tex] \frac{6}{7} [/tex]

Step-by-step explanation:

C. [tex]2 - \frac{12}{16} [/tex]

[tex] = 2 - \frac{3}{4} [/tex]

[tex] = \frac{8 - 3}{4} [/tex]

[tex] = \frac{5}{4} [/tex]

D. [tex] \frac{20}{22} \times \frac{33}{35} [/tex]

[tex] = \frac{10}{11} \times \frac{33}{35} [/tex]

[tex] = 10 \times \frac{3}{35} [/tex]

[tex] = 2 \times \frac{3}{7} [/tex]

[tex] = \frac{6}{7} [/tex]

Answer:

17minutes 10sec

Step-by-step explanation:

Total time running and walking

= time ran + time walked

= 11 minutes 24 sec + 5 minutes 48sec

= 16minutes 70sec

( now we know 60 sec = 1 min) so..

= 17minute 10sec