10788 divided by 31 what it the answer

Answer:

[tex]{x}^{5} + 40{x}^{4} + 640{x}^{3} + 5120 {x}^{2} + 20480{x}^{}+ 32768 [/tex]

Step-by-step explanation:

This too follows the as same process as

recall binomial theorem,

[tex] \displaystyle (a + b {)}^{n} = \sum _{k = 0} ^{n} \binom{n}{k} {a}^{n - k} {b}^{k} [/tex]

Given binomial:

comparing it to (a+b)ⁿ , we acquire:

Now substitute:

[tex] \displaystyle (x +8 {)}^{5} = \sum _{k = 0} ^{5} \binom{n}{k} {a}^{5- k} {b}^{k} [/tex]

To convert the summation into a sum, substitute the values from k=0 to k=5 into the expression which yields

[tex] \displaystyle (x + 8{)}^{5} = \binom{5}{0} {x}^{5 - 0} \cdot {8}^{0} + \binom{5}{1} {x}^{5 - 1} \cdot {8}^{1} + \binom{5}{2} {x}^{5 - 2} \cdot {8}^{2} + \binom{5}{3} {x}^{5 - 3} \cdot {8}^{3} + \binom{5}{4} {x}^{5- 4} \cdot {8}^{4} + \binom{5}{5} {x}^{5 - 5} \cdot {8}^{5} \\ \implies(x + 8 {)}^{5} = \binom{5}{0} {x}^{5} \cdot 1 + \binom{5}{1} {x}^{4} \cdot {8} + \binom{5}{2} {x}^{3} \cdot 64+ \binom{5}{3} {x}^{2} \cdot 512 + \binom{6}{4} {x}^{1} \cdot 4096+ \binom{5}{5} {x}^{0} \cdot 32768\\ \implies(x + 8{)}^{5} = 1 \cdot {x}^{5 } \cdot 1 + 5\cdot{x}^{4} \cdot {8} + 10 \cdot {x}^{3} \cdot 64+ 10 \cdot {x}^{2} \cdot 512 + 5 \cdot{x}^{1} \cdot 4096+ 1 \cdot {x}^{0} \cdot 32768 \\ \implies \boxed{ (x + 8 {)}^{5} = {x}^{5} + 40{x}^{4} + 640{x}^{3} + 5120 {x}^{2} + 20480{x}^{}+ 32768 }[/tex]

and we're done!

Step-by-step explanation:

first fine 2% of the initial salary since he is paid that every year

2/100×69400=2×694=1388

so for 17 years = 1388×17

=23596

Answer:

[tex]\frac{21}{40}n[/tex] + [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

The important part to understand about this problem is that you need to find a common denominator. You can ONLY add two fractions if they have the same denominator. A way to change the denominator of a fraction is to multiply the numerator and denominator of the fraction by the same number.

So, You want to make the 2/5n and 1/8n to have the same denominator so you can add them. An easy rule of thumb is multiply the one of the fraction by the other fraction's denominator, so in this problem:

[tex]\frac{2 * 8}{5*8} n[/tex] and [tex]\frac{1*5}{8*5}n[/tex]

this comes out as

16/40n and 5/40n

NOW, they have the same denominator and you can add the numerators together to make it one happy fraction

[tex]\frac{16}{40} + \frac{5}{40} = \frac{16+5}{40} = \frac{21}{40}[/tex]

Then, for the 3/6, you can simplify this fraction into:

1/2

This is because if you divide the top and bottom of the fraction by 3 like so:

[tex]\frac{3/3}{6/3}[/tex] (Always make sure you do the same for the top as you do to the bottom)

This comes out as

[tex]\frac{1}{2}[/tex]

Then for the full equation:

[tex]\frac{21}{40} n + \frac{1}{2}[/tex]

The gross monthly income for 4 weeks is $1,887.20

We have given that Scott earns $16. 85 per hour at his job.He works 7 hours per day then,

Gross income= Earning per hour × number of hours works per day × number of days works per week × number of weeks

Gross income= $16.85 × 7 × 4 × 4

Gross income= $1,887.20

Therefore, the gross monthly income for 4 weeks is $1,887.20.

To learn more about the gross monthly income visit:

https://brainly.com/question/25623677

Total interest:-

Answer:

2 is the next number in the sequence

Step-by-step explanation:

in this pattern, you go down by one decimal spot ( zero)

this is a geometric sequence since there is a common ratio between each term.

Answer:

7 units

Step-by-step explanation:

(Background info, skip if not interested or needed for you)

The equation for distance on a cartesian plane coordinate system is based off the pythagorean theorem.

[tex]a^2 + b^2 = c^2[/tex]

a and b being sides of a right triangle, c being the hypotenuse.

When we are solving for distance we are solving for c essentially.

[tex]c[/tex] = [tex]\sqrt{a^2 + b^2}[/tex]

Because a and b are side lengths of the right triangle, we need to find a way to find that in terms of coordinates. So here we might say that a is equal to the horizontal distance between the 2 points or Δx, and we would say that b is the vertical distance between the 2 points Δy.

(solutions)

So essentially distance is:

[tex]d = \sqrt{(x_2 - x_1)^2+ (y_2-y_1)^2 }[/tex]

Now we just use the values given to us, and sub in the x and y values respectively.

(-2,4) [tex]x_1 = -2, y_1 = 4[/tex]

(5,4)[tex]x_2 = 5, y_2 = 4[/tex]

plug these values in:

[tex]d = \sqrt{((5) - (-2))^2+ (4-4)^2 } = \sqrt{(7)^2+ (0)^2 } = \sqrt{7^2 } = 7[/tex]

Therefore the distance is 7 units.

Answer:

1080÷9=120

hope it helps!

Answer:

b i took this exam 90% sure its B

Step-by-step explanation:

B

B

B

second 1

Answer:

1376.1 ft^3

Step-by-step explanation:

The volume of a sphere formula: V=4/3πr^3

r = 6.9 ft

V = 4/3 * π * (6.9^3) = 1,376.055

to the nearest tenth it's 1376.1 ft^3

Answer:

C. 3

is the answer :)

hopefully this helps

Answer:

D: 4

Step-by-step explanation:

1) Make the 1/4 into 5/20 by multiplying top and bottom by 5/5

x/5 - 5/20 = 11/20

2) Move the 5/20 to the other side

x/5 = 11/20 + 5/20

3) Add the 2 fractions on the right

x/5 = 16/20

4) Make the fraction on the right have a denominator of 5 by dividing top and bottom by 4/4

x/5 = 4/5

5) Multiply both sides by 5

x = 4

The missing numerator is 4.

Answer:

2.30 cm

Step-by-step explanation:

Circumference of circle= πD, where D is the diameter.

Substitute all the given information into the formula:

7.22= 3.14D

Divide both sides by 3.14:

D= 7.22 ÷3.14

D= 2.30 (3 s.f.)

Thus, the diameter is 2.30 cm. (rounded off to 3 significant figures)

The value of sin(80°)cos(20°) – cos(80°)sin(20°) using the trignometry property is √3/2.

The difference formula in trignometry for the sine funciton is given as,

[tex]\sin(A-B)=\sin(A)\cos(B) -\cos(A)\sin(B)[/tex]

The trignometric equation given in the problem is,

[tex]\sin(80^o)\cos(20^o) -\cos(80^o)\sin(20^o)[/tex]

Compare this equation with the above eqution, we get,

[tex]A=80^o\\B=20^o[/tex]

Thus, this equation can be written as,

[tex]\sin(80^o)\cos(20^o) -\cos(80^o)\sin(20^o)=\sin(80-20)\\\sin(80^o)\cos(20^o) -\cos(80^o)\sin(20^o)=\sin(60)\\\sin(80^o)\cos(20^o) -\cos(80^o)\sin(20^o)=\dfrac{\sqrt{3}}{2}[/tex]

Hence, the value of sin(80°)cos(20°) – cos(80°)sin(20°) using the trignometry property is √3/2.

Learn more about the difference formula in trignometry here;

https://brainly.com/question/2142049

Answer:

m= [tex]\frac{7}{4}[/tex]

Step-by-step explanation:

[tex]m=\frac{y2-y1}{x2-x1} \\\\m=\frac{5--2}{7-3} \\m=\frac{5+2}{4}\\ m=\frac{7}{4}[/tex]

First, define what equation needs to be used. We need to use the slope formula to find the answer.

Next, we substitute the x and y values into their respective places.

Last, simplify the equation!

378 inches squared

its (18x15)+(6x18)

Answer:

1.

+4

number: 11

2.

x × 3

number: 48

3.

+5

number 46

4.

÷2

number: 19

5.

-1.5

number: 19.5

6.

-0.2

number: 31.2

Answer:

240 Minutes

Step-by-step explanation:

0.6 per minute × 2 = 1.2 gallons .

120 balloons × 2 mins= 240 mins

Answer:

ABCDEFG = 3211000

Step-by-step explanation:

A counts the number of zeroes, and there are 3 zeroes (E, F, G), so A = 3.B counts the number of ones, and there are 2 ones (C, D), so B = 2.C counts the number of twos, and there is 1 two (B), so C = 1.D counts the number of threes, and there is 1 three (A), so D = 1.There is no four, five, six in, so E, F, G are all zeroes.

Answer:

[tex]588mm^3[/tex]

Step-by-step explanation:

Each side of the blue pyramid is 3 times the size of the red pyramid.

Instead of just dividing by 3 for the volume we must divide by 9 instead because we're working in cubes.

Hey there!

In order to evaluate this expression, we need to plug in the value of x (-2)

So we have

-x²+4x+1

plug in -2

-(-2)²+4(-2)+1

-4-8+1

-12+1

-11

Hence, the answer's

[tex]\boxed{\boxed{\bold{-11}}}[/tex]

Hope everything is clear.

Let me know if you have any questions!

#ILoveLearning

:-)

Answer:

Your answer would be:
13.25

128 books in use + 84 books in the collection box =212 reference books on the shelf

212 books / 16 shelves =13.25 per shelf

Logically the answer 13.25 wouldn't make sense because you can't put a 25th of a book on a shelf, so that means you will need to put the "0.25 book" away. Technically your answer would be 13. Due to the question, however, it would be 13.25.

Step-by-step explanation:

Have a great rest of your day
#TheWizzer

The answer is: Yes, all conditions for inference are met.

1 1⁄3

Step-by-step explanation:

In order to find how far was she from her destination

We substract 4 2⁄3 from 3 1⁄3

=> 4 2⁄3 - 3 1⁄3

=> 1 1⁄3 (Decimal: 1.333333)

Answer:

1 1/3 miles

Step-by-step explanation:

2-1

4 2/3-3 1/3= 1-----------

3

=1 1/3miles

1st question

volume of the bottle in inches ?

cylinder volume = area x height

                           = pi x r² x h

                           = 3,14 x 4,5² x 9,10

the bottle volume is 578,62 in³

then

3 ounces of water...........2 in³

? ounces of water..........578,62 in³

? = 3 x 578,62 : 2

? ≈ 868 ounces of water

The distance between Samir and Ayisha is 2 ft.

Samir and Ayisha are on one side of a river. Since they are on the same side, they may likely be close to each other.

Katia is on the other side of the river. It is likely Katia is far from Samir and Ayisha.

The distance between Samir and Katia is 82 ft. Therefore, the distance between Ayisha and Katia is 80 ft.

The distance between Samir and Ayisha = 82 ft - 80 ft

The distance between Samir and Ayisha = 2 ft

learn more on distance here:https://brainly.com/question/8387377

Step-by-step explanation:

[tex] \frac{dA}{dx} = 3 {(x - 1)}^{2} \\A = ∫3 {(x - 1)}^{2}dx \\ = ∫3 {x}^{2} - 6x + 3 \: dx \\ = \frac{3 {x}^{3} }{3} - \frac{6 {x}^{2} }{2} + 3x + c \\ = {x}^{3} - 3 {x}^{2} + 3 + c[/tex]

Now substitute in A=10 and X=3, to find the value of c

[tex]10 = {3}^{3} - 3 {(3)}^{2} + 3(3) + c \\ c = 1[/tex]

Hence,

[tex]A = {x}^{3} - 3 {x}^{2} + 3x + 1[/tex]

Answer:

made a mistake in step 3

Step-by-step explanation:

there, he should have gotten y=5-2x which is then translated to y=-2x+5

this means the y-intercept is correct, but the slope is actually -2