Determine whether the sequence converges or diverges. If it converges, give the limit.

50, 25/2, 25/8, 25/32, ...

The Pascal triangle terms and binomial are related by the binomial theorem fomrula:

The row of the Pascal triangle is the same as

where n is the same as the row of the Pascal triangle.

For example,

.

is the same as the 2nd row of the Pascal triangle.

.

Also know the leading coefficient and last term degree will be the nth row of the Pascal triangle.

The first term, a will be 1 less than the previous terms and the second term, b will be 1 more than the previous terms. For example, look at

.

Another example is

.

The third row of Pascal Triangle

.

.

Pascal's triangle provides a systematic way to determine the coefficients of binomial expansions, making it a valuable tool in algebra and combinatorics.

Binomial expansions are directly related to Pascal's triangle.

Pascal's triangle is a triangular arrangement of numbers in which each number is the sum of the two numbers directly above it. The first and last numbers in each row of Pascal's triangle are always 1.

The coefficients of the terms in a binomial expansion correspond to the numbers in Pascal's triangle. Each row of Pascal's triangle represents the coefficients of the corresponding power of the binomial.

For example, in the expansion of (a + b)², the coefficients are 1, 2, and 1. These coefficients can be found in the third row of Pascal's triangle: 1, 2, 1. Similarly, in the expansion of (a + b)³, the coefficients are 1, 3, 3, and 1, which can be found in the fourth row of Pascal's triangle: 1, 3, 3, 1.

In summary, Pascal's triangle provides a systematic way to determine the coefficients of binomial expansions, making it a valuable tool in algebra and combinatorics.

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Answer:

Here we have:

g(x) = 2*√x

And we know that it is related to a parent function, where the parent functions are:

Linear Function: f(x)=x.

Quadratic Function: ݂f(x)=x^2.

Square Root function: f(x)= √x.

Absolute Value function: f(x)=|x|

Cubic function: f(x)=x^3.

Cube Root function: f(x) = ∛x

Logarithmic function: f(x)=log x or f(x)=In x.

Exponential function: f(x) = a^x.

a) Because g(x) = 2*√x

We can see that it is related to the square root function, then the parent function is:

f(x) = √x

b) now we want to write g(x) in terms of f(x)

we have:

g(x) = 2*√x

we can replace √x by f(x)

then we get:

g(x) = 2*f(x)

Now we have g(x) in terms of f(x)

Answer:

83,55,41

Step-by-step explanation:

1/10 : 1/15 : 1/20

180/10 : 180/15 : 180/20

18 : 12 : 9

=> 6 : 4 : 3

Sum of the ratios = 6 + 4 + 3 = 13

1st ratio: (6/13) * 180 = 83       (approximately)

2nd ratio: (4/13) * 180 = 55     (approximately)

3rd ratio: (3/13) * 180 = 41       (approximately)

∴ Three parts of 180 in the ratio 6 : 4 : 3 is 83, 55 and 41

Answer:

1.55

Step-by-step explanation:

p =nc-e

p=3750, n=3000, e=900, c=?

3750 = 3000c - 900

3750 + 900 = 3000c

4650 = 3000c

3000c = 4650

c = 4650/3000

c = 1.55

Answer:

Step-by-step explanation:

Hamamadou

Answer:

202.5

Step-by-step explanation:

[tex]\frac{L}{45}[/tex] = [tex]\frac{90}{20}[/tex] → [tex]\frac{L}{45}[/tex] = [tex]\frac{9}{2}[/tex]

9 x 45 = 405 → 2L=405

L=[tex]\frac{405}{2}[/tex] → L = 202.5

-4-3-2

1

2

3

4

5 6

x

-2gbhdfcjfghu

Answer:

3 loaves 2 bananas left.

Step-by-step explanation:

The answer is asking how many loaves of three bananas Seth can make. 11 can be divided by 3 a total of 3 times, leaving a remainder of 2 bananas that would not be enough to make another loaf.

Answer:

Im guessing its

C

Step-by-step explanation:

Option B - $20

Total guests = 15

Total Money = $300

Per Guest Cost = 300/15

= $20

Therefore she will spend $20 per guest

Answered by Gauthmath must click thanks and mark brainliest

here's the answer to your question

Answer:

∠ JFK = 57°

Step-by-step explanation:

∠ JFK and ∠ GFH are vertically opposite and congruent , then

∠ JFK = ∠ GFH = 57°

Answer:

40

Step-by-step explanation:

200% x 20

200/100 x 20

(200 ÷ 100) x 20

200 x 20 ÷ 100

4,000 ÷ 100 = 40

This is a polynomial in [tex]2^x[/tex] that can be factorized:

[tex]2^{2x}-5\cdot2^x+4 = 0[/tex]

[tex]\left(2^x\right)^2-5\cdot2^x+4=0[/tex]

[tex]\left(2^x-4\right)\left(2^x-1\right)=0[/tex]

[tex]2^x-4=0\text{ or }2^x-1=0[/tex]

[tex]2^x=4\text{ or }2^x=1[/tex]

Since 4 = 2² and 1 = 2⁰, you get the two solutions x = 2 and x = 0.

Answer:

It is 36

Step-by-step explanation:

Hopefully this help

             Have a good day bye

Answer:

3 a) solution:-

Discount=Rs 1,200

S .P =RS 4,000

M P=?

we know that,

Discount= M.P - S.P

or, Rs 1,200= M.P - Rs 4,000

or, M.P = RS (4,000-1,200 )

M.P = RS 2,800

In no. 3 all we have to make like this .........

Hope it helps

Answer:

Step-by-step explanation:

2)a) M.P =₹ 5000

S.P = ₹4000

Discount amount = M.P - S.P

                            = 5000 - 4000

                            = ₹1000

Discount percent = [tex]\frac{discount \ amount}{M.P}*100[/tex]

                             [tex]= \frac{1000}{5000}*100\\[/tex]

                             = 20%

3)a) Discount = ₹ 1200

S.P = ₹ 4000

M.P = S.P + discount

      = 4000 + 1200

      =  ₹ 5200

4)a ) Discount rate = 15%

S.P= ₹ 4000

[tex]M.P = \frac{100+Discount rate}{100}*S.P\\\\=\frac{115}{100}*4000[/tex]

= ₹ 4600

The current price of the mask is $1 per mask and there is expected demand of 6000 masks per week.

If the company plans to increase the price the demand for the masks will decrease.

Revenue  = 6000 * x

Total revenue will be  $6,000 if the price of mask is $1. If price of mask increase by 10% then quantity will be declined to 5850 masks [6000 - 150].

New price = $ 1 * 110% = $1.10

Revenue = 5850 masks * $ 1.10 = $6,435.

Then correct answer is Revenue will increase if price of mask is increased.

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5a+2b-3a+4

= (5a-3a)+2b+4

= 2a + 2b + 4

Answered by Gauthmath must click thanks and mark brainliest

Answer:

29 feet

Step-by-step explanation:

14 × 3 = 42

100 - 42 = 58

58 ÷ 2 = 29

One of the longer chains is 29 feet long.

Hope this helps.

Answer:

The 5x^2 vs -5x^2 will reflect over "X" axis

the +1 vs -2 will shift the graph down three units

the first answer is the correct answer

Step-by-step explanation:

Answer: 20.58

Step-by-step explanation:

Answer:

You could set up the relation as a table of ordered pairs. Then, test to see if each element in the domain is matched with exactly one element in the range. If so, you have a function!

Step-by-step explanation:

Answer:

see image

Step-by-step explanation:

put a point on .5 on the x axis and a point on -3 on the y axis draw a line through them and shade the space under the line

Step-by-step explanation:

3(t-3)=5(2t-1)

= 3t-9=10t-5

= 3t-10t = -5+9

= -7t = 4

= -t = 4/7

= - 4/7 Answer

hope it helps

Hi there!

[tex]\large\boxed{\frac{1}{5}, \frac{21}{5}}[/tex]

In order to set each equation equal to each other, we must have them both equal the same variable.

Rearrange the top equation to make it equal to y:

x - y = -4

Add 4 to both sides and add y to both sides:

x + 4 = y

Now, we can set both equations equal to each other:

x + 4 = 5(x + 1)² - 3

Begin solving by expanding the square binomial:

x + 4 = 5(x² + 2x + 1) - 3

Simplify:

x + 4 = 5x² + 10x + 5 - 3

x + 4 = 5x² + 10x + 2

Bring all terms to one side:

0 = 5x² + 9x - 2

Factor:

0 = (5x - 1)(x + 2)

Set the other factor equal to 0:

5x - 1 = 0

5x = 1

x = 1/5

Plug in this value of x into an original equation:

1/5 - y = -4

1/5 + 4 = y

1/5 + 20/5 = y

y = 21/5

Answer:

x = -1/2

Step-by-step explanation:

4x^2 + 4x + 1 = 0

Factor

(2x+1)(2x+1) =0

Using the zero product property

2x+1 = 0 2x+1 =0

2x = -1  2x=-1

x = -1/2   x = -1/2

lllStep-by-step explanation:

Answer:

y = -x + 15

Step-by-step explanation:

if an item is priced at $9 per item then 6 items are sold.

Thus, the input is 9 while the output is 6.

Thus, we can say; x, y = (9, 6)

4 items are sold for $11 per item. Thus, the coordinate is; (11, 4)

Now,slope is;

m = (y2 - y1)/(x2 - x1)

m = (4 - 6)/(11 - 9)

m = -2/2

m = -1

We know that slope intercept form is;

y = mx + c

Let's try the first point.

Thus;

6 = -1(9) + c

6 + 9 = c

c = 15

Thus, equation of line is;

y = -x + 15

Answer:

Option A: T(-3, -4)

Step-by-step explanation:

For a general point (x, y), if we apply the transformation:

T(a, b)

at that point, the new point that we will get is:

T(a,b)[ (x, y) ] = (x + a, y + b)

Notice that if w take the difference between the new point (x + a, y + b) and the original point (x, y)

we get:

(x + a, y + b) - (x, y) = (x + a - x, y + b  y) = (a, b)

These are x-value and y-value that describe our transformation T(a, b).

Then if we know that the original point is B (-2, 1)

and the transformed point is B'( -5, -3)

We can just take the difference to get:

(-5, -3) - (-2, 1) = (-5 - (-2), -3 - 1) = (-5 + 2, -4) = (-3, -4)

Then the transformation applied is:

T(-3, -4)

The correct option is A.