Answer:
-1 and 1
Step-by-step explanation:
Reciprocal means "one divided by...".
1/-1 = -1 and 1/1 = 1
If each interior angle of a regular polygon measures 160°, how many sides does it have?
Answer:
18
Step-by-step explanation:
Each exterior angle is the supplement of the adjacent interior angle, so is ...
180° -160° = 20°
The total of all n of these exterior angles is 360°, so we have ...
n(20°) = 360°
n = 18 . . . . . . . . . divide by 20°
The polygon is an 18-gon. It has 18 sides.
Answer:
18 Sides
Step-by-step explanation:
Each interior angle = 160°
Each exterior angle = 180° - 160° = 20°
The sum of the exterior angles = 360°
Hence the number of exterior angles =360°/20°
= 18
The polygon has 18 sides (since it has 18 exterior angles).
Hope this helps.
Please mark me as Brainliest.
NEED HELP ASAP PLEASE!! The graph of F(x), shown below, resembles the graph of G(x) = x2, but it has
been stretched and shifted. Which of the following could be the equation of
Fx)?
10
G(X) = x2
10
Fx) = ?
Answer:
D. F(x) = ( (1/5)x)^2 - 4
Step-by-step explanation:
The standard transformation with a stretch and a shift is
F(x) = f(x/b) + k
The red curve has a vertex at (0,-4), and cuts the x-axis at (10,0)
That means that before the vertical shift (of k=-4), the vertex was at (0,0), and the curves passes through (10,4).
Substituting in the equation
F(10) = (10/b)^2 -4 = 0
solve for b
(10/b)^2-4 = 0
(10/b)= sqrt(4) = 2
b = 10/2 = 5
Therefore the transformation equation is
F(x) = (x/5)^2-4
The answer is
F(x) = ( (1/5)x)^2 - 4
The numbers of words defined on randomly selected pages from a dictionary are shown below. Find the mean, median, mode of the listed numbers. 72 58 62 38 44 66 42 49 76 52 What is the mean? Select the correct choice below and ,if necessary ,fill in the answer box within your choice.(around to one decimal place as needed)
Answer:
72 58 62 38 44 66 42 49 76 52 ( arrange it!)
38 42 44 49 52 58 62 66 72 76 (done!)
Median: Find the number in the middle after we arranged, so the answer is (52+58)/2= 110/2 = 55
Mode : None (there is no number appear more than other number)
Mean = (38+42+44+49+52+58+62+66+72+76)/10
=559/100
=5,5
Hope it helps ^°^
PLS HELP !!
Define two terms, each containing the variables x and y, with exponents on each. (For Example : 10x³y–⁵)Find the quotient of the two terms. Explain step-by-step how you found the quotient
Answer:
Step-by-step explanation:
Two such terms are 7x^3*y^9 and -3x*y^5
Their quotient is
7x^3*y^9
--------------
-3x*y^5
This can be simplified as follows:
The numerical coefficients become -7/3.
x^3/x = x^3*x^1 = x^(3 - 1) = x^2 (we subtract the exponent of x in the denominator from the exponent of x in the numerator).
Next, y^9*y^5 = y^4.
The quotient in final reduced form is then (-7/3)x^2*y^4
the height of a soccer ball that is kicked from the ground can be approximated by the function:
y = -12x^2 + 60x
where y is the height of the soccer ball in feet in x seconds after it is kicked. Find the time, in seconds, it takes from the moment soccer is kicked until it returns to the ground
Answer:
5 seconds
Step-by-step explanation:
Well we know that when the soccer ball is on the ground the height will be 0.
So we replace y with 0 and solve for x.
0=-12x²+60x
factor out and divide x, (this x is x=0, which is before he kicked it)
0=-12x+60
subtract 60 from both sides
-60=-12x
x=5
PLEASE HELP ME I DONT HAVE THAT MANY POINTS AND ITS DUE TODAY I NEED HELP ASAP
The table contains the data for your first weeks sales. Complete the table by calculating your commission and earnings for each day of the week
Answer with explanation:
Sales Commission(10% of sales)
$2,200 0.1×$2,200= $220
$2,000 0.1× $2,000= $200
$3,134 0.1×$3,134=$313.4
$2,417 0.1×$2,417=$241.7
$2,579 0.1×$2,579 =$257.9
The completed table is given as follows
Day Sales Commission Non-Sales pay Earning
(10% of sales) (Commission +Non Sales pay)
Mon $2,200 $220 $9.50 $220+ $9.50=$229.50
Tue $2,000 $200 $9.50 $200 +$9.50=$209.50
Thurs $3,134 $313.4 $9.50 $313.4+ $9.50=$322.9
Fri $2,417 $241.7 $9.50 $241.7+$9.50= $251.2
Sat $2,579 $257.9 $9.50 $257.9+$9.50=$267.4
Karim has two investments, one in Company A, and another in Company B. Karim purchased 3,000 shares in company A at $2.65 per share. Since purchasing the shares, the price per share increased to $2.95 per share, after which point Karim decided to sell, realizing a profit. At the same time, Karim purchased 2,000 shares in Company B at $1.55 per share. Since purchasing the shares, the share price fell to $1.30 per share, after which Karim decided to sell the shares, suffering a loss. Karim is required to pay tax at a rate of 28% on the combined profit from both investments. Calculate how much tax Karim must pay.
Answer:
A:$2478
B:$728
Total:$3206
Step-by-step explanation:
2.95x3000=8850
1.30x2000=2600
8850x0.28=2478
2600x0.28=728
2478+728=3206
Can somebody please solve this problem for me!
Answer:
x = 200.674
Step-by-step explanation:
tan∅ = opposite/adjacent
Step 1: Find length of z
tan70° = 119/z
ztan70° = 119
z = 119/tan70°
z = 43.3125
Step 2: Find length z + x (denoted as y)
tan26° = 119/y
ytan26° = 119
y = 119/tan26°
y = 243.986
Step 3: Find x
y - z = x
243.986 - 43.3125 = x
x = 200.674
The sum of 8 times a number and 7 equals 9!
Answer:
0.25*8+7=9
Step-by-step explanation:
8x+7=9
2/8=x
0.25=x
Prove that for all integers m and n, m - n is even if, and only if, both m and n are even or both m and n are odd.
Answer:
Below
Step-by-step explanation:
Suppose that m and n are both even numbers.
So we can express them as the product of 2 and another number.
● n = 2×a
● m = 2×b
● m-n = 2b-2a
● m-n = 2(b-a)
m-n is an even number since it is divisible by 2.
■■■■■■■■■■■■■■■■■■■■■■■■■■
Suppose that both n and m are odd numbers.
● n = 2a+1
● m = 2b+1
● m-n = 2b+1-(2a+1)
● m-n = 2b+1-2a-1
● m-n = 2b-2a
● m-n = 2(b-a)
So m-n is even since it is divisible by 2.
■■■■■■■■■■■■■■■■■■■■■■■■■■
Suppose that m is odd and n is even ir vice versa
● n = 2a or n= 2a+1
● m = 2b+1 or m = 2b
● m-n = 2b+1-2a or m-n = 2b-2a-1
● m-n = 2(b-a) +1 or m-n = 2(b-a)-1
In both cases m-n isn't even.
■■■■■■■■■■■■■■■■■■■■■■■■■■
So m-n is even if and only if m and n are odd or m and are even
Answer:
Case 1
both m and n are even
Therefore m/2 and n/2 are integers
Then,
m-n
=2(m/2 - n/2)
Since m/2 and n/2 are integers
Then m/2 - n/2 will be an integer
Therefore,
m-n = 2(Z)
Where Z is an integer
Since 2 is a factor of m-n
Therefore m -n is even
Case 2
Both m and n are odd
m-n
= 2(½m - ½n)
When an odd number is divided by 2 it gives an integer and a remainder of 1
Therefore
½m = Y + ½
And
½n = Z + ½
Where Y and Z are integers
Then
m-n = 2(Y+½-Z-½)
= 2(Y-Z)
Y-Z will also be an integer
m-n= 2A
Therefore m-n is even
Case 3
One is odd and the other even
m-n = 2(m/2 - n/2)
Assume m is even and n is odd
From the discussions above
m-n = 2(Y - Z - ½)
m-n = 2(A - ½)
Hence m-n is not even because when is divided by two it doesn't give an integer.
Therefore for all integers m and n, m - n is even if, and only if, both m and n are even or both m and n are odd.
A sandman earns a commission of 26%. One week he had sales of $24400. Find the commission for the week.
Answer:
6344
Step-by-step explanation:
Find 26% of 24400
24400 * 26%
24400 * .26
6344
There are 4 roads leading from Bluffton to Hardeeville, 10 roads leading from Hardeeville to Savannah, and 5 roads leading from Savannah to Macon. How many ways are there to get from Bluffton to Macon
Answer: 200 ways
Step-by-step explanation:
From the given information:
Total number of roads leading from Bluffton to Hardeeville = 4
Total number of roads leading from Hardeeville to Savannah = 10
Total number of roads leading from Savannah to Macon = 5
We need to find the total number of ways to get from Bluffton to Macon.
Total number of ways to get from Bluffton to Macon = 4 * 10 * 5
= 200
Therefore, there are 200 required number of ways to get from Bluffton to Macon.
The chief business officer of a construction equipment company arranges a loan of $9,300, at 12 1 /8 % interest for 37.5 months. Find the amount of interest. (Round to the nearest cent)
a. $2,761.21
b. $3,583.83
c. $3,523.83
d. $3,722.47
Answer:
C). $3523.83
Step-by-step explanation:
loan of principles p= $9,300,
at rate R= 12 1 /8 % interest
Rate R = 12.125%
for duration year T = 37.5 months
T= 37.5/12 = 3.125 years
Interest I=PRT/100
Interest I =( 9300*12.125*3.125)/100
Interest I = (352382.8125)/100
Interest I = 3523.83
Interest I= $3523.83
In the figure below. MN is the arc of a circle with center L. If the length of arc MN is 6π, what is the area of sector LMN?
On a number line, the coordinates of X, Y, Z, and W are −7, −2, 2, and 7, respectively. Find the lengths of the two segments below. Then tell whether they are congruent. XY and
In a two-factor analysis of variance, the F-ratios for factor A, factor B, and the AxB interaction _____. Group of answer choices may have different df values but they all have the same denominator all have the same df values and they all have the same denominator may have different df values and may have different denominators all have the same df values but they may have different denominators
Answer:
may have different df values but they all have the same denominator
Step-by-step explanation:
In a two-factor analysis of variance, the F-ratios for factor A, factor B, and the AxB interaction _____. may have different df values but they all have the same denominator
In two--factor analysis of variance, the estimates of the variance can be obtained by partitioning the total sum of squares into three components corresponding to the three possible sources of variation , viz; Between Rows, Between Columns, and Within Samples or error.
As the number of rows and columns may differ the degrees of freedom differ with them.
In other words
Total df= Rows df + Columns df + Error df
Since the variance is identically the same for each row of the c values and variance is the same for each observation in the jth column of r values the sum of squares becomes an identity.
Therefore it may have different df values but they all have the same denominator.
Find the sum of 1 + 3/2 + 9/4 + …, if it exists.
Answer:
Option (4)
Step-by-step explanation:
Given sequence is,
[tex]1+\frac{3}{2}+\frac{9}{4}..........[/tex]
We can rewrite this sequence as,
[tex]1+\frac{3}{2}+(\frac{3}{2})^2.............[/tex]
There is a common ratio between the successive term and the previous term,
r = [tex]\frac{\frac{3}{2}}{1}[/tex]
r = [tex]\frac{3}{2}[/tex]
Therefore, it's a geometric sequence with infinite terms. In other words it's a geometric series.
Since sum of infinite geometric sequence is represented by the formula,
[tex]S_{n}=\frac{a}{1-r}[/tex] , when r < 1
where 'a' = first term of the sequence
r = common ratio
Since common ratio of the given infinite series is greater than 1 which makes the series divergent.
Therefore, sum of infinite terms of a series will be infinite Or the sum is not possible.
Option (4) will be the answer.
f(x)=3x2+10x-25 g(x)=9x2-25 Find (f/g)(x).
Answer:
[tex](f/g)(x) = \frac{x + 5}{3x + 5} [/tex]
Step-by-step explanation:
f(x) = 3x² + 10x - 25
g(x) = 9x² - 25
To find (f/g)(x) divide f(x) by g(x)
That's
[tex](f/g)(x) = \frac{3 {x}^{2} + 10x - 25 }{9 {x}^{2} - 25 } [/tex]
Factorize both the numerator and the denominator
For the numerator
3x² + 10x - 25
3x² + 15x - 5x - 25
3x ( x + 5) - 5( x + 5)
(3x - 5 ) ( x + 5)
For the denominator
9x² - 25
(3x)² - 5²
Using the formula
a² - b² = ( a + b)(a - b)
(3x)² - 5² = (3x + 5)(3x - 5)
So we have
[tex](f/g)(x) = \frac{(3x - 5)(x + 5)}{(3x + 5)(3x - 5)} [/tex]
Simplify
We have the final answer as
[tex](f/g)(x) = \frac{x + 5}{3x + 5} [/tex]
Hope this helps you
A researcher wishes to see if the average weights of newborn male infants are higher than the
average weights of newborn female infants. She selects a random sample of 12 male infants and
finds the mean weight is 7.70 pounds. She selects a random sample of 9 female infants and finds
that the mean Leight is 7.80 pounds. Assume that the variables are normally distributed and the
population standard deviation is 0.5 for each group.
Using alpha=0.05 to test if the mean weight of the males is higher than the mean weight of the
females, the pvalue of the test is:
Answer:
The p-value is [tex]p-value = 0.62578[/tex]
Step-by-step explanation:
From the question we are told that
The sample size of male infant is [tex]n_1 = 12[/tex]
The sample size of female infant is [tex]n_2= 9[/tex]
The sample mean of male infant is [tex]\= x_1 = 7.70 \ lb[/tex]
The sample mean of female infant is [tex]\= x_2 = 7.80 \ lb[/tex]
The population standard deviation is [tex]\sigma = 0.5[/tex]
The significance level is [tex]\alpha = 0.05[/tex]
The null hypothesis is [tex]H_o : \mu_ 1 = \mu_2[/tex]
The alternative hypothesis is [tex]H_1 : \mu_1 > \mu_2[/tex]
The test statistics is mathematically represented as
[tex]t =\frac{\= x_1 - \= x_2 }{\sqrt{\frac{\sigma }{n_1} } + \frac{\sigma }{n_2} } }[/tex]
=> [tex]t = \frac{7.70 -7.80}{\sqrt{\frac{0.5 }{12} } + \frac{0.5 }{9} } }[/tex]
=> [tex]t = -0.3207[/tex]
From the z-table the p-value is obtained, the value is
[tex]p-value = P(Z > -0.3207) = 0.62578[/tex]
[tex]p-value = 0.62578[/tex]
What is the approximate area of the unshaded region under the standard normal curve below? Use the portion of the standard normal table given to help answer the question.
A normal curve with a peak at 0 is shown. The area under the curve shaded is 1 to 2.
z
Probability
0.00
0.5000
1.00
0.8413
2.00
0.9772
3.00
0.9987
0.14
0.16
0.86
0.98
Answer:
0.14
Step-by-step explanation:
The z score is a score used in statistics to determine by how many standard deviations ti the raw score above or below the mean. If the raw score is above the mean then the z score is positive while If the raw score is below the mean then the z score is negative, It is given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
From the normal distribution table, The area under the curve shaded is 1 to 2 = P(1 < z < 2) = P(z < 2) - P(z < 1) = 0.9772 - 0.8413 = 0.1359 ≈ 0.14
The area under the curve shaded is 1 to 2 is 0.14
What are probabilities?Probabilities are used to determine the chances of an event
The shaded region represents the probability of the z-scores
The shaded region 1 to 2 is represented as:
P(1 < z < 2) =
Using the probability of z-score, we have the formula
P(1 < z < 2) = P(z < 2) - P(z < 1)
From the given standard normal table:
P(z < 2) = 0.9772
P(z < 1) = 0.8413
So, we have:
P(1 < z < 2) = 0.9772 - 0.8413
P(1 < z < 2) = 0.1359
Approximate
P(1 < z < 2) = 0.14
Hence, the area under the curve shaded is 1 to 2 is 0.14
Read more about normal distribution at:
https://brainly.com/question/4079902
Need help!!!! Show work plz
Answer:
24 units²
Step-by-step explanation:
A rhombus is divided into 4 right triangles when it's two diagonals intersect at right angles. All the sides are of equal lengths.
Therefore, a simple method to use to find the area of the given rhombus is to calculate the area of one of the right triangles, and multiply by 4.
Area of right triangle = ½*base*height
Height = 3
Base = [tex]\sqrt{5^2 - 3^2} = \sqrt{16} = 4[/tex] (Pythagorean theorem)
Area of right triangle = ½*4*3 = 2*3 = 6 units²
Area of rhombus = 4(6 units²) = 24 units²
Write the quadratic in a verbal sentence. PLEASE HELP I’m super stuck!! If you can explain how to do this as well that would help so much!!
Answer:
n = 8
Step-by-step explanation:
Follow the question when turning the word equation into an equation
Because we know this is a quadratic equation, the product is a result of n multiplied by itself
[tex]n^{2} -4=60[/tex]
Solve for n
[tex]n^{2} =64[/tex]
[tex]\sqrt{n^{2} } =\sqrt{64}[/tex]
n = 8
the angle theta is in the second quadrant and cos theta = -2/√29 determine possible coordinates for point P on the terminal arm of theta a. (2,5) b. (-2,√29) c. (-5,2) d. (-2,5)
[tex] \cos(\theta)=-\frac{2}{\sqrt{29}}[/tex] and $\theta$ lies in $2^{\text{th}}$ quadrant.
where, $x-$ coordinate is negative, and $y-$ coordinate is positive
so it can't a.
now, cosine means, side adjacent over the hypotenuse, in Cartesian plane, that will be $x-$ coordinate over the distance from origin.
Assume the triangle , with base $2$ units and hypotenuse $\sqrt{29}$ and it's in second quadrant. (so [tex] \cos(\theta)=-\frac{2}{\sqrt{29}}[/tex])
now, the leftmost point on $x-$ axis is , obviously $(-2,0)$
and by Pythagoras theorem, we can find the perpendicular side, that will be $y^2=(\sqrt{29})^2-(2)^2\implies y=5$
so the coordinates of the upper vertex is $(-2,5)$, each point lying on this "ray" should have equal ratio of respective coordinates. i.e. $\frac25=\left|\frac xy\right| $
and it should lie on second quadrant, so $x<0 \, y>0$
Option d satisfies this.
What is the value of the product (3 – 2i)(3 + 2i)?
Answer:
13
Step-by-step explanation:
(3 - 2i)(3 + 2i)
Expand
(9 + 6i - 6i - 4i^2)
Add
(9 - 4i^2)
Convert i^2
i^2 = ([tex]\sqrt{-1}[/tex])^2 = -1
(9 - 4(-1))
Add
(9 + 4)
= 13
Answer:
13.
Step-by-step explanation:
(3 - 2i)(3 + 2i)
= (3 * 3) + (-2i * 3) + (2i * 3) + (-2i * 2i)
= 9 - 6i + 6i - 4[tex]\sqrt{-1} ^{2}[/tex]
= 9 - 4(-1)
= 9 + 4
= 13
Hope this helps!
Can someone do this assuming that it is infinite and as well as assuming it's not infinite? Thanks!
Answer:
see below
Step-by-step explanation:
4,7,12,19
We are adding 3,5,7,9..... each time
The sequence is not arithmetic because we are not adding a constant. It is not geometric since we are not multiplying by a constant term each time
There is no common difference or common ratio.
The explicit formula is
an =n^2 +3
The recursive formula is
(n+1)^2 +3 - (n^2 +3)
n^2 +2n+1+3 - ( n^2+3)
2n+1
a sub(n+1) = a sub( n) + 2n+1
The 10th term
an = n^2 +3
Let n=10
an = 10^2+3
= 100+3
= 103
summation
see image
since the numbers are increasing and greater than 1 the sum does not exist
If f(x)=ax+b/x and f(1)=1 and f(2)=5, what is the value of A and B?
Answer:
[tex]\huge\boxed{a=9 ; b = -8}[/tex]
Step-by-step explanation:
[tex]f(x) = \frac{ax+b}{x}[/tex]
Putting x = 1
=> [tex]f(1) = \frac{a(1)+b}{1}[/tex]
Given that f(1) = 1
=> [tex]1 = a + b[/tex]
=> [tex]a+b = 1[/tex] -------------------(1)
Now,
Putting x = 2
=> [tex]f(2) = \frac{a(2)+b}{2}[/tex]
Given that f(2) = 5
=> [tex]5 = \frac{2a+b}{2}[/tex]
=> [tex]2a+b = 5*2[/tex]
=> [tex]2a+b = 10[/tex] ----------------(2)
Subtracting (2) from (1)
[tex]a+b-(2a+b) = 1-10\\a+b-2a-b = -9\\a-2a = -9\\-a = -9\\a = 9[/tex]
For b , Put a = 9 in equation (1)
[tex]9+b = 1\\Subtracting \ both \ sides \ by \ 9\\b = 1-9\\b = -8[/tex]
If sin∠M = cos∠N and m∠N = 30°, what is the measure of ∠M?
Step-by-step explanation:
sin∠M = cos∠N
sin∠M = cos(30°)
sin∠M = √3 / 2
m∠M = 60° or 120°
If ∠M is acute, m∠M = 60°.
Answer: The measure of ∠M is 60°
Step-by-step explanation:
The complement of 30° is 60°
sin∠M =cos∠N
sin∠60°=cos∠30°
the measure of ∠M is 60°
Given that f(x) = x + 4 and g(x) = x + 7, find (g - 4(x).
Answer: The value of [tex](g - f)(x)=4 .[/tex]
Step-by-step explanation:
Given functions : [tex]f(x) = x + 4[/tex] and [tex]g(x) = x + 7[/tex]
To find : [tex](g - f)(x)[/tex]
Difference between two functions: [tex](u-v)(x)=u(x)-v(x)[/tex]
Then, [tex](g-f)(x)=g(x)-f(x)[/tex]
[tex]=(x+7)-(x+4)=x+7-x-4\\\\=7-4=3[/tex]
Hence, the value of [tex](g - f)(x)=4 .[/tex]
can you help me with this homework please?
Answer:
hey I was wondering if you still needed help?
line and passes through C -2,0 in the 1, -3) Quetion of the line in standard form
Answer:
[tex]\huge\boxed{x+y=-2}[/tex]
Step-by-step explanation:
The standard form of an equation of a line:
[tex]Ax+By=C[/tex]
The point-slope form of an equation of a line:
[tex]y-y_1=m(x-x_1)[/tex]
where
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have two points (-2, 0) and (1, -3).
Substitute:
[tex]x_1=-2;\ y_1=0;\ x_2=1;\ y_2=-3[/tex]
[tex]m=\dfrac{-3-0}{1-(-2)}=\dfrac{-3}{1+2}=\dfrac{-3}{3}=-1\\\\y-0=-1(x-(-2))\\\\y=-(x+2)[/tex]
[tex]y=-x-2[/tex] add x to both sides
[tex]x+y=-2[/tex]
Compute (3/4)*(8/9)*(15/16)*(24/25)*(35/36)*(48/49)*(63/64)*(80/81)*(99/100) Express your answer in the simplest way possible. (Suggestion: First, try computing 3/4*8/9 then 3/4*8/9*15/16 and so on. Look for patterns.
Answer:
[tex](\frac{3}{4})*(\frac{8}{9})*(\frac{15}{16})*(\frac{24}{25})*(\frac{35}{36})*(\frac{48}{49})*(\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}) = \frac{11}{20}[/tex]
Step-by-step explanation:
Given
[tex](\frac{3}{4})*(\frac{8}{9})*(\frac{15}{16})*(\frac{24}{25})*(\frac{35}{36})*(\frac{48}{49})*(\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100})[/tex]
Required
Simplify
For clarity, group the expression in threes
[tex]((\frac{3}{4})*(\frac{8}{9})*(\frac{15}{16}))*((\frac{24}{25})*(\frac{35}{36})*(\frac{48}{49}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))[/tex]
Evaluate the first group [Divide 8 by 4]
[tex]((\frac{3}{1})*(\frac{2}{9})*(\frac{15}{16}))*((\frac{24}{25})*(\frac{35}{36})*(\frac{48}{49}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))[/tex]
[Divide 9 by 3]
[tex]((\frac{1}{1})*(\frac{2}{3})*(\frac{15}{16}))*((\frac{24}{25})*(\frac{35}{36})*(\frac{48}{49}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))[/tex]
[tex]((\frac{2}{3})*(\frac{15}{16}))*((\frac{24}{25})*(\frac{35}{36})*(\frac{48}{49}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))[/tex]
[Divide 15 by 3]
[tex]((\frac{2}{1})*(\frac{5}{16}))*((\frac{24}{25})*(\frac{35}{36})*(\frac{48}{49}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))[/tex]
[Divide 16 by 2]
[tex]((\frac{1}{1})*(\frac{5}{8}))*((\frac{24}{25})*(\frac{35}{36})*(\frac{48}{49}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))[/tex]
[tex](\frac{5}{8})*((\frac{24}{25})*(\frac{35}{36})*(\frac{48}{49}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))[/tex]
Evaluate the second group [Divide 35 and 25 by 5]
[tex](\frac{5}{8})*((\frac{24}{5})*(\frac{7}{36})*(\frac{48}{49}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))[/tex]
[Divide 49 by 7]
[tex](\frac{5}{8})*((\frac{24}{5})*(\frac{1}{3})*(\frac{4}{7}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))[/tex]
[Divide 24 by 3]
[tex](\frac{5}{8})*((\frac{8}{5})*(\frac{1}{1})*(\frac{4}{7}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))[/tex]
[tex](\frac{5}{8})*((\frac{8}{5})*(\frac{4}{7}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))[/tex]
Merge the first and second group
[tex]((\frac{5}{8})*(\frac{8}{5})*(\frac{4}{7}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))[/tex]
[tex](1*(\frac{4}{7}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))[/tex]
[tex](\frac{4}{7})*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))[/tex]
Evaluate the last group [Divide 99 by 9]
[tex](\frac{4}{7})*((\frac{63}{64})*(\frac{80}{9})*(\frac{11}{100}))[/tex]
[Divide 63 by 9]
[tex](\frac{4}{7})*((\frac{7}{64})*(\frac{80}{1})*(\frac{11}{100}))[/tex]
[Divide 64 and 80 by 8]
[tex](\frac{4}{7})*((\frac{7}{8})*(\frac{10}{1})*(\frac{11}{100}))[/tex]
[Divide 10 and 4 by 2]
[tex](\frac{4}{7})*((\frac{7}{4})*(\frac{5}{1})*(\frac{11}{100}))[/tex]
[Divide 100 by 5]
[tex](\frac{4}{7})*((\frac{7}{4})*(\frac{1}{1})*(\frac{11}{20}))[/tex]
[tex](\frac{4}{7})*((\frac{7}{4})*(\frac{11}{20}))[/tex]
[tex](\frac{4}{7})*(\frac{7}{4})*(\frac{11}{20})[/tex]
[tex]1*(\frac{11}{20})[/tex]
[tex]\frac{11}{20}[/tex]
Hence;
[tex](\frac{3}{4})*(\frac{8}{9})*(\frac{15}{16})*(\frac{24}{25})*(\frac{35}{36})*(\frac{48}{49})*(\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}) = \frac{11}{20}[/tex]
