The most appropriapriate choice for factorization will be given by-
[tex](x^2+12+4x)(x^2+12-4x)[/tex] is the required factorization.
What is factorization?
The process of breaking an algebraic expression into product of different factors is called factorization.
Here,
The factorization of [tex]x^4+8x^2+144[/tex] has been shown below-
[tex]x^4+8x^2+144[/tex]
[tex](x^{2} )^2 + 24x^2 +144 -16x^2\\(x^{2} )^2 + 2\times x^2\times 12+ 12^2-16x^2\\(x^2+12)^2 - (4x)^2\\(x^2 + 12+4x)(x^2+12-4x)[/tex]
This is the required factorization
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Exponential Growth and Decay : Growth Formula : y = a(1 + r)', Decay Fórmula: y = a(1 – r) 1. Suppose you deposited $5,500.00 at a bank with an annual interest rate of 5%. What would be the amount in the bank after 20 years?
in this case we have that it is growth formula, so we have that r= 0.05 and a =5500. Therefore the formula is
[tex]y=5500\cdot(1.05)^t[/tex]we only need to replace t by 20 and calculate
[tex]y=5500\cdot1.05^{20}=14593.13[/tex]so after 20 years we hace $14593.13 in our bank account
The miles Jack has driven, y, varies directly with x, the number of hours driven. If Jack drove 175 miles in 2.5 hours, find the number of hours it would take Jack to travel 665 miles.
If the miles Jack has driven, y, varies directly with x, the number of hours driven. If Jack drove 175 miles in 2.5 hours, the number of hours it would take Jack to travel 665 miles is 9.5 hours.
Determining the number of hours to travelLet x represent the number of hours it would take Jack to travel
Formulate an equation
175 / 2. 5 = 665 / x
The denominator cannot equal 0 because the fraction is defined
so,
x ≠ 0
Hence,
1750 × 25x / 25 = 665 × 25x /x
Reduce the fraction
1750x = 665 × 25
1750x = 16,625
Divide both side by 1750x
x = 16,625 / 1750
x = 9.5
Therefore it will take Jack 9.5 hours.
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In 9.5 hours Jack can travel for 665 miles.
What is a unitary method?A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.
Suppose 2 pens cost 10 dollars, therefore 1 pen costs (10/2) = 5 dollars.
From this unitary value, we can determine the cost of any no. of pens.
Given, Jack drove 175 miles in 2.5 hours.
∴ In one hour Jack can drive (175/2.5) miles.
= 70 miles.
So, to travel 665 miles Jack needs (665/70) hours.
= 9.5 hours or 9 hours and 30 minutes.
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ਦੀ ਲੋੜ ਹੀ I — I — Alls – PRAAT
The given polynomial is:
[tex]30x^3-13x^2-40x-12[/tex]Substitute x = -2/5 into the expression:
[tex]30\left(-\frac{2}{5}\right)^3-13\left(-\frac{2}{5}\right)^2-40\left(-\frac{2}{5}\right)-12=0[/tex]Therefore by the remainder theorem x = -2/5 is a root.
[tex]\begin{gathered} x=-\frac{2}{5} \\ multiply\text{ both sides by 5} \\ 5x=-2 \\ 5x+2=0 \end{gathered}[/tex]Hence, the factor is
5x + 2
A
Answer:
A
Step-by-step explanation:
[tex]{ \tt{ {30x}^{3} - {13x}^{2} - 40x - 12}}[/tex]
- For a value to be a factor of a function, the function range must be zero if the factor is substituted into it.
Testing with 5x+2
[tex]{ \tt{5x + 2 = 0}} \\ { \tt{x = - \frac{2}{5} }}[/tex]
Therefore;
[tex]{ \tt{ = 30( - \frac{2}{5}) {}^{3} - 13( - \frac{2}{5} ) {}^{2} - 40( - \frac{2}{5}) - 12 }} \\ \\ = { \tt{0}}[/tex]
hence 5x + 2 is a factor
Solve simultaneously:y = 5x + 210y - 50x = 20
ANSWER
Infinitely many solutions (0 = 0)
EXPLANATION
We have the two equations and we are to solve them simultaneously.
We have:
y = 5x + 2 ___(1)
10y - 50x = 20 ___(2)
Put (1) in (2):
We have that:
10(5x + 2) - 50x = 20
50x + 20 - 50x = 20
=> 50x - 50x = 20 - 20
=> 0 = 0
This kind of solution implies that there are infinitely many solutions to this equation.
3 to 5 men and total of 224 people how many are men
When there are 3 women to to 5 men and there is a total of 224 people, the number of men will be 140 men.
How to illustrate the information?From the information, it was stated that there are 3 women to to 5 men and a total of 224 people.
Therefore, it should be noted that the fraction for men that illustrates the information will be:
= 5/(3 + 5) × 224
= 5/8 × 224
= 5 × 28
= 140
Therefore, the number of men is 140 men.
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how could you use a graph of a proportional relationship to find any ratio in the the proportional relationship why does this work?
It should be emphasized that a connection is proportional if its graph is a line that passes through its origin.
How should the information be illustrated?If the graph of a connection is a line passing through the origin, the connection is proportionate. If it is not a line or ray that fails to achieve this, the ratio is not proportional.
The equation for the proportionality constant is K = y/x. This is the same equation used to get the slope of a straight line with respect to the origin.
If the graph of a connection is a line or ray that goes through the origin, the relationship is proportional. If the line or ray does not pass through the origin, it is not proportional.
Additionally, if anything is not linear, it is not proportional.
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Renu's brother is 5 years younger than Renu. Now he is 30 years old. Connect their ages
The age of Renu and her brother is 35 and 30 years respectively.
Let the age of Renu be x
Then,
The age of her brother will be x-5
According to the question,
Age of Renu's brother is 35
So,
x-5 = 30
x = 30+5
x= 35
Hence, the age of Renu and her brother is 35 and 30 years respectively.
This question is related to the topic age problem. These problems aim is to find the age of certain people.
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When $\dfrac{2}{13}$ is written as a decimal, what is the $2000^\text{th}$ digit after the decimal point?
The 2000th digit after the decimal point is 5. See the explanation below.
What is the explanation that resolved the above problem?
First, we divide the fraction to get the decimal number.
2/13 = 0.15384615384
Paying close attention, you'd notice that after the 6th number forms the decimal point, the number forms a loop that repeats again. That is:
0.153846 153846 154...
Hence, to detect the 2000th number,
we divide 2000/6
we are left with 2
(that is 333 x 6 = 1998)
Hence we count two from the decimal and that gives us the 2000th digit.
That is: 5
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Full Question:
[tex]When $\dfrac{2}{13}$ is written as a decimal, what is the $2000^\text{th}$ digit after the decimal point?[/tex]
Please help I’ll mark you as brainliest if correct!
Answer:
A is 729,2187,6561 and it would be geometric
B is 46,55,64 and is arithmetic
C is 32,36,40 and is arithmetic
Write an expression for the sequence of operations described below.
triple u, multiply v by the result, then multiply what you have by t
Need to know what goes in the 4 boxes above, and the last box
Given that Owen moves half the number of boxes moved by Ariana.
So you can put 2 in the left side upper box, and 1 in the left side lower box.
Now, it is mentioned that Owen mobes 12 boxes. So the corresponding number of boxes moved by Arianna is to be obtained.
So you have to put 12 in the right side lower box. And a variable (say 'x') in the right side upper box.
The vaue of 'x' is to be calculated.
Cross multiply the terms,
[tex]\begin{gathered} 1\cdot x=2\cdot12 \\ x=24 \end{gathered}[/tex]Thus, the value of 'x' is 24.
Therefore, Arianna can move 24 boxes in the time when Owen moves 12 boxes.
A circular disc has a circumference of 141 meters. If we multiply the radius of the circular disc by 12, what will be the circumference of the new disc? OA) 168 m OB) 248 m OC) 4147 m OD) 352 m
Kate paid 2.50 for 8 juice boxes how much should kate be expected to pay for 24 juice boxes
====================================================
Work Shown:
(2.50 dollars)/(8 juice boxes) = (x dollars)/(24 juice boxes)
2.50/8 = x/24
2.50*24 = 8x
60 = 8x
8x = 60
x = 60/8
x = 7.50
----------------
Another approach:
She paid $2.50 for 8 juice boxes. The unit price is 2.50/8 = 0.3125 dollars per juice box. Multiply this by 24 to get 24*0.3125 = 7.50
----------------
Yet another method:
We know the cost for 8 juice boxes is $2.50
We want to know the cost for 24 juice boxes.
The jump from 8 to 24 is "times 3". So we'll multiply the $2.50 cost by 3 to get 3*2.50 = 7.50
We can think of it like this
[tex]\frac{2.50 \ \text{dollars}}{8 \ \text{juice boxes}}=\frac{3*2.50 \ \text{dollars}}{3*8 \ \text{juice boxes}}=\frac{7.50 \ \text{dollars}}{24 \ \text{juice boxes}}[/tex]
24. Jenna wants to purchase a new guitar for $375. She currently has $45 in her savings account. If she plans to save $35 each week, how many weeks will it take her to save enough money to purchase the guitar? Choose the inequality that best represents this situation. A 45 + 35x < 375 B 35 + 45x < 375 C 45 + 35x > 375 D 35 + 45x > 375
Here, we want to select the inequality that best represents the situation
Let the number of weeks be x
Total value saved in x weeks at $35 per week will be 35 * x = 35x
Adding this to what she had initially, the total expression becomes 35x + 45
This sum must be the same or greater than what she plans to save
The inequality is thus;
[tex]35x\text{ + 45}\ge\text{ 375}[/tex]Gary is buying a $1,250 computer on the installment plan. He makes a down payment of $150. He has to make monthly payments of $48.25 for 2 years. What is the total finance charge?
The total finance charge on the computer purchased on finance by Gary is $58.00
What is finance charge?
The finance charge on the computer purchase is the excess of the total payments over the principal of the loan, where the principal is the purchase price of $1,250 minus the down payment of $150
principal=purchase price-down payment
principal=$1,250-$150
principal=$1,100
total payments=monthly payment*number of months in 2 years
total payments=$48.25
total payments=$48.25*24
total payments=$1,158.00
total finance charge=total payments-principal
total finance charge=$1,158.00-$1,100.00
total finance charge=$58.00
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Please help for number 1 2 and 3 and an explanation because I don't understand
The product of the numbers are-
107×11 = 117772×13 = 936466×27 = 12582What is defined as the product of number?In mathematics, a product is defined as the result of multiplying two or more numbers together.The amount of objects in a group is referred to as a multiplicand, and the number of these equal groups is referred to as a multiplier.A multiplier, a multiplicand, as well as the product comprise a multiplication expression.For the given number;
Part a: 107 × 11
1 0 7
× 1 1
---------
1 0 7
+ 1 0 7 x
-------------
1 1 7 7
--------------
Thus, 107×11 = 1177
Part b: 72×13
7 2
× 1 3
---------
2 1 6
+ 7 2 x
-------------
9 3 6
--------------
Thus, 72×13 = 936
Part c: 466×27
4 6 6
× 2 7
---------
3 2 6 2
+9 3 2 x
-------------
1 2 5 8 2
--------------
Thus, 466×27 = 12582
Therefore, product of the number are found.
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Sonya drinks a 32 oz energy drink containing 80 calories per 12 oz how many calories did she drink
Answer:
213
Step-by-step explanation:
First we decide how many ounces 12 has in 32 (2.6)
Then we multiply 2.6 to 80 calories and get 213 calories
A cylindrical bucket contains 314 cubic inches of water. the height of the water is 4 inches. What is the radius of the bucket, to the nearest whole number
The radius of the cylindrical bucket which contains 314 cubic inches of water and 4 inch height of water is 5 inches.
What is the radius of the cylindrical bucket?A cylinder is simply a 3-dimensional shape having two parallel circular bases joined by a curved surface.
The volume of a cylinder is expressed as;
V = π × r² × h
Where r is radius of the circular base, h is height and π is constant pi ( π = 3.14 )
Given the data in the question;
Volume V = 314 in³Height h = 4 inRadius r = ?To determine the radius r, plug the given values into the volume formula above and solve r.
V = π × r² × h
314 in³ = 3.14 × r² × 4
314 in³ = r² × 12.56 in
Divide both sides by 12.56 in
r² = 314 in³ / 12.56 in
r² = 25 in²
Take the square root of both sides
r = √( 25 in² )
Radius r = 5 in
Therefore, the radius r of the cylindrical bucket is 5 inches.
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Factor 8mn2 + 12mn completely. A 42mn’ +3mn) B 4mn(2 + 3n) C 4mn(2mn + 3) D 4mn(2n + 3)
Question 1Step 1: Problem
[tex]\text{Factor 8mn}^2\text{ + 12mn}[/tex]Step 2: Concept
Factor the highest common factor out.
Step 3: Method
[tex]8mn^2\text{ + 12mn = 4mn( 2n + 3)}[/tex]Step 4: Final answer
4mn(2n + 3)
Question 2
Step 1: Question
[tex]\text{Simplify }\frac{(1.24\text{ }\times10^2\text{ ) (3.6 }\times10^{-3})}{1.8\text{ }\times\text{ 10}}[/tex]Step 2: Concept
Apply laws of exponent
[tex]\begin{gathered} \text{Division law } \\ \frac{m^x}{m^y}=m^{x\text{ - y}}^{} \\ \text{Multiplication law} \\ m^x\text{ }\times m^y=m^{x\text{ + y}} \end{gathered}[/tex]Step 3: Method
[tex]\begin{gathered} =\text{ }\frac{(1.24\text{ }\times10^2\text{ )(3.6 }\times10^{-3})}{1.8\text{ x 10}} \\ =\text{ }\frac{1.24\text{ }\times\text{ 3.6 }\times10^{2\text{ + (-3)}}}{18} \\ =\text{ }\frac{4.464\text{ }\times10^{2\text{ - 3}}}{18} \\ =\text{ }\frac{4.464\text{ }\times10^{-1}}{18} \\ =\text{ }\frac{4.464}{18}\text{ }\times10^{-1} \\ =\text{ 0.248 }\times10^{-1} \\ =\text{ 2.48 }\times10^{-2} \end{gathered}[/tex]Step 4: Final answer
Option D is the correct answer
[tex]2.48\text{ }\times10^{-2}[/tex]
In a 7-card poker, played with a standard 52-card deck, 52C7, or 133,784,560, different hands are possible. The probability of being dealt various hands is the number of different ways they can occur divided by . Shown to the right is the number of ways a particular type of hand can occur and its associated probability. Find the probability of not being dealt this type of hand.
If the probability of being dealt this type of hand is 7654/133,784,560. the probability of not being dealt this type of hand is: 0.999944..
ProbabilityProbability of complement of the event A =P (Ac) = 1- P(A)
A = event of the particular type of hand
Probability of A :
P(A) = n (A) / n(S)
P(A) = 7480 / 133,784,560
Ac = event of not being dealt of this type of hand
Probability of Ac:
P (Ac) = 1- P(A)
P (Ac) = 1- 7480 / 133,784,560
P (Ac) = 133, 777,080 / 133,784,560
P (Ac) = 0.999944
Therefore the probability of not being dealt this type of hand is 0.999944.
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The complete question is :
In 7 card poker,played with a standard 52 card deck 52C7 or 133,784,560 different hands are possible. The probability of being dealt various hands is the number of different ways they can occur divided by 133,784,560. The probability of being dealt this type of hand is 7654/133,784,560. Find the probability of not being dealt this type of hand.
Type a paragraph in which you use at least two linking commas, two semicolons, and one colon.
Need two commas (,,)
two semicolons (;;)
one colon (:)
and not run on sentences and of course put period.
TRUE OR FALSE? For any real number x > 0 log 3 x > log ₂ x.
======================================================
Explanation:
We can use a counter-example.
Pick any positive real number you want to replace x.
I'll pick x = 7
Use the change of base formula to get the following
[tex]\log_{3}(\text{x}) = \frac{\log(\text{x})}{\log(3)}\\\\\log_{3}(7) = \frac{\log(7)}{\log(3)}\\\\\log_{3}(7) \approx \frac{0.8451}{0.4771}\\\\\log_{3}(7) \approx 1.7713\\\\[/tex]
and
[tex]\log_{2}(\text{x}) = \frac{\log(\text{x})}{\log(2)}\\\\\log_{2}(7) = \frac{\log(7)}{\log(2)}\\\\\log_{2}(7) \approx \frac{0.8451}{0.3010}\\\\\log_{2}(7) \approx 2.8076\\\\[/tex]
---------------------------
So if x = 7, then we have,
[tex]\log_{3}(\text{x}) > \log_{2}(\text{x})\\\\\log_{3}(7) > \log_{2}(7)\\\\1.7713 > 2.8076\\\\[/tex]
The last statement is false, so the first statement is false when x = 7.
It turns out that you could pick any positive real number for x and will always get a false statement when saying [tex]\log_{3}(\text{x}) > \log_{2}(\text{x})[/tex]
The cholesterol levels of an adult can be described by a normal model with a mean of 185 mg/dL and a standard deviation of 29. What percent of adults do you expect to have cholesterol levels over 190 mg/dL?
Given
mean = 185 mg/dL
standard deviation = 29
Required: The percent of adults that have cholesterol levels over 190 mg/dL
Step 1: Find the z-score for the given cholesterol level using the formula:
[tex]\begin{gathered} z\text{ = }\frac{x\text{ - }\mu}{\sigma} \\ Where\text{ }\mu\text{ is the mean} \\ and\text{ }\sigma\text{ is the standard deviation} \end{gathered}[/tex]Substituting the given values:
[tex]\begin{gathered} z\text{ = }\frac{190-\text{ 185}}{29} \\ z\text{ = 0.1724} \end{gathered}[/tex]Step 2: Using a normal distribution table, find the probability of a random value greater than 0.1724
[tex]P(x\text{ >}0.1724)\text{ = 0.43156}[/tex]Step 3: Convert to percent by multiplying by 100%
[tex]\begin{gathered} =\text{ 0.43156 }\times\text{ 100} \\ =\text{ 43.156}\% \\ \approx\text{ 43.2\%} \end{gathered}[/tex]Hence, the percent of adults that should have a cholesterol level greater than 190 mg/dL is 43,2%
PLEASE HELP ASAP Solve for y, z, x, or t: z-a=z/b if b does not equal 1
On solving the equation z-a = z/b if b≠1 , for z we get z=ab/(b-1) .
in the question ,
the equation is given as
z-a = z/b
adding "a" to both the sides
we get
z-a+a = z/b + a
z = z/b + a
subtracting z/b from both the sides , we get
z - z/b [tex]=[/tex] z/b - z/b + a
z - z/b = a
taking z common
z(1-1/b) = a
taking LCM as b and solving further , we get
z (b-1)/b = a
on cross multiplication we get
z = ab/(b-1)
Therefore , on solving the equation z-a = z/b if b≠1 , for z we get z = ab/(b-1) .
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Which of the following numbers could not be used to describe a distance walked? O 19 feet 0-140 feet 0 -125 feet 12 feet
NSWER
140 Ffeet
EXPLANATION
istance is an absolute value wquantity, so it is expressed either as a positive value or an absolute value of a negative number.
find the standard error mean if O = 64 and n = 64
The standard error mean if σ = 64 and n = 64 is 8.
How can we obtain the standard error mean?The standard error mean is given by the formula σ/√N. In the question provided, we need to note that the standard error mean is designated by σM.
Now applying the formula, we will have this:
σM = 64 ÷√64
The root of 64 = 8.
Therefore, the standard error mean is equal to 64 divided by 8 which is 8.
So, we can arrive at the conclusion that given the standard error mean of σ = 64 and n = 64, the standard error mean will be 8.
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Set up a proportion and solve.
Find the cost of 3 scarves if 2 scarves cost $22.80.
Answer:
Proportion: 22.80/2=x/3
x= 34.20
Step-by-step explanation:
First find what the value of one scarf is:
22.80/2=11.40
Then multiple by 3 to get $34.20
Answer:
Proportion : 1 scarf = $11.40
Cost of 3 scarves = $34.20
Step-by-step explanation:
GIVEN: 2 SCARVES = 22.80
LET X = # OF SCARVES
2X=22.80
X=$11.40
$11.40(3) = cost of 3 scarves
$34.20 = cost of 3 scarves
a picture is 5inches wide and 8inches tall:A photographer wants to use a scale factor of 2.5to enlarge a picture.what will the area of the picture be after it is elarged
We can determine the area of the enlarged picture as follows:
*First, we determine the new dimensions, that is:
[tex]5\cdot2.5\text{ = 12.5}[/tex][tex]8\cdot2.5=20[/tex]*Secondly, we find the area using the formula of area for a rectangle, that is:
[tex]A=20\cdot12.5\Rightarrow A=250[/tex]From this, we have that the area of the picture after being enlarged equals 250 in^2.
What is the slope of a line perpendicular to the line whose equation is 3x-12y=-108
Answer:
-4
Step-by-step explanation:
Given:
Equation of line is 3x-12y = -108.To Find:
Slope of line perpendicular to the given line.Concept used:
For a line ax+by+c = 0 , the slope is equal to -a/b.Slope of a line perpendicular to a line say ax+by+c = 0 will be b/a.For the given equation, we have
a = 3, b = -12 and c = 108
So, Slope of line perpendicular to given line = -12/3 = -4
So, the slope of required line is -4.
The slope of a line perpendicular to the line whose equation 3x - 12y = - 108 will be negative 4.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
The equation is given below.
3x - 12y = - 108
Convert the equation into a slope intercept, then we have
3x - 12y = - 108
12y = 3x + 108
y = (1/4)x + 9
The product of the slopes of the perpendicular line will be a negative one. Then we have
(1/4)m = -1
m = - 4
The slope of a line perpendicular to the line whose equation 3x - 12y = - 108 will be negative 4.
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A catering service offers 8 appetizers, 9 main courses, and 3 desserts. A customer is to select 6 appetizers, 6 main courses, and 2 desserts for a banquet. Inhow many ways can this be done?
Given:
Number of appetizers offered = 8
Number of appetizers customer is to select = 6
Number of main courses offered = 9
Number of main courses customer is to select = 6
Number of desserts offered = 3
Number of desserts the customer is to select = 2
Let's determine how many ways this can be done.
This is a combination problem.
To determine the number of ways this can be selected, apply the combination formula below:
[tex]_nC_r=\frac{n!}{r!(n-r)!}[/tex]Thus, we have:
[tex]_nC_r=_8C_6\ast_9C_6\ast_3C_2[/tex]Solving further, let's apply the formula and combine:
[tex]\begin{gathered} _8C_6\ast_9C_6\ast_3C_2=\frac{8!}{6!(8-6)!}\ast\frac{9!}{6!(9-6)!}\ast\frac{3!}{2!(3-2)!} \\ \\ _8C_6\ast_9C_6\ast_3C_2=\frac{8!}{6!(2)!}\ast\frac{9!}{6!(3)!}\ast\frac{3!}{2!(1)!} \end{gathered}[/tex]Solving further:
[tex]\begin{gathered} _8C_6\ast_9C_6\ast_3C_2=\frac{8\ast7\ast6!}{6!(2\ast1)}\ast\frac{9\ast8\ast7\ast6!}{6!(3\ast2\ast1)}\ast\frac{3\ast2!}{2!(1)} \\ \\ _8C_6\ast_9C_6\ast_3C_2=\frac{8\ast7}{2\ast1}\ast\frac{9\ast8\ast7}{3\ast2\ast1}\ast\frac{3}{1} \\ \\ _8C_6\ast_9C_6\ast_3C_2=\frac{56}{2}\ast\frac{504}{6}\ast\frac{3}{1} \\ \\ _8C_6\ast_9C_6\ast_3C_2=28\ast84\ast3 \\ \\ _8C_6\ast_9C_6\ast_3C_2=7056 \end{gathered}[/tex]herefore, there are