a. 6! = 6 x 5 x 4 x 3 x 2 x 1 = 720. b. 20! = 20 x 19 x 18 x ... x 2 x 1. c. There are 16 zeros at the end of the decimal representation of (20!)2.
a. 6! = 6 x 5 x 4 x 3 x 2 x 1 = 720
b. 20! = 20 x 19 x 18 x ... x 2 x 1. To write this in factored form, we can identify the prime factors of each number and write the product using exponents. For example, 20 = 2² x 5, so we can write 20! as:
20! = (2² x 5) x 19 x (2 x 3²) x 17 x (2² x 7) x 13 x (2 x 2 x 3) x 11 x (2³) x (3) x (2) x 7 x (2) x 5 x (2) x 3 x 2 x 1
Simplifying, we get:
20! = 2¹⁸ x 3⁸ x 5⁴ x 7² x 11 x 13 x 17 x 19
c. The number of zeros at the end of (20!)² in decimal form is determined by the number of factors of 10, which is equivalent to the number of factors of 2 x 5. Since there are more factors of 2 than 5 in the prime factorization of (20!)², we only need to count the number of factors of 5. There are four factors of 5 in the prime factorization of 20!, which contribute four factors of 10 to the square. Therefore, (20!)²ends in 8 zeros when written in decimal form.
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Find the value of f(4) for the function F(a) = 4 (a+3)-8
determine all minors and cofactors of -6 -6 -3 -7 9 5 -5 -1 -9 . , , , , , , , , , , , , , , , , , .
The minors and cofactors of the given matrix are:
|882 270 -72| |-490 194 198| |78 -44 -72|
To find the minors and cofactors of the given matrix, we first need to understand what a minor and a cofactor are.
The minor of an element a_ij is the determinant of the submatrix obtained by deleting the i-th row and j-th column of the original matrix.
The cofactor of an element a_ij is the minor of a_ij multiplied by (-1)^(i+j).
Using this definition, we can find the minors and cofactors of the given matrix as follows:
Minor of a_11:
|-7 9 5 -1|
|-5 -9 -7 9|
|-6 -3 -7 9|
Minor = (-7)(-9)(-7) + (9)(-7)(-6) + (5)(-5)(-3) + (-1)(-6)(9) = 882
Cofactor of a_11:
Cofactor = (-1)^(1+1) * 882 = 882
Minor of a_12:
|-6 -3 -7 9|
|-5 -9 -7 9|
|-5 -1 -9 5|
Minor = (-6)(-9)(-9) + (-3)(-7)(5) + (-7)(-5)(-1) + (9)(-5)(-5) = -270
Cofactor of a_12:
Cofactor = (-1)^(1+2) * (-270) = 270
Minor of a_13:
|-6 -6 -3|
|-5 -9 -7|
|-5 -1 -9|
Minor = (-6)(-9)(-9) + (-6)(-7)(-1) + (-3)(-5)(-1) + (-9)(-5)(-6) = -72
Cofactor of a_13:
Cofactor = (-1)^(1+3) * (-72) = 72
Minor of a_21:
|-5 -9 -7 9|
|-6 -3 -7 9|
|-5 -1 -9 5|
Minor = (-5)(-7)(-9) + (-9)(-5)(-5) + (-7)(-5)(-1) + (9)(-1)(-5) = 490
Cofactor of a_21:
Cofactor = (-1)^(2+1) * 490 = -490
Minor of a_22:
|-6 -6 -3|
|-5 -1 -9|
|-5 -1 -9|
Minor = (-6)(-9)(-1) + (-6)(-1)(-5) + (-3)(-5)(-1) + (-9)(-5)(-5) = 194
Cofactor of a_22
Cofactor = (-1)^(2+2) * 194 = 194
Minor of a_23:
|-6 -6 -3|
|-5 -9 -7|
|-5 -1 -9|
Minor = (-6)(-9)(-7) + (-6)(-7)(-1) + (-3)(-5)(-1) + (-7)(-5)(-6) = 198
Cofactor of a_23:
Cofactor = (-1)^(2+3) * (-198) = 198
Minor of a_31:
|-5 -9 -7|
|-6 -3 -7|
|-5 -1 -9|
Minor = (-5)(-3)(-9) + (-9)(-5)(-1) + (-7)(-6)(-1) + (-6)(-1)(-7) = -78
Cofactor of a_31:
Cofactor = (-1)^(3+1) * (-78) = 78
Minor of a_32:
|-6 -6 -3|
|-5 -1 -9|
|-5 -1 -9|
Minor = (-6)(-9)(-1) + (-6)(-1)(-5) + (-3)(-5)(-1) + (-1)(-5)(-5) = 44
Cofactor of a_32:
Cofactor = (-1)^(3+2) * 44 = -44
Minor of a_33:
|-6 -6 -3|
|-5 -9 -7|
|-6 -3 -7|
Minor = (-6)(-9)(-7) + (-6)(-7)(-3) + (-3)(-6)(-1) + (-7)(-5)(-6) = -72
Cofactor of a_33:
Cofactor = (-1)^(3+3) * (-72) = -72
Therefore, the minors and cofactors are:
|882 270 -72| |-490 194 198| |78 -44 -72|
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when a child turns 18 years old the money in the account will be a birthday gift. The grandfather's choosing in between two options. option one and account that grows by 10.5% each year or option two and account that grows by $20 each year. which option will result in a better 18th birthday gift explain your reasoning.
10.5% is better because 20 dollers is good but it not gonna increase like 10.5%
it takes 6 painters 4 1/2 to paint these classroom. calculate how long 3 painters will take to complete the same job
which direction does the gradient v point in the direction of maximum increase or maximum decrease in v
The negative of the gradient (-grad f(x)) points in the direction of the maximum decrease of f from x.
The gradient of a scalar-valued function is a vector that points in the direction of the maximum increase of the function.
In other words, if we consider a point in the domain of the function and take the gradient at that point, the direction of the gradient vector indicates the order in which the function increases the most from that point. Conversely, the negative gradient points in the direction of the maximum decrease of the function.
Specifically, let f be a scalar-valued function of n variables [tex](f: R^n - > R),[/tex]and let x be a point in the domain of f. The gradient of f at x is defined as the vector:
[tex]grad f(x) = (∂f/∂x1, ∂f/∂x2, ..., ∂f/∂xn)[/tex]
where ∂f/∂xi denotes the partial derivative of f with respect to xi evaluated at x, the direction of the gradient vector grad f(x) at x is the direction in which f increases the most from x, and the magnitude of the gradient vector is the rate of change of f at x in that direction.
The negative of the gradient (-grad f(x)) points in the direction of the maximum decrease of f from x.
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Esmanol A spinner with 12 equally sized slices has 4 yellow slices, 3 red slices, and S blue slices. The dial is spun and stops on a slice at random. What is the probability that the dial stops on a slice that is not yellow?
The probability of spinning a slice that is not yellow is equal to the total number of non-yellow slices divided by the total number of slices.
Total number of non-yellow slices = 9 (3 red + 5 blue)
Total number of slices = 12
Therefore, the probability of spinning a slice that is not yellow is 9/12 or 75%.
determine if the transformation is one to one and/or onto. justify your answers. give an explanation for each of these properties.
To determine whether a transformation is one-to-one or onto, one must analyze its behavior and properties, such as passing the horizontal line test for one-to-one or checking if the range equals the codomain for onto.
In mathematical terms, a transformation refers to a function that maps elements from one set, called the domain, to another set, called the range. A transformation is said to be one-to-one if no two distinct elements in the domain are mapped to the same element in the range. This means that each element in the range is associated with a unique element in the domain.
On the other hand, a transformation is onto if every element in the range is mapped to by at least one element in the domain. In other words, for each element in the range, there exists at least one element in the domain that maps to it.
To determine whether a transformation is one-to-one or onto, one can analyze its properties and behavior. For example, a transformation is one-to-one if and only if it passes the horizontal line test. This means that no two points in the domain map to the same point on a horizontal line. To determine if a transformation is onto, one can check if the range of the transformation equals the codomain.
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The given question is incomplete, the complete question is:
How to determine the transformation is one to one and/or onto?
The number of the words formed with letters of the word 'PROBLEM' with neither start with O nor end with E.
The number of words formed with letters of the word 'PROBLEM' which neither start with O nor end with E is 3600.
The word PROBLEM has 7 letters, which can be arranged in 7! (factorial) ways, i.e. [tex]7*6*5*4*3*2*1 = 5040.[/tex]
Now to calculate the number of words formed with letters of the word 'PROBLEM' which neither start with O nor end with E, we can first calculate the number of words which start with O or end with E.
For words starting with O, there are 6 letters left and these can be arranged in 6! ways, i.e.[tex]6*5*4*3*2*1 = 720.[/tex]
For words ending with E, there are again 6 letters left and these can be arranged in 6! ways, i.e. [tex]6*5*4*3*2*1 = 720[/tex].
Now the total number of words which start with O or end with E will be the sum of two, i.e. 720 + 720 = 1440.
Therefore, the number of words formed with letters of the word 'PROBLEM' which neither start with O nor end with E will be the total number of words minus the total number of words which start with O or end with E, i.e. 5040 - 1440 = 3600.
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25 POINTS, PLS EXPLAIN! Which sum or difference is modeled by the algebra tiles? Select the correct answer. (-2x + 3) + (3x − 4) (-2x + 3) − (3x − 4) (2x − 3) + (-3x + 4) (2x − 3) − (-3x + 4)
Answer: Consider the expression (2x − 3) − (-3x + 4).
First, distribute the negative sign and rewrite the expression:
2x − 3 + 3x – 4.
Then, model the polynomial.
There are no zero pairs, so the difference is 5x − 7.
Step-by-step explanation:
PLATO
A system of equations is shown. 2x-y= 15 y=9 What is the value of x in the solution to this system?
Answer:
x=12
Step-by-step explanation:
2x-y=15
y=9
2x-9=15
2x=24
x=12
For numbers 3, 4, and 5, find the value of the indicated length(s) in ⨀C. A and B are points of tangency. Simplify all radicals.
I just need help with these three problems!
As a result, AB = 52 and AC = BC = 5 as AC and BC are both the circle's radii since A and B are points of tangency .
what is circle ?A circle is a closed object made up of all points in a plane that are separated from the center by a predetermined distance, known as the radius. The diameter is the distance across the circle that passes through its center, while the circumference is the distance around the circle. The ratio of a circle's circumference to its diameter is always pi (), or roughly 3.14. Pi is also known as the proportionality constant. Circles are significant geometric forms that are used frequently in mathematics, science, and daily life.
given
AC and BC are both the circle's radii since A and B are points of tangency. Hence, AC = BC = 5.
We can apply the Pythagorean theorem to segment AB as follows:
[tex]AB^2 = 52 + 52 \\AB^2 = AC^2 + BC^2[/tex]
AB² = 50
AB = √50 = 5√2
As a result, AB = 52 and AC = BC = 5 as AC and BC are both the circle's radii since A and B are points of tangency .
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a man allowed 10 discount on the fixed price of an piece of a land and offered 5 commision to the broker if he received 256500 what was the fixed price of land
The fixed price of the land is 296257.50.
What is discount?
Discount is the state of having a bond's price lower than its face value. The difference between the purchase price and the item's par value is the discount.
Discounts are different types of price reductions or deductions from a product's cost. It is frequently employed in consumer transactions when consumers receive discounts on a range of goods. The % discount rate is provided.
Here the discount on the fixed price = 10%
Commission for the broker = 5%
If total amount = 100%+10% = 110%
Then received amount = [tex]\frac{110}{100}\times256500[/tex]
=> Received amount = 282150
Now 5% commission then,
=> [tex]\frac{105}{100}\times 282150[/tex] = 296257.50.
Hence the fixed amount of the land before discount is 296257.50.
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ANSWER THIS QUESTION FAST WILL GIVE BRAINLIEST
In each triangle, M, N, and P are the midpoints of the sides. Name a segment parallel to the one given.
Answer: MN || VT
Step-by-step explanation:
We can see that MN is vertical, and the only angle that is vertical, is VT. And we can see that they don't obstruct their lines (meaning that they don't intersect), and keep going for infinity. So, VT would be the only parallel line to the one given.
Hope this helps
find the following answers
Answer:
hope it helps
Step-by-step explanation:
based on the given condition formulate
The number 0 is an element of the set of natural numbers.
OA. True
B. False
SUBI
it is false. 0 is not a natural number. it is a whole number
What is the answer? Need help!!!
Use the given acceleration function to find the velocity vector v(t), and position vector r(t). Then find the position at time t = 4.
a(t) = eti − 6k
v(0) = 2i + 9j + k, r(0) = 0
The velocity vector and position vector and position vector at t=4 is r(4) = (e₄+2)i+36j - 44k.
a(t) = eti - 6k
Since we know that v(t) = ∫ a(t) dt
= ∫ (eti - 6k) dt
= ∫6ti-6tk+c
where c is the arbitrary vector valued constant
since it is given that
v(0) = 2i + 9j + k
therefore from above
v(0) = e * 0i - 6(0) * k + c
2i + 9j + k =i+c
C= i +9j+k
therefore,
v(t) = eti - 6tk + i + 9j + k
= (et + 1) * i + 9j + (- 6t + 1) * k
Since we know that velocity vector can be found by integration of acceleration vector.
Since, v(t) = (et + 1) * i + 9j + (- 6t + 1) * k
and we know that
R(t) = ∫ v(t)dt
= ∫ of [(a + 1)i + 9j+(-6t + 1)k]dt =(a+t)i+9tj+(-3ta+t)k+C
where C is an arbitrary vector constant.
Now,
Since it given that r(0)=0 therefore
r(0) =(e0+1)+9(0)j)+(-3(0)2+0)x+C
0=2i+ C
C= -2i
therefore
r(t)= (et+t)i+9tj+(-3t+t)k-2i
r(t)=(a+t-2)1+9tj+(-3t+t)k
Since we know that position vector can be found by integration of velocity vector
r(4) = (e4+4-2)i+9(4)j + (-3(4)+4)k
r(4) = (e4+2)1+36j-44k
Now we have found the velocity vector and position vector and position vector at t=4 which are as follows:
v(t) =(et+1)i+9j+(-6t+1)k
r(t) =(et+t-2)i+9tj+(-3t2+t)k
r(4) = (e₄+2)i+36j - 44k
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Lisa records the amount of time she plans to spend for each reading session during a one month period on the line plot
5. If Lisa redistributes the total time
equally over all her reading sessions,
how long will each session be?
Answer:
Step-by-step explanation:
mathematicians divide the world of numbers into at least seven subsets. list seven subsets and define each
Mathematicians divide the world of numbers into seven subsets, namely natural numbers, whole numbers, integers, rational numbers, irrational numbers, real numbers, and complex numbers.
Natural numbers: These are the counting numbers, starting from 1 and continuing indefinitely. They can also be denoted as "N" or "ℕ".
Whole numbers: These are the natural numbers, as well as zero. They can also be denoted as "W" or "ℤ⁺⁰".
Integers: These are the whole numbers, as well as their negative counterparts. They can also be denoted as "Z" or "ℤ".
Rational numbers: These are numbers that can be expressed as a fraction, where the numerator and denominator are integers (and the denominator is not zero). They can also be denoted as "Q" or "ℚ".
Irrational numbers: These are numbers that cannot be expressed as a fraction of two integers. They are often represented by decimal expansions that neither terminate nor repeat. Examples include π and the square root of 2.
Real numbers: These are all the rational and irrational numbers, taken together. They can also be thought of as numbers that can be located on a number line. They are often denoted as "R" or "ℝ".
Complex numbers: These are numbers of the form a + bi, where a and b are real numbers and i is the imaginary unit (defined as the square root of -1). Complex numbers can be added, subtracted, multiplied, and divided, just like real numbers. They are often denoted as "C" or "ℂ".
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Graph the system below and write its solution
Y=1/4x-3
-x+4y=-4
The graph of the system of equations is shown below:
The solution of the system is given by the point of intersection of the two lines which is (20/7, -7/2).
Let f(x)=3-x and g(x)=1/x.
f/g(x)
In Exercise 5.1, we determined that the joint distribution of Y1, the number of contracts awarded to firm A, and Y2, the number of contracts awarded to firm B, is given by the entries in the following table.
The marginal probability function of Y1 was derived in Exercise 5.19 to be binomial with n = 2 and p = 1/3. Find
a E ( Y 1 ).
b V ( Y 1 ).
c E ( Y 1 − Y2).
Reference
Contracts for two construction jobs are randomly assigned to one or more of three firms, A, B, and C. Let Y1 denote the number of contracts assigned to firm A and Y2 the number of contracts assigned to firm B. Recall that each firm can receive 0, 1, or 2 contracts. a Find the joint probability function for Y1 and Y2.
b Find F(1, 0).
The marginal probability function E(Y1) = 2/3, variance of a binomial distribution is V(Y1) = 4/9, and E(Y1-Y2) = 0, using the joint probability function for Y1 and Y2 and the fact that they have binomial distributions with n=2 and p=1/3.
The marginal probability function of Y1 is binomial with n=2 and p=1/3, as given in Exercise 5.19. Therefore, we have:
E(Y1) = np = 2(1/3) = 2/3.
The variance of a binomial distribution with parameters n and p is given by np(1-p), so we have:
V(Y1) = np(1-p) = 2(1/3)(2/3) = 4/9.
We can use the linearity of expectation to find E(Y1-Y2):
E(Y1 - Y2) = E(Y1) - E(Y2)
We know that E(Y1) = 2/3 from part (a), but we need to find E(Y2). Using the same reasoning as in part (a), we find that the marginal probability function of Y2 is also binomial with n=2 and p=1/3. Therefore, we have:
E(Y2) = np = 2(1/3) = 2/3.
Substituting these values into the expression for E(Y1-Y2), we get:
E(Y1 - Y2) = 2/3 - 2/3 = 0.
Therefore, E(Y1-Y2) is equal to 0.
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have to 4. Thandi works for an organisation that packs food parcels for the poor. A company has donated 19 boxes of assorted tins, each containing 55 cans. Calculate how many cans each family will receive if there are 95 families to feed
If there are 95 families to feed then each family will receive 11 cans of assorted tins.
What is assorted tins?Assorted tins typically refer to cans or containers of food items that come in different varieties or flavors.
According to question:To calculate the number of cans each family will receive, we need to first determine the total number of cans in the 19 boxes.
19 boxes × 55 cans per box = 1045 cans
Now we can divide the total number of cans by the number of families to determine the number of cans each family will receive:
1045 cans ÷ 95 families = 11 cans per family (rounded to the nearest whole number)
Therefore, each family will receive 11 cans of assorted tins.
For example, a box of assorted tins may contain cans of different types of vegetables, fruits, soups, or other food items. The specific assortment may vary depending on the context and the supplier. In the context of the given question, the 19 boxes of assorted tins likely contain cans of different types of food that will be packed into food parcels for the poor.
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This year, the ratio of Alan's age to Bernice's age is 1:2. Four years ago, the total age of Alan and Bernice was 55 years. How old is Alan this year?
Answer:
21 years old
Step-by-step explanation:
Set Alan's age as x, Bernice's age as y
2x=y
x-4+y-4=55
x+y=63
3y=63
x=21
y=42
Between 11pm and midnight on Thursday night Mystery pizza gets an average of 5.9 telephone orders per hour
URGENT
Answer:157
Step-by-step explanation:
it just is =]
What is the solution for those?
And if you can please add the explanations
The required simplified forms are 3x - 1, 6x , 2x² - 10x , a + 2b , 15x - 8 , x² + 2x + 6 , x² - y² , 6x² - 22x.
What is Equation?the definition of an equation is a mathematical statement that demonstrates that two mathematical expressions are equal. For instance, the equation 3x + 5 = 14 consists of the two expressions 3x + 5 and 14, which are separated by the 'equal' symbol.
According to question:Simplified forms of the equation are
[tex]$c: 3(x-2)+5=3x-6+5=3x-1$[/tex]
[tex]$f: 2x(3-x)+x^2=6x-x^2+x^2=6x$[/tex]
[tex]$i: 7x^2-5x(x+2)=7x^2-5x^2-10x=2x^2-10x$[/tex]
[tex]$c: 2a-(a-2b)=2a-a+2b=a+2b$[/tex]
f: [tex]$3x-4(2-3x)=3x-8+12x=15x-8$[/tex]
[tex]$x(x+4)-2(x-3)=x^2+4x-2x+6=x^2+2x+6$[/tex]
[tex]$x(x+y)-y(x+y)=(x-y)(x+y)=x^2-y^2$[/tex]
[tex]$o: 4x(x-3)-2x(5-x)=4x^2-12x-10x+2x^2=6x^2-22x$[/tex]
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Question 25 (2 points)
Suppose the Math Department has 17 full-time faculty members. If 3 are selected to
attend a conference in Las Vegas, in how many different ways can you selected the 3
individuals?
3
17
680
4080
Answer:
680 ways
Step-by-step explanation:
C(17, 3) gives 17! / (14! 3!), or (17*16*15)/6 = 680 ways to select the 3 individuals.
Hope this helped!
Label all of the angle measures on the transversal.
Remember you can find all of the angles since you know one of them is 45 degrees.
The transversal angle of 45 is angle6.
What are angles?Two lines intersect at a location, creating an angle.
An "angle" is the term used to describe the width of the "opening" between these two rays. The character is used to represent it.
Angles are frequently expressed in degrees and radians, a unit of circularity or rotation.
In geometry, an angle is created by joining two rays at their ends. These rays are referred to as the angle's sides or arms.
An angle has two primary components: the arms and the vertex. T
he two rays' shared vertex serves as their common terminal.
Hence, The transversal angle of 45 is angle6.
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What is this question asking? What does it mean by floor plan? A step-by-step explanation would be very much appreciated.
Answer:
this is when you want to draw a sketch of a building
June uses 192 jellybeans for every dozen (12) plastic eggs she fills. How many plastic eggs can she fill with 1,152 jellybeans?
Answer: June uses 192 jellybeans for every dozen (12) plastic eggs she fills, which means she uses 192/12 = <<192/12=16>>16 jellybeans per plastic egg.
To find how many plastic eggs can be filled with 1,152 jellybeans, we can divide 1,152 by the number of jellybeans per egg:
Number of eggs = 1,152 ÷ 16 = <<1152/16=72>>72
Therefore, June can fill 72 plastic eggs with 1,152 jellybeans.
Step-by-step explanation: