How many divisors of 7! = 7:6:5.4.3.2.1 are divisible by 7 ? (Example: 14 has
two divisors, 7 and 14, that are divisible by 7.)
Answers
Answer:
30
Step-by-step explanation:
7! = 7*(2*3)*5*(2*2)*3*2*1 = [tex]7*5*3^{2}*2^{3}[/tex]
Ignoring the 7, there are 24 factors of this number as you will multily each of the factors of 6! by 7 to get each of the factors of 7! divisble by 7. But since you ignored the 7, you need to bring back the possible values of 7*6, 7*5, 7*4, 7*3, 7*2, 7*1.
24 + 6 = 30 divisors
There are 60 divisors of 7!.
What is factorial?The factorial function can be used to determine the ordered set of numbers or how many different ways things can be arranged. Daniel Bernoulli discovered the factorial function's well-known interpolating function. Numerous mathematical concepts, including probability, permutations and combinations, sequences and series, and so on, make use of the factorial idea.
Given 7!
We must first write 7! as the product of prime numbers, as shown below. The highest power of a prime number is typically divided by N! is given by [tex]s_{p}[/tex](N!)=N/p + N/p² + N/p³ +.......
Since you want to count the number of terms that are multiples of p and contribute one p to N!, the first term appears. However, when you have multiples of p², you are not simply multiplying one p; rather, you are multiplying two primes p to the product. Therefore, you now count and add the number of multiples of p² that are less than N.
let for p =2
[tex]s_{p}[/tex](7!) = 7/2 + 7/4 + 7/8 + ......... = 3 +1 = 4
we have to repeat this process for 3,5,7
we get 7!=2⁴ x 3² x5¹ x7¹
Now, the number of divisors of 7 is equivalent to number of ways of selecting zero or more objects from the group of identical objects
=(4 +1)(2 + 1)(1 + 1)(1 + 1) = 60 includes 1 and 7.
Hence the divisors of 7! is 60.
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Related Questions
Simplify the following:
(3i-3)(3i+3) and (4i+7)(-6i+20)
Answers
1. -18
2. 164+38i
Bill drove his car at a constant speed while on a trip. Kevin drove his car at a different constant speed while on the same trip. The graph and the table show information about the trips Bill and Kevin took.
Which sentence correctly compares the rates Bill and Kevin drove on their trips
Answers
What do you think?
What is the solution for the equation -5/2 equals 3/4+ n
Answers
Answer:
3/4+n=-5/2
n=-10/4-3/4
n=-13/4
Step-by-step explanation:
Answer:
n = -13/4
Step-by-step explanation:
-5/2 equals 3/4+ n => -5/2 = 3/4+ n
Recognize that the LCD here is 4. Multiply all three terms by 4, obtaining:
-10 = 3 + 4n
Combining the constants results in
-13 = 4n, so that n = -13/4
A system of equations where both X and Y cancel and you are left with just a number is called
Answers
It has been estimated that a certain stream can support 85,000 fish if it is pollution-free. It has further been estimated that for each ton of pollutants in the stream, 1700 fewer fish can be supported. Assuming the relationship is linear, write the equation that gives the population of fish p in terms of the tons of pollutants x.
Answers
Answer:
[tex]p = 85000 - 1700x[/tex]
Step-by-step explanation:
Given
[tex]Initial\ Fish = 85000[/tex]
[tex]Rate = 1700[/tex]
Required
Determine the equation
For 1 ton, there is a reduction of 1700 fishes
This implies that:
For x tons, there will be a reduction of 1700x fishes
So, the function is:
[tex]p = Initial\ Fishes - Rate * x[/tex]
We used minus because the number of fishes reduced.
So, we have:
[tex]p = 85000 - 1700*x[/tex]
[tex]p = 85000 - 1700x[/tex]
Hence, the function is: [tex]p = 85000 - 1700x[/tex]
If the graph of a line goes from the upper left corner of the graph to the lower right corner what can you say about its slope ?
Answers
Answer: You can say that the slope is negative since the graph is decreasing.
Step-by-step explanation:
A baker makes apple tarts and apple pies each day. Each tart, t, requires 1 apple, and peach pie, p, requires 8 apples. The baker receives a shipment of 184 apples every day. If the baker makes no more than 40 tarts per day, which system of inequalities can be used to find the possible number of pies and tarts the baker can make?
t ≤ 40
p ≤ 184
t ≤ 40
8p ≤ 184
t ≤ 40
p + 8t ≤ 184
t ≤ 40
8p + t ≤ 184
the answer is D is the answer
Answers
Answer:
i think 8p+tLess equal to 184
The inequality system may be used to determine the maximum number of pies and tarts the baker is capable of producing is t ≤ 40 and 8p + t ≤ 184.
What is inequality?It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.
We need to define variables initially in this situation. Thus, we have the number of tarts and the number of pies, which are p and t respectively.
Apples are needed for each tart, abbreviated t, and for each pie, abbreviated p.
It is given that every day, a supply of 184 apples is sent to the baker
8p + t ≤ 184
The baker only produces up to 40 tarts every day as a result
t ≤ 40
Thus, the inequality system may be used to determine the maximum number of pies and tarts the baker is capable of producing is t ≤ 40 and 8p + t ≤ 184.
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8. What is the value of x?
82
(4x + 4)
(2x + 4)
Answers
Answer:
x = 12 and 1/3
Step-by-step explanation:
At a deli, Joe bought 2.2 pounds of coleslaw for $7.15. What was the unit price?
Answers
Answer:
$3.25 for 1 pound of coleslaw
Step-by-step explanation:
i think,.
Mrs. Hanson has a potato salad recipe that calls for 2 3/8 pounds of potatoes, but she wants to make 1 1/2 times as much as the recipe calls for. The diagram represents the number of pounds of potatoes that Mrs. Hanson needs. How many pounds of potatoes does Mrs. Hanson need? Enter your answer as a mixed number in simplest form by filling in the boxes. Need an answer fast!!!
Answers
The pounds of potatoes that Mrs. Hanson needs is 3 9/16 pounds.
How many pounds of potatoes does Mrs. Hanson need?A mixed number is number that consists of a whole number and a proper fraction. A proper fraction is a fraction in which the numerator is less than the denominator. An example of a mixed number is 2 3/8.
In order to determine the pounds of potatoes that Mrs. Hanson needs, multiply 2 3/8 by 1 1/2. Multiplication is the mathematical process that is used to determine the product of two or more numbers. The sign that is used to represent multiplication is x.
Pounds of potatoes that Mrs Hanson needs = 2 3/8 x 1 1/2
Pounds of potatoes that Mrs Hanson needs = 19/8 x 3/2
Pounds of potatoes that Mrs Hanson needs = 57 / 16 = 3 9/16 pounds
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Find the midpoint of the segment with the following endpoints
(9.9) and (1.-1)
Answers
Answer:
(5,4)
Step-by-step explanation:
To find midpoint you just find out how far apart the points are and divide it by half. For example our x values are 9 and 1. 9 and 1 are 8 points away. Half of 8 is four so 9-4 is 5. Remember midpoint is the MIDDLE.
Pls help i will mark please dont answer if you don’t know please
Answers
Answer:
35.84
Step-by-step explanation:
32x1.12=35.84
Answer:
$35.84
Step-by-step explanation:
Hi! Ace here.
The easiest way to do this is to use benchmark fractions.
10% of 32 = 3.2
1% of 32 = .32
1% of 32 = .32
Add up all the numbers:
3.2 + .32 + .32 = 3.2 + 64 = 3.84
Since it's a mark up, we do:
32 + 3.84 = $35.84
You can also use percent proportions which would look like this. I'm not going to explain it that much because I think that's what the other person did.
[tex]\frac{x}{112} =\frac{32}{100}[/tex]
[tex]x=\frac{112*32}{100} \\\\x=\frac{3584}{100} \\\\x=35.84[/tex]
Please let me know if you have any questions.
can someone help me ?!
Answers
Answer:
Gavin is incorrect. Divide 1/3 by 4, or multiply by 1/4. each friend gets 1/12 of the cake
Step-by-step explanation:
There are only red counters and blue counters in a bag
in the bag
the number of red counters: the number of blue counters = 5.7
What fraction of the counters in the bag are red?
Answers
Answer:
[tex]Red\ Fraction = \frac{5}{12}[/tex]
Step-by-step explanation:
Given
[tex]Red:Blue = 5 : 7[/tex]
Required
Determine the fraction of red
To do this, we make use of:
[tex]Red\ Fraction = \frac{Red}{Red + Blue}[/tex]
This gives:
[tex]Red\ Fraction = \frac{5}{5+7}[/tex]
[tex]Red\ Fraction = \frac{5}{12}[/tex]
1. Given the following relation, determine the inverse relation.
a. {(-1,0), (- 4,5), (3,2), (-3,5)}
b. f(x) =x + 3
2. Represent the inverse of the following relation algebraically and graphically.
f(x) = 2x - 4
Answers
Answer:
1. a
2. [tex]f^{-1} (x)=\frac{x}{2} +2[/tex]
Step-by-step explanation:
1. Since there is one value of y for every value of x in (−1,0),(−4,5),(3,2),(−3,5), this relation is a function.
2. To find the inverse, interchange the variables and solve for y.
[tex]f^{-1} (x)=\frac{x}{2} +2[/tex]
1. Lily wants to buy 4 pounds of cereal for her camping trip. The boxes are each 18 ounces. According to the number line, how many boxes will she need to buy to have at least 4 pounds? 18 36 72 +++ 26 32 48 80
1: 2 boxes
2: 5 boxes
3: 3 boxes
4: 4 boxes
Answers
Answer: 4 boxes.
Step-by-step explanation:
We know that each box has 18 ounces of cereal.
We know that:
1 lb = 16 oz
Then:
1 = (1lb/16oz)
Then we can write:
18 oz = 18oz*(1lb/16oz) = (18/16) lb
This means that each box has (18/16) pounds of cereal.
Now, how many boxes we need to buy if we want to have at least 4 pounds of cereal?
If we buy N boxes, we will have N*(18/16) lb boxes of cereal.
Let's find N such that:
N*(18/16) lb = 4lb
N = 4*(16/18) = 3.56
But you can not have a 0.56 of a box, so we should round our number up to the next whole number, then we get:
N = 4.
She should buy 4 boxes.
Answer:
4
Step-by-step explanation:
Good Luck
Jared bought a 15-pound bag of turkey for Thanksgiving. His family ate 6 ⅗ pounds of the food on the morning of Thanksgiving and 4 ⅘ for dinner. Jared decided to use ½ of the remaining turkey to make sandwiches for lunch. How much turkey, in pounds, did Jared use to make sandwiches?
Answers
Answer:
1 4/5 pounds
Step-by-step explanation:
15-6= 9
9-4=5
3/5+4/5=7/5 or 1 2/5
5-1=4
4-2/5=3 3/5
half of 3 is 1.5 or 1 5/10
3/5=6/10 half of 6/10 is 3/10
3/10+5/10= 8/10
simplify 1 8/10= 1 4/5
Evaluate m2 + 12q if m= 5 and q =-3 plz
Answers
Answer:
-11
Step-by-step explanation:
m²+12q
= (5)² + 12(-3)
= 25 -36
= -11
5² + 12(-3)
25 + (-36)
25 -36
= -11
Jonas is buying fencing to surround his garden. If his garden has a perimeter of 36 feet, and fencing costs
$10.00 a yard, how much money will he need for the fencing?
Answers
Answer:
Step-by-step explanation:
$120
which of the following is a quadratic equation in one variable. a.7x^2-15=32x b.x^2+y+9=0 c.3x+2y=8. d. 5x -15=0
Answers
Answer:
a. 7x^2-15=32x
Step-by-step explanation:
a standard form quadratic equation is written as ax^2+bx+c=0
7x^2-15=32x can be rewritten into 7x^2-32x-15=0 by subtracting 32x on both sides.
options b and c don't work because they include another variable, y
option d is a linear equation, not a quadratic
PLEASE ANSWER THIS QUESTION CORRECTLY AND ILL MARK BRAINLY
Answers
You forgot the image attached to the question. I will edit my answer after you edit the question
Help pre- algebra
:DD
Answers
Answer:
Calzones are $ 8 and an Empanada costs $12
Step-by-step explanation:
2x+3y=52
4x+3y=68
Multiply by -1
-2x-3y=-52
4x+3y=68
combine
2x=16
x=8
plug in 8
4(8)+3y=68
32+3y=68
3y=36
y=12
Step-by-step explanation:
step 1. 2c + 3e = 52, 4c + 3e = 68.
step 2. this is a system of equations. solve the system.
step 3. subtract the 1st equation from the 2nd.
step 4. 2c = 16, therefore c = 8.
step 5. 2(8) + 3e = 52. 3e = 36. e = 12.
step 6. calzones = 8, empanadas = 12.
Sandy works at a clothing store. She makes $8 per hour plus earns 10% commission on her sales. She worked 76 hours over the last two weeks and had a total of $1,942 in sales before taxes.
Which of the following is closest to how much she will earn in hourly wages and commission for those two weeks? PLEASE HELP DUE AT 12!
Answers
per hour Sandy earns (together with commission):
8 + 0.15*8 = 1.15*8 = $9.2 per hour
for the 74 hours worked she will earn total of:
74*9.2 = $680.8
A $592 is the closest.
Pls help
Solve the equation —3x —12 = —39 for x, and show all steps.
Answers
Answer:
x=9
Step-by-step explanation:
-3x-12=-39 Add the like terms (if you add 12 to negative 12 it cancels out)
+12 +12
-3x=-27 Now divide
/-3 /-3
x=9
For every quad, there are 4 wheels. Complete the
chart to show how many wheels there would be,
following this pattern.
Answers
What is the volume of the cone below?
O A. 132pi units3
O B. 264pi units3
O C. 396pi units3
O D. 792pi units3
Answers
Answer:
B. 264π units³
Step-by-step explanation:
Volume of the cone = ⅓πr²h
Where,
r = 6
h = 22
Plug in the values
Volume = ⅓×π×6²×22
Volume = ⅓×π×36×22
Volume = 264π units³
A large pizza costs $17.99. A second large pizza is 14 off. Using an estimate, approximately how much will it cost for 2 large pizzas?
Answers
Answer:
$22
Step-by-step explanation:
17.99 round up so 18
a second large pizza is 14 dollars off of the original price of 18 so 4
18+4 is 22
so 2 large pizzas would cost $22
Can you help, I will give you alot of points. 50 to be exact
Answers
Answer:
Part 1
190/38 = 5 minutes266/38 = 7 balloonsPart 2
266/190 = 1.4 balloons/min1.4*10 = 14 balloons / 10 minLcm of 20, 3 quick math
Answers
Answer:
least common multiple of 20 and 3? it would be 60.
3. What is the probability that Austin will spin a number less than 3?
A 40%
B 45%
C 60%
D 2