Answer: 33
======================================================
Explanation:
The exclamation mark means factorial.
Factorial's are operations in which we start with the given number, then count our way down to 1, multiplying along the way.
Examples:
7! = 7*6*5*4*3*2*14! = 4*3*2*1The original number must be a positive whole number (side note: other inputs are possible but we have to involve more complicated math which I'll ignore for this solution).
Let's expand out the first few terms. I'll leave them in factored form and not multiply out the values
1! = 1
2! = 2*1
3! = 3*2*1
4! = 4*3*2*1
5! = 5*4*3*2*1 ... note the 3 and 5 in bold
6! = 6*5*4*3*2*1
7! = 7*6*5*4*3*2*1
This keeps going until we reach 100!
As you can see in the factors above, we have 3 and 5 show up as soon as we reach 5! which means we'll have 3*5 = 15 as a factor of the following items: {5!, 6!, 7!, 8!, ..., 99!, 100!}
Each higher factorial just builds in the last factorial so to speak.
So what this means is that we can write this
15q = 5!+6!+7!+...+99!+100!
where q is some integer. We don't need to worry about what q is
--------------
Therefore,
1!+2!+3!+4!+5!+6!+7!+...+99!+100!
1!+2!+3!+4!+( 5!+6!+7!+...+99!+100! )
1!+2!+3!+4! + 15q
1+2+6+24 + 15q
33+15q
15q+33
--------------
Recall that if we divide integers x and y, then
x/y = q remainder r
x/y = q + r/y
x = yq+r
Where q and r are the quotient and remainder.
Since 1!+2!+3!...100! = 15q+33, we're in the form yq+r showing that r = 33 is the remainder.
find the value of x
Answer:
[tex] \frac{28}{3x - 1} = \frac{24}{x + 7 } \\ 24(3x - 1) = 28(x + 7) \\ 72x - 24 = 28x + 196 \\ 72x - 28x = 24 + 196 \\ 44x = 220 \\ x = 5[/tex]
Find the value of x
X + 90
100°
Anyone, can help me with this question?
25)
9514 1404 393
Answer:
A) Positive (4, 2, 0), negative (0)
Step-by-step explanation:
Descartes' rule of signs tells you the number of positive real roots is equal to the number of sign changes in the coefficients (with allowance for an even number of roots possibly being complex).
The signs of the coefficients are ...
- + - + -
so there are 4 sign changes. The number of positive real roots will be 4, 2, or 0.
__
Changing the signs of odd-degree terms, you can use the same method to determine the number of negative real roots. With those signs changed, the signs of the coefficients are ...
- - - - -
so there are 0 sign changes. The number of negative real roots is 0.
_____
The graph shows there are no real roots of either sign. All the roots are complex.
Write the following using algebraic notation, using the letter x for any
unknown numbers:
I think of a number, add seven, then divide by five.
Answer:
(x+7)÷5
Step-by-step explanation:
since the number is unknown, it becomes X. Because we first add 7 then divide by 5, the expression will be a bracketed (X+7), followed by the division by 5. This makes sense because of the BODMAS rule to which, in coherence with the BODMAS rule, we first solve the expression in the brackets then move on outside them.
Help please !! I need to find x
Answer:
6
Step-by-step explanation:
12x + 3 = 11x + 9 because these two angles are corresponding angles
12x - 11x = 9 - 3
x = 6
What is 22.5 subtract by 2.5
Answer:
The answer is 20 hope this helps
Step-by-step explanation:
22.5 divided by 2.5 = 20
Write the equivalent fraction with a denominator of 100.
9/10 = ?/100.
Answer:
90
Step-by-step explanation:
Find common denominators. Note that what you multiply to the denominator (bottom number of the fraction), you must also multiply to the numerator (top number of the fraction).
In this case, you are multiply 10 to both the numerator and denominator, as:
100/10 =10
Multiply 10 to the numerator:
? = 9 * 10
? = 90
90 is your answer.
~
Since the fractions are equivalent to each other, they must have the same simplified value. It means they can be multiple or divisor of each other.
Here, we have to find the numerator of the second fraction for which we have to multiply with the same number with which we multiplied the denominator.
➝ 10 × 10 = 100
The denominator was multiplied with 10, So the numerator will be multiplied with 10 too.
➝ 9 × 10 = 90
➝ [tex] \dfrac{9 \times 10}{10 \times 10} = \dfrac{90}{100} [/tex]
Thus, the required numerator is 90
Carry On Learning !
Multiply.
3⋅3/5
Enter your answer as an improper fraction, in simplified form, by filling in the boxes.
Answer:
9/5
Step-by-step explanation:
3/1 x 3/5 = 9/5
:HOPE THIS HELPS
Simplify the expression.
Exact Form:
9
_ 9 over 5
5
Decimal Form:
1.8
Mixed Number Form:
1 4/5
the cost of old boiler is £775 per year,the new one is £1850 ,the cost of using a new boiler will be 1/5 less than the cost of using the opd boiler. how many years will it take for the savings feom cost of using nthe new boiler to total £1850
Answer:
I think its 12.3 years
Step-by-step explanation:
a fifth of 775 is 155 and 155 x 12.3 = 1850
What is 7 7//8 + 2 1/4=
Answer:
14.875
Step-by-step explanation:
77/8 = 9.625 and 21/4 = 5.25
So, 9.625+5.25 =14.875
Answer: 10 1/8
............................
mr peters drives 266 miles in 3.5 hours what is the rate mr peters travels
Answer:
The answer is 76
Step-by-step explanation:
I just divided 266 by 3.5 - *I used a calculator*
HELP ASAP 15 POINTS
Look i know this isnt mathematics but its an easy 15 points if your good a rhyming or if you just know the basics.
I need a rap or song about the six main nutrients (water, protein, carbohydrates, fats, minerals, and vitamins)
Answer:
I hope this helps
Step-by-step explanation:
carbonhydrates protein water fats minerals and vitamins
1. Five more than twice a number is 7.
Answer:
5+2n=7
Step-by-step explanation:
5+2n=7
7-5=2n
2=2n
2÷2=1
n=1
Find the interest on the following loan.
$5350 at 9%; loan made on August 15 and due December 18
The simple interest for this loan is $
(Round to the nearest cent as needed.)
Answer for 2020: loan maturity in days 125
Actual Interest is $164.90
Step-by-step explanation:
loan x Interest x Time (in days =Total interest
the simple interest on the loan is approximately $161.28.
To calculate the interest on the loan, we need to determine the time period in years and multiply it by the principal amount and the interest rate.
The loan period runs from August 15 to December 18, which is a total of 4 months. To convert this into years, we divide 4 by 12 (since there are 12 months in a year), resulting in 1/3 or approximately 0.3333 years.
The principal amount is $5350, and the interest rate is 9% or 0.09 as a decimal.
Using the formula for simple interest: Interest = Principal x Rate x Time
Interest = $5350 x 0.09 x 0.3333 ≈ $161.28
Therefore, the simple interest on the loan is approximately $161.28.
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How man ten thousand are in 440000
What is the slope of the linear equation Y-5=3/7(x+2)
Answer:
[tex]y=\frac{3}{7} x+\frac{41}{7}[/tex]
Slope is 3/7
Step-by-step explanation:
y-5+5=3/7x+6/7+5
y=3/7x+41/7
Describe the relationship between integers and rational numbers.
Answer:
Integers are a subset of Rational Numbers because all Integers are Rational Numbers.
Step-by-step explanation:
Hope this helped mark me as brainliest (:
Answer: Every integer is a rational number, since each integer n can be written in the form n/1. For example 5 = 5/1 and thus 5 is a rational number. However, numbers like 1/2, 45454737/2424242, and -3/7 are also rational, since they are fractions whose numerator and denominator are integers
Step-by-step explanation:
Help please you will get 20 points
Answer:
Part B:
His measure is incorrect because the interior angles of every triangle result up to 180°. His measures (50+90+38) added up to 178; so his measures are false.
Which numbers have been rounded correctly to the nearest ten thousand? Choose a the correct answers.
A. 13,500 ➡️ 10,000
B. 78, 210 ➡️ 78,000
C. 620,499 ➡️ 600,000
D. 456,234 ➡️ 460,000
E. 129,302 ➡️ 129,000
F. 324,985 ➡️ 320,000
|4x-1|=2x+13
what does x equal
Answer:
2x+13=4x-1
2x=14
x=7
another solution
2x+13=-(4x-1)
2x+13 =-4x+1
6x=-12
x =-2
so solutions are 7,-2
Quadratic formula
x2 + 3x - 5 = 0
Answer:
2x +3x- 5= 0
5x-5=0
5x=0+5
5x=5
x=5÷5
x=1
Where’s my smart friends??
I had $3.00.
My Mom gave me $10.00.
My Dad Gave me $30.00.
My Aunt & Uncle gave me $100.00.
I had another $7.00.
How much did I have?
Answer:
$10 Its asking how much you had not how much was given to you. So the answer is you had 10
I have $150
In order to determine the amount you have, add the amounts you are given to the original amount. This is because the money you have increases by the amounts you are given
Total sum of money = amount you have + amount given by mum + amount given by dad + amount given by uncle and aunt
$3 + $10 + $30 + $100 + $7 = $150
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write the first 4 terms of the arithmetic sequence With first term 37 and common difference 9
Answers:
first term = 37
second term = 46
third term = 55
fourth term = 64
==========================================
Explanation:
Start at 37. Add 9 to this term to get the second term. Add 9 to that result to get the next term, and so on.
first term = 37
second term = 37+9 = 46
third term = 46+9 = 55
fourth term = 55+9 = 64
-----------
The nth term formula is
a(n) = 9n+28
It can be found by plugging a = 37 and d = 9 into the general form
a(n) = a + d*(n-1)
The four terms of the arithmetic sequence with a first term of 37 and a common difference of 9 are: 37, 46, 55, and 64.
An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms remains constant.
Given:
First term (a1) = 37
Common difference (d) = 9
The arithmetic sequence can be represented as follows:
[tex]a_1[/tex]= 37
[tex]a_2[/tex] = [tex]a_1[/tex] + d
= 37 + 9 = 46
[tex]a_3[/tex] = [tex]a_2[/tex] + d
= 46 + 9 = 55
[tex]a_4[/tex] = [tex]a_3[/tex]+ d
= 55 + 9 = 64
So, the first four terms of the arithmetic sequence are: 37, 46, 55, and 64.
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Susie filled up at the gas station where it costs $3.14 per gallon. She put 22.5 gallons of gas in her vehicle. She also bought a fountain drink for $0.99. How much did she spend at the gas station?
A. $66.00
B. $70.65
C. $71.64
D. $141.30
What is the zero of the function that is graphed below?
Answer:
a which is -2
Step-by-step explanation:
that's the answer
Please help me out fast.
Convert 4 to a percent.
Step-by-step explanation:
0.04 is ur answer ..........
Fill in the blanks from the attachment.
Answer: why was 8 scard of 7
Step-by-step explanation: becues
789
What is the value of y?
7-120
56"
7-2030 x g x 65 -=65 65 65 65
Joshua quick made a deposit to his checking and recieved $50 in cash. His deposit slip shows a total deposit of $90. If Joshua deposited checks worth six times the value of the coins he deposited, how much did he deposit in (a) coins and (b) checks?
Joshua deposited
(a). $12.85 in coins
(b). $77.14 in checks
Linear equation in one variable?
The linear equation in one variable is an equation which is expressed in the form of ax + b = 0, where a and b are two integers, and x is a variable and has only one solution.
According to the given question
Joshua deposited checks worth six times the value of the coins he deposited.
Let Joshua deposit the value of coins be x. Then the value of x will be 6x
There is total deposit of $90.
⇒ x + 6x = 90
⇒ 7x = 90
⇒ [tex]x = \frac{90}{7}[/tex] =$12.85
Therefore,
[tex]6x = \frac{90(6)}{7} =\frac{540}{7}[/tex] = $77.14
Hence, he deposit total $12.85 in coins and $77.14 in checks.
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