Find the sum of integers from 33 to 47:
Answer:
Step-by-step explanation:There are formulas to work this out, but you can also suss out an answer by a liberal application of critical thinking.
Okay, you want to add 51 + 52 + 53 + … + 99 + 100, right? (The … represents all the numbers in between, in case you were wondering.)
Well, that’s a total of 50 numbers. And if you know anything about addition, you know that it doesn’t matter what order you add them.
So you could also say 51 + 100 + 52 + 99 + 53 + 98 + … and so on.
Let’s see what happens. 51 + 100 = 151. So far so good.
Then, 52 + 99 also equals 151. And 53 + 98 also equals 151. Since there are 50 numbers, that’s 25 pairs that are going to add up to 151.
151 + 151 + 151 + 151 + … (21 more instances of 151).
So we can simplify our workload a bit. Instead of adding up all the numbers by hand, we can just multiply 151 by 25.
151 x 25 = 3775
From that, we can work out a generic formula that will allow you to add any sequence of numbers…without actually adding.
Let a be the first number in the sequence, and let n be the last number in the sequence. The number of numbers is (n - a) + 1. (You have to add 1, because if you just subtract, it’s like you’re losing the lowest number in the sequence).
So…you get the sum by adding the first and last number in the sequence, and then multiplying that result by half of the total number of numbers.
(a+n)((n−a)+12)
an−a2+a+n2−an+n2
−a2+a+n2+n2
−a(a−1)+n(n+1)2
Let’s check to see if it works!
−51(51–1)+100(100+1)2
−51(50)+100(101)2
−2550+10,1002
75502
3775
Note that if the starting number were 1, the formula would simplify to n(n+1)2
Following are the calculation to the sum of integers:
Given:
33 to 47
To find:
Sum of integers=?
Solution:
Given numbers:
33 to 47
[tex]\to \bold{33,34,35,36,37,38,39,40,41,42,43,44,45,46,47}[/tex]
Using formula:
[tex]\bold{S = \frac{n(a + l)}{2}}[/tex]
[tex]n=15\\\\a=33\\\\l=47 \\\\ \bold{S = \frac{15(33 + 47)}{2}}\\\\[/tex]
[tex]\bold{= \frac{15(80)}{2}}\\\\\bold{= \frac{1200}{2}}\\\\\bold{= 600}[/tex]
Therefore, the sum of the integers "600".
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Terry is feeling crafty and wants to put a ribbon border on her boring clock to jazz it up a bit. If the clock has a radius of 15inches, how many inches of ribbon will Terry need to use to surround the clock? Round your answer to the nearest hundredth
EMERGENCY! Please give me the correct answer!
Answer:
6^10
Step-by-step explanation:
6^0 is 1 so 6^10 x 1 is just 6^10
(04.05)Erika calculated that she would spend $115 on school supplies this year. She actually spent $82.50 on school supplies. What is Erika’s percent of error?
28.3%
2.8%
39.4%
32.5%
Answer:
28.3
Step-by-step explanation:
Help please!!! This is due in a couple hours!
I will give you brainliest
Answer:
I believe it would be 60
Step-by-step explanation:
Every triangle equals up to 180 degrees and this triangle is equal on all sides.
180÷3
Hope this helps! :)
a football stadium, 55% of the crowd is cheering for Team A, and 48 % of the crowd is female . 19% of the crowd is cheering for Team A and female . What is the probability that a randomly selected Person from the crowd are cheering for Team A or female?
Answer:
67%
Step-by-step explanation:
I added 48%+19%
If g(n) = 3n - 2, then what is the value of g(10)?
Answer:The answer would be 28 the value of g would
be 2.8
Step-by-step explanation:
The expression 937(1+x) gives the markup price of a computer, where x is the percent of the markup written in decimal form.
What does 1 + x represent in the expression?
Answer:
It represents 1 + the percent of the markup written in decimal form
Answer:
percent of original price being paid
I NEED HELP ASAP
The equation y+6
- 5(x-9) is written in point-slope form. What is the equation written in slope-intercept form
If Hector is 8 years old and Mary is 3 years old, how old will Mary be when Hector is 16? Can I use proportional reasoning in here
Answer: Mary will be 11, and yes you can
Step-by-step explanation: hector will be 16 in 8 years so you just add the 8 on to the 3
Is the table a function?
Answer:
Yes!
Step-by-step explanation:
Vocabulary Which statements are true about opposites? Choose all that apply.
Answer:
where are the options?
Step-by-step explanation:
i need help with linear functions can anybody help me?
I can help you! Just let me how what the questions are
How would you solve this?
Answer:
24k 21j37
Step-by-step explanation:
((0 - (22k3 • (j6)))2) • k15j25
k6 multiplied by k15 = k(6 + 15) = k21
j12 multiplied by j25 = j(12 + 25) = j37
25 POINTS!!
Consider a square and a regular hexagon (a six sided figure with sides of equal length). One side of the square is 8 feet longer than a side of the hexagon, and the two figures have the same perimeter. What are the lengths of the sides of each figure?
Answer:
The hexagon has sides of 8 feet and the square 's sides are 16 feet long..
Step-by-step explanation:
If the side of the hexagon is x feet then the side of the square = x+8 feet.
So as the perimeters are equal:
8x = 4(x + 8)
8x = 4x + 32
8x - 4x = 32
4x = 32
x = 8 = side of hexagon so the square side = 16 feet.
Answer:
6
Step-by-step explanation:
subscribe to DLO Aryan
-0.8b = 10.4
What is b and how does it make this equation true......?
Answer:
-13.375 is the answer
Trickets to the zoo cost $12 for adults and $8 for children. The school has a budget of $240 for the field trip. An equation representing the budget for the trip is 240=12x+8y where x representing the number of adults and y represents the number of children. Get your own graph of this equation
So select all the statement that are true
A. If 12 children go to the zoo, then 20 adults can go
B. If 18 children go to the zoo then 8 adults can go
C. If 4 adults go to the zoo then 30 children can go
D. If 16 adults go to zoo then 6 children can go
Answer:
is B
Step-by-step explanation:
If you multiplied 18 childrens x $8 and 8 adults x $12 you get 240
Answer:
The correct Answer is B
Step-by-step explanation:
Just did the Test.
factor each trinomal. write prime if it is not factorable
1. y2+14y+48
2. m2+8m+12
3. y2-12y+60
4. 12y2+17y-5
5. 10x2+31x+15
Answer:
ARMY-BTS
Step-by-step explanation:
The art club is raising money for a new equipment. They need $842.36 to purchase new supplies and have received a $300.00 donation. The remaining amount will be equally divided among 4 different fundraisers throughout the summer. How much money will each fundraiser need to raise in order to purchase the new net and equipment?
Answer: Each fundraiser need to raise $ 135.59 in order to purchase the new net and equipment.
Step-by-step explanation:
Money required = $ 842.36
Donation amount = $ 300.00
Amount left to arrange = (Money required - Donation amount )
= $ (842.36- 300.00)
= $ 542.36
Number of fundraisers = 4
Money required to arrange by each fundraiser = (Amount left to arrange) ÷4
= $ (542.36÷4)
= $ 135.59
Hence, each fundraiser need to raise $ 135.59 in order to purchase the new net and equipment.
How do I do this problem im confused?
Answer: 54800
Step-by-step explanation: plug in 6 instead of t in both the equations. Start with the first equation
-300t+150000
-300(6)+150000= 148200
Then do the other equation
500t+200000
500(6)+200000= 20300
Subtract both
203000-148200= 54800
Rewrite each expression in its equivalent form.
8pq - 3pq
ASAP PLZ HELPPP
Answer:
i believe its 5pq
Step-by-step explanation:
if you do the math of it it should still be the same
Answer:
5pq
Step-by-step explanation:
Step 1: Write expression
8pq - 3pq
Step 2: Combine like terms.
Since both have a pq term in it, we can simply subtract.
8 - 3 = 5
5pq
Math is hard please help, and explain i need to learn this.
Answer:
c
Step-by-step explanation:
Answer:
C is the answer
Step-by-step explanation:
Pls Help again I have to post separately
The six lowest temperatures for a certain date were listed
in an almanac as -32, -14, -28, -19, -38, and -21. Which of
these temperatures is the COLDEST?
Answer: -38 is the coldest because it is the lowest.
Is 1.75 x 10^6 written in scientific notation?
Answer:
yes it is
<3
Red
Answer:
yep it is ❤
Step-by-step explanation:
:)
hope this helps
♡
Jose desea cubrir los gastos del tratamiento del Cov.19 de un familiar,para ello solicita un préstamo de una entidad bancaria un moto que asciende de s/.5000 cantidad a pagar con un interés de 1.5% trimestral,ha previsto pagar con los intereses incluido en un plazo de dos años ¿Cuanto pagara jose por interés del dinero prestado? ¿Cuando sera el monto total que pagara Jose?
Answer:
Step-bynznsbsjsjsbsisksbbd-step explanation:bdndnsoansjj hi rodn
Answer:
gkssjsjsjssisndrishddhdsusucjdjejuzuxuddid
Which expression is equivalent to ^3 sqrt x^10?
Answer:
D
Step-by-step explanation:
Just did it, the other person was wrong.
The expression is equivalent to [tex]\sqrt[3]{x^{9}x }[/tex].
What is expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows:
Expression: (Math Operator, Number/Variable, Math Operator)
Given an expression, [tex]\sqrt[3]{x^{10} }[/tex]
to find the equivalent of x¹⁰,
x¹⁰ = x⁵.x⁵
by property aⁿ.aᵇ = aⁿ⁺ᵇ
so x¹⁰ = x⁹.x
=> x⁹⁺¹ = x¹⁰
[tex]\sqrt[3]{x^{10} }[/tex] = [tex]\sqrt[3]{x^{9}x }[/tex]
Hence equivalent expression is [tex]\sqrt[3]{x^{9}x }[/tex].
Learn more about expressions;
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1. f(x) = 2^-2x + 3
T-chart:
End behavior:
2. f(x) = (½)^ (x - 1)
T-chart:
End behavior:
3. j(x) = -2 (3/2)^x
T-chart:
Asymptotes:
End behavior:
4. g(x) = -3x
T-chart:
End behavior:
Step-by-step explanation:
Make sure all words are spelled correctly.
Try different keywords.
Try more general keywords.
Try fewer keywords.
-3(-2y-4)-5y-2
Please help
Answer:
y+10
Step-by-step explanation:
someone please help me asap
Answer: I think it’s 3868000000
Step-by-step explanation:
You move the decimal 9 places to the right