Find the sum of integers from 33 to 47:

Answers

Answer 1

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

Answer 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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Related Questions

Phil would like to make a profit of $250 this summer mowing his grandfather’s lawn. If he plans to mow 20 times and estimates that his fuel costs will be $30 for the entiresummer,which equation could be used to determine how much should he charge for each mowing?

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Answer:

which principle prevents a brach from abusing  its power

Step-by-step explanation:

which principle prevents a brach from abusing  its power

Answer:

20x - 30 = 250

Step-by-step explanation:

20x - 30 = 250

20x = 280

x = 14

POSSIBLE PO In a bag there are 10 red marbles, 5 green marbles, and 5 blue marbles. Wh at is the ratio IN FRACTION FORM of RED marbles to the total?​

Answers

Answer:

10/20 = 1/2

There are a total of 20 marbles, and ten of those are red = 10/20

Which, is half of the total.

If the selling prices of 20 pens are equal to the cost price of 25 pens, what is the gain percentage?

Answers

The gain percentage is 25%

[tex]\huge\bold\red{Answer:-}[/tex]

No(0)Let the cost price of the 20 pens be ₹100.

Cost of each pen=₹100/20=₹5

Selling price of each 25 pens sold=₹100/25=₹4.

%LOSS:

If cost of each pen. = 5=100%

..selling price of each pen. = 4= ?%.

Cross multiply:5? =400

?=80%

So,%loss= 100%-80%=20%

FOLLOW ME ♥️

if x=-2, y=-6 and z=4, Find the value of 4xy 3marks

Answers

Answer:

Step-by-step explanation:

4xy=4*(-2)*(-6)

4xy=48

At the start of the football game, there were 840 fans in the stadium. It began to rain during halftime, so 10% of the fans went home.
During the 3rd quarter of the game, the visiting team scored five touchdowns, so 25% of the remaining fans went home.
How many fans were in the stadium after the 3rd quarter?

Answers

After the third quarter there were 567 fans in the stands
840x.90(total-part)=756 fans at 1/2 time
756x.75= 567 fans after the third quarter

Which quadrant contains the point named by (2,5)

Answers

quadrant 1 contains that point! hope this helps

Answer:

Quadrant 4

Step-by-step explanation:

A rectangular garden has length and width as given by the expressions below.
Length: 4 - 7(3x + 4y)
Width: 3x(-2y)
Write a simplified expression for the perimeter of the rectangle.

Answers

2[4 − 7(3x + 4y)] + 2[3x(−2y)]
2[4 - 21x -28y] + 2[-6xy]
8 - 42x - 56y -12xy

the perimeter of given rectangular garden is (8 - 42x - 56y -12xy).

6. 108 is how many times as large as 2. 103?

Answers

Answer:

54 times larger than 2

Step-by-step explanation:

108 divided by 2 is 54

54 times larger than 2

solve each equation for x:
-5(3x + 4) = 25
4(x + 2) - 3(2x - 4) = 10
-4x - 3 = -1

Answers

Answer:

1.  x = -3

2.  x = 5

3.  Exact Form:   x = −1/2

Decimal Form:   x = −0.5

Step-by-step explanation:

Answer:

1. -3

2. 2/3

3. 1/2

Can someone help me?​

Answers

Answer:

x = 10

Step-by-step explanation:

50 + 4x = 90

4x = 40

x=10

X=10 because it has to add up to 180 so 4 x 10 would equal 40 and 40 + 50=180

Solve the equation for b. Use lowercase letters and no spaces when typing in the equation. a+b/3= C type your answer...​

Answers

Multiply both sides of the equation by 3

3a+b=3c

Subtract 3a from both sides

B= 3c-3a


I’m not 100% sure about this answer, but I hope it helps anyways :)

Complete the statements below that show y = 8x2 + 32x + 17 being converted to vertex form.

Factor out the leading coefficient.

y = 8(x2 + 4x) + 17

Form a perfect-square trinomial.

Answers

Answer:

y = 8(x + 2)^2 + -15

Step-by-step explanation:

Factor out the leading coefficient.

y = 8(x2 + 4x) + 17

Form a perfect-square trinomial.

y = 8(x2 + 4x + 4) + 17 + -32

Write in vertex form.

y = 8(x + 2)^2 + -15

Answer:

4, -32

Step-by-step explanation:

what is -6 divided by (-3) • (-5)

Answers

Answer:

d

Step-by-step explanation:

-10
Pls mark brainliest

Determine whether the equation below has a one solutions, no solutions, or an
infinite number of solutions. Afterwards, determine two values of x that support your
conclusion.
2 – 3 = -3 + 2

Answers

Answer:

one solution

Step-by-step explanation:

5,2,-1,-4,-7 arithmetic

Answers

easy it’s 6 9 your welcome i’m happy i could help u

A right rectangular prism is packed with cubes of side length fraction 1 over 8 inch. If the prism is packed with 16 cubes along the length, 8 cubes along the width, and 6 cubes along the height, what is the volume of the prism?

Answers

Answer:

768

Step-by-step explanation:

16x8x6=768 because volume equals length times width times height ! :)

combining like terms: -7x+x HELP ASAP​

Answers

Answer:

Hello!!! Princess Sakura here ^^

Step-by-step explanation:

When you combine like terms you see the ones that are similar then you add or subtract, depends on what the signs are. For this one -7x is similar to x so in this case you would add x to the -7x which will give you -6x.

You have $300 to spend on school clothes shirts cost $15 and pants $20

Answers

265 should be correct

Answer

19 pants and 6 shirts

Find x- and y-intercepts. Write ordered pairs representing the points where the line crosses the axes.

y= 1/3 x− 2/3

Answers

Answer:

y-intercept = (0,-2/3)

x-intercept = (2,0)

Step-by-step explanation:

*X-intercept touches the x-axis & y-intercept touches the y-axis*

You can identify the y-intercept by looking at the equation.

The slope is 1/3x and the y-intercept is -2/3.

I'm not sure how to solve for the x-intercept, but you can make a graph with the y-intercept and the slope points. By doing this you should be able to find the x-intercept.

Hope this helped!!!  :)

PS: Check out the Desmos Graphing Calculator

This website helps a lot with these types of problems. You can type the equation, and it will show you a graph. If you look at the graph, you'll be able to determine the slope, the x-intercept, and the y-intercept.

what ordered pair is the solution​

Answers

The solution is C both (1,2) and (2,4) because for (1,2) both sides = 9 which is true and for (2,4) both sides equal 18 which is true

james painted 3/4 of his bedroom wall in 2/3 of an hour. How much of the wall could he paint in ONE full hour? (WRITE YOUR ANSWER AS A SIMPLIFIED IMPROPER FRACTION) Use either strategy to solve.

Answers

Answer:3/3 i think

Step-by-step explanation:

Answer:

Step-by-step explanation:

First, we need to find the common denominator between 3/4 and 2/3. The least common factor of these fractions is 12. Now we can turn 3/4 into 9/12, and 2/3 into 8/12, simply by multiplying. To figure out what one third is, we can divide by 2 to get 4/6 and 3/6... And now I'm lost (* ̄∀ ̄) *embarrassed face lol*

-10+1= plssssss help meeeeeee

Answers

Answer:

-9

Step-by-step explanation:

-10 - (-1) = -9

A rectangle has coordinates A(-4,3). B(0,0), C(6,8) and D(2,11)

Answers

Answer:

what is the question

Step-by-step explanation:

Two​ pulleys, one with radius r 1r1 and the other with radius r 2r2​, are connected by a belt. The pulley with radius r 1r1 rotates at omega 1ω1 revolutions per​ minute, whereas the pulley with radius r 2r2 rotates at omega 2ω2 revolutions per minute. Show that StartFraction r 1 Over r 2 EndFraction equals StartFraction omega 2 Over omega 1 EndFraction r1 r2

Answers

Answer:

r1/r2 = 2ω2/ω1

Step-by-step explanation:

The velocity of each pulley is expressed as v = ωr where;

v is the linear velocity of the pulley

ω is the angular velocity of the pulley

r is the radius of the pulley.

For the two pulleys, the velocity I'd both pulleys are the same.

v1 = v2

v1 is the linear velocity of first pulley

v2 is the linear velocity of the second pulley.

v1 = ω1r1

v2 = 2ω2(r2)

r1 and r2 is the radius of pulley 1 and pulley 2 respectively.

Since v1 = v2

ω1r1 = 2ω2(r2)

Divide both sides by r2

ω1r1/r2 = 2ω2(r2)/r2

ω1r1/r2 = 2ω2

Divide both sides by ω1

ω1r1/r2/ω1= 2ω2/ω1

r1/r2 = 2ω2/ω1

is 3/17 rational or irrational

Answers

Answer:

A rational number is a number that can be put in the form p / q where p and q are integers.

3 and 17 are integers

3 / 17 is rational

-8≤8+y for the solution?

Answers

Answer:

- 16 ≤ y

Step-by-step explanation:

- 8 ≤ 8 + y

- 8   -8

- 16 ≤ y

Answer:

Y>-16

The > is a greater than or equal to i just can’t put it in since I’m on my phone

Step-by-step explanation:

If you’re solving for y that should be the answer

Roxy is multiplying 18 by 43.

Use the drop-down menu to complete the statement.




1
4
1
The product × will be
.

8
3
8

Answers

Answer:

774,

Step-by-step explanation:

At the beginning of the school year, Jamie had $500 in her savings account. She wants to have at least $200 left in the account at the end of the school year. Each week, she withdraws $30 for spending money. To determine how many weeks she can spend $30, Jamie wrote and solved this inequality. 500 − 30x ≥ 200 −500 −500 −30x ≥ −300 x ≥ 10 Review Jamie's work. What was her error?

Answers

Answer:

Step-by-step explanation:

Given the inequality solved by H=Jamie expressed as:

500 − 30x ≥ 200

We need to calculate the range of x of the inequality to determine the number of weeks she can spend $30 as shown:

500 − 30x ≥ 200

Subtract 500 from both sides

500 − 30x - 500≥ 200 - 500

− 30x ≥ -300

Divide both sides by -30

− 30x/-30 ≥ -300/-30

x ≤ 10 (note that the inequality sign changes after dividing both sides by a negative sign)

Jamie's error was that she didn't change the sense of inequality after dividing both sides by -30 hence rendering her solution incorrect

Hence the number of weeks is less than or equal to 10.

Answer:

Answer is B

Step-by-step explanation:

Jamie should have reversed the inequality when using the division property of inequality. is the right answer hope it helps

I may or may not be dumb in the brain... I'll give brainliest to whoever answers first and correctly.​

Answers

Answer:

23 degrees

Step-by-step explanation:

6x + 42 = 180

x = 23

Answer:

23 Degrees

Step-by-step explanation:

6x + 42 = 180

-42. -42

6x = 138

/6. /6

× = 23

Identify the like term(s) in the following expression...
-11d-12z-5+9m+8d+2z
A) +8d and 11d, +2z and -12z
B) -11d and +8d, +2z and -12z
C) -11d and +8d, +2z and 12z
D) -11d and +8d, +2z and -12z, +9m

Answers

Answer:

If Im correct B). is the correct answer

B) -11d and +8d, +2z and -12z

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