Mathematics College

2E What is the greatest whole number less than 1000 that:
(1) can be expressed as the sum of two consecutive whole numbers, and
(2) can be expressed as the sum of three consecutive whole numbers, and
(3) can be expressed as the sum of five consecutive whole numbers

Answers

Answer 1

Answer:

(1) 499 and 500 are the greatest consecutive whole numbers whose sum is less than 1000.

(2) 332, 333 and 334 are the greatest consecutive whole numbers whose sum is less than 1000.

(3) 197, 198, 199, 200 and 201 are the greatest consecutive whole numbers whose sum is less than 1000.

Step-by-step explanation:

(1) Let be [tex]n \in \mathbb{Z}[/tex], such that:

[tex]n + (n+1) < 1000[/tex]

[tex]2\cdot n +1 < 1000[/tex] (Eq. 1)

Then we solve the inequation by algebraic means:

[tex]2\cdot n < 999[/tex]

[tex]n < \frac{999}{2}[/tex]

[tex]n < 499.5[/tex]

Which means that greatest value of [tex]n[/tex] is 499. In consequence, 499 and 500 are the greatest consecutive whole numbers whose sum is less than 1000.

(2) Let be [tex]n \in \mathbb{Z}[/tex], such that:

[tex]n+(n+1)+(n+2) < 1000[/tex]

[tex]3\cdot n + 3 < 1000[/tex] (Eq. 2)

Then we solve the inequation by algebraic means:

[tex]3\cdot n < 997[/tex]

[tex]n < \frac{997}{3}[/tex]

[tex]n < 332.333[/tex]

Which means that greatest value of [tex]n[/tex] is 332. In consequence, 332, 333 and 334 are the greatest consecutive whole numbers whose sum is less than 1000.

(3) Let be [tex]n \in \mathbb{Z}[/tex], such that:

[tex]n +(n+1)+(n+2)+(n+3)+(n+4) < 1000[/tex]

[tex]5\cdot n + 10 < 1000[/tex] (Eq. 3)

Then we solve the inequation by algebraic means:

[tex]5\cdot n <990[/tex]

[tex]n < \frac{990}{5}[/tex]

[tex]n < 198[/tex]

Which means that greatest value of [tex]n[/tex] is 197. In consequence, 197, 198, 199, 200 and 201 are the greatest consecutive whole numbers whose sum is less than 1000.

Related Questions

find the original price of a pair of shoes if the sale price is $40 after a 60% discount

Answers

Answer:

Thus, the original price of the pair of shoes was $100.

Step-by-step explanation:

Percentages

After a 60% discount, the sale price is now valued at 100-60=40% of its original price.

If the sale price is $40, then the original price is calculated as

$40 / 40 * 100 = $100

Thus, the original price of the pair of shoes was $100.

Verify applying 60% discount:

$100 - 60*$100/100 =  $40

Select the correct answer from the drop-down menu.
Javier has a basket of oranges and apples. The number of oranges is 2 more than twice the number of apples in the basket. The difference of half the number of oranges and half the number of apples is 4.
An equation created to find the number of apples Javier has in the basket will have
A One Solution
B No solution
c Infinite Solution

Answers

Answer:

one solution

Step-by-step explanation:

Answer:

one solution

Step-by-step explanation:

What is the formula for the area of a square?

Answers

Answer:

Area of a square = side times side. Since each side of a square is the same, it can simply be the length of one side squared. If a square has one side of 4 inches, the area would be 4 inches times 4 inches, or 16 square inches. (Square inches can also be written in2.)

Answer:

lxwxtor you can up it in the calculator

Cho flipped a coin 20 times. The coin landed on tails 8 times. What is the ratio of the number of times the coin landed on heads to the number of flips?​

Answers

Answer:

The answer is

A ) 12 to 20

Step-by-step explanation:

Cho flipped heads 12 times. She flipped the coin a total of 20 times, making the ratio 12 to 20.

I hope this helped you! If it did, please consider rating, pressing thanks, and giving my answer 'Brainliest.' Have a fantastic day! :)

please
help i’ve been stuck on
this all day

Answers

Answer:

CPB

Step-by-step explanation:

acute is less than 90 degrees and right is 90 degrees and obtuse is over 90 degrees

Answer: The answer is CPB

helpppp it’s my friends birthday

Answers

-2(13/20)
there you go

Find the variance for the given data. Round your answer to one more decimal place than the original data.

{12.4, 10.7, 14.5, 10.1, 16.5}

Answers

Answer:

5.6864

Step-by-step explanation:

Find the variance for the given data. Round your answer to one more decimal place than the original data.

{12.4, 10.7, 14.5, 10.1, 16.5}

hELLPPLPLP PLEASEE answer 1-3 and please show the work on how to get it

Answers

Answer:

Step-by-step explanation:

Milk consumed in 4 weeks = 20 jugs

Milk consumed in 1 week = 20 ÷ 4 = 5 jugs

Milk consumed in 8 weeks = 5 * 8  = 40 jugs

2) Cost of 20 sets of crayons =  $ 60

Cost of 1 set of crayon  =   60 ÷ 20  = $ 3

Cost of 9 sets of crayons =  3 * 9 = $ 27

3) Number of tomatoes required to make soup for two guest  = 4

Number of tomatoes required to make soup for one guest  = 4 ÷ 2  = 2

Number of tomatoes required to make soup for 6 guests= 2*6= 12 tomatoes

A pool drains 5000 gallons of water over the course of 5 hours. How many gallons of water, on average, does the pool drain each hour?

A. -5000 gallons per hour
B. -1000 gallons per hour
C. -100 gallons per hour
D. 1000 gallons per hour

Answers

Answer:

D. 1000 gallons per hour

Step-by-step explanation:

5000 / 5 = 1000

Answer: If it drained 5000 gallons and there were 5 hours, then 5000 divided by 5 is 1 so that would be answer D.

Hoped this helped!

PLEASE HELP ME ASAP​

Answers

Answer:

The answer is Option D

Step-by-step explanation:

Supplementary angles are angles that sum up to 180 °

538 = ? hundred + ? tens + ? ones


What is the answer?
(I am doing this cause my friend won't stop saying that 8 is in the tens

Answers

Answer:

500 (or 5) is in the hundreds place, 30 (or 3) is in the tens place, and 8 is in the ones place.

Step-by-step explanation:

500 is five-hundred, 30 is a ten (10, 20, 30, 40...), and 8 is a one because it is a single digit number and no other numbers come before it, unless it is a decimal.

HELP!!! Parallel Line Proofs

Answers

They add to 180 when you connect the two lines

a water park is designing an incline for guests to boogie board on as shown below
PLEASE HELP

Answers

the answer would be ≈43.7

Simplify x^-5

please please I need it please please please please please please

Answers

Answer:

[tex]1/x^5[/tex]

Step-by-step explanation:

[tex]x^-^y = 1/x^y[/tex]

Answer:

1/x^5

Step-by-step explanation:

When you have a negative exponent, you have to put 1 over that power without the negative sign in the exponent. You put 1 over x^5

Answer: 1/x^5

what is 2+2 my brain has been in circles about this

Answers

Answer:

hey  welcome to Brainly, and 2 + 2 = 4

Step-by-step explanation:

2+2=4

3+3=6

4+4=8

5+5=10

and so on just keep adding 2

identiy why trade improved during the middleages.
this is the question.

Answers

Answer:

intermarriage

Step-by-step explanation:

people from different part intermarried

Answer:

dont know

Step-by-step explanation:

Write an equation to match this graph

Answers

Answer:

its y=x+7

Step-by-step explanation:

Whoever answers this gets brainlist!

Answers

Answer: 5^5.

Step-by-step explanation: Using the equation x^a*x^b = x^(a+b), we find that 5^2*5^3 is equal to 5^5.

29 + 15x = -x - 3. Simplified

Answers

for this equation the answer is x= -2
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