(sum of 50 different whole numbers, each less than 51)-(sum of 45 different whole numbers, each less than 51)is at most
A:10
B:15
C:240
D:285

Answers

Answer 1
The whole numbers less than 51 are {0, 1, 2, ...50}, which makes 51 of them.

The sum of the first 50 consecutive positive integers, 1+2+3+4+...+50 is given by the Gauss formula for addition:

[tex] \frac{50*51}{2}=25*51= 1275[/tex]

To maximize "(sum of 50 different whole numbers, each less than 51)-(sum of 45 different whole numbers, each less than 51)":

we need to maximize the first part, and minimize what we are subtracting.

That is:

we need to maximize "sum of 50 different whole numbers, each less than 51" which is done by subtracting the smallest one, that is 0, from 1275

and minimize "sum of 45 different whole numbers, each less than 51"
which is done by subtracting the greatest 6 numbers from 1275, that is:

1275-50-49-48-47-46-45=990

Thus, the difference is at most: 1275-990=285

Remark: we need to subtract 6 numbers because there are in total 51, and we are adding the smallest 45 of them.


Answer: D: 285

Related Questions

The area of a square mirror is 256in^2. A rectangular mirror has a width the same as the square mirror's width. Its length is two inches longer than its width. What is the area of the rectangular mirror?

Answers

256 = l×w

l = 2 + w

substitute the "l" in the first equation with the second equation (2+w) and solve for "w". Once you find it, plug into the second equation to find "l". Use the area formula for rectangles to find the area. Hope this helps!

Angie has laid out a design for a garden consisting of two triangular areas as shown. The points are A (0,0), B (0,5), C(3,5), D(6,5), E(6,0). Name the type of congruence transformation for the preimage ABC to EDC.

A.) reflection
B.) rotation
C.) translation
D.) none of these

Answers

I think the correct answer would be A. The type of congruence transformation for the preimage ABC to EDC would be a reflection. It is a transformation where you basically flip the preimage or the original shape ove a line which is called the line of reflection. So, the image would be a mirror image of the preimage. By plotting the points, you will see that triangle EDC is just a mirror image of triangle ABC and the line of reflection would be at x = 3. It could not be a rotation since the preimage was not turned or rotated around a center of rotation. Also, it cannot be a translation since the preimage was not just moved left, right, up or down.

Why cant you add the exponnents in the product 12 exponent 3 × 11 exponent 3

Answers

Because you are multiplying the bottom numbers and not adding it so it would be 132 in the exponent of 9

which of the following are valid names for the given triangle ? check all that apply

Answers

B, D, and E are all valid names for the triangle

Answer: B.  ΔMLZ

D.  ΔLMZ

E. ΔZML

Step-by-step explanation:

In the given picture we have one triangle with three vertices as

Vertex L

Vertex M

Vertex Z

To name a triangle we use the labels of the vertices of the triangle, which are commonly written in capital letters.

When we name a triangle, we can start with any vertex but we need to keep the letters in order as you go around the triangle.

Therefore, the possible names of the triangle are :-

ΔLMZ   Δ LZM    ΔMLZ    ΔMZL   ΔZLM    ΔZML

A car dealership increased the price of a certain car by 11%

The original price was $39,600.

Fill in the blank to write the new price in terms of the original price.
Write your answer as a decimal.

New price= ? x original price

Use your answer in part (a) to determine the new price.
New price: $?

Answers

43956 yu take the original price and times it by .11 then at that to the price f the original and that is your new price
Move 11% to the left 2 times = 0.11
Next, add 1 + 0.11 = 1.11
Then, multiply 39,600 * 1.11 = 43,956
43,956 will be your answer

Mariah had owed her grandfather $2.25 but was recently able to pay him back $1.50. How much does Mariah currently owe her grandfather.

Answers

2.25-1.50=.75.He already paid 1.50 so he has only .75 left to pay

Thanks for the points! BTW, I have the same question.

A scale on a map shows that 2 inches = 25 miles.
Part A
How many inches on the map represent 60 miles?
Enter your answer in the box.
Part B
How many miles are represented by 1/4inch on the map?
Enter your answer in the box.

Answers

2 inches = 25 miles
?,,,,,,,,,,,,,,,60 miles

60 x 2 / 25 = 4.8 inches

1/4 = 0.25 inches

0.25 x 25 / 2 = 3.125 miles

answer

How many inches on the map represent 60 miles?
Enter your answer in the box.
answer: 4.8 inches

Part B
How many miles are represented by 1/4inch on the map?
Enter your answer in the box.
answer: 3.125 miles

Barry orders a wallet for $12.99, a sweater for $20.99, and a watch for $66.49 from a mail-order catalog. He adds $12.06 for tax, shipping, and handling. What is the total cost of Barry’s order?

Answers

Hi!

To answer this, simply add all of the values together to get the final answer. 

12.99 + 20.99 + 66.49 + 12.06 = 112.53

The answer is 112.53

Hope this helps! :)

Which of the following is the inverse of the relation {(1, 5), (2, 6), (1, 7), (4, 8)}? Select the correct answer below. A. {(1, 5), (2, 6), (7, 1), (8, 4)} B. {(5, 1), (6, 2), (7, 1), (8, 4)} C. {(2, 6), (1, 5), (8, 4), (7, 1)} D. {(1, 7), (1, 5), (2, 6), (8, 4)}

Answers

B. {(5, 1), (6, 2), (7, 1), (8, 4)}

winston's soup recipe make 6 servings and uses 4 carrots and 2 potatoes. how many will winston need for 15 servings

Answers

Hello there!
We have the following equation:
c + p = 15 (c = carrots, p = potatoes)
Previously, we had this equation:
2 + 4 = 6.
2 is 1/3 of 6, and 4 is 2/3 of 6. The sum of these two fractions make a whole.

Let's apply this rule to 15 servings.
Since we are looking for thirds, divide 15 by 3 to solve for 1/3, or "p".
15 / 3 = 5
We have 5 potatoes.

Now, we must remember that the amount of carrots is twice the amount of potatoes.
Divide 15 by 3, then multiply that quotient by 2.
15 / 3 = 5
5 * 2 = 10

We have 10 carrots.


Your final answer is:
Winston will need 5 potatoes and 10 carrots.

I hope this helps!

2x+3y=-5
3x-5y=21

The value of y that satisfies the system of the equations above is
A) 2
B)7
C) -3
D)There is no solution

Answers

You have to find a way to eliminate either x and y. We'll eliminate x:

2x + 3y = -5
3x - 5y = 21

2x*3 + 3y*3 = -5*3
3x*-2 + -5y*-2 = 21*-2

6x + 9y = -15
-6x + 10y = -42

19y = -57

y = -3

How much longer is the hypotenuse

Answers

x= sqrt(6^2 +8^2)

sqrt ( 100)

x=10

10-6 = 4

it is 4 feet longer than the shortest leg

AB² = 6² + 8² = 36 + 64 = 100
AB = √100 = 10 ft

Shorter leg is AC=6 ft

AB - AC = 10 - 6 = 4 ft

The hypotenuse is 4 ft longer than the shorter leg.

Devaughn's age is two times Sydney's age. The sum of their ages is 30

. What is Sydney's age?

Answers

D=2S

D+ S = 30

2s+S = 30

3S=30

S=30/3 = 10

Sydney is 10

Devaughn is 2*10 = 20

A training field is formed by joining a rectangle and two semicircles, as shown below. The rectangle is 89m long and 66m wide. Find the area of the training field. Use the value 3.14 for π , and do not round your answer. Be sure to include the correct unit in your answer.

Answers

The area of the field will be given by:
Area=[area of the semi circle]+[area of rectangle]
Area of semicircle is given by:
Area=πr^2
where;
radius,r=66/2=33 m
thus;
Area=3.14*33^2
3,419.46 m^2

The area of the rectangle is given by:
Area=89*66
=5,874 m^2
Hence the area of the field will be:
A=(5,874)+(3,419.46)
A=9,293.46 m^2

Answer:9953.46M squared

Step-by-step explanation:

what is the 8th term of this geometric sequence 6,48,384,3072

Answers

common ratio can be found by dividing the 2nd term by the first
r = 48/6
r = 8

an = a1 * r^(n-1)
n = term to find = 8
a1 = first number = 6
r = common ratio = 8
now we sub
a(8) = 6 * 8^(8-1)
a(8) = 6 * 8^7
a(8) = 6 * 2097152
a(8) = 12582912 <==

Find the greatest possible pair of numbers such that one integer is 5 more than twice the other and the sum is less than 30.

Answers

8 and 21 = 29 which is < 30
8 * 2 + 5 = ?
16 + 5 = 21

12 and 17 are the greatest integers less than 30

You need to cut a 9 foot piece of plywood into 12 inch sections. Every cut also removes 1/8 inch. How much of the plywood will be left after cutting the 12 inch sections?

Answers

There are 9 feet so it would usually be nine 12" pieces but since each cut takes away 1/8, you can only cut 8 pieces equal to 12 inches. 

Considering this fact, each cut would take away 0.125 inches. If you're cutting 8 times, you would in all be taking away 1 inch.

So aside from the eight 12" sections, you would have a leftover of 11 inches.

11 inches of  the plywood will be left after cutting the 12 inch sections.

What is Fraction?

A fraction represents a part of a whole.

Given that we need to cut a 9 foot piece of plywood into 12 inch sections and every cut also removes 1/8 inch.

We are to find the quantity of plywood that will be left after cutting the 12 inch section.

We know that  1 foot = 12 inches.

So, 9 foot = 12 × 9 = 108 inches.  

Since each cut removes 1/8  inch at ever cut, so the number of 12 inch sections will be 8.

Quantity of plywood that remained after cutting the 12 inch sections will be 108-12×8-8×1/8=11

Hence, 11 inches of  the plywood will be left after cutting the 12 inch sections.

To learn more on Fractions click:

https://brainly.com/question/10354322

#SPJ3

What is the rounding or compatible number

of 256+321

Answers

Compatible numbers for 256...
1. Rounded to the nearest hundred = 200
2. Rounded to the nearest tens place = 260

Compatible numbers for 321...
1. Rounded to the nearest hundred = 300
2. Rounded to the nearest tens place = 320

I hope this helps! :)


256 would round to 300 and 321 would round to 300. 300+300 = 600
Hope thats what you were looking for!

Triangle JKL is isosceles. The meansure of angle J is 72degrees and the measure angle K is 36 degrees. Which satement describes angle L?

Answers

Angle L in triangle JKL is [tex]\( 180^\circ - (72^\circ + 36^\circ) = 72^\circ \)[/tex]. Therefore, angle L measures [tex]\( 72^\circ \).[/tex]

1. Start with the fact that triangle JKL is isosceles, which means that angles J and K are congruent.

2. Given that angle J measures [tex]\( 72^\circ \)[/tex] and angle K measures \( 36^\circ \), the sum of angles J and K is [tex]\( 72^\circ + 36^\circ = 108^\circ \).[/tex]

3. Since the triangle is isosceles, the base angles (angles J and K) are congruent, so each measures half of the sum of angles J and K, which is [tex]\( \frac{108^\circ}{2} = 54^\circ \).[/tex]

4. Since angle L is the remaining angle in the triangle and the sum of the angles in a triangle is \( 180^\circ \), we subtract the sum of angles J and K from [tex]\( 180^\circ \)[/tex] to find the measure of angle L: [tex]\( 180^\circ - 108^\circ = 72^\circ \)[/tex].

5. Therefore, angle L measures [tex]\( 72^\circ \)[/tex].

answer both questions to get brain if u don't see all the answers is don't matter all u need is the question

Answers

3) area = pi x r^2

113 = 3.14 x r^2

r^2 =113/3.14 = 35.98726

r = sqrt(35.98726) = 5.9989 round to 6 inches

answer is C 6 inches


4) G = 2.5 times smaller than 18.04

18.04/2.5 = 7.216

 answer is B0 7.216 cm

Write down three different improper fractions for the number four

Answers

1, 3, and 5 I think. You should maybe search it up 

Which linear inequality is represented by the graph?

y ≤ 2x + 4
y ≤ 1/2x + 3
y ≥ 1/2x + 3
y ≥ 2x + 3
The graph is a solid line. It is crossing through (0,3) and it's shaded below it.

Answers

the answer is the second one, the y-intercept is 3 and its is less than or euqal to so you shade below

SOMEONE PLEASE GIVE ME THE RIGHT ANSWER!
The Baldwin family walked four over five of a mile in four over nine of an hour. What is their unit rate in miles per hour?

A.) four-ninths over four-fifths equals four over nine miles per hour
B.) four-fifths over four-ninths equals one and four-fifths miles per hour
C.) four-ninths over four-fifths equals one and four-fifths miles per hour
D.) four-fifths over four-ninths equals four over nine miles per hour

Answers

(4/5) / (4/9) = 4/5 * 9/4 = 36/20 = 9/5 = 1 4/5 miles per hour

so B.) one and four-fifths mph

Answer:

B.

Step-by-step explanation:

4/5 go over 4/9 because you are trying to find the unit rate of miles per hour. Since 4/5 is the mile, put that over 4/9. Then, simply divide the two fractions. Which is 1 over 4/5.

Help me quick plz thanks

Answers

add 12-3 = 9

 the difference is 9

 

How do variables help you model real-world situations? Give an example of a model that uses variables and explain how it helps people make predictions.

Answers

Variables are an integral part of the equations. 
With equations, you can simulate almost any process. For example, you can take the formula for payroll. (P)Payment=(T)the number of hours multiplied by the (R)rate per hour.P=T*R.In this formula, rate per hour (R) is constant (sometimes  revised, of course).And the Number of hours worked is variable. Every month the number of hours changes. So, to calculate the payroll helps modeling with the use of a formula.

Misha used a probability simulator to pull 3 colored marbles from a bag and flip a coin 50 times. The results are shown in the tables below: Color of Marble Number of Times Rolled Blue 20 Green 18 Yellow 12 Heads Tails 28 22 Using Misha's simulation, what is the probability of pulling a blue marble and the coin landing tails up?

Answers

To solve this problem, let us first remember that probability is:

Probability = number of successful events / number of total events

 

Now, let us first calculate the probability of getting a blue marble. There are 20 blue marbles out of 50 total marbles, therefore the probability is:

P (blue marble) = 20 / 50 = 0.4

 

Next, let us calculate for the probability of landing tails up. There are 22 tails success out of 50 times the coin was tossed, therefore the probability is:

P (tails) = 22 / 50 = 0.44

 

Finally, since we want to find the Probability of getting blue and Probability of landing tails, we multiply the two:

P (blue and tails) = 0.4 * 0.44

P (blue and tails) = 0.176               (ANSWER)

 

Now if the choices are in fraction:

P (blue and tails) = (20 / 50) (22 / 50) = 440 / 2500

Answer:

The answer is 440/2500

Step-by-step explanation:

Stuck on this problem

Answers

step 2 would be 10

step 4 would be 10x-x = 9x =7

 x = 7/9

Step 2: 10
Step 4: 9x
7/9

Hope this helps (;

Which is not a true statement? A 346.91 < 347 B 586.0041 < 586.0004 C 637.750 = 637.75 D 959.0059 < 959.006

Answers

B because 586.0041 is more than 586.0004 not less than.

Diego wanted to find the 7% sales tax on purchases that total $15.99. On his calculator the display showed $1.1193 as the tax. How much sales tax will Diego pay?

Answers

If I understand this question correctly, Diego will pay $1.12 because the 9 rounds the 1 up to a 2.

Find the 4th term if the sequend in which a1 = 2 and a n+1 = -4a n + 2.

Answers

The given sequence is
[tex]a_{1}=2 \\ a_{n+1}=-4a_{n}+2[/tex]

Write the first 4 terms.
When n=1, obtain
a₁ = 2
When n=2, obtain
a₂ = -4a₁ + 2
    = -4(2) + 2 = -8 + 2
    = -6
When n=3, obtain
a₃ = -4a₂ + 2
    = -4(-6) + 2 = 24 + 2
    = 26
When n=4, obtain
a₄ = -4a₃ + 2
   = -4(26) + 2 = -104 + 2
   = -102

Answer:  a₄ = -102

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