[tex]x > \ln(x)[/tex] for all [tex]x[/tex], so[tex]\displaystyle \lim_{x\to\infty} (\ln(x) - x) = - \lim_{x\to\infty} x = \boxed{-\infty}[/tex]Similarly, [tex]\displaystyle \lim_{x\to\infty} (x-e^x) = - \lim_{x\to\infty} e^x = \boxed{-\infty}[/tex]We can of course see the limits are identical by replacing [tex]x\mapsto e^x[/tex], so that[tex]\displaystyle \lim_{x\to\infty} (\ln(x) - x) = \lim_{x\to\infty} (\ln(e^x) - e^x) = \lim_{x\to\infty} (x - e^x)[/tex]You can also rewrite the limands to accommodate the application of l'Hpital's rule. For instance,[tex]\displaystyle \lim_{x\to\infty} (x - e^x) = \ln\left(\exp\left(\lim_{x\to\infty} (x - e^x)\right)\right) = \ln\left(\lim_{x\to\infty} e^{x-e^x}\right) = \ln\left(\lim_{x\to\infty} \frac{e^x}{e^{e^x}}\right)[/tex]Using the rule, the limit here is[tex]\displaystyle \lim_{x\to\infty} \frac{(e^x)'}{\left(e^{e^x}\right)'} = \lim_{x\to\infty} \frac{e^x}{e^x e^{e^x}} = \lim_{x\to\infty} \frac1{e^{e^x}} = 0[/tex]so the overall limit is[tex]\displaystyle \lim_{x\to\infty} (x - e^x) = \ln\left(\lim_{x\to\infty} \frac{e^x}{e^{e^x}}\right) = \ln(0) = \lim_{x\to0^+} \ln(x) = -\infty[/tex]

Mathematics College

Evaluate the limits

Answers

Answer 1

[tex]x > \ln(x)[/tex] for all [tex]x[/tex], so

[tex]\displaystyle \lim_{x\to\infty} (\ln(x) - x) = - \lim_{x\to\infty} x = \boxed{-\infty}[/tex]

Similarly, [tex]\displaystyle \lim_{x\to\infty} (x-e^x) = - \lim_{x\to\infty} e^x = \boxed{-\infty}[/tex]

We can of course see the limits are identical by replacing [tex]x\mapsto e^x[/tex], so that

[tex]\displaystyle \lim_{x\to\infty} (\ln(x) - x) = \lim_{x\to\infty} (\ln(e^x) - e^x) = \lim_{x\to\infty} (x - e^x)[/tex]

You can also rewrite the limands to accommodate the application of l'Hôpital's rule. For instance,

[tex]\displaystyle \lim_{x\to\infty} (x - e^x) = \ln\left(\exp\left(\lim_{x\to\infty} (x - e^x)\right)\right) = \ln\left(\lim_{x\to\infty} e^{x-e^x}\right) = \ln\left(\lim_{x\to\infty} \frac{e^x}{e^{e^x}}\right)[/tex]

Using the rule, the limit here is

[tex]\displaystyle \lim_{x\to\infty} \frac{(e^x)'}{\left(e^{e^x}\right)'} = \lim_{x\to\infty} \frac{e^x}{e^x e^{e^x}} = \lim_{x\to\infty} \frac1{e^{e^x}} = 0[/tex]

so the overall limit is

[tex]\displaystyle \lim_{x\to\infty} (x - e^x) = \ln\left(\lim_{x\to\infty} \frac{e^x}{e^{e^x}}\right) = \ln(0) = \lim_{x\to0^+} \ln(x) = -\infty[/tex]

Related Questions

phoebe needs to use 3/4 cups of sugar to make one batch of cookies. how many batches can she make with 12 cups of sugar?

Answers

Answer:

16 batches

Step-by-step explanation:

we can divide 12 by 3/4 or 0.75: 12/0.75 = 16

Make sure but I’m pretty sure it’s 16

A drink bottle is 3/8 full. It contains 240 millilitres of water. How much water does the bottle contain when it is half-full?

Answers

Answer: 320 mL

Step-by-step explanation:

Given information

The bottle is currently 3/8 full

Current Volume = 240 mL

Concept:

Imagine the water in the bottle being separated into 8 parts

Currently, 3 parts are being occupied

Determine the volume for 1 part

3 parts = 240 mL

1 part = 240 / 3 = 80 mL

Determine the volume for half-full (4 parts)

1 part = 80 mL

4 parts = 80 × 4 = [tex]\Large\boxed{320~mL}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Please help!
Express the area of the region bounded by the x-axis, y = 1/2x - 2 and y equals the cubed root of x, using definite integrals.

Answers

The integral which expresses the area of the region bounded by y = ¹/₂x - 2 and y = ∛x is; ∫⁸₀((x^(1/3)) - ¹/₂x + 2

How to integrate between two curves?

We are given the functions as;

y = ¹/₂x - 2

y = ∛x

Now, from the graph the coordinate of the point where both curves intersect is at; (8, 2)

Thus, the x-coordinate here is x = 8

∛x - (¹/₂x - 2)

∛x - ¹/₂x + 2

Similarly, another point of intersection of both curves is at the coordinate (0, -2). Thus, the x-coordinate here is; x = 0

Thus, the integral which expresses the area of the region bounded by y = ¹/₂x - 2 and y = ∛x is; ∫⁸₀((x^(1/3)) - ¹/₂x + 2

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|x - 1| > 4 is equivalent to which of the following?
a. -3 < x < 5
b. x > 5
c. x > 5 or x < −3
d. x < 5

*show your work*

Answers

Answer:

C. x > 5 or x < - 3

Step-by-step explanation:

|x - 1| > 4

Step 1:

x - 1 > 4

x > 4 + 1

x > 5

Step 2:

x - 1 < -4

x < -4 + 1

x < -3

HP: {x > 5 or x < -3} (c)

Please help solve this equation?

Answers

[tex]{ \red{ \bold{cos \: y \: }}}[/tex]

Step-by-step explanation:

[tex]{ \green{ \tt{ \frac{1 \: + \: \cos \: y \: }{1 \: + \: \sec \: y \: }}}} \: → {eq}^{n} (1)[/tex]

But, as you know that

[tex]{ \blue{ \tt{sec \: y \:}}} = { \green{ \tt{\frac{1}{ \ \cos \: y }}}} [/tex]

Then the equation (1) becomes

[tex]{ \green{ \tt{ \frac{1 \: + \: cos \: y }{1 \: + \: \frac{1}{cos \: y} }}}} \: [/tex]

Multiply Numerator and Denominator by [tex] \frac{cos \: y}{cos \: y} [/tex]

then,

[tex]{ \green{ \tt{( \frac{cos \: y}{cos \: y})}}} \: { \green{ \tt{ \frac{1 \: + \: cos \: y}{1 \: + \: \frac{1}{cos \: y}}}}} [/tex]

[tex] = { \green{ \tt{ \frac{cos \: y \: + \: {cos}^{2} \: y }{cos \: y \: + \: 1 }}}}[/tex]

take cos y as common, then

[tex]{ \green{ \tt{cos \: y}}} \: { \green{ \tt( \frac{1 \: + \: cos \: y}{cos \: y \: + \: 1} )}}[/tex]

Here, (1+cos y/cos y + 1) gets cancelled.

Then the remaining answer is cos y.

A garrison has provision for 10 days. At the end of 2 days 1/2 of the men left the garrison. how long the food will now last?

Please answer with explanation?

Answers

After half of the men go away, the provisions will last for another 16 days.

how long the food will now last?

First, we know that the garrison has provisions for 10 days.

2 days after that, the garrison has provisions for another 8 days. Here we know that the number of men on the garrison is reduced to its half. Then, the time that the provisions in the garrison will last is multiplied by 2.

So we just need to solve the product:

2*8 days = 16 days.

After half of the men go away, the provisions will last for another 16 days.

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what is 4,928 will rounded to the nearest hundred

Answers

If you mean 4.928 rounded to the nearest hundredth, that would be 4.93

Answer:

The answer is 4900, because the next number is less than five, due to that we don't have to add a number (+1).

---

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I hope help you :)

Kind regards, Antonio.

Directions: Factor the following trinomials containing negative numbers. Follow the rules for operations with signed numbers to identify the correct binomial factors.

1. x2 + 6x - 7

2. x2 - 5x + 6

3. x2 - 6x - 7

4. x2 + 5x - 6

5. x2 + x - 12

6. x2 - 2x - 8

7. x2 - 4x - 5

8. x2 + 2x - 3

9. x2 - 16

10. x2 - x - 12

11. x2 -9x + 18

12. x2 -5x - 14

13. x2 - 7x + 10

14. x2 -11x + 24

15. x2 - x - 30

Answers

The factored form of the given quadratic expressions are

1. (x -1)(x +7)

2. (x -2)(x -3)

3. (x +1)(x -7)

4. (x -1)(x +6)

5. (x -3)(x +4)

6. (x +2)(x -4)

7. (x +1)(x -5)

8. (x -1)(x +3)

9. (x +4)(x -4)

10. (x +3)(x -4)

11. (x -3)(x -6)

12. (x +2)(x -7)

13. (x -2)(x -5)

14. (x -3)(x -8)

15. (x +5)(x -6)

Factoring quadratic expressions

From the question we are to factor the given quadratic expressions

1. x² + 6x - 7

x² +7x -x - 7

x(x +7) -1(x +7)

(x -1)(x +7)

2. x² -5x +6

x² -3x -2x +6

x(x -3) -2(x -3)

(x -2)(x -3)

3. x² -6x -7

x² -7x +x -7

x(x -7) +1(x -7)

(x +1)(x -7)

4. x² +5x -6

x² -x +6x -6

x(x -1) +6(x -1)

(x -1)(x +6)

5. x² + x - 12

x² +4x -3x -12

x(x +4) -3(x +4)

(x -3)(x +4)

6. x² -2x -8

x² -4x +2x -8

x(x -4) +2(x -4)

(x +2)(x -4)

7. x² -4x -5

x² -5x +x -5

x(x -5) +1(x -5)

(x +1)(x -5)

8. x² + 2x - 3

x² +3x -x -3

x(x +3) -1(x +3)

(x -1)(x +3)

9. x² - 16

(x +4)(x -4)

10. x² -x -12

x² -4x +3x -12

x(x -4) +3(x -4)

(x +3)(x -4)

11. x² -9x +18

x² -6x -3x +18

x(x -6) -3(x -6)

(x -3)(x -6)

12. x² -5x -14

x² -7x +2x -14

x(x -7) +2(x -7)

(x +2)(x -7)

13. x² -7x +10

x² -5x -2x +18

x(x -5) -2(x -9)

(x -2)(x -5)

14. x² -11x +24

x² -8x -3x +24

x(x -8) -3(x -8)

(x -3)(x -8)

12. x² -x -30

x² -6x +5x -30

x(x -6) +5(x -6)

(x +5)(x -6)

Hence, the factored form of the given quadratic expressions are

(x -1)(x +7)

(x -2)(x -3)

(x +1)(x -7)

(x -1)(x +6)

(x -3)(x +4)

(x +2)(x -4)

(x +1)(x -5)

(x -1)(x +3)

(x +4)(x -4)

(x +3)(x -4)

(x -3)(x -6)

(x +2)(x -7)

(x -2)(x -5)

(x -3)(x -8)

(x +5)(x -6)

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The value of your stock investment in a certain company decreased 10 % over the last year. If the value of your stock investment is $7000
today, then what was the value of your stock investment a year ago

Answers

The value of the stock a year ago is $7778

How to determine the value of the stock a year ago?

The given parameters are:

Depreciation rate, r = 10%

Value of investment today, V(t) = $7000

The value of the stock a year ago is then calculated as:

Value of investment today = Value of investment last year * (1 - Depreciation rate)

Substitute the known values in the above equation

7000 = Last year * (1 - 10%)

Evaluate the difference of 1 and 10%

7000 = Last year * (90%)

Divide both sides by 90%

Last year = 7778

Hence, the value of the stock a year ago is $7778

Answers

Answer:

yes

Step-by-step explanation:

yes

three hens lay 3 eggs any 3 days. in how many days will 3n hens lay at this rate 9nk eggs? please i need answer fast!!! will give brainliest!

Answers

If three hens lay 3 eggs any 3 days. The number of days that 3 Hens give in 9 eggs is: 9days.

Number of days that three hens lay 9 eggs

Given:

3 hens lay 3 eggs in 3 days

First step is to determine the number of egg one hen lay in 3 days

1 hen in 3 days lays 3/3

1 hen in 3 days lays=1 egg

Second step is to determine the number of egg 3 hens lay 1 day

1 hen in 1 day lays 1/3 egg

3 hens in 1day lay=(1×3)/3

3 hens in 1day lay=1 egg

Third step is to determine the number of eggs 3 hens lay in 9 days

3 hens in 9 days lay=(1×9)

3 hens in 9 days lay=9 eggs

Therefore assuming three hens lay 3 eggs any 3 days. The number of days that 3 Hens give in 9 eggs is: 9days.

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Work out the upper quartile of this list of numbers: 3,4,1,2,9

Answers

Answer:

23 24

it is the answer it is answered

JD Scott I have no idea how to go but she is kind I don't really care about

f(x)=2x-6 Match each transformation of f(x) with its description

Answers

The transformation of the function is illustrated below

How to match the transformation?

Parent function is: f(x) = 2x - 6

Transformations are:

shifts f(x) 4 units down

f(x) → f(x) - 4 ⇒ g(x)= 2x - 6 - 4 = 2x - 10

stretches f(x) by a factor of 4 away from the x-axis

f(x) → 4*f(x) ⇒ g(x) = 4(2x - 6) = 8x - 24

shifts f(x) 4 units right

f(x) → f(x - 4) ⇒ g(x) = 2(x - 4) - 6 = 2x - 14

compresses f(x) by a factor of toward the y-axis (must be 4)

f(x) → f(4x) ⇒ g(x) = 2*4x - 6 = 8x - 6

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Identify the theorem or postulate that is related to the measures of the angles in the pair, and find the unknown angle measure.

m∠1=(50x−50)∘, m∠2=(20x+70)∘
Alt. Ext. ∠s Thm.
m∠1 = 130°, m∠2 = 130°

Same-Side Int. ∠s Thm.
m∠1 = 130°, m∠2 = 130°

Alt. Int. ∠s Thm.
m∠1 = 150°, m∠2 = 150°

Corr. ∠s Post.
m∠1 = 150°, m∠2 = 150°

Answers

The theorem used and the angle measures are:

D. corresponding angles postulate

m∠1 = 150°, m∠2 = 150°

What is the Corresponding Angles Postulate?

According to the corresponding angles postulate, if two angles lie on same relative corner along a transversal that cuts two parallel lines (corresponding angles), then their measures are equal.

Thus, ∠1 and ∠2 are corresponding angles, therefore:

m∠1 = m∠2 [corresponding angles postulate]

Given the following:

m∠1 = (50x − 50)∘,

m∠2 = (20x + 70)∘

Therefore, we would have:

50x − 50 = 20x + 70

Subtract 20x from both sides

50x − 50 - 20x = 20x + 70 - 20x

30x − 50 = 70

Add 50 to both sides of the equation

30x − 50 + 50 = 70 + 50

30x = 120

Divide both sides by 30

30x/30 = 120/30

x = 4

Plug in the value of x

m∠1 = (50x − 50) = 50(4) − 50 = 150°

m∠2 = (20x + 70)∘ = 20(4) + 70 = 150°

Thus, the answer is: D. corresponding angles postulate

m∠1 = 150°, m∠2 = 150°

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Give that m/_ y=39, find the measures of angles a and b

Answers

Answer:

∠a = 39°

∠b = 129°

Step-by-step explanation:

Vertical angles are congruent. An exterior angle of a triangle is equal to the sum of the remote interior angles.

Application

Angle y and angle 'a' are vertical angles, so congruent.

∠a = ∠y = 39°

The angle marked 'b' is an exterior angle to the triangle. Its remote interior angles are 'a' and the one marked 90°.

∠b = ∠a +90° = 39° +90°

∠b = 129°

[tex] \huge\mathbb{ \underline{SOLUTION :}}[/tex]

Given:[tex]\longrightarrow\bold{m<a= \: 39}[/tex] ✓

[tex]\longrightarrow\bold{m<b= \: 141}[/tex]

In the given figure, angles a and y are vertically opposite angles. The measure of vertical angles is equal, therefore :-

[tex]\small\longrightarrow\sf{m<a = m<y}[/tex]

[tex]\small\longrightarrow\sf{m<a= \: 39^\circ}[/tex]

Next, angles a and 90° are the opposite interior angles to the exterior angle b. By the triangle theorem below :-

[tex]\small\longrightarrow\sf{m<b=m<a+90^\circ}[/tex]

[tex]\small\longrightarrow\sf{39^\circ+90^\circ}[/tex]

• [tex]\small\longrightarrow\sf{m<b= 129^\circ}[/tex]

[tex]\huge \mathbb{ \underline{ANSWER:}}[/tex]

m<a= [tex]\large\sf{\boxed{\sf 39^\circ}}[/tex]

m<b = [tex]\large\sf{\boxed{\sf 129^\circ}}[/tex]

The sum of three numbers is 100. The second number is 2 times the third. The third number is 8 less than the first. What are the numbers?

Answers

Answer:

Step-by-step explanation:x+y+z=100(let x ,y,z represent the first second and third numbers respectively)

Therefore,y=2z

z=x-8

y=2x-16

substituting the values of x,y and z into the question,we have

x+(2x-16)+(x-8)=100

Simplifying,we have

4x-24=100

adding 24 to both sides of the equation,

4x=100+24

4x=124

dividing both sides of the equation by the co-efficient of x,we have

4x/4=124/4

4.31=124

therefore,x=31.

Anyone know the answer to this?

Answers

Slope = 3/1 =3
Point = (-1, 2)
Point slope form = y - y_1 = m (x - x_1)
Equation = y - 2 = 3 (x + 1)

Answer: y = 3x+5, 3, (-1,2)

Step-by-step explanation:

y = mx + c where m is the slope, so we must find the slope

Slope = rise/run = (5-2)/(0-(-1)) = 3

So y = 3x + c

To find c, we have to substitute one of the coordinates on the graph into the equation, (-1,2), the point that is marked

2 = 3(-1) + c

c = 5

So the equation of the graph is y = 3x + 5

Draw out a two column proof for each problem below. Complete all problems on one page and upload ONE photo of the entire assignment Make sure your file/image is clear (not blurry) and easy to read. Problem 1. Congruent Triangle Proof (10 Points) Given: NQ is the bisector of MNP and NMQ ~ ZNPQ| Prove: A MNQA PNQ 0 Problem 2. Proof Involving CPCTC (14 Points) Given: S is the midpoint of QR QR PS and RSP and QSP are right angles. Prove: PR PQ S 0

Answers

Two or more triangles are congruent if on comparison, they have equal lengths of sides, and measure of angles.

Therefore, the required proofs for each question are shown below:

Problem 1:

Congruent triangles are triangles with equal lengths of corresponding sides and measures of internal angles.

Thus,

STATEMENT REASON

1. <NMQ ≅ <NPQ Any point on a perpendicular bisector

makes equal measure of angle with the

two ends of the line segment.

2. NQ ⊥ MP Definition of a line.

3. MQ ≅ PQ Equal segments of a bisected line.

4. MN ≅ PN Any point on a perpendicular bisector

is at the same distance to the

two ends of the line segment.

5. <MNQ ≅ <PNQ Equal measure of the bisected angle.

Problem 2:

A line segment is the shortest distance between two points.

STATEMENTS REASONS

1. m<PSR ≅ m<PSQ A perpendicular bisector is always at a right

angle to the bisected line segment.

2. m<RPS ≅ m<QPS Equal measure of the bisected angle.

3. RS ≅ QS Property of a bisected line segment.

4. PR ≅ PQ Any point on a perpendicular bisector

is at the same distance to the two ends of

the line segment.

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Find all of the zeros for f(x).
f(x) = 6x³ + 25x² + 2x − 8
Arrange your answers from smallest to largest.

Answers

(-4, 0)

(-0.667, 0)

(0.5, 0)

3x + 3 = 6 + 6. solve for x

Answers

Answer:

x = 3

Step-by-step explanation:

3x + 3 = 6 + 6

3x + 3 = 12

3x = 12 - 3

3x = 9

x = 3

3 (3) + 3 = 6 + 6

9 + 3 = 12

12 = 12

given the quadriatic equation
x² + 6x + 9 = 4kx
find the set values for which k has real roots

Answers

Answer:

⇒ The given quadratic equation is x2−kx+9=0, comparing it with ax2+bx+c=0

∴ We get, a=1b=−k,c=9

⇒ It is given that roots are real and distinct.

∴ b2−4ac>0

⇒ (−k)2−4(1)(9)>0

⇒ k2−36>0

⇒ k2>36

⇒ k>6 or k<−6

∴ We can see values of k given in question are correct.

Can u guys please give me the correct answe

Answers

Answer:

Step-by-step explanation:

Since the two sides are equal in a parallelogram angle B = y ,so we have angle to be equal to 145°

We sum both angles and divide from

360° - [145° +145°]

360° - 290° = 70

Since the left sides( X And Z) are equal then we divide what we got into 2

70 ÷ 2 = 35

therefore angle X equals 35

Which graph shows a system with no solutions?
Graph A
Graph B
y
201
OA. Graph B
OB. Graph C
OC. Graph A
5
5
Graph C
Y
5
5+
y=2x-1
5
2y=4x-2

Answers

Answer:

i belive its graph B

f(x)=x3 −4x even odd or neither

Answers

Answer:

The function would be odd

The answer is neither.

Let's take an odd number and substitute.

f(3) = 3³ - 4(3)f(3) = 27 - 12f(3) = 15 (odd)

Now, let's take an even number.

f(4) = 4³ - 4(4)f(4) = 64 - 16f(4) = 48 (even)

Since both even and odd numbers are possible, it is neither.

How many milliliters are contained in 3 liters of fluid?

Answers

Answer:

3000

Step-by-step explanation:

1 liter = 1000 milliliters

3 liters = 3000 milliliters

------------------------

1 : 1000 = 3 : x

x = 3 * 1000 : 1

x = 3000

Answer: 3000 mL

Step-by-step explanation:

1 L = 1000 mL

3x1000 = 3000

You are on the Arithmetic Reasoning section.
Q: If the following series continues the same pattern. What is the next
number in the series 1, 10, 7, 16?

Answers

Answer:

Step-by-step explanation:

This problem is a type of puzzle called a Number Pattern. Number patterns always follow a specific pattern. In this case, its +9, -3.

The first number in this pattern is 1.

The second number in this pattern is 10.

That is an increase of +9.

The third number in this pattern is 7

That is a decrease of -3.

The fourth number in this pattern is 16.

That is an increase of +9.

Therefore, we can conclude that the next number will have to be a decrease of -3.

16 - 3 = 13

That is your answer. I hope I helped. If you feel like this is the best answer, please rate brainliest.

please help 30 points

Answers

See attachment for the graph of the function y = 5 sin(4x)

How to graph the trigonometry function?

The trigonometry function is given as:

y = 5 sin(4x)

To plot the graph, we use the following domain:

x > 0

This represents the minimum value of x

Also, we use

x < π/2

This represents the maximum value of x

When the domain are combined, we have:

0 < x < π/2

This means that the domain that gives a complete cycle is 0 < x < π/2

See attachment for the graph of the function

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what is the greatest number that can divide 13,17 and 21 and have one as a remainder

Answers

Answer:

Step-by-step explanation:

this is the same question as what number can divide

13-1 = 12, 17-1 = 16 and 21-1 = 20 and has 0 remainder ?

the greatest number that can do that is 4.

we can easily see that, but formally, let's do prime factorization :

12 ÷ 2 = 6

6 ÷ 2 = 3

3 ÷ 2 no

3 ÷ 3 = 1 finished

12 = 2×2×3

16 ÷ 2 = 8

8 ÷ 2 = 4

4 ÷ 2 = 2

2 ÷ 2 = 1 finished

16 = 2×2×2×2

20 ÷ 2 = 10

10 ÷ 2 = 5

5 ÷ 2 no

5 ÷ 3 no

5 ÷ 5 = 1 finished

20 = 2×2×5

so, the largest common factor is the combination of the longest streaks per factor they have in common.

they only have 2s in common.

and the longest common streak is 2×2 = 4.

hence the answer

Which two tables represent the same function

Answers

Answer:

A and D

Step-by-step explanation:

Let's find the slope of the functions in all tables.

A. -1/2

B. -1/2

C. -1/2

D. 1

E. -1/2

Option D. is out since it has a different slope.

The answer has to be two tables out of A, B, C, and E.

Start with Table A.

As x goes from 8 to 6, y goes up by 1.

We can create points for x = 0 and x = 2

x = 2, y = 9

x = 8, y = 6

This is exactly table D.

Answer: Tables A and D

Suppose you are in charge of setting up tables and ordering
appetizers and cookies for an awards dinner. The principal
expects 168 seventh-graders and 112 eighth-graders to attend
the dinner. Each grade will have dinner in a separate room.
1. Decide how many tables and how many chairs per table you will need, based on
the following criteria:
• No more than 15 tables in each room, and no more than 15
chairs per table.
• All tables in both rooms must have the same number of chairs.
Only 280 chairs can be ordered.
●

Answers

Answer: 10 tables in each room 14 kids at each table

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