A new school has x day students and y boarding students.
The fees for a day student are $600 a term.
The fees for a boarding student are $1200 a term.
The school needs at least $720 000 a term.
Show that this information can be written as x + 2y ≥ 1200.​

Answers

Answer 1

Given:

The fees for a day student are $600 a term.

The fees for a boarding student are $1200 a term.

The school needs at least $720000 a term.

To show:

That the given information can be written as [tex]x + 2y\geq 1200[/tex].​

Solution:

Let x be the number of day students and y be the number of boarding students.

The fees for a day student are [tex]\$600[/tex] a term.

So, the fees for [tex]x[/tex] day students are [tex]\$600x[/tex] a term.

The fees for a boarding student are [tex]\$1200[/tex] a term.

The fees for [tex]y[/tex] boarding student are [tex]\$1200y[/tex] a term.

Total fees for [tex]x[/tex] day students and [tex]y[/tex] boarding student is:

[tex]\text{Total fees}=600x+1200y[/tex]

The school needs at least $720000 a term. It means, total fees must be greater than or equal to $720000.

[tex]600x+1200y\geq 720000[/tex]

[tex]600(x+2y)\geq 720000[/tex]

Divide both sides by 600.

[tex]\dfrac{600(x+2y)}{600}\geq \dfrac{720000}{600}[/tex]

[tex]x+2y\geq 1200[/tex]

Hence proved.


Related Questions

A tether ball is attached to the top of a 15-foot pole. Maddy holds the ball 3 feet off the ground and 4 feet from the pole. How long is the rope that the tether ball is attached to?

Answers

Answer:

15.52 ft

Step-by-step explanation:

the length of the rope can be determined using Pythagoras theorem

The Pythagoras theorem : a² + b² = c²

where a = length

b = base

c =  hypotenuse

√15² + 4²

= √225 + 16

=√ 241

= 15.52 ft

Answer:

the answer is b the square root of 160

Step-by-step explanation:

i did it on the assignment

Diego deposited \$ 10,000$10,000 for 44 years at a rate of 6\%6% simple interest. ​Find the amount of interest Diego earned after four years.

Answers

Answer:

$2,400

Step-by-step explanation:

Note: The correct years is 4 not 44

The Principal  = $10,000

Time period = 4 years

Rate = 6 % p.a.

Simple Interest = Principal * Rate * Time

Simple Interest = $10,000 * 6% * 44

Simple Interest = $2,400

So, the amount of interest Diego earned after four years is $2,400

I need help. Someone please figure it out

Answers

Answer:

[tex]\frac{1}{2^{n} }[/tex]

Step-by-step explanation:

The rules of exponents state that

[tex]a^{-m}[/tex] = [tex]\frac{1}{a^{m} }[/tex] and [tex]a^{0}[/tex] = 1

Thus

[tex]2^{-5}[/tex] = [tex]\frac{1}{2^{5} }[/tex] = [tex]\frac{1}{32}[/tex]

[tex]2^{-4}[/tex] = [tex]\frac{1}{2^{4} }[/tex] = [tex]\frac{1}{16}[/tex]

[tex]2^{-3}[/tex] = [tex]\frac{1}{2^{3} }[/tex] = [tex]\frac{1}{8}[/tex]

and so on , to

[tex]2^{0}[/tex] = 1

a. 1.3
b. 9.6
c. 13
d. 1

Answers

Answer:      I believe the answer would be 1.3

           HOWEVER, if you do have to round to the nearest tenth then the answer would be 1

Step-by-step explanation:    

2x+7 = 12x - 6

(subtract 2x from both sides)

7 = 10x - 6

(add 6 to both sides)

13 = 10x

(divide 13/10)

1.3 = x

a bag contains 3 white balls and 4 red balls. A.second bag contains 4 white balls and 3 red balls. If a bag is picked at random from each bag. Find the probability that both are white

Answers

Answer:

12/49 chance that they are both white

Step-by-step explanation:

We have 2 events going on:

The first bag that contains: 3 white, 4 red

The second bag that contains: 4 white, 3 red

First let's find the probability of picking a white ball from each individual bag (not combing the chances yet):

For the 1st bag, there are 3 white balls out of 7 balls (add 3 and 4).

That means there's a 3/7 chance you'll get a white ball from the 1st bag.

For the 2nd bag, there are 4 white balls out of 7 balls (add 4 and 3).

That means there's a 4/7 chance you'll get a white ball from the 2nd bag.

To find the probability of getting both white from both of the bags, multiply 3/7 & 4/7:

3/7 * 4/7 = 12/49

You can't simplify 12/49 further, so that's your answer!

Hope it helps (●'◡'●)

Answer:

2/6

Step-by-step explanation:

_______________________________hope it helps________

the answer is... 2/6

Does anybody know the answer to this ?

Answers

Answer:

A

Step-by-step explanation:

C is the answer I believe.

Choose the answer that is equivalent to the quotient.
(-4x3 + 16x2 21x + 22) divided by (2x – 3)
0-222 +51 - 3+
13
21-3
o 22 – 3+3
O-212 + 52 - 3+
16
21-3
0-222 + 52 - 3

Answers

I believe it would be B sorry if I’m wrong

if a real estate company gives 3% commission on to it's agents. if an agent sold a piece of land for 12,50,000, how much cccommision did the agent get ?​

Answers

Answer:

$37500

Step-by-step explanation:

Given data

Selling price=$1250000

Commission= 3%

Let us find 3% of 1250000

=3/100*1250000

=0.03*1250000

=$37500

Hence the commission will be $37500

I need help
Please
I hate math

Answers

Hey
Here it is

We can do this exercise in two ways

1°) We can make an expression:

3 markers ———> 5,79$
13 markers ——> x $

So x = ( 13 x 5,79 )/ 3

2°) 3/5,79 = 13/x

So x = ( 13 x 5,79 )/ 3

Answer: C

Cual de las siguientes fracciones es equivalente a 6/18
1/3

2/3

3/18

3/6

Answers

Answer:

the answer is going to be 1/3

1/3 is the correct answer

If the volume of a sphere is 36t cubic units, what is the radius?

Answers

Answer:

Volume of sphere = 4/3 * π * r³

Since 36π = 4/3 * π * r³, r³ = 27 and r = 3.

Step-by-step explanation:

There are 3 feet in 1 yard. This is equivalent to 12 feet in 4 yards. Which proportion can be used to represent this?
12th
$
12
Save and Exit
Next
Submit
Mark this and return

Answers

Answer:

divide 3 by the amount of feet to get to the yards

Step-by-step explanation:

For every three feet, there's always one yard

so to do this only given feet, we'll need to divide the amount of feet by 3 to represent the amount of yards

Jesse spends 1/2 of his pocket money on Monday.
On Tuesday, he spends 2/3 of what is left.
On Wednesday, he spends 1/4 of what remains.
What fraction of the pocket money does he have left? Choose the most
reasonable answer

Answers

Answer:

The fraction of the pocket money she left is 1/8.

Step-by-step explanation:

Let the total pocket money is p.

Spent on Monday = p/2

Amount left = p - p/2 = p/2  

Spent on Tuesday = 2/3 of p/2 = p/3

Amount left = p/2 - p/3 = p/6

Spent on Wednesday = 1/4 of p/6 = p/24

Amount left = p/6 - p/24 = p/8

So, the fraction of the pocket money she left is 1/8.  

Help me please correct answers only

Answers

Answer:

well your answer should be "F"

Step-by-step explanation:

we have

Y<-2x+10  -----> inequality A

The solution of the inequality A is the shaded area below the dashed line

Y = -2x+10

The y-intercept of the dashed line is (0,10)

The x-intercept of the dashed line is (5,0)

Y<1/2x-2 ----> inequality B  

The solution of the inequality B is the shaded area below the dashed line

Y= 1/2x-2

The y-intercept of the dashed line is (0,-2)

The x-intercept of the dashed line is (4,0)

The solution of the system of inequalities is the shaded area between the two dashed lines

Remember that

If a ordered pair is a solution of the system of inequalities, then the ordered pair must lie on the shaded area of the solution

therefore

The solution are the points

E, F and G

i hope this helps

Step 3: Let LM = x. We know the lengths of the radii of each circle, so KL = 12 +
8 = 20. Add the length of KL to the diagram.
J
12 K
20
L
X
M
12
00
8
N

Answers

Answer:

Step-by-step explanation:

Step 3:

Let LM = x

OK = KP = 12 units [Radii of circle K]

LN = LP = 8 units [Radii of circle L]

Therefore, KL = KP + PL

KL = 12 + 8

     = 20 units

Step 4:

Since, ΔKOM and ΔLNM are the similar triangles,

By the property of two similar triangles, corresponding sides of these similar triangles will be proportional.

[tex]\frac{OK}{NL}=\frac{KM}{LM}[/tex]

[tex]\frac{12}{8}=\frac{x+20}{x}[/tex]

12x = 8(x + 20) [By cross multiplication]

12x = 8x + 160

12x - 8x = 160

4x = 160

x = 40

Find the missing side or angle. Round to the nearest tenth. C=95° a=5 c=6 A=[?]° ​

Answers

Answer:

Missing angle A = 56.1° (approximately)

Step-by-step explanation:

<A = arcsin(a×sin(C)/c)

= arcsin(5×sin 95/6)

= 56.1154084° ≈ 56.1°

Answered by GAUTHMATH

someone help me please with this algebra homework

Answers

Answer:

the answer with the salad and dressing that has 100 calories per oz.

Step-by-step explanation:

a.20
b.25
c.15
d.1
help me

Answers

it's a little hard to see but it looks like A

hope that helps :)

1/5 + 3/4 + 1/2
please helpppo asap

Answers

Answer:

29/20 or 1 9/20 or 1.45

Answer:

[tex]\frac{1}{5}+\frac{3}{4}+\frac{1}{2}[/tex]

lease common multiplier of 5,4,2 is 20

[tex]\frac{4}{20}+\frac{15}{20}+\frac{10}{20}[/tex]

[tex]Add\: 4+15+10= 29[/tex]

[tex]1/5+3/4+1/2=29/20[/tex]

[tex]Answer :\frac{29}{20}[/tex]

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

hope it helps

have a great day!!

A cinema is doing a promotion to celebrate their 50th anniversary for 1 week. They give

away a free drink to every 98th customer, a free bag of popcorn to every 112th customer and

a free cinema ticket to every 224th customer. Which lucky customer will be the first to

receive all 3 items?​

Answers

Answer:

1,568 customer

Step-by-step explanation:

Find the lowest common multiple of 98, 112, and 224

98 = 98, 196, 294, 392, 490, 588, 686, 784, 882, 980, 1078, 1176, 1274, 1372, 1470, 1568, 1666

112 = 112, 224, 336, 448, 560, 672, 784, 896, 1008, 1120, 1232, 1344, 1456, 1568, 1680, 1792, 1904

224 = 224, 448, 672, 896, 1120, 1344, 1568, 1792, 2016, 2240

The lowest common multiple of 98, 112, and 224 is 1568

Therefore, the 1,568th customer will be the first to receive all 3 iitem

∆ABC transforms to produce ∆A'B'C'. Which transformation did NOT take place?


A.
rotation 180° counterclockwise about the origin
B.
reflection across the origin
C.
rotation 180° clockwise about the origin
D.
reflection across the line y = -x

Answers

Answer: The answer is (D) Reflection across the line y = -x.

Step-by-step explanation: In figure given in the question, we can see two triangles, ΔABC and ΔA'B'C' where the second triangle is the result of transformation from the first one.

(A) If we rotate ΔABC 180° counterclockwise about the origin, then the image will coincide with ΔA'B'C'. So, this transformation can take place here.

(B) If we reflect ΔABC across the origin, then also the image will coincide with ΔA'B'C' and so this transformation can also take place.

(C) If we rotate ΔABC through 180° clockwise about the origin, the we will see the image will be same as ΔA'B'C'. Hence, this transformation can also take place.

(D) Finally, if we reflect ΔABC across the line y = -x, the the image formed will be different from ΔA'B'C', in fact, it is ΔA'D'E', as shown in the attached figure. So, this transformation can not take place here.

Thus, the correct option is (D).

Write an equation in slope-intercept form for the line that passes through the given point and is perpendicular to the given line. (4,-2); y=3

Answers

Answer:

y = -1/3x - 2/3

Step-by-step explanation:

y = -1/3x + b

-2 = -1/3(4) + b

-2 = -4/3 + b

-2/3 = b

The 23 members of a track team are trying to raise at least $2226.00 to cover the traveling cost for a holiday tournament. If they have already raised $465.00, at least how much should each member still raise, on average, to meet the goal?

Answers

I think it would be $76.50

I NEED HELP ASAP. find the value of the variable that results in congruent triangles.
A. 80
B. 10
C. 50
D. 30​

Answers

Answer:

A) 80°

Step-by-step explanation:

55° + 45° + (5x + 30)° = 180°

55° + 45° + 30° + 5x = 180°

130 + 5x = 180°

5x = 50°

x = 10°

=> (5x + 30)° = 5*10° + 30° = 50° + 30° = 80

Find the length of UC

A. 54
B. 4
C. 39

Answers

Answer:

54

Step-by-step explanation:

It is the answer to this question

Wait waaaait Hol' up.

Answer:

Its 18.

Complete the steps to solve the inequality:

0.2(x + 20) – 3 > –7 – 6.2x

Use the distributive property:
Combine like terms:
Use the addition property of inequality:
Use the subtraction property of inequality:
Use the division property of inequality:




0.2x + 4 – 3 > –7 – 6.2x

0.2x + 1 > –7 – 6.2x

6.4x + 1 > –7

6.4x > –8

Answers

Answer:

x>-1.25

Step-by-step explanation:

0.2x+4-3>-7-6.2x

0.2x+1>-7-6.2x

0.2x+6.2x>-7-1

6.4x>-8

x>-1.25

or x>-5/4,x>-1 1/4, xE(-1.25, infinite)

The solution to the inequality is x > -1.25.

The complete steps are:

the distributive property: 0.2x+4-3>-7-6.2x

Combine like terms: 0.2x+1>-7-6.2x

the addition property of inequality: 0.2x+6.2x +1 >-7 => 6.4x + 1 > –7

the subtraction property of inequality: 6.4x > -7 - 1 => 6.4x>-8

the division property of inequality: (6.4x)/6.4 > (-8)/6.4 => x>-1.25

Here, we have,

To solve the inequality 0.2(x + 20) - 3 > -7 - 6.2x,

let's go through the steps:

Step 1: Use the distributive property:

0.2x + 4 - 3 > -7 - 6.2x

Step 2: Combine like terms:

0.2x + 1 > -7 - 6.2x

Step 3: Use the addition property of inequality:

0.2x + 1 + 6.2x > -7

6.4x + 1 > -7

Step 4: Use the subtraction property of inequality:

6.4x > -7 - 1

6.4x > -8

Step 5: Use the division property of inequality:

Divide both sides of the inequality by 6.4 to isolate x:

(6.4x)/6.4 > (-8)/6.4

x > -8/6.4

Simplifying further, we have:

x > -1.25

Therefore, the solution to the inequality is x > -1.25.

To learn more on inequality click:

https://brainly.com/question/28841069

#SPJ5

Danny’s dog weighs 45.33 pounds. His cat only weighs 14.89 pounds. About how much more does his dog weigh?
rounding

Answers

Answer:

30.44 pounds.  

Step-by-step explanation:

to find the answer you have to subtract 45.33 and 14.89

so 45.33-14.89= 30.44

so now you would have to round. the number after the decimal is NOT greater then 5 so Therefore, we simply remove the 4 an d the the whole number as: 30

SO your answer ROUNDING wise is 30

Hope this helps

What is the value of y

Answers

Answer: C

Step-by-step explanation: A straight angle is 180 degrees:

180-130 = 50

Triangle angles equal up to 180.

50 + 2y =180

y =65

QUESTION -> What is the value of y

ANSWER :-

SUM OF INTERIOR OPPOSITE ANGLES = EXTERIOR ANGLE .

[tex]130 = y + y \\ 130 = 2y \\ \frac{130}{2} = y \\ \frac{ \cancel{130}^ { \tiny \: \: \: \: 65} }{ \cancel{2}} = y \\ y = 65 \degree[/tex]

Is the graph increasing, decreasing, or constant?

Answers

Answer:

it's increasing.

Step-by-step explanation:

I'm not sure what else write here, it's obvious it's increasing

Answer:

Increasing

Step-by-step explanation:

You can see the line moving up on the graph starting from its origin (0,0) then moving to (1,1) then moving slowly up then finally ending at (12,3).

5. Nicholas bought a map of a city. It uses a scale of 1 inch to 8 miles.
Nicholas's house and school are 1/2 inches apart on the map. How far apart
would his house and school be on the map if the scale was 1 inch to 6 miles?
What’s the answer to this?

Answers

Scale is 1 inch to 6 mile.

So, ½ inch = 6 mile/2 = 3 mile

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