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.
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?
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
Cual de las siguientes fracciones es equivalente a 6/18
1/3
2/3
3/18
3/6
Answer:
the answer is going to be 1/3
∆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
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).
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
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
a.20
b.25
c.15
d.1
help me
Does anybody know the answer to this ?
Answer:
A
Step-by-step explanation:
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
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
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?
Scale is 1 inch to 6 mile.
So, ½ inch = 6 mile/2 = 3 mile
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
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
1/5 + 3/4 + 1/2
please helpppo asap
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!!
Danny’s dog weighs 45.33 pounds. His cat only weighs 14.89 pounds. About how much more does his dog weigh?
rounding
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
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
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
I NEED HELP ASAP. find the value of the variable that results in congruent triangles.
A. 80
B. 10
C. 50
D. 30
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
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
a. 1.3
b. 9.6
c. 13
d. 1
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 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?
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
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
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.
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.
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
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 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
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:
2/6Step-by-step explanation:
_______________________________hope it helps________the answer is... 2/6
If the volume of a sphere is 36t cubic units, what is the radius?
Answer:
Volume of sphere = 4/3 * π * r³
Since 36π = 4/3 * π * r³, r³ = 27 and r = 3.
Step-by-step explanation:
What is the value of y
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
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]
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 ?
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
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?
Help me please correct answers only
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
Find the missing side or angle. Round to the nearest tenth. C=95° a=5 c=6 A=[?]°
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
Find the length of UC
A. 54
B. 4
C. 39
Answer:
54
Step-by-step explanation:
It is the answer to this question
Wait waaaait Hol' up.
Answer:
Its 18.
someone help me please with this algebra homework
Answer:
the answer with the salad and dressing that has 100 calories per oz.
Step-by-step explanation:
I need help
Please
I hate math
Is the graph increasing, decreasing, or constant?
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).
