PLEASE HELP!! ALGEBRA! For a movie theater 4,000 tickets were sold, and the proceeds were $37,000. Tickets for children 16 and younger, were $10, adults were $12, and seniors 60 and older were $8. There were 4 times more seniors than adults at the movie theater. What system of equations represents the number of children, c, adults, a, and seniors, s, that attended the movie theater?
Answers
Answer: Fourth answer choice
c+a+s = 4000
10c+12a+8s = 37000
4a = s
==========================================
Explanation:
The first equation
c+a+s = 4000
is fairly straightforward. We add the individual counts of children (c), adults (a) and seniors (s) to get the total number of people (4000) who attended
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If 1 child ticket costs $10, then 2 of them cost 20, and so on. If we don't know how many children there are, then we say 10c is the total cost for just the children alone. The c is a placeholder for some number.
Similarly, 12a represents the total cost for just the adults since 1 adult pays $12
8s is the total cost for all the seniors only
10c+12a+8s is the total cost of everyone and this total cost is 37000 dollars
The second equation is therefore
10c+12a+8s = 37000
----------------
We're told that "There were 4 times more seniors than adults at the movie theater" meaning
number of seniors = 4*(number of adults)
s = 4a
which is the same as 4a = s since we can flip both sides. So this is the third equation of our system.
------------------
We found these three equations
c+a+s = 4000
10c+12a+8s = 37000
4a = s
Related Questions
In how many distinct ways can the letters of the word DALLAS be arranged?
Answers
Answer:
720ways
Step-by-step explanation:
DALLAS = 6!
6x 5 x 4 x 3 x 2 x 1
720 ways
The letters of the word DALLAS can be arranged in 720 distinct ways.
What is the fundamental principle of multiplication?Multiplication is the mathematical operation that is used to determine the product of two or more numbdistinctn event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.
A word has n letters. then there are m repeating letters, each of them repeating r0, r1, r2.. times
So the number of distincts ways the letters DALLAS can be arranged are:
DALLAS = 6!
= 6x 5 x 4 x 3 x 2 x 1
= 720 ways
The letters of the word DALLAS can be arranged in 720 distinct ways.
Learn more about multiplications;
https://brainly.com/question/14059007
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is 2 square root of 5 plus three rational or irrational
Answers
Answer:
It is irrational
Step-by-step explanation:
It is irrational.
Find the equation of a line containing the given points (4,3) and (8,1). Write the equation in slope-intercept form.
Answers
Answer:
y= -1/2x +5
Step-by-step explanation:
Tina is saving to buy a notebook computer. She has two options. The first option is to put $200 away initially and save $10 every month. The second option is to put $100 away initially and save $30 every month. After how many months would Tina save the same amount using either options? How much would she save with either option?
Answers
Answer: In five months,she will save the same money which is $250.
Step-by-step explanation:
Using the first statement we can generate the function y=10x + 200 and using the second statement we can also generate the function y = 30x + 100 . Now using the two equations solve for x and y to determine how many months they cost the same.
y = 10x + 200
y = 30x + 100
Substitute the value of x in the first equation into the second equation.
30x + 100= 10x + 200 now solve for x
-100 -100
30x = 10x + 100
-10x -10x
20x = 100
x= 5
This means in five months Tina will save the same amount. Now to find out how much the amount is, plot the value of x into one of the equations and solve for y.
y = 10(5) + 200
y = 50 + 200
y = 250
She will save $250 with either option.
Find the distance. V(X2-X.)2+(2-Y.)?
(1,2)(5,4) (-3,5)(2,3)
Answers
Answer: If you divide a trinomial by a monomial the result is a bionomial
A. True
B. False
Step-by-step explanation: tell me the correct answer and I'll tell you
Answer:
The distance formula is an algebraic expression used to determine the distance between two points with the coordinates (x1, y1) and (x2, y2).
Example
Find the distance between (-1, 1) and (3, 4).
This problem is solved simply by plugging our x- and y-values into the distance formula:
Sometimes you need to find the point that is exactly between two other points. This middle point is called the "midpoint". By definition, a midpoint of a line segment is the point on that line segment that divides the segment in two congruent segments.
If the end points of a line segment is (x1, y1) and (x2, y2) then the midpoint of the line segment has the coordinates: HOPES THIS HELPS
Step-by-step explanation:
solve for x if 10/4x-3 = 2
Answers
Answer:
We need to solve this equation:
[tex]\frac{10}{4x}-3=2[/tex]
We pass -3 to the right summing:
[tex]\frac{10}{4x} = 2 + 3[/tex]
[tex]\frac{10}{4x}=5[/tex]
We pass the 4x that is dividing to the right multiplying:
[tex]10 = 5*4x[/tex]
[tex]10=20x[/tex]
We pass the 20 of the right to the left dividing:
[tex]\frac{10}{20}=x[/tex]
[tex]x=\frac{1}{2}[/tex]
Now, we know [tex]x=\frac{1}{2}[/tex], so we can verify:
[tex]\frac{10}{4*\frac{1}{2}}-3 = 2[/tex]
[tex]\frac{10}{2}-3=2[/tex]
[tex]5 - 3 = 2[/tex] TRUE
Answer:
Kindly see attached picture
hope it helped you:)
A rectangular box with no top is to be built from 1728 square meters of material. Find the dimensions of such a box that will enclose the maximum volume.
Answers
Answer:
given surface area with no top as 1728
We say
V= X x Y x Z
So
yz = a(y+2z)
xz = a(x+2z)
Then using partial derivatives
xy = a(2x+2y)
xy+2xz+2yz = 1728
So
xy+2yz = xy+2xz
x=y
So
4xz = x²+ 2xz
x = 2z
4z²+4z²+4z²= 1728
z² = 432
z = 20.8m
x = y = 41.6m
A random sample of 100 cars was taken and data were recorded on the miles per gallon (mpg) in the city and on the highway. The mean city mpg was 28 with a standard deviation of 9.2. The mean highway mpg was 35 with a standard deviation of 8.6. The correlation coefficient between city mpg and highway mpg is 0.95. Although a scatterplot is not show, it has been determined that a linear equation is appropriate for the data. Determine the correct value of the slope for the linear model that predicts highway mpg based on city mpg and interpret it in context.
Answers
Answer:
0.89
Step-by-step explanation:
Nunber of samples = 100
City mpg :
Mean = 28
Standard deviation =9.2
Highway mpg:
Mean = 35
Standard deviation = 8.6
correlation Coefficient (r) between city mpg and highway mpg = 0.95.
The value of the slope of the regression line that predicts highway mpg based on city mpg can be obtained by:
(Standard deviation of highway mgp / standard deviation of city mpg) × correlation Coefficient
Slope = (8.6 / 9.2) × 0.95
Slope = (0.934782 × 0.95) = 0.8880
Slope = 0.89 ( two decimal place)
A supermarket has 148 shrubs on their property, but they are having trouble mowing grass so they need to pay to have cut down shrubs each year until the property has less than 30 shrubs. If they can pay to have only three shrubs cut down this year, but six shrubs cut down every year after that, in how many years will they have less than 30 shrubs on their property?
Answers
Answer: 21 years
Step-by-step explanation: After the first year, it’s down by 3 so 145. For the next 20 years, you go down 6 shrubs a year. At year 20 it will be 31 shrubs so at year 21 it will be at 25 shrubs.
Answer:
21 years.
Step-by-step explanation:
All equations are written in bold so you can find them easier.The first thing we do is subtract the 3 shrubs from the first year from the total 148.
148 - 3 = 145
We then take 29 from 145, as the supermarket wants less than 30 shrubs on their property, so the maximum amount they want to keep is actually 29.
145 - 29 = 116
The supermarket can pay to have 6 shrubs cut down every year, excluding the first, so we need to do then is divide 116 by 6.
116 ÷ 6 = 19.333.
Because that equation leaves us with a decimal, we have to round up to get a whole number because the answer has to be in years, not years and months.
19.333 rounded up is 20.
So that's 20 years of paying for 6/per year. We have to add on the one year they only payed for 3 shrubs to be cut down, making the answer;
21 years.We can further confirm we have the right answer by doing;
6 × 20 = 120
145 - 120 = 25
Because we're going down in 6's, we know that 20 is the lowest amount of years it would take to get less than 30 shrubs, because 25 + 6 = 31.
what doesIf 7! = 7x6x5x4x3x2x1 then 5! =
Answers
Answer:
Step-by-step explanation:
5!=5*4*3*2*1=20*6=120
Answer:
Hey!
5! Is equal to 5×4×3×2×1
So your answer is 120!
Step-by-step explanation:
7! Is 5040!
HOPE THIS HELPS!
Is 12 + 6 + 15= 12 +15+6 commutative property of addition
Answers
Answer:
yes
Step-by-step explanation:
answer above
What details can you determine about the dive from the coordinates of the point (5, −8)?
Answers
Answer:
(See explanation below for further details)
Step-by-step explanation:
A. What details can you determine about the dive from the coordinates of the point (5, -8)?
First component corresponds to time and second component to depth with respect to sea level. The diver is 8 feet below sea level at 5 seconds.
B. What is the average speed of the diver in the water? How can you tell from the graph?
The average speed of the diver ([tex]\bar v[/tex]), measured in feet per second, can be calculated by the following expression:
[tex]\bar v = \frac{x_{f}-x_{o}}{t_{f}-t_{o}}[/tex]
Where:
[tex]x_{o}[/tex], [tex]x_{f}[/tex] - Initial and final depth of diver, measured in feet.
[tex]t_{o}[/tex], [tex]t_{f}[/tex] - Initial and final instant, measured in seconds.
There are three different average speeds: (i) Descent ([tex]t = 1\,s[/tex] to [tex]t = 5\,s[/tex]), (ii) Ascent ([tex]t = 5\,s[/tex] to [tex]t = 9\,s[/tex]), (iii) Descent + Ascent ([tex]t = 1\,s[/tex] to [tex]t = 9\,s[/tex])
(i) Descent ([tex]t = 1\,s[/tex] to [tex]t = 5\,s[/tex])
[tex]x_{o} = 0\,ft[/tex] and [tex]x_{f} = -8\,ft[/tex]
[tex]\bar v_{i} = \frac{-8\,ft-0\,ft}{5\,s-1\,s}[/tex]
[tex]\bar v_{i} = -2\,\frac{ft}{s}[/tex]
(ii) Ascent ([tex]t = 5\,s[/tex] to [tex]t = 9\,s[/tex])
[tex]x_{o} = -8\,ft[/tex] and [tex]x_{f} = 0\,ft[/tex]
[tex]\bar v_{ii} = \frac{0\,ft-(-8\,ft)}{9\,s-5\,s}[/tex]
[tex]\bar v_{ii} = 2\,\frac{ft}{s}[/tex]
(iii) Descent + Ascent ([tex]t = 1\,s[/tex] to [tex]t = 9\,s[/tex])
[tex]x_{o} = 0\,ft[/tex] and [tex]x_{f} = 0\,ft[/tex]
[tex]\bar v_{iii} = \frac{0\,ft-0\,ft}{9\,s-1\,s}[/tex]
[tex]\bar v_{iii} = 0\,\frac{ft}{s}[/tex]
C. Which point on the graph shows the starting location of the diver?
The initial location is when [tex]t = 0\,s[/tex], which corresponds to the intercept of the line on y-axis.
Find the rate of change.
Answers
Answer:
It add up by 6.
Step-by-step explanation:
6 plus 6 is 12 plus another is 18 and it keeps going.
Answer:
time x 6 = your distance
Step-by-step explanation:
Time x 6 = distance
EXample:
2 x 6 = 12
Hope this helps!
PLS HELP BEST ANSWER GETS BRAINLIEST Find the height of the triangle whose base is 1/4 inch and its area is 7/8 square inches?
Answers
Answer:
7
Step-by-step explanation:
Half the base (.25) times x = 7/8
.25x = 7/8
7/8 divided by .125 = 7
how'd I do?
I hope I got it correct
identify the perfect square that is closest . ex square 76 ; 81 ;8 ,9
Answers
Answer:
Perfect squares = 9 and 81
Step-by-step explanation:
[tex]\sqrt{76} = 2\sqrt{19} \\\sqrt{81} =9\\\sqrt{8} =2\sqrt{2} \\\sqrt{9} =3[/tex]
Use scientific notation to find the product of 20.5 × 10^7 and 0.000036.
73.8 × 10 2
7.38 × 10 2
5.69 × 10 12
7.38 × 10 3
Answers
7.38 x 10^3
Explanation:
20.5 x 10^7 = 205000000
205000000 x 0.000036 = 7380
7380 = 7.38 x 10^3
Hannah's car used of a tank of gas to
cross Arizona. The gas tank on her car hold
15 42 gallons. ABOUT how many gallons did
it take to cross Arizona? (Round to the
nearest whole number)
Answers
Answer:
There are 30 halves in 15, plus the extra half
Step-by-step explanation:
= 31 / 2; 31 / 2 times 3 / 4 = 93 / 8 = your answer. Hope this helps
Which statement accurately describes lines of laditude also called parallels on a map? A. They measure distance east and west of the equator B. They measure the distance east and west of the prime meridian C. They measure distance north and south of the prime meridian D. They measure distance north and south of the equator
Answers
Answer:
A
Step-by-step explanation:
they measure the distance east to west of the equator
The Tigers had twice as many hits as the yanks.Let x= number of hits by yanks.Then ?= number of hits by tigers
Answers
Answer: 2x = ? is the question
In the figure above, the radius of the inscribed circle is inches (in.). What is the perimeter of square CABD?
Answers
Answer:
perimeter of the square is 32 inches
which agrees with the last answer in your list of options.
Step-by-step explanation:
Notice that the radius of the circle is exactly half of the side of the square, therefore, each side of the square must be 8 inches long.
Then, the perimeter of the square (addition of its four sides) is :
4 x 8 inches = 32 inches
Answer:
Step-by-step explanation:
32
There were 3 apple, 1 mixed fruit, 2 grape, and 4 tropical fruit juice boxes in the cooler at the picnic. What is the probability that, when Jill reaches into the cooler to grab two juice boxes without replacing them, she grabs two that are grape? StartFraction 1 over 100 EndFraction StartFraction 1 over 50 EndFraction StartFraction 1 over 45 EndFraction StartFraction 1 over 25 EndFraction
Answers
There are 10 total juice boxes with 2 grape ones.
Picking the first grape would be 2/10 which can reduce to 1/5
Then there would be 9 juice boxes left with 1 grape.
Picking the second grape would be 1/9
Picking both would be 1/5 x 1/9 = 1/45
Answer:
1/45
Step-by-step explanation:
i think it would possibly be d because there are 3 of the apple and 2 of the grape and 4 for the tropical one so it least has a chance... im sorry if its wrong i just started i hope i helped....
plz give me brainlist
(5a^3-2a^2)+(6a^3+9a^2+8a)
Answers
Answer:
11a^3 + 7a^2 + 8a
Step-by-step explanation:
( 5a^3 - 2a^2 ) + ( 6a^3 + 9a^2 + 8a )
= 5a^3 + 6a^3 + -2a^2 + 9a^2 + 8a
= 11a^3 + 7a^2 + 8a
A school district's superintendent wants to administer a test of life skills to a sample of students. The superintendent has ample time and resources to conduct the study, as well as access to detailed information about all students' addresses, courses, grades, and attendance. Which of the following would be the worst sampling method for the superintendent to use?
-Cluster Sampling
-Convenience Sampling
-Stratified Sampling
-Systematic Sampling
Answers
Answer:
-Convenience Sampling
Step-by-step explanation:
Convenience Sampling is a sampling method that is employed simply because the samples are easy to reach or access. It is a non-probability system of sampling and not a very strong method of sampling. For a serious research such as the one being conducted by the Superintendent, who has ample time to perform the research, this is not a very good sampling method. A Convenience style of research would mean that he can just walk into a cafeteria with students and administer the test to them.
Since he has detailed information of the students, he should choose any of the other mentioned sampling techniques in the options provided to randomly select the subjects. This would help to prevent bias, and enable him to make generalizations with the result of the research.
Flaws in a carpet tend to occur randomly and independently at a rate of one every 270 square feet. What is the probability that a carpet that is 8 feet by 14 feet contains no flaws
Answers
Answer:
Probabilty= 0.0015355
Step-by-step explanation:
Flaws in a carpet tend to occur randomly and independently at a rate of one every 270 square feet.
Probabilty= 1/270
Probabilty= 0.0037
carpet that is 8 feet by 14 feet
Area=8*14
Area=112 square feet
Probabilty= 0.0037*(112/270)
Probabilty= 0.0037*0.415
Probabilty= 0.0015355
Write the opposite of the number. -4/5 (The four is not negative, the whole fraction is)
Answers
Answer:
4/5.
Step-by-step explanation:
The opposite of -4/5 is 4/5.
Answer:
4/5
Step-by-step explanation:
The opposite of a number is that number with the opposite sign.
The opposite of a positive number is a negative number. The opposite of a negative number is a positive number. The opposite of zero is zero since -0 means 0.
Examples:
opposite of -5 is 5
opposite of 1/2 is -1/2
opposite of 28 is -28
opposite of -sqrt(5) is sqrt(5)
Your problem:
opposite of -4/5 is 4/5
The distance around a figure is called _____
Answers
The distance around a figure is the perimeter, although around a circle is the perimeter is actually called the circumference.
Answer:
PerimeterStep-by-step explanation:
Is it possible for one ray to be shorter in distance than another ray
Answers
Answer:
please mark my answer brainliest
Step-by-step explanation:
no...because it extends to infinity from one side
Why Is 3 times 1/10 less than 3 times 10?k
Answers
3 times 1/10 is equal to 3/10, whereas 3 times 10 is equal to 30.
3/ 10 is less than 30.
We can write this as 3 * 1/10 compared to 3 * 10
If we divide both sides by 3, we then compare 1/10 and 10.
1/10 is less than 10, so 3 times 1/10 is less than 3 times 10.
We can rewrite 1/10 = 0.1, so 3 * 0.1 is 0.3 whereas 3 * 10 = 30.
Answer:
See Explanation
Step-by-step explanation:
When you multiply 3 * 1/10, 3 goes in the numerator so you get 3/10 which is 0.3
On the other hand 3*10 is 30.
0.3 is less than 30 that's why.
Here's the thing you had one pizza slice (equal to 1/10), and your parents gave you three times more the pizza slice. You will have three slices of pizza (each slice being 1/10) not 30 pizzas.
Hope that makes sense. I can explain again if you need me to!
if X = a^1/3 - a^-1/3 , show that x^3 + 3x = a - 1/a
Answers
Answer:
Step-by-step explanation:
Hello,
[tex](a^{1/3}-a^{-1/3})^3=a-3a^{1/3}+3a^{-1/3}-\dfrac{1}{a}=-3x+a-\dfrac{1}{a}\\\\<=> x^3+3x=a-\dfrac{1}{a}[/tex]
Thanks
Select the statements that are true based on the following given information. D = {x | x is a whole number} E = {x | x is a perfect square < 36} F = {x | x is an even number between 20 and 30} a) The expression D ∩ E is {1, 4, 9, 16}. b) The expression D ∩ F is {12, 14, 16, 18}. c) D ∪ (E ∩ F) is {all whole numbers}. d) (E ∩ F) is the empty set. e) The expression D ∩ (E U F) is 25
Answers
==========================================================
Explanation:
Let's write the roster notation of each set
D = {0, 1, 2, 3, ...} the dots indicate the pattern goes on forever
E = {0, 1, 4, 9, 16, 25} = list of perfect squares smaller than 36
F = {20, 22, 24, 26, 28, 30} = even numbers between 20 and 30
----------------
If we intersect sets D and E, we're looking for what numbers are in both sets at the same time. Therefore, D ∩ E = {0, 1, 4, 9, 16, 25} which is the exact same as set E. This is because all of set E is inside of set D. We say that set E is a subset of set D. So, D ∩ E = E.
Choice A is very close to being true. The problem is that 25 is missing from the set {1,4,9,16}. So this is why choice A is false.
----------------
Now let's intersect sets D and F. The numbers they have in common are {20, 22, 24, 26, 28, 30} which is exactly what set F is. So set F is a subset of set D. We can write D ∩ F = F in much the same way we can say D ∩ E = E.
D ∩ F = {12,14,16,18} is not true. A number like 12 is not between 20 and 30, so it cannot be in set F.
Choice B is false so we cross it off the list.
----------------
Choice C is true and here's why
D ∪ (E ∩ F) is the same as saying D ∪ G where G is the set of intersecting E and F together. In other words, G = E ∩ F
We don't really need to even worry about sets E, F or G. All that matters here is set D.
When we write D ∪ (E ∩ F) or D ∪ G, we're saying "a number is in set D, or it is in set G". If it is in D, then it's a whole number. Otherwise, it's in a subset of whole numbers.
Overall, D ∪ G and D ∪ (E ∩ F) form the entire set of whole numbers.
------------------
Choice D is true.
E and F have nothing in common
E = {0, 1, 4, 9, 16, 25}
F = {20, 22, 24, 26, 28, 30}
So intersecting them leads to the empty set. This is the set with nothing inside it, not even 0.
------------------
Choice F is false
These two sets below
E = {0, 1, 4, 9, 16, 25}
F = {20, 22, 24, 26, 28, 30}
union together to get
H = {0,1,4,9,16,20,22,24,25,26,28,30}
just toss all of the numbers together into one big set
Notice how each of these numbers are whole numbers, so they are part of set D. This means set H is also a subset of set D.
When we intersect sets D and H, we end up with set H. We do not simply end up with the set with 25 only inside it.