PLEASE PLEASE HELP!
Movies.
Your parents drop you off at the movies and you have $40 to spend. Admission to the movies costs you $14.50 and you buy a drink and popcorn for $7.75. You want to play a video game that costs $0.75.
1. Write a verbal inequality model that represents this situation.
2. Write an algebraic inequality model that represents this situation.
3. Show all work to solve the inequality.
4. Graph the inequality.
5. Describe the possible numbers of times you can play the same video game.
Answers
Answer:
3
Step-by-step explanation:
and the answer is 17
Answer:
1. The total cost of movie and the total cost of refreshments purchased and the total cost of video games played cannot exceed 40
2. 14.50 + 7.75x + 0.75y ≤ 40
3. y ≤ 34 - 10.333x
4. See attached graph
5.
one refreshment means you can play 23 times
two refreshments means you can play 13 times
three refreshments means you can play 3 times
Step-by-step explanation
We have to assume that you can see one movie but but buy multiple refreshments and play multiple video games. A refreshment is considered to be one drink and one popcorn.
If not we have a situation where we have three unknowns and it will be difficult to solve in a 2D context
1. Verbal inequality model
The total cost of one movie and the total cost of refreshments purchased and the total cost of video games played cannot exceed 40
2. Algebraic Inequality Model
Since the cost of a movie is 14.50 and you are seeing only 1 movie, the cost is 14.50(1) = 14.50
Assume you are going to buy x refreshments. Total cost of refreshments = 7.75x
Assume you are going to play y video games. Total cost of video games played = 0.75y
This cannot be greater than 40 i.e ≤ 40
So the algebraic inequality is
14.50 + 7.75x + 0.75y ≤ 40
3. Solving the inequality
Subtracting 14.50 from both sides we get
7.75x + 0.75y ≤ 25.50
Subtracting 14.50 from both sides we get
7.75x + 0.75y ≤ 25.50
Subtract 7.75x from both sides:
0.75y ≤ 25.50- 7.75x
Divide both sides by 0.75
y ≤ 25.50/0.75 - 7.75x/0.75
which is
y ≤ 34 - 10.333x
3. Graph of Inequality
This is an inequality in 2 variables and can be graphed.
See attached graph. The shaded portion represents the inequality
y ≤ 34 - 10.333x
Note that since neither x nor y can be < 0, we should not consider any portion of the shaded area which would mean two more constraints x ≥ 0 and y ≥ 0 but in this case I have stuck to only the above one inequality
5. Possible number of times you can play the same video game
Again we consider only 1 movie and multiple refreshments and video games
Using the inequality y ≤ 34 - 10.33x
If x = 1 refreshment,
y ≤ 34 - 10.33 x 1
y ≤ 23.67 or max 23 times you can play the video game max
If x = 2,
y ≤ 34 - 10.33 x 2
y ≤ 13.34 or maximum 13 times
If x = 3
y ≤ 34 - 30.99
y ≤ 3.01 or maximum 3 times
Related Questions
Tony's Used Car Dealership is selling a car for $12,000. This price represents a 20%
reduction from the original price of the car. What was the original price of the car?
Answers
The original price of the car is $15,000
Let us assume the original price of car be x. So, forming the equation to find the value of x and hence the original price of the car.
Equation -
x - 20% × x = 12000
x - 20/100×x = 12000
Cancelling zero as common in both numerator and denominator, on the left hand side of the equation
x - x/5 = 12000
Taking LCM on Left Hand Side of the equation
(5x - x)/5 = 12000
Rewriting the equation
4x = 12000 × 5
Performing multiplication on Right Hand Side of the equation
4x = 60,000
x = 60,000 ÷ 4
Performing division
x = 15,000
Therefore, the original price of the car is $15,000.
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Answer these 3, please. ( Statistics )
Answers
1) This narrative is an example of a sample survey.
2) This narrative is an example of an experiment.
3) This narrative is an example of an observational study.
What is the type of Statistical study?
There are some common methods of data collection in statistical studies which are sample survey, observational study, experiments e.t.c
A sample survey is a survey that is done by taking a sample of people or items that represent a larger population.
An observational study is a type of study whereby a researcher utilizes observed information to gain more information about a group of individuals.
An experiment is where a researcher purposely applies different treatments to different groups and then does a comparison of the groups to determine if there is any difference in a specific variable of interest.
1) This narrative is an example of a sample survey because he studied a sample of 50 people who exercise regularly to determine if their blood pressures are low or average.
2) This narrative is an example of an experiment because we see that he studies 20 people who exercise and another 20 who don't exercise and uses the result to generate a conclusion about both groups.
3) This narrative is an example of an observational study because he is using the information he gets from the question he asks every fifth patient to learn about a group of individuals.
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Six friends each use $2-off coupons to but themselves a movie ticket. They spend a total of $42. What is the price of one movie ticket without coupon?
Answers
Modelling the situation, it is found the price of the ticket without the coupon is of $9 when all the six friends spent $ 42 to buy the tickets.
Total money spent by 6 friends on purchasing of the movie tickets = $ 42
So, the money spent for the purchase of 1 ticket will be calculated by dividing the $ 42 by 6.
So, cost of 1 ticket = 4 42 / 6 = $ 7
Coupon is of $2-off.
This means that with the coupon, $2 is subtracted from the ticket price.
So, price of ticket will be = $ 7 + $ 2 = $ 9.
Therefore, the price of the ticket without the coupons will be $ 9.
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Ann and Ben translate documents from German into English.
A set of documents that would take Ann 10 days would take Ben 12 days.
Ann starts to translate the documents.
After 2 days Ann and Ben both work on translating the documents.
How many more days will it take to complete the work?
You must show your working.
Answers
Using the together rate, it will take more 3.45 days to complete the work.
Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.
The together rate is given by the sum of each separate rate.
For this problem, the rates are given as follows,
Ann,1/10 = 0.1
Ben,1/12 = 0.0833
Together,1/x
Hence the amount completed in 2 days is:
2 x (0.1 + 0.0833) = 0.3666
The amount it would take them to complete 100% of the project working together is found by the together rate as follows,
x = 60/11
x = 5.45 days.
The time it would take to do the remaining 100 - 36.66 = 63.34% of the project is,
0.6334 x 5.45 = 3.45 days.
It will take more 3.45 days to complete the work.
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There are 35 students in a class. Fifteen of them are men and 20 of them are women. The mean height of the men is 69.65 inches, and the mean height of all 35 students is 66.85 inches. What is the mean height of the women?
Answers
Answer:
64.75
Step-by-step explanation:
The total heights of men is m
so m/15 = 69.65 => m = 1044.75
The total heights of all students is s
so s/35 = 66.85 => s = 2339.75
so the total heights of women = 2339.75 - 1044.75 = 1295
The mean height of women = 1295/20 = 64.75
Please answer the screenshot
Answers
The set of ordered pairs that represents a function is the third option.
{ (4, 1), (-6, 6), (5, -2), (-4, 1)}
Which set of ordered pairs represents a function?
For a relation that maps elements x (inputs) into elements y (outputs), we will have ordered pairs of the form (x, y) that define the relation.
Now, a relation is only a function if input are only mapped to only one output.
For example, if you look at the first set of ordered pairs, you can see that the input x = -4 appears twice with two different outputs, then this relation does not represent a function.
For the second set the same thing happens for the input x = -8, and for the last set the same happens for the input x = -8
The only set where each input appears only once is the third one:
{ (4, 1), (-6, 6), (5, -2), (-4, 1)}
This relation represents a function, so this is the correct option.
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which statements about doubling in investment are true check all that apply an investment of $5000 will double in six years at an annual compound interest rate of 12% An investment of $1000 will double at an annual compound interest rate of 18% in six years an investment of $350 will double in nine years At a compound interest rate of 8% an investment of $2000 will double at a simple interest rate of 5% in 20 years and investment of $700 will double in 12 years at a simple interest rate of 6%
Answers
The following statement are true:
An investment of $5,000 will double in 6 years at an annual compound interest rate of 12%.An investment of $350 will double in 9 years at a compound interest rate of 8%. An investment of $2000 will double at a simple interest rate of 5% in 20 years.What is rule 72?It's an easy way to calculate just how long it's going to take for your money to double. Just take the number 72 and divide it by the interest rate you hope to earn. That number gives you the approximate number of years it will take for your investment to double.
Using the formula
time for doubling money= 72/R
First, An investment of $5,000 will double in 6 years at an annual compound interest rate of 12%.So, 72/12 = 6 years
Thus, It will take 6 years to double the investment. This statement is true.
Second, An investment of $1000 will double at an annual compound interest rate of 18% in 6 years.So, 72/18 = 4 years
Thus, It will take 4 years to double the investment. This statement is not true.
Third, An investment of $350 will double in 9 years at a compound interest rate of 8%.so, 72/8= 9 years.
Thus, It will take 9 years to double the investment. This statement is true.
Fourth, An investment of $2000 will double at a simple interest rate of 5% in 20 years.So, interest = PRT/100
I = (2000 × 0.05 × 20)
I = $2000
Thus, This statement is true.
Fifth, An investment of $700 will double in 12 years at a simple interest rate of 6%Interest = ( 700 × 0.06 × 12 ) = $504
Amount after 12 years
=700 + 504
= $1204.
Thus, This statement is not true.
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Jackie buys 6 packs of 100 post-its, 4 packs of 10 post-its, and 4 fancy post-its by themselves.
Then, her friend gives her 3 more fancy post-its. How many post-its does she have now?
Answers
Step-by-step explanation:
Number of post-it's = 6*100=600+4*10+4+3=647post-its
A line passes through the point (-2, 6) and has a slope of -8.
Write an equation in slope-intercept form for this line.
Answers
The given equation of the straight line is y +8x+10=0
We are required to find the equation of a straight line passing through the point (-2, 6) and has a slope of -8.
An equation of a straight line can be easily found if the slope and any of the points is given
The general form of equation is given by
y-y1 = m (x-x1)
where x1,y1 is the coordinate of the known point
m is the slope of the line
It is given that the coordinate of the known point is (-2,6)
the slope is given to be -8
Thus using these values to form the equation,
y-6 = -8 (x--2)
y-6 = -8 (x+2)
y-6 = -8x-16
y+8x-6+16=0
y+8x+`10=0
Hence, The straight line equation is y +8x+10=0
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whats 20,973 rounded to the nearest thousand
Answers
Answer:
21000
Step-by-step explanation:
21000
PLEASE HELP ME TY!!!!!!
Answers
Answer:
3.82×10^7
Step-by-step explanation:
3.82e+7= 3.82×10^7
Step by step
3.82 x 10^7
Change from scientific to standard form
This is a positive power of 10 so your decimal will go to the right 7 places
3.82 to
38200000.
If the power of 10 was a negative, you move the decimal to the left creating a decimal number less than 1
THE TRIANGLE SHOWN HERE IS REFLECTED IN X-AXIS AND THEN IN Y-AXIS. WRITE THE FINAL COORDINATES OF TRIANGLE:
Answers
Answer:
Option 4
Step-by-step explanation:
This is the same as a rotation of 180° about the origin, which means we can negate the x and y coordinates of the preimage to get the coordinates of the image.
An English instructor asserted that students' test grades are directly proportional to the amount of time spent studying.
Lisa studies 6 hr for a particular test and gets a score of 76. At this rate, how many hours would she have had to
study to get a
score of 91?
Answers
Answer:
7.18421051
Step-by-step explanation:
76 ÷ 6 = 12.6666667
91 ÷ 12.6666667 = 7.18421051
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How many even 2 digit positive integers can be written using the numbers 2,4,5,8
Answers
Answer: 12 different even 2 digit positive numbers can be witten
Step-by-step explanation:
the even numbers are 44, 24, 54, 84, 22, 42, 52, 82, 28, 48, 58, 88
There are 15 floors of an office building each floor is 10 2/5 feet tall 24 9/10 feet of the building are completed 1 1/4 feet of the building can be finished each day how many days are needed to complete the building
Answers
The days it would take to complete the building is 104 22/25 days.
How many days would it take to complete the building?A fraction is a non-integer that has a numerator and a denominator. The numerator is the number above. While the denominator is the number below. An example of a fraction is 1/4.
A mixed number is a number that has a whole number and a proper fraction. A proper fraction is a non-integer in which the numerator is less than the denominator. An example of a mixed number is 3 1/2.
The first step is to determine the total height of the office bulding = height of each floor x total number of floors
15 x 10 2/5
15 x 52/5 = 780 /5 = 156
The next step is to determine the floors left to complete the office building :
156 - 24 9/10 = 131 1/10 feet
The last step is to divide the feet that can be built each day by the number of floors needed to complete the builfing :
1311/10 ÷ 1 1/4
1311 / 110 ÷ 5/4
1311 / 10 x 4/5 = 104 days 44/50
104 22/25 days
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Un terreno tiene 205 metros y cada metro cuesta 315 cuánto vale el terreno
Answers
Answer:
64,765
Step-by-step explanation:
multiplicas porque dice que uno cuesta 315 entonces si hay 205 hay 64,765
9. Your family is looking for a new Internet company. Comcast has a $50 installation fee
and $60 per month for Internet. Centurylink has no installation fee and $60 per month.
Your grandparents decide to register with Comcast the sametime your family registers
with Centurylink. At what month will your family pay the same as your grandparents?
Answers
Answer:
in the heaven or hell hhhvgvcgdgghh
ANSWER RIGHT AWAY PLEASE!
question one: simply the exponents. (show your work)
- 21^0 = ?
- (2/3)^-2 = ?
question two: Solve the problem. (leave your answer as a base number with an exponent and show your work)
- 4^6 / 4^2 = ?
question three: Convert the number into numerical form. (show your work)
- 8.723 x 10^-10 = ?
question four: Solve the problem. (leave your answer in scientific notion and show your work)
- 5.1 x 10^8 - 2.3 x 10^3 = ?
- 6 x 10^5 x 1.1 x 10^7 = ?
PLEASE ANSWER I WILL GIVE 100 POINTS TO ANYONE WHO ANSWERS AND MARK BRAINLIEST AT LEAST ANSWER THE ONES YOU KNOW
Answers
Answer:
1. 1, 9/4
2. 4^4
3. -0.0000000008723
4. -5100023*10^2, -6.6*10^(12)
Step-by-step explanation:
[tex]21^0 = 1;\ n^0\ always\ is\ 1.\\(\frac{2}{3})^{-2} = (\frac{3}{2})^2 = \frac{3^2}{2^2} = \frac{9}{4}; n^m\ is\ performed\ by\ doing\ n*n,\ m\ times.\\i.e.,\\ n^2=n*n;\\n^3=n*n*n;\\ n^4=n*n*n*n\\\\\frac{4^6}{4^2};\ original\\\\\frac{(4^2)^3}{4^2};\ (n^{mc}\ can\ be\ rewritten\ as\ (n^m)^c\\\\\frac{4^2}{4^2}*\frac{(4^2)^2}{1};\ split\ the\ fraction\ into\ two\ parts\ because\ of\ multiplication\ rules.\\\\1*4^4;\ \frac{n}{n}\ can\ be\ written\ as\ 1.\ \frac{n}{1}\ can\ be\ written\ as\ n.\\\\4^4[/tex]
Technically, [tex]4^4[/tex] is 256, but the answer is requested as a number with an exponent.
-8.723 * 10^-10 would be -0.0000000008723.
10^-10 = [tex]\frac{1}{10^{10}}[/tex], which would mean you must move your decimal left by the number of places indicated by the exponent.
[tex]-5.1*10^8-2.3*10^3 = x\\-51*10^7-23*10^2 = x\\10^7=10^{5+2}=10^5*10^2\\-5100000*10^2-23*10^2=x\\-5100023*10^2=x;\ combine\ like\ terms.\\-6*10^5 * 1.1*10^7 = x\\-6*1.1*10^5*10^7;\ rewrite\ for\ simplification.\\-6.6*10^{12}=x[/tex]
How many inches are in 75 mm
Answers
Answer: 2.95 I think
Step-by-step explanation:
0.50x +0.15(30) = 23.5
Answers
Explanation:
Isolate the x
Multiply the .15x30=4.5
.50x + 4.5 = 23.5
Subtract 4.5
.50x = 19
Divide by .50
19/.50 = 38
X = 38
Answer: x=38
Step-by-step explanation:
SOLVE FOR X
STEPS FOR SOLVING LINEAR EQUATION
0.50x+0.15(30)=23.5
Multiply 0.15 and 30 to get 4.5.
0.5x+4.5=23.5
Subtract 4.5 from both sides.
0.5x=23.5−4.5
Subtract 4.5 from 23.5 to get 19.
0.5x=19
Divide both sides by 0.5.
[tex]x=\frac{19}{0.5}[/tex]
Expand [tex]\frac{19}{0.5}[/tex] by multiplying both numerator and the denominator by 10.
[tex]x=\frac{190}{5}[/tex]
Divide 190 by 5 to get 38.
x=38
1000 divided by 3 answer
Answers
Answer:333R1 or as a mixed fraction 33 1/3. I believe this is right :]
Step-by-step explanation:
. Compare the value of the 4's in this number
64,432
Write your statement
Answers
The 4 on the right is 10 times larger than the 4 on the left! (=^.^=)
The angles of a triangle add up to 180 degrees.
The second angle is 20 degrees larger than the smallest angle.
The third angle is 3 times as big as the smallest angle.
Find the measure of the smallest angle (in degrees).
Answers
Answer:
32 degrees
Step-by-step explanation:
You want the smallest angle of a triangle in which the other two angles are 20 degrees larger than the smallest, and 3 times the smallest.
SetupThe sum of angles is 180 degrees. The three angles are x, (x+20), and (3x). Their sum is ...
x +(x +20) +3x = 180
SolutionCollecting terms gives ...
5x +20 = 180
5x = 160 . . . . . . subtract 20
x = 32 . . . . . . divide by 5
The smallest angle is 32 degrees.
7h
t: h²k²
-7k
k² - h²
Answers
Answer:
i'm pretty sure it's the second option
Step-by-step explanation:
what is |x|-7=1 what is the answer
Answers
Answer:
it is x=8 or x=-8
Step-by-step explanation:
|x|-7=1
+7 +7
x=8 or x=-8
i'm doing absolute value in math rn so this should be right!! have a good day
Find the volume generated by rotating the given region about the specified line. I tried it 4 different times and have 1 try left! Please help only if you're sure of how to do it
Answers
Using integrals, the volume generated by rotating the given region about the specified line is of 0.8π cubic units.
How to use integrals to find the volume of a curve?Rotating a function f(x) around a function g(x), the volume is given by the following integral:
[tex]V = \pi \int_{a}^{b}[f(x) - g(x)]^2 dx[/tex]
In which a and b are the intersection points of the curve.
For this problem, from the graph, we have that:
[tex]f(x) = 2\sqrt[4]{x}[/tex].g(x) = 2x.a = 0.b = 1.Hence:
[tex]V = \pi \int_{0}^{1}[2\sqrt[4]{x} - 2x]^2 dx[/tex]
[tex]V = \pi [\int_{0}^{1} 4\sqrt{x} - 8x\sqrt{x} + 4x^2 dx][/tex]
[tex]V = \pi \left[\frac{8}{3}x^{\frac{3}{2}} - \frac{16}{5}x^{\frac{5}{2}} + \frac{4}{3}x^3}\right]_{x=0}^{x=1}[/tex]
[tex]V = \pi \left[\frac{8}{3} - \frac{16}{5} + \frac{4}{3}\right][/tex]
[tex]V = \pi \left[4 - \frac{16}{5}\right][/tex]
[tex]V = \frac{4\pi}{5}[/tex]
V = 0.8π cubic units.
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Which of the following is an existential quantifier?
Oa) Few
Ob) None
Oc) Every
O d) All
Answers
Answer:
A
Step-by-step explanation:
It might be the best one!
Draw LMN with vertices L(2,-2), M(7,-3), and N(5,2). Find the coordinates of the vertices after a 90 degree rotation about the origin and about each of the points L, M, and N.
Answers
The rotation of the vertices L(2,-2), M(7,-3), and N(5,2) are L'(-2, -2), M'(-7, -3), and N'(5, 2) respectively.
How does rotation by 90 degrees changes coordinates of a point if rotation is with respect to origin?Let the point be having coordinates (x,y).
If the point is in first quadrant:
Subcase: Clockwise rotation:
Then (x,y) → (y, -x)
Subcase: Counterclockwise rotation:
Then (x,y) → (-y, x)
We know that the rotation of a point (x,y) about the origin by 90° is (-y,x).
Given vertices of ΔLMN are L(2,-2), M(7,-3), and N(5,2).
Let consider the rotations of L, M, and N are L', M', and N' respectively.
The rotation of a point L(2,-2) about the origin by 90° is L'(-2,-2).
The rotation of a point M(7,-3) about the origin by 90° is M'(-7,-3).
The rotation of a point N(5,2) about the origin by 90° is N'(5,2).
Hence, the points L'(-2, -2), M'(-7, -3), and N'(5, 2) are the rotation of vertices.
Therefore, L, M, and N of ΔLMN about the origin by 90°.
Hence, The rotation of the vertices L(2,-2), M(7,-3), and N(5,2) are L'(-2, -2), M'(-7, -3), and N'(5, 2) respectively.
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Use the graph of the line to answer the questions. what is an equation of the line in slope-point form? _____
How can the point-slope form be written in function notation?
_______
Answers
The slope-point form is y + 1 = (1/4) (x +2)
The function notation for the point-slope form is f(x) = -1 + (1/4) (x +2)
From the graph, we get two points (x₁, y₁) = (-2, -1) and (x₂, y₂) = (2,0)
Slope, m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
= [tex]\frac{0 --1}{2--2}[/tex]
= 1/4
The slope-point form of a line is (y-y₁) = m(x-x₁), where (x, y) is the general point on the line, (x₁, y₁) is a given point on the line and m, the slope of the line.
So here the slope-point form of the line is,
(y- -1) = 1/4(x- -2)
⇒ y + 1 = (1/4) (x +2)
For the function notation, we put y = f(x) simply and write it as,
f(x) = -1 + (1/4) (x +2)
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the first one is c
the second is B
Step-by-step explanation:
6216÷21 please show me the work
Answers
Therefore, on dividing 6216 by 21 we get 126
Given 6216 / 21
21 ) 6216 ( 296
42
(-)................... (By subtracting these two numbers we get )
201
189
(-)..................
126
126
.(-)..........................
0
Therefore 6216 / 21 = 126
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