To find the number of children, students, and adults attending the movie theater, we can solve the system of equations based on the given information.
Let's assume the number of children attending the movie theater is C. Since there are half as many adults as children, the number of adults attending is A = C/2. Let's denote the number of students attending as S.
From the seating capacity of the theater, we have the equation C + S + A = 379. Since there are half as many adults as children, we can substitute A with C/2 in the equation, which becomes C + S + C/2 = 379.
To solve for C, S, and A, we need another equation. We know the ticket prices for each category, so the total ticket sales can be calculated as 5C + 7S + 12A. Given that the total ticket sales amount to $2746, we can substitute the variables and obtain the equation 5C + 7S + 12(C/2) = 2746.
Now we have a system of two equations with two variables. By solving this system, we can find the values of C, S, and A, which represent the number of children, students, and adults attending the movie theater, respectively.
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what does it mean if x=1?
The meaning of the equation x=1 is that the numerical value of variable X is; 1.
What is the meaning of x=1?It follows from the task content that the mathematical meaning of the equation x=1 be explained.
By virtue of the equality sign, it follows that the numerical value of variable x is 1 and hence, 1 can be substituted for variable x in any mathematical expression within the context of discuss.
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PLESSEE HELP ME ASAPP
Answer:
option A. is the midpoint of the graph
Select the correct answer. A line t runs upward to the right through two parallel horizontal lines r and s, forming 8 angles numbered from 1 to 8. Given: Transversal t passes through parallel lines r and s. Prove: ∠3 ≅ ∠6 ∠4 ≅ ∠5 Statement Reason 1. r || s given
2. ∠3 ≅ ∠7 ∠4 ≅ ∠8 For parallel lines cut by a transversal, corresponding angles are congruent.
3. What is the next step in the proof? Choose the most logical approach.
A. Statement: ∠1 ≅ ∠8 and ∠2 ≅ ∠7 Reason: Congruent Supplements Theorem
B. Statement: m∠3 + m∠4 = 180° and m∠7 + m∠8 = 180° Reason: Linear Pair Theorem
C. Statement: m∠3 + m∠5 = 180° and m∠4 + m∠6 = 180° Reason: definition of supplementary angles
D. Statement: ∠7 ≅ ∠6 and ∠8 ≅ ∠5 Reason: Vertical Angles Theorem Reset Next
The the next step in the proof is D. Statement: ∠7 ≅ ∠6 and ∠8 ≅ ∠5 Reason: Vertical Angles Theorem.
How to illustrate the angle?It should be noted that vertical angles are the angles that are opposite each other when the two line cross.
In this case, 7 ≅ ∠6 and ∠8 ≅ ∠5 Reason: Vertical Angles Theorem.
In conclusion, the correct option is D.
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15. The sides of a parallelogram are 100 m each and the length of the longest diagonal is 160 m. Find the area of the parallelogram.
Answer:
Area of parallelogram = 9600 m²
Step-by-step explanation:
• We can find the measure of angle x using the cos rule:
[tex]160^2 = 100^2 +100^2 -2(100)(100) \cdot cos (x)[/tex]
Make x the subject of the equation:
⇒ [tex]20000 \cdot cos(x) = 100^2 +100^2 - 160^2[/tex]
⇒ [tex]cos(x) = -0.28[/tex]
⇒ [tex]x = cos^{-1} (-0.28)[/tex]
⇒ [tex]x = 106.26 \textdegree[/tex]
• Now we can find the area of one the triangles formed using the formula:
[tex]Area =\frac{1}{2} ab \cdot sin \theta[/tex]
where a and b are two sides of a triangle, and θ is the angle between them (angle x).
Substituting the values:
Area of one triangle = [tex]\frac{1}{2}[/tex] × (100)(100) × sin(106.26°)
= 4800 m²
• Since the parallelogram is formed by two such triangles, we have to double the area of the triangle to find the parallelogram's area:
Area of parallelogram = 2 × 4800
= 9600 m²
GEOMETRY HELP ASAP PLEASE!!)
Chad had a garden that was in the shape of a rectangle Its original width was 3 feet and its original length was 8 feet.
He decided to make a new garden that was 3 feet wider and 2 feet longer than his first garden.
How much larger is the area, in square feet, of his new garden compared to his original garden?
Fill in the blank by entering only a number for your answer.
Answer:
36
Step-by-step explanation:
Chad's original garden is 3 ft x 8 ft.
original area = 3 x 8 = 24 square feet
Chad's super Chadly new garden is 3 feet wider, and 2 feet longer.
new width = 3 + 3 = 6
new length = 8 + 2 = 10
new Area = 6 x 10 = 60 square feet
To find how much larger the new area is, subtract the original area.
60 – 24 = 36 square feet
LaQuinta is in the French club with 25 other students. Three exchange
students will be attending her school from France. If the French teacher
chooses a student at random to guide each of the visiting students, what is
the probability that LaQuinta will NOT be picked as a guide?
Answer: 23/26
Step-by-step explanation:
Let’s say we have 3 spots, one for each of the three exchange students. It doesn’t matter who goes with who, we’re just going to choose people.
If LaQuinta is NOT one of the people chosen, then there are 25 possible people left to become tour guides. We will need to choose 3 of them, so there are (25 choose 3) = 2,300 ways.
With no restrictions, there are 26 people to choose from and 3 spots to fill. Therefore there are (26 choose 3) = 2,600 ways to fill these 3 spots with no restrictions.
The total probability is 2,300/2,600, which simplifies to 23/26.
. A special safe lets you choose from 9 symbols for a 3-symbol-long pass code. You may enter a symbol any number of times. How many potential pass codes are there
The question is an illustration of combination and there are 729 potential pass codes available
How to determine the number of potential pass codes?The given parameters are
Symbols available = 9
Length of pass code = 3
From the question, we understand that a symbol may be entered any number of times.
This means that each of the 9 available symbols can be used three times
So, the number of potential pass codes is
Passcodes = 9 * 9 * 9
Evaluate the product
Passcodes = 729
Hence, there are 729 potential pass codes available
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A doctor claims that the mean number of hours of sleep that seniors in high school get per night differs from the
mean number of hours of sleep college seniors get per night. to investigate, he selects a random sample of 50
high school seniors from all high schools in his county. he also selects a random sample of 50 seniors from the
colleges in his county. he constructs a 95% confidence interval for the true mean difference in the number of hours
of sleep for seniors in high school and seniors in college. the resulting interval is (0.57, 1.25). based upon the
interval, can the doctor conclude that mean number of hours of sleep that seniors in high school get per night
differs from the mean number of hours of sleen college seniors net ner night?
In light of the provided confidence interval, the following is the best answer on the outcome of the hypothesis test:
Yes, because 0 is not in the confidence interval.
What are the hypotheses tested?At the null hypotheses, it is tested if the difference is equals to zero, that is:[tex]$H_{0}: \mu=0$[/tex]
At the alternative hypotheses, it is tested if it is different, hence:[tex]$H_{1}: \mu \neq 0$[/tex]
The confidence interval is (0.57, 1.25). Since it does not contain 0, there is enough evidence that the difference is different of 0.yes, because 0 is not in the confidence interval
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The acts in a talent competition consist of 4 instrumentalists, 10 singers, and 6 dancers. If the acts are ordered randomly, what is the probability that a dancer performs first
Answer:
[tex] \frac{6}{20} = \frac{3}{10?} [/tex]
Step-by-step explanation:
total amount of acts = 4+10+6 = 20
amount of dancers = 6
probability of picking a dancer = number of dancers / total number of talents = 6/20 = 3/10
The probability that a dancer performs first is 3/10.
What is probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.
The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
The degree to which something is likely to happen is basically what probability means.
Given:
The acts in a talent competition consist of 4 instrumentalists, 10 singers, and 6 dancers.
Total participants = 4+ 10 +6 = 20
So, the probability that a dancer performs first
= 6 /20
= 3/10
Hence, the probability that a dancer performs first is 3/10.
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standard deviation sign and the mean sign
Answer:
standard deviation sign is σ
mean sign is x , and sometimes it have a hyphen directly above x.
Step-by-step explanation:
Greetings!standard deviationIn statistics, the standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean of the set, while a high standard deviation indicates that the values are spread out over a wider range.
MeanIt is the sum (total) of all the values in a set of data, such as numbers or measurements, divided by the number of values on the list. To find the mean, add up all the values in the set. Then divide the sum by how many values there are.
summationThe symbol ∑ indicates summation and is used as a shorthand notation for the sum of terms that follow a pattern.
If $25, 000 is invested into an account paying 4.5% per year, compounded quarterly, how much money can be withdrawn from the account every two months for the next 6 years?
The money can be withdrawn from the account every two months for the next 6 years is $20, 625, 000
What is compound interest?
The formula for compound interest is given as;
[tex]A = P ( 1 + \frac{r}{n} )^n^t[/tex]
P = principal interest = $25, 000
r = rate = 4. 5%
n = 2 months
t = 6 years
A = [tex]25, 000 ( 1 + \frac{4. 5}{2} )^2 ^*^6[/tex]
A = [tex]25, 000(1 + 0. 75)^1^2[/tex]
A = [tex]25, 000( 825. 00)[/tex]
A = $20, 625, 000
Thus, the money can be withdrawn from the account every two months for the next 6 years is $20, 625, 000
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Find the solution of the differential equation that satisfies the given initial condition. du dt = 2t + sec2(t) 2u , u(0) = â2
It looks like the equation is
[tex]\dfrac{du}{dt} = 2t + \dfrac12 \sec^2(t) u[/tex]
with initial value [tex]u(0) = \frac\pi2[/tex].
Rearrange the equation to
[tex]\dfrac{du}{dt} - \dfrac12 \sec^2(t) u = 2t[/tex]
Multiply both sides by the integrating factor
[tex]\displaystyle \mu = \exp\left( \int -\frac12 \sec^2(t)\,dt\right) = \exp\left(-\frac12\tan(t)\right)[/tex]
and solve for [tex]u[/tex].
[tex]\implies e^{-\frac12 \tan(t)} \dfrac{du}{dt} - \dfrac12 \sec^2(t) e^{-\frac12 \tan(t)} u = 2t e^{-\frac12 \tan(t)}[/tex]
[tex]\implies \dfrac{d}{dt}\left[e^{-\frac12 \tan(t)} u\right] = 2t e^{-\frac12 \tan(t)}[/tex]
By the fundamental theorem of calculus, integrating both sides yields
[tex]e^{-\frac12\tan(t)} u = e^{-\frac12\tan(t)} u \bigg|_{t=0} + \displaystyle \int_{\xi=0}^{\xi=t} 2\xi e^{-\frac12 \tan(\xi)} \, d\xi[/tex]
[tex]\implies e^{-\frac12\tan(t)} u = 1\times\dfrac\pi2 + \displaystyle \int_{0}^{t} 2\xi e^{-\frac12 \tan(\xi)} \, d\xi[/tex]
[tex]\implies \boxed{\displaystyle u = \frac\pi2 e^{\frac12\tan(t)} + 2e^{\frac12\tan(t)} \int_0^t \xi e^{-\frac12 \tan(\xi)} \, d\xi}[/tex]
can you help me with this
Given the choice between doing an oral and written report ,18 of the 28 students chose to do an oral report find the ratio of written to oral report
Answer:
5:9
Step-by-step explanation:
So since 18 chose to do oral report, that means (28-18) or 10 students decided to do a written report.
To find the written to oral report ration, we need to find for each student that did a written report, how many did an oral report? We can express this as a fraction and simplify to get the simplified ratio. So the the written will be the numerator and the oral will be the denominator: 10/18, to simplify this simply divide both sides by 2, to get 5/9 which gives us the simplified ratio of 5:9 meaning that for every 5 students who decided to do a written report 9 students decided to do an oral report.
A pizza company is building a rectangular solid box to be able to deliver personal pan pizzas. The pizza company wants the volume of the delivery box to be 756 cubic inches. The length of the delivery box is 6 inches less than twice the width, and the height is 2 inches less than the width. Determine the width of the delivery box.
The width of the delivery box is 9 inches.
Given that volume of delivery box is 756 cubic inches,length is 6 inches less than twice the width, height is 2 inches less than width.
let width be x
Length = 2x- 6
Height = x - 2
Width = x
We can find the value of x by putting values one by one and then we will be able to get the value of x which is width.
Because the delivery box is cuboid in shape so the volume is equal to product of length,breadth and height.
When x=7: Volume=7 x (7 - 2) x (2x7 - 6) = 7 x 5 x 8 = 280
When x=9,Volume will be 9 x (9 - 2) x (2x9 - 6) = 9 x 7 x 12 = 756
Therefore, the width of the delivery box is 9 inches.
Hence the width of the delivery box is 9 inches.
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Question 4 of 5
Which values are solutions to x < 7?
OA. x= 1 and x = 6
OB. x= 8 and x = 12
OC. x = 6 and x = 12
OD. x=8 and x = -1
HELP ASP please
Another copy machine also has the ability to reduce image dimensions, but by a different percentage. This graph shows
the results found when copying a design x times. Use the graph to write the equation modeling this relationship.
-10
2 3 4
6 7 8
Enter the correct answer in the box by feplacing the values of a and b.
The correct values for a and b which models this relationship through an exponential function are 8 and 2 respectively.
What is an exponential function?An exponential function can be defined as a mathematical function whose values are generated by a constant that is raised to the power of the argument. Mathematically, an exponential function is represented by this formula:
f(x) = eˣ
How to write an equation modeling this relationship?Based on the information provided, we can logically deduce that the other copy machine can reduce image dimensions by a different percentage and this is defined by the following exponential function:
f(x) = abˣ
From the graph (see attachment), we have;
When x = 0, y = f(x) = 8. Thus, f(0) = 8
f(x) = abˣ
8 = ab⁰
8 = a × 1
a = 8.
Also, from the graph (see attachment), we have;
When x = 1, y = f(x) = 4
f(x) = abˣ
4 = 8b¹
4 = 8 × b
4 = 8b.
b = 8/4
b = 2.
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the area of a rectangle is (16x^2 - 9y^2) square units
Please help me quickly.
Thank you
Answer:
[tex]x = \bf -7[/tex]
Step-by-step explanation:
[tex]\frac{3}{4} (x + 21) = 10\frac{1}{2}[/tex]
• Divide both sides by [tex]\frac{3}{4}[/tex] :
⇒ [tex]x + 21 = 10\frac{1}{2} \space\ \div \frac{3}{4}[/tex]
⇒ [tex]x + 21 = 10\frac{1}{2} \space\ \times \frac{4}{3}[/tex]
⇒ [tex]x + 21 = 14[/tex]
• Subtract 21 from both sides:
⇒ [tex]x = 14 -21[/tex]
⇒ [tex]\boxed {x = \bf -7}[/tex]
A couple quick algebra 1 questions for 50 points!
Only answer if you know the answer, quick shout-out to Subtomex0, tysm for the help!
Answer:
Question 6) Neither (Not an inverse variation)
Question 7) Inverse variation
Question 8) Inverse variation
Step-by-step explanation:
These are the two formulas we need to know prior to solving the question.
Direct variation: c times x
Inverse variation: c times 1/x --> c/x
- Here, c is the constant
6. y = x + 7
This is neither. It is not in the form of a direct, or inverse variation, so it does not belong in any category.
7. 14 = xy
This equation is an inverse variation.
xy = 14
y = 14/x
14 is the constant, and the format is the same as for an inverse variation.
8. x = -8/y
This equation is an inverse variation.
yx = -8
y = -8/x
-8 is the constant, and the format is the same as for an inverse variation.
So we can conclude that questions 7 and 8 is an inverse variations, while question 6 isn't.
General forms
Direct
y=KxInverse
y=k/xso
#6
y=x+7Not inverse and direct also as 7 is present
#7
14=XYy=14/xYes
#8
x=-8/yy=-8/xYes
Which equation represents the line that is perpendicular to y = 1/4 and passes through (-6,-9)? OA X=-9 OB. Oc y=-9 D. y=-4
Which graph shows y < x² +1?
O
4) Intro
•
What is inequality?
In Algebra, inequality shows the relation between two expressions using the inequality symbol.
The graph shows the equation y<x^2+1 is attached
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The graph at option 1 shows the given inequality y < x² + 1. The domain and range of the given inequality is {x: x ∈ (-∞, ∞)} and {y: y ∈ [1, ∞)}.
How to graph an inequality?The steps to graph an inequality equation are:
Solve for the variable y in the given equationGraph the boundary line for the inequalityShade the region that satisfies the inequality.Calculation:The given inequality is y < x² + 1
Finding points to graph the boundary line by taking y = x² + 1:
When x = -2,
y = (-2)² + 1 = 4 + 1 = 5
⇒ (-2, 5)
When x = -1,
y = (-1)² + 1 = 2
⇒ (-1, 2)
When x = 0,
y = (0)² + 1 = 1
⇒ (0, 1)
When x = 1,
y = (1)² + 1 = 2
⇒ (1, 2)
When x = 2,
y = (2)² + 1 = 5
⇒ (2, 5)
Plotting these points in the graph forms an upward-facing parabola.
So, all the points above the vertex of the parabola satisfy the given inequality. Thus, that part is shaded.
From this, the graph at option 1 is the required graph for the inequality y < x² + 1. The boundary line is dashed since the inequality symbol is " < ".
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Given a population comprised of 30 bats, 15 gloves, and 60 balls, if sampling is random and one at a time without replacement, what is the probability of obtaining a bat and a ball in that order if two objects are sampled from the populationGroup of answer choices
The probability would be 3/125 in the given conditions.
As there are 105 items, of which 30 are bats. The probability for that draw is 30/105.
There are now 104 items remaining, of which 15 are gloves. The probability of getting a glove now is 15/104.
There are now 103 items remaining, of which 60 are balls. The probability of getting a ball now is 60/103.
The probability of all three occurring = product of three
15/104* 30/105* 60/103
= 3/125
Hence the probability is 3/125.
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If i start my trip driving at x mph for a hours and then go 5 mph slower for the next 2 hours what is the total distance i traveled.
Total distance travelled = (x.a + 2x -10) miles .
How to solve such time related questions?
The key concept for solving such questions is the relationship between speed, distance and time.
The relationship between them is Distance = Speed X Time
The whole trip can be divided into two parts
Part 1 :- Speed = x mph and time = a hours
∴ Distance = x .a miles
Part 2 :- Speed = x -5mph and time = 2 hours
∴ Distance =(x-5).2 = (2x -10)miles
Total distance = (x.a + 2x -10) miles
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Divide quotient and remainder (image)
Answer:
Hi, I'm not for sure but I think for sure for the answer is, I haven't done this math in a while btw I like math lol, but I will try my best for this answer:
The quotient: x + 4
The remainder: - 2
Step-by-step explanation:
I hope this helps you and have a lovely day of learning!
helpppppppp. look at pic
Answer:
h (1) = $140
Step-by-step explanation:
10x + 150
-10 -10
150-10
=140
so the answer must be $140
So it is definitely the first one
H(12)=$270
The design pattern on a blanket has 3 circles followed by 4 triangles. this pattern repeats across the entire blanket. move a number or word to each blank to describe the ratio relationship between the circles and triangles.
The ratio between the circle and triangle is described as 3:4.
What is ratio?An ordered pair of numbers a and b, written as a / b, is a ratio if b is not equal to 0.A proportion is an equation that sets two ratios at the same value.In this section, the terms ratio and proportion are defined. Both ideas play a significant role in mathematics. Numerous examples where the concept of the ratio is highlighted may be found in daily life, such as the rate of speed (distance/time) or price (rupees/meter) of a substance.An equation for proportion establishes the equality of the two provided ratios.Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects. A ratio is indicated by the symbol A fraction, like 2/5, can be used to represent a ratio. In our daily lives, we come across many comparisons, or ratios.As a result, the ratio can be expressed in three distinct ways, including:a to ba : ba/bKnow more about ratio and proportion numerical
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20 POINTS
please help and have a good weekend
A = 6 cm; B = 3 cm; C = 8 cm; D = 10 cm
The Surface area of the prism = 120 cm².
How to Find the Surface Area of Triangular Prism?Surface area = Area of A + B + C + D
The side lengths are:
A = 6 cm
B = 3 cm
C = 8 cm
D = 10 cm
Surface area of the prism = 2(area of triangular face) + area of rectangle 1 + area of rectangle 2 + area of rectangle 3
Area of triangular face = 1/2(b)(h) = 1/2(8)(6) = 24 cm
Area of rectangle 1 = (length)(width) = (10)(3) = 30 cm²
Area of rectangle 2 = (length)(width) = (6)(3) = 18 cm²
Area of rectangle 3 = (length)(width) = (8)(3) = 24 cm²
Surface area of the prism = 2(24) + 30 + 18 + 24 = 120 cm².
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Two students compared the scores on their math tests. Their results on 9 tests are shown in the box plots below.
Compare the box plots. Which statements are true? Check all that apply.
Ben has the smaller range of test scores.
The lower quartile and upper quartile of Nadia’s data are both higher than the lower quartile and upper quartile of Ben’s data.
The median of Nadia’s data is equal to the median of Ben’s data.
Nadia had the highest score on a test.
Ben’s lowest score was equal to Nadia’s lowest score
The statements that are true for the box plots are:
C. The median of Nadia’s data = median of Ben’s data.
D. Nadia had the highest score on a test
How to Find the Median of a Box Plot?The median of a data set is the center value, which is indicated on a box plot by a vertical line that divides the box.
Given the two box plots, we can conclude that:
Median for the data of Nadia is 92, which is the same for Ben.
The extreme whisker to the right for Nadia is at 100, which is the highest value for Nadia while that of Ben is 99.
The true statements are:
C. The median of Nadia’s data = median of Ben’s data.
D. Nadia had the highest score on a test
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Answer:
"C" and "D"
Step-by-step explanation:
took test on edge 2023
Erin’s car uses 6 gallons of gas for every 138 miles she drives.which equation could be used to find how many gallons,g, Erin needs to drive 92 miles. Answer choice A : 23=92g B:23=183g C:92=23g D:138=23g
The equation that could be used to find how many gallons Erin would need to drive 92 miles is 92 = 23g (option c)
How many gallons is needed to drive 92 miles?
The first step is to determine the gallons needed to drive 1 mile. To do this, divide the 6 gallons by 138 miles. Division is the process of grouping a number into equal parts using another number. The sign used to denote division is ÷.
Gallons needed for 1 mile = 6/138
In order to determine the gallons needed for 92 miles, multiply the ratio gotten in the previous step by 92
(6/138) x 92 = 4 gallons
The option that gives 4 gallons is : 92 = 23g
g = 92 / 32 = 4
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