The drama club is selling tickets to their play to raise money for the show's expenses. Each student ticket sells for $6.50 and each adult ticket sells for $11. The auditorium can hold a maximum of 130 people. The drama club must make a minimum of $1100 from ticket sales to cover the show's costs. Also, they can sell at least 90 adult tickets. If x x represents the number of student tickets sold and y y represents the number of adult tickets sold, write and solve a system of inequalities graphically and determine one possible solution.
Answers
The graph for the inequality is attached below.
What is Inequality?Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
Given:
Each student ticket sells for $6.50 and each adult ticket sells for $11.
let the number of student ticket sold be x and number of adult ticket sold be y.
so, the inequality is
x + y < 130
and, 6.5x + 11y >1100.
Solving the inequality we get
x= 73.33 and y = 56.667
Now, if they sell at least 90 adult tickets then they sell at most 40 children ticket.
Hence, the solution is (73.33, 56.667).
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Related Questions
Solve the polynomial congruence x^2-3x+2 is congruent to 0 mod 5. Solve for x=? or x=?,when k is any integer
Answers
The solutions of x² - 3x + 2 ≡ mod 5 does not exist.
How to solve Polynomial Congruence?
We are given the Polynomial;
x² - 3x + 2 ≡ mod 5
Finding the roots of the equation gives;
x² - 2x - x + 2 = 0(mod 5)
x(x - 2) - 1(x - 2) = 0(mod 5)
Thus, RHS = 0(mod 5) = 0
The roots of the equation are;
x = 1 and x = 2
Thus, the solutions of x² - 3x + 2 ≡ mod 5 does not exist.
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Explain how to solve 4^(x + 3) = 7 (x+3 being an exponent) using the change of base formula. Include the solution for x in your answer—round your answer to the nearest thousandth.
Answers
Using natural logarithms properties, we will see that:
x = -1.596
How to solve the equation?
Here we can use the property:
[tex]ln(a^b) = b*ln(a)[/tex]
Now we have the equation:
[tex]4^{x + 3 }= 7[/tex]
If we apply the natural logarithm in both sides, we get:
[tex]ln(4^{x + 3 })= ln(7)\\\\(x + 3)*ln(4) = ln(7)\\\\x + 3 = ln(7)/ln(4)\\\\x = ln(7)/ln(4) - 3 = log_4(7) - 3 = -1.596[/tex]
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Emily can read 30 pages in 45 minutes. At this rate, how many pages
will she read in 3 hours?
Answers
60x3=180(Number of minutes in 3 hours)
180/45=4
4x30=120
What is the distance between the points (4,3) and (1,-1) on the coordinate
plane?
A. 10 units
B. 50 units
C. 5 units
D. 25 units
Answers
Answer:
The distance between the points (4,3) and (1,-1) is C. 5 units.
Step-by-step explanation:
C.
(5 Units)
Explanation
Distance formula: square root of (x2-x1)^2+ (y2-y1)^2
(4-1)^2+ (3--1)^2
3^2 + 4^2
9 + 16
25
square root of 25 is 5
Can someone pls pls PLS, help me out? ASAP!! (Geometry)
“Complete the proof”
Answers
1) [tex]\overline{AB} \perp \overline{BD}[/tex], [tex]\overline{AB} \cong \overline{DB}[/tex], [tex]\overline{AC} \cong \overline{DE}[/tex] (given)
2) [tex]\angle ABD[/tex] is a right angle (perpendicular lines form right angles)
3) [tex]\triangle ABD[/tex] and [tex]\triangle DEB[/tex] are right triangles (a triangle with a right angle is a right angle)
4) [tex]\triangle ABD \cong \triangle DEB[/tex] (HL)
5) [tex]\angle ACB \cong \angle DEB[/tex] (CPCTC)
11y^2-xy dxUse the method for solving homogeneous equations to solve the following differential equation.
Answers
The solution to the homogenous differential equation, (11y² - xy)dx + x²dy = 0, is [tex]y = \frac{x}{11 ln (x) + C}[/tex].
A homogeneous differential equation has a homogeneous function as one of its components, if f(λx, λy) = λⁿf(x, y), for any non-zero constant λ, the function is said to be homogenous. The homogeneous differential equation's generic form is of the type f(x, y).dy + g(x, y).dx = 0. The degree of the homogeneous differential equation is the same for the equation's variables x and y.
In the question, we are asked to solve the homogeneous differential equation, (11y² - xy)dx + x²dy = 0.
The given equation can be solved as follows:
Grouping by differentials, gives us: x²dy = (xy - 11y²)dx.We now substitute, u = yx, making y = ux, or, dy = u.dx + x.du.Making the substitutions, we get: x²(u.dx + x.du) = (u - 11u²)x²dx.Expanding the parentheses, we get: ux².dx + x³.du = ux².dx - 11u²x².dx.Reducing ux².dx, we get: x³.du = -11u²x².dx.Dividing by x³ and u², we get du/u² = -11/x.Now, we integrate both sides of the equation: [tex]\int \frac{1}{u^2}du = \int -\frac{11}{x}dx[/tex]Calculating the resulting integrals, we get: -1/u = C - 11 ln(x).Undoing the substitution, u = y/x, we get: -x/y = C - 11 ln(x)The final solution is: [tex]y = \frac{x}{11 ln (x) + C}[/tex]Thus, the solution to the homogenous differential equation, (11y² - xy)dx + x²dy = 0, is [tex]y = \frac{x}{11 ln (x) + C}[/tex].
The provided question is incomplete. The complete question is:
"Use the method for solving homogenous equations to solve the following differential equation.
(11y² - xy)dx + x²dy = 0".
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Is the point (−2, 10) on the circle with radius 5 and center (2, 13)?
Answers
Answer:
yes
Step-by-step explanation:
The point can be demonstrated to lie on the circle by plotting both on a graph. It can also be shown to lie on the circle by showing the distance from center is equal to the radius.
GraphThe attachment shows a graph of the circle. Its equation is ...
(x -h)² +(y -k)² = r² . . . . . . for center (h, k) and radius r
We have (h, k) = (2, 13) and r = 5, so the equation is ...
(x -2)² +(y -13)² = 25 . . . . graphed equation
The point in question is also graphed, and is shown to lie on the circle.
DistanceIf the given point satisfies the circle's equation, it lies on the circle.
For (x, y) = (-2, 10), we find ...
(-2 -2)² +(10 -13)² = (-4)² +(-3)² = 16 +9 = 25 . . . . . the equation is satisfied
The area of the triangle shown is represented by A=s(s−12)(s−9)(s−7)−−−−−−−−−−−−−−−−−−−√, where s is equal to half the perimeter. What is the height h of the triangle? Round your answer to the nearest hundredth. (25 points to answer!! please))
Answers
The height h of the triangle is 5.42 ft
How to find height of a triangle?The height of the triangle can be found using the formula below:
Area = 1 / 2 bh
where
b = baseh = heightTherefore,
A = √s(s - a)(s - b)(s - c)
Hence,
s = 14 + 7 + 11 / 2 = 32 / 2 = 16
A = √16(16 - 11)(16 - 7)(16 - 14)
A = √1440
A = 37.947331922
A = 37.95 ft²
37.95 = 1 / 2 × 14 × h
h = 37.95 / 7
h = 5.42104741743
h = 5.42 ft
Therefore, the height h of the triangle is 5.42 ft
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Does anyone know how to do this
Answers
Considering the area of the rectangle, we have that the length is of 8 units and the width is of 10 units.
What is the area of a rectangle?The area of a rectangle of length l and width w is given as follows:
A = lw.
In this problem, the area is of 80 square units, while the length and the width are consecutive even integers, hence:
A = 80.w = l + 2.Then:
l(l + 2) = 80
l² + 2l - 80 = 0
(l + 10)(l - 8) = 0.
We need the positive measure, hence:
l - 8= 0 -> l = 8 units.
w = l + 2 = 10 units.
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Solve for xxx in the diagram below.
Answers
Answer:
x = 34
Step-by-step explanation:
The three angles form a straight line and are thus supplementary angles. The sum of a supplementary angles is always 180, so we can use the equation 180 = x + 12 + 100 + x to find x:
180 = 2x + 112
68 = 2x
x = 34
please put it in expanded form and solve it
Answers
Answer:
1/xyz^3
Step-by-step explanation:
exponents are subtracted when divided
x^0 is 1
negative exponents are positive in the denominator
(4x^0y^-2z^-3) / (4xy-1)
(4xy^-2z^-3) / (4xy^-1)
x-1y^-1z^-3
1/xyz^3
Can 1775 dollars buy 2 large balloons and 16 small balloons 1 large balloon = 300 cubic feet 1 small balloon - 40 cubic feet helium costs $1.60 per cubic foot
Answers
No, 1775 dollars cannot buy 2 large balloons and 16 small balloons if helium costs $1.60 per cubic foot.
Calculating the Costs of Balloons
It is given that,
Helium costs $1.60 per cubic foot.
Volume of one large balloon = 300 cubic feet
Thus, the price of one large balloon = $1.60 × 300
= $480
Volume of one small balloon = 40 cubic feet
Thus, the price of one small balloon = $1.60 × 40
= $64
How much buying 2 large and 16 small balloons costs?
So, as calculated above,
One large balloon costs $480, and one small balloon costs $64
Therefore, the cost of two large balloons = $480 × 2
= $960
Cost of 16 small balloons = $64 × 16
= $1024
Total cost of balloons = $960 + $ 1024
= $1984
Since, $1984>$1775,
Therefore, $1775 cannot buy all those balloons if helium costs $1.60 per cubic foot.
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The sum of 225 consecutive positive integers only has digits 1 or 0. What is the smallest possible value of the sum?
Answers
Answer:
1 +10=11 (since 0 is neither negative or positive the first and second positive integerswith 1 or 0
Find the probability of winning a lottery by selecting the correct six integers, where the order in which these inte
Answers
The probability of winning a lottery by selecting the correct six integers, are
[tex]\begin{aligned}&(a) 1.68 \times 10^{-6} \\&(b) 5.13 \times 10^{-7} \\& (c) 1.91 \times 10^{-7} \\&(d)8.15 \times 10^{-8}\end{aligned}[/tex]
What is binomial distribution?The binomial distribution is a type of probability distribution that expresses the probability that, given a certain set of characteristics or assumptions, a value would take one of two distinct values.
Part (a); positive integers not exceeding 30.
To calculate the probability, use binomial coefficients. Pick six of the six accurate integers and none of the other twenty-four.
[tex]\frac{\left(\begin{array}{c}6 \\6\end{array}\right)\left(\begin{array}{c}24 \\0\end{array}\right)}{\left(\begin{array}{c}30 \\6\end{array}\right)}=\frac{1}{\left(\begin{array}{c}30 \\6\end{array}\right)}=1.68 \times 10^{-6}[/tex]
Part (b); positive integers not exceeding 36.
To calculate the probability, use binomial coefficients. Pick six of the six accurate integers and none of the other thirty.
[tex]\frac{\left(\begin{array}{l}6 \\6\end{array}\right)\left(\begin{array}{c}30 \\0\end{array}\right)}{\left(\begin{array}{c}36 \\6\end{array}\right)}=\frac{1}{\left(\begin{array}{c}36 \\6\end{array}\right)}=5.13 \times 10^{-7}[/tex]
Part (c); positive integers not exceeding 42.
To calculate the probability, use binomial coefficients. Pick six of the six accurate integers and none of the 36 other integers.
[tex]\frac{\left(\begin{array}{l}6 \\6\end{array}\right)\left(\begin{array}{c}36 \\0\end{array}\right)}{\left(\begin{array}{c}42 \\6\end{array}\right)}=\frac{1}{\left(\begin{array}{c}42 \\6\end{array}\right)}=1.91 \times 10^{-7}[/tex]
Part (d); positive integers not exceeding 48.
To calculate the probability, use binomial coefficients. Choose six of the six accurate integers and none of the other 42.
[tex]\frac{\left(\begin{array}{l}6 \\6\end{array}\right)\left(\begin{array}{c}42 \\0\end{array}\right)}{\left(\begin{array}{c}48 \\6\end{array}\right)}=\frac{1}{\left(\begin{array}{c}48 \\6\end{array}\right)}=8.15 \times 10^{-8}[/tex]
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The complete question is-
Find the probability of winning a lottery by selecting the correct six integers, where the order in which these integers are selected does not matter, from the positive integers not exceeding a) 30. b) 36. c) 42. d) 48.
A boat traveled north for 28 miles, then turned x° southwest and traveled for 25 miles before stopping. When it stopped, the boat was 18 miles from its starting point.
A triangle shows the course of a boat. Starting at the dock, it travels 18 miles to the left, then 25 miles up and to the right, and then 28 miles down and back to the dock. The angle between 25 miles and 28 miles is x degrees.
Law of cosines:
By how many degrees did the direction of the boat change when it made its first turn? Round to the nearest degree.
30 degrees
39 degrees
46 degrees
Answers
The number of degrees that the direction of the boat change when it made its first turn is 39°.
How to calculate the value?From the information given, we would use the cosine function to solve the information.
This will be:
18² = 28² + 25² - 2(28)(25)(cos x)
324 = 784 + 625 - 1400cosx
x = 39.19
Therefore, the value is 39°.
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Which of the following statements about angles is NOT correct?
Complementary angles are two angles whose sum is 90 degrees.
The measure of an obtuse angle is always greater than the measure of an acute angle.
The measure of an acute angle and the measure of an obtuse angle added together will always
be supplementary.
Two right angles that share a leg are supplementary.
Answers
ANSWER: The third statement appears to be incorrect.
Can someone please help me on this
Answers
Answer:
? = 38°
Step-by-step explanation:
We can use the property of sine to find the missing angle value.
sin (angle) = opposite / hypotenuse
sin (?) = 16 / 26 <----- Insert values
? = sin⁻¹(16 / 26) <----- Rearrange
? = 37.97... <----- Solve
? = 38° <----- Round
Line $m$ is parallel to line $n$ and the measure of $\angle 1$ is $\frac 18$ the measure of $\angle 2$. What is the degree measure of $\angle 5$?
Answers
The angle of m∠5 is 116 degrees.
How to find angles when parallel lines are cut by a transversal?When parallel lines are cut by a transversal, angle relationships are formed. This include corresponding angles, alternate angles , vertical angles etc.
Therefore, line m and n are parallel lines cut by the a transversal.
Hence,
m∠2 = 64 degrees
Therefore,
m∠5 = m∠4 (alternate angles)
Therefore,
m∠5 + m∠2 = 180
m∠5 = 180 - 64
m∠5 = 116 degrees.
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The degree measure of the angle labelled 5; m<5 = 116°.
What is the measure of the angle labelled 5 in the task content?The angle measure of the angle labelled 5 as in the complete task content in the attached image can be determined as follows;
It follows from the complete task content that; that the measure of angle 2 is; 64°.
On this note, it follows from the sum of angle measures on a straight line theorem that; m<4 = 180° - 64° = 116°.
Additionally, it follows from the congruence of alternate angles theorem that <4 and <5 are congruent and hence, their measures are equal.
Therefore, m<5 = 116°.
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Determine the intercepts of the line. Do not round your answers. 7x-5=4y-6
x intercept: (_),(_)
y intercept: (_),(_)
Please help!
Answers
The intercepts are x intercept: (-1/7,0) and y intercept: (0,1/4)
How to determine the intercepts?The function is given as:
7x-5=4y-6
Set y = 0 to determine the x-intercept
7x - 5 = -6
Add 5 to both sides
7x = -1
Divide by 7
x = -1/7
Set x = 0 to determine the y-intercept
- 5 = 4y - 6
Add 6 to both sides
4y = 1
Divide by 4
y = 1/4
Hence, the intercepts are x intercept: (-1/7,0) and y intercept: (0,1/4)
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Solve the following system of equations:
3x-5y=-11
7x+2y=-12.
Express your answer as an ordered pair. (x, y)
Answers
Answer: (-2, 1)
Step-by-step explanation:
We will graph the given equations. The point of intersection is the solution to the system of equations. See attached.
They intersect at the point (-2, 1) giving us an answer of x = -2 and y = 1, but this question asks for the answer as an ordered pair so we leave it as is.
What are the solutions of sin(2theta)+sin(theta)=cos(theta) on the interval [0, 360]
Answers
The solutions are: θ = 90º, 270º, 30º, and 150º
Given,
sin2θ = cosθ
sin2 θ = 2sinθ cosθ
2sinθ cosθ = cosθ
2sinθ cosθ - cosθ = 0
factor
cosθ(2sinθ-1) = 0
cosθ = 0 or 2sinθ - 1 = 0
cosθ = 0 when θ=90º or θ=270º (look on the unit circle)
2sinθ - 1 = 0
2sinθ = 1
sinθ = 1/2
look at the unit circle and see that sinθ=1/2 when θ=30º
sin is positive in Quadrant2 as well as Quadrant 1
180º-30º=150º
θ=150º
answers: θ=90º, 270º, 30º, and 150º
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The lengths of three sides of a triangle are 2x + 1/5 feet , 4x + 1/2 feet , and x+ 1 5 . what is the perimeter of the triangle? the drondown menuto complete the answer
Answers
Answer:
7x + 9/10 ft
Step-by-step explanation:
To find the perimeter of a triangle, add the lengths of the three sides
P = 2x + 1/5 + 4x + 1/2 + x+ 1/ 5
Combine like terms
P = 7x + 2/5 +1/2
Get a common denominator
P = 7x + 2/5(2/2) + 1/2 * (5/5)
= 7x + 4/10 + 5/10
= 7x + 9/10
What is the approximate side length of the square? 3.0 units 3.5 units 4.2 units 4.9 units
Answers
Answer:
(っ◔◡◔)っ ♥ the answer is C ♥
Step-by-step explanation:
Read the excerpt from Chapter 3 of Wheels of Change . In 1881, as women in the United States continued to struggle with hoops and corsets and other fashion architecture, their counterparts in England formed the Rational Dress Society. This society called for more reasonable clothing solutions, including limiting the weight of a woman's undergarments to seven pounds. Why was the Rational Dress Society formed? to advocate for more functional cycling and athletic gear for women to push for more beautiful, intricate styles of clothing for women to encourage English women to dress differently than American women to promote safer, more comfortable styles of dress for women
Answers
Step-by-step explanation:
Chapter 3 of Wheels of Change .
But the bicycle craze had a more lasting impact on women’s clothing than just the use of bloomers. Thanks in large part to cycling, the innovation of rational dress reformers were starting to take effect by the end of the 1890s. Corsets were on their way out, dresses were getting shorter, and women no longer wore the heavy, bulky undergarments that gave them round, unnatural shapes. These changes went a long way toward unburdening women and setting the stage for them to be healthier and more active in the coming century.
Based on the excerpt, women in the 1890s became more independent and their lives improved as a result of
a rise in the popularity of bicycles.
a rise in the popularity of corsets.
cycling becoming less socially acceptable.
clothing becoming more restrictive.
Answer:
to promote safer, more comfortable styles of dress for women
Step-by-step explanation:
to promote safer, more comfortable styles of dress for women
The duration of shoppers' time in BrowseWorld's new retail outlets is normally distributed with a mean of 41.8 minutes and a standard deviation of 17.3 minutes. How long must a visit be to put a shopper in the longest 20 percent
Answers
A visit must be of at least 56.33 minutes to put a shopper in the longest 20 percent.
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula. In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z=\frac{X-\mu}{\sigma}[/tex]
How long must a visit be to put a shopper in the longest 20 percent?
Here [tex]\mu=41.8 , \sigma=17.3[/tex]
The 100-20=80th percentile, which is X when Z has p-value of 0.8, so Z=0.84
[tex]Z=\frac{X-\mu}{\sigma}[/tex]
[tex]0.84=\frac{X-41.8}{17.3}[/tex]
14.532=X-41.8
X=14.532+41.8
X=56.33
A visit must be of at least 56.33 minutes to put a shopper in the longest 20 percent.
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Determine if y varies directly with x. Give the constant of variation, when appropriate. (picture below)
A) Does y vary directly with x?
B) What is the constant of variation?
Answers
Based on the given variation, y does not vary directly with x and the constant of variation are 8, 3.2 and 1.25 respectively.
Variationy = k × x
where,
k = constant of proportionality
y = -40
x = -5
y = k × x
-40 = k × -5
-40 = -5k
k = -40/-5
k = 8
when,
y = 8 and x = 2.5
y = k × x
8 = k × 2.5
8 = 2.5k
k = 8/2.5
k = 3.2
when,
y = 5 and x = 4
y = k × x
5 = k × 4
5 = 4k
k = 5/4
k = 1.25
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This system of equations has been placed in a matrix:
y = 700x + 200
y = 5,000 − 75x
Complete the matrix by filling in the missing numbers.
Answers
Answer:
Hello,
Step-by-step explanation:
here is the answer in a picture.
Write two expressions to show the total area of advertisement space on one page.
Answers
The area covered by the advertisement on the page is [tex]ab \ unit^2[/tex].
What is the definition of area of a rectangle?The area of a rectangle covers is the space it takes up inside the boundaries of its four sides. The dimensions of a rectangle determine its area. In general, the area of a rectangle is equal to the product of its length and breadth of the rectangle.
The formula of area of rectangle is [tex]length \times breadth[/tex] [tex]unit^2[/tex]
let the given page represents a rectangle.
We take the length of the advertisement is [tex]a[/tex] unit and breadth of the advertisement is [tex]b[/tex] unit.
The area of the advertisement [tex]=a \times b \ unit^2[/tex]
[tex]=ab \ unit^2[/tex]
Therefore, the area covered by the advertisement on the page is [tex]ab \ unit^2[/tex]
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The graph below shows two polynomial functions, f(x) and g(x): Graph of f of x equals x squared minus 2 x plus 1. Graph of g of x equals x cubed plus 1 Which of the following statements is true about the graph above? (4 points) f(x) is an even degree polynomial with a negative leading coefficient. g(x) is an even degree polynomial with a negative leading coefficient. f(x) is an odd degree polynomial with a positive leading coefficient. g(x) is an odd degree polynomial with a positive leading coefficient.
Answers
Last option. The correct statement about the graph is g(x) is an odd degree polynomial with a positive leading coefficient.
How to solve the questionWe have the function as
[tex]f(x) = x^2 - 2x + 1[/tex]
The polynomial that we have here is of an even degree. The highest degree we have here is 2. The coefficient that has the highest degree is 1.
Hence all of the options that have f(x) are incorrect.
The answer to the question is option 4.
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Identify the factors of 6ab − 8a 21b − 28. (2a 4)(3b − 7) (2a − 4)(3b 7) (2a 7)(3b − 4) (2a − 7)(3b 4)
Answers
Answer: ) (2a+7)(3b- 4)
Step-by-step explanation: