A school show had sold the ticket sales of first and second nights. The price of a student ticket is $3.54, a So, the correct answer is option (d).
Total sale on tickets at the first night = $1345
Total sale on tickets at the second night = $935
Let the price of student ticket and adult ticket in school show be "$x" and "$y" respectively. According to problem,
On first night total sale,
180x + 110y = $1345 --(1)
On Second night total sale,
100x + 90y = $935 --(2)
we have to determine the price of student ticket i.e x and price of adult ticket i.e y .. We have a system of linear equation which consists two equations (1) and (2) . Now, we solve these equations using Substitution method,
From equation (2), 100x = 935 - 90y
=> x = (935 - 90y )/100 --(*)
Substitute the value of x in equation (1) 180x + 110y = $1345
=> 180(935 - 90y )/100 + 110y = 1345
Simplify ..
=> 168120 - 16200y + 11000y = 134500
=> 168120 - 134500 = 16200y - 11000y
=> 33620 = 5200y
=> y = 33620/5200
=> y = 6.46
put the value of y in equation (*) we get,
x = (935 - 90× 6.46)/100 = 3.536
Hence, the value of x is $3.536 and value of y is $6.46..
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edges 1. at the world tic-tac-toe championship, each player must play against 7 other players. new games start every hour. how many hours will the tournament take?
Each game starts every hour then 28 games will be occurred in 28 hours and therefore the tournament will take 28 hours for completion.
Given, there are total 8 players playing the tournament of world tic-tac-toe championship.
Also, new game start each hour.
We have to find the number of hours the tournament will take to complete.
Total games occurred be,
we will use the concept of A.P. to find the total number of games
First player will play with 7 players, second player will play with 6 players and so on.
Total games = 8/2[14 + 7×(-1)]
Total games = 4×7
Total games = 28
Now, if each game start every hour then 28 games will occurred in 28 hours and therefore the tournament will take 28 hours for completion.
Hence, the tournament will take 28 hours for completion.
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Find the exponential growth model that fits the following two points:
(0, 2720)and (8, 10,225)
The exponential growth model below that fits the points (0, 2720) and (8, 10,225) as [tex]y = 2720 \times0.039^t.[/tex]
To find the exponential growth model that fits the points (0, 2720) and (8, 10,225), we need to find the values of the constants k and y0 in the equation [tex]y = y_0e^(kx)[/tex]. We can do this by substituting the coordinates of the two points into the equation and solving for the constants.
First, we substitute the coordinates of the first point into the equation:
[tex]2720 = y_0e^(k\times0)[/tex]
We can simplify this expression by substituting 1 for e⁰: 2720 = y⁰ˣ¹
This equation tells us that y0 = 2720.
Next, we substitute the coordinates of the second point into the equation: [tex]10,225 = y_0e^(k\times8)[/tex]
Substituting the value of y0 that we found above, we get: [tex]10,225 = 2720e^(k\times8)[/tex]
To solve for k, we divide both sides of the equation by 2720: [tex]\dfrac {10,225}{2720} = e^(k\times8)[/tex]
We can take the natural logarithm of both sides to get: ln(10,225/2720) = k8
Dividing both sides of the equation by 8, we get: k = ln(10,225/2720)/8
We can approximate the value of k by using a calculator to evaluate the logarithm: k ≈ 0.039
We now have the values of the constants k and y0, so we can write the exponential growth model that fits the given points: [tex]y = 2720 \times0.039^t.[/tex]
This is the exponential growth model that fits the points (0, 2720) and (8, 10,225).
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PLEASE ANSWER ASAP! WILL GIVE 30 POINTS!
The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
m is the slope.b is the y-intercept.Given two points, the slope is given by the change in y divided by the change in x, hence the slope of segment RS is given as follows:
m = (16 - 4)/(9 - 3) = 2.
When two lines are perpendicular, the multiplication of their slopes is of -1, hence the slope of the perpendicular bisector is obtained as follows:
2m = -1
m = -1/2.
The midpoint of a segment is given by the mean of the coordinates, hence:
x = (3 + 9)/2 = 6.y = (4 + 16)/2 = 10.The perpendicular bisector is a linear function with slope of -1/2 going through the point (6,10), hence the intercept b is calculated as follows:
10 = -0.5(6) + b
b = 13.
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20% of the teachers at Francis Middle School teach science. If there are 6 science
teachers, how many teachers are at Francis Middle School?
Answer: A total of 30 teachers
Step-by-step explanation:
20% = 6 (science) teachers
20x5= 100
6x5=30 teachers
Hope this helps you!
Answer:
30 teachers
20% is 2/10 of 100
20 x 5 = 100
6 x 5 = 30
Therefore, 30 teachers.
What is the value of the expression 1/2 + 2/3 when b = -5?
-17/6
-1/6
23/6
I don't know.
Answer:
1st answer is correct
Step-by-step explanation:
[tex]\sf \frac{1}{2} +\frac{2b}{3}[/tex]
Given that,
b = -5
To find the value of the above expression, replace b with -5.
[tex]\sf \frac{1}{2} +\frac{2b}{3}\\\\\sf \frac{1}{2} +\frac{2*(-5)}{3}\\\\\sf \frac{1}{2} +\frac{-10}{3}[/tex]
Now, to solve the above fractions, you have to make the denominator the same.
For that, multiply both the numerator and denominator of (1/2) & (-10/3) by 3 & 2 respectively.
Let us solve it now.
[tex]\sf \frac{1}{2} +\frac{-10}{3}\\\\\sf \frac{1}{2} -\frac{10}{3}\\\\\sf \frac{1*3}{2*3} -\frac{10*2}{3*2}\\\\\sf\frac{3}{6} -\frac{20}{6} \\\\\sf\frac{-17}{6}[/tex]
How Do You Solve 2 linear equations?
There are six methods to solve linear equations;
Graphical MethodElimination MethodSubstitution MethodCross Multiplication MethodMatrix MethodDeterminants MethodGiven,
Solving Linear equations;
To find a linear equation's solution is to solve a linear equation. Here, the techniques for solving the three primary forms of linear equations—linear equations with one variable, linear equations with two variables, and linear equations with three variables—are described.
We have to find the methods to solve linear equations;
There are six methods to solve linear equations;
Graphical MethodElimination MethodSubstitution MethodCross Multiplication MethodMatrix MethodDeterminants MethodLearn more about solving linear equations here;
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PLEASE HELP ME WITH MY MATH HOMEWORK
ill give you brainliest
Answer: [tex]H = -16s(s-6)[/tex]
Work Shown:
[tex]H = -16s^2+96s\\\\H = -16s*s+16s*6\\\\H = -16s(s-6)\\\\[/tex]
The answer can be confirmed by using the distributive rule to multiply -16s by each term inside the parenthesis. You should get [tex]-16s^2+96s[/tex] after distributing.
Find the standard form of the equation of the parabola satisfying the given conditions.
Focus: (5,0); Directrix: x = -5
The standard equation of parabola that has focus (5, 0) and directrix x = -5 is y² = 20x.
What is parabola ?Any point in a parabola has an identical distance from the fixed point, making it resemble a curve.
Given that,
The focus of the parabola is (5, 0).
And Directrix x = -5
Since the directrix is horizontal here, use the standard equation of parabola,
(y - k)² = 4 p (x - h)
Vertex = (h, k)
= ((x coordinate of focus + directrix)/2 , 0)
= ((5 - 5)/2, 0)
= (0, 0)
p = distance from focus to the vertex = 5 - 0 = 5
The required equation of parabola,
(y - 0)² = 4 × 5(x - 0)
y² = 20x
The equation of parabola is y² = 20x.
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Find all real solutions for the equation n² + 20n +96= 0.
Answer:
n = -8 , n = -12
Step-by-step explanation:
First we factorise the quadratic using the factorisation method :
n²+8n+12n+96 = 0
n(n+8)+12(n+8) = 0
(n+12)(n+8) = 0
Now we equate each bracket to 0 :
Either
n + 12 = 0
n = -12
OR
n + 8 = 0
n = -8
So the real solutions for that equation is
n = -8 , n = -12
If 12% of a number is 150, find 2% of that number.
Answer:
25
Step-by-step explanation:
To find the value of a number given that 12% of it is 150, we can set up the following equation:
0.12x = 150
Solving for x, we get:
x = 150 / 0.12 = 1250
To find 2% of that number, we simply multiply 1250 by 0.02:
2% of 1250 = 0.02 * 1250 = 25.
Therefore, 2% of the number for which 12% is 150 is 25.
suppose the mean number of earthquakes per year in a certain region is 8 . what is the probability that in a given year more than 5 earthquakes occur ?
the probability that in a given year more than 5 earthquakes occur is 72.1%.
What is probability?
By simply dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula. Because the favorable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1.
Let X denotes the number of earthquakes during the next year in this area
X ~ Poisson(2)
The probability mass function of X is
The probability that there will be 1 to 3 (inclusive) earthquakes during the next year in this area P(1 ≤X≤3)
P = 0,721
Hence the probability that in a given year more than 5 earthquakes occur is 72.1%.
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What are the 3 forms of an equation?
Answer:
There are three major forms of linear equations: point-slope form, standard form, and slope-intercept form.
if n 1 integers are chosen from the set {1, 2, 3, , 2n}, where n is a positive integer, must at least one of them be even?
Yes, One of them must be even and this is because Pigeonhole Principle.
What is Pigeonhole Principle?
According to the pigeonhole principle, at least one container must hold more than one item if n things are placed into m containers, where n > m. As an illustration, if one has three gloves (none of which are ambidextrous or reversible), at least two of them must be right-handed or left-handed as there are three items but only two categories of handedness to classify them into. It is possible to establish potentially surprising consequences using this seemingly obvious assertion, a type of counting argument.
From series {1,2......2n}, we need to select 'n+1' integers.
Even integers series from above series is {2,4,6..........2(n-1), 2n}
Odd integers series from above series is {1,3,5......2(n-2), 2n-1}
We can choose only n odd integers from the series. Therefore, if we choose n+1 integers, at least one of them must have to be even integer.
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What is the slope of a line parallel to 1 2?
The slope of a line parallel to 1 2 is also 1 2. The equation for a line parallel to the line with equation y = mx + b is y = mx + b + c, where c is any constant.
The slope of a line parallel to 1 2 is the same as the slope of 1 2, which is 1 2.
The slope of a line is calculated by dividing the change in the y-values by the change in the x-values. In the case of 1 2, this is (2-1)/(2-1), which equals 1/1, or 1 2. So the slope of any line parallel to 1 2 is also 1 2. Parallel slope intercept form is a form of linear equation that describes a line parallel to a given line. It is written as y = mx + b, where m is the slope of the line and b is the y-intercept of the line. This form is useful for finding equations of lines that are parallel to a given line.
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If a polynomial function, f(x), with rational coefficients has roots 0, 4, and , what must also be a root of f(x)?.
The remaining root of f(x) will be 3 - [tex]\sqrt{11}[/tex]
To answer this question we have to find the conjugate of 3+[tex]\sqrt{11}[/tex],
For example, the conjugate of p+q will be p-q or vice versa.
Let us consider x= 2+[tex]\sqrt{11}[/tex]
To simplify the equation let us subtract 3 on both sides of the equation
x - 3 = 3+[tex]\sqrt{11}[/tex] - 3
x - 3 = [tex]\sqrt{11}[/tex]
Square both,
[tex](x - 3)^{2}[/tex] = 11
[tex](x - 3)^{2}[/tex] - 11 =0
Now we will use the principle of Square difference to factorize both sides-
[tex](d^{2} - e^{2}) = (d - e)(d + e)[/tex]
(x - 3) - 11 × (x - 3) + 11 = 0
on solving the equation we get,
(x - 3) - 1 = 0 let us consider this first equation
or (x - 3) + 11 = 0 let us consider this second equation
Add [tex]\sqrt{11}[/tex] on both sides of the first equation,
[tex]x - 3 = \sqrt{11}[/tex]
Subtract [tex]\sqrt{11}[/tex] on both sides of the second equation,
[tex]x - 3 = -\sqrt{11}[/tex]
Now by adding 3 on both sides of the first and second equation,
[tex]x = 3 + \sqrt{11}[/tex] or [tex]x = 3 - \sqrt{11}[/tex]
Therefore, the remaining root of f(x) will be = [tex]3 - \sqrt{11}[/tex]
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Complete Question - If a polynomial function f(x), with rational coefficients, has roots 0, 4, and 3 + [tex]\sqrt{11}[/tex], what must also be a root of f(x)?.
Question 10 (1 point)
(01.03 MC)
What is the simplified expression for 54.53 55?
5²
53
54
55
Answer:
5 to the second power
Step-by-step explanation:
5 to the power of 4 is 625
5 to the power of 3 is 125
5 to the power of 5 is 3,125
So the expression is now 625 x 125/ 3,125
625 x 125 = 78,125
78,125/3,125= 25
5 to the second power equals 25
The park plans to cover the shaded portion of the ramp in wood.
Approximately how much wood, in square feet, will the park need to cover the shaded portion of the ramp?
(MGSE9-12.G.SRT.8)
The area that park will need to cover 67.95 square feet of the ramp.
What are trigonometric ratios?The trigonometric ratios are defined for a right angled triangle.
The example of these ratios are sin, cos, tan, cosec, sec and cot.
The trigonometric ratios are useful in determining the heights and distances of the large objects.
Suppose the length of the wood be x.
The length of wood forms the right triangle as shown in the figure.
Apply trigonometric ratio to the triangle to get,
Cos (28°) = 12/x
⇒ x = 12/Cos (28°) = 13.59
Now, the area of the wood is given as,
Length × width
⇒ 13.59 × 5 = 67.95
Hence, the area of wood required is 67.95 square feet.
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What is the equation in point − slope form of the line passing through 1 2 and 2/5 )? 5 points?
The equation in point-slope form of the line passing through [tex](1,2)[/tex] and [tex](2,5)[/tex] is [tex]y=3x-1[/tex]
To find the slope of the line is
[tex]m=\frac{y_{2} -y_{1} }{x_{2} -x_{1} } \\m=\frac{5-2}{2-1} \\m=\frac{3}{1} \\m=3[/tex]
The equation of the line is given by
[tex]y=mx+c.........(1)[/tex]
We have to use one point form to find the equation
The point [tex](1,2)[/tex] satisfies the equation
plug in the value of m, the equation becomes
[tex]2=3(1)+c\\2=3+c\\c=2-3\\c=-1[/tex]
Put the value of m,c in (1) equation
[tex]y=3x-1[/tex]
The equation of the line is [tex]y=3x-1[/tex].
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-4x² + x - 7 = y
2x + 8 = -y ( solve by elimination )
A technique for solving an equation system is elimination.
What is elimination method ?Elimination is a method of solving a system of equations. In elimination, the goal is to eliminate one of the variables by adding and subtracting equations in order to create an equation with a single variable. This equation can then be solved for the single variable. For example, given the system of equations 2x + 8 = -y and 4x² + x - 7 = y, we can use elimination to solve for the variables x and y. To do this, we first need to multiply the first equation by -4, giving us -8x - 32 = 4y. We then add the two equations together, which gives us 4x² + 9x - 39 = 0. This equation can be solved using the quadratic formula, which gives us x = -3. To solve for y, we can plug x = -3 into either of the original equations. Plugging this value into the first equation gives us 2(-3) + 8 = -y, which simplifies to -6 + 8 = -y, and therefore y = 2. This method of using elimination to solve a system of equations can be used to solve any system of equations with two variables.2x + 8 = -y
-4x² + x - 7 = -y
Subtracting 2x + 8 from both sides:
-4x² - x + 15 = 0
(4x - 5)(x + 3) = 0
4x - 5 = 0
x = 5/4
x + 3 = 0
x = -3
Solutions:
x = 5/4 and x = -3
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in chemistry class, samantha finds that she can make a certain solution by mixing $.04$ liters of chemical a with $.02$ liters of water (this gives her $.06$ liters of the solution). she wants to make a total of $.48$ liters of this new solution. to do so, how many liters of water will she use?
For a 0.48 liter solution, Samantha will use 0.16 liters of water.
Given that
she can make a certain solution by mixing 0.04 liters of chemical a with 0.02 liters of water
she wants to make a total of 0.48 liters of this new solution.
a quantity 0.48/0.06 = 8 times greater than that produced by one recipe.
Water in the amount of 0.02 liters is required.
Samantha will require 0.16 liters of water, or 8 times as much water, to create the solution.
For a 0.48 liter solution, Samantha will use 0.16 liters of water.
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Employees at a company are given £1,500 to spend on items for the office. They decide to buy a coffee machine and as many bean bags as possible. Bean bags cost £75 with an offer of "Buy at least 15 get 10% off the price." The coffee machine costs £210. How much will they have left over from the £1,500?
278.5 if im not wrong
Step-by-step explanation:
75 x 15 1125 ten percent of that is 133.5 take 1125 - 133.5 =1011.5 take that add 210 get 1221.5 -1500 and you have 278.5
Find the slope of the tangent line to the given polar curve at the point specified by the value of theta.
r = 6 cos(theta),
theta = ????/3
The slope of the tangent line to the given polar curve at the point specified by the value of theta is m= 1/√3.
What is meant by tangent line?A straight line that just touches a plane curve at a particular location is referred to as the tangent line (or tangent) to the curve in geometry. It was described by Leibniz as the line connecting two points on the curve that are endlessly near to one another. A line passes through the point (c, f(c)) on the curve and has a slope of f'(c), where f' is the derivative of f. This is more properly referred to as being a tangent of the curve y = f(x) at a point x = c. Curves in n-dimensional Euclidean space and curves in space have a comparable definition.
The tangent line is "passing" through the point of tangency—the intersection of the tangent line and the curve as it travels.
Given,
r=6cosθ
f'(θ)=-6sinθ
θ=π/3
dy/dx=(f'(θ)sinθ+f(θ)cosθ)/(f'(θ)cosθ-f(θ)sinθ)
dy/dx=( -6sinθsinθ+6cosθcosθ)/(-6sinθcosθ-6cosθsinθ)
=(6cos²θ-6sin²θ)/-12 sinθcosθ
=6(cos²θ-sin²θ)/-6(2sinθcosθ)
=6cos2θ/-6sin2θ
=-cos2θ/sin2θ
=-cot2θ
Slope of the given polar curve at θ=π/3 is
m=dy/dx
m= -cot(2(π/3))
m = cot(-2π/3)
m= 1/√3
Therefore, the slope of the tangent line to the given polar curve at the point specified by the value of theta is
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HELPPPPPP PLEASEEE I NEED HELP
The volume of pyramid with square base is 15466.67 cm³.
What is pyramid?A three-dimensional shape is a pyramid. A pyramid's flat triangular faces unite at a common point known as the apex and have a polygonal base. The bases are joined to the peak to create a pyramid. The lateral face is a triangle face formed by the connection of each edge of the base to the apex.
Given, the pyramid has square base.
And the side of square is 40 cm
And the height is 29cm.
The volume of the pyramid with square base
V = base area x height/3
V = (40 x40) x 29/3
V = 15466.67 cm³
Therefore, the volume of pyramid with square base is 15466.67 cm³.
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What is the theorem of SSS?
Answer:
read below :)
Step-by-step explanation:
SSS is the side side side theorem.
It states that if the three sides of a triangle are equal in length to the three sides of another triangle, they must be congruent.
The ratio of roses to lilles in a garden is 3 to 2 what percentage of the gardens flowers are roses
Answer:
To find the percentage of roses in the garden, we first need to determine the total number of flowers in the garden. We can do this by adding the number of roses and lilies, and then multiplying that number by the ratio of roses to lilies. For example, if there are 3 roses and 2 lilies in the garden, the total number of flowers would be 5 (3 + 2 = 5). To determine the percentage of roses, we would then divide the number of roses by the total number of flowers, and multiply by 100. In this case, the percentage of roses would be 60% (3 / 5 * 100 = 60).
Which of the following is the equation of the ellipse with a vertical major axis, center at (1, –3), a = 7, and b = 5?
(Don't mind the answer that is already selected.)
The required equation of the ellipse is (x - 1)² / 49 + (y + 3)² / 25 = 1. which is the correct answer would be an option (A).
What is the equation of the ellipse?The equation of an ellipse with a vertical major axis and center at (h, k) is given by the formula (x - h)² / a² + (y - k)² / b² = 1, where a is the length of the major axis and b is the length of the minor axis.
As per the question, the ellipse has a vertical major axis and center at (1, -3), a = 7, and b = 5.
Substituting these values into the formula, we get:
(x - 1)² / 7² + (y + 3)² / 5² = 1
Simplifying this expression, we get:
(x - 1)² / 49 + (y + 3)² / 25 = 1
Thus, the required equation of the ellipse is (x - 1)² / 49 + (y + 3)² / 25 = 1.
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Is root 2 a rational number?
The [tex]\sqrt{2}[/tex] is not a rational number, it is an irrational number
The number is [tex]\sqrt{2}[/tex]
The rational number is the number that can be written in the form of p/q where q ≠ 0
Therefore assume [tex]\sqrt{2}[/tex] is a rational number
[tex]\sqrt{2}[/tex] = p/q
Find the square of the both side
2 = p^2 / q^2
2q^2 = p^2
The value of p^2 will be the multiple of 2
p will be the multiple of 2
Consider the multiple as m
p = 2m
p^2 = 4m^2
Substitute the values in the above equation
2q^2 = 4m^2
q^2 = 2m^2
Therefore the value of the q will be the multiple of 2
The p and q is the multiple of 2, therefore they have coprime
Our assumption is wrong, [tex]\sqrt{2}[/tex] is an irrational number
Therefore, the [tex]\sqrt{2}[/tex] is not a rational number
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How to you turn 9 less than six times a number into an expression
Answer:
6x-9
Step-by-step explanation:
you do
Answer: 6x-9
Step-by-step explanation:
We know that the word than is a switch word. Therefore, the nine will go after the minus sign. X is the variable (unknown number). Times is a multiplication word but you do not put a multiplication symbol when there is just a variable.
Hence, our answer is 6x - 9
Elise said that 0.1 equals 1% complete the explanation of her mistake
Help please, it’s hard and I’m having a difficult time!
Answer:
1) Median
2) Mode
3) Mean
(Hope this is correct :D )
Step-by-step explanation:
Mode is the number that is most repeated in the data set, and it would best describe the center of the data for the second one.
The first one has an outlier of 50 at the start, so the median would be most appropriate for this.
The last one is basically equal for each value, so the mean would best describe the center for this one.