A small theatre's profit, P(x), from selling concert tickets is P(x) = −15x2 + 60x + 30, where x is the number of $2 price increases of each ticket. Use the graph below to answer the question.
Graph of function p of x equals negative 15 x squared plus 60 x plus 30. The graph has the x-axis labeled as number of price increases, and the y-axis labeled as profit. The curve begins at (0, 30) and increases to (2, 90) and then decreases through (4.449, 0).
How many price increases maximized the theatre's profit?
0
1.5
2
4.5
Using the vertex of the quadratic equation, it is found that the profit will be maximized when each ticket price is sold for $2.
What is the vertex of a quadratic equation?A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.
Considering the coefficient a, we have;
If a < 0, the vertex is a maximum point.
If a > 0, the vertex is a minimum point.
In this question, the function is modeled as follows, considering x as the price divided by $2.
P(x) = -15x² + 60x + 30.
The coefficients are a = -15 < 0, b = 60, c = 30, therefore the x-value of the vertex is given by:
V = -b/2a
V = -60/2(-15)
V = -60/-30
V = 2
Hence, the profit will be maximized when each ticket price is sold for $2.
More can be learned about the vertex of a quadratic equation at brainly.com/question/24737967
#SPJ1
the difference between two numbers is 547. one is 268 find the larger
Answer:
279
Step-by-step explanation:
Please I need help to doing this pleaseee help me
The equation of line in the given graph with coordinate points (2,-2) and (-3,-6) is 4x-5y=18.
What is equation of line?A straight line's general equation is y = mx + c, where m is the gradient and y = c is the value at which the line intersects the y-axis. This value c is known as the y-axis intercept. Linear equations are classified into three types: point-slope, standard, and slope-intercept. The equation of a two-dimensional line is ax+by=c; it is fair to predict that the equation of a three-dimensional line is ax+by+cz=d; reasonable, but incorrect—it turns out that this is the equation of a plane. A plane, unlike a line, does not have a clear "direction."
Here,
The coordinates of line will be (2,-2) and (-3,-6).
slope m=(-6-(-2))/(-3-2)
=-4/-5
=4/5
(y-y1)=m(x-x1)
y+2=4/5(x-2)
5(y+2)=4(x-2)
5y+10=4x-8
4x-5y=18
4x-5y=18 is the equation of the line in the given graph with coordinate points (2,-2) and (-3,-6).
To know more about equation,
https://brainly.com/question/10413253?referrer=searchResults
#SPJ1
Which of the given formulas for the general term of the sequence 8, 5, 2, –1, –4, ...
is correct?
a. tn = −3n + 11
b. tn = 3n + 11
c. tn = 3n + 8
d. tn = 3n − 8
The term is tn=-3n+11
From the question, we have
The sequence is 8, 5, 2, –1, –4, ...
d = 5-8 = -3
t1 = 8
tn = t1+(n-1)d
tn=8+(n-1)(-3)
tn=8-3n+3
tn=-3n+11
Addition:
The phrase "the addition" refers to combining two or more numbers. Adding two numbers is indicated by the plus sign (+), therefore adding three is written as three plus three. Additionally, the number of times the plus symbol (+) is used is up to you. For example, 3 + 3 + 3 + 3. Mathematical addition is a crucial component of the learning curriculum for kids. In primary school, students learn simple addition sums such as one-digit facts,
Math addition sums, and double-digit Math addition sums. One of the most fundamental and interesting
Math concepts for elementary school children is addition sums. Math is a fascinating subject, and children first learn basic mathematical concepts like adding numbers in their early years.
To learn more about addition visit: https://brainly.com/question/680614
#SPJ1
Please help with the following question.
Answer:
Step-by-step explanation:
C
If h = 7 find value of h2
Step A
Let x = Elijah’s age.
x + 4 = James’s age
2(x +4) = Bryan’s age.
Step B
x + x + 4 + 2(x +4) = 80.
Step C 4x + 12 = 80
X = 17
Step D James is 21.
1. Above is a solution to a verbal problem on the Algebra 1 test. Write the word problem that the student was solving.
2. If the equation in step B had been 2(x + 4) = 80, would the wording of the word problem change or stay the same? If it changed, what would it say now?
1. Elijah is the smallest sibling among his brother who is 4 years older than her and Bryan is the eldest sibling who is twice as James, what is his age of James if the sum of their ages is 80 years?
2. If the equation in step B had been 2(x + 4) = 80, the changed statement would be Bryan is 80 years old.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Here we are converting a numerical expression into a statement.
Given,
Step A
Let x = Elijah’s age.
x + 4 = James’s age
2(x +4) = Bryan’s age.
Step B
x + x + 4 + 2(x +4) = 80.
Step C 4x + 12 = 80
X = 17
Step D James is 21.
The verbal problem to the algebra test can be stated as
Elijah is the smallest sibling among his brother who is 4 years older than her and Bryan is the eldest sibling who is twice as James, what is the age of James if the sum of their ages is 80 years?
If the equation in step B had been 2(x + 4) = 80, the changed statement would be Bryan is 80 years old.
learn more about numerical expressions here :
https://brainly.com/question/29199574
#SPJ1
3. Cameron has been given 4 boxes with samples
of soil. If all of the samples can either be
classified as mineral-rich, mineral-neutral, or
mineral-poor, how many different ways could
Cameron possibly classify all 4 samples, given
that they could all be classified as the same type
if that were the case?
A. 3
B. 4
C. 12
D. 81
Answer: D. 81
Step-by-step explanation:
Box A: 3 possibilites
Box B: 3 possibilites
And so on, so you get 3^4, which is 81
Given: AB is parallel to CD and BD bisects AC.
Prove: triangle ABE is congruent to triangle CDE.
Check the picture below.
Diana is packing a lunch that will include an orange. Diana has 3 navel oranges, 5 mandarin oranges, and 4 Valencia oranges. If Diana selects an orange at random, what is the probability that she selects a navel orange?
Give your answer as a simplified fraction.
Answer:
Step-by-step explanation:
1. Ok. Probability is something out of all. Add to get the bottom base of the probability.
3+4+5= 12
2. Probability is something out of something so 3 navel oranges can be represented out of 12 oranges.
3 out of 12
3. Make as fraction:
3 out of 12=
3/12=
1/4 or 25 Percent!
Answer: 1/4 or 25% ( If wanted as Percent)
Answer:
1/4
Step-by-step explanation:
Number of navel oranges = 3.
Number of mandarin oranges = 5.
Number of Valencia oranges = 4.
Let N be an event that Diana selects navel orange.
The total number of oranges Diana has:
n(T)=3+5+4=12n(T)=3+5+4=12
Number of navel Oranges is:
n(N)=3n(N)=3
The probability that Diana selects a navel orange is:
P(N)=n(N)n(T)=312=14P(N)=n(N)n(T)=312=14
Hence, the probability that Diana selects a navel orange is 1414.
HElp using trigonometry how do I solve this?
By using trignometry we got the side p as 6.67
Use the cosine rule of trignometry to find side p
p² = r² + q² - 2rqcosP
To find the angle of p we will simply subtract angle R and angle Q from 180.
180 - 47.28 - 40 = 92.72
p² = 8² + 7² + 2(8)(7)cos(92.72)
p² = 107.685
p = √107.685
p = 10.38
Let's suppose that the shortest distance of R from PQ is .
look at the diagram I gave
since the line I made makes a right angled triangle, we can use SOH CAH TOA
for the angle 40, is opposite and 10.38 is hypotenuse
which means we will have to use SOH
sin40 = O/H
sin40 =x /10.38
0.6428 = x/10.38
0.6428 × 10.38 = x
x = 6.67
Hence, by using trignometry we got the side p as 6.67
To learn more about heights and distance refer here
https://brainly.com/question/25748640
#SPJ1
Disclaimer,
The given question is incomplete, the answer is done based upon a similar question. The question is given in the image attached.
How many different 10-letter words (real or imaginary) can be formed from the following letters? cbqgvlbbgc
Using mathematical permutation, there 30240 number of 10-letter words that can be formed from the arrangement of letters cbqgvlbbgc
What is permutation?Permutation is simply the manner of arrangement or selection of elements.
We shall calculate for the permutation of the letters cbqgvlbbgc as follows:
There are total of 10 letters
c = 2
b = 3
g = 2
q = 1
v = 1 and,
l = 1
permutation of cbqgvlbbgc = 10!/(2! × 2! × 3!)
permutation of cbqgvlbbgc = (10 × 9 × 8 × 7 × 6 × 5 × 4 × 3!)/(2! × 2! × 3!)
dividing common factors of the numerator and denominator, we have
permutation of cbqgvlbbgc = 10 × 9 × 8 × 7 × 6 × 5
permutation of cbqgvlbbgc = 30240
Therefore by permutation, we derived 30240ways 10-letter words can be arranged from the letters cbqgvlbbgc.
Know more about permutation here: https://brainly.com/question/12468032
#SPJ1
The bookshop received a shipment of identification books. 1/3 of them were bird books, 1/2 of the rest of the books
were about plants, and 1/4 of the remaining books were mammal books. The 12 books that were left were insect
books. How many books were in the shipment?
Answer:
48
Step-by-step explanation:
1/3+(1/2*2/3)+(1/4*1/3)=3/4
1-3/4=1/4
So 12 book were 1/4 of the shipment.
So 48 book sis total.
Which is equivalent to 644 ?
4x^{2}+16y^{2}-24x+64y+36=0
The center is:
The vertices are:
The foci are:
For the given equation,4x²−y²−24x−4y+28=0.The center is (h,k)=(3,−2), vertex (h+a,k)=(4,−2) and (h−a,k)=(2,−2), foci is (h+c,k)=(5.23,−2) and (h−c,k)=(0.77,−2)
What is the equation?An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.
It is given that, the equation of the hyperbola is,
4x²−y²−24x−4y+28=0
Comparing the equation with the standard equation we get,
Center (h,k)=(3,−2)
Vertex (h+a,k)=(4,−2) and (h−a,k)=(2,−2)
Foci (h+c,k)=(5.23,−2) and (h−c,k)=(0.77,−2)
Asymptotes y=2x−8 and y=−2x+4
Thus, for the given equation,4x²−y²−24x−4y+28=0.The center is (h,k)=(3,−2), vertex (h+a,k)=(4,−2) and (h−a,k)=(2,−2), foci is (h+c,k)=(5.23,−2) and (h−c,k)=(0.77,−2)
Learn more about the equation here,
https://brainly.com/question/10413253
#SPJ2
can someone pls help me
Answer: AAS
Step-by-step explanation:
Because of the pair of vertical angles, there are two pairs of congruent angles and one pair of congruent sides. This means the triangles are congruent by AAS.
A basic cellular package costs $40 /month for 60 minutes of calling with an additional charge of $0.20 /minute beyond that time. The cost function C(x) for using x minutes would be
If you used 60 minutes or less, i.e. if if x≤60 , then C(x)=40 (the base charge).
If you used more than 60 minutes, i.e. (x−60) minutes more than the plan came with, you would pay an additional $0.20 for each of those (x−60) minutes. Your total bill would be C(x)=40+0.20(x−60) .
If you want to keep your bill at $50 or lower for the month, what is the maximum number of calling minutes you can use?
Answer:
78
exclamation is that if 50 is lower than 60 which it is meaning that 78 is the correct answer if you multiply 18 + 34 that is not the right answer but there should be a right answer under this question you shouldn't trust me because I do not give a what the answer is I do not suggest you write down this answer but you do your top G
The maximum number of calling minutes you can use to keep your bill at $50 or lower is 110 minutes. If you use 110 minutes or less, your bill will not exceed $50.
To keep your bill at $50 or lower for the month, you need to set up an inequality using the cost function C(x):
C(x) = 40 + 0.20(x - 60)
Since you want to keep the cost at or below $50, the inequality is:
C(x) ≤ 50
Now, substitute the expression for C(x) into the inequality:
40 + 0.20(x - 60) ≤ 50
40 + 0.20x - 12 ≤ 50
0.20x + 28 ≤ 50
Now, isolate the term with "x" on one side by subtracting 28 from both sides:
0.20x ≤ 50 - 28
0.20x ≤ 22
Finally, divide both sides by 0.20 to solve for "x":
x ≤ 22 / 0.20
x ≤ 110
The maximum number of calling minutes you can use to keep your bill at $50 or lower is 110 minutes. If you use 110 minutes or less, your bill will not exceed $50.
Learn more about maxima here:
https://brainly.com/question/12870695?
#SPJ2
10x+2y=41
Solve for y and x
Answer:
{x,y}={25/7,41/7}
Step-by-step explanation:
Michael is working two summer jobs, making $19 per hour lifeguarding and making
$14 per hour clearing tables. In a given week, he can work at most 17 total hours and
must earn a minimum of $280. If a represents the number of hours lifeguarding and
y represents the number of hours clearing tables, write and solve a system of
inequalities graphically and determine one possible solution.
The possible solutions are 8 hours and 9 hours.
The number of hours for lifeguarding is 8 hours.
The number of hours for clearing tables is 9 hours.
What is inequality?It shows a relationship between two numbers or two expressions.
There are commonly used four inequalities:
Less than = <
Greater than = >
Less than and equal = ≤
Greater than and equal = ≥
We have,
Two summer jobs:
Lifeguarding.
x = number of hours
= $19 per hour
Cleaning tables.
y = number of hours
=$14 per hour
Total hours in a week = 17 hours
Minimum earning = $280
The inequality represents the above situation.
x + y ≥ 17
19x + 14y ≥ 280
Solving for x and y.
x + y = 17 _____(1)
x = 17 - y
19x + 14y = 280 ______(2)
Putting (1) in (2) we get,
19(17 - y) + 14y = 280
323 - 19y + 14y = 280
323 - 5y = 280
323 - 280 = 5y
43 = 5y
y = 43/5
y = 8.6
y = 9
Now,
x = 17 - y
x = 17 - 8.6
x = 8.4
x = 8
Thus,
The possible solutions are 8 hours and 9 hours.
The number of hours for lifeguarding is 8 hours.
The number of hours for clearing tables is 9 hours.
Learn more about inequalities here:
https://brainly.com/question/20383699
#SPJ1
A truck travels 50 m/s in a 30 second time frame what is the average speed
The average speed of the truck is 50 m/s .
We know that the average speed of any vehicle is calculated by total distance divide by total time.
Now the truck travels at 50 m/s for 30 seconds.
Distance covered in 30 seconds = 50 × 30 = 1500 meters
Time taken = 30 seconds
average speed = 1500 / 30 = 50 m/s
The average speed now accounts for the majority of the distance travelled. Average speed is essentially a method for calculating distance and the rate of transit time.
Knowing the average speed is crucial because it is clear that the pace will vary throughout the voyage. The average speed of a vehicle or an object can be determined using a variety of methods.
That is the most popular and simple way for figuring your average speed. It functions best when the object's speed remains constant throughout the journey, never rising or falling.
To learn more about average speed visit:
brainly.com/question/4657663
#SPJ1
Explain what the vertical line test is and how it is used
Answer:
You take a pencil and slowly go across the graph from left to right. If any two points are under the pencil at any one time, the relations is not a function. For a relations to be a function, every input must have only one output, so there will be no two points graphed vertically on top of each other.
Step-by-step explanation:
HI i need this questions answer as soon as possible WITH STEPS PLEASE
Answer:
210
Step-by-step explanation:
200 × (5% + 1)
=200 × (0.05 + 1)
=200 × 1.05
=210
yan po hope it helps
The length of the rectangular lot is 25 ft longer than twice the width. If the perimeter of the lot cannot exceed 350 ft, what is the greatest width possible?
The greatest width possible if the length of the rectangular lot is 25 ft longer than twice the width and if the perimeter of the lot cannot exceed 350 ft is 50 ft.
We are given,
The length of the rectangular lot is 25 ft longer than twice the width.
The perimeter of the lot cannot exceed 350 ft.
Let the width of the rectangular lot be x.
So, the length of the rectangular lot = 2x + 25
We know that the perimeter of the rectangle is given by:
P = 2(L + W)
Substitute the given values in the above formula;
350 = 2(2x +25 + x)
350 / 2 = 3x + 25
175 - 25 = 3x
x = 150 / 3
x = 50 ft
So, the width of the rectangular lot = 50 ft
And, the length of the rectangular lot = 2 * 50 + 25 = 125
Thus, the greatest width possible if the length of the rectangular lot is 25 ft longer than twice the width and if the perimeter of the lot cannot exceed 350 ft is 50 ft.
To learn more about rectangle visit:
https://brainly.com/question/27722891
#SPJ1
The lifeguards on a beach in Hawaii found a correlation between the height of a wave (y) and the number of surfers on the beach (x). The equation they calculated was y = 0.95x + 20. If the wave height was 4 feet, about how many surfers would be on the beach?
Answer:
Step-by-step explanation:
hope this helps
I need an answer ASAP. A football player runs the ball from the 20-yard line on one side of the field to the 20-yard line on the other side. How many yards did the player run?? 100 pts and the brainliest.
The player ran 60 yards on the football field
How to find the distance covered by the playerA football field measures a length of 100 yards, using subtraction the required dimensions are calculated
The player started form 20 yards line to 20 yard of the other end of the field
The player did not ran the initial 20 yards and the finial 20 yards
this added to give 40 yards
Length covered by the player
100 yards - 40 yards = 60 yards
Learn more about football field here:
https://brainly.com/question/29399743
#SPJ1
a certain species of bird migrates 10,000 miles in 75 days a person race walking can walk 20 kilometers in 100 minutes
who goes faster
A person race walking a distance of 20 kilometers in 100 minutes is more faster with a speed of 0.2 kilometer per minutes.
How to determine who is faster?Mathematically, the speed of a physical object or body can be calculated by using this formula;
Speed = distance/time
Next, we would convert the unit of distance covered by the bird in miles to kilometers as follows:
1 mile = 1.60934 kilometer.
10,000 miles = X kilometer.
Cross-multiplying, we have:
X kilometer = 10,000 miles × 1.60934 kilometer.
X kilometer = 16,093.4 kilometer.
Also, we would convert the unit of time in days to minutes as follows:
1 day = 1,440 minutes
75 days = X minutes
Cross-multiplying, we have:
X minutes = 75 days × 1,440
X minutes = 108,000 minutes.
Now, we can calculate the speed of this bird as follows:
Speed = 16,093.4/108,000
Speed = 0.1490 kilometer per minutes.
For the speed of the person, we have:
Speed = 20/100
Speed = 0.2 kilometer per minutes.
Read more on speed here: brainly.com/question/8163450
#SPJ1
please help!! i do not understand
Answer:
Step-by-step explanation:
Hi, Julia, they are trying to ask about error, or the confidence that there is not an error. It's kinda like saying, we're 100% sure the answer is correct, mostly :DDDD which really lowers your confidence about the 100% correct statement. Anyway, sooo then they give the way to show deviation, from something. if you've had Calculus one, this is the same thing as the Delta , Epsilon thing, about a small distance away from the target is still with in a certain range. I feel like if they had written the inequality like this...
( p' - E) < p < (p'+E) it would be clearer about the inequality. E is just a tiny distance away in the positive and negative direction. E plays the role of epsilon. the numbers they give are the range of the confidence. I don't think they ask a very clear question.
0.056<p<0.112
p is kinda like our "best guess" answer, and we're giving it this range that it's probably within, for a certain level of confidence. You can see, that as the confidence goes down, that range can become bigger.
During the time Tommy eat two bowls of ice cream, Robert eats three bowls of ice cream. The two boys ten bowls of ice cream in one hour. How many bowls did Tommy eat? Show working
Answer:20
Step-by-step explanation:
Given f(x) = x³ + kx + 3, and x + 3 is a factor of f(x), then what is the value of
k?
If (x + 3) is a factor of f(x) = x³ + kx + 3 , then the value of k is -8 .
In the question ,
it is given that ,
the function is f(x) = x³ + kx + 3 ,
and also given that (x+3) is a factor of f(x) , that means
x + 3 = 0
x = -3
x = -3 should satisfy the function ,
So , substituting x = -3 in the function f(x) = x³ + kx + 3,
we get
f(-3) = (-3)³ + k(-3) + 3 = 0
-27 -3k + 3 = 0
-3k - 24 = 0
-3k = 24
k = 24/(-3)
k = -8
Therefore , If (x + 3) is a factor of f(x) = x³ + kx + 3 , then the value of k is -8 .
Learn more about Factors here
https://brainly.com/question/19438583
#SPJ1
How many times did the team score less than 60 points?
Stem
4
5
6
7
Leaf
2,5,9
3,4,6,8,8,9
0,2,3,4,4,6,8
0,0,1,2