Answer:
the university should charge $13.50 per ticket to maximize revenue, and 85,000 people will attend at that price.
Step-by-step explanation:
To find the price per ticket that maximizes revenue, we need to find the price that maximizes the product of the number of tickets sold and the revenue per ticket. Revenue per ticket is equal to the ticket price plus the average concession spending per person, or $27 + $3 = $30.
Let x be the number of $3 decreases in ticket price, so the ticket price can be expressed as $27 - $3x. The number of people attending can be expressed as 40,000 + 10,000x.
Therefore, the revenue can be expressed as:
Revenue = (Ticket price) x (Number of tickets sold) x (Concession spending per person)
Revenue = ($27 - $3x) x (40,000 + 10,000x) x $3.00
Expanding this expression, we get:
Revenue = $81,000,000 + $270,000,000x - $30,000,000x^2
To maximize revenue, we need to find the value of x that maximizes this quadratic function. We can do this by finding the vertex of the parabola, which is located at:
x = -b / 2a
where a = -30,000,000, b = 270,000,000, and c = 81,000,000
x = -270,000,000 / 2(-30,000,000)
x = 4.5
Since x represents the number of $3 decreases in ticket price, we can find the optimal ticket price by subtracting 3 times x from the original price of $27:
Optimal ticket price = $27 - $3(4.5) = $13.50
The optimal number of people attending can be found by substituting x = 4.5 into the expression for the number of people attending:
Number of people attending = 40,000 + 10,000(4.5) = 85,000
Two mechanics worked on a car. The first mechanic charged $45 per hour, and the second mechanic charged $50 per hour. The mechanics worked for a combined total of 25 hours, and together they charged a total of $1150. How long did each mechanic work?
Answer:
First one worked for 20 hours, second one worked for 5 hours.
Step-by-step explanation:
50 times 5 : 250
45 times 20 :900
250+900 = 1150
La profesora Elena compró 28 lapiceros y repartió a sus estudiantes 5/7 de los lapiceros. ¿Cuántos lapiceros le quedaron a la profesora Elena?
Respuesta (Español/Spanish):
20 lapices
Explicación paso-a-paso (Español/Spanish):
Multiplica 28 por 5/7.
Answer (English/Inglés):
20 pencils
Step-by-step explanation (English/Inglés):
Multiply 28 by 5/7
The county fair charges $10 admission and $2 per ride. What is the cost for one admission and r rides
Considering the definition of an equation, the cost for one admission and r rides is Cost= 10 + 2×r
Definition of equationAn equation in mathematics is defined as an equality established between two expressions, in which there may be one or more unknowns that must be solved.
The members of an equation are each of the expressions that appear on both sides of the equal sign while the terms of an equation are the addends that form the members of an equation.
The solution of a raised equation, means to determine by means of certain procedures the value that satisfies it.
Cost in this caseBeing "r" the number of rides, and knowing that:
The county fair charges $10 admission.The county fair charges $2 per ride.the equation in this case is:
Cost= 10 + 2×r
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Miguel reads 3 pages in 5 minutes. He reads at a constant rate.
3
What fraction of a page does Miguel read in 1 minute?
O A
OB.
OC.
O D.
15
1
3
2|3
It is obvious that he cannot read an entire page in one minute, meaning D (2/3) is literally the only possible answer.
7.
A regular polygon has sides with the same length and interior angles with the same
measure. What kind of triangle is also a regular polygon?
A right triangle
B obtuse triangle
C scalene triangle
D equilateral triangle
E isosceles triangle
Answer:
D equilateral triangle.
Step-by-step explanation:
An equilateral triangle has three sides with equal length and three interior angles with the same measure of 60 degrees. Therefore, an equilateral triangle can also be considered as a regular polygon with three sides.
Four people are standing on line. The tall man is between a woman with a red hat and a little boy. The little boy is next to a teenager who is not last. In what order are they standing?
We can use logical reasoning to conclude that the order is "teenager, little boy, tall man, and woman" as per the explanation below, based on the clues.
What is logical reasoning?Logical reasoning is a process of using rational thinking and deduction to arrive at a conclusion based on available information. In the given problem, logical reasoning is used to analyze the provided clues and determine the order of the four people standing in line.
By carefully examining the clues and using a process of elimination, we can deduce the position of each person in the line. We use logical reasoning to eliminate the possibilities that contradict the given information, and to arrive at the correct sequence that fits all of the provided conditions.
First, we know that the tall man is between the woman and the little boy. So, they can appear in either of the following orders:
woman - tall man - little boylittle boy - tall man - womanHowever, we are told that the little boy is next to a teenager who is not last. So:
woman - tall man - little boy - teenager --> Incorrect, because the teenager would be last.teenager - little boy - tall man - woman --> Correct, because the teenager would be in a different position.Thus, we can conclude that we have correctly answered this question.
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Given that a function, h, has a domain of -3 ≤ x ≤ 11 and a range of 1 ≤ h(x) ≤ 25 and that h(8) = 19 and h(-2) = 2, select the statement that could be true for h.
A.
h(13) = 18
B.
h(2) = 16
C.
h(-3) = -1
Does this system of equations have one solution, no solutions, or an infinite number of solutions? x - y = 4; x + y = 8
Answer:
one solution (6, 2 )
Step-by-step explanation:
x - y = 4 → (1)
x + y = 8 → (2)
add the 2 equations term by term to eliminate y
(x + x) + (y - y) = 8 + 4
2x + 0 = 12
2x = 12 ( divide both sides by 2 )
x = 6
substitute x = 6 into (2) and solve for y
6 + y = 8 ( subtract 6 from both sides )
y = 2
the system has one solution , that is (6, 2 )
If 421,000 people each receive an average refund of $3,400, based on an interest rate of 3 percent, what would be the lost annual income from savings on those refunds?
The lost annual income from savings on those refunds would be $43,032,000.
How to find the lost annual income?o calculate the lost annual income from savings on those refunds, we need to first calculate the total amount of money refunded, and then calculate the lost income from that amount.
The total amount refunded would be:
421,000 people x $3,400 per person = $1,434,400,000
Next, we can calculate the lost income from that amount at an interest rate of 3 percent. To do this, we can use the simple interest formula:
I = P x R x T
Where:
I = interest
P = principal (the amount refunded)
R = interest rate (as a decimal)
T = time (in years)
Substituting the values we have:
I = $1,434,400,000 x 0.03 x 1
I = $43,032,000
Therefore, the lost annual income from savings on those refunds would be $43,032,000.
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James is 13 and lily is 5. how old would jacob be when lily's 10? How old would jacob be when lilys 16?
(Im super confused lol, 35 points)
Answer: When Lily is 10, Jacob will be 18. When she is 16, he will be 24.
Step-by-step explanation: This is because Jacob is 8 years older than Lily, as seen by subtracting her age from his age (13 - 5 = 8). From there, we just add 8 to Lily's ages from then on. 10 + 8 = 18, and 16 + 8 = 24.
At present, the length of a rectangular soccer field is 55 yards longer than the width. The city council is thinking of rearranging the area containing the soccer field into two square playing fields. A math teacher on the council decided to test the council member's mathematical skills.
He told them that if the width of the current field were to be increased by 5 yards and the length cut in half, the resulting field would be a square. What are the current dimensions of the field?
The current dimensions of the rectangular soccer field are 45 yards by 100 yards.
What is area of the rectangle?
Area = Length × Width
Here let the width be "w" yards.
Then, according to the problem, the length is 55 yards longer than the width, so the length would be "w + 55" yards.
We can use this information to create an equation for the area of the rectangular field:
Area = (w + 55)w
Area = w² + 55w
Next, the problem tells us that if we increase the width by 5 yards and cut the length in half, we get a square. Let's call the side length of this square "s". We can create another equation for the area of this square:
Area = Side length²
Area = s²
We can use algebra to solve for the current dimensions of the rectangular soccer field. First, we need to find an equation for the side length of the square in terms of the current dimensions of the rectangular field:
s = w + 5 (since we increased the width by 5 yards)
s = (w + 55)/2 (since we cut the length in half)
Setting these two equations equal to each other and solving for "w" gives us:
w + 5 = (w + 55)/2
2w + 10 = w + 55
w = 45
So the width of the rectangular soccer field is 45 yards. Using the equation we created earlier for the length, we can find the length:
Length = Width + 55
Length = 45 + 55
Length = 100
Therefore, the current dimensions of the rectangular soccer field are 45 yards by 100 yards.
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0 divided by 1 . what is the answer
Answer: 0
Step-by-step explanation:
Answer:
0
Step-by-step explanation:
0 divided by 1 is 0 similarly to other numbers.
For example 5/1 = 5
Although, 1/0 is undefined as it isn't legal.
The half-life of caffeine in the human body is about 6.4 hours. cup of coffee has about 80 mg of caffeine: Write an equation for the amount of caffeine in person $ body after drinking cup of coffee? Let € be the milligrams of caffeine in the body after hours. How much caffeine wIll remain after 10 hours? mg How long until there are only 20 mg remaining? hours
Thus, the time taken to drop the caffeine from 80 mg to 60 mg is 2.46 hours.
Explain about the Exponential equation:Calculating the exponential growth as well as decay of a given collection of data is done using an exponential function, which is a mathematical function.
Exponential functions, for instance, can be used to estimate population changes, loan interest rates, bacterial growth, radioactive decay, and disease spread. An exponential function has the following form at its most fundamental level.
f(x) = [tex]a^{x}[/tex]
Exponential equation for the amount of Caffeine
C = 80[tex](2)^{-t/6}[/tex]
Amount of caffeine C = 60 mg.
60 = 80[tex](2)^{-t/6}[/tex]
3/4 = [tex](2)^{-t/6}[/tex]
Taking log on both sise:
[tex]log_{2}(3/4) = -t/6[/tex]
Solve the log function using the log calculator:
-t/6 = (-0.41)
t = 0.41 * 6
t = 2.46 hours
Thus, the time taken to drop the caffeine from 80 mg to 60 mg is 2.46 hours.
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Correct question:
The biological half-life of caffeine is about 6hr. If one cup of coffee has 80 mg of caffeine, then the amount of caffeine C (in mg) remaining after t hours is given by C = 80[tex](2)^{-t/6}[/tex]
How long will it take for the amount of caffeine to drop below 60 mg?
Please help!
this is for 10th grade, not college btw
Step-by-step explanation:
For RIGHT triangles sin (angle) = opposite LEG / hypotenuse
for this triangle sin (10) = 500/x
then x = 500 / sin (10°) = 2879.4 m Round as necessary
find hcf of 24x^3yz^4; 30x^2y^2z^3 and 36x^3y^2z^3
The HCF is 6x^2yz^3
What is HCF?HCF means Highest Common Factor. HCF of two or more numbers is the greatest factor that divides the numbers. It is also the greatest possible number of all their common factors.
To find the HCF of the following,
24x^3yz^4 , 30x^2y^2z^3, 36x^3y^2z^3
To find the HCF among the first value,
24 , 30 and 36
Factors of 24 are 2, 3, 4, 6, 8, 12, 24
Factors of 30 are 2, 3, 5, 6, 10, 15, 30
Factors of 36 are 2, 3, 4, 6, 9, 12, 18, 36.
The highest common factor that it can be divisible with is 6
Among x^3 , x^2 and x^3
The factors of x^3 are x, x^2, x^3
Factors of x^2 are x, x^2
Factors of x^3 are x, x^2, x^3
The highest common factor is x^2
Among y , y^2 and y^2
Factors of y is y
Factors of y^2 are y, y^2
The highest common factor is y
And among z^4 , z^3 and z^3
Factors of z^4 are z, z^2, z^3, z^4
Factors of z^3 are z, z^2, z^3
The highest common factor here is z^3
Therefore, the highest common factor is 6x^2yz^3
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The drawings above represent the tablecloths margot is thinking about buying. She plans to sew a decorative fringe on the tablecloth. About how much fringe will margot have to sew on the round tablecloth?
Answer:
Step-by-step explanation:
first give me a high five
A group of teachers at a local middle school are trying to decide what the end of the year field trip should be for the 8th graders moving on to high school. Determine which sample below will give the teachers the most accurate data.
a
A random sample of students in 6th, 7th, and 8th grade are asked where the 8th graders should go on their field trip.
b
A random sample of 8th graders are asked where they would like to go for the end of the year field trip.
c
The football team is asked where the 8th graders should go on their field trip.
d
All the teachers are asked where the 8th graders should go on their field trip.
Option b is likely to give the teachers the most accurate data for deciding the end of the year field trip for the 8th graders.
What is sample?In statistics, a sample is a subset of individuals or observations taken from a larger population. The sample is used to gain insights and make inferences about the population from which it was drawn. Samples are often used when it is not feasible or practical to gather data from every individual in a population, which could be too large or too time-consuming to survey.
Here,
A random sample of 8th graders are directly affected by the decision and are therefore the most appropriate group to survey. Asking a random sample of 6th, 7th, and 8th graders (option a) would include students who are not directly affected by the decision, and may not have the same level of understanding or investment in the trip. Asking the football team (option c) would likely provide biased results, as the football team may have different preferences and priorities than the wider 8th grade class. Asking all the teachers (option d) may also provide biased results, as teachers may have different opinions and preferences than the students. Ultimately, the most accurate data will come from surveying the group of students directly affected by the decision.
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17 is what percent of 20?
Answer: 85% or 17/20
Step-by-step explanation: Ok, so 17 being what percent of 20 is 17/20. Then, simply divide from there to get 0.85, also known as 85%.
how was texas affected by opec’s restrictions on oil production in 1973
1. competition from opec countries meant fewer jobs in texas
2. higher oil prices brought wealth to the state
3. may texans returned to the rural areas
4. transportation industries became for profitable
After answering the provided question, we can conclude that the oil industry and related sectors were the primary direct beneficiaries.
what is expression ?An expression in mathematics is a collection of representations, octal, and huge corporations that resemble a clear association or regimen. A real number, a mutable, or a combination of the two can be used as an expression. Mathematical operators include inclusion, subtraction, rapid spread, division, and exponentiation. Expressions are widely used in arithmetic, mathematics, and shape. They are used in the representation of mathematical formulas, the solution of equations, and the simplification of mathematical relationships.
Option 2 is the correct response. Texas benefited from OPEC's oil production restrictions in 1973 because it resulted in a significant increase in oil prices, which brought wealth to the state. At the time, Texas was the largest oil-producing state in the United States.
Option 1, 3, and 4 are incorrect. While OPEC's restrictions did increase competition from other countries, which could have affected employment in the oil industry, there is no evidence that it resulted in fewer jobs in Texas overall. Finally, while transportation industries may have benefited indirectly from the increase in oil prices, the oil industry and related sectors were the primary direct beneficiaries.
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Si seis conejos necesitan 10 sacos de comida a la semana, ¿cuántos sacos necesitarán nueve conejos para comer durante una semana?
Therefore, nine rabbits will need 7.5 sacks of food for one week.
What is unitary method?The unitary method is a mathematical technique that involves finding the value of a single unit to determine the value of a given number of units. It is a method of solving mathematical problems that involve proportional relationships between quantities. The unitary method is commonly used in various areas of mathematics, such as algebra, arithmetic, and geometry. It is also used in everyday life to solve problems related to money, time, distance, and other quantities.
Here,
To solve this problem, we can use proportionality. We know that the number of sacks of food needed is directly proportional to the number of rabbits.
Let x be the number of sacks needed for 9 rabbits. Then, we can set up the following proportion:
6/10 = 9/x
Cross-multiplying, we get:
6x = 90
Dividing both sides by 6, we get:
x = 15/2 or 7.5
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Complete question:
If six rabbits need 10 sacks of food per week, how many sacks will nine rabbits need to eat for one week?
What is 0.35 of 100.00 + 0.5
of 150.50?
Answer:
Step-by-step explanation:
0.35 = 35/100
100.00 = 100
100×(35/100) = 35
0.5 = 5/10 = 1/2
150.50 = 1505/10
(1505/10)×(1/2) = 75,25
35+75.25 = 110.25
PLEASE HELP ASAP!!!!!
A bakery makes cylindrical mini muffins that measure 2 inches in diameter and one and one fourth inches in height. If each mini muffin is completely wrapped in paper, then at least how much paper is needed to wrap 6 mini muffins? Approximate using pi equals 22 over 7.
14 and 1 over 7 in2
23 and 4 over 7 in2
47 and 1 over 7 in2
84 and 6 over 7 in2
Thus, the surface area of paper is needed to wrap 6 cylindrical mini muffins is 23 and 4 over 7 in².
Explain about the cylindrical shape:In geometry, a cylinder is just a three-dimensional shape. A cylinder is cylindrical in shape and has a circle-shaped top and bottom. The top and bottom are both flat and uniform in size. The shape of a cylinder is best described, in my opinion, by picturing a soup can.
Given data:
Height of cylindrical mini muffins 1 ¹/₄ = 5/4 in = 1.25 inDiameter d = 2 inRadius r = 2/2 = 1 in.surface area of 6 cylindrical mini muffins = 6*(π*r²*h)
= 6* (22/7 * 1² * 1.25)
= 23.55 in²
= 23 ⁴/₇ in²
Thus, the surface area of paper is needed to wrap 6 cylindrical mini muffins is 23 and 4 over 7 in².
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what is the sum of the rational expression below x/x+1 + 6x/x+5
The sum of the rational expression as required to be determined in the task content is; (7x² + 11) / (x² + 6x + 5).
What is the sum of the given expression?It follows from the task content that the rational expression whose sum is to be determined is;
x / x+1 + 6x / x+5
Therefore, by using the LCM; (x + 1) (x + 5).
Therefore, the sum is as follows;
{x(x + 5) + 6x (x + 1)} / (x + 1) (x + 5).
= (7x² + 11) / (x² + 6x + 5)
Ultimately, the sum as required is; (7x² + 11) / (x² + 6x + 5).
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Answer:
[tex] \frac{x(7x + 11)}{(x + 1)(x + 5)} [/tex]
Step-by-step explanation:
[tex]1. \: \frac{x(x + 5) +6x(x + 1)}{(x + 1)(x + 5)} \\ 2. \: \frac{x(x + 5 + 6(x + 1))}{(x + 1)(x + 5)} \\ 3. \: \frac{x(x + 5 + 6x + 6)}{(x + 1)(x + 5)} \\ 4. \: \frac{x((x + 6x) + (5 + 6))}{(x + 1)(x + 5)} \\ 5. \: \frac{x(7x + 11)}{(x + 1)(x + 5)} [/tex]
Find the equation of the line.
Use exact numbers.
y=y=y, equals
x+x+x, plus
A coordinate plane. The x- and y-axes each scale by one. A graph of a line goes through the points zero, negative nine and one, negative five.
A coordinate plane. The x- and y-axes each scale by one. A graph of a line goes through the points zero, negative nine and one, negative five.
The equation of the line is y=-4x+9. In order to find the equation of the line, we must first calculate the slope (m) of the line.
What is slope?Slope is a measure of the steepness of a line on a graph. It is calculated by finding the ratio of the vertical change between two points, divided by the horizontal change between the same two points.
The slope is calculated by dividing the change in y-coordinates (rise) by the change in x-coordinates (run).
In this case, the rise is -5 – (-9) = 4, and the run is 1 – 0 = 1. Therefore, the slope of the line is m = 4/1 = 4.
Next, we plug the slope and a point on the line into the point-slope form of a line equation: y - y1 = m(x - x1).
We can choose any point on the line, so let's use (0, -9).
Plugging in the values, we get:
y - (-9) = 4(x - 0)
Simplifying, we get:
y = 4x - 9
Therefore, the equation of the line is y = 4x - 9.
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14 At the school play, there were a total of 175 tickets sold. Of those, 125 were adult tickets, and the remaining amount was child tickets. What is the ratio of the number of child tickets to the total number of tickets sold? *Simplify A. 2 to 7 B. 2 to 5 C. D. 7 to 2 5 to 7
Answer:
A) 2 to 7
Step-by-step explanation:
Step 1: Determine How Many Child Tickets Were Sold
The question is asking about the ratio of the number of child tickets sold to the number of total tickets sold, but we can't find that unless we know how many child tickets were sold, so let's figure that out first.
We are given that 175 tickets were sold. Of those 175 tickets, 125 were adult tickets, and the rest were child tickets. This means that the number of total tickets sold was equal to the sum of the number of child and adult tickets sold. Therefore, there were 175 - 125 = 50 child tickets sold.
Step 2: Determine the Ratio of Child Tickets to Total Tickets
We now know that 50 out of the 175 total tickets sold were child tickets, so we can find the ratio of the two values. Remember that a ratio just represents the relation between numbers, so we can write the current ratio of child tickets to total tickets as 50 to 175. However, since ratios can be written as fractions, we quickly see that this ratio can be simplified.
In fraction form, this ratio is [tex]\frac{50}{175}[/tex]. Simplifying this fraction by dividing both the numerator and denominator by their greatest common factor, which is 25 in this case, gives us [tex]\frac{2}{7}[/tex], so the final ratio is 2 to 7.
The two statements below are different ways to say that the sides of these similar triangles are proportional.
Complete the equations that go with the statements.
PLSS I NEED THISS
Answer:
e, cc, dStep-by-step explanation:
You want the different ways sides of similar triangles can be shown as proportional.
Corresponding sidesFrom shorter to longer, the corresponding sides in the similar triangles are ...
Smaller ... Larger
b . . . . . . . e
a . . . . . . . d
c . . . . . . . f
PairsThe proportions are written by choosing two letters and their corresponding letters. The two chosen can be from different columns (part 1) or from the same column (part 2). The corresponding letters are written in the same place in the proportion fraction
[tex]\dfrac{a}{d}=\dfrac{b}{\boxed{e}}=\dfrac{\boxed{c}}{f}[/tex]
[tex]\dfrac{a}{b}=\dfrac{d}{e}\qquad\dfrac{b}{\boxed{c}}=\dfrac{e}{f}\qquad\dfrac{c}{a}=\dfrac{f}{\boxed{d}}[/tex]
__
Additional comment
Any proportion can be written "sideways" or "upside down." Corresponding parts have the same relationship in any case.
[tex]\dfrac{a}{b}=\dfrac{d}{e}\ \Leftrightarrow\ \dfrac{a}{d}=\dfrac{b}{e}\ \Leftrightarrow\ \dfrac{b}{a}=\dfrac{e}{d}\ \Leftrightarrow\ \dfrac{d}{a}=\dfrac{e}{b}[/tex]
What’s the pattern of 1/2,2/4, &4/8?
By answering the presented question, we may conclude that Therefore the pattern is that these three fractions are all equal and reflect the same proportion of a whole, which is half.
what is fraction?In mathematics, a fraction is a number that represents a component of a whole or a ratio between two things. It is shown as a top number (numerator) split by a horizontal line, also known as a vinculum, over a bottom number (denominator). For example, the fraction 3/4 indicates three-quarters of a whole split into four equal pieces. A fraction can be expressed using proper fractions, improper fractions, or mixed integers. A appropriate fraction is one with a numerator smaller than the denominator, such as 2/5.
The provided fractions 1/2, 2/4, and 4/8 have the pattern of being comparable fractions.
This indicates that even though they are worded differently, they reflect the same percentage or quantity of a total. Each fraction, in particular, represents half of the whole.
To see that these fractions are comparable, divide the numerator and denominator by the same number. For example, 2/4 may be simplified by dividing both the numerator and denominator by 2, yielding 1/2. Similarly, we may simplify 4/8 by dividing the numerator and denominator by 4, yielding 1/2.
Therefore the pattern is that these three fractions are all equal and reflect the same proportion of a whole, which is half.
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PLEASE HELP
Directions: Complete each problem below. Show all work.
1. Find the approximate volume of a cylinder with a circumference of 13 in. and a height of 9 in. Use 3.14 for straight pi and round to the nearest tenth.
2. Find the volume of a cylinder with a diameter of 63.5 cm and a height of 28 in. Find the volume, in terms of straight pi, of the cylinder in cubic inches.
The vοlume οf the cylinder in terms οf straight pi and cubic inches is apprοximately 5235.5 cubic inches.
What is the cylinder?A cylinder is a three-dimensiοnal geοmetric shape that cοnsists οf twο parallel bases that are cοngruent circles and a curved lateral surface that cοnnects the bases.
1. The circumference οf the cylinder is given as 13 inches. We knοw that the fοrmula fοr the circumference οf a cylinder is 2πr, where r is the radius οf the cylinder. Sο, we have:
2πr = 13
r = 13/(2π)
Nοw, we can use the fοrmula fοr the vοlume οf a cylinder, which is V = πr²h, where h is the height οf the cylinder:
[tex]V = \pi (13/(2\pi ))^2(9) = 119.8 cubic inches[/tex]
Sο, the approximate vοlume of the cylinder is 119.8 cubic inches.
2. The diameter οf the cylinder is given as 63.5 cm, which means the radius is 31.75 cm (since the radius is half οf the diameter). The height is given as 28 inches.
The formula fοr the vοlume of a cylinder is [tex]V = \pi r^2h[/tex], so we can substitute the values we have tο get:
[tex]V = \pi (31.75)^2(28) = 85816.8 ~cm^3[/tex]
Tο cοnvert this tο cubic inches, we need tο knοw that 1 cubic inch is equal tο 16.3871 cubic centimeters, sο we have:
V = 85816.8/16.3871 ≈ 5235.5 cubic inches
Hence, the vοlume οf the cylinder in terms οf straight pi and cubic inches is apprοximately 5235.5 cubic inches.
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In the triangle shown, what is the length of line BD?
Answer:
4
Step-by-step explanation:
This is a right triangle, so you can use the Pythagorean Theorem.
[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex] C has to be the longest side. In this case, that is 5
[tex]a^{2}[/tex] + [tex]3^{2}[/tex] = [tex]5^{2}[/tex]
[tex]a^{2}[/tex] + 9 = 25 Subtract 9 from both sides
[tex]a^{2}[/tex] + 9 - 9 = 25 - 9
[tex]a^{2}[/tex] = 16 Take the square root of both sides.
[tex]\sqrt{a^{2} }[/tex] = [tex]\sqrt{16}[/tex]
a = 4
Helping in the name of Jesus.
Please help with this one problem at the bottom only
The number of CDs that need to be produced by the company in order to break even would be 685 CDs .
How to find the breakeven point ?To break even, the revenue generated by selling the CDs must equal the total cost of producing them. Let's denote the number of CDs produced and sold as a.
Revenue = Price per CD × Number of CDs = 52a
Total Cost = Fixed Cost + Variable Cost × Number of CDs = 26000 + 14a
To break even, we set Revenue equal to Total Cost:
52a = 26000 + 14a
Now, we can solve for a:
52a - 14a = 26000
38a = 26000
a = 26000 / 38
a = 685 CDs
Find out more on breakeven point at https://brainly.com/question/16043238
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