The repeating decimal produced by the fraction 3/9 is 0.33333..., with the digit 3 repeating infinitely.
What is fraction?A fraction is a way of expressing a part of a whole or a ratio between two quantities. It is represented as one quantity divided by another quantity, with a horizontal line called a fraction bar between them.
According to question:The fraction 3/9 can be simplified to 1/3 by dividing both the numerator and denominator by their greatest common factor, which is 3.
When we divide 1 by 3, we get a quotient of 0.3, and a remainder of 1. To continue the long division, we add a decimal point and a zero, and bring down the next digit, which is also a zero. We then divide 10 by 3, which gives us a quotient of 3, and a remainder of 1. We repeat the process, adding a decimal point and another zero, and bringing down another zero. We continue this process infinitely, getting a sequence of 3s that repeat without end.
Therefore, the repeating decimal produced by the fraction 3/9 is 0.33333..., with the digit 3 repeating infinitely.
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What is the value of f^{-1}(4)f
−1
(4)f, start superscript, minus, 1, end superscript, left parenthesis, 4, right parenthesis?
The value of f^−1(4)f is the result of applying the inverse of the function f to 4.
To calculate f^−1(4)f, the inverse of the function f must be applied to 4.
Firstly, the inverse function of f, denoted as f^−1, is obtained by exchanging the x and y coordinates of all points on the graph of f. This means that the equation of f^−1 is obtained by solving the equation of f for y.
Next, 4 is substituted into the equation of f^−1 and the resulting equation is solved for x. This gives the value of f^−1(4).
Finally, the value of f^−1(4) is then substituted into the equation of f and the resulting equation is solved for y. This gives the value of f^−1(4)f.
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diego earned $1,393.74 commission on weekly sales of $15,486 as a salesperson at the computer store. what is his rate of commission
Answer:
Step-by-step explanation:
Rate of commission = commission / total sales
Rate of commission = $1,393.74 / $15,486
Rate of commission = 0.0898 or 8.98%
Diego's rate of commission is 8.98%.
Write the equation of the parabola that has its x intercepts at (5,0) and (-6,0) and its y intercept at (0,-1)
The equation of parabola for the given equation through which it satisfied the relation is [tex]( \frac{1}{30} )x^2 + (\frac{1}{30} )x - 1[/tex].
What about parabola?
A parabola is a U-shaped curve that is formed by the graph of a quadratic function of the form y = [tex]ax^2 + bx + c[/tex]. The parabola is symmetric around its axis of symmetry, which is a vertical line passing through the vertex of the parabola. The vertex is the point where the parabola changes direction, either from increasing to decreasing or from decreasing to increasing. The direction of the opening of the parabola (upward or downward) is determined by the sign of the coefficient a in the quadratic equation. Parabolas are used in various fields, such as physics, engineering, and mathematics, to model various real-life phenomena.
Define equation:
An equation is a statement that shows the equality of two expressions, typically separated by an equals sign (=). It represents a mathematical relationship between two or more variables or constants, and is used to solve problems and make predictions.
In mathematics, equations can take various forms, including linear equations, quadratic equations, trigonometric equations, differential equations, and more. Depending on the type of equation, the variables may represent real or complex numbers, vectors, matrices, functions, or other mathematical objects.
According to the given information:
As, we know about the condition of the parabola,
Hence:
[tex]y = Ax^2 + Bx + C y-intercept: x=0 and y = -1\\\\ C = -1 y = Ax^2 + Bx - 1 (5,0) \\ \\0 = 25A + 5B - 1 (-6,0) \\\\ 0 = 36A - 6B - 1 1 \\\\ = 25A + 5B1 = 36A - 6B \\ \\ 0 = -11A - 11B 11B = -11A B = -A kX^2 - kx - 1 , k=A=-b (5,0)\\\\25k + 5k - 1 = 030k = 1k = 1/30 \\\\(-6,0)36k - 6k - 1 = 0\\\\30k = 1k=30 (\frac{1}{30} )x^2 + (\frac{1}{30} )x - 1 ,[/tex]
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Answer:
it's above
Step-by-step explanation:
yeah
Derive the formula for the Pythagorean theorem in 3 dimensions. Math help ASAP
The formula for the Pythagorean theorem in 3 dimensions is [tex]d^2 = a^2 + b^2 + c^2.[/tex]
What is Pythagorean theorem?
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be extended to 3 dimensions using the same principle.
In the case of a cube with base a, width b, and height c, we can imagine a right triangle that is formed by one of the diagonals of the cube and one of the faces. Let d be the length of this diagonal.
By the Pythagorean theorem in 3 dimensions, we have:
[tex]d^2 = a^2 + b^2 + c^2[/tex]
To see why this is the case, imagine that we have a right triangle in three dimensions, with sides of length a, b, and c.
The hypotenuse of this triangle is the diagonal of a rectangular box with sides of length a, b, and c. By the Pythagorean theorem, the square of the length of the diagonal is equal to the sum of the squares of the lengths of the other two sides, which gives us the formula above.
Therefore, the formula for the Pythagorean theorem in 3 dimensions is [tex]d^2 = a^2 + b^2 + c^2.[/tex]
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Don't *quite* know how to solve this one. Any help would be great, and please explain your answer ^w^
Answer:
127°
Step-by-step explanation:
I added a photo of my solution
Answer:
x = 127°--------------------------------
The formed quadrilateral has two right angles, because of tangent segments.
One angle is marked as 53°, and the missing angle is x.
We know the sum of interior angles of a quadrilateral is 360°.
Find the missing angle:
x + 53 + 180 = 360x + 233 = 360x = 360 - 233x = 127A toy rocket is launched from the top of a building 98 feet tall at an initial velocity of 224 feet per second.
a) Give the function that describes the height of the rocket in terms of time t.
b) Determine the time at which the rocket reaches its maximum height, and the maximum height in feet.
c) For what time interval will the rocket be more than 702 feet above ground level?
d) After how many seconds will it hit the ground?
a)The function that describes the height of the rocket in terms of time t can be expressed as: h(t) = -16t² + 224t + 98
b) the maximum height of the rocket is 1378 feet at t=7sec.
c)the rocket will be more than 702 feet above ground level during the time interval [1.95, 18.55].
d)14.13 seconds will take it to hit the ground
Define quadratic formulaThe quadratic formula is a formula that gives the solutions (or roots) of a quadratic equation of the form ax^2 + bx + c = 0, where a, b, and c are coefficients, and x is the variable:
x = (-b ± √(b² - 4ac)) / (2a)
a) The function that describes the height of the rocket in terms of time t can be expressed as:
h(t) = -16t² + 224t + 98
where h(t) represents the height of the rocket (in feet) at time t (in seconds).
The -16t² term represents the effect of gravity, which causes the rocket's height to decrease over time. The 224t term represents the initial velocity of the rocket, which causes its height to increase over time. The constant term 98 represents the initial height of the rocket (at t = 0).
b) To determine the time at which the rocket reaches its maximum height, we need to find the vertex of the parabolic function h(t). The x-coordinate of the vertex is given by:
t = -b / (2a)
where a = -16 (the coefficient of t²) and b = 224 (the coefficient of t). Substituting these values, we get:
t = -224 / (2×(-16)) = 7
Therefore, the rocket reaches its maximum height at t = 7 seconds.
To find the maximum height, we can substitute t = 7 into the function h(t) and simplify:
h(7) = -16(7)²+ 224(7) + 98 = 1378
Therefore, the maximum height of the rocket is 1378 feet.
c) To find the time interval during which the rocket is more than 702 feet above ground level, we need to solve the inequality:
h(t) > 702
Substituting the expression for h(t), we get:
-16t² + 224t + 98 > 702
Simplifying and rearranging terms, we get:
16t² - 224t - 604 < 0
Using the quadratic formula, we can solve for the roots of the equation:
t = [224 ± √(224²- 4(16)(-604))] / (2(16))
t ≈ 1.95 or t ≈ 18.55
Therefore, the rocket will be more than 702 feet above ground level during the time interval [1.95, 18.55].
d) To find the time at which the rocket hits the ground, we need to find the root(s) of the function h(t) where h(t) = 0. This occurs when the rocket returns to ground level (i.e., h(t) = 0) after reaching its maximum height.
Substituting the expression for h(t), we get:
-16t²+ 224t + 98 = 0
Using the quadratic formula, we can solve for the roots of the equation:
t = [224 ± √(224² - 4(-16)(98))] / (2(-16))
t ≈ 14.13 or t ≈ -0.38
the rocket hits the ground after approximately 14.13 seconds.
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Angle x and y are complementary. Angle x is supplementary to a 128° angle. What are the measures of angle x and angle y.
Answer:
Step-by-step explanation:
Short answer? x is 52 degrees and y is 38 degrees.
But how did I get it you probably did not ask?
Let's run it back to the definitions of complementary and supplementary angles.
Complementary angles: 2 angles that add to get you a CLEAN 90 degrees
Supplementary angles: 2 angles that add to get you a CLEAN 180 degrees
So if x is supplementary to 128 degrees, it has to be 52 degrees to fit the definition. So yeah 180-128= 52 degrees
Now for x to be complementary to y, y has to 38 degrees. 90-52=38 degrees.
x: 52 degrees
y: 38 degrees
I teleport here again should you have anymore questions.
A pitcher has 6.2 L of water in it. Raji pours water from the pitcher into 7 glasses. Each glass has 0.275 L of water in it. How much water is left in the pitcher? Solve the problem, and show your thinking.
Answer:
4.275 L
Step-by-step explanation:
Pitcher starts with 6.2 L.
7 glasses
each glass has 0.275 L
total water in 7 glasses: 7 × 0.275 L = 1.925 L
water remaining in pitcher: 6.2 L - 1.925 L = 4.275 L
Answer: 4.275 L is left in the pitcher.
Solve the equation
9 - x = 11
Select the statement that is true about the line plot.
A line plot with the title Read a Thon. Below the line is the label Measurement in Hours. The line begins at 5 and ends at 8. Each whole is partitioned into four equal parts. There are two marks above five, zero marks above five and one fourth, zero marks above five and two fourths, five marks above five and three fourths, four marks above six, two marks above six and one fourth, one mark above six and two fourths, two marks above six and three fourths, three marks above seven, zero marks above seven and one fourth, four marks above seven and two fourths, two marks above seven and three fourths, and zero marks above eight.
The median is six and one fourth.
The mode is seven and two fourths.
The range is five and three fourths.
There are 23 values in the data set.
The correct statements are:
The median is six and one-fourth.
The mode cannot be determined from the given information.
The range is five and three-fourths.
What is the median?The median measures the central tendency in a dataset, which is the middle value when the data is arranged in order from lowest to highest (or highest to lowest). If the dataset has an odd number of values, the median is the middle value. If there is an even number of values in the dataset, the median is the average of the two middle values.
The median is six and fourth: This statement is true based on the given information that there are 11 marks on the line plot above 6 and fourth, and 11 marks below.
The mode is seven and two-fourths: This statement is false based on the given information. The mode is the value that appears most frequently in the dataset, and there are no values that appear more than once in the given data.
The range is five and three-fourths: This statement is true based on the given information. The range is the difference between the highest and lowest values in the dataset, which in this case is 5 and three-fourths (8 minus 2 and one-fourth).
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Waymon's weekly earnings for working 40 hours plus 3 hours of working overtime was
S479.27. If $48.47 of that paycheck was overtime pay, what was his hourly rate for the first
40 hours of work?
Waymon's hourly wage for the first 40 hours of labour was thus S9.68. equation
Equation: What is it?An equation in mathematics is a declaration of the equality of two expressions. Two sides of an equation are divided using the algebraic symbol (=). As an example, the assertion "2x + 3 = 9" is supported by the argument that it is true. Finding the value or values of the variable(s) needed to make the equation true is the aim of equation solving. It is possible to create regular or nonlinear, straightforward or complex equations that include one or more elements.
Let's name Waymon's usual hourly wage for the first 40 hours of labour "x". Based on the facts provided, we can then construct the following equation:
[tex]40x + 3(x + 1.5x) = 479.27[/tex]
Waymon's normal compensation for 40 hours of work is represented by the first term, while his overtime pay for 3 hours of work at time-and-a-half is represented by the second term (or 1.5 times his regular rate).
When we simplify this equation, we get:
[tex]40x + 4.5x = 479.27 - 48.4744.5x = 430.80 \\x = 9.68[/tex]
Waymon's hourly wage for the first 40 hours of labour was thus S9.68.
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Suppose you have $50 in a savings account and deposit an additional $10 each week.
a) Write a recursive formula to represent the sequence.
b) Write an explicit formula to represent the sequence.
c) How much money do you have in savings after 26
weeks? Show all work.
How do I put this in order?
Simplify. (y^3)^5 • y^4
1. y^12
2. y^19
3. y^32
4. y^60
Answer:2
Step-by-step explanation:
When raising an exponential expression to a power, you need to multiply the exponents. Applying this rule to (y^3)^5, we get (y^3)^5 = y^(3*5) = y^15.
So, (y^3)^5 • y^4 = y^15 • y^4 = y^(15+4) = y^19.
Therefore, the simplified expression is y^19, and the answer is 2.
Please help me set this question up so I can solve by quadratic equation and by completing the square.
When the length of each side of a
square is increased by 10 cm, the area
is increased by 200 cm². What was
the length of each side of the original
square?
Answer:
Step-by-step explanation the answer will be 20 each
:
Please help!!!!!!!!!!!!!!!!!!
Kaleb, Clarissa, and Patrick are all playing frisbee at the park. Kaleb had started at the top of the triangle shown but has slowly been moving closer to Clarissa and Patrick while they have been playing. Kaleb is now at point K and remains equidistant from each of his friends. Determine the distance between Clarissa and Patrick.
Patrick and Clarissa are 5 yards apart.
Patrick and Clarissa are 2 yards apart.
Patrick and Clarissa are 10 yards apart.
Their distance cannot be determined.
The distance between Patrick and Clarissa cannot be determined as only one variable has been given in the question. Not sufficient data provided.
Using congruency, length of the missing side of the triangle =- 8.5 units.
Define congruency of triangles?The dimensions of the sides and angles of two or more triangles determine whether they are congruent. A triangle's size and shape are determined by its three sides and three angles, respectively. If pairings of corresponding sides and corresponding angles are equal, two triangles are said to be congruent. They are the exact same size and form. Triangles can satisfy a wide variety of congruence requirements.
In the 1st image:
The distance between Patrick and Clarissa cannot be determined as only one variable has been given in the question. Not sufficient data provided.
In the 2nd image:
Let x be the missing length of the triangle.
As the ray is an angle bisector,
Due to congruency:
11.9/7 = x/5
⇒ (11.9 × 5)/7 = x
⇒ x = 8.5 units.
Therefore, length of the missing side of the triangle =- 8.5 units.
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The average of the first 6 scores was 12. The average of the next 12 scores was 36.
What was the overall average ?
Answer:
28
Step-by-step explanation:
Average of first 6 scores is 12, so the total of those 6 scores is 6 × 12 = 72.
Average of next 12 scores is 36, so the total of those 12 scores is 12 × 36 = 432.
Total of all 18 scores is 72 + 432 = 504.
Overall average is 504 ÷ 18 = 28.
What is the slope of the line that passes through the points (8, -6)(5,−1)? Write your answer in simplest form.
Answer:
[tex]-\frac{5}{3}[/tex]
Step-by-step explanation:
[tex]m (slope)=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]m=\frac{-1-(-6)}{5-8}[/tex]
[tex]m=-\frac{5}{3}[/tex]
bonsoir aider moi plus vite possible
3+?=0
Answer: -3
Step-by-step explanation: 3-3=0
Answer:
-3Step-by-step explanation:
bonsoir aider moi plus vite possible
3+?=0
3 + x = 0
x = -3
When playing baseball, Chad misses on 60% of the pitches he receives. Describe
how to use random digits to simulate the probability that he will get a hit on more
than 2 of every 10 pitches he receives.
This proportion represents the estimated probability that Chad will get a hit on more than 2 of every 10 pitches he receives.
what is probability?
Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.
To simulate the probability that Chad will get a hit on more than 2 of every 10 pitches he receives using random digits, follow these steps:
1. Divide the pitches into groups of 10. For each group of 10 pitches, record the number of hits that Chad gets.
2. Generate a random digit between 0 and 9 for each pitch in the group. If the digit is 0, 1, 2, or 3, consider it a hit. If the digit is 4, 5, 6, 7, 8, or 9, consider it a miss. Repeat this process for each group of 10 pitches.
3. Count the number of groups of 10 pitches in which Chad gets more than 2 hits.
4. Repeat steps 2 and 3 a large number of times (for example, 1000 times) to get an estimate of the probability that Chad will get a hit on more than 2 of every 10 pitches he receives.
5. Calculate the proportion of times in which Chad gets more than 2 hits in a group of 10 pitches.
Therefore, this proportion represents the estimated probability that Chad will get a hit on more than 2 of every 10 pitches he receives.
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please i need help with this geometry hmw
Answer:
Step-by-step explanation:
The triangles are similar so the ratio of their corresponding sides will be the same. That is, TV/RV is equal to TS/RQ. This gives us the equation 12/x+6=16/x+1. Cross multiplying, this becomes 12x+12=16x+96. Simplifying, we get x=21. Therefore, RV=12+x-6=x+6=21+6=27.
Answer:
TV/RV=TS/RQ, 12/x+6=16/x+1, 12x+12=16x+96, x=21. Therefore, RV=12+x-6=x+6=21+6=27.
Step-by-step explanation:
please help and show work! thank you <3
Answer: 2
Step-by-step explanation:
7x-5 =3x+9
x = 4
7x4-5= 23
3x4+9=21
∠PQT=∠PQS+∠SQT
23=21+∠SQT
∠SQT=2
For each set of points given below, write a possible equation of a quadratic function in standard form.
A: (3/4,0) and (-2,0).
B: (negative square root of 5,0), (square root of 5, 0), and (-3,12)
The equations of the functions from the zeros are f(x) = 4x² + 5x - 6 and f(x) = 3x² - 15
Calculating the equation of the functionsFunction (a)
Given that
(3/4,0) and (-2,0).
Since the two points have the same y-coordinate of 0, the quadratic function is of the form
f(x) = (x - p)(x - q), where p and q are the x-coordinates of the two points.
Plugging in the given values, we get
f(x) = (x - 3/4)(x + 2)
So, we have
f(x) = 4x² + 5x - 6
Function (b)
Here we have
(-√5, 0), (√5, 0) and (-3, 12)
This function can be represented as
f(x) = a(x - p)(x - q)
So, we have
f(x) = a(x - √5)(x + √5)
Expand
f(x) = a(x² - 5)
Using the last point, we have
a((-3)² - 5) = 12
4a = 12
a = 3
So, we have
f(x) = 3(x² - 5)
Expand
f(x) = 3x² - 15
Hence, the function is f(x) = 3x² - 15
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a company receives an average of .64 purchase orders per minute. assuming a poisson distribution for the number of purchase orders per minute, what is the standard deviation for this distribution?
The standard deviation for the given Poisson distribution is 0.8.
A Poisson distribution is used to model the number of events occurring in a fixed time interval when the events occur independently and at a constant rate. The mean and variance of a Poisson distribution are equal, and both are given by λ, the rate parameter.
Here, the given information is that the company receives an average of 0.64 purchase orders per minute. Therefore, λ = 0.64.
The formula for the variance of a Poisson distribution is σ² = λ, where σ is the standard deviation. Thus, substituting λ = 0.64 in this formula, we get σ² = 0.64. Taking the square root of both sides, we get σ = √0.64 = 0.8.
Therefore, the correct answer is 0.8.
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Marcus wants to find the volume of a rectangular prism. He multiplies the height times the height times the height. Explain how to fix Marcus's mistake.
Answer:
Marcus has to multiply the height times the length times the width.
Step-by-step explanation:
The formula for the volume of a rectangular prism is the following:
Volume of rectangular prism = length x width x height
f(x) = (x + 2)²
What is f(4)?
21
36
13
89
Answer:
36
Step-by-step explanation:
f(4) = (4+2)² = (6)² = 36
In the diagram below, quadrilateral RSTU is inscribed in circle V. Find the
measure of T.
The measure of angle T in the given quadrilateral is 92.5 degrees.
What is quadrilateral inscribed in circle?A quadrilateral is said to be inscribed in a circle if all four of its vertices are located on the circumference of the circle. In other terms, the quadrilateral is "enclosed" by the circle. The opposing angles of a quadrilateral are supplementary (add up to 180 degrees) and the product of the measurements of the two diagonals equals the sum of the products of the measures of the pairs of opposite sides when a quadrilateral is inscribed in a circle, both of which are important features. Inscribed quadrilateral geometry difficulties can be resolved by using these characteristics.
The sum of the angles in a quadrilateral is 360 degrees.
angle R + angle S + angle T + angle U = 360 degrees
79 degrees + 96 degrees + x + angle U = 360 degrees
Angle T and angle U are opposite angles in quadrilateral RSTU, therefore congruent.
175 degrees + 2x = 360 degrees
2x = 185 degrees
x = 92.5 degrees
Hence, the measure of angle T is 92.5 degrees.
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PLEASE ANSWER ASAP!!!
The compressions in a sound wave are very close together, and the energy supplied by the vibrating source decreases. Which statement best describes how this will affect the wave and what you hear?
The wavelength will decrease, and the sound will become quieter.
The amplitude will decrease, and the sound will become quieter.
The frequency will decrease, and the pitch will become lower.
The intensity will decrease, and the pitch will become lower.
Step-by-step explanation:
The correct statement is: The amplitude will decrease, and the sound will become quieter.
When the compressions in a sound wave are very close together, the amplitude of the wave decreases. Amplitude is the measure of the maximum displacement of the particles of the medium from their rest position. As the amplitude of the wave decreases, the energy supplied by the vibrating source decreases, and the sound becomes quieter.
A particular type of cell doubles in number every hour.
Write an exponential function that can be used to find
the number of cells present, y, at the end of x hours if
there are initially 4 of these cells?
A particular type of cell doubles in number every hour.Write an exponential function that can be used to findthe number of cells present, y, at the end of x hours ifthere are initially 4 of these cells?The exponential function that can be used to find the number of cells present, y, at the end of x hours, given that there are initially 4 cells is: y = 4 * 2^x This is because the number of cells doubles every hour, so if there are 4 cells to start with, after one hour there will be 8 cells (doubling the initial number), after two hours there will be 16 cells (doubling the number after one hour), and so on. The exponent in the function represents the number of hours elapsed, and the base of the exponent is 2, representing the doubling of cells every hour.
A store sells prepackaged popcorn in two sizes
The package for the small size can be modeled by a cone with a height of 6 inches and a diameter of 4 inches
The package for the larger size can be modeled by a cone with a height of 9 inches and a diameter of 5 inches
Which of the following are true?
Select all that apply
A. The small popcorn has a volume of about 25.13 cubic inches
B. The small popcorn has a volume of about 75.40 cubic inches
C. The volume of two small popcorn is less than the volume of one large popcorn
D. The volume of two small popcorns is greater than the volume of one large popcorn
E. The volume of a large popcorn is about 135.09 cubic inches greater than the volume of the small popcorn
The answer is ,the statement that are true are: A. The small popcorn has volume of about 25.13 cubic inches , C. The volume of two small popcorn is less than volume of one large popcorn , E. The volume of large popcorn is about 34.68 cubic inches greater than volume of small popcorn (135.09 - 25.13 = 109.96).
What is Cone?A cone is three-dimensional geometric shape that tapers smoothly from flat, usually circular base to point called the apex or vertex. The base of cone can be any closed shape, but is usually a circle. A cone can be right or oblique, depending on whether or not the axis passing through the apex and the center of the base is perpendicular to the base.
The formula for volume of cone are V = (1/3)πr^2h, where r is radius and h is height.
For the small popcorn cone:
radius =diameter/2 =4/2=2 inches
V = (1/3)π(2²)(6) ≈ 25.13 cubic inches
For the large popcorn cone:
radius = diameter/2 = 5/2 = 2.5 inches
V = (1/3)π(2.5²)(9) ≈ 59.81 cubic inches
Therefore, the statements that are true are:
A. The small popcorn has volume of about 25.13 cubic inches
C. The volume of two small popcorn is less than volume of one large popcorn
E. The volume of large popcorn is about 34.68 cubic inches greater than volume of small popcorn (135.09 - 25.13 = 109.96)
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