Select the correct answer.
A container is made by cutting off the bottom of a cone. The container has a diameter of 30 centimeters and a height of 20 centimeters. The
small cone that was removed has a diameter of 10 centimeters and a height of 6 centimeters.
What is the volume of the container, to the nearest cubic centimeter?
A. 6,126 cm³
B. 6,283 cm³
C. 5,812 cm³
D. 5,969 cm³
Answers
The volume of the container is 5969 cm³. The correct option is D. 5,969 cm³
Calculating VolumeFrom the question, we are to determine the volume of the container
Volume of the container = Volume of the cone - Volume of the small cone
The volume of a cone is given by the formula,
V = 1/3πr²h
Where V is the volume
r is the radius
and h is the height
From the given information,
For the small cone,
Diameter = 10 cm
∴ Radius, r = 10cm/ 2 = 5 cm
h = 6 cm
For the big cone
diameter = diameter of the container = 30 cm
∴ Radius = 30cm/ 2
Radius = 15cm
h = height of small cone + height of container
h = 6 cm + 20 cm
h = 26 cm
Putting the parameters into
Volume of the container = Volume of the cone - Volume of the small cone
We get,
Volume of the container = 1/3π × 15² ×26 - 1/3π × 5² × 6
Volume of the container = 1/3π (15² ×26 - 5² × 6)
Volume of the container = 1/3π (5850 - 150)
Volume of the container = 1/3π (5700)
Volume of the container = 1/3 × π × 5700
Volume of the container = 5969.026 cm³
Volume of the container ≈ 5969 cm³
Hence, the volume of the container is 5969 cm³. The correct option is D. 5,969 cm³
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Related Questions
Look at the pic and show your work
Answers
We kindly invite to check the image attached below to see the representation of the exponential function. This function shows exponential growth.
How to graph exponential functions
In this occasion we must plot the graph of exponential functions of the form:
y = a · bˣ (1)
Where:
a - Initial valueb - Base of the functionx - Independent valuey - Dependent valueFirst, we need to follow this procedure to create the graph of the curve on Cartesian plane:
Evaluate the function at every x-value.Fill the blanks on table.Mark the rectangular points (x, y) on the Cartesian plane.Match the points.Therefore, we build the exponential curve with the help of a graphing tool (i.e. Desmos), whose result is shown in the image attached below.
From (1) we must understand that exponential functions report growth for b > 1 and decay for 0 < b < 1. Thus, the exponential function y = 3ˣ shows exponential growth according to graphical and analytical findings.
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(pls help me with this)
4. The points C and D are (4, 5) and (p, q) respectively,
a) Write down, in terms of p and q, the coordinates of the midpoint of CD.
b) Given that the midpoint of CD is (7, 1), find the coordinates of D.
Answers
A. The coordinates of the midpoint of CD in terms of p and q is [(4 + p) / 2 , (5 + q) / 2]
B. The coordinates of D, Given that the midpoint of CD is (7, 1) is (10 , -3)
A. How to determine the mid pointCoordinate of C = (4, 5)Coordinate of D = (p, q)Mid point =?Mid point = (X , Y)
X = (x₁ + x₂) / 2
X = (4 + p) / 2
Y = (y₁ + y₂) / 2
Y = (5 + q) / 2
Thus,
Mid point = (X , Y)
Mid point = [(4 + p) / 2 , (5 + q) / 2]
B. How to determine the coordinates of DMid point = (7, 1)Coordinates of D =?Mid point = (7, 1) = (X , Y)
X = (4 + p) / 2
7 = (4 + p) / 2
Cross multiply
7 × 2 = 4 + p
14 = 4 + p
Collect like terms
p = 14 - 4
p = 10
Y = (5 + q) / 2
1 = (5 + q) / 2
Cross multiply
1 × 2 = 5 + q
2 = 5 + q
Collect like terms
q = 2 - 5
q = -3
Coordinates of D = (p, q)
Coordinates of D = (10 , -3)
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Becca's car engine has a capacity of 3.6 quarts and
contains 1.2 quarts of engine oil. One bottle of engine oil is
0.5 quart. Approximately how many bottles of engine oil
does Becca need to completely fill her car engine?
Answers
Becca needs approximately 5 bottles of engine oil to completely fill her car engine.
How to determine the number of bottles of engine oil?Since Becca's car engine has a capacity of 3.6 quarts and contains 1.2 quarts of engine oil, the remaining space left in her car engine is given by:
Space = 3.6 - 1.2
Space = 2.4 quarts.
By applying direct proportion, we have:
1 bottle = 0.5 quart.
x bottles = 2.4 quarts.
Cross-multiplying, we have:
0.5x = 2.4
x = 2.4/0.5
x = 4.8 ≈ 5 bottles.
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15-point question. Pls help
Answers
Answer:
44
Step-by-step explanation:
x + (22 - 13) = 53
x + 9 = 53
x = 44
Answer:
44
Step-by-step explanation:
x+(22-13)=53
x+22-13=53
x+9=53
x=44
A set of golf clubs and bag cost $225. The clubs cost $60 more than the bag. How much do the clubs cost?
Answers
Answer:
$142.5
Step-by-step explanation:
225-60=165
165/2=82.5
82.5+60=142.5
The number of pollinated flowers as a function of time in days can be represented by the function. f(x)
Answers
The average increase in the number of flowers pollinated per day between days 4 and 10 is 39, given that the number of pollinated flowers as a function of time in days can be represented by the function [tex]f(x) = (3)^{\frac{x}{2} }[/tex].
In the question, we are asked for the average increase in the number of flowers pollinated per day between days 4 and 10, given that the number of pollinated flowers as a function of time in days can be represented by the function [tex]f(x) = (3)^{\frac{x}{2} }[/tex].
To find the average increase in the number of flowers pollinated per day between days 4 and 10, we use the formula {f(10) - f(4)}/{10 - 4}.
First, we find the value of the function [tex]f(x) = (3)^{\frac{x}{2} }[/tex], for f(10) and f(4).
[tex]f(x) = (3)^{\frac{x}{2} }\\\Rightarrow f(10) = (3)^{\frac{10}{2} }\\\Rightarrow f(10) = 3^5 = 243[/tex]
[tex]f(x) = (3)^{\frac{x}{2} }\\\Rightarrow f(4) = (3)^{\frac{4}{2} }\\\Rightarrow f(10) = 3^2 = 9[/tex]
Thus, the average increase
= {f(10) - f(4)}/{10 - 4},
= (243 - 9)/(10 - 4),
= 234/6
= 39.
Thus, the average increase in the number of flowers pollinated per day between days 4 and 10 is 39, given that the number of pollinated flowers as a function of time in days can be represented by the function [tex]f(x) = (3)^{\frac{x}{2} }[/tex].
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For complete question, refer to the attachment.
The distance from the Sun to Mercury is approximately 57910000 km.
Assuming Mercury has a circular** orbit around the Sun, find the distance Mercury travels in orbiting the Sun through an angle of 2.65 radians.
Answers
Mercury travels a distance of 153 461 500 kilometers on its orbit.
How much distance did Mercury travel on its orbit?
The statement indicates that Mercury has a circular orbit and indicates the central angle covered by translation. The distance traveled is found by definition of circular arc:
s = (2.65 rad) · (57 910 000 km)
s = 153 461 500 km
Please notice that the radius of translation is the distance from the Sun to Mercury.
Mercury travels a distance of 153 461 500 kilometers on its orbit.
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Jorge wrote the equation negative 6 x 4 x = 8. what is the value of x? –4 –2 2 4
Answers
Option (A) - 4 is the correct answer.
The value of x for linear equation -6x + 4x = 8 is - 4.
What is linear equations in one variable?If a variable's maximum power constantly equals 1, the equation is considered linear equation. Another name for it is a one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0. Here, A is a coefficient, B is a constant, and x is a variable.
The given equation is -6x + 4x = 8.
Simplifying the above equation.
-2x = 8
Now, dividing both sides by -2.
x = -4
Therefore the value of x in equation -6x + 4x = 8 is -4.
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I understand that the question you are looking for is " Jorge wrote the equation -6x + 4x = 8. What is the value of x?
(A) –4
(B) –2
(C) 2
(D) 4 "
Answer: (A): -4
Step-by-step explanation:
It's the correct option.
Find the measure of the arc or angle indicated by the question mark.
Answers
Answer:
FP is 70 degrees 35 times 2 so PD is 180 half a turn minus 70 = 110 degrees
Step-by-step explanation:
Consider the series one-fourth, startfraction 1 over 16 endfraction startfraction 1 over 64 endfraction startfraction 1 over 256 endfraction ellipsis which expression defines sn? limit of (one-fourth) superscript n baseline as n approaches infinity limit of (1 minus (one-fourth) superscript n baseline) as n approaches infinity limit of one-third (1 minus (one-fourth) superscript n baseline) as n approaches infinity limit of one-third (one-fourth) superscript n baseline as n approaches infinity
Answers
The sum of the series is: (c) lim n⇒∝ 1/3(1 - (1/4)^n)
How to evaluate the sum of the series?The complete question is added as an attachment
The given series is a geometric series. So, we first calculate the common ratio (r) using:
r = T2/T1
From the series, we have:
T1 = 1/4 and T2 = 1/16
Substitute the known values in the above equation
r = (1/16)/(1/4)
So, the equation becomes
T = 1/16 / 1/4
Rewrite as product
T = 1/16 * 4
Evaluate the product
r = 1/4
The formula to calculate the sum of a geometric series of is:
Sn = a(1 - r^n)/(1 - r)
Where
a = 1/4 -- the first term
r = 1/4 --- the common ratio
Substitute the known values in the above equation
Sn = 1/4 * (1 - (1/4)^n)/(1 - 1/4)
Simplify the denominator
Sn = 1/4 * (1 - (1/4)^n)/(3/4)
Divide 1/4 by 3/4
Sn = 1/3 * (1 - (1/4)^n)
Take the limit to infinity of the series
Sn = lim n⇒∝ 1/3(1 - (1/4)^n)
We can conclude that, the sum of the series is: (c) lim n⇒∝ 1/3(1 - (1/4)^n)
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Answer:
Step-by-step explanation:
B
please help
Which reason completes the proof for step 6?
Answers
The reason that completes the proof for step 6 is (a) Definition of median
How to complete step 6?From the graph, point R' to be the midpoint of points M' and O'
Also, points P' and Q' are the midpoints of lines M'N' and N'O', respectively
This means that the three points are the median of the sides of the triangle
The line drawn through the three medians meet at point S
Hence, the reason that completes the proof for step 6 is (a) Definition of median
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Answer: median
Step-by-step explanation:
Prior to September, 2000, taxi fares from Washington DC to Maryland were described as follows: $2.00 up to and including 1⁄2 mile, $0.70 for each additional 1⁄2 mile increment.
-Write the piecewise function for 0 to 2 miles.
f(x) = ?
Answers
The piecewise function is
f(x) = 2, 0 < x ≤ 1/2
f(x) = 2 + 0.7x, x > 1/2
How to determine the piecewise function?From the question, we have:
Fares = $2.00 ⇒ up to (and including) 1/2 miles
Fares = $0.70 increment ⇒ greater than 1/2 miles
Let x represent the number of miles, and f(x) the fares.
So, we have:
f(x) = 2, 0 < x ≤ 1/2
f(x) = 2 + 0.7x, x > 1/2
The above represents the piecewise function
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Find the missing length of the triangle (Side AC)
Answers
Answer: 17.3 cm
Step-by-step explanation:
[tex]\tan 68^{\circ}=\frac{AC}{7}\\\\AC=7\tan 68^{\circ}\\\\AC \approx 17.3[/tex]
20 points
please help me i am in a rush
Answers
Answer:
Khan Academy.
Step-by-step explanation:
You can go on khan academy and search up "percentages and numbers." The videos should immediately pop up. there are also lessons if you don't want to risk getting your problem wrong. If you are still confused and do not understand please just comment and I will respond.
We have to find the areas of both circles, and subtract the area of the smaller one from the bigger one. That will be the answer.
Area of a circle = pi times radius^2
So
Small circle:
A = 3.14 x 18 x 18
A = 1,017.36
Bigger circle:
A = 3.14 x 23 x 23
A = 1,661.06
So then we do:
1,661.06 - 1,017.36 which equals 643.7. That’s the area of the ring.
I hope this helped! (:
1. Find the Principal when S.l. = 100 Rate = 5% per annum Time = 2 years.
Answers
The principal is 1000
SI = PRT/100
Simple interest = 100
Rate = 5%
Time = 2 years.
SI = PRT/100
100 = (P × 5 × 2)/100
10000 = 10P
P = 10000/10
P = 1000
Here are the scores of 14 students on a geography test. 58, 60, 65, 67, 68, 72, 79, 79, 80, 81, 82, 86, 86, 87 Notice that the scores are ordered from least to greatest. Give the five-number summary and the interquartile range for the data set.
Five-number summary
Minimum:
Lower quartile:
Median:
Upper quartile:
Maximum:
Interquartile range:
Answers
The five-number summary are as follows:
Minimum = 58Lower quartile(Q₁) = 67Median = 79Upper quartile(Q₃) = 82Maximum = 87Interquartile range = 15How to solve for five-number summary?The five-number summary is a set descriptive statistics which consist of the minimum, maximum, median, upper quartile, and lower quartile of a data distribution.
Therefore,
Given:
58, 60, 65, 67, 68, 72, 79, 79, 80, 81, 82, 86, 86, 87
Therefore,
Minimum = 58
Lower quartile(Q₁) = 67
Median = 79 + 79 / 2 = 79
Upper quartile(Q₃) = 82
Maximum = 87
Interquartile range = Q₃ - Q₁ = 82 - 67 = 15
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Which bag has more fruit? Use the ratios to justify your answer.
Answers
The bag that has more fruits is the second bag, because the ratio is greater.
Which bag has more fruits?Ratio expresses the relationship between two or more numbers. It shows the frequency of the number of times that one value is contained within other value(s).
Number of fruits in the first bag : (3/8) x 60 = 22.50
Number of fruits in the second bag :(7/17) x 60 = 24.71
Here is the complete question:
Tamika has two bags of trail mix. Each has a combination of 60 pieces of fruit and nuts. Ratio of fruit to nuts in the first bag:3 5 Ratio of fruit to nuts in the second bag:7 10 Which bag has more fruit? Use the ratios to justify your answer. The first bag, because the ratio is greater. The first bag, because the ratio is smaller. The second bag, because the ratio is greater. The second bag, because the ratio is smaller.
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A grocery store sells a bad of 4 oranges for $1.04. how much would it cost for 11 oranges?
Answers
If a grocery store sells a bag of 4 oranges for $1.04 then it will cost $2.86 for 11 oranges.
Given that a grocery store sells a bag of 4 oranges for $1.04 means revenue is $1.04 with no profits.
We have to find the cost of 11 oranges. We have assumed that there are no profits as we are require to find cost. But there is huge difference between cost and profits.
We know that average cost is total cost divided by number of items.
Cost of 4 oranges=$1.04
cost of 1 orange=1.04/4
=$0.26 per orange
Cost of 11 oranges=0.26*11
=$2,86.
Hence if a grocery store sells a bag of 4 oranges for $1.04 then it will cost $2.86 for 11 oranges.
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Six sophomores and 14 freshmen are competing for two alternate positions on the debate team. which expression represents the probability that both students chosen are sophomores? startfraction (20 c 6) (19 c 5) over 20 c 2 endfraction startfraction (20 p 6) (19 p 5) over 20 p 2 endfraction
Answers
The probability expression is [tex]\frac{^{6}C_2}{^{20}C_2}[/tex]
How to determine the probability expression?The given parameters are
Sophomore = 6Freshmen = 14The total number of people is
n = 20
2 of the 20 people are to be selected.
So, the number of selection is
[tex]n = ^nC_r[/tex]
This gives
[tex]n = ^{20}C_2[/tex]
The expression that represents both students being sophomore is
[tex]n = ^{6}C_2[/tex] --- i.e. 2 students selected from 6
The probability is then represented as:
[tex]\frac{^{6}C_2}{^{20}C_2}[/tex]
Hence, the probability expression is [tex]\frac{^{6}C_2}{^{20}C_2}[/tex]
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Answer:
a
Step-by-step explanation:
edge 2023
4x-6y=-20
-2x+4y=6
8th grade pre algebra
Answers
The values of x and y that are solutions to the simultaneous equations are; x = -11 and y = -4
How to Solve Simultaneous Equations?
We are given the simultaneous equations;
4x - 6y = -20 -----(eq 1)
-2x + 4y = 6 -----(eq 2)
Multiply equation 2 by 2 and eq 1 by 1 to get;
-4x + 8y = 12 -----(eq 3)
Add eq 3 to eq 1 to get;
2y = -8
y = -4
Thus;
4x - 6(-4) = -20
4x + 24 = - 20
4x = -20 - 24
4x = -44
x = -44/4
x = -11
Thus, the values of x and y that are solutions to the simultaneous equations are; x = -11 and y = -4
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Your dad says you can have a new puppy if you build the dog house. Before building, you need to determine the dimensions. Choose the dimensions of the base, the length, and the width of the dog house. Choose dimensions that you think are reasonable for whatever type of puppy you would get. Once you plan the base and walls, you need to decide on the height of the roof (represented by the dotted line in the image below). The roof is a triangle with two sides that are the same length.
Find the height of the roof using the dimensions you chose. You are hoping to put shingles on the roof and need to know what the square footage of the roof will be. Use the dimensions to calculate the area of the roof.
Hint: Remember to find the area of the entire roof.
Answers
Step by step
Roof is 36” x 24” which is 3’ x 2’
So 3 x 2 = 6 multiplied by 2 sides of roof
Total is 12 sq feet
————-
I made the roof peak with a 3” overhang over the entrance
I made the roof overhang the sides with 4”
—————-
So to find the hypotenuse (diagonal of the roof) I used the Pythagorean theorem.
a^2 + b^2 = c ^2
15^2 + 13^2 = c^2
394 = c^2
Take square root of both sides
C= 19.8 rounded to 20
I then added 4” overhang to each side for total diagonal of 24”
The area of Entire roof is 12 feet².
What is Pythagorean theorem?The well-known Pythagorean Theorem states that the square on the hypotenuse of a right triangle equals the sum of the squares on its legs (the side opposite the right angle)
Given:
As, the roof peak with a 3 and the roof overhang the sides is 4.
Now, Using Pythagorean theorem.
a² + b² = c ²
15² + 13² = c²
c² = 225+ 169
c = 19.8 (or 20)
So, the length of diagonal is 24.
Roof Dimension 36 x 24 or (
Area of Roof = 3 x 2
= 6 unit²
and, area of the entire roof = 2 x6 = 12 ft²
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(FIRST TO ANSWER GETS BRAINLIEST OR 5 STARS) For consecutive weeks, the manager of a local restaurant collected data on the number of cheese pizzas sold each week. The data is shown in the scatterplot below.
(scatterplot is below)
Can the given line be used to make reasonable predictions of the number of cheese pizzas that will be sold in upcoming weeks? Explain your reasoning.
Answers
Yes, the line can be used to make reasonable predictions of the number of cheese pizzas that would be sold in the upcoming weeks. This is because the line is the line of best fit
Line of best fitFrom the question, we are to determine if the line can be used to make reasonable predictions of the number of cheese pizzas that would be sold in the upcoming weeks
In the graph, we have a scatterplot.
The line drawn is the line of best fit
Hence,
Yes, the line can be used to make reasonable predictions of the number of cheese pizzas that would be sold in the upcoming weeks. This is because the line is the line of best fit.
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In a class of 48 students, one fourth of them regularly watch a particular tv programme. how many of the students do not regularly watch the programme?
Answers
36 students does not watch regularly the programme.
Lets simplify the problem,
Total students = 48
Regular students 1//4*48
=> 12 students
Through Simple Subtraction method,
Irregular students = Total students - regular students
Irregular students = 48-12
=36
Hence 36 students does not watch regularly the programme.
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Which function is negative for the interval [-1, 1]?
ty
3
2
-3-2-11
-3
ty
O
Intro
123
x
3
2
1
-3-2-1₁
-3
O
x
23
2,
-3-2-1
2 of 11
O
x
123
321
-3-2-11
-2
MAR
-3
ty
x
23
Done
O
Answers
Answer:
Graph number 2
Step-by-step explanation:
See attached image.
find the inverse of
f(x) = -6xˆ2 + 24x - 100
Answers
Answer:
See below
Step-by-step explanation:
y = -6x^2 + 24x-100
solve for 'x'
y + 100 = -6x^2 + 24x = -6(x^2-4x) complete the square for x
(y+100) /(-6 ) = (x-2)^2 -4 add 4 to both sides
(y+100)/(-6) +4 = (x-2)^2 sqrt both sides
sqrt [ ( y+100)/(-6) + 4 ] + 2 = x change x and y
y = ± sqrt [ (x+100)/(-6) + 4 ] + 2 simplify (if needed)
y = ± sqrt( -x/6 -12.666) + 2
Question 4 (2 points)
The function y = sin has been transformed. It now has amplitude of 3.4, a
period of 28, a phase shift of 6.5 units to the right, a vertical translation of 6 units
is a point in the parent
down, and is reflected over the x-axis. Given that
(²
1
62
function, use mapping notation to determine the y-coordinate of its image point in
the transformed function.
Enter the numerical value of the y-coordinate only in the box below rounded to two
decimals.
Answers
n this activity, you will apply your understanding of permutations and combinations to calculate probabilities. Use the information in this scenario to answer the questions that follow. Coach Bennet’s high school basketball team has 14 players, consisting of six juniors and eight seniors. Coach Bennet must select three players from the team to participate in a summer basketball clinic.
Answers
In order to determine the number of different groups of three players that are possible for Coach Bennet to select from, we would use a mathematical model referred to as combination.
Mathematically, combination is given by this mathematical equation:
[tex]_nC_r = \frac{n!}{r!(n-r)!}[/tex]
Where:
n is the number of items.r is the number of times of choosing items.Substituting the given parameters into the formula, we have;
Number of groups = (⁶C₃ × ⁸C₀) + (⁶C₂ × ⁸C₁) + (⁶C₁ × ⁸C₂) + (⁶C₀ × ⁸C₃)
Number of groups = 20 + 120 + 168 + 56
Number of groups = 364 different groups.
Therefore, there are 364 different groups of three players possible for Coach Bennet to select.
In conclusion, we can infer and logically deduce that this is a combination because the order in which the players are selected isn't important.
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Complete Question:
In this activity, you will apply your understanding of permutations and combinations to calculate probabilities. Use the information in this scenario to answer the questions that follow. Coach Bennet’s high school basketball team has 14 players, consisting of six juniors and eight seniors. Coach Bennet must select three players from the team to participate in a summer basketball clinic.
How many different groups of three players are possible for Coach Bennet to select?
At a 95-percent confidence level, what should be the cutoffs from the left and right sides of a normal distribution?
Answers
The cutoffs from the left and right sides of normal distribution at a 95-percent confidence level are 1.96.
What is the confidence level?The confidence level, which is used in statistics, describes the likelihood that the estimation of a statistical parameter's location in a sample survey is also true for the population.
Confidence levels must be decided upon in advance when surveying since they affect the survey's essential scope and error margin. Confidence intervals of 90, 95, and 99 percent are widely employed in surveys.
If the confidence level were set at 95%, there is a very good likelihood that the population's arithmetic mean, as a statistical number, will fall within the survey's established margins of error.
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If a and b are rational numbers and a+b√3=1/2-√3,find a:b=?
Answers
The value of the ratio a:b is 2:1
What is a surd?Surds are values of a square roots that cannot be simplified as whole numbers or integers. They are usually called irrational numbers.
Example of some surds are the square root of prime numbers.
Analysis:
a + b[tex]\sqrt{3}[/tex] = [tex]\frac{1}{2 - \sqrt{3} }[/tex]
Rationalizing the right hand side by the conjugate surd which is 2 + [tex]\sqrt{3}[/tex]
[tex]\frac{1}{2 - \sqrt{3} }[/tex] x [tex]\frac{2 + \sqrt{3} }{2 +\sqrt{3} }[/tex] = [tex]\frac{2 + \sqrt{3} }{4 -2\sqrt{3} +2\sqrt{3} -3}[/tex] = [tex]\frac{2 + \sqrt{3} }{1}[/tex] = 2 + [tex]\sqrt{3}[/tex]
Equating,
a + b[tex]\sqrt{3}[/tex] = 2 + [tex]\sqrt{3}[/tex]
Comparing the variables,
a = 2, b[tex]\sqrt{3}[/tex] = [tex]\sqrt{3}[/tex], b = 1
The ratio, a: b = 2:1
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WILL MAKE BRAINLIEST!! Solve for x
Answers
Answer:
5
Step-by-step explanation:
6x+4=34
6x=30
x=5
hope this helps <3