A sculpture is shaped like a sphere with 4 cones attached to it. Several dimensions of the sculpture, in feet, are shown in the diagram below. The total height of the sculpture from top to bottom is 12 feet. What is the volume of the sculpture, to the nearest cubic foot?
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volume of the center sphere = 4/3*PI*r^3
r = 3 ( given in the picture)
so 4/3 * 3.14 *3^3 = 113.04 cubic feet
volume of 1 cone: pi *r^2 *h/3
r = 3 and h=3 ( given in the picture)
so 3.14 * 3^2 * 3/3 = 28.26 cubic feet
there are 4 cones so 28.26* 4 = 113.04 cubic feet
113.04 + 113.04 = 226.08 cubic feet
rounded to nearest cubic foot = 226 cubic feet
Related Questions
How long will it take for $2800 to grow to $24,900 at an interest rate of 5.6% if the interest is compounded continuously? round the number of years to the nearest hundredth?
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What is the reason for each step in the solution of the inequality? −2(x+3)−4>4x+30 Select the reason for each step from the drop-down menus.
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The second blank is Combine like terms.
The third blank is Addition Property of Order
The reason for each step in the solution of the inequality must be mathematical operations such as; the distributive property
What is a solution set to inequality or an equation?If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solutions to that equation or inequality.
We have given that -2(x + 3) - 4 > 4x + 30
First, apply the distributive property
-2x - 6 - 4 > 4x + 30
Now combine like terms;
-2x - 10 > 4x + 30
Then subtraction property
-6x - 10 > 30
The addition property
-6x > 40
The division property
x < -20/3
Hence, we get the answer equal to x < -20/3.
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terrell wants to drive his car at a speed of 50 miles per hour for 2.75 hours. his car has a fuel efficiency of 25 miles per gallon. How many gallons of fuel does terrell need for his journey
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Yolanda is saving money to buy a game. so far she has saved $30 , which is five-sixths of the total cost of the game. how much does the game cost?
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Final answer:
To find the total cost of the game based on Yolanda's savings of $30, which is five-sixths of the cost, multiply $30 by the reciprocal of 5/6, resulting in a total cost of $36.
Explanation:
The question asks how much a game would cost if Yolanda has already saved $30, which is five-sixths of the total cost of the game. To find the total cost of the game, we consider the amount saved ($30) as five-sixths of the total cost (which we'll call x).
So the equation to solve is 5/6 * x = $30. To find x, we divide $30 by 5/6, which is the same as multiplying $30 by the reciprocal of 5/6 (which is 6/5). Therefore, x = $30 * (6/5) = $36. Thus, the total cost of the game is $36.
Explain the difference between exponential growth and exponential decay
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[tex]y = a^{x} , a\ \textgreater \ 1[/tex]
Exponential decay is the function
[tex]y = a^{x} , 0\ \textless \ a\ \textless \ 1[/tex]
So, the basic difference is that in growth the base is more than 1, and in decay the base is more than 0 but less than 1.
Final answer:
Exponential growth occurs when a population increases at an increasing rate, whereas exponential decay involves a decrease at a rate proportional to the current size. Logistic growth, adding the concept of carrying capacity, more accurately reflects natural populations with initial exponential increase followed by a plateau as resources become limited.
Explanation:
The key difference between exponential growth and exponential decay lies in the direction and rate at which a quantity changes over time. Exponential growth occurs when a population grows at an increasing rate as time passes, often depicted as a J-shaped curve, whereas exponential decay describes a process of decrease at a rate proportional to the current value, leading to a rapid reduction in size or quantity over time.
In the context of biology and population growth, exponential growth describes how populations can grow dramatically when there are no limits to resources or space. This type of growth can be formalized as a mathematical model where the population after n time periods has increased by a factor of 2n when the base growth rate is 2. In natural populations, this is idealized and does not usually last long as resources become depleted and other limiting factors come into play. On the other hand, exponential decay in biology might refer to the rapid loss of a population due to harsh conditions, lack of resources, or other negative impacts.
please help and explain to me!
Answers
- do we need to be on the left or the right side of the line to find points that satisfy the equation?
- is the line itself included or not
To start with the second question, since y has to be greater than and not equal, the line itself is NOT included in the solution area. This means the correct answer has to have a dashed line.
The general way to know on which side of the line you have to be, is to fill in one easy point and see if the equation holds. Let's fill in (0,0), (but any point will do).
you get: 0 > 1 - 3*0, which is NOT true. So (0,0) is in an area that is not our solution. The top-right picture is therefore not the answer.
What remains is the bottom-right picture, that is the correct shaded area. All points in the shaded area satisfy the equation.
Jasmine is 23 years old. jasmine is 3 years less than half of george's age. write and solve an equation to find george's age.
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take 23 and multiply by 3 then divide by 2 and your answer should be x34
Which soap dispenser shows that 64% of its soap has been used?
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16/25 x 4/4 = 64/100
64/100 = 0.64, or 64%
Your answer is Dispenser C
hope this helps
The width of a rectangle is 2m less than the length. the area is 48m squared. find the dimensions
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Then the width, W = L - 2
A = LW
48 = L(L - 2)
48 = L^2 - 2L
L^2 - 2L - 48 = 0
(L - 8)(L + 6) = 0
L - 8 = 0 or L + 6 = -6
L = 8 or L = -6
Since the length of a rectangle cannot be a negative number,
we discard the -6.
The length is 8m
The width is 2 m less than the length, so the width is 6 m.
The length of the rectangle is 8m and the width is 6m
This question involves the area of a rectangle and we can use the formula to solve this problem.
Data given;
A = 48m^2w = (L - 2)mAreaThe area of a rectangle is given as
[tex]A = L * W[/tex]
l = lengthw = widthsubstitute the values and solve
[tex]A = lw\\48 = L * ( L - 2)\\48 = l^2 -2l\\l^2 -2l - 48 = 0[/tex]
solve this quadratic equation to find the length
a = 1, b = -2, c = -48
[tex]l = \frac{-b+-\sqrt{b^2 - 4ac} }{2a} \\l = \frac{-(-2)+-\sqrt{(-2)^2-4*1*(-48)} }{2*1} \\l = 8[/tex]
Taking only the positive value of l, l = 8
but we also know that
[tex]w = l -2\\w = 8 -2\\w= 6[/tex]
from the above, the length of the rectangle is 8m and the width is 6m
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What is 7,433,654 to the nearest 10,000
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So, you just want to round that to the nearest ten thousand.
(10,000, 20,000, 30,000, 40,000, etc.)
So we want to see which of those 33,654 is closest to.
In this case it would be closest to 30,000, as it is only 3,654 away from it.
And then we can just add it back in the number.
7,430,000 would be your answer.
This graph of a function is a translation of y = 2/x . What is an equation for the function?
A. y = 2/(x - 6) – 3
B. y = 2/(x – 6) + 3
C. y = 2/(x – 3) - 6
D: y = 2/(x – 3) + 6
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Answer: The answer is C, the rest of the answers are
1:B
2:C
3:A its a graph
4:C y=2/x-3 -6
5:D19, as of 2019
Step-by-step explanation:
Answer:
The correct option is C) [tex]y=\frac{2}{x-3}-6[/tex]
Step-by-step explanation:
Consider the provided information.
Transformation:
The graph of parent function f(x) move up b unit for f(x)+b.
The graph of parent function f(x) move down b unit for f(x)-b.
The graph of parent function f(x) move left b unit for f(x+b).
The graph of parent function f(x) move right b unit for f(x-b).
Since, the graph of the parent function moves down, Therefore Option Option B and D are incorrect.
Here, we can observe that vertical asymptote shifted from x = 0 to x = 3.
Horizontal Shift: Right 3 Units
Vertical Shift: Down 6 Units
Therefore, the correct option is C) [tex]y=\frac{2}{x-3}-6[/tex]
Debra travels a distance of 2 miles in 1 minute. how much distance can she cover in 25 minutes? choose the correct equivalent rate.
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Debra traveled 50 miles in 25 minutes at a rate of 2 miles per minute.
What is a unitary method?A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.
Given, Debra travels a distance of 2 miles in 1 minute.
Which is already in unit measure, therefore to determine the distance traveled by Debra in 25 minutes we'll multiply the distance traveled in 1 minute and the total time Debra traveled.
= (2×25) miles.
= 50 miles.
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You select a card at random from the cards that make up the word replacement. On each card, there is one letter. Without replacing the card, you choose a second card. Find the probability of choosing a vowel and then not a vowel
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4 of them are vowels : e, a, e, e
7 of them are not vowels : r, p, l, c, m, n, t
The probability of getting a vowel the first try is 4/11.
The probability of getting something that is not a vowel is 7/10. The denominator is one less because the vowel card is not replaced, meaning there is one less card to choose from.
Multiply.
4/11*7/10
=28/110
=14/55
The probability is 14/55.
Hope this helps!
If HE = 3p + 7, /, LP = 5p – 19, and /, find the values of p and q for which quadrilateral HELP is a parallelogram. A. p = 18, q = 13 B. p = 13, q = 8 C. p = 8, q = 18 D. p = 13, q = 1
Answers
HE = LP : 3p + 7 = 5p - 19
Solving for the value of p
3p - 5p = -19 - 7
-2p = -26
p = 13
We determined the value of p, the answer is either B or D.
Which quadrilateral HELP is a parallelogram? The corrsect answer is P=13, q=18
to construct the midpoint of a segment, fold the paper so that the given line segment lies on itself and
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Answer:
The endpoints of the line segment lie on each other
Explanation
To understand the question, follow the practical steps below
1. Take a sheet of plane paper
2. Label the edges of the top of the paper A and B
3. Fold the paper in such a way that edge A lies on B.
You'll notice the following;
1. The top of the paper lies in itself; hence, we can say that the line segment lies on itself
2. You have a new line at the centre of the paper. The point at the top of this center line is the midpoint of the line segment
3. The edges that lie on each other translates to the endpoints lying on each other.
Number (3) above is the required observation and the right answer.
Which list contains ONLY rational numbers?
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Feel free to ask anymore questions at branily.com
Answer:
B. [tex]0.4166\overline{6}[/tex], [tex]\sqrt{81}[/tex], [tex]\frac{1}{8}[/tex].
Step-by-step explanation:
We are asked to find the list that contains only rational numbers.
We know that a number is known as rational, when it can be expressed as a fraction.
Upon looking at our given choices, we can see that option B is the correct choice.
In [tex]0.4166\overline{6}[/tex], the digit 6 has a bar on it, this means that it is repeating. We know that a repeating decimal is a rational number.
[tex]\sqrt{81}=9[/tex]. We can represent 9 as a fraction: [tex]\frac{9}{1}[/tex].
[tex]\frac{1}{8}[/tex] is already written as a fraction, therefore, it is a rational number.
The leukemia and lymphoma society sponsors a 5k race to raise money it receives $55 per race entry and $10000 in donations but it must spend $15 per race entry to cover the cost of the race write and solve an inequality to determine the number of race entries the charity needs to raise at least 55,000
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Helpppppppppppppppppp
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When an exponent is negative, the answer is 1 over x
Do the usual for 5^2, which equals 25
x = 25
1/25 is your answer
hope this helps
What is the area of △ABC?
Enter your answer as a decimal in the box. Round only your final answer to the nearest tenth.
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We have the b at 25m, but to find the h we need to drop an altitude or apothem down that is perpendicular to the base (90°). Now we have to do some trig to determine that h.
Since we're given that AB is 40m, and <B is 80°, we can set up a SOH-CAH-TOA equation:
The hypotenuse = 40m, and our height is opposite <B, therefore sin (80) = h/40,
h = 40 × sin (80) = 40 × 0.985 = 39.39m
Now, a = 1/2bh = 1/2 (25m)(39.4m)
[tex]a \: = 492.40 \: {m}^{2} [/tex]
Answer: smh
Step-by-step explanation:
Can you help me solve #s 43 an 44 pleeeease
Answers
Based on a poll, 5050% of adults believe in reincarnation. assume that 44 adults are randomly selected, and find the indicated probability. complete parts (a) through (d) below.
a. what is the probability that exactly 33 of the selected adults believe in reincarnation? the probability that exactly 33 of the 44 adults believe in reincarnation is
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To solve this problem, we use the formula for binomial probability:
P = [n! / (n – r)! r!] p^r * q^(n – r)
where,
n = total number of adults = 4
r = number of adults who believe in reincarnation = 3
p = chance of believing in reincarnation = 50% = 0.50
q = 1 – p = 0.50
P = [4! / (4 – 3)! 3!] 0.50^3 * 0.50^(4 – 3)
P = 0.25 = 25%
Answer:
Answer is 0.096
Step-by-step explanation:
Here 44 adults are randomly selected.
Each adult selected is independent of the other to believe in reincarnation.
Also there are only two outcomes, probability for success in each trial = 0.50
Hence X no of adults who believe in reincarnation is binomial with n =50 and p = 0.50
[tex]a) P(X=23) = 50C23 (0.5)^{50} =0.096[/tex]
Working notes:
50C23 =108043253365600
0.5^50) = 8.8178x10^(-14)
Simplifying we get answer as 0.096
In the diagram below XY is the perpendicular bisector of JK. Which of the following statements must be true?
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(1) A is true.
(2) B is true.
(3) C is false. Since line segment XY is the perpendicular bisector, it is not necessary that P should be its midpoint.
(4) D is true.
(5) E is false. The same explanation as that of C, P is not necessarily at the center of the line segment XY.
(6) F is true.
Answer:
Step-by-step explanation:
A B D F
in what quadrant does the angle 11 pi / 4 terminate?
Answers
Help me with this question plzzzz
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V = 1/4 * 2/3 * 3/5
V = (1 * 2 * 3) / (4 * 3 * 5)
V = 6/60 reduces to 1/10 m^3 <==
Find the number of hours it would take to drive 510 miles at 55 mph. Round to the nearest tenth of an hour. i THINK ITS 9.3 BUT IM NOT SURE?
Answers
hope this helps.
Answer: It would take 9.3 hours to take 510 miles.
Step-by-step explanation: We are given to find the number of hours it would take to drive 510 miles at 55 mph.
We will be using the UNITARY method to solve the given problem.
According to the given information, we have
Number of hours taken to drive 55 miles = 1 hour.
So, number of hours taken to drive 1 mile will be
[tex]\dfrac{1}{55}~\textup{hour}.[/tex]
Therefore, the number of hours it would take to drive 510 miles is given by
[tex]\dfrac{1}{55}\times510=\dfrac{102}{11}=9.27~\textup{hour}.[/tex]
Rounding to nearest tenth of an hour, we get
9.27 hour ≈ 9.3 hour.
Thus, it would take 9.3 hours to take 510 miles.
South of the White House in Washington, D.C., is the President’s Park South, or the Ellipse, which hosts events such as the White House Garden Tours. The Ellipse is 880 ft from north to south and 1057 ft from east to west. Write an equation in standard form for the Ellipse, centered at the origin.
Note: If any values of a2 or b2 are greater than 1,000, include the comma.
Answers
(x^2/a^2)+(y^2/b^2)=1
Where a is one half of one axis, and b is one half of the other.
The problem states that one axis is 1057 ft, and the other is 880 ft, so divide these values by 2 and square them. This results in:
(x^2/279,312.25)+(y^2/193,600)=1
For verification, if you have a graphing calculator, solve for y, set the size of the window so it should perfectly fit the ellipse, and check (it does)
Given the dimensions of the Ellipse, the major axis is the east-west distance (1057 ft) and the minor axis is the north-south distance (880 ft). Taking half these lengths as 'a' and 'b' respectively, the equation of the ellipse in standard form centered at the origin is (x^2/(528.5^2)) + (y^2/(440^2)) = 1.
Explanation:The given dimensions of the Ellipse represent the lengths of the major and minor axes. In an ellipse centered at the origin, the equation in standard form is given by:
(x^2/a^2) + (y^2/b^2) = 1
where 'a' is half the length of the major axis and 'b' is half the length of the minor axis. Here, since the measurement from east to west (1057 ft) is greater than the measurement from north to south (880 ft), 'a' will have a value of 1057/2 and 'b' will have a value of 880/2. Consequently, the ellipse equation would be:
(x^2/(528.5^2)) + (y^2/(440^2)) = 1
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I need this asap! Please help me!! Brainliest answer! The line plot below represents the frequency distribution of the number of book reports done by students in grades nine and ten. Each x represents 3 students. How many students did less than 4 or more than 17 reports?
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THE TOTAL COST OF A SUIT AND 4 TIES IS $292. THE SUIT COST $200. eACH TIE COST THE SAME AMOUNT. fIND THE COST OF ONE TIE
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a suit = 200
4 ties = 292 - 200
4 ties = 92
4T = 92
4T/4 = 92/4
T = 23
Each tie costs 23 dollars
hope this helps
292-200=92
92÷4=23
23×4=92
so one tie would equal $23 dollars
hope this helps!
If milk costs $1.97 per gallon and a bread recipe uses 6 fl. ounces, how much do those 6 fl. ounces cost?
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128 ounce milk costs $1.97 (Note:1gallon fluid=128ounce)
6 ounce bread costs=1.97/128 multiples 6
=2.56x10^-3
HOPEFULLLY its works
How does the radius of a positive and negative ion compare to a neutral atom?
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A neutral atom contains equal amount of proton and electron.
A negative ion contains extra electrons hence there is additional outer shell so it is expected that the radius is bigger than that of a neutral atom.
While a positive ion contains less electron so there is less outer shell so the radius is smaller than that of a neutral atom.
Arranging the radius in increasing order:
positive ion, neutral atom, negative ion