Answers
Answer:
Volume of sphere = 4.187x³
Step-by-step explanation:
[tex]\textsf {Volume of a sphere = $\dfrac{4}{3} \pi {r^2 }$}[/tex]
Here r = x
[tex]\textsf {Volume = $\dfrac{4}{3} \pi {x^2 }$}[/tex]
[tex]\textsf {Volume of cuboid = $4x^3$}\\[/tex]
[tex]\textsf {volume of sphere = $\dfrac{4}{3}\pi \cdot x^3$}[/tex]
[tex]\textsf {Since $\pi \approx 3.14$, this is} \approx \dfrac{4\cdot (3.14)}{3} x= 4.187x[/tex]
So volume of sphere of radius x = 4.187x³ is greater than cuboid volume of 4x³
Related Questions
What is the mean of the data set rounded to the nearest tenth
0.7,1.1,0.8,1.6,2.2,1.1
Answers
Answer:
1.3 is the correct answer
Step-by-step explanation:
The sum of three consecutive even integers is 312. Find the integers.
OA. 103, 104, 105
OB. 100, 102, 104
OC. 104, 106, 108
D. 102, 104, 106
Answers
The total of three consecutive even numbers is 312.
The correct option is A.
Briefing:Three numbers totaling 312 are consecutive, one of which being 104. Take one of the other numbers from 104=103 and add one to 104=105 for the third.
103 + 104 + 105 = 312.
What are consecutive even integers?Consecutive even numbers are consecutive even integers that differ by 2. If x is an even number, then x + 2, x + 4, and x + 6 are also even numbers. The difference between consecutive even numbers is two.
How do you find a series of consecutive integers?The formula for successive integers is quite simple. If x is the first consecutive integer, x+1 is the next, x+2 is the third, x+3 is the fourth, and so on. Consider the following example. 45 is 'x if it is the first consecutive integer in either a series of numbers.
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Find the points on the curve y = 2x3 + 3x2 − 12x + 3 where the tangent line is horizontal.
Answers
the tangent is only horizontal at the critical points of the equation, so
[tex]y=2x^3+3x^2-12x+3\implies \cfrac{dy}{dx}=6x^2+6x-12\implies \cfrac{dy}{dx}=6(x^2+x-2) \\\\\\ \stackrel{\textit{setting the derivative to 0}}{0=6(x^2+x-2)}\implies 0=x^2+x-2 \\\\\\ 0=(x+2)(x-1)\implies \boxed{x= \begin{cases} -2\\ 1 \end{cases}} \\\\[-0.35em] ~\dotfill\\\\ y=2(-2)^3+3(-2)^2-12(-2)+3\implies y=-16+12+24+3\implies \boxed{y=23} \\\\\\ y=2(1)^3+3(1)^2-12(1)+3\implies y=2+3-12+3\implies \boxed{y=-4} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \text{\LARGE (-2~~,~~23)\qquad (1~~,~~-4)}~\hfill[/tex]
There are 2 numbers with a sum of 43. The first number is 2 less than twice the second. What is the SECOND number?
Answers
The value of the number is 15.
How to compute the value?Let the first number be represented by x.
The second number will be:
(2 × x) - 2 = 2x - 2
Therefore, the addition of the numbers will be:
= x + 2x - 2 = 43
3x - 2 = 43
3x = 43 + 2
3x = 45
Divide
x = 45/3
x = 15.
Therefore, the number is 15
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Find the angle in degrees between the two planes
x − 10y − 8z = 11
and
2x + 5y + 8z = 1.
(Round your answer to two decimal places.)
Answers
The angle in degrees between the two planes is approximately 159.460°.
What is the angle between two planes?
The equation of the plane, whose form is a · x + b · y + c · z = d is equivalent to this vectorial form (a, b, c) • (x, y, z) = d, where (a, b, c) is the vector of coefficients. The angle between the two planes:
θ = cos⁻¹ [[(a₁, b₁, c₁) • (a₂, b₂, c₂)] / [||(a₁, b₁, c₁)|| · ||(a₁, b₁, c₁)||]]
If we know that (a₁, b₁, c₁) = (1, - 10, - 8) and (a₂, b₂, c₂) = (2, 5, 8), then the angle between the two planes is:
θ = cos⁻¹ [[(1, - 10, - 8) • (2, 5, 8)] / [√165 · √93]]
θ = cos⁻¹ [(-2 - 50 - 64) / √15345]
θ = cos⁻¹ (- 116 / √15345)
θ ≈ 159.460°
The angle in degrees between the two planes is approximately 159.460°.
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Which is the equation of the given line?
Question options:
A. x = –2
B. y = –2x
C. x = 2
D. y = –2
Answers
Answer:
Option D: [tex]y=-2[/tex]
Step-by-step explanation:
The line is horizontal, which means the slope is 0. The line also crosses the y-axis at (0,-2). Thus y at 0 is equal to 2.
T(x,y,z)=x^2yz^3 với M(1,1,1)
Answers
Answer:
A= (2xy^2)^3. (-1/2x^2yz) (gạch chéo là phần)
B=(-4x3y2z)( x2y3)3xy
Step-by-step explanation:
ok :)
In AOPQ, PQ = 19, QO = 11, and OP = 20. Which statement about the angles of AOPQ
must be true?
Answers
The true statement about the angles of the triangle OPQ is the third statement that is m∠P < m∠O < m∠Q.
It is given that:-
In triangle OPQ,
PQ = 19
QO = 11
OP = 20
We have to find which one of the six statements given in the question is correct.
We know that, in a triangle, if one side of the triangle is longer than the other side, then the angle opposite to the longer side will be larger than the angle opposite the shorter side.
Hence,
In triangle OPQ,
Angle opposite to side OP = ∠Q
Angle opposite to side PQ = ∠O
Angle opposite to side QO = ∠P
As,
QO < PQ < OP , Hence,
m∠P < m∠ O < m∠Q
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Which angles of rotation will map the figure onto itself? Explain your reasoning and/or show your work.
Answers
The angles of rotation will map the figure onto itself are 60, 120, 180....
How to deternine which angles of rotation will map the figure onto itselfIn geometry, transformation involves changing the angle, position and/or size of a shape.
The figure that completes the question is added as an attachment
The given parameter is the shape in the figure
From the figure, we can see that the shape has 6 congruent sides
This means that the shape is a regular hexagon
The angle of rotation will map the figure onto itself is calculated as
Angle = 360/Number of sides
So, we have
Angle = 360/6
Evaluate
Angle = 60
The other angles must be a multiple of 60
i.e. 60, 120, 180....
Hence, the angles of rotation will map the figure onto itself are 60, 120, 180....
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Apply the indicated series of transformation to the triangle image and draw its final placement on the graph: *(x,y)—>(x+6,y-2) *reflect across y=2 (this part confuses me)
Please tell me in steps
(Photo attached)
Answers
Answer:
See the answer below
Step-by-step explanation:
Solve for the system of equations.
Y=2x+3
2y-x=12
Answers
For the system of equations y = 2 x + 3 and 2 y - x = 12, the solution will be x = 2 and y = 7.
We are given the system of equations:
y = 2 x + 3 … (1)
2 y - x = 12 …. (2)
We need to solve it to find the values of x and y.
Putting the value of y from equation (1) in equation (2), we get that:
2 y - x = 12
2 (2 x + 3) - x = 12
Multiplying the brackets, we get that:
4 x + 6 - x = 12
3 x + 6 = 12
Subtract 6 from both the sides, we get that:
3 x + 6 - 6 = 12 - 6
3 x = 6
Divide both sides by 3. we get that:
3 x / 3 = 6 / 3
x = 2
y = 2 x + 3
y = 2 (2) + 3
y = 4 + 3
y = 7
Therefore, we get that, for the system of equations y = 2 x + 3 and 2 y - x = 12, the solution will be x = 2 and y = 7.
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How do you write 14 programming errors for every 56 programmers as a rational number? Select the simplified rational number that represents this scenario.(1 point)
14
56
14/56
1/4
Answers
The simplified rational number that represents this scenario is 1/4
How to determine the simplified rational number that represents this scenario?The given parameters are:
14 programming errors for every 56 programmers
The above means:
Error : Actual = 14 : 56
Express as fraction
Error/Actual = 14/56
Simplify the ratio
Error/Actual = 1/4
Hence, the simplified rational number that represents this scenario is 1/4
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9
)
14+(−9)+(−9)14, plus, left parenthesis, minus, 9, right parenthesis, plus, left parenthesis, minus, 9, right parenthesis.
Answers
The value of (9)14+(−9)+(−9)14 is -9
The concept is used to Solve is BODMAS
(9)14+(−9)+(−9)14
126-9-126=-9
BODMAS, also known as the order of operations, is a series of operations in an arithmetic statement. Math is all about logic and certain common principles that help us with our calculations. So BODMAS is one of the basic principles for simplifying multi-operator formulations.
An expression or equation in arithmetic has two components:
Numbers \Operators
A character that combines two integers to form an expression or equation is known as an operator. The most popular operators in mathematics are Addition (+), Subtraction (-), Multiplication (), and Division (). Finding the solution to mathematical statements or equations with only one operator is rather straightforward.
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Find a counterexample to show that the following statement is false.
The sum of three multiples of 5 will always end in a 5.
Answers
Answer:
5 + 10 + 15 = 30
Step-by-step explanation:
You want a sum of three multiples of 5 that does not end in 5.
Multiples of 5Any odd multiple of 5 will end in 5. An even multiple will not.
In order for the sum to not end in 5, the total of the multipliers must be even:
1×5 +2×5 +3×5 = 6×5 = 30
5 +10 +15 = 30 . . . . . . three multiples of 5 whose sum does not end in 5
Solve the equation. 7x=35 x=
Answers
Answer:
x=
Step-by-step explanation:
Answer:
5
Step-by-step explanation:
A school board member surveys parents to learn how they feel about the new school boundaries. What are a random sample and a non-random sample for this situation?
Answers
A random sample and a non-random sample for this situation are given below:
Mrs.Donovan could have taken opinions from the first 50 parents to answer.Mr.Giles could have taken 10 Parents from each grade in the school and used that as his example.What is a Random Sample?This refers to the statistical population where there is an equal chance of being selected by members of a population.
Hence, we can see that a random sample and a non-random sample for this situation are given above and this shows that each of them have equal chances of being selected (random sampling)
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Find the volume of a sphere with a diameter of 6 centimeters.gi
12 cubic centimeters
288 cubic centimeters
97 cubic centimeters
O 367 cubic centimeters
Answers
Answer:V≈113.1
Step-by-step explanation:
d Diameter 6
V=4
3πr3
d=2r
Solving forV
V=1
6πd3=1
6·π·63≈113.09734
Number between 50 and 80 that has exactly 4 factors one which is 2
Answers
58, 62 and 74 are the numbers between 50 and 80 that has exactly 4 factors with 2 being one of them 4.
As per the question statement, we are required to find out the numbers between 50 and 80 that has exactly 4 factors with 2 being one of the factors.
To solve this question, we need to know that every or any number in the number system as has at least 2 factors: 1 and the number itself.
Since we are to find numbers with exactly 4 factors, 2 being one of the factors and as per the above mentioned concept, two of the remaining three factors will be 1 and the number itself, the fourth factor has to be a prime number as prime numbers have no other factors than 1 and itself.
That is, we will have to find prime numbers (say "n") which when multiplied by 2 lies within the range of 50 and 80,
[tex]or, 50\leq (n*2) \leq 80\\or, \frac{50}{2}\leq n\leq \frac{80}{2}\\ or, 25\leq n\leq 40[/tex]
That is, we will need to find the prime numbers between 25 and 40; They are 29, 31 and 37.
Hence, our required numbers are [(29 * 2) = 58], [(31 * 2) = 62] and
[(37 * 2) = 74]. They lie between 50 and 80 that has exactly 4 factors with 2 being one of them.
Factors: In mathematics, a factor "x" of a number, say "y" is such a number that, "y" when divided by "x", the division leaves no remainder.Prime Numbers: Any number greater than 1, that has only two factors, 1 and the number itself is known as a prime number.To learn more about Factors, click on the link below.
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find the dimensions of a rectangle with an area of 12 ft.² and a diagonal of 5 feet
Answers
The dimensions of a rectangle with an area of 12 ft.² and a diagonal of 5 feet are 4 feet and 3 feet.
How to calculate the value?From the information, we are given that the dimensions of a rectangle with an area of 12 ft.² and a diagonal of 5 feet.
It should be noted that the number will be:
= 4 × 3 = 12 ft²
It should be noted that 4² + 3² = 25 and the square root will give 5 which is also the diagonal.
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Can someone tell me if this is right if it’s not can you tell me where I messed up at
Answers
Using translation concepts, the vertices of the triangle after the rotation are given as follows:
G'(2,-2), E'(5,-4), F'(5,-1).
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.
The rule for a 90º counterclockwise rotation around the origin is:
(x,y) -> (-y,x).
Hence the vertices should be given by:
G': (-2,-2) -> (2,-2).E': (-4,-5) -> (5,-4). (here you committed a mistake, should be one left and one up to where you positioned).F': (-1,-5) -> (5,-1). (here you committed a mistake).The correct translation is graphed at the end of the question. You are doing a good job, just there was two small mistakes on the rule :).
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The length of a rectangle parking area is three times the width.The perimeter is 280 yd.Find the length and width of the parking are.
Answers
Answer:
length = 105 yd
width = 35 yd
Step-by-step explanation:
Let L = length and W = width.
L = 3W
perimeter = 2(L + W)
280 =2(L + W)
L = 3W
We have a system of 2 equations. Let's use the substitution method to solve it. Substitute 3W for L in the first equation.
280 = 2(3W + W)
140 = 4W
W = 35
L = 3W = 3(35) = 105
length = 105 yd
width = 35 yd
what number is 1/10th of 8,000,000
Answers
Answer:
800,000
Step-by-step explanation:
To do this, simply divide the number by 10. 8000000/10 = 800,000.
999,999 + 1=1,000,000 show work
Answers
Answer:
use a calculator
Step-by-step explanation: the calculator doesn't lie I used a calculator
Answer:
1,000,000
Step-by-step explanation:
Which expression is equivalent to the given expression [tex]\sqrt{45}[/tex]
Answers
Answer:
6.7
Step-by-step explanation:
√45 = 6.7
.................
Cassie and Amy are playing a card flash game. Cassie has a card with the fraction - 2/7 and Amy has a card with the fraction - 3/4. Write an equation to represent the product of theirs fractions then solve that equation.
( The minus is not plain -3 or -2 it’s the whole fraction)
Answers
The equation representing the product of theirs fractions is -
(- 2/7) x (- 3/4) and on solving this expression, we get 3/14.
What is a Fraction?In mathematics, fractions are represented as a numerical value, which defines a part of a whole.
Given that Cassie and Amy are playing a card flash game such that Cassie has a card with the fraction - 2/7 and Amy has a card with fraction - 3/7.
The equation that represent the product of their fractions is -
(- 2/7) x (- 3/4)
Now, solving the above expression, we get -
(- 2/7) x (- 3/4)
(1/7) x (3/2)
3/14
Therefore, the equation representing the product of theirs fractions is -
(- 2/7) x (- 3/4) and on solving this expression, we get 3/14.
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benjamein writes an expression for the sum of 1 cubed, 2cubed and 3 cubed. what is the value of the expression
Answers
The expression for the sum of 1 cubed, 2cubed and 3 cubed is 1² + 2³ + 3³ and the value is 36.
How to compute the value?It should be noted that the information is to find the expression for the sum of 1 cubed, 2cubed and 3 cubed.
This will be:
= 1³ + 2³ + 3³
= 1 + 8 + 27
= 36
Therefore, the correct answer is 36.
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Determine the interval(s) for which f(x) ≥ 0. f(x) = x − 2
Answers
The interval(s) for which f(x) ≥ 0. is x ≥ 2
How to determine the interval(s)?The function is given as:
f(x) = x - 2
Also, we have:
f(x) ≥ 0
This means that
x − 2 ≥ 0
Add 2 to both sides of the inequality
x ≥ 2
Hence, the interval(s) for which f(x) ≥ 0. is x ≥ 2
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Find the measures of the central tendency of the data: (Round the answer to 2 decimal places)
7 14 9 10 10 7 13
Mode:
(Enter DNE if there are no modes)
Mean:
Median:
Answers
Mean: 10
Median: 10
3. The lip balm costs about $16 to make. What is
the cost per ounce?
Answers
Using proportions, it is found that the cost per ounce is of $0.8.
What is the missing information?The missing information is the number of ounces in the balm, that is of 20.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.
The cost per ounce is given by the proportion of the cost by the number of ounces, hence:
Cost: $16.Number of ounces: 20.Then:
$16/20 = $0.8.
The cost per ounce is of $0.8.
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if f(x)=2x2+5 then f(-3)=
Answers
The function f ( x ) = 2 x² + 5 will have the value 23 for f (- 3).
We are given the function:
f ( x ) = 2 x² + 5
We need to find the value of f ( -3 ).
We will do this by substituting the value of x = - 3 in the function and then evaluating the expression.
Putting x = -3 in the function, we get that:
f ( x = - 3 ) = 2 (- 3)² + 5
Solving the square, we get that:
f (- 3) = 2 ( 9 ) + 5
Simplifying the expression, we get that:
f (- 3) = 18 + 5
f (- 3) = 23
Therefore, we get that, the function f ( x ) = 2 x² + 5 will have the value 23 for f (- 3).
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