Final answer:
The volume of a sphere increases by 72.8%, which after calculations, results in a 20% increase in the radius of the sphere.
Explanation:
The volume of a sphere is given by the formula V = (4/3)πr³, where r is the radius of the sphere. An increase in volume by 72.8% implies that the new volume V' is equal to 1.728 times the original volume V. To find the percentage increase in the radius, we use the relationship between volume and radius:
V' = (4/3)πr'^3, where r' is the new radius after increase. Since V' = 1.728V, we have:
1.728 (4/3)πr³ = (4/3)π[tex]r'^3[/tex]Therefore, [tex]r'^3[/tex] = 1.728r³.After taking the cube root of both sides, we obtain:
r' = ∛1.728 * r ≈ 1.200 * rThus, the new radius is approximately 120% of the original radius, which means there is a 20% increase in the radius.
Final answer:
To calculate the percentage increase in the radius of the sphere when the volume is increased by 72.8%, we can use the formula for volume and solve for the new radius in terms of the original radius. The percentage increase in radius is then calculated by comparing the new and original radius.
Explanation:
The volume of a sphere is given by the formula V = (4/3)πr³, where r is the radius of the sphere. If the volume of the sphere is increased by 72.8%, we can calculate the new volume by multiplying the original volume by 1 + 0.728. Let's denote the original radius as r1 and the new radius as r2.
The formula for volume can be written as V = (4/3)πr³. Substituting r1 and r2 into the formula, we get:
Original volume: V1 = (4/3)πr1³New volume: V2 = (4/3)πr2³Since the two volumes are related by the percentage increase (1 + 0.728), we can write the equation:
(1 + 0.728)V1 = V2
Now, let's solve for r2 in terms of r1:
(1 + 0.728)V1 = (4/3)πr2³
r2 = ([(1 + 0.728)V1] * (3/4π))^(1/3)
Finally, we can calculate the percentage increase in the radius by comparing r2 to r1:
Percentage increase in radius = (r2 - r1) / r1 × 100%
(f) how many ways are there to place a total of m indistinguishable balls into n distinguishable urns, with some urns possibly empty or with several balls?
Write the standard form of the line that contains a slope of -1/2 and y intercept of 1
what is the slope the line cantains the points (-1,2) and (3,3)?
does anyone know
2x=8y=7
4x-2y=9
classify each pair of labeled angles as complementary, supplementary, or neither.
Answer: supplementary, complementary, neither.
Step-by-step explanation:
Which of the following measurements is equivalent to 5 quarts? 25 cups 40 fl. oz. 10 pt. 1 gal.
What is 42/100 simplified?
Solve fro the Equation below:
7+2(x-3)=-3(x+1)-4
A country has a Gross Domestic Product (GDP) of $225. If the GDP deflator is 3, what would be the real GDP of the country? The real GDP of the country is
A. $225
B. $150
C. $200
Write each rational number as a repeating decimal.
1. -7/9
2. 11/15
3. 8/3
Final answer:
To write a rational number as a repeating decimal, perform long division. -7/9 as a repeating decimal is -0.7777..., 11/15 is 0.7333..., and 8/3 is 2.6666...
Explanation:
To write a rational number as a repeating decimal, you need to perform a long division. Let's go through each of the given rational numbers:
1. -7/9
When you divide -7 by 9, you get -0.7777… with the 7s repeating. So, -7/9 as a repeating decimal is -0.7777…
2. 11/15
When you divide 11 by 15, you get 0.7333… with the 3s repeating. So, 11/15 as a repeating decimal is 0.7333…
3. 8/3
When you divide 8 by 3, you get 2.6666… with the 6s repeating. So, 8/3 as a repeating decimal is 2.6666…
5x-4(2x+11)=13
solve for x
show all work please
The measure of each interior angle of a regular polygon is 140 degrees, how many sides does the polygon have
The regular polygon with an interior angle of 140 degrees has 9 sides. This conclusion can be reached by using the formula for the interior angle of a polygon, which is (n-2)*180/n, where 'n' represents the number of sides.
Explanation:
The number of sides in a regular polygon can be determined using the formula for the interior angle of a polygon, which is (n-2)*180/n, where 'n' represents the number of sides. This formula comes from the fact that a polygon can be divided into (n-2) triangles, each of which has angles summing up to 180 degrees.
In this particular case, an interior angle of 140 degrees is given. So we will set up an equation: 140 = (n-2)*180/n. Solving for 'n', we get a value of 9.
Therefore, the regular polygon with an interior angle of 140 degrees has 9 sides.
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-4.31 x 3.09 + (-0.98)
What is a methodical step by step procedure that guarantees solving a problem?
?PLEASE HELP!!!!
The table shows the relationship between the number of bracelets made and the number of beads used: Number of bracelets Number of beads 3 24 5 40 7 ? 9 72 The number of beads used to make 7 bracelets is _______.
The number of beads used to make 7 bracelets will be equal to 56 beads.
What are arithmetic Operations?The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or even more items.
Included in them is the study of integers, especially the order of operations, which is important for all other areas of mathematics, notably algebra, data management, and geometry.
As per the data given in the question,
Three bracelets have 24 beads, so start with the lowest number. Finding out how often beads are on a single bracelet will help you locate the solution the quickest. We shall know the answer on 24/3.
24/3=8.
Then multiplying 56 by 7 to get.
Then confirm that your response still makes sense.
3 x 8 = 24
5 x 8 = 40
7 x 8 = 56
9 x 8 = 72
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solve the equation 17=-13-8x with steps
The solution for given equation 17=-13-8x is x = -15/4.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions by connecting them with the equal sign = .
The given equation is,
17 = -13 - 8x
Now to solve the equation following steps are followed :
adding 13 both the sides of the equation,
17 + 13 = -13 - 8x + 13
or, 17 + 13 = -13 + 13 - 8x
Solving them we get,
30 = - 8x
or, - 8x = 30
multiplying -1 both side
- 8x*(-1) = 30*(-1)
Solving them we get,
8x = -30
dividing both side by 2
8x/2 = -30/2
Solving them we get,
4x = -15
dividing both side by 4
4x/4 = -15/4
Solving them we get
x = -15/4
Hence,the solution for given equation 17=-13-8x is x = -15/4.
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how do u solve using the ratios !
If 2x-5=10, then 2x=
Convert the radian measure to degree measure. use the value of π found on a calculator and round answers to two decimal places. five pi divided by six
What is the sine of angle a?
a. 12/13
b. 5/13
c. 5/12
d. 13/12
What is the equation of a line passing through the points 6,3 and -4,3 so y=?
Answer:
y=3
Step-by-step explanation:
The required line will be y = 3 which is passing through points (6,3) and (-4,3)
What is the slope of the line?The slope of the line is defined as the gradient of the line. It is denoted by m
Slope m = (y₂ - y₁)/(x₂ -x₁ )
Assume two points on a line—Point 1 and Point 2. Point 1 has coordinates (x₁,y₁) and Point 2 has coordinates (x₂, y₂)
To determine the line of passing through points (6,3) and (-4,3)
We have been given two points :(6,3) and (-4,3)
Let the required line will be:
(y - y₁) = [(y₂ - y₁)/(x₂ -x₁ )](x -x₁ )
Here
x₁ = 6, y₁ = 3
x₂ = -4, y₂ = 3
(y - y₁) = [(y₂ - y₁)/(x₂ -x₁ )](x -x₁ )
Substitute values in the above formula
(y - 3) = [(3 - 3)/(-4 -6 )](x -6 )
(y - 3) = [(0)/(-10 )](x -6 )
(y - 3) = 0
y = 3
Therefore, the required line will be y = 3
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Which of these equations describe the line shown below check all that apply . plz don't give me the formula and tell me do it that way I'm not good at math I'll give 5 stars if you just give me the answer thanks
If you have a distribution of 50 scores, and you want 5 intervals, what should be the size of your class interval?
The rule (x,y)→(2x,2y) maps △DEF to △D′E′F′.
Which statement correctly describes the relationship between △DEF and △D′E′F′ ?
the triangles are congruent because △D′E′F′ is a rotation of △DEF , and a rotation is a rigid motion.
The triangles are congruent because △D′E′F′ is a reflection of △DEF , and a reflection is a rigid motion.
The triangles are not congruent because △D′E′F′ is a dilation of △DEF , and a dilation is not a rigid motion.
The triangles are not congruent because △D′E′F′ is a translation of △DEF , and a translation is not a rigid motion.
Which figure shows how a shape can be rotated about an axis to form the given object?
The figure that shows how a shape can be rotated about an axis to form a disc is (c) rectangle
How to determine the figure?The shapes in the figures are given as:
A. Rectangle
B. Semicircle
C. Inscribed semicircle
D. Another Rectangle
When the first rectangle is rotated about the axis, it forms a spiral shape
Rotating a semi-circle and the inscribed semi-circle about its axis would form a hemisphere
However, when a rectangle that has one of it sides on the axis is rotated, it forms a cylinder or disc
Hence, the figure is (d) rectangle
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Two cars leave new york at the same time traveling in opposite directions. one travels at an average speed of 77 mph and the other at 63 mph. in how many hours will they be 280 miles apart?
The number of hours will they be 280 miles apart will be 2 hours.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
Two vehicles leave new york simultaneously going in inverse headings. one goes at a typical speed of 77 mph and the other at 63 mph.
The relative speed is given as,
S = 77 + 63
S = 140 miles per hour
The number of hours will they be 280 miles apart will be calculated as,
Time = 280 / 140
Time = 2 hours
The number of hours will they be 280 miles apart will be 2 hours.
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How is the distance formula like the pythagorean theorem explain?
The distance formula is
simply a variation of the theorem. The method is the same with the Pythagorean
however we are now dealing with 2 sets of points instead of 2 lengths.
In the distance formula, the lengths are derived from the
(x1,y1)->(x2,y2) coordinate points and the formula simplified. We still
square the difference of x’s and difference of y’s to get our two squares then
square root the sum to give our length. While the Pythagorean theorem is
directly the sum of the square of the other two sides.
Nevertheless, both formulas work on the same principle.
Answer:
Both formulas can be used to find the distance between two points on the coordinate plane. The vertical leg of the right triangle represents the difference in the y values of the two points. The horizontal leg of the right triangle represents the difference in the x values of the two points. The hypotenuse of the right triangle represents the distance between the two points.
Step-by-step explanation:
The scale on a map of Texas shows that 1 inch represents 20 miles. The actual distance from Austin to Dallas is 195 miles. On the map, how many inches apart are the two cities?
To calculate the map distance between Austin and Dallas with a scale of 1 inch representing 20 miles, and an actual distance of 195 miles, set up a proportion and solve to find that Austin and Dallas would be 9.75 inches apart on the map.
Explanation:To find out how many inches Austin is from Dallas on the map, we need to set up a proportion. The scale given on the map is 1 inch represents 20 miles. We know the actual distance between Austin and Dallas is 195 miles. To calculate the distance on the map, we use the proportion 1 inch / 20 miles = x inches / 195 miles.
Cross-multiply to solve for x:
(1 inch) * (195 miles) = (20 miles) * (x inches)
195 inch-miles = 20x inch-miles
Now, divide both sides by 20 miles to solve for x:
x = 195 inch-miles / 20 miles
x = 9.75 inches
So, on the map, Austin and Dallas would be 9.75 inches apart.
Graph the following inequality and then select the correct graph below. x + y < 1
( first answer choice is a dotted vertical graph shaded down)
(second answer is a vertical line graph shaded up)
plsss help
Answer:
Given inequality,
[tex]x+y<1[/tex]
For graphing the inequality :
The related equation of the given inequality,
x + y = 1
Having the x-intercept = (1,0),
y-intercept = (0,1),
Also, at (0,0),
0 + 0 < 1 ( True )
⇒ The area of the given inequality x + y < 1 must contain the origin.
Now, '<' show the dotted line.
Thus, by the above explanation we can plot the graph of the given inequality.
A couch and coffee table cost a total of $1053. The cost of the couch is two times the cost of the coffee table. Find the cost of each item.