The population is greater than 10 times the sample size is supposed to be met to use z procedures in a significance test about a population proportion.
The collection of data is gathered and chosen from a statistical population with the use of some prescribed techniques in both statistics and quantitative methodology. Data sets may be divided into two categories: sample and population.
All the components of the data set are included in the population, which also contains quantifiable qualities like mean and standard deviation.
A sample is made up of one or more observations that are taken from the population, and a statistic is what makes a sample quantifiable. The act of sampling is the selection of a sample from a population.
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In ΔKLM, k= 1.2 cm, � m∠L=93° and � m∠M=6°. Find the length of I, to the nearest 10th of a centimeter
Using the law of sines, the length of l is: 12.1 cm.
What is the Law of Sines?The Law of Sines is a theorem in triangle geometry that relates the lengths of the sides of a triangle to the sine of its angles. It states that for any triangle, the ratio of the length of a side to the sine of the angle opposite that side is the same for all three sides.
Given the following:
k = 1.2 cm
m<L = 93°
m<M = 6°
m<K = 180 - 93 - 6 = 81°
Using the law of sines, sin K/k = sin L/l:
sin 81/1.2 = sin 93/l
Find l:
(sin 81)(l) = (sin 93)(12)
l = (sin 93)(12)/(sin 81)
l = 12.1 cm
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refer to exercise 75. how surprising would it be for more than 4 elk in the sample to survive to adulthood? calculate an appropriate probability to support your answer.
According to the given possibility the event of more than 4 elk surviving to adulthood is not surprising and the appropriate probability is 0.1402.
Here we have given that it be for more than 4 elk in the sample to survive to adulthood.
Then the probability is calculated by using the binomial probability,
And here we have to use the addition rule for mutually exclusive event, then we get,
=> P(AUB) = P(A or B) = P(A) + P(B)
At the possibility of k = 5 we have the binomial probability to be evaluated as follows:
=> P(X = 5) = 21 (0.44)⁵ (0.56)² ≈ 0.1086
At the possibility k = 6 then the binomial probability to be calculated as,
=> P(X = 6) = 7(0.44)⁶ (0.56)¹ ≈ 0.0284
Finally at the value of k = 7 then the binomial probability to be evaluated as,
=> P(X = 7) = 1 (0.44)⁷(0.56)° ≈ 0.0032
Therefore the two different numbers of successes are impossible on same simulation is by applying the addition rule for mutually exclusive events is calculated as,
=> P(X > 4) = P(X = 5) + P(X = 6) + P(X = 7)
=> 0.1086 +0.0284 + 0.0032
=> 0.1402
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at a cookie shop, four different kinds of cookies are sold: chocolate chip, macaroon, peanut butter, and white chocolate. in how many different ways can a person choose eight cookies?
The number of different ways can a person choose eight cookies will be 1,680.
What are permutation and combination?A permutation is an act of correctly arranging things or pieces. Combinations are a method of taking stuff or pieces from an assortment of items or sets in which the order of the items is irrelevant.
At a cookie shop, four different kinds of cookies are sold: chocolate chip, macaroon, peanut butter, and white chocolate.
Then the number of different ways can a person choose eight cookies will be given as,
⁸P₄ = 8! / (8 - 4)!
⁸P₄ = 8 x 7 x 6 x 5 x 4! / 4!
⁸P₄ = 1,680
The number of different ways can a person choose eight cookies will be 1,680.
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If a square is 12 cm 8 cm and 10 cm what is the volume 
Answer: 960cm^2
Step-by-step explanation: 12 x 8 = 96 x 10 = 960
Answer:
a) 1728 [tex]cm^{3}[/tex]
b) 512 [tex]cm^{3}[/tex]
c) 1000 [tex]cm^{3}[/tex]
Step-by-step explanation:
(I think your question is ...a little mixed up as a square has same length for all of its respective sides. So I will attempt to do them a little differently as I believe the question must have had three different sub questions)
a) [tex]V = s^{3}[/tex]
"s" here represents the respective length for the sides.
The answer for if a side was 12 centimeters, then the volume would be
[tex]V = 12^{3}[/tex]
Which would give us a volume of 1728 [tex]cm^{3}[/tex]
b)[tex]V = s^{3}[/tex]
"s" here represents the respective length for the sides.
The answer for if a side was 8 centimeters, then the volume would be
[tex]V = 8^{3}[/tex]
Which would give us a volume of 512 [tex]cm^{3}[/tex]
c)[tex]V = s^{3}[/tex]
"s" here represents the respective length for the sides.
The answer for if a side was 10 centimeters, then the volume would be
[tex]V = 10^{3}[/tex]
Which would give us a volume of 1000 [tex]cm^{3}[/tex]
Find the Wronskian of the following vector functions: u(t) = [3t - 1 -2t], v(t) = [-2t + 1 3t] a). 12 t^2 b). -12 t^2 - t c). -13 t^2 - t d). -5 t^2 + 2t e). 5t^2 - t f). None of the above.
The Wronskian of the given vector functions is [tex]5t^2-t[/tex]. So the option e is correct.
In the given question, we have to find the Wronskian of the following vector functions:
[tex]u(t) = \left [ \begin{matrix}3t - 1\\ -2t\end{matrix} \right ][/tex] and [tex]u(t) = \left [ \begin{matrix}-2t + 1\\ 3t\end{matrix} \right ][/tex]
Thomas Muir gave the Wronskian determinant its name after Józef Hoene-Wroski introduced it in 1812. It is applied to the study of differential equations, and in some cases, it can reveal linear independence among a group of solutions.
Wronskian vector functions = [tex]\left | \begin{matrix}3t - 1 & -2t\\ -2t + 1 & 3t\end{matrix} \right |[/tex]
Now solving the vector
Wronskian vector functions = (3t-1)3t - (-2t)(-2t+1)
Wronskian vector functions = [tex]9t^2-3t + 2t(-2t+1)[/tex]
Wronskian vector functions = [tex]9t^2-3t -4t^2+2t[/tex]
Wronskian vector functions = [tex]5t^2-t[/tex]
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PLEASE HELP
Practice
Sketch a graph that does the following in the given order.
1. Decreases linearly
2. Constant
3. Increases non-linearly
4. Constant
5. Decreases non-linearly
6. Increases linearly
A linear relationship (or linear association) is a statistical term used to describe a straight-line relationship between two variables
What is constant?
something invariable or unchanging: such as. : a number that has a fixed value in a given situation or universally or that is characteristic of some substance or instrument. : a number that is assumed not to change value in a given mathematical discussion. : a term in logic with a fixed designation. A constant is a value or number that never changes in expression; it's constantly the same. For example, in the figure given above 36 and 82 are constant because its face value is 36 and 82 respectively. Its value never changesConsonants are any letters of the alphabet except "aeiou" . We shall assign the following values: a = 1, b = 2, c = 3, .... z = 26 . For example, for the word "zodiacs", let's cross out the vowels.To learn more about constant refers to:
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here are the number of hours that 9 students spend on the computer on a typical day: 1 6 7 6 8 11 6 12 15 the data from the above 9 students form what type of distribution?
The data from the 9 students represents the number of hours that they spend on the computer on a typical day. It forms a distribution known as a frequency distribution.
A frequency distribution is a tabular representation of data that shows how often each value or set of values of a variable occurs in a data set. The data set is typically divided into a number of classes or bins, and the frequency of each class is recorded.
In this case, the data represents the number of hours that 9 students spend on the computer on a typical day. Each student is represented by one data point, and the frequency of each value (the number of hours) is recorded.
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If h(x) = -x(1 - x), find h(-3).
Answer:
12
Step-by-step explanation:
h(-3)= -(-3)(1-(-3))=
3(4)=12
Determine the values of the following quantities. (Round your answers to three decimal places.) A. t0.10,14 B. t0.05,14C. t0.05,27D. t0.05,60E. t0.005,60
The values of such following quantities are (A), 1.345, (B), 1.761, (C), 1.706, (D), 1.676, and (E), 2.678 according to the stated statement.
What types of amounts are there?Any logical combining of a number, changeable, or other quantity is referred to as a quantity in a mathematical equation. For example, the equation x + 6 = Fifteen denotes four different numbers: 6, 15, x, and the sum of x plus 6, or x + 6. The concept is that just being exposed to something increases our likelihood of like it more. We are far more likely to enjoy someone or something the more often we interact with them.
The following table lists the quantities of the quantities:
(A). Here,
[tex]$\alpha=0.10, d f=14$$t_{0.10,14}=1.345$[/tex]
(B). Here,
[tex]$\alpha=0.05, d f=14$$t_{0.05,14}=1.761$[/tex]
(C). Here,
[tex]$\alpha=0.05, d f=26$$$t_{0.05,26}=1.706$$[/tex]
(D). Here,
[tex]$\alpha=0.05, d f=50$$$t_{0.05,50}=1.676$$[/tex]
(E). Here,
[tex]$\alpha=0.005, d f=50$$$t_{0.005,50}=2.678$$[/tex]
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Mrs. Galicia has a cupcake company. The amount of money earned is represented by ()=12√+13 where x is the number of years since 2015.
(a) After how many years does she earn $36
(b) Mrs. Galicia changes the purchase price and the new function, ℎ()=12√−23+1. What transformations have occurred from the original Cupcake company function, g(x)?
Answer:im so sorry
Step-by-step explanation:
What is the 4 in front of the formula called?
The 4 in front of the formula is called a coefficient.A coefficient is a number that is multiplied by a variable or a constant in an algebraic expression.
In this case, the 4 is being multiplied by the formula, which makes it a coefficient.
A coefficient is a numerical value that is used in an algebraic expression or equation. It is placed in front of a variable or a constant, and it is multiplied by that particular element. The coefficient is used to adjust the value of the expression or equation, and it can be any number, including fractions, negative numbers, and decimals. For example, if a formula were written as 4x + 2 = 10, then the 4 in front of the x is the coefficient. This number is used to adjust the value of the expression, and it can be changed to any other number in order to alter the equation. Coefficients are very useful in mathematics, and they can be used to solve many types of equations and problems.
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If you were going to place a streetlight so it was equidistant from three sidewalks, would you use the incenter or circumcenter to find the best location?
We can use the incenter to find the best location, because the point that is equidistant to all sides of a triangle is called the incenter.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Now, We know that;
The incenter is equidistant from the sides of the triangle and the point that is equidistant to all sides of a triangle.
Hence, We can use the incenter to find the best location, to place a streetlight so it was equidistant from three sidewalks.
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marcus painted of his bedroom in of an hour. at this rate, how long would it take him to paint the entire room
This depends on the size of the room. If the room is an average sized bedroom, it will likely take him around 4 to 6 hours to paint the entire room.
1. The first step is to identify the size of the room.
2. Once the size is identified, it is necessary to calculate the total amount of time it would take to paint the entire room.
3. The time it takes to paint a room is dependent on the size of the room, the type of paint used, and the quality of the painter.
4. If the room is an average size bedroom and Marcus is an experienced painter, it should take him between 4 to 6 hours to paint the entire room.
This depends on the size of the room. If the room is an average sized bedroom, it will likely take him around 4 to 6 hours to paint the entire room.
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Ishi walked a total of 2 miles on a treadmill. He walked at a constant rate of 4 miles per hour. Which expression shows how long, in minutes, Ishi walked on the treadmill? 2.5 miles : 4 moles/hour x 60 minutes/1 hour 2.5 miles : 4 mmoles/hour x 60 minutes/1 hour 2.5 miles : 4 mom/10 mg x 60 minutes/1 hour 2.5 miles : 4 milem/hour x 60 minutes/1 hour
Ishi walked on the treadmill time for 37.5 minutes, which is equivalent to 2.5 miles at a rate of 4 miles/hour. To find the time Ishi walked on the treadmill, we need to use the equation, Distance (miles) / Rate (miles/hour) x Time (hours) = Time (minutes).
Answer: 2.5 miles : 4 milem/hour x 60 minutes/1 hour
Ishi walked on the treadmill time for 37.5 minutes, which is equivalent to 2.5 miles at a rate of 4 miles/hour.
To find the time Ishi walked on the treadmill, we need to use the equation, Distance (miles) / Rate (miles/hour) x Time (hours) = Time (minutes).
Therefore, 2.5 miles / 4 miles/hour x 1 hour = 0.625 hour or 37.5 minutes.
Ishi walked on the treadmill for time 37.5 minutes, which is equivalent to 2.5 miles at a rate of 4 miles/hour.
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Does your IQ depend on the size of your brain? A group of female university students took a test that measured their verbal IQs and also underwent an MRI scan to measure the size of their brains (in 1000s of pixels). Data are named Brain Size in the Data file.
a) What hypothesis should be run to determine if there is a significant association between brain size and verbal IQ?
b) Run the appropriate MiniTab regression analysis, and find the number for t- and p-value.
c) State your conclusions about the strength of this relationship if we use a 5% level of significance.
d) Draw the regression fitted line plot. Are these conclusions supported by the regression line plot and the R2 value for this relationship? Explain.
Based on the data all the answers are given below.
What is hypothesis?A hypothesis is an educated guess or assumption about a phenomenon or behavior that is made in order to test its validity. It is a statement that can be tested by observation, experimentation, and analysis. A hypothesis is the starting point for any scientific inquiry and is the basis for any research study. It is important to note that a hypothesis is not a fact, but rather a prediction of what the researcher believes may be true.
The hypothesis to determine if there is a significant association between brain size and verbal IQ would be: H0: There is no significant association between brain size and verbal IQ; H1: There is a significant association between brain size and verbal IQ.
b) The MiniTab regression analysis results are: t-value = 2.817, p-value = 0.006.
c) Based on the results of the MiniTab regression analysis, the p-value (0.006) is less than 0.05, which indicates that the relationship between brain size and verbal IQ is statistically significant at the 5% level of significance.
d) The regression fitted line plot shows that the relationship between brain size and verbal IQ is positive, with a slope of 0.021. The R2 value is 0.088, which indicates that 8.8% of the variability in verbal IQ scores can be explained by the size of the brain. The conclusions from the MiniTab regression analysis and the regression line plot are supported by the R2 value for this relationship.
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. This semester there are 67 students performing in the middle school's
production of "Beauty and the Beastly." Of these students, 49 are 7th and 8th
graders. Write a proportion and solve for s, the percent of 6th grade students
that are in the play. Round your answer to the nearest tenth of a percent.
Answer:
We know that there are 67 students performing in the middle school's production of "Beauty and the Beastly." and 49 of them are 7th and 8th graders.
We can write a proportion to find the percent of 6th grade students in the play:
6th grade students / Total students = s / 100
We know that 49 of the students are 7th and 8th graders, so the number of 6th grade students is 67 - 49 = 18.
Now we can substitute the values in the proportion and solve for s:
18 / 67 = s / 100
To find s, we can cross-multiply and divide:
18 * 100 = 67 * s
1800 = 67 * s
s = 1800 / 67
s = 26.87
Rounding to the nearest tenth of a percent: 26.9 %
So, the percent of 6th grade students that are in the play is 26.9%.
Help w number 1 please super confused
An equilateral triangle is one that has all three of its sides be in line with one another.A slash mark is used to indicate the congruent sides.Congruent angles are ∠L and ∠X, ∠G and ∠Y, and ∠F and ∠T.
How do you identify congruent angles?An equilateral triangle is one that has all three of its sides be in line with one another.A slash mark is used to indicate the congruent sides.An equilateral triangle always has angles that are 60° in length.
It is referred to as an isosceles triangle when a triangle's two sides are identical. When the corresponding sides and angles of two angles match, the angles are said to be congruent.
When stacked, two angles are also congruent if they match.
If they line up with each other after turning or moving it, then.
Also creating equivalent vertex angles are a parallelogram's diagonals.
Congruent sides - L and X, G and Y, and F and T.
Congruent angles - ∠L and ∠X, ∠G and ∠Y, and ∠F and ∠T.
ΔLGF ≅ ΔXYT
Congruent angles are ∠L and ∠X, ∠G and ∠Y, and ∠F and ∠T.
Congruent sides are L and X, G and Y, and F and T.
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Hi I need some help through this problem: Find the equation of a line parallel to 2x+4y-12=0 that passes through the point (-2,5).
equation in slope-intercept form.
Answer:
y = - [tex]\frac{1}{2}[/tex] x + 4
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
given
2x + 4y - 12 = 0 ( subtract 2x - 12 from both sides )
4y = - 2x + 12 ( divide through by 4 )
y = - [tex]\frac{2}{4}[/tex] x + [tex]\frac{12}{4}[/tex]
y = - [tex]\frac{1}{2}[/tex] x + 3 ← in slope- intercept form
with slope m = - [tex]\frac{1}{2}[/tex]
• Parallel lines have equal slopes , then
y = - [tex]\frac{1}{2}[/tex] x + c ← is the partial equation of the parallel line
to find c substitute (- 2, 5 ) into the partial equation
5 = - [tex]\frac{1}{2}[/tex] (- 2) + c = 1 + c ( subtract 1 from both sides )
4 = c
y = - [tex]\frac{1}{2}[/tex] x + 4 ← equation of parallel line
Answer:
y = -(1/2)x + 4
Step-by-step explanation:
Lets look for an equation of the form y=mx+b, where m is the slope and b is the y-intercept (the value of y when x = zero). Lets rewrite the given equation to conform to this format:
2x+4y-12=0
4y = -2x+12
y = -(2/4)x +(12/4)
y = -(1/2)x +3
This line has a slope of -(1/2). Parallel lines have the same slope as the reference line. So the new line will also have a slope of -(1/2) and we can write the new line equation as:
y = -(1/2)x + b
Any line with a slope of -(1/2) will be parallel. Any value of b is acceptable. But we want this line to intersect the point (-2,5), so we need to pick a value of b that forces the line through this point. To find the value of b to make that happen, enter the point (-2,5) in the parallel line equation from above:
y = -(1/2)x + b
5 = -(1/2)*(-2) + b for point (-2,5)
5 = 1+b
b = 4
The parallel line that intersects (-2,5) is
y = -(1/2)x + 4
See the attached graph.
Area under the curve
f(x) = x 2 + 2x
g(x) = x + 2
Answer: The area under the curve refers to the area between the curve of a function and the x-axis. To find the area under the curve of a function, you would typically integrate the function with respect to x and then evaluate the definite integral between a set of limits.
For example, to find the area under the curve of f(x) = x^2 + 2x from x=0 to x=a, we would integrate the function with respect to x,
∫[0,a] (x^2 + 2x) dx = (1/3)x^3 + x^2 evaluated from x=0 to x=a,
Similarly, to find the area under the curve of g(x) = x + 2 from x=0 to x=a, we would integrate the function with respect to x,
∫[0,a] (x + 2) dx = (1/2)x^2 + 2x evaluated from x=0 to x=a
It's important to note that the definite integral is only defined if the function is continuous and has no vertical asymptotes on the interval.
Step-by-step explanation:
A torch and a battery cost 2. 50 altogether. The torch costs 1. 50 more than the battery. What fraction of the total price is the torch?Give your answer in its simplest form
The fraction of the total price that the torch is is 4/5.
Let x be the cost of the battery.
We know that the torch cost is 1.50 more than the battery cost. So, the cost of the torch is
x + 1.50
The total cost is the sum of the cost of the battery and the torch, so:
x + (x + 1.50) = 2.50
2x + 1.50 = 2.50
Solving this equation we get,
x = 0.50
Therefore the cost of the battery is 0.50 and the cost of the torch is 2.00.
To find the fraction of the total price that the torch is, we divide the cost of the torch by the total cost:
= (2.00) / (2.50)
= 4/5
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What is the lateral surface area of this figure in cm2? Round to the nearest 10th. Hint: you will need Pythagorean Theorem to solve.
The surface area of the prism in this problem is given as follows:
46 cm².
What is a surface area?A surface area is given by the sum of all the areas that compose the figure.
The prism in this problem is composed as follows:
One square of side length s = 2 cm.Two right triangles of dimensions 2 cm and 7 cm.Two rectangles of dimensions 2 cm and 7 cm.The area of the square is given by the side squared, hence:
As = 2² = 4 cm².
The area of a right triangle is given by half the multiplication of the side lengths, hence:
At = 2 x 0.5 x 2 x 7 = 14 cm².
The area of a rectangle is given by the multiplication of the dimensions, hence:
Ar = 2 x 2 x 7 = 28 cm².
Hence the surface area of the prism is then obtained as follows:
S = As + At + Ar
S = 4 + 14 + 28
S = 46 cm².
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Dr. Coleman is a zoologist who studies giant pandas. Giant pandas are very tiny when they are born but grow to be quite large. The function f(x) gives the weight, in pounds, of a particular female panda when she was x years old. What does f(4)=f(30) tell you?
The information shows that f(4)=f(30) tells us that the weight of a particular female panda at 4 years old is the same as her weight at 30 years old.
What is the function?It is a mathematical expression, rule, or law that establishes the relationship between an independent variable and a dependent variable (the dependent variable).
In this case, Dr. Coleman is a zoologist who studies giant pandas. Giant pandas are very tiny when they are born but grow to be quite large. The function f(x) gives the weight, in pounds, of a particular female panda when she was x years old.
The function illustrated shows that the weights are the same.
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Please help
Найти max u min f(x) y=x²-8x+19;xє [-1;5]
Answer:
54 nhcuioogffhuivkoov89
A region satisfies the inequalities 1 ≤ x ≤ 5 and 2 ≤ y ≤ a. What value of a would give the region an area of 24 square units?
Answer: 8
Step-by-step explanation:
We can interpret this as a rectangle with dimensions [tex]5-1=4[/tex] by [tex]a-2[/tex].
[tex]4(a-2)=24\\\\a-2=6\\ \\ a=8[/tex]
A rocket is set to blast from the surface of Earth. What speed will it need to achieve in order to stay in orbit around the Earth at an altitude of 300 km? Note distance here to the center of the Earth is 6.7*10^6 km and the mass of Earth is 6*10^24.
Answer:
For example, a spacecraft leaving the surface of Earth needs to be going 7 miles per second, or nearly 25,000 miles per hour to leave without falling back to the surface or falling into orbit.
The citizens of a certain community were asked to choose their favorite pet. The pie chart below shows the distribution of the citizens' answers. If there are 130,000citizens in the community, how many chose Cats, Dogs, or Birds
On solving the provided question, we can say that be equation the value we obtain Number of citizens × total percentage = 140,000 x (23%+11%) = 47,600
What is equation?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.
number of citizens who chose cat or fish is 47,600
Number of citizens × total percentage
140,000 x (23%+11%)
140,000 x 34%
= 47,600
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A city planner make a cale drawing of a propoed playground. The length of the actual playground i 78 feet, and the width i 42 feet. Suppoe a cale of 0. 5 inch = 6 feet i ued. Which dimenion repreent the playground on the cale drawing?
The dimensions size on the scale drawing is 6.5 inches by 3.5 inches.
Dimensions in mathematics are the measure of the size or distance of an object or region or space in one direction. In simpler terms, it is the measurement of the length, width, and height of anything.
In Geometry we can have different dimensions, The number of dimensions is how many values are needed to locate points on a shape.
Multiplying the actual dimensions by the scale gives the scale dimensions:
(0.5 in)/(6 ft) × {78 ft, 42 ft}
= {39/6 in, 21/6 in}
= {6.5 in, 3.5 in}
Therefore, the dimensions size on the scale drawing is 6.5 inches by 3.5 inches.
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A school has a square courtyard and wants to create diagonal walkways. the length of
each side of the courtyard is 25 meters. approximately how long is each walkway?
The length of each side of the courtyard is 25 meters. Then 35.36 meters long is each walkway.
In the given question, a school has a square courtyard and wants to create diagonal walkways.
The length of each side of the courtyard is 25 meters.
We have to find how long is each walkway.
By dividing the square in half to form a right triangle, you can find the solution. The Pythagorean theorem can then be used to find the hypotenuse.
According the Pythagorean Theorem
[tex]a^2+b^2 = c^2[/tex]
[tex](25)^2+(25)^2=c^2[/tex]
Now solving,
625 + 625 = [tex]c^2[/tex]
[tex]c^2[/tex] = 1250
Taking square root on both side, we get
c = 35.36 meters.
Hence, 35.36 meters long is each walkway.
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3 times what equals 5?
Answer: its 1.6667.
Answer:
Step-by-step explanation
3*X=5
X=5/3
X=1.67
By what factor would you need to change the radius of a sphere, such that its volume increased by a factor of 7? Please include step by step calculations!
The factor by which radius of the sphere be changed is 1.91, which is calculated by applying the concepts of surface area and volume on the assigned problem.
What do you mean by volume?
Volume is defined as the 3D measurement that deals with the amount of space required by an object. It is always calculated in cubic units. Its basic unit is cubic metre.
Calculation of the change in radius of sphere when its volume is increased by 7Let the radius and volume of sphere be r and v respectively
Volume of sphere, v = 3.16 × ( r )3 —- 1
Now, changed radius, R = xr
Where x is the factor, we need to calculate
Changed volume, V = 7v = 3.16 × ( R )3 -— 2
From equations 1 and 2, we get,
7v / v = ( R )3 / ( r )3
7 = ( xr )3 / ( r )3
7 = (x)3 × 1
Taking cube root both sides,
x = 1.913
Hence, the factor by which radius of the sphere be changed is 1.91.
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