Answers
SOLUTION:
Case: Volume of a Sphere
The volume of a sphere is the capacity it has. It is the space occupied by the sphere. The volume of a sphere is measured in cubic units, such as m3, cm3, in3, etc. The shape of the sphere is round and three-dimensional. It has three axes as x-axis, y-axis and z-axis which defines its shape. All the things like football and basketball are examples of the sphere which have volume.
Given:
The radius of the sphere is 2.2cm
Method:
The Volume of a sphere is given as:
[tex]V=\frac{4}{3}\pi r^3[/tex][tex]\begin{gathered} V=\frac{4}{3}\pi(2.2)^3 \\ V=\frac{4}{3}\pi\times2.2\times2.2\times2.2 \\ V=\frac{42.592}{3}\pi \\ V=14.1973\pi \\ V=44.6 \end{gathered}[/tex]Final answer:
The Volume of the Sphere to the nearest tenth is 44.6 cubic centimeters
Related Questions
In the United States, 1000 residents aged 15 or older were surveyed and 870 replied that they were satisfied with the water quality. The 90% confidence interval estimate of all U.S residents satisfied with their water quality is _________.
Answers
Given:
Here In the United States, 1000 residents aged 15 or older were surveyed and 870 replied that they were satisfied with the water quality is given.
Required:
Interval of 90% confidence level.
Explanation:
The formula to find the interval of confidence level is as below
[tex]=(p^{\prime}-z*\sqrt[]{\frac{p^{\prime}(1-p^{\prime})}{n}},\text{p' }+z*\sqrt[]{\frac{p^{\prime}(1-p^{\prime})}{n}})[/tex]Now we have to find the value of all
z=1.64485
p'=870/1000=0.87
n=1000
Now put the all values
[tex](0.87-1.64485*\sqrt[]{\frac{0.87(1-0.87)}{1000}},0.87+1.64485*\sqrt[]{\frac{0.87(1-0.87)}{1000}})[/tex][tex](0.87-0.0175,0.87+0.0175)[/tex][tex](0.8525,0.8875)[/tex]Final answer:
Confidence interval is (0.8525,0.8875)
Mary has been getting up extra early on school days so far she has woken up 6 out of 80 school days what percent of the days has she get been getting up early
Answers
Let's begin by identifying key information given to us:
Number of times she woke early (e) = 6
Total number of days (t) = 80 days
The percentage of days she's been getting up early is given by:
[tex]\begin{gathered} \text{\%}n\text{=}\frac{e}{t}\cdot100\text{\%} \\ \text{\%}n=\frac{6}{80}\cdot100\text{\%} \\ \text{\%}n=7.5\text{\%} \end{gathered}[/tex]Mary has gotten up early 7.5% of the days
how to solve 5x+5=2x+20
Answers
To do this you can subtract 5 from both sides of the equation
[tex]\begin{gathered} 5x+5=2x+20 \\ 5x+5-5=2x+20-5 \\ 5x=2x+15 \end{gathered}[/tex]Now you can subtract 2x from both sides of the equation
[tex]\begin{gathered} 5x=2x+15 \\ 5x-2x=2x+15-2x \\ 3x=15 \end{gathered}[/tex]Finally, you can divide by 3 both sides of the equation
[tex]\begin{gathered} \frac{3x}{3}=\frac{15}{3} \\ x=5 \end{gathered}[/tex]On the other hand, to check you replace the value of x found in the original expression
[tex]\begin{gathered} 5x+5=2x+20 \\ 5(5)+5=2(5)+20 \\ 25+5=10+20 \\ 30=30 \end{gathered}[/tex]Since a true equality is obtained, then it is true that the value of x is 5.
Find the greatest common factor of the following function 15x3+9x2-30x
Answers
ok
[tex]undefined[/tex]Consider ADEF with vertices D(-6,4) E(0,8), and F(2,-2) Find the coordinates of the vertices of the final image of ADEF after the similarity transformation Translation: (x,y) - (x + 8y + 4) Dilation: (x,y)-(1/2x, 1/2y) centered at (0,0) The coordinates of the vertices of the final image are D'' E" and F"
Answers
D''(1, 4), E"(4, 6) and F"(5, 1)
Explanation:Coordinates of original image: D(-6,4), E(0,8) and F(2,-2)
Translation: (x,y) to (x + 8, y + 4)
The coordinate becomes:
D(-6,4) = (-6+8, 4+4) = (2, 8)
E(0,8) = (0+8, 8+4) = (8, 12)
F(2,-2) = (2+8, -2+4) = (10, 2)
Dilation: (x,y) to (1/2x, 1/2y) centered at (0,0)
D" = (2, 8) to 1/2(2), 1/2(8) = (1, 4)
E" = (8, 12) to 1/2(8), 1/2(12) = (4, 6)
F" = (10, 2) to 1/2(10), 1/2(2) = (5, 1)
The coordinates of the vertices of the final image are D''(1, 4), E"(4, 6) and F"(5, 1)
Question 10The physical plant at the main campus of a large state university recieves daily requests to replace florecentlightbulbs. The distribution of the number of daily requests is bell-shaped and has a mean of 56 and a standarddeviation of 11. Using the Empirical Rule rule, what is the approximate percentage of lightbulb replacementrequests numbering between 56 and 89?Do not enter the percent symbol.ans =%
Answers
We know that the empirical rule states that 99.7% of the area is in the interval:
[tex](\mu-3\sigma,\mu+3\sigma)[/tex]In this case we notice that we are looking at the interval (56,89) in a normal distribution with mean 56 and standard deviation 11, which means that we area in the interval:
[tex](\mu,\mu+3\sigma)[/tex]which means that we have half the area of the interval mentioned before. Therefore, the approximate percentage between 56 and 89 is 49.85%
List the side lengths of △TUV in order from smallest to largest.
Answers
The sum of angles in a triangle is 180°
From the given angles given, if we are to determine the sizes of the angles from least to the highest, we will simply add the angles together and then equate to 180°
Solution
[tex](P+60)+(44P)+(P+74)=180[/tex][tex]\begin{gathered} 2P+44P+134=180 \\ 46P=180-134 \\ 46P=46 \\ P=\frac{46}{46} \\ P=1 \end{gathered}[/tex]The next step will be to find the values of each angle
[tex][tex][tex]Since we have the values of each angle of the triangles, we can list out the sides of the triangles from smallest to largest
we will have
The smallest to be UV
The bigger will be UT
The biggest will be TV
Thus, the order is
[tex]UVWhich side lengths represent the side of a right triangle
Answers
ANSWER
B) 7, 24, 25
EXPLANATION
The sides of a right triangle always satisfy the Pythagorean Theorem,
[tex]c^2=a^2+b^2[/tex]Where a and b are the legs, and c is the hypotenuse - which is the longest side.
Thus, to answer this question, we have to see for what set of lengths the sum of the squares of the shortest ones is equal to the square of the longest one.
• For 2, 3, 5,
[tex]\begin{gathered} 5^2=2^2+3^2 \\ 25=4+9 \\ 25=13\rightarrow FALSE \end{gathered}[/tex]So, this set does not represent a right triangle.
• For 7, 24, 25,
[tex]\begin{gathered} 25^2=7^2+24^2 \\ 625=49+576 \\ 625=625\rightarrow TRUE \end{gathered}[/tex]So, this set does represent a right triangle.
• For 7, 23, 25,
[tex]\begin{gathered} 25^2=7^2+23^2 \\ 625=578\rightarrow FALSE \end{gathered}[/tex]This set does not represent a right triangle.
• For 12, 16, 21,
[tex]\begin{gathered} 21^2=12^2+16^2 \\ 441=400\rightarrow FALSE \end{gathered}[/tex]This set does not represent a right triangle.
Hence, the side lengths that represent the lengths of the sides of a right triangle are 7, 24, 25.
Hi!! I have a homework problem i am not sure how to do.. I have missed some school due to health related issues so i’m a little behind. Thank you so much. I also have an example of the answer i have to give i can send to you
Answers
We need to find a quadratic model from the news or social media.
We can model the number of people watching a story after t time of posting it.
When you post it, there are no people watching it, it starts at y=0. Throughout the day more people are watching, but when time passes, the number of people starts to decrease.
The situation can be modeled by the quadratic function:
[tex]y=-0.5x^2+10x[/tex]Where x is the time in hours after posting the story, and y is the number of new people who watched the story in the past hour.
If we graph the function it looks like this:
As can be seen, at the beginning the number of people watching the story starts to increase, but after some time the number of people you reach out to with your story starts to decrease until no one will watch it.
The quadratic term of the function is:
[tex]-0.5x^2[/tex]The coefficient of the quadratic term determines how wide or narrow the graphs are, and whether the graph turns upward or downward. As we have a negative coefficient, then the parabola opens down.
The linear term is 10x, and it determines the position of the vertex.
There is a maximum value and it occurs at t=10 when you reach out to 50 people: (10,50).
The domain of the function is the set of possible x-values, as can be seen in the graph, it is [0,20], which means after 20 hours no one will watch your story.
The range is the set of y-values the function takes. It is [0,50]. It means you start with 0 people and the maximum number of people you reach out to in one hour is 50.
Question 3 of 10Which of the following are exterior angles? Check all that apply.
Answers
The possible angles are exterior angles:
[tex]\measuredangle2,\text{ }\measuredangle4\text{ and }\measuredangle6[/tex]The inner angles of the triangle are:
[tex]\measuredangle5\text{ and }\measuredangle1[/tex]We also can see that:
[tex]\measuredangle1\text{ }\cong\measuredangle3\text{ and }\measuredangle2\text{ }\cong\measuredangle4[/tex]Since
[tex]\measuredangle1\text{ and }\measuredangle3\text{ }[/tex]They are vertical angles formed by two intersecting lines, and 1 is congruent to 3. So, 3 is a
if measure of arc JI= (3x+2), measure of arc HLK= (15x+36), and measure of angle HMK=(8x-1), find the measure of arc HLK.
Answers
Step 1: Problem
If the measure of arc JI= (3x+2), a measure of arc HLK= (15x+36), and a measure of angle HMK=(8x-1), find the measure of arc HLK.
Step 2: Concept
Apply secant theorem
[tex]\text{HMK = }\frac{1}{2}(\text{ }JI\text{ + HLK )}[/tex]Step 3: Method
Given data
[tex]\begin{gathered} 8x\text{ - 1 = }\frac{1}{2}\text{ ( 3x + 2 + 15x - 36 )} \\ (8x\text{ - 1 ) }\times\text{ 2 = 18x - 34} \\ 16x\text{ - 2 = 18x - 34} \\ 34\text{ - 2 = 18x - 16x } \\ 32\text{ = 2x} \\ x\text{ = 32/2} \\ x\text{ = 16} \end{gathered}[/tex]The measure of arc HLK = 15x - 36
= 15(16) - 36
= 240 - 36
= 204
Step 4: Final answer
arc HLK = 204
Which of the graphs is represented by the following table:X-2 -1 0 1 2y1 2 3 4 5Click the button BELOW the correct graph.2+23442++22++2-3+432++2Show
Answers
Let us prepare the table from the deduced information as shown below:
We can use a graphing calculator to plot the points.
The graph is shown below:
What is the greatest common factor of 63, 84, and 105?
Answers
Answer:
Explanation:
The factors of 63 are: 1, 3, 7, 9, 21, 63
The factors of 84 are: 1, 2, 3, 4, 6, 7, 12, 1
Find the mean, median, mode, and range of this data: 47, 56, 57, 63, 89, 44, 56. If the answer is not a whole number, round to the nearest tenth.
Answers
The data given are 47, 56, 57, 63, 89, 44, 56
To calculate the mean:
The mean of the data can be defined as
[tex]undefined[/tex]You are playing a dice game and wondering whatnumber has been rolled the most so far.Find the mode of the following rolls:2, 1, 5, 6, 6, 3, 1, 4, 4, 3, 2, 1, 5, 1, 5, 3
Answers
Solution:
Concept:
Definition of mode:
Mode: The most frequent number—that is, the number that occurs the highest number of times.
The numbers are given below as
[tex]2,1,5,6,6,3,1,4,4,3,2,1,5,1,5,3[/tex]By rearranging the numbers, we will have
[tex]1,1,1,1,2,2,3,3,3,4,4,5,5,5,6,6,[/tex]From the set of numbers above, we will see that the number that occurs most is 1
Hence,
The mode of the rolls is
[tex]\Rightarrow1[/tex]A 12 ounce can of beans costs $0.88. What is the unit price per ounce?
Answers
To find the unit price per ounce of beans, you just need to divide the cost of the 12 ounce can by the number of ounces of beans in the can, it means, 12.
[tex]\frac{0.88}{12}=0.0733[/tex]The unit price per ounce is $0.0733, that rounded to the nearest hundredth is $0.07.
Malaysia hits a softball straight up at a speed of 120 ft / sec. Her bat contacts the ball at a height of 3 ft above the ground. This scenario can be modeled by the function f(x) = -16x^2 + 120x +3, where x represents the time elapsed (in seconds) since the ball was hit and f(x) represents the ball's height (in feet) a. What do the x intercepts represent in this scenario? b. When does the ball reach its maximum height? (What feature is being requested in this question?) a. x coordinate of vertex b. у coordinate of vertex C. x coordinate of roots d. y coordinate of roots c. Justify your answer to #b.d. What is the value of 3 in the context of the question?
Answers
a. x intercepts represent the time that the ball was at 0 feet.
b. answer is a. x coordinate of vertex
c. Since it is time you need, it is the x coordinate of vertex (maximum height)
I need help checking my answers to simplifying expressions. -2n-(9-10n)
Answers
We are given the following expression
[tex]-2n-(9-10n)[/tex]We are asked to simplify the above expression.
First of all, expand the parenthesis.
[tex]\Rightarrow-2n-9+10n[/tex]Now, combine the like terms together and simplify
[tex]\begin{gathered} \Rightarrow10n-2n-9 \\ \Rightarrow8n-9 \end{gathered}[/tex]Therefore, the simplified expression is
[tex]8n-9[/tex]I need help with a question for my math practice but I will have to see the picture to show you
Answers
The dependent variable is Y because the value depends on the number of people(x) who buy tickets
and y is the total cost of the tickets
Then the right option is D
the volume of the cone.Radius: 5 m, Height: 5 mnd to the nearest whole number.Volume[ ? ] m³
Answers
EXPLANATION
The volume of the cone is given as;
[tex]V=\frac{1}{3}\pi r^2h=\frac{1}{3}\pi\times5^2\times5=\frac{125}{3}\pi\approx131m^3[/tex]Answer: 131 cubic meteres
ActivityPlane A is descending toward the local airport, and plane B is ascending from the same airport. Plane A is descending at a rate of 2,500 feet perminute. Plane B is ascending at a rate of 4,000 feet per minute. If plane A is currently at an altitude of 14,000 feet and plane B is at an altitude of1,000 feet, how long will it take them to be at the same altitude? Represent time in minutes as the x-variable and altitude in thousands of feet asthe y-variable.
Answers
Let:
y1 = altitude of the plane A
y2 = altitude of the plane B
Let's find the equation for plane A:
[tex]\begin{gathered} m1=-2500 \\ y1=-2500x+b \\ for \\ 14000=-2500(0)+b \\ b=14000 \\ y1=-2500x+14000 \end{gathered}[/tex]And for plane B:
[tex]\begin{gathered} m2=4000 \\ y2=4000x+b \\ for \\ 1000=4000(0)+b \\ b=1000 \\ y2=4000x+1000 \end{gathered}[/tex]So:
[tex]\begin{gathered} y1=y2 \\ -2500x+14000=4000x+1000 \\ solve_{\text{ }}for_{\text{ }}x\colon_{} \\ 6500x=13000 \\ x=\frac{13000}{6500} \\ x=2 \end{gathered}[/tex]Answer:
2 minutes
What is the process between the second and third step? I don’t get how step 3 has 10^2 power.
Answers
ANSWER
Base raised to logarithm rule
EXPLANATION
Between the second and third steps, a property of logarithms was applied, the base raised to logarithm rule. This property states that when the base of the logarithm is raised to the logarithmic expression, the result is the argument,
[tex]a^{\log_a(x)}=x[/tex]In this case, we can see that it only says "log", so we can assume that the base of this logarithm is 10. To get from step 2 to step 3, we have to raise the base (10) to each side of the equation,
[tex]10^{\log(\frac{x+2}{x+1})}=10^2[/tex]And then, by the property stated above, we have the third line of this solution,
[tex]\frac{x+2}{x+1}=10^2[/tex]In the picture, the equation is inverted, but since there is an equal sign it is equivalent.
twice a number increased by 7 is 35 . find the number
Answers
Hello there. To solve this question, we'll have to remember how to translate a statement to a mathematical equation and then solve the equation for a number.
Twice a number increased by 7 is 35. We want to find that number.
In this case, say this number is n.
Twice this number is the same as multiplying this number by 2, hence
[tex]2n[/tex]Now increasing it by 7 is the same as adding 7 to the expression, therefore
[tex]2n+7[/tex]And this must be equal to 35
[tex]2n+7=35[/tex]Now we have to solve this equation for n.
Subtract 7 on both sides of the equation
[tex]2n=28[/tex]Divide both sides of the equation by a factor of 2
[tex]n=14[/tex]This is the number we're looking for.
x = 23 is a solution for the equation x/2 = 10 true or false
Answers
False
Here, we want to check if x = 23 is a solution for the equation
Firstly, we need to understand that what we have is a linear equation, an equation in which the highest power of the variable is 1. For this type of equations, what we expect is a single solution.
Thus;
[tex]\begin{gathered} \frac{x}{2}\text{ = 10} \\ \\ x\text{ = 2 }\times\text{ 10} \\ \\ x\text{ = 20} \end{gathered}[/tex]Since x = 20 is the only possible solution, then x = 23 as a solution must be incorrect and false
Solve for x ...........
Answers
We are given an equation
2(4x - 9) = 14
To solve for x
Firstly, we need to open the parenthesis
2 *4x - 2*9 = 14
8x - 18 = 14
Collect the like terms
8x = 18 + 14
8x = 32
Divide both sides by 8
8x/8 = 32 / 8
x = 32/8
x = 4
The answer is 4
The amount of medication in a patient's bloodstream decreases exponentially from the time the medication is administered. For a particular medication, a function that gives the amount of medication in Use this a patient's bloodstream t hours after taking a 100 mg function to find the amount of medication remaining after 2 hours. 39 mg 59 mg 49 mg 29 mg 1 2 3 4 5 28
Answers
Let's solve the function for when t = 2
[tex]\begin{gathered} A(2)=100(\frac{7}{10})^2 \\ A(2)=100\cdot\frac{7^2}{10^2} \\ A(2)=100\cdot\frac{49}{100} \\ A(2)=49 \end{gathered}[/tex]The answer would be 49mg
Which is the best buy?3-kilogram bag of lollipops for $10.505-kilogram bag of lollipops for $18.672-kilogram bag of lollipops for $9.224-kilogram bag of lollipops for $12.64
Answers
Given
3-kilogram bag of lollipops for $10.50
5-kilogram bag of lollipops for $18.67
2-kilogram bag of lollipops for $9.22
4-kilogram bag of lollipops for $12.64
Required
we need to find which among these is the best buy.
Explanation
For 3-kilogram bag for $10.50
[tex]\text{ cost of 1 kg bag=}\frac{10.50}{3}=3.5[/tex]For 5-kilogram bag of lollipops for $18.67
[tex]\text{ cost of 1 Kg bag=}\frac{18.67}{5}=3.73[/tex]for 2-kilogram bag of lollipops for $9.22
[tex]\text{ cost of 1 Kg bag=}\frac{9.22}{2}=4.61[/tex]for 4-kilogram bag of lollipops for $12.64
[tex]\text{ cost of 1 Kg bag =}\frac{12.64}{4}=3.16[/tex]Here the minimum cost per kg is for 4-kilogram bag of lollipops for $12.64. So it is the best buy.
Debbie has already taken 2 pages of notes on her own, and she will take 1 page during each hour of class. In all, how many hours will Debbie have to spend in class before she will have a total of 16 pages of notes in her notebook?
Answers
Based on the given information, we can define the following expression
[tex]y=2+1x[/tex]Where x represents hours and y represents pages.
For 16 pages, we have
[tex]\begin{gathered} 16=2+x \\ 16-2=x \\ x=14 \end{gathered}[/tex]Debbie will have to spend 14 hours to have 16 pages of notes.A cylinder popcorn tin had lid with a circumference of approximately 25.12 inches which expression can be used to describe the relationship between circumference and the diameter of the popcorn tin lid.
Answers
Answer:
The last choice: 25. 12 / pi
Explanation:
The relationship b
You are a game manufacturer. You and your team are trying to find the best pair of dice for a new board game you have made. You are examining the possible results of using one 12-sided die and one 12-sided die and rolling them together. If the random variable is defined as the sum of the two dice when rolled, what are the random variables?
Answers
As per given by the question,
There are given that, two 12-sided die and rolling together.
Now,
If there are two 12-sided die, and rolling together,
Then the total oucomes of the both die is,
[tex]12\times12=144[/tex]Now,