The correct statement regarding the volumes is given as follows:
B. The volume of half the sphere is 2/3 the volume of the cylinder.
How to obtain the volumes?The volume of a cylinder of radius r and height h is given by the equation presented as follows:
V = πr²h.
The volume of a sphere of radius r is given by the equation presented as follows:
V = 4πr³/3
The diameter is twice the radius, however they have the same unit, hence we can keep using the radius for the formulas.
If the diameter and the radius of the cylinder are equal to the height, the volume is given as follows:
V = πr² x r = πr³.
Hence the volume of the sphere is of 4/3 the volume of the cylinder, hence the volume of half the sphere is 2/3 the volume of the cylinder, meaning that option B is correct.
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Melissa is hosting a dinner party. She is making the main course and is assigning the invited guests to bring the following items: appetizer, side dish, salad, beverage, or dessert. Suppose there are nine guests invited to the party. Each is assigned to bring one of the items mentioned, and more than one guest can be assigned to an item so that each guest brings something to the dinner party.
a. Explain why assigning each guest an item to bring to the party is an example of a function.
Each guest being assigned to bring an item to the party is an example of a function because a unique output (the item to bring) is assigned to each input (the guest).
Why is this a function ?In this case, each guest is the input, and the item they are assigned to bring is the output. Each guest is assigned exactly one item, and there are no two guests assigned to bring the same item. This means that for each guest, there is a unique item that they are assigned to bring, and no two guests are assigned to bring the same item.
Therefore, the assignment of guests to items to bring to the dinner party is an example of a function because it assigns a unique output (the item) to each input (the guest), and it meets the mathematical definition of a function.
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three of the sides will require fencing and the fourth wall already exists. if the farmer has 100 feet of fencing, what are the dimensions of the region with the largest area?
Therefore, a maximum area the farmer can enclose with the 144 feet of fencing will be1250 square feet.
Let the length of the field = feet
And the width of the field = feet
Therefore, area of the rectangular field = Length × Width
A = x*y square feet
Since, length of the fence = 100 feet
And the farmer has to enclose three sides of the rectangle as shown in the figure attached.
Therefore, length of the fence = length + 2(width)
= (x+2y) feet
Hence, (x+2y)=100
x=100-2y
By substituting the value of 'x' in the expression for the area of the rectangular field.
A=(100-2y)y
A=-2y^2+144y
Find the derivative of the expression with respect to y ,
A'= -4y+100
A'=0
4y=100
y=25
A=-2*625+2500
A=2500-1250
A=1250 square feet
Therefore, maximum area the farmer can enclose with the 144 feet of fencing will be1250 square feet.
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how many distinct rectangles are there with integer side lengths such that the numerical value of area of the rectangle in square units is equal to $5$ times the numerical value of the perimeter in units? (two rectangles are considered to be distinct if they are not congruent.)
There are a total of 5 distinct rectangles that can be formed whose area is equal to 5 times the numerical value of the perimeter.
The area of a rectangle is given by:
A = L*W, where L- length of rectangle and W- width of rectangle,
The perimeter of a rectangle is given by:
P = 2*(L + W)
Since area of rectangle in square units is equal to 5 times the numerical value of the perimeter of the rectangle, on substituting the perimeter in terms of the area, we get:
P = 2(L + W) = 2( √(A/5) * √(5A))
Since the length of the sides must be integers, the possible values of area can be 5, 25, 125, and so on.
For each value of A, there can only be one possible rectangle that is formed. Therefore, only 5 distinct rectangles with integer side lengths that can be formed which meets the provided criteria.
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the length of a rectangle is five inches more than four times the width. the perimeter is inches. find the length and width.
In rectangle , The width is 8 and the length is 37.
What is a rectangle ?
A rectangle is a sort of quadrilateral with parallel sides that are equal to one another and four vertices that are all 90 degrees apart. Because of this, it is also known as an equiangular quadrilateral.
The term "parallelogram" can also be used to describe a rectangle because the opposing sides are equal and parallel.
90 = 2(x + 5 + 4x)
90 = 2(5x + 5)
90 = 10x + 10
80 = 10x
x = 8
So the width is 8 and the length is 37.
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The complete question is -
The length of a rectangle is five inches more than four times it’s width. If the perimeter is 90 inches, find its dimensions
there are 48 students in the kennedy middle school student council. the number of 8th graders is 12 fewer than three times the number of 7th graders
Answer:
3 * 15 - 12 = 33 So, the equation is saying that the result of 3 times 15 minus 12 is equal to 33.
Step-by-step explanation:
Let's call the number of 7th graders "x". Then, the number of 8th graders is 3 * x - 12.
The total number of students in the student council is 48, so we can set up an equation:
x + (3 * x - 12) = 48
Expanding and simplifying:
4x - 12 = 48
Adding 12 to both sides:
4x = 60
Dividing both sides by 4:
x = 15
So, there are 15 7th graders and 3 * 15 - 12 = 33 8th graders in the Kennedy Middle School student council.
Answer: 36 8th graders and 12 7th graders
Step-by-step explanation:
48-12=36
36 divided by 3=12
With this information, 12 7th graders and 36 8th graders
determine the most suitable system of coordinates to describe the spherical shell between two concentric spheres centered at (4,1,2). the inner sphere has a radius of 7 and the outer sphere has a radius of 13.
The spherical coordinate system is the most suitable system of coordinates to describe the spherical shell between two concentric spheres centered at (4,1,2).
A system of coordinates is a set of numbers used to describe the position of a point in space. There are different types of coordinate systems, each with its own advantages and disadvantages.
The spherical shell is the region of space between two spheres with the same center, but different radii. In this case, the center of both spheres is at (4,1,2) and the inner sphere has a radius of 7 while the outer sphere has a radius of 13.
One of the most commonly used coordinate systems for describing spheres is the spherical coordinate system.
To use this system of coordinates to describe the spherical shell, we first need to determine the radial distance for each point in the shell. This distance is between 7 and 13, since the shell lies between the inner and outer spheres.
Therefore, to describe a point in the spherical shell using spherical coordinates, we use the radial distance, polar angle, and azimuthal angle. These coordinates can then be used to plot the spherical shell and understand its geometry and properties.
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To select 10 students our of the class of 40 students, 40 names are placed in a hat and 10 names are drawn out of the hat. what type of sample is this?
In selecting 10 students out of the class of 40 students, if 40 names are placed in a hat and 10 names are drawn out of the hat, the type of sample is:
a random sampling.
Random sampling is a type of sampling method where each member of the population has an equal chance of being selected.
In this case, the population is the class of 40 students and the sample size is 10. By randomly selecting 10 names out of a hat, each student has an equal chance of being chosen for the sample.
This ensures that the sample is representative of the entire population, without any bias.
Random sampling is a widely used method for selecting a representative sample from a larger population.
It is important to use random sampling when conducting research or surveys in order to ensure that the results are reliable and accurate.
Random sampling helps to eliminate any potential bias that might be present in the sample if it was chosen through some other method. This is why it is important to use random sampling when selecting a sample from a larger population.
Complete Question:
"To select 10 students out of the class of 40 students, 40 names are placed in a hat and 10 names are drawn out of the hat. what type of sample is this?"
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in july, claire rode her bike 15 miles in 72 minutes, at her constant speed. a how long did it take her to ride 10 miles? show or explain your thinking.
To find the time it took Clare to ride 10 miles, we can use the concept of speed, which is defined as distance divided by time. In this case, Clare's constant speed was 15 miles in 72 minutes, so her speed is 15/72 miles per minute.
Using this speed, we can calculate the time it took her to ride 10 miles by dividing the distance by the speed:
Time = Distance / Speed
Time = 10 miles / (15/72 miles per minute)
Time = 10 * 72 / 15 minutes
Time = 43.2 minutes
So, it took Clare approximately 43.2 minutes to ride 10 miles at her constant speed of 15 miles in 72 minutes.
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Dana tried to evaluate an expression. Here is her work:
45 [(4 + 3) (60 ÷ 12 - 2)]
-
=
= 45 [7 (60+ 10)]
= 45 - [7.6]
= 45 - 42
= 3
Is Dana's work correct?
Step 1
Step 2
Step 3
Step 4
Dana is not correct, she has done mistake in the second step.
What is Expression?An expression is combination of variables, numbers and operators.
The given expression is 45 [(4 + 3) (60 ÷ 12 - 2)]
45 [(4 + 3) (60 ÷ 12 - 2)]
The first step is 45 [7 (60÷ 10)], it is correct
The second step 45- [7.6] is wrong because 45 is a multiple of [7 (60÷ 10)]
45(42)
When we multiply 45 with 42 we get
1890
Hence, Dana is not correct, she has done mistake in the second step.
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The ratio of the measures of the angles in a triangle is 8:3:4. Find the measure of the largest angle.
BOTH QUESTIONS IN THE PICTURE
Will give brainliest !!!
Answer:
Only can do the first one
Let's call the measures of the angles in the triangle x, 3x, and 4x.
According to the ratio, we have:
x : 3x : 4x = 8 : 3 : 4
To find the value of x, we can set up a proportion:
8/x = 3/(3x) = 4/(4x)
Cross multiplying, we get:
8x = 12
So, x = 12/8 = 3
Therefore, the measures of the angles in the triangle are 3x, 3(3x), and 4(3x).
The measure of the largest angle is 4x = 4(3) = 12.
Complete the frequency table:
Method of Travel to School
Walk/Bike Bus Car Row totals
Under age 15 18 165
Age 15 and above 65 195
Column totals 152 110 98 360
What percentage of students age 15 and above travel to school by bus? Round to the nearest whole percentage.
36%
26%
45%
50%
The percentage of students age 15 and above travel to school by bus is given as follows:
25.64%.
How to obtain the percentage?The percentage is obtained applying the proportions in the context of this problem.
A proportion is applied because a percentage is calculated with the division of the number of desired outcomes by the number of total outcomes, a result which is then multiplied by 100%.
The total outcomes are given as follows:
195 students 15 and above that travel by bus.
The desired outcomes are given as follows:
195 - 65 - (98 - 18) = 50 students 15 and above that travel by bus.
Hence the percentage is given as follows:
50/195 x 100% = 25.64%.
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the u shaped curve created by a quadratic equation
Answer: it is called a parabola
Step-by-step explanation:
Simplify a/2b times bc/a
Answer:
[tex]\dfrac{c}{2}[/tex]
Step-by-step explanation:
We can simplify the given expression by canceling like terms.
Remember that anything divided by itself is 1.
ex:
[tex]\dfrac{2x}{x} = 2 \cdot \dfrac{x}{x} = 2 \cdot 1 = 2[/tex]
Applying this logic to the given expression:
[tex]\dfrac{a}{2b} \cdot \dfrac{bc}{a}[/tex]
↓ simplify multiplication of fractions
[tex]\dfrac{a \cdot bc}{2b \cdot a}[/tex]
↓ rewrite to align like variables
[tex]\dfrac{a \cdot b \cdot c}{a \cdot b \cdot 2}[/tex]
↓ separate out variables that are divided by each other
[tex]\dfrac{a}{a} \cdot \dfrac{b}{b} \cdot \dfrac{c}{2}[/tex]
↓ represent them as 1
[tex]1 \cdot 1 \cdot \dfrac{c}{2}[/tex]
↓ rewrite without unnecessary 1's
[tex]\dfrac{c}{2}[/tex]
The amount Troy charges to mow a lawn is proportional to the time it takes him to mow the lawn. Troy charges $50 to mow a lawn that took him 1.5 hours to mow. Which equation models the amount in dollars, d, Troy charges when it take him, h, hours to mow a lawn? Group of answer choices h = 50d d = 75h d = 50h h = 75d
The equation d = (100/3)h models the amount in dollars, d, Troy charges when it take him, h, hours to mow a lawn.
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
For example, 3x – 5 = 16 is an equation.
Given,
Troy charges $50 to mow the lawn that took him 1.5 hours to mow
Charges are proportional to time.
If charges are d and time is h
then,
Ratio of Charges to time
⇒ d/h = 50/1.5
⇒ d/h = 100/3
⇒ d = (100/3)h
Hence, d = (100/3)h is the equation that can be used to calculate the amount with time.
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Which one of the following simplifications is incorrect ?
94 0 16x4 = 12x4
. در 0
3/ 3.
26 = 22
=
0 2 0 42 = 2017
3
O 264 0 481 = 12
The expression that is incorrectly simplified is given as follows:
[tex]\sqrt[4]{9x^4} \times \sqrt[4]{16x^4} = 12x^4[/tex]
How to simplify the expressions?The expressions in this problem involve roots, which also can be written as exponents, hence exponential rules such as multiplication of terms with same base and different exponents, along with the power of power rule, are used.
For the first expression, we have that the fourth root can be expressed as an exponent of 1/4, hence:
fourth root of 9x^4 = (9x^4)^(1/4).fourth root of 16x^4 = (16x^4)^(1/4).The coefficients however, stay inside the root, meaning that the result of 12 is false, and the statement is incorrect.
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How do I solve this question?
The percentage of total budget for insurance, housing and entertainment is 3%. 13.3% and 4% respectively.
What is percentage?A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.
The total budget given is $4100 for the month.
The percentage of total budget for insurance is:
123/ 4100 (100) = 3%
The percentage of total budget for housing is:
574/ 4100 (100) = 13.3%
The percentage of total budget for entertainment is:
164/4100 (100) = 4%
Hence, the percentage of total budget for insurance, housing and entertainment is 3%. 13.3% and 4% respectively.
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There is a strong positive correlation between the number of umbrellas sold in a town and the water levels in nearby rivers.
What is a possible reason for why this correlation exists?
Question 9 options:
A melting glacier upstream of the rivers
A large number of tourists in the area
A new shopping mall opened in the area
High levels of rainfall
A possible reason for the strong positive correlation is high levels of rainfall. (fourth option)
What is correlation?Correlation is a measure used in statistics to measure the linear relationship that two variables have.
When two variables have a positive correlation, it means that the two variables move in the same direction. In this question, the number of umbrellas sold increase when water levels in streams increase. An reason for this could be that the increased water levels lead to higher rate of rainfall which would lead to people buying more umbrellas.
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Stone runs 1 mile five times a week. How many miles does 4 he run each week? Write the equation you would use to solve. Then, fill in the grid with your answer. Tip: Fill in your answer as a fraction greater than 1.
The number of miles in 4 weeks is 20 mules
How to determine the number of milesFrom the question, we have the following parameters that can be used in our computation:
Stone runs 1 mile five times a week
This means that the rate is
Rate = 1 mile * 5 per week
So, we have
Rate = 5 miles per week
For 4 weeks, we have
Distance = 5 * 4
Evaluate
Distance = 20 miles
Hence, the distance is 20 miles
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What do I do I need help and answers ASAP class ending in 2 mins
Answer:
Step-by-step explanation:
5=19600
10=17200
15=14800
20=12400
it should take about 46 mins to land and the final question should be B
find the difference of 24 - 3k and 5k - 11
Answer:
35 - 8k
Step-by-step explanation:
(24 - 3k) - (5k - 11)
= 24 - 3k - 5k + 11
= 35 - 8k
PLEASE HELP! EASY MATH!
The length of PR in the triangle is 229 feet.
How to find sides of similar triangle?To indirectly measure the distance across a river, Savannah stands on one side of the river and uses sight lines to a landmark on the opposite bank. Savannah draws the diagram below to show the lengths and angles that she measured. Let's find PR, the distance across the river.
Triangle PRE is similar to triangle POC. Therefore, similar triangles are the triangles that have corresponding sides in ratio to each other and corresponding angles congruent to each other.
Hence,
PR = x
165 / 255 = x / x + 125
cross multiply
165(x + 125) = 255x
165x + 20625 = 255x
165x - 255x = - 20625
-90x = - 20625
divide both sides of the equation by -90
x = - 20625 / - 90
x = 229.166666667
Therefore,
PR = 229 ft
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Directions: Based on the information given in the following problem, compute the gross pay.
Regular hours worked: 40
Overtime hours worked: 8
Regular rate of pay: $7.75 per hour
gross pay: $
The gross pay based on the given information is $372.
What is gross pay?Gross Salary is the amount of salary after adding all benefits and allowances but before deducting any tax, Net Salary is the amount that an employee takes home.
Given that, regular hours worked: 40 and overtime hours worked: 8.
Regular rate of pay: $7.75 per hour
So, gross pay = 40×7.75+8×7.75
= $372
Therefore, the gross pay is $372.
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What does a correlation coefficient of 0 indicate?
Answer:
the coefficient of 0 indicates that there is no relationship between the two values
Proving Rectangles, Rhombi, and Squares in the Coordinate Plane
Classify as the most specific shape possible
1. A(8,3) B(7,8) C(2,7) D(3,2)
What formulas do I use to solve this? (My own question not in text)
The most specific shape is rhombus for the co-ordinates A(8,3) B(7,8) C(2,7) D(3,2).
What is a rhombus?A rhombus is one type of parallelogram and has 4 sides and 4 vertices.
Every side is equal in length and opposite angles are equal.
We have four co-ordinates,
A(8,3) B(7,8) C(2,7) D(3,2).
The length of the segment AB = √{(8 - 7)² + (3 - 8)²} = √26 units.
The length of the segment BC = √{(7- 2)² + (8- 7)²} = √26 units.
The length of the segment CD = √{(2 - 3)² + (7 - 2)²} = √26 units.
The length of the segment AD = √{(8 - 3)² + (3 - 2)²} = √26 units.
That means, all the sides are equal.
Now, let the slope of AC = slope of BD
(7 - 3)/(2 - 8) ≠ (2 - 8)/(3 - 7)
The slope of the diagonal is not equal.
Therefore, the shape is rhombus.
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. Seth’s father is thinking of buying his son a six-month movie pass for $40. With the
pass, matinees cost $1.00. If matinees are normally $3.50 each, how many times must
Seth attend in order for it to benefit his father to buy the pass?
Seth must attend the move 17 times
How to find the number of times Seth have to attendThe difference in price of matinee is
= price of matinee normally - price of matinee with movie pass
= 3.50 - 1
= 2.5
We divide to find the number of times
= 40 / 2.5
= 16
In other that Seth's father benefits Seth must attend at least 17 times
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What is -a^-2 if a=-5?
Answer:
-0.04ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ
Answer:
1/-25
Step-by-step explanation:
First we plug it in
-(-5)^-2
Then since the exponent is negative, we take the equation and put it under one which makes it a positive.
1/-(-5)^2
Then we solve the exponent
1/-(25)
Since it's a negative outside the parenthesis we treat it as multiplying it by -1 in which case we'd get
1/-25
Estimate the number of rabbits at the farm in 2016
the Estimated number of rabbits will be 80 in the year 2016.
What is the function?A relationship between a group of inputs and one output is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function. Typically, f(x), where x is the input, is used to represent a function.
Given a table of Rabit at a zoo in the table below,
2008 14
2009 24
2010 30
2011 39
2012 45
2013 57
M: 2010.5 M: 34.8333
To estimate the number of rabbits in the zoo in 2016 we need to find the linear equation;
Sum of X = 12063
Sum of Y = 209
Mean X = 2010.5
Mean Y = 34.8333
Sum of squares (SSX) = 17.5
Sum of products (SP) = 143.5
Regression Equation = ŷ = bX + a
b = SP/SSX = 143.5/17.5 = 8.2
a = MY - bMX = 34.83 - (8.2*2010.5) = -16451.26667
ŷ = 8.2X - 16451.26667
For x = 2016
y = 8.2* 2016 - 16451.26667
y = 79.933 or 80
therefore, the Estimated number of rabbits will be 80 in the year 2016.
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Complete question:
Convert each equation to slope intercept form, then determine if the lines are parallel, perpendicular, or neither(intersecting).
A) 2x + 3y = 9
B) 2y - 3x = 8
The slope-intercept form of the equations are y = -2x/3 + 3 and y = 3x/2 + 4 and the line are perpendicular to each other.
What is the slope intercept form of an equation of a line?The meaning of slope intercept form is the equation of a straight line in the form y = mx + b where m is the slope of the line and b is its y-intercept.
Given that two equations, we need to find their slope intercept form, and determine if the lines are parallel, perpendicular, or neither (intersecting).
The given equations are;
A) 2x + 3y = 9
B) 2y - 3x = 8
The general equation of a line, in a slope intercept form, is given by,
y = mx + c, where m is the slope of the line and c is the y-intercept,
A) 2x + 3y = 9
3y = 9-2x
y = -2x/3 + 3....(i)
B) 2y - 3x = 8
2y = 3x+8
y = 3x/2 + 4.....(ii)
Here, the slope are -2/3 and 3/2, we can say that both the slopes are negative reciprocal of each other,
We know that slopes of two perpendicular lines are negative reciprocal of each other,
Therefore, the given two line are perpendicular to each other.
Hence, the slope-intercept form of the equations are y = -2x/3 + 3 and y = 3x/2 + 4 and the line are perpendicular to each other.
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Please help thank u!!
Answer:
see below
Step-by-step explanation:
shift B right by 4units & up by 2 units to have point B overlap point A so the 2 circles center will be overlapped
* image is provided*
I know it might be hard to see but I really need help I’ll give points!!!!
Plssss help!!!!
From the data analytics of this table, the right statements are A,C and D.
What is called data in mathematics?In mathematics, data is a collection of facts and figures that can take any shape, whether it be numerical or not. You can calculate numerical data, which is always gathered in number form and includes things like student test results, employee salaries, football team member heights, etc.
Given in the table of students which are watching movies or not
Yes No Total
Boys 6 8 14
Girls 9 7 16
Total 15 15 30
Statement (A): 27% of sampled students are boys who did not watch a movie?
27% of total students = 27 * 30/100
= 810/100
≈ 8 boys
So the statement (A) is true.
Statement (B): 30% of sampled girls watched a movie?
30% of sampled girl = 30 * 16/100
= 480/100
≈ 5 girls
So the statement (B) is false.
Statement (C): 50% of sampled students did not watch a movie?
50% of total students = 50 * 30/100
= 1500/100
= 15 students
So the statement (C) is true.
Statement (D): 57% of sampled boys did not watch a movie?
57% of total students = 57 * 14/100
= 798/100
≈ 8 boys
So the statement (D) is true.
SO that, the right statements are A,C and D.
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