The area of hemisphere is given by 3πr² and the volume of the hemisphere is given by 2/3πr³.
When we divide the sphere into two equal halves, we get a hemisphere. The curved surface area of the hemisphere plus the base area will add up to the hemisphere's total surface area. Here, the foundation has a circular shape. We may discover many examples of hemispheres in daily life, such as how our planet Earth is divided into the southern and northern hemispheres.
A hemisphere's surface area is the sum of all of its faces. When a sphere is cut along a plane that runs through its centre, a three-dimensional shape known as a hemisphere is created. A hemisphere is, in other terms, one-half of a sphere.
3πr²
A hemisphere has one flat circular base and a curving surface. The quantity of unit cubes that can fit inside a hemisphere is known as its volume.
2/3πr³.
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let r be the region bounded by the following curves. find the volume of the solid generated when r is revolved about the y-axis.
The volume of the solid generated when r is revolved about the y-axis is 3.2π.
Volume of Solid:
The volume of a solid is a measure of the space occupied by an object. This article explains how to calculate the volume of solids and the volume of regular and irregular solids.
According to the Question:
We know that:
A ( y ) = π × (f₁ (y)² - f₂ (y)²)
where,
f₁ (y) is the function further away from y axis
f₂ (y) is the function closer to y axis
f₁ (y) = 2
f₂ (y) = 2y²
A ( y ) = π × [2² - (2y)²]
A (y) = π × (4 - 4y²)
A (y) = 4π (1 - y²)
Now,
Computing V (y)
[tex]V =\int\limits^1_0 {A(y)} \, dy[/tex]
[tex]V = 4\pi \int\limits^1_0 {(1-y^2)} \, dx[/tex]
V = 4π (1 - 0.2)
V = 3.2π
Therefore, The volume of the solid generated when r is revolved about the y-axis is 3.2π.
Complete Question:
Let R be the region bounded by the following curves. Use the disk or washer method to find the volume of the solid generated when R is revolved about the y-axis. y= square root of (x/2) , y=0 , x=2
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What is the result 3 x 6 ?
Answer:
Step-by-step explanation:
3*6=18
9 people on a bus in Seattle and the average of their yearly income is $65,000. At the next stop, the highest paid person on the bus (with an income of $120,000 per year) gets off and Bill Gates gets on. Mr. Gates makes 7.6 Billion dollars a year. What is the new average and median salary of people on the bus?
The new average salary of the people on the bus is $84,44,96,111.11 and the median salary will not change and will remain same.
Given, we know that average salary of the 9 people on the bus is $65,000.
Formula for Average = sum of salary of all people/ the number of people.
Let us say average salary of first 8 people is 'S'. Given, salary of the 9th guy on the bus is $120,000 Now, we can write it like this :
⇒$65,000 = (S + $120,000)/9
⇒585,000 = S + $120,000
⇒S = $465,000
Therefore, average salary of 8 people is $465,000 after the 9th guy gets off. Now Bill Gates enters the bus with a salary of $7,600,000,000. New average salary :
⇒ (S + $7,600,000,000) / 9
⇒$84,44,96,111.11
Median will not change since, The median of a set of numbers is the number in the middle when you list them in order. For example, the median of {1, 3, 6, 9, 13} is 6. If you replace the highest number with a different number, the median will not change. In this example, {1, 3, 6, 9, 100} still has a median of 6.
Therefore, the new average yearly income of the people on the bus along with Bill Gates is $84,44,96,111.1111.
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A ball is thrown upwards in the air. The height h(t) in feet, of the ball above ground t seconds after being thrown is determined by the expression h(t)=-16t^2+20t+2.
What is the meaning of 2 in the expression?
Answer:
1. The ball is thrown from a height of 2 ft
Step-by-step explanation:
Since 2 does not have a variable that would be the y-intercept; the y-intercept it where the ball is first getting thrown from.
Rob has $7,869 in an account that earns 13% interest compounded annually.To the nearest cent, how much will he have in 5 years?
Step-by-step explanation:
Principal (P)=$7869
Rate (R)= 13%
Time (T)= 5 years
Compound Interest (CI)=?
We know that,
CI = P { (1+R/100)^T -1}
= $7869 {(1+13/100)^5 -1}
= $7869 {(113/100)^5 -1}
= $7869 {(1.13)^5 -1}
= $7869 {1.84-1}
= $7869 × 0.84
= $6609.96
Compound Amount= CI+p
= $6609.96+7869
= $14478.96
Therefore, he will have $14478.96 after 5 years.
The following table shows different choices for making a shake at a restaurant. DeeDee will randomly select one dairy, one fruit, and one topping choice. What is the probability that DeeDee's shake will be made with yogurt, pineapple, and cherries?
Answer:
1/27
Step-by-step explanation:
Probability of DeeDee choosing Yogurt in diary = 1/3
Probability of DeeDee choosing pineapple as fruit = 1/3
Probability of DeeDee choosing cherries as toppings = 1/3
So the Probability of DeeDee's shake being made with yogurt pineapple and cherries = 1/3×1/3×1/3 = 1/27
Faith is going to use a computer at an internet cafe. The cafe charges $0. 80 for every minute using a computer on top of an initial charge of $3. Make a table of values and then write an equation for C,C, in terms of t,t, representing the total cost of using a computer for tt minutes at the internet cafe. Number of Minutes Total Cost to Use Computer
00 3\hspace{3px}\color{green}{\checkmark}3✓3
11 3. 80\hspace{3px}\color{green}{\checkmark}3. 80✓3. 80
22 4. 60\hspace{3px}\color{green}{\checkmark}4. 60✓4. 60
33 5. 40\hspace{3px}\color{green}{\checkmark}5. 40✓5. 40
Answer: C=C=
The equation for the total cost of using a computer for t minutes at the internet cafe is C = 0.80t + 3
The cost of using a computer at the internet cafe can be represented by a linear equation, where C is the total cost and t is the number of minutes used. The equation can be written as C = 0.80t + 3, where 0.80 is the cost per minute and 3 is the initial charge.
To make a table of values, we can plug in different values of t into the equation and solve for C
Number of Minutes (t) Total Cost to Use Computer (C)
0 C = 0.80(0) + 3 = 3
1 C = 0.80(1) + 3 = 3.80
2 C = 0.80(2) + 3 = 4.60
3 C = 0.80(3) + 3 = 5.40
So the equation for the total cost of using a computer for t minutes at the internet cafe is C = 0.80t + 3.
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The value where the histogram balances when supported at that point is called ____.
The value where the histogram balances when supported at that point is called the mode of the distribution.
The mode of distribution is the value that appears most frequently in the data set. It is often used as a measure of central tendency, along with the mean and median. The mode is especially useful when dealing with categorical or discrete data, where the possible values are limited and well-defined.
For example, the mode of a list of test scores might be the score that occurs most frequently, indicating the most common level of performance. In a histogram, the mode is the value where the distribution is highest, or where the histogram balances when supported at that point.
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Solve ( x + 6 ) ^2 = 64
A . X = 8 or x = -8
B . X = 2 or x = -2
C . X = 2 or x = -14
D . X = 4 or x = -16
The required solutions to the equation are x = 2 or x = -14.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
Starting with the equation:
(x + 6)² = 64
Taking the square root of both sides, we get:
x + 6 = ±8
Solving for x, we have two cases:
Case 1:
x + 6 = 8
x = 8 - 6
x = 2
Case 2:
x + 6 = -8
x = -8 - 6
x = -14
Therefore, the solutions to the equation are x = 2 or x = -14.
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39.5 Degrees Celsius to Fahrenheit
To convert temperatures in degrees Celsius to Fahrenheit, multiply by 1.8 (or 9/5) and add 32.
39.5 degrees Celsius is equal to 103.1 degrees Fahrenheit.
Temperatures, across the worlequal td, are measured either in Fahrenheit(the US temperature scale) or Celsius(the metric scale), two of the most popular and widely used scales.Temperature Conversion – Degrees Celsius into Degrees Fahrenheit.
Celsius to Fahrenheit conversion formula is all about converting the temperature denoting in Celsius to Fahrenheit. As mentioned earlier, the temperature of boiling (hot) water in Celsius is 0 degrees and in Fahrenheit is 21 degrees, the formula to convert C to F is
F = C x (9/5) + 32To convert 39.5 degrees Celsius to Fahrenheit, you can use the formula:
°F = (°C × 9/5) + 32
Substituting 39.5 for °C, we get:
°F = (39.5 × 9/5) + 32
°F = (71.1) + 32
°F = 103.1
Therefore, 39.5 degrees Celsius is equal to 103.1 degrees Fahrenheit.
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Find the slope of the line tangent to the y-intercept of the parabola:y=(x+2)^2−4
The slope of the line tangent to the parabola's y-intercepty = [tex](x+2)^2-4[/tex] is 4.
We must first get the parabola's y-intercept in order to determine the slope of the line tangent to it.
We enter x=0 into the equation to obtain the y-intercept:
[tex]y = (x + 2)^2 - 4[/tex]
[tex]y = (0 + 2)^2 - 4[/tex]
y = 4 - 4
y = 0
Hence, the parabola's y-intercept is (0, 0).
The derivative of the parabola's equation must then be determined.
[tex]y = (x + 2)^2 - 4\\y = x^2 + 4x + 4 - 4\\y = x^2 + 4x[/tex]
dy/dx = 2x + 4
By adding x=0 to the derivative, we can now get the slope of the tangent line to the y-intercept:
dy/dx = 2x + 4
dy/dx = 2(0) + 4
dy/dx = 4
Hence, the slope of the line tangent to the parabola's y-intercepty = [tex](x+2)^2-4[/tex] is 4.
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Solve the system by substitution.
y=-7x-3
5x+4y= -35
Answer: (x,y)=(1,-10)
Step-by-step explanation:
y=-7x-3
5x+4y=-35
substitute the value of y
5x+4(-7x-3)=-35
solve the equation
x=1
substitute the value of x
y=-7 x 1-3
solve the equation
y=-10
A possible solution is
(x,y)=(1,-10)
Check the solution
-10=-7 x 1-3
5 x 1+4 x (-10)=-35
simplify
-10=-10
-35=-35
The ordered pair is a solution
(x,y)=(1,-10)
Based on the results, what is the probability of needing more than 6 rolls to get doubles??
___
The probability of needing more than 6 rolls to get doubles is,
⇒ 3 / 20
What is mean by Probability?The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.
Given that;
Each student in Mr. Jones class has two standard number cubes.
Hence, The probability of needing more than 6 rolls to get doubles is,
Total number of cubes = 20
More than 6 rolls = 3
Thus, The probability of needing more than 6 rolls to get doubles is,
⇒ 3 / 20
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Due nowww please help mee
Answer:
Step-by-step explanation:
I cant see
Rob has $7,869 in an account that earns 13% interest compounded annually.To the nearest cent, how much will he have in 5 years?
Answer:
$14,498.1
Step-by-step explanation:
To find the amount Rob will have in 5 years with compound interest, we can use the formula:
A = P (1 + r/n)^(nt)
where:
A = the future value of the investment
P = the principal amount invested
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the number of years
In this case, we have:
P = $7,869 (the principal amount)
r = 13% or 0.13 (the annual interest rate)
n = 1 (the interest is compounded annually)
t = 5 (the number of years)
Substituting these values into the formula, we get:
A = $7,869 (1 + 0.13/1)^(1*5)
A = $7,869 (1.13)^5
A = $14,964.92
Therefore, to the nearest cent, Rob will have $14,964.92 in 5 years.
how to convert 151 cm in feet?
On converting the length , 151 centimeter is equivalent to 4.954 feet .
The Units of measuring the length are used to measure the distance between two points of an object. There are several units of measuring length , which are : meter , centimeter , kilometer , feet .
We have to convert 151 cm to feet,
So , we use the conversion factor of 0.03281 feet per centimeter , which means that there are approximately 0.03281 feet in 1 centimeter.
So , to convert 151 cm to feet, we multiply the number of centimeters by this conversion factor ;
Using this method, we get ;
⇒ 151 cm × 0.03281 feet/cm = 4.954 feet ;
Therefore, 151 cm is equal to approximately 4.954 feet.
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If the inflation rate was 3% last year and John's salary grew 4%, how much did the purchasing power of his salary change?
John's purchasing power increased by 0.97%.
What is the inflation?
The definition of inflation in the field of economics is "mean increased money supply, but the general public often refer to a sustained increase in the general price level of goods and services in an economy over a period".
If the inflation rate was 3% and John's salary grew 4%, his salary increased more than the rate of inflation. However, his real increase in purchasing power depends on the difference between his salary growth rate and the inflation rate.
To calculate the change in John's purchasing power, we can use the following formula:
Change in purchasing power = (1 + Salary growth rate) / (1 + Inflation rate) - 1
Plugging in the values, we get:
Change in purchasing power = (1 + 0.04) / (1 + 0.03) - 1
Change in purchasing power = 1.01 / 1.03 - 1
Change in purchasing power = 0.0097 or 0.97%
Hence, John's purchasing power increased by 0.97%.
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Greg is building birdhouses in shop class. The amount of wood he has on hand determines how many birdhouses he can build. w = the amount of wood Greg has on hand b = the number of birdhouses Greg can build Which of the variables is independent and which is dependent?
Answer:
Step-by-step explanation:
w is the independent
b is the dependent
Think of it this way: the number of birdhouses depends on the amount of wood available.
what is the 58 percentage conversion in decimal ?
The conversion value of the given quantity 58 percentage in decimals is equal to 0.58.
Percentage is that quantity of mathematics which represents the fraction of 100.One percentage converted to decimals is written as :
1 percentage = ( 1 / 100 )
= ( 0.01 )
Now Get the value in decimals for 58 percentage using conversion factor we have ,
= 58 percentage
= ( 58 / 100 )
= ( 0.58 ) in decimal form
Therefore, the value which we get after conversion of percentage to decimals is equal to 58 percentage = 0.58 in decimals.
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Which graph shows the solution to the system of linear equations?
y = 2x
y=x-2
The solution to the system of linear equations y = 2x and y = x - 2 is (2, 0).
Please help me
five subtracted from the product of 6 and a number is less than or equal to 29. Write as an inequality
Answer:
6x-5 ≤ 29
Step-by-step explanation:
Let translate each part of the sentence into an equation or expression.
1. "five subtracted from the product of 6 and a number"
Lets say the "number" is x. The product of 6 and a number would be: 6x'five subtracted from" would be -5So the "five subtracted from the product of 6 and a number" would be 6x-5.2. "is less than or equal to 29"
using just math symbols, this would be ≤ 293. Assemble the two expression into an equation
Combine parts 1 and 2 into an equation.
6x-5 ≤ 29
=============
Extra
6x-5 ≤ 29 can be simplified:
6x ≤ 29+5
6x ≤ 36
x ≤ 6
A ballet company has sold 540 tickets for the next performance. Tickets for the center section are $56 while tickets for the left and right sections are $38. They have sold $24,120 in tickets. How many $56 and $38 tickets were sold?
The number of $56 dollar tickets to center section was 200 and the number of tickets costing $38 to the left and right sections were 200.
Let us consider the number of tickets to the center section be x and right and left sections be y.
Here the total number of tickets sold are 540.
So, x+ y = 540 ---------> i
The cost of tickets cost $56 will be 56x
The cost of tickets cost $38 will be 38y.
The total cost was given as $24120
So, 56x+ 38y = 24120 -----------> ii
Multiplying equation i with 56,
56x + 56y = 30240 ------------> iii
Subtracting equation ii from equation iii
56x+ 56y = 30240
- 56x + 38y = 24120
So 18y = 6120
y = 6120/18 = 340
Since x+ y = 540
x+ 340 = 540
x = 540- 340 = 200
So the number of $56 ticket sold is 200 and the number of $38 ticket sold is 340.
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Anyone can help? Please..
The correct option is A: A linear pair is two adjacent, supplementary angles.
Describe Supplementary Angles?Supplementary angles are a pair of angles whose measures add up to 180 degrees. In other words, if we place two angles side by side, and their measures add up to 180 degrees, then they are said to be supplementary.
For example, if we have an angle with a measure of 120 degrees, then its supplementary angle would have a measure of 60 degrees, since 120 + 60 = 180. It's important to note that the two angles in a pair of supplementary angles do not have to be adjacent, meaning they can be located anywhere in a figure, as long as their measures add up to 180 degrees.
Supplementary angles play an important role in geometry and mathematics, especially when it comes to solving problems involving angles. For instance, if we know that two angles are supplementary, and we know the measure of one of the angles, we can easily calculate the measure of the other angle by subtracting the known measure from 180 degrees.
In addition, supplementary angles are often used in real-life situations, such as when designing buildings, bridges, or other structures that require precise measurements of angles. Overall, understanding the concept of supplementary angles is crucial for anyone who wants to study and understand geometry and mathematics.
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how much is 140 lbs in kg
On converting the weight of 140 lbs to Kilogram , we get that 140 lbs is equivalent to 63.49 Kg .
The Conversion Factors is used to convert the weight between pounds and kilograms. that means : To convert 1 pound to kilograms , We multiply the number of pounds by 0.4535 .
In this case , we have to convert 140 pounds to kilograms ;
So , we multiply the given weight in pounds with 0.4535 .
On multiplying ,
We get ;
⇒ 140 pounds = 140 × 0.4535 Kg ;
⇒ 140 pounds = 63.49 Kg .
Therefore , 140 lbs is approximately equal to 63.49 Kg .
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i need help on this equation
Answer:
c
Step-by-step explanation:
DO THE MATH!!!!!!!PLEASE
A shipment of 8 tons of sugar is separated into containers of equal size. If the shipment fills 3 3/5 containers, how much sugar can one container hold?
THIS IS TIMED HELP ME OUT
Therefore, one container can hold 20/9 tons of sugar.
To simplify this expression, we can convert the mixed number 3 3/5 to an improper fraction:
3 3/5 = (5*3 + 3)/5 = 18/5
So the expression becomes:
8 tons / (18/5) containers
To divide by a fraction, we can multiply by its reciprocal:
8 tons / (18/5) containers = 8 tons * (5/18) containers
Now we can simplify the expression and solve for the amount of sugar in one container:
8 tons * (5/18) containers = 40/18 tons/container = 20/9 tons/container
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The Olson family uses up a
1/2
-gallon jug of milk every 3 days. At what rate do they drink milk?
The Olson family drinks milk at a rate of 1/6 gallon per day.
To find the rate at which the Olson family drinks milk, we need to divide the amount of milk they drink by the time it takes them to drink it.
They use up a 1/2-gallon jug every 3 days, so their rate of milk consumption is:
(1/2 gallon) ÷ (3 days) = 1/6 gallon per day
A gallon is a unit of volume measurement commonly used in the United States and some other countries. There are different types of gallons, but the most commonly used ones are:
US liquid gallon (abbreviated as "gal" or "US gal"): This is a unit of volume used for measuring liquid substances. It is defined as exactly 3.785411784 liters or approximately 0.83267418 Imperial gallons.
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David is doodling on a rectangular sheet of paper. Beginning in a corner, David draws a line along the long edge of the paper, a distance of 77 cm. Next, David draws a line along the width of the paper, a distance of 36 cm. Finally David draws a diagonal line straight back to the original corner. At this point, David has drawn a total of ___ cm of lines
David has drawn a total of 177 cm of lines.
According to given conditions :We can use the Pythagorean theorem, which tells us that in a right triangle, the square of the length of the hypotenuse (the diagonal line) is equal to the sum of the squares of the lengths of the other two sides (the lines along the long edge and the width).
In this case, the length of the hypotenuse is the distance from the starting corner to the end of the diagonal line, which we can calculate as follows:
d = √(77² + 36²) ≈ 85.99 cm
Therefore, David has drawn a total of 77 cm + 36 cm + 85.99 cm = 198.99 cm of lines. However, we should subtract the length of the starting corner to the end of the first line, which is 77 cm, since it was counted twice (once as part of the diagonal line and once as part of the line along the long edge).
So, the total length of lines that David has drawn is 77 cm + 36 cm + 85.99 cm - 77 cm = 177 cm.
What is Pythagoras Theorem ?Pythagoras' theorem is a fundamental theorem in mathematics that relates to the sides of a right triangle. It states that in any right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
This can be expressed as:
a² + b² = c²
where a and b are the lengths of the two legs of the right triangle, and c is the length of the hypotenuse.
Pythagoras' theorem can be used to solve a variety of problems involving right triangles, such as finding the length of a missing side or determining whether a triangle is a right triangle. It is also the basis for the distance formula in two and three-dimensional Euclidean space.
Pythagoras' theorem has applications in many fields, including physics, engineering, and computer graphics, and it is one of the most important and widely used theorems in mathematics.
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Express 4 + ln 2 - ln 4 as a single natural logarithm.a. ln 2b. ln 4 c. ln 64
The single natural logarithm for the expression 4 + ln 2 - ln 4 is ln(2). So, correct option is A.
To express 4 + ln 2 - ln 4 as a single natural logarithm, we can use the properties of logarithms to combine the terms.
First, we can use the rule that ln(a) - ln(b) = ln(a/b) to simplify ln 2 - ln 4:
ln 2 - ln 4 = ln(2/4) = ln(1/2)
Now, we can rewrite the expression as:
4 + ln(1/2)
We can use another logarithmic property, ln(a) + ln(b) = ln(ab), to write this as:
4 + ln(2^(-1))
Simplifying further:
4 - ln(2)
Therefore, 4 + ln 2 - ln 4 can be expressed as a single natural logarithm of:
ln(2^2 / 2) = ln(2)
So, the answer is (a) ln 2.
In general, when simplifying expressions involving logarithms, it's helpful to remember the logarithmic properties and rules, such as the product, quotient, and power rules, as well as the fact that ln(e) = 1. By applying these rules systematically, we can simplify complex expressions into simpler forms that are easier to work with.
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Can you help me with this problem quickly? Thank you ✨
Answer:
pair c has the inverse functions
