Answer:
3.229 revolutions per minute
Step-by-step explanation:
The angular velocity of an object is the rate at which it rotates around a fixed axis. In this case, the hamster wheel is rotating.
To find the angular velocity of the wheel, we need to convert the linear velocity of the hamster into angular velocity.
The linear velocity of the hamster is given as 17 centimeters per second. This means that for every second, the hamster moves 17 centimeters along the circumference of the wheel.
To find the angular velocity, we need to find the distance traveled along the circumference of the wheel in one revolution. The circumference of a circle is given by the formula C = 2πr, where r is the radius of the wheel.
In this case, the radius of the wheel is 10 centimeters. So, the circumference of the wheel is C = 2π(10) = 20π centimeters.
Since the hamster runs at a speed of 17 centimeters per second, in one revolution of the wheel, it covers a distance of 20π centimeters.
Now, we can find the angular velocity by dividing the linear velocity by the distance traveled in one revolution.
Angular velocity = linear velocity / distance traveled in one revolution
Angular velocity = 17 centimeters per second / (20π centimeters per revolution)
Simplifying the expression, we get:
Angular velocity = 17 / (20π) revolutions per second
To convert the angular velocity from revolutions per second to revolutions per minute, we need to multiply it by 60 (since there are 60 seconds in a minute).
Angular velocity in revolutions per minute = (17 / (20π)) * 60
Calculating the value, we get:
Angular velocity in revolutions per minute ≈ 3.229 revolutions per minute
Therefore, the wheel will s
AI-generated answer
The angular velocity of an object is the rate at which it rotates around a fixed axis. In this case, the hamster wheel is rotating.
To find the angular velocity of the wheel, we need to convert the linear velocity of the hamster into angular velocity.
The linear velocity of the hamster is given as 17 centimeters per second. This means that for every second, the hamster moves 17 centimeters along the circumference of the wheel.
To find the angular velocity, we need to find the distance traveled along the circumference of the wheel in one revolution. The circumference of a circle is given by the formula C = 2πr, where r is the radius of the wheel.
In this case, the radius of the wheel is 10 centimeters. So, the circumference of the wheel is C = 2π(10) = 20π centimeters.
Since the hamster runs at a speed of 17 centimeters per second, in one revolution of the wheel, it covers a distance of 20π centimeters.
Now, we can find the angular velocity by dividing the linear velocity by the distance traveled in one revolution.
Angular velocity = linear velocity / distance traveled in one revolution
Angular velocity = 17 centimeters per second / (20π centimeters per revolution)
Simplifying the expression, we get:
Angular velocity = 17 / (20π) revolutions per second
To convert the angular velocity from revolutions per second to revolutions per minute, we need to multiply it by 60 (since there are 60 seconds in a minute).
Angular velocity in revolutions per minute = (17 / (20π)) * 60
Calculating the value, we get:
Angular velocity in revolutions per minute ≈ 3.229 revolutions per minute
Therefore, the wheel will spin at a rate of approximately 3.229 revolutions per minute.
Yung’s taxable income is $36,558. He is filing as head of household, and he has already paid $4802 in federal taxes. What will he receive or pay after he figures his taxes for the year?
A. He will pay $64.
B. He will receive a refund of $64.
C. He will pay $57.
D. He will receive a refund of $57.
Answer:
He needs to pay back $64
Step-by-step explanation:
He has already paid $4802, and according to the chart that goes with this question, he owed $4866.
What he owes: $4866
subtract what he has paid: $4802
4866-4802=64
So he needs to pay the IRS $64
You can use subtraction here to get to the correct option.
The correct option for the given condition is
Option A: He will pay $64
How to get what is Yung left to do with his income?Since the chart that goes along with the given question says that Yung had to give $4866 for the taxes, and since it is given that Yung already paid $4802, we see that he didn't paid full tax yet since 4802 < 4866.
So he has to pay the remaining amount of the tax.
To get the remaining amount he has to pay, we will use subtraction.
Thus:
Remaining amount = Total amount to pay - amount already paid
Remaining amount = $4866 - $4802 = $64
Thus,
The correct option for the given condition is
Option A: He will pay $64
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The amount in a savings account increased from $150 to $156. What was the percent of increase?
The amount in a savings account increased from $150 to $156. The percent of increase is equal to 4%.
The percentage simply means out of 100. It means proportionating a value out of another value to be out of 100. Percentage facilitates comparison since the base of all values becomes equal.
To find the increase in value, we first need to calculate the increase in numbers i.e., new value minus the original value. Divide it by the original value and multiply by 100, and you get the required result.
Original amount in savings account = $150
increased amount in savings account = $156
Increase in amount = $156 - $150 = $6
The increase in percent = [tex]\frac{increase}{original \ amount }*100[/tex] = [tex]\frac{6}{150} * 100 = 4%[/tex]%
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x + y = -9
5x - 2y = 32
The solution is x = 2 and y = -11
Solution:
Given system of equations are:
x + y = -9 --------- eqn 1
5x - 2y = 32 ------------- eqn 2
We have to solve the system of equations
We can solve the system by substitution method
From eqn 1,
x + y = -9
Isolate "y" to one side
y = -9 - x ---------- eqn 3
Substitute eqn 3 in eqn 2
5x -2(-9 - x) = 32
5x + 18 + 2x = 32
Combine the like terms
7x = 32 - 18
7x = 14
x = 2
Substitute x = 2 in eqn 3
y = - 9 - 2
y = -11
Thus the solution is x = 2 and y = -11
What is the solution for 3x-4=-1/2x+3
Answer:
2
Step-by-step explanation:
3x-4 =-1/2x+3
3x+1/2x=3+4
6x+x/2=7
6x+x=14
7x=14
x=14/2
x= 2
Answer:
X = 2
Step-by-step explanation:
- Add 1/2 to both sides
3x - 4 + 1/2x = -1/2x + 3 + 1/2x
7/2x - 4 = 3
- Add 4 to both sides
7/2x - 4 + 4 = 3 + 4
7/2x = 7
- Multiply both sides by 2/7
(2/7) X (7/2x) = (2/7) X (7)
x = 2
The table shows the relationship between the height of a tomato plant and the number of days since it has been planted
Days Height (cm)
2 3
5 4
8 6
12 9
18 13
22 15
25 16
30 20
32 21
35 24
What does the y-intercept represent in this problem situation? Explain your answer.
Answer:
The y-intercept represent Height
Step-by-step explanation:
In a graph the independent variable is plotted on the X axis and attain only certain discrete values. The Dependent variable is plotted against the Y axis and may be discrete or continuous.
Here in the given question
Days: 2,5,8,12,18,22,25,30,32,35
Height: 3,4,6,9,13,15,16,20,21,24
The height is a dependant variable because we are trying to determine a relationship between the Days and the height. In particular, we are trying to see how the height depends upon what day it is or what is the height of the pant on the particular day.
The day can be only discrete values where height can be both discrete and continuous.
So height can be represented along Y axis
Answer:
The height at the beginning of the experiment.Step-by-step explanation:
The relation that the problem shows is between Days (x) and Height (y).
Remember that a y-incercept is a point with the form (0, k), where k is a real number.
In this case, the y-intercept represents the height of a tomato plant at day zero. In other words, it represents the initial condition, the height at the beginning of the experiment.
The angles below are supplementary. What is the value of x?
Answer:
see the attached picture please
Which of the following is a source of water pollution?
a. sewage
b. oil spills
C. fertilizers
d. all of the above
Answer:
D
Step-by-step explanation:
all of the above
The solution is Option D.
The sources of water pollution are sewage , oil spills and fertilizers
What is water pollution?Water contamination is the tainting of bodies of water, typically as a result of human activity, which has a detrimental impact on their uses. Aquifers, reservoirs, lakes, rivers, seas, and groundwater are all examples of bodies of water. When contaminants are introduced into these water bodies, water contamination results. It causes illnesses: consuming contaminated water can lead to serious health problems. From diarrhoea, cholera, hepatitis A, typhoid, to death.
Given data ,
Water scarcity is the situation when available water is not sufficient
And , the sources of water pollution are mainly sewage , oil spills and fertilizers thrown out into the ocean and other water bodies by humans
Toxic substances from farms, towns, and factories readily dissolve into and mix with it, causing water pollution.
Ground water , surface water and ocean water pollution are the three water bodies caused by water pollution
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Briana has 1,438 likes for the picture posted online of her dog dressed up like a superhero.How many more likes does Briana need to reach 2,000 likes?
Answer:Briana needs 562likes to reach 2000
Step-by-step explanation:
The number of likes Briana has = 1438
The number of likes Briana wants to reach = 2000
The remaining of likes she needs= 2000-1438 = 562
Hence, Briana needs 562 more likes to reach 2000likes on her picture
Final answer:
Briana needs 562 more likes to reach 2,000 likes on her dog's picture, calculated by subtracting her current likes from the target amount.
Explanation:
Briana currently has 1,438 likes on a picture of her dog dressed as a superhero. To determine how many more likes Briana needs to reach 2,000 likes, we perform a simple subtraction operation:
2,000 (desired amount of likes) - 1,438 (current amount of likes) = 562 more likes needed.
Therefore, Briana needs 562 additional likes to reach her goal of 2,000 likes on the picture of her dog.
(-22) - 14 - (-22) + 14
Answer:
-28
Step-by-step explanation:
(-22)-14= -36. (-22)+14= -8. -36-(-8)= -28.
Find the coordinates of a point on the directed segment from (3,-2) to (8,0) that divides it into a ratio of 3:1.
a.
(6.75,-0.5)
b.
(6, -0.75)
c.
(4, -1.5)
d.
(5, -1.5)
The coordinates of a point on the directed segment from (3,-2) to (8,0) that divides it into a ratio of 3:1 is (6.75, -0.5). The correct option is A.
What are coordinates?A coordinate system in geometry is a system that employs one or more integers, or coordinates, to define the position of points or other geometric components on a manifold such as Euclidean space.
Let the line be represented as AB, therefore, the coordinates of points A and B are (3,-2) and (8,0), respectively. The coordinate of the point m that divides the line AB in a ratio of 3:1 is,
x = [(x₂×m)+(x₁×n)]/(m+n)
x = [(8×3)+(3×1)]/(3+1)
= (24+3)/4
= 6.75
y = [(y₂×m)+(y₁×n)]/(m+n)
y = [(0×3)+(-2×1)]/(3+1)
= (0-2)/4
= -0.5
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Final answer:
The coordinates of the point that divides the directed segment from (3,-2) to (8,0) in the ratio of 3:1 are a) (6.75, -0.5), using the section formula.
Explanation:
When finding the coordinates of a point on a directed segment that divides it into a specific ratio, such as 3:1, the formula for the section formula in coordinate geometry is used. This formula allows us to calculate the coordinates of the point that divides the segment internally or externally in a given ratio (m:n) using the coordinates of the endpoints (x1,y1) and (x2,y2). The formula for the point (x, y) that divides the segment internally in the ratio m:n is:
x = (mx2 + nx1) / (m + n)
y = (my2 + ny1) / (m + n)
For the directed segment from (3, -2) to (8, 0) and a ratio of 3:1, we find the point by this method:
x = (3×8 + 1×3) / (3 + 1) = (24 + 3) / 4 = 27 / 4 = 6.75
y = (3×0 + 1×(-2)) / (3 + 1) = (0 - 2) / 4 = -2 / 4 = -0.5
Thus, the coordinates of the point that divides the segment in the ratio 3:1 are a) (6.75, -0.5).
-16t^2+vt+h Find a function
Answer:
Step-by-step explanation:
What is the equation of the inverse of the function?
f(x)=3x8+1
options:
f−1(x)=83x−13
f−1(x)=83x−83
f−1(x)=83x−1
f−1(x)=38x−1
Final answer:
The inverse of the function f(x) = 3x^8 + 1 is found by reversing the operations: subtract 1, divide by 3, and take the eighth root. The correct equation for the inverse is f⁻¹(x) = ⁸√((x - 1) / 3), which simplifies to f⁻¹(x) = ((x - 1) / 3)^(1/8). The options provided do not match this result.
Explanation:
The question asks for the equation of the inverse of the given function f(x) = 3x^8 + 1. To find the inverse function, f⁻¹(x), we must reverse the operations of the original function on x. First, you would subtract 1 from both sides to undo the addition, and then divide by 3 to undo the multiplication, followed by taking the eighth root to reverse the exponentiation. The correct inverse function will therefore reverse all these operations in that order.
Here's the step-by-step solution:
Start with y = 3x^8 + 1
Subtract 1 from both sides: y - 1 = 3x^8
Divide both sides by 3: (y - 1) / 3 = x^8
Take the eighth root of both sides: x = ⁸√((y - 1) / 3)
Therefore, the inverse function is f⁻¹(x) = ⁸√((x - 1) / 3), which simplifies to f⁻¹(x) = ((x - 1) / 3)^(1/8). However, none of the options provided fully match this result, implying there might be a typo or mistake in the question or options provided.
Find the cosine of L
Answer:
0.42
Step-by-step explanation:
use the attached as reference
recall that for a right (90°) triangle, with any acute angle θ,
cos θ = length of adjacent side / length of hypotenuse
in our case, for angle I, the adjacent side is HI = 36 units and the hypotenuse is IJ = 85 units
by the above formula,
cos I = length of adjacent side / length of hypotenuse
= 36 / 85
= 0.42353
= 0.42 (rounded to nearest hundredth)
how can you come up with a tree diagram
Answer:
Create a tree diagram
1. Click File > New > Templates > General, and then open Block Diagram.
2. From the Blocks and Blocks Raised stencils, drag block shapes onto the drawing 3.page to represent stages in a tree structure.
5 .To add text to a shape, select the shape, and then type.
6. Indicate relationships between the blocks by connecting the shapes:
Step-by-step explanation:
And kind of like this but you can do whatever get creative:) here’s the picture
A tree diagram is a form of graphical representation that visually displays possible outcomes of an experiment or event. It is particularly useful in solving complex probability problems. An example would be if you were to draw balls from an urn multiple times and wanted to visualize all the possible outcomes.
Explanation:A tree diagram is a graphical representation used to determine the outcomes of an experiment. It consists of multiple branches, typically representing different possible outcomes or choices.
As an example, let's consider an urn with 11 balls: 3 red and 8 blue. If you were to draw two balls, one at a time, with replacement (putting the first ball back before the second draw), a tree diagram would show all possible outcomes. Your first set of branches would represent the color of the first ball drawn (red or blue) and from each of those branches, a second set would signify the color of the second ball drawn.
So branch one could show red for the first draw, and from that branch you would have two further branches, red and blue, showing the possibilities for the second draw. The same would be done for the first draw being blue. This tree diagram illustrates the different scenarios of this experiment.
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Roberto can read 4 pages in 6 minutes casey can read 6 pages in 9 minutes.Is roberto’s ratio of pages to minutes equivalent to Casey’s ratio of pages to minutes?
Answer:
Yes
Step-by-step explanation:
Roberto 4:6 = 2:3
divisor 2. 4/2=2 6/2=3
Casey 6:9 = 2:3
divisor 3
6/3=2 9/3=3
solve for x
4x = -48
Answer:
-12
Step-by-step explanation:
4x=-48. use inverse operations here so divide -48 by 4
x=-12
Betty has a sister named Anne. Betty's sister, Anne, is 3 years younger than twice Betty's age.
Write an equation to represent the relationship between Anne's age and Betty's age. Let a represent Anne's age and b represent Betty's age.
The equation that represents the relationship between Anne's age and Betty's age is a = 2b - 3. The equation indicates that Anne's age is 3 years less than twice Betty's age.
Explanation:The relationship between Anne's age and Betty's age is expressed through the given information: 'Anne is 3 years younger than twice Betty's age'. This can be translated into an equation using 'a' to represent Anne's age and 'b' to represent Betty's age. Accordingly, the equation becomes a = 2b - 3.
The equation shows that to get Anne's age, you have to double the age of Betty and then subtract 3 years. For example, if Betty was 10 years old, Anne would be 2*10 - 3 = 17 years old.
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−2(2x+3)=−4(x+1)−2
x = ___
(type your answer as a number, "no solution" or "infinite solutions")
Answer:
infinite solutions
Step-by-step explanation:
−2(2x+3)=−4(x+1)−2 multiply -2 and -4 with inside the parenthesis
-4x -6 = -4x -4 -2 now add like terms
-4x -6 = -4x -6 ➡ -4x +4x = -6+6
that makes equation 0 = 0 this is called infinite solutions which means whatever number you use instead of x there will always be a solution.
What is the solution of the system of equations?
y = -2x + 5
-5y = 10x + 20
(1,3)
no solution
infinitely many solutions
(0, 20)
The correct answer is "no solution."
Let's first rewrite the second equation in the system in slope-intercept form (y = mx + b) to make it easier to work with:
[tex]\[ -5y = 10x + 20 \][/tex]
Divide both sides by -5:
[tex]\[ y = -2x - 4 \][/tex]
Now we have the system of equations:
[tex]\[ y = -2x + 5 \][/tex]
[tex]\[ y = -2x - 4 \][/tex]
To find the solution to the system, we can set the two equations equal to each other since they both equal y:
[tex]\[ -2x + 5 = -2x - 4 \][/tex]
Now, we can solve for x:
[tex]\[ 5 = -4 \][/tex]
This equation is not true, which means there is no value of x that satisfies both equations simultaneously. Therefore, the system has no solution.
Does anyone know what this answer is?
0.3x − 2.7 =
Answer:
the answer is 9
Step-by-step explanation:
why it 9 Add '2.7' to each side of the equation.
-2.7 + 2.7 + 0.3x = 9 + 2.7
Combine like terms: -2.7 + 2.7 = 0.0
0.0 + 0.3x = 9 + 2.7
0.3x = 9 + 2.7
Combine like terms: 9 + 2.7 = 11.7
0.3x = 11.7
Divide each side by '0.3'.
x = 39
Simplifying
x = 39
The price decreased by nine dollars
Answer: -9
Step-by-step explanation: it is a negative because it is minus 9$ from the price just like adding -9
Answer:
t - 9 = ?
Step-by-step explanation:
Mt. McKinley, which is the highest elevation in North America, is 20,320 feet above sea level. Death Valley, which is the lowest elevation in North America, is 282 feet below sea level. What is the difference in height between the top of Mt. McKinley and the bottom of the death valley?
Answer:
20,602 feet is the difference in height between the top of Mt. McKinley and the bottom of the Death Valley.
Step-by-step explanation:
Given:
Mt. McKinley, which is the highest elevation in North America, is 20,320 feet above sea level.
Death Valley, which is the lowest elevation in North America, is 282 feet below sea level.
Now, to find the difference in height between the top of Mt. McKinley and the bottom of the death valley.
Height of Mt. McKinley above sea level = 20,320 feet.
Height of Death Valley below sea level = 282 feet.
Now, to get the difference in height between the top of Mt. McKinley and the bottom of the Death Valley by adding both the heights:
[tex]20320+282[/tex]
[tex]=20602\ feet.[/tex]
Therefore, 20,602 feet is the difference in height between the top of Mt. McKinley and the bottom of the Death Valley.
Answer:
20,602 feet.
Step-by-step explanation:
What is the common difference of 80,60,45,33.75
Answer:
The common difference (or common ratio) = 0.75
Step-by-step explanation:
i) let the first term be [tex]a_{1}[/tex] = 80
ii) let the second term be [tex]a_{2}[/tex] = [tex]a_{1}[/tex] . r = 80 × r = 60 ∴ r = [tex]\frac{60}{80}[/tex] = 0.75
iii) let the third term be [tex]a_{3}[/tex] = [tex]a_{2}[/tex] . r = 60 × r = 45 ∴ r = [tex]\frac{45}{60}[/tex] = 0.75
iv) let the fourth term be [tex]a_{4}[/tex] = [tex]a_{3}[/tex] . r = 45 × r = 33.75 ∴ r = [tex]\frac{33.75}{45}[/tex] = 0.75
Therefore we can see that the series of numbers are part of a geometric progression and the first term is 80 and the common ratio = 0.75.
Fill in the plank to make an equivalent fraction 2/6 equals blank /30
Answer:
10
Step-by-step explanation:
multiply both numbers by same number
Help me with this please!
Answer:
Step-by-step explanation:
Increases weight = 80 - 40 = 40 lbs
Percent increase = (40/40)*100 = 1*100 = 100%
Answer:
The percent change is 50%.
Step-by-step explanation
1) 80-40=40
2) 40 divided by 80 which equals 0.5
3) 0.5 multiplied by 100
4) 0.5 x 100=50
The formula for percent change is change divided by the original amount then multiply the answer from that problem by 100.
Solve the system of equations.
2x + 3y = 1
5x + 2 = 8
What is the solution?
Answer:
x = 2, y = -1
Step-by-step explanation:
2x + 3y = 1.....(1)
5x + 2y = 8.....(2)
multiply equation (1) by 5 and equation (2) by 2
10x + 15y = 5 .......(3)
10x + 4y = 16......(4)
solving by elimination method
we subtract equation (4) from (3)
hence ...
11y = -11
dividing both sides by 11
y = -1
substituting y = -1 in equation (1) to solve for the value of x
2x + 3(-1) = 1
2x - 3 = 1
rearranging,
2x = 3 + 1
2x = 4
dividing both sides by 2
x = 2
(1.6z+4) -4(-0.5+5z) no parentheses
Answer:
-18.4z+6
Step-by-step explanation:
Express 60 as the product of its prime factors. Write the prime factors in ascending order and give your answer in index form.
Answer: 2.2.3.5 = 60 are the prime factors in ascending order
In a certain town there were 332 robberies last year. This year the number of robberies has gone down 14%. How many robberies were there this year, to the nearest whole number?
To find the number of robberies this year, we need to calculate 14% of last year's total and subtract it from that total. This results in an estimated 286 robberies this year.
Explanation:The question asks for the number of robberies this year given a 14% decrease from the prior year's total of 332 robberies. To calculate this, you would multiply last year's number of robberies by 14% (or 0.14) to find the decrease in robberies. Then, subtract this decrease from the original number of robberies.
First, calculate the decrease: 332 * 0.14 = 46.48. This rounds down to 46 robberies, as it would be unlikely to have a fraction of a robbery.
Next, subtract this from the original amount: 332 - 46 = 286. There were approximately 286 robberies this year, rounded to the nearest whole number, assuming a 14% decrease from 332.
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On Monday Luke’s business lost $15. on Tuesday it made $8 .on Wednesday it broke even what is the total profit or loss during those 3 days?
Answer:
He lost 7 dollars
Step-by-step explanation:
In Luke’s business, total loss in business during three days = $7
What is profit and loss ?The profit is defined as the amount gained by selling a product, which should be more than the cost price of the product.
The amount the seller incurs after selling the product less than its cost price is mentioned as a loss.
Given,
Loss on Monday = $15
Profit on Tuesday = $8
On Wednesday, no profit or loss
Total profit or loss = Profit + ( - loss)
=$8+(-$15)
= -$7
Hence, there was total loss of $7 during three days in Luke’s business.
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