Final answer:
To partition a number line into fourths, divide it into four equal segments, with each representing 1/4. To decompose 3/4 into 6 equal lengths, divide 3/4 into six parts where each part is 1/8 of the whole.
Explanation:
Partitioning a Number Line into Fourths and Decomposing Fractions
To partition a number line from 0 to 1 into fourths, you would divide the line into four equal segments. Each segment represents a value of 1/4. Now, to decompose 3/4 into 6 equal lengths, realize that each 1/4 is being divided into two parts (since 6 divided by 3 equals 2), which means each part is 1/8 in length. Therefore, 3/4 divided into 6 equal lengths gives us 6 segments, each of length 1/8.
Step-by-Step Solution
Draw a number line from 0 to 1.
Mark off four equal lengths between 0 and 1, each representing 1/4.
Find 3/4 on the number line. It is three of these fourths.
Divide each fourth into two equal lengths to decompose 3/4 into 6 equal parts.
Mark these new lengths on the number line, showing that each length is 1/8.
If the original 24 m edge length x of a cube decreases at the rate 5m/min, when x=3 at what rate does the cube's surface area change
The change in the cube's surface area is -180 m^2/min when the edge length is 3 m. This is found by differentiating the surface area with respect to time and substituting the given values.
Explanation:The subject of the question is related to rates of change in the context of the geometry of a cube. To address this problem, we use the formula for a cube's surface area, which is given by A = 6x^2, where x represents the length of an edge. If x changes with respect to time, we denote this change as dx/dt, which is given as -5m/min. You want to find how quickly the surface area, A, changes when x = 3.
First, let us differentiate the surface area A with respect to time t. By the chain rule of differentiation, dA/dt = dA/dx * dx/dt. Given A = 6x^2, dA/dx = 12x. substituting x=3 and dx/dt=-5, we find that dA/dt = 12*3*-5, which equals -180m^2/min.
Therefore, the change in the cube's surface area is -180 m^2/min when the edge length is 3 m.
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A vegetable farmer fills 2/3 of a wooden crate with 5/7 pound of tomatoes. How many pounds of tomatoes can fit into one crate?
Explain the rules for multiplication and division to convert units. How do you know when to multiply and when to divide to convert untis of measurement?
2 to the x power equals 512
How can you find the surface area of a composite solid made up of prisms
in 3/4 identify the role of 3. Then explain how to read tbis number
Answer:
The 3 is the numerator, To read the number is "three-fourths"
Step-by-step explanation:
I hope this helps!
"how few colors can be used so that each room is painted a color so in which no two adjacent rooms are the same color?"
We can see here that to guarantee that no two adjacent rooms are the same color, a minimum of four colors is generally needed.
To determine the minimum number of colors needed to paint each room in a way that no two adjacent rooms have the same color, we can use a coloring algorithm known as the "Four Color Theorem." According to this theorem, it is possible to color any map on a plane using at most four colors, ensuring that no two adjacent regions have the same color.
Applying this concept to the rooms, we can conclude that a minimum of four colors is needed to satisfy the given condition. By using these four colors, we can ensure that no two adjacent rooms share the same color.
Suppose that the polynomial function A(x) = - 0.0082x2 + 0.06x approximates a person's blood-alcohol level x hours after drinking 5 ounces of 80-proof whiskey. What is the person's blood-alcohol level after 3 hours?
what is the rate of decay, as a percent, for the following function n(x)=7(0.067)^x
Answer: The rate of decay is 93.3%.
Step-by-step explanation:
Since we have given that
The exponential function is given by
[tex]n(x)=7(0.067)^x[/tex]
As we know the general equation of exponential function that is given by
[tex]n(x)=a(1-b)^x[/tex]
Here, a denotes the initial value
1-b denotes the rate of decay.
So, On comparing both the equations, we get that
[tex]1-b=0.067\\\\b=1-0.067\\\\b=0.933=0.933\times 100=93.3\%[/tex]
Hence, the rate of decay is 93.3%.
William runs 5 meters in 20 steps. How many kilometers will he run if he takes 1,000 steps ?
9ax+9b-6=21
based on the equation above what is the value of ax+b
The value of equation ax + b is 3.
What is an equation?An equation contains one or more terms with variables connected by an equal sign.
Example:
2x + 4y = 9 is an equation.
2x = 8 is an equation.
We have,
To find the value of ax + b, we need to isolate that expression on one side of the equation.
Starting with:
9ax + 9b - 6 = 21
We can add 6 to both sides:
9ax + 9b = 27
Then, we can factor out 9 from the left-hand side:
9(ax + b) = 27
Dividing both sides by 9, we get:
ax + b = 3
Therefore,
The value of equation ax + b is 3.
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Enrique charges $5 for every 1/5 hour he spends walking dogs.in the morning he walks buttons for 2/5 hour bruno for 1/5 hour and pepper for 3/5 hour. Monday thru friday. On saturdays he takes mimi diva and coco to the dog park for 4/5 of an hour. On wendsday this week it rained and pepper wanted to stay out for only 1/5 hour. How many hours did enrique spend with the dogs this week. Explain your method
Shondra found large candles on sale at her favorite store. She has a large family and many friends, so she bought as many of the candles she could fit in her trunk to give as gifts. Her trunk is 2 feet deep, 4 feet wide, and 3 feet long. If each candle comes in a cube box with 1 foot edges, how many candles will fit in her trunk? A) 9 candles B) 10 candles C) 14 candles D) 24 candles
which equation is the inverse of y=100-x2
Answer:
Inverse of y = [tex]f^{-1}(x)[/tex] = [tex]\sqrt{100 -x}[/tex].
Step-by-step explanation:
Given : f(x) = y = 100 - x²
To find : Find inverse.
Solution : We have given that :
f(x) = y = 100 - x²
Step1) : Replace every x with a y and replace every y with an x .
x = 100 - y².
Step 2): Solve for y
On subtracting 100 from both sides
x - 100 = -y²
On multiplying both side by -1
100 -x = y²
Taking square root both sides and switching sides
y = ± [tex]\sqrt{100-x}[/tex].
Step3 ) : Replace y with [tex]f^{-1}(x)[/tex].
[tex]f^{-1}(x)[/tex] = ± [tex]\sqrt{100-x}[/tex].
Therefore, inverse of y = [tex]f^{-1}(x)[/tex] = ± [tex]\sqrt{100-x}[/tex].
Answer:
A on edge
Step-by-step explanation:
A swimmer swam 49 kilometers in d days. what is the value of d if the swimmer swam an average of 3.2 kilometers daily?
There are fewer than 8 gallons of gas in the tank how do I write an inequality for that
which number produces an irrational number when multiplied by 0.5
Find the equation of the plane through the point p=(5,5,4)p=(5,5,4) and parallel to the plane 5x+2y−z=−6.
If changes are made to a signature while using version 5.x signature files, are they visible in the router running the configuration?
Which expression is equivalent to 10b - 25? 10(b - 15) 5(b - 5) 5(5b - 20) 5(2b - 5)
The diagonals BF and CE divide the hexagon ABCDEF into two equilateral triangles and a square. Find the perimeter of the hexagon if BF = 3 cm. Answer: P = cm
Answer: The perimeter of the hexagon is 18 cm.
Step-by-step explanation: As given in the question, hexagon is shown in the attached figure.
The diagonals g and h divides the hexagon into two two equilateral triangles and one square .
Also, length of diagonal g = 3 cm.
We are to find the perimeter of hexagon.
We know that all the sides of a square are equal, so we have
length of b = length of h = length of e = length of g = 3 cm.
Since the two triangles are equilateral, so all their sides will be equal.
That is, length of a = length of f = length of g =length of c =length of d = length of h = 3 cm.
We know that the perimeter of a polygon is equal to the sum of the lengths of its sides.
Therefore, the perimeter of hexagon is given by
P = a + b + c + d + e + f = 3 + 3 + 3 + 3 + 3 + 3 = 18 cm.
Thus, the perimeter of the hexagon is 18 cm.
a rectangle that is 2 inches by 3 Inches has been scaled by factor of 7 suppose you want to scale the copy back to its original size what scale factor would you use?
This is about transformation of objects.
Scale factor back to original size = 1/7
We are told that the rectangle was scaled by a factor of 7.What this means is that if the length and width are x and y respectively, then the new scaled measurements will be;
7x and 7y.
Now,for us to scale back to the original size, all we need to do is to divide the new scale measurements by a factor of 7.This means the original size will be;
Length = 7x × 1/7
Width = 7y × 1/7
Thus,the scale factor will be 1/7 back to the original size.Read more at; https://brainly.com/question/17292295
A school sold small and large boxes of fruit as a fundraiser. One student sold 5 small boxes and 13 large boxes for $232. Another student sold 12 small boxes and 7 large boxes for $218. Let x represent the price of a small box and y represent the price of a large box. Solve the system to determine the price of each size box of fruit.
A The price of a small box of fruit is $10 and the price of a large box of fruit is $14.
B The price of a small box of fruit is $8 and the price of a large box of fruit is $14.
C The price of a small box of fruit is $10 and the price of a large box of fruit is $16.
D The price of a small box of fruit is $14 and the price of a large box of fruit is $16.
The answer is y=14 and x= 10
What is the solution to a linear equation?The solution of a linear equation is defined as the points, in which the lines represent the intersection of two linear equations. In other words, the solution set of the system of linear equations is the set of all possible values to the variables that satisfies the given linear equation.
Given here: One student sold 5 small boxes and 13 large boxes for $232. Another student sold 12 small boxes and 7 large boxes for $218.
Then we have 5x+13y=232
12x+7y=218
Solving these two equations here we get y=14 and x= 10
Hence, The answer is y=14 and x= 10
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Shoe store A is having a sale in which every pair of shoes is 40% off the regular price.
Shoe store B is having a sale in which $40 is deducted from the regular price.
Richard is comparing the price of the same pair of shoes in both shoes in both stores.In both stores, the shoes normally sell for $120. Which store has the better bargain?
which relation defined by mapping diagram is a function
Margaret wants to call her friend overseas. There is a connection fee of $2 and a charge of $1.50 per minute. So the cost of the call is 2 + 1.5t dollars for t minutes.
A Broadway musical was attended by a total of 2,838 people, including men, women, and children. The number of women who attended the event was 5 more than 3 times the number of children, while the number of men was 3 less than 4 times the number of women. Write an equation to model this situation. Then, use the equation to find the number of men, women, and children who attended the musical.
a triangle has an area of 54 m2 and a height of 9m how long is the base of the triangle entered your answer in the box
Which is a correct way of evaluating the expression 25x + 40x for x = 4?
Five hummingbirds drink 7.5 ounces of sugar water a day. How much sugar water is needed for 14 hummingbirds?