A rectangular carpet measures 10 m by 6m
Part of the carpet is covered by a square rug of length 2 m
2m
10m
Diagram not drawn accurately
6m
What fraction of the carpet is
covered by the rug?
Give your answer in its simplest form.
Optional working
Answer:
Answers
Hope it helps …
The fraction of the carpet covered by the rug will be 1/15.
What is the area of the rectangle?Let W be the rectangle's width and L its length.
The area of the rectangle is the multiplication of the two different sides of the rectangle. Then the rectangle's area will be
Area of the rectangle = L×W square units
A rectangular carpet estimates 10 m by 6m. Some portion of the rug is covered by a square rug of length 2 m.
The area of the carpet is given as,
A = 10 x 6
A = 60 square meters
The area of the rug is given as,
a = 2 x 2
a = 4 square meters
A fraction of the carpet is covered by the rug is given as,
⇒ 4 / 60
⇒ 1 / 15
A fraction of the carpet covered by the rug will be 1/15.
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The missing diagram is attached below.
Related Questions
eight congruent equilateral triangles, each of a different color, are used to construct a regular octahedron. how many distinguishable ways are there to construct the octahedron? (two colored octahedrons are distinguishable if neither can be rotated to look just like the other.)
Answers
There are 1680 ways to construct the octahedrons.
Here,
Eight congruent equilateral triangles, each of a different color, are used to construct a regular octahedron.
An octahedron has 8 equilateral triangles.
We have to find number of ways to construct the octahedron.
What is Regular octahedron?
An octahedron is a polyhedron with eight faces. The term is most commonly used to refer to the regular octahedron, a Platonic solid composed of eight equilateral triangles, four of which meet at each vertex.
Now,
An octahedron has 8 equilateral triangles.
We have to fix 2 faces before applying the colors.
So, the first face that can be fixed for any of the 8 faces but each faces are similar.
Hence, there are 8/8 ways.
And, When we fix one face, three adjoining faces are similar.
So, we have 7 colors for the second face.
Hence, 7/3 ways
Now, we can place any color anywhere, it will be different arrangement.
So, 6! ways.
Hence, Total number of ways = (8/8) * (7/3) * 6! = 7 * 6 * 5 * 4 *2 = 1680
So, There are 1680 ways to construct the octahedrons.
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Simplify 4(11 - 6) + 2
Answers
Step-by-step explanation:
Distribution first y=44-24+2
Simplify y=22
Hope this helps!
If you have any other questions feel free to ask!
Answer:
22
Step-by-step explanation:
Hey there!
To solve this, you need to follow PEMDAS
We do Parenthesis first:
44 - 24 + 2
Now we can simplify:
20 + 2
22
This table represents function f. If function g is a quadratic function that contains the points and , which statement is true over the interval ? A. The average rates of change of f and g cannot be determined from the given information. B. The average rate of change of f is less than the average rate of change of g. C. The average rate of change of f is the same as the average rate of change of g. D. The average rate of change of f is more than the average rate of change of g.
Answers
If function g is a quadratic function that contains the points (-3, 5) and (0, 14), the statement which is true over the interval [-3, 0] is: B. The average rate of change of f is less than the average rate of change of g.
What is an average rate of change?An average rate of change is also referred to as slope and it can be defined as a type of function that describes the average rate at which a quantity changes (decreases or increases) with respect to another quantity, over a given interval.
In Mathematics, the average rate of change of f(x) on a closed interval [a, b] is given by this formula:
Average rate of change = [f(b) - f(a)]/(b - a)
Next, we would determine the average rate of change of function f over the interval [-3, 0]:
a = -3; f(a) = -4.5
b = 0; f(b) = 0
Substituting the given parameters into the formula, we have;
Average rate of change = (0 - (-4.5))/(0 - (-3))
Average rate of change = 4.5/3
Average rate of change = 1.5.
Also, we would determine the average rate of change of function g over the interval [-3, 0]:
a = -3; f(a) = 5
b = 0; f(b) = 14
Substituting the given parameters into the formula, we have;
Average rate of change = (14 - 5)/(0 - (-3))
Average rate of change = 9/3
Average rate of change = 3.
In conclusion, the average rate of change of function f is less than the average rate of change of function g.
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Answer:
The average rate of change of f is less than the average rate of change of g.
Step-by-step explanation:
Plato/Edmentum
− 2/ 3 is a/an . (check all that applies.) \sqrt{5} 5 is a/an . (check all that applies.) natural number integer rational number real number irrational number
Answers
The -2/3 is an integer and rational number.
It is required to choose the number.
What is real number?Real numbers are numbers that include both rational and irrational numbers. Rational numbers such as integers (-2, 0, 1), fractions(1/2, 2.5) and irrational numbers such as √3, π(22/7), etc., are all real numbers.
Given:
-2/3 is an integer and rational number.
The square root of 25 is 5 is an Natural numbers, whole number, integer, and rational number.
Natural numbers are positive whole numbers (1, 2, 3, 4, 5, ...)
Whole numbers are positive numbers start with zero (0, 1, 2, 3,...)
Integers are positive and negative whole numbers or zero (..., -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5...)
Rational numbers include all integers as well as positive or negative numbers that have fractional parts ( -2.0, -3/4, 0.25, 2.1, 5, etc.)
Irrational numbers are numbers that can not be written as a simple fraction. Its decimal goes on forever without repeating (π = 3.14159....)
5 is a natural number, whole number, integer, and rational number.
Therefore, the -2/3 is an integer and rational number.
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You want your daily sodium intake to be less than 2300 milligrams. For breakfast, you eat a cereal bar with the nutrition label shown. What are the possible amounts of sodium you can eat during the rest of the day? Nutrition Facts Serving Size Servings Per Container Amount Per Serving Calories 120 Total Fat 3g 1 Bar (37g) Calories from Fat 30 % Daily Value* 5% 3% Saturated Fat 0.5g Trans Fat Og Cholesterol Omg Sodium 125mg 0% 5% The possible amounts of sodium you can eat during the rest of the day should be less than mg
Answers
According to the information in the nutritional table, it can be inferred that the amount of milligrams of sodium that we should consume during the rest of the day must be less than 2,175mg,
How to calculate the amount of sodium we can consume?To calculate the amount of sodium that we can consume during the rest of the day after breakfast, we must subtract the value of sodium consumed to the amount of total sodium that we want to ingest as shown below:
2300mg - 125mg = 175mgAccording to the above, it can be inferred that after consuming the cereal bar at breakfast, we should consume an amount less than or equal to 2,175mg of sodium in the other meals of the day (lunch, dinner and snacks).
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gabriel types 3 1/5 pages in 1/2 of an hour how many pages can he type in one hour
Answers
Answer:
6 2/5 pages
Step-by-step explanation:
Since we know how much he can type in half an hour, for a full hour you simply add two of the same value:
3 1/5 + 3 1/5
3+3 = 6, and 1/5 + 1/5 = 2/5
So the final answer would be 6 2/5 pages
I hope this helps :)
A piece of machinery depreciates at a fixed rate of 12% per year for 7 years. If the machinery is valued at $100,000 after 7 years, how much would the machinery have initially cost rounded to the nearest dollar?
a.
$113,636
d.
$45,235
b.
$40,868
e.
$244,692.86
c.
$244,693
Answers
The price the machinery have initially cost rounded to the nearest dollar is $244,693
Exponential equationThe formula for calculating depreciation is expressed according to the formula:
P(t) = P0e^-rt
Given the following parameters
P(t) = $100,000
rate = 12% = 0.12
time =7 years
Substitute
100,000 = P0e^-(0.12)(7)
100000 = P0e^0.84
P0 = 100000/e^0.84
P0 = $244,693
Hence the price the machinery have initially cost rounded to the nearest dollar is $244,693
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Meri paid $19.24 for 10.5 gallons of
gas. What was the cost of one
gallon?
Answers
A tennis player hits the ball with an initial speed of 55 feet per second at an angle of 17°, from a height of 1.8 feet. How far away does the ball land in feet?
Answers
The range of the tennis player hitting the ball will be 172.43 meters away from the initial point.
What is the projectile motion?An item or particle that is thrown toward the planet's surface and moves somewhere along a curved route only under the influence of gravity is said to be experiencing projectile motion.
Let u be the initial speed and θ be the angle at which the ball hits. Then the range of the call is given as,
R = (u² sin 2θ) / g
Where 'g' is the acceleration due to gravity.
A tennis player strikes the ball at a height of 1.8 feet with an initial speed of 55 feet per second and an angle of 17°.
R = [55² x sin (2 x 17°) ] / 9.81
R = [3025 x sin 34° ] / 9.81
R = 172.43 meters
The range of the tennis player hitting the ball will be 172.43 meters away from the initial point.
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Answer:
61.988 feet
Step-by-step explanation:
I took the test and got it right :)
What is four hundred in standard form
Answers
standard form
Answer: 4x10²
Step-by-step explanation:
Find car A and car B speed in km/h
Answers
Answer:
72 km/h and 48 km/hStep-by-step explanation:
Let the speed of the cars be x and y.
When moving in opposite directions, the speeds add up and when moving in the same direction the speeds subtracted.
Convert time from minutes to hour:
4 minutes = 4*1/60 hr = 1/15 hr20 minutes = 20*1/60 hr = 1/3 hrOpposite direction(x + y)*1/15 = 8x + y = 8*15x + y = 120Same direction(x - y)*1/3 = 8x - y = 8*3x - y = 24Add up the two equations and find the value of x:
x + y + x - y = 120 + 242x = 144x = 72Find y:
72 + y = 120y = 120 - 72y = 48can someone answer 2 1/8 x 1 7/9 =
Answers
Answer:
Exact Form: 34/9
Mixed-Number Form: 3 7/9
Step-by-step explanation:
Hope this helps.
Answer:
3 7/9
Step-by-step explanation:
2 1/8
convert mixed numbers to improper fractions
2x8+1/8 = 17/8
1 7/9
1x7+9/9 =16/9
17/8 x 16/9
Factor the number 16=8x2
17x8x2/8x9
cancel the common factor =8
=17x2/9
=34/9
convert improper fractions to mixed numbers
34/9 =3 remainder of 7
34/9 = 3 7/9
Solve the given word problem.
Ms. Enriquez asked a carpenter to construct a rectangular bulletin board for his classroom. She told the carpenter that the length of the board is 7 ft. Longer than its width and its area is 18 square feet. Find the dimensions of the given bulletin board.
Pls solve the question
Answers
The dimensions of the bulletin board is 2 ft and 9 ft.
Let the width of board = x
Then, the length of board = 7+x
Area of board = 18 ft²
Area of rectangle = L×W
so, (7+x) × x = 18 ft²
7x + x² = 18 ft²
7x + x² + 18 = 0
x² + 9x -2x -18 = 0
x(x+9) -2(x+9) = 0
(x+9) (x-2) = 0
x+9 =0, x -2 = 0
Dimension can not be in negative number, so
x = 2, Width = 2 ft
Length = 2+7 = 9 ft
Hence, the dimensions of board will be:
The width of board = 2 ft
And, the length of bard = 9 ft.
Hayley wants to be a marine biologist when she grows up. Her entire room is ocean-themed, so she is painting her bed frame blue to match. She estimates that she will need 800 milliliters of paint, but the hardware store only sells paint in liters. If Hayley buys 1 liter of paint, how many milliliters will she have left?
Answers
Answer:
Hayley will have 200 milliliters of paint left.
Step-by-step explanation:
1 liter=1000 milliliter
1000-800=200
Answer:
305
Step-by-step explanation:
There are 1,000 milliliters in 1 liter.solveYou need to find how many milliliters of blue paint Annie has left. But first, you need to know how many milliliters she started with.There are 1,000 milliliters in a liter, so multiply 0.5 liters by 1,000.0.5×1,000=500Annie started with 500 milliliters of blue paint.Now, add to find how much blue paint Annie used for her beach painting. She used 75 milliliters of blue paint for the sky and 120 milliliters for the ocean.75+120=195Annie used 195 milliliters of blue paint in all.Now, find how much blue paint Annie has left. She started with 500 milliliters. Subtract the 195 milliliters she used.500–195=305Annie has 305 milliliters of blue paint left.
B is the midpoint of AC and E is the midpoint of BD. If A(-9, -4), C(-1, 6), and E(-4, -3), find the coordinates or D
Answers
The coordinates of point D is (- 3, - 7).
How to determine the coordinates of a endpoint of a line segment divided by a midpoint
A midpoint is a point that partitions a line segment in two parts of equal length. First, we must find the coordinates of point B by using the midpoint formula:
B(x, y) = 0.5 · A(x, y) + 0.5 · C(x, y)
B(x, y) = 0.5 · (- 9, - 4) + 0.5 · (- 1, 6)
B(x, y) = (- 4.5, - 2) + (- 0.5, 3)
B(x, y) = (- 5, 1)
And the location of point D is found by using the midpoint formula again:
E(x, y) = 0.5 · B(x, y) + 0.5 · D(x, y)
(- 4, - 3) = 0.5 · (- 5, 1) + 0.5 · D(x, y)
(- 4, - 3) = (- 2.5, 0.5) + 0.5 · D(x, y)
(- 8, - 6) = (- 5, 1) + D(x, y)
D(x, y) = (- 8, - 6) - (- 5, 1)
D(x, y) = (- 3, - 7)
The coordinates of point D is (- 3, - 7).
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7. Health experts recommend the average female older than 50 years of age to
consume about 1,800 calories per day.
• Mrs. Keith has already consumed 950 calories today.
She plans to consume the same number of calories per hour for
the next 5 hours.
.
Which inequality represents d, the number of calories Mrs. Keith could eat each hour
for the next 5 hours without exceeding her recommended daily caloric intake?
Answers
i need help on 7 and 8.
Answers
Answer:
7 is 48b-4 and 8 is mn+4m
Step-by-step explanation:
38) "the quotient of a number and 2, increased
by 9 is -15"
Answers
Answer: x=48
i know the answer bc i just did it
Create an equivalent expression for 1.5 cubed over 1.3 raised to the fourth power all raised to the power of negative six.
15 points to whoever can answer this pleeease help
Answers
Answer:
1.3^24 / 1.5)^18
Step-by-step explanation:
[1.5^3 / 1.3^4]^-6
= 1.5^(3*-6) / 1.3^(4*-6)
= 1.5^(-18) / 1.3^(-24)
= 1.3^24 / 1.5)^18
part a a wall is covered with 6 wood panels. each panel is a square with a side length of x feet. write an expression to represent the total area, in square feet, covered by the wood panels.
Answers
The expression that represent the total area in square feet covered by the wood panels is: 6x² feet²
The formula and procedure to solve this geometry exercise is:
A = s²
Where:
A = area of the squares = sideProblem information:
A = ?s = x feetNo. panels= 6Using the formula of the square area we get the area of 1 panel:
A(1 panel) = s²
A(1 panel) = (x feet)²
A(1 panel) = x² feet²
Calculating the total area of the 6 wood panels we get:
A(total): No. panels * A(1 panel)
A(total): 6x² feet²
What is the area?Is the measure of the space occupied by a body bounded by an environment called perimeter, the same is expressed in units of squared side. Example: ft2, m2
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in a random sample of 77 residents of the state of california, the mean waste recycled per person per day was 1.71.7 pounds with a standard deviation of 0.360.36 pounds. determine the 99�% confidence interval for the mean waste recycled per person per day for the population of california. assume the population is approximately normal.
Answers
A simple random sample is a subset of a statistical population in which each member of the subset has an equal probability of being chosen. A simple random sample is meant to be an unbiased representation of a group.
Random sampling, or probability sampling, is a sampling method that allows for the randomization of sample selection, i.e., each sample has the same probability as other samples to be selected to serve as a representation of an entire population.
Simple random sampling is the randomized selection of a small segment of individuals or members of a whole population. It provides each individual or member of a population with an equal and fair probability of being chosen. The simple random sampling method is one of the most convenient and simple sample selection techniques.
Simple random samples are determined by assigning sequential values to each item within a population, then randomly selecting those values.
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please help
see attached picture
Answers
Answer:
See Explanation
Step-by-step explanation:
For cement block:Given is a square cement block, thus, it's width and height would be equal.-> length (l)= h, width (w)= 2x, height (h) = 2x [tex]V_{cement \: block} = lwh[/tex][tex]\implies V_{cement \: block} = h(2x)(2x)[/tex][tex]\implies V_{cement \: block} = 4x^2h.....(1)[/tex]For cylinder:Radius (r) = 2x/2 = x, height (h) = h[tex]V_{cylinder} = \pi r^2 h[/tex][tex]\implies V_{cylinder} = \pi x^2 h.....(2)[/tex]Subtract (2) from (1), we find:[tex]V_{cement \: block}-V_{cylinder} = 4x^2h- \pi x^2 h[/tex][tex] V(cement \: block\: without\: cylinder)= x^2h(4- \pi)[/tex]Thus proved To solve 6.2.1 and 6.2.2 plug the given values in [tex]x^2h(4- \pi)[/tex] and calculate.Describe the pattern, then list the next three numbers in the sequence.
4.5, 7, 12, 22, 42 __, __, __
Answers
Answer:
82 , 162, 322
Step-by-step explanation:
So basically add the number by two and then subtract that number by 2. 4.5(2)=9 9-2=7 and 7(2)=14 14-2=12 and so on
Determine the general solution of cos(x-30°) = 2 sin x.
Answers
Answer:
I’m not sureee
Step-by-step explanation:
Look at the simultaneous equations below.
(1)
x - 2y = 15
(2) x = 3 = 4y
a) Rearrange equation (2) to make x the
subject.
b) Using your answer to part a), solve the
simultaneous equations using substitution.
Answers
Answer:
x_2y=15
x_4y=_3
_6y=12
divide both sides by 6
y=_2
substitute y for x
In equation 1
x_2y=15
x_2 (_2)=15
x+4=15
x=15_4
x=11
Is the mixed number 1 1/6 rational or irrational?
Answers
Answer:
rational
Step-by-step explanation:
1 1/6 can also be expressed in the form 7/6
any number that can be expressed in a form of a/b is a rational number
Write a function g with the parent function f(x) = /x/ that has a vertex at (-2, 4)
Answers
The answer for the given function g(x) is |x - 4|² - 2.
Given parent function is f(x) = |x|
Given vertex (h, k) = (-2, 4)
The simplest function in a family of functions, a parent function maintains the definition of the entire family.
The parent function that has vertex must be used to create the function of g, as shown below.
vertex form can be written as
a ( x - k )² + h
Here a = 1 , k = 4, h = -2
Now the function g(x) = | x -4 |² + ( -2)
g(x) = |x - 4|² - 2
Therefore, the function g(x) is found to be |x - 4|² - 2.
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Maria needs to be at the airport terminal at 16:15. It will take 1 1/3
hours to drive to the airport from her home, and a further 25 minutes to park and get to the terminal.
What is the latest time she should leave home?
Give your answer as a time in the 24-hour clock.
Answers
Maria should leave home for the airport terminal at 14:30.
How to convert hour into minutes?Local time is the time of a location as determined by the apparent motion of the sun. The fixed time for locations on the same meridian set by law in a country is referred to as standard time. Changes in real time as longitude changes. The same applies to a specific country.We all know that one hour equals sixty minutes.
As a result, 6 hours = (6 × 60) minutes = 360 minutes.
For, the given question;
The time at which Maria need to be at airport terminal is 16:15.
Time taken for the driving is 1 1/3 = 4/3 hours.
convert this in minutes;
= 4×60/3
= 80 minutes.
Now, extra 25 minutes is requires to park.
Total time = 80 minutes + 25 minutes
Or we can write 60 minutes + 45 minutes.
Total time = 1 hour + 45 minutes.
The time at which Maria has to reach = 16:15 - 1:45 = 14:30
Therefore, the time at which Maria must reach the airport is 14:30 in 24-hour clock.
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Help me pleasee
Questions r in picture
Answers
[tex] \large \bf\implies\frac{12}{61} [/tex]
Step-by-step explanation:Given :[tex] \tt \frac{8}{101} , \frac{9}{91} , \frac{10}{81} , \frac{11}{71} ...[/tex]
To Find :nth termSolution :We have to add 1 in numerator and -10 in denominator because
[tex] \tt \frac{8}{101} , \frac{9}{91} , \frac{10}{81} , \frac{11}{71} ...[Given][/tex]
[tex] \frac{8 \: + \: 1}{101 \: - \: 10} = \frac{9}{91} \\\\ \frac{9 + 1}{91 - 10} = \frac{10}{81} \\ \\ \frac{10 + 1}{81 - 10} = \frac{11}{71} \\ \\ \frac{11 + 1}{71 - 10} = \frac{12}{61} ...[/tex]
The difference is 1 in numerator so we add 1 and the difference is -10 in denominator so we subtract -10.
40 . a guest orders a drink that contains 4 ½ ounces of 80-proof liquor. approximately how many drinks does this beverage contain?
Answers
Number of drinks = 3
From the question we are told that:
Ordered drink 4 1/2 ounces of 80-proof liquor
Generally,
80-proof liquor contains 40\% alcohol
Giving the drink a standard 1.5 ounce of distilled spirit
Therefore,
Number of drinks = 4.5 / 1.5
So, Number of drinks = 3
What do you mean by ounces?A number of distinct units of mass, weight, or volume are derived from the uncia, an ancient Roman unit of measurement, including the ounce, which is almost unmodified. The avoirdupois ounce, or precisely 28.349523125 g, is 116 of an avoirdupois pound and is used in both the United States and the United Kingdom. Although it is frequently used outside of the Anglosphere, it is predominantly employed in the United States to measure packaged foods and food portions, postal items, the areal density of fabric and paper, boxing gloves, and other items. Although the avoirdupois ounce is the standard unit of mass for most applications.
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