Write and simplify polynomial expressions that represents the perimeter and area of the cornfield (7y) (6x)
The expressions that represent the perimeter and area of the cornfield are: Perimeter = 14y + 12x,Area = 42xy
What is Area of rectangle ?
Area of rectangle can be defined as product of length and breadth of a rectangle.
The given expression represents the dimensions of a rectangular cornfield, where one side measures 7y units and the other side measures 6x units.
The perimeter of a rectangle is the sum of the lengths of all its sides. Therefore, the perimeter of this cornfield is:
P = 2(7y) + 2(6x) = 14y + 12x
To find the area of a rectangle, we multiply its length by its width. Therefore, the area of this cornfield is:
A = (7y) (6x) = 42xy
Therefore, the expressions that represent the perimeter and area of the cornfield are: Perimeter = 14y + 12x,Area = 42xy
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A car averages 60 miles per hour on a road trip. Use the graph to represent the relationship between the time and the distance traveled.
please tell me the coordinates for the graphing because you have to graph it.
the picture is the graph I have to use :>
Using the speed formula, the coordinates to plot on the graph are (0, 0), (1, 60), (2, 120), (3, 180), and (4, 240).
What is the speed?
Speed is defined as the distance traveled per unit of time. It is the slope of the distance vs time graph. The formula for speed is:
Speed = Distance / Time
Where:
Speed is the speed of the object, usually expressed in units such as meters per second (m/s)
Distance is the distance traveled by the object, usually expressed in units such as meters
Time is the duration of travel, usually expressed in units such as seconds
To graph the relationship between the time and the distance traveled by the car, we can use the following formula:
Distance Traveled = Rate x Time
In this case, the rate (or speed) of the car is 60 miles per hour, and the distance traveled is a function of time.
So we can write the equation as:
Distance Traveled = 60 x Time
To graph this equation, we can plot a series of points using different values of time. For example:
At 0 hours, the distance traveled is 0 miles. Coordinate: (0, 0)
At 1 hour, the distance traveled is 60 miles. Coordinate: (1, 60)
At 2 hours, the distance traveled is 120 miles. Coordinate: (2, 120)
At 3 hours, the distance traveled is 180 miles. Coordinate: (3, 180)
At 4 hours, the distance traveled is 240 miles. Coordinate: (4, 240)
These points can be plotted on a graph with time on the x-axis and distance traveled on the y-axis. The resulting graph would be a straight line with a slope of 60 (which represents the rate or speed of the car) and passing through the origin (0, 0).
So the coordinates to plot on the graph are:
(0, 0), (1, 60), (2, 120), (3, 180), (4, 240)
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What angle does m make with the x-axis?
Therefore , the solution of the given problem of angle comes out to be x = 30°.
What does an angle mean?In Euclidean geometry, the barrier's centre and top separate two spherical faces, which make both of the sides of a tilt. Two rays may combine to create an angle where they collide. Another result of two things interacting is an angle. They most closely resemble dihedral shape. Two line beams can be arranged in different ways at their extremities to form a two-dimensional curve.
Here,
Given : a line making angle with x axis:
We have to find the angle with x axis.
So,
=> tan x = p/b
=> tanx = 1/√3
=> x = tan⁻¹(1/√3)
=> x = 30°
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Solve 19(1.12^x)=8(1.18^x). Show work.
Answer:
x≈12.6
Step-by-step explanation:
We have the equation:
19(1.12^x) = 8(1.18^x)
Divide both sides by 8:
19/8 (1.12^x) = (1.18^x)
Take the natural logarithm of both sides:
ln[19/8 (1.12^x)] = ln[1.18^x]
Using the properties of logarithms, we can simplify the left side:
ln(19/8) + ln(1.12^x) = x ln(1.18)
Substituting y = 1.12^x, we get:
ln(19/8) + ln(y) = ln(1.18) y
Now we can solve for y:
ln(y) = ln(1.18) y - ln(19/8)
Using a numerical method or a graphing calculator, we can find that y ≈ 10.584.
Substituting back to solve for x:
1.12^x ≈ 10.584
Taking the logarithm base 1.12 of both sides:
x ≈ ln(10.584)/ln(1.12)
x ≈ 12.6
Therefore, the solution to the equation is x ≈ 12.6.
Find the area of a circle with a circumference of 31. 42 centimeters
From the given data in the question, the circumference of a circle is 31.42 centimeters then the area of the circle is 78.5 cm².
To find the area of a circle with a given circumference, we need to use the formula:
Circumference = 2πr
where π is the mathematical constant pi (approximately 3.14) and r is the radius of the circle. In this case, the circumference is given as 31.42 centimeters. So we can write:
31.42 = 2πr
To solve for r, we can divide both sides by 2π:
r = 31.42 / (2π)
r = 5
So the radius of the circle is 5 centimeters.
Now, to find the area of the circle, we can use the formula:
Area = πr²
Substituting the value of r, we get:
Area = π(5²)
Area = 25π
Area = 78.5 square centimeters
Therefore, the area of the circle with a circumference of 31.42 centimeters is approximately 78.5 square centimeters.
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Do you mind if someone would answer number 21 part a and b
I would really appreciate if you would
The value at the 60th percentile is 72°F. According to the given question.
What is whisker plot?
A whisker plot, also known as a box and whisker plot, is a graphical representation of a dataset that shows the distribution of values. It is often used to summarize and compare datasets, and to identify outliers or extreme values.
The plot is constructed using a rectangular box that represents the middle 50% of the data (the interquartile range or IQR). The box extends from the lower quartile (the value below which 25% of the data falls) to the upper quartile (the value below which 75% of the data falls). A line inside the box represents the median (the value below which 50% of the data falls).
Part A:
Here is a box and whisker plot representing the given data:
| + |
75 -+ + |
| | |
70 -+ | |
| | |
65 -+-------------+-------------------+
| S M T W | T F S |
The plot is divided into four sections: the lowest 25% of the data (the lower quartile), the next 25% of the data (the second quartile or median), the next 25% of the data (the third quartile), and the highest 25% of the data (the upper quartile). The box represents the middle 50% of the data, and the whiskers extend to the lowest and highest values that are not outliers.
Part B:
To determine which value is at a given percentile, we need to sort the data in ascending order and count how many values are less than or equal to the percentile we are interested in. Then we find the corresponding value in the sorted list.
For example, to find the value at the 60th percentile, we first calculate 60% of the total number of values, which is:
0.60 * 7 = 4.2
Since we cannot have a fraction of a value, we round up to the next integer, which is 5. This means that the value at the 60th percentile is the fifth value in the sorted list:
65, 66, 68, 70, 72, 74, 75
Therefore, the value at the 60th percentile is 72°F.
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Which is the better buy? 3-pound bag of rice for $2.25 9-pound bag of rice for $6.66
Answer:
Step-by-step explanation:
To see which bag is the better buy, calculate how much each pound of rice would cost.
To do that divide the price by the amount of costs for each then compare those numbers
$2.25/3 = $0.75 per pound
$6.66/9 = $0.74 per pound
So the 9 pound bag of rice would cost 1 cent less per pound making it the better buy.
Norris living room table is a shape of a trapezoid the bottom of the table top measure 613. 5 inches and the top measures 11. 3 inches theme part of the table top is 12 inches the paint she will buy covers 12 in. ² per kid how many whole cans of paint does she need to buy the cover the table top
Norris living room table is a trapezoid shape with a bottom length of 613.5 inches, a top length of 11.3 inches, and a height of 12 inches.
To find the area of the tabletop, we need to calculate the average of the lengths of the top and bottom, and then multiply that by the height.
Average of lengths = (613.5 + 11.3)/2 = 312.4 inches
Area of table top = (312.4) x 12 = 3748.8 square inches
Since one can of paint covers 12 square inches, we can find the number of cans of paint needed by dividing the area of the table top by the coverage per can:
Number of cans of paint = 3748.8/12 = 312.4 cans
However, we need to round up to the nearest whole can, so Norris needs to buy 313 cans of paint to cover the entire table top.
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how is a condominium different than a single family dwelling
a. occupants pay rent to the landlord who owns the property
b.occupants are investors who own shares in the entire property and not individual unit
c.occupants individually own both the home and the land
b.occupants jointly own the common parts of the property and individually own their own units
Option d. occupants jointly own the common parts of the property and individually own their own units is the correct answer .A condominium is a type of housing where individuals own their own unit or apartment
what is condominium?
A condominium, often shortened to "condo," is a type of housing arrangement where individuals own their own unit or apartment within a larger building or community, and jointly own the common areas and facilities of the property with other owners.
In the given question,
A condominium is a type of housing where individuals own their own unit or apartment and jointly own the common areas of the property, such as hallways, elevators, and recreation areas. This is different from a single-family dwelling where the occupant individually owns both the home and the land.
In a condominium, occupants are not renting from a landlord who owns the property, nor are they investors who own shares in the entire property. Instead, each occupant owns their own individual unit and has a shared interest in the common areas of the property.
Additionally, in a condominium, occupants are typically required to pay fees to the condo association to cover the maintenance and upkeep of the common areas, which is not typically required in a single-family dwelling.
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find the cost in dollars of the operating a 100- w w lamp continuously for 1 week when the power utility rate is 16 cents/kwh c e n t s / k w h . express your answer using two significant figures.
Operating a 100-watt lamp for a week when the power utility rate is 16 cents/k
Wh can be calculated as follows:
Power of the lamp = 100 watts
Time of usage = 1 week = 7 days
Power utility rate = 16 cents/kWh
1 kW = 1000 watts
Power consumed by lamp = 100 watts
Total time of usage in hours = 7 days x 24 hours/day = 168 hours
Energy consumed = Power x Time= 100 watts x 168 hours= 16,800
watt-hours (Wh) = 16.8 kWh
Cost of operating the lamp = Energy consumed x Power utility rate= 16.8 kWh x 16 cents/k
Wh= 2.688 dollars= $2.7 (approx)
Therefore, the cost of operating a 100-watt lamp continuously for 1 week when the power utility rate is 16 cents/kWh is approximately $2.7 using two significant figures.
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Fill in the gaps in the following sentences using the options below:
Two objects are similar if they have
Two objects are congruent if they have 1)the same shape.
2) different shapes.
3)the same shape and size.
4)different shapes and sizes
Answer:
Two objects are similar if they have the same shape.
(1): Two objects are similar if they have the same shape.
(2): Two objects are congruent if they have the same shape and size.
(3): Two objects are congruent if they have the same shape and size.
(4): Two objects are congruent if they have different shapes and sizes.
Hope this helps! I'm sorry if it's wrong. If you need more help, ask me! :]
7. The sides of a rectangle are in the ratio 5:2. If the perimeter of the rectangle is 42 cm, find the area of the rectangle.
Answer:
90 cm²
Step-by-step explanation:
Let the greater side be the length L and the smaller side the width W
Given L : W = 5 : 2
we can rewrite this as a fraction
[tex]\dfrac{L}{W} = \dfrac{5}{2}[/tex]
Cross-multiplying we get
2L = 5W
The perimeter of a rectangle
= 2(L + W)
= 2L + 2W
and we are told it is 42 cm
Therefore
2L + 2W = 42
Substitute 5W for 2L to get
5W + 2W = 42
7W = 42
or
W = 42/6 = 6
Given 2L + 2W = 42, substitute 6 for W to get
2L + 2(6) = 42
2L + 12 = 42
2L = 42 - 12= 30
L = 30/2 = 15
So length L = 15
Just to check
L/W = 15/6 = 5/2 by dividing both numerator and denominator by 3
Area of the rectangle
= L x W
= 15 x 6
= 90 cm²
F(x)=4x^2+2
a) F(1)=
B) F(-1)=
C) F(-4)
D) F(-7/2)=
Answer:
F(1) = 6
F(-1) = 6
F(-4) = 66
F(-7/2) = 51
14. EXTENSION QUESTION
A GIVE WAY sign in the shape of an equilateral triangle is 110cm in height. Find the length of one
of its sides. Include a diagram.
The length of one of the sides of the GIVE WAY sign, equilateral triangle is approximately 200.89cm.
What is an equilateral triangle?
An equilateral triangle in geometry is a triangle with equally long sides. The three angles opposing the three equal sides are equal in size because the three sides are equal. As a result, with each angle measuring 60 degrees, it is sometimes referred to as an equiangular triangle. Equilateral triangles have the same area, perimeter, and height formula as other kinds of triangles.
Given that the triangle is an equilateral triangle, thus all sides are equal.
Let us suppose the sides = x.
The height of the equilateral triangle is given by:
height = (√3/2) x side length
Substituting the values:
110 = (√3/2) x (x)
x = 110 / (√3/2)
x ≈ 200.89cm
Hence, the length of one of the sides of the GIVE WAY sign is approximately 200.89cm.
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in a group more than 1/2 are boys but there are less than 2/3 of the group can there be 4 people
The minimum number of people in the group should be 3.
In a group more than 1/2 are boys but there are less than 2/3 of the group.
Let the number of people in the group be x.
Therefore, the number of boys in the group is greater than 1/2 × x or x/2.
The number of people in the group is less than 2/3 × x or 2x/3.
As per the question, x > x/2 and x < 2x/3
multiply both sides by 2,
so we get:
2x > x and 2x < 4x/3.
Now, simplify the above equations as follows:
2x > x ⇒ x > 0 and
2x < 4x/3 ⇒ 6x < 4x ⇒ 0 < -2x ⇒ x < 0
Thus, it is not possible to have a group of 4 people as the number of people in the group is greater than 0.
Therefore, the minimum number of people in the group should be 3.
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Write the following ratio in its simplest form: 64:18
Answer:
32:9
Step-by-step explanation:
64 :18
32: 9
So 32: 9 is its simplest form.
Answer:
32:9
Step-by-step explanation:
64 : 18
Divide both sides by a common number 2
32 : 9
This cannot be further divided
an angle measures 2.8 radians and the initial ray of the angle points in the 3-o'clock direction. a circle with a radius 2.6 cm long is centered at the angle's vertex. the terminal point is how many radii to the right of the circle's center? radii the terminal point is how many cm to the right of the circle's center? cm
Therefore, the terminal point is 0.26 radii to the right of the circle's center and 0.67 cm to the right of the circle's center.
The angle in question has an initial ray pointing in the 3-o'clock direction and measures 2.8 radians. It is centered at the vertex of a circle with a radius of 2.6 cm. To calculate the number of radii and the number of cm the terminal point is to the right of the circle's center, we need to use the formula for arc length. Arc length is equal to the circumference of the circle multiplied by the central angle's measurement, divided by 2π.
So, the arc length of this angle is equal to 2.6 cm times 2.8 radians divided by 2π, or[tex]2.6 x 2.8 / 6.28 = 0.67 cm.[/tex] The terminal point is 0.67 cm to the right of the circle's center, which is equal to [tex]0.67/2.6 = 0.26 radii.[/tex]
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A bottle filling machine fills 25 bottles per minute. A second machine fills 15 bottles per minute. The second machine starts filling bottles 20 minutes after the first machine starts. Both machines stop filling bottles after 300 minutes after the first machine started. Which equation represents the situation of how many bottles will be filled?
A) 300(25)+290(15)
B) 300(25)+280(25)
C) 300(25)+300(25)
D) 300(25)+280(15)
25 bottles every minute are filled using a filling and capping machine in [tex]11700[/tex]
What use does a machine serve?Even though both pressures and movements are involved in a machine's functioning, one of its principal functions can either be force amplification or motion modification. A lever essentially adds force, but a gearbox often acts as a speed reducer.
What in mathematics is a machine diagram?A machine diagram represents a function operation on a variable x to create a variable output y diagrammatically. If x falls inside the scope of the f(x, the machine will accept x as an input and output y in accordance with the function's rules.
[tex]25 bottles/minute * 20 minutes = 500 bottles.[/tex]
During the remaining [tex]280[/tex] minutes, both machines are running and together they fill
[tex]25 bottles/minute + 15 bottles/minute = 40 bottles/minute[/tex]
So, the total number of bottles filled during this period is
[tex]40 bottles/minute * 280 minutes = 11,200 bottles.[/tex]
[tex]500+ 11,200= 11,700[/tex]
None of the given options represents this equation.
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The diameter of a circle is 6 kilometers. What is the length of a 30 degree arc
Hence, in answering the stated question, we may say that As a result, the circle length of a 30-degree arc of a 6-kilometer-diameter circle is approximately 1.57 kilometers.
What is circle?Each spot that is a particular distance from yet another point creates a circle in the plane (center). As a result, it is a curve composed of points separated in the plane by a given distance. Furthermore, at all angles, it is circumferentially symmetric the about centre. Every couple of points in such a circle's closed, two at least plane is evenly spaced out from the "centre." A round symmetry line is formed by tracing a line through circle. Furthermore, at all angles, it is rotationally equal about the centre.
The circumference of a circle can be calculated using the formula C = d, where d is the circle's diameter. Because the diameter in this case is 6 kilometres, the circumference is:
C = d = (6) = 18.85 km (rounded to two decimal places)
1/12 = 30 degrees / 360 degrees
As a result, the length of the 30 degree arc is:
1.57 km length = (1/12) * C = (1/12) * 18.85 km (rounded to two decimal places)
As a result, the length of a 30-degree arc of a 6-kilometer-diameter circle is approximately 1.57 kilometres.
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which equality represents a proportional relationship
The answer is B hope it helps
Consider the following linear programming problem:Maximize 6x+5y (OBJ)Subject tox+y≤6 (1)2x+y≤8 (2)y≤5 (3)
The maximum value of the objective function is 33, which occurs at the corner point (3, 3)
According to the question we have to maximize 6x+5y (OBJ)Subject tox+y≤6 (1)2x+y≤8 (2)y≤5 (3).Linear programming is a mathematical method that aims to maximize or minimize an objective function subject to a set of linear constraints. In this problem, we are asked to maximize the objective function 6x + 5y subject to the constraints given by the inequalities 1, 2, and 3.
The inequalities 1, 2, and 3 define a feasible region in the xy-plane, which is a region that satisfies all the constraints. The feasible region can be found by graphing the three inequalities and shading in the region that satisfies all of them.
In this case, the feasible region is a triangle with vertices (0, 0), (3, 3), and (4, 1), as shown below:
The objective function 6x + 5y is evaluated at each corner point as follows:
At (0, 0), 6(0) + 5(0) = 0, At (3, 3), 6(3) + 5(3) = 33, At (4, 1), 6(4) + 5(1) = 29. Thus, the optimal solution is x = 3 and y = 3, and the maximum value of the objective function is 33.
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Find the missing information for the triangle. *not drawn to scale
The measure of the angle x is 60 degrees and the sides of the triangle is 4√3 and 8.
What is sum of interior angles of triangle?According to the triangle sum theorem, a triangle's internal angles can be added up to 180 degrees. The triangle sum theorem, often referred to as the angle sum theorem of the triangle, states that the total of the measures of a triangle's internal angles in a Euclidean space adds up to 180 degrees, whether the triangle is acute, obtuse, or right. The smallest polygon with three sides and three internal angles, one at each vertex, and bordered by two neighbouring sides is a triangle.
Given that, angle B = 30 degrees and angle m = 90 degrees.
The sum of all the angles of a triangle is 180 degrees.
Thus,
30 + 90 + angle x = 180
120 + angle x = 180
angle x = 180 - 120
angle x = 60
The sides is thus a triangle with angle 30-60-90.
For this case the sides are in the ratio:
x : x√3 : 2x
From the figure we see that, x = 4.
Thus, the remaining sides are:
x√3 = 4√3 and 2x = 2(4) = 8
Hence, the measure of the angle x is 60 degrees and the sides of the triangle is 4√3 and 8.
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What is the area of a sector with a central angle of 30° and a radius of 12.5 cm?
Use 3.14 for π and round your final answer to the nearest hundredth.
Enter your answer as a decimal in the box.
The area of the sector is equal to 40.89 cm².
How to calculate the area of a sector?Mathematically, the area of a sector can be calculated by using this formula:
Area of sector = θπr²/360
Where:
r represents the radius of a circle.θ represents the central angle.Substituting the given parameters into the area of a sector formula, we have the following;
Area of sector = θπr²/360
Area of sector = 30(3.14/360) × (12.5)²
Area of sector = 0.2617 × 156.25
Area of sector = 40.89 cm²
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Please help me find the missing sides to solve this equation
Trigonometry is a branch of mathematics that deals with the relationships and properties of triangles, particularly the relationships between their sides and angles.
What is trigonometry?1) sin 30 = 10/u
u = 10/sin 30
u = 20
Cos 30 = v/20
v = 20cos 30
v = 17
2) cos 30 = 4√3/m
m = 4√3/√3/2
m = 4√3 * 2/√3
m = 8
Sin 30 = n/8
n = 8 sin 30
n = 4
3) sin 60 = x/7
x = 7 sin 60
x = 6
Cos 60 = y/7
y = 7 Cos 60
y = 3.5
4) Tan 30 = v/10√3
v = 10√3 * 1/√3
v = 10
Cos 30 = 10√3/u
u = 10√3/Cos 30
u = 10√3/√3/2
u = 10√3 * 2/√3
u = 20
5) Sin 60 = x/6√3
x = 6√3Sin 60
x = 6√3 * √3/2
x = 3
Cos 60 = y/6√3
y = Cos 60 * 6√3
y = 6√3 * 1/2
y = 3√3
6) Sin 60 = x/4√2
x = Sin 60 * 4√2
x = 4√2 * √3/2
x = 2√6
Cos 60 = y/4√2
y = Cos60 * 4√2
y = 1/2 * 4√2
y = 2√2
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A large game cube with a three inch side length is wrapped with shrink wrap how much shrink wrap will be used to wrap ten game cubes
The quantity of shrink wrap that will be used to wrap ten game cubes is 540 square inches
To calculate the amount of shrink wrap needed to wrap ten game cubes, we need to first find the surface area of one game cube, and then multiply it by 10.
The surface area of a cube can be found by multiplying the length of one side by itself, and then multiplying that by 6 (since there are six faces on a cube). In this case, the length of one side is 3 inches, so the surface area of one cube is:
Surface area of one cube = 3 x 3 x 6 = 54 square inches
To wrap ten cubes, we need to multiply the surface area of one cube by 10:
Surface area of ten cubes = 54 x 10 = 540 square inches
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Antonio participa en la restauración del salón comunal. Pinta una pared de 15m² de la siguiente manera 4m² de color melón 5m² de color verde y 6m² de color blanco ¿Que fracción de la pared pinta de cada color ? EXPRESE CADA UNA DE LAS FRACCIONES DEL EJERCICIO EN NOTACION DECIMAL
Antonio painted about 27% of the wall with melon color, 33% with green color, and 40% with white color.
Antonio painted a wall with an area of 15 square meters. He painted 4 square meters with melon color, 5 square meters with green color, and 6 square meters with white color.
To find the fraction of the wall that Antonio painted with each color, we need to divide the area painted with each color by the total area of the wall:
Fraction painted with melon color = 4 / 15 = 0.2666... ≈ 0.27
Fraction painted with green color = 5 / 15 = 0.3333... ≈ 0.33
Fraction painted with white color = 6 / 15 = 0.4
So Antonio painted about 27% of the wall with melon color, 33% with green color, and 40% with white color.
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Complete Question:
Antonio is participating in the restoration of the communal room. He paints a wall of 15m² in the following way: 4m² of melon color, 5m² of green color, and 6m² of white color. What fraction of the wall does he paint with each color? EXPRESS EACH OF THE FRACTIONS IN THE EXERCISE IN DECIMAL NOTATION.
A shop sells bottles of orange juice for £1.60, but will take 20% off the total cost when you buy more than 20 bottles. How much does it cost, in pounds (£), to buy 40 bottles of orange juice?
Answer: 51.2 pounds
Step-by-step explanation: The problem states that 20% of the total cost is taken when you purchase more than 20 bottles.
We start by finding the total cost without the 20% off
Multiply the unit price by the number of bottles
[tex]1.60*40 = 64 pound[/tex]
Next use the discount, since we are getting 20% off we only have to pay 80% of it and 80/100 simplifies to 4/5 so we can just multiply 64 by that.
[tex]64*4/5 = 51.2[/tex]
The cost of buying 40 bottles of orange juice, with a 20% discount, is £51.20.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
The cost of one bottle of orange juice is £1.60.
To find the cost of 40 bottles of orange juice
40 bottles x 1.60 per bottle = £64
The total cost without the discount would be £64.
To calculate the discount, we can multiply the total cost by 20% or 0.20:
Discount = 20% x £64 = £12.80
The discount on 40 bottles of orange juice is £12.80.
To find the final cost, we need to subtract the discount from the total cost:
Final cost = Total cost - Discount
= £64 - £12.80
= £51.20
Therefore, the cost of buying 40 bottles of orange juice, with a 20% discount, is £51.20.
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The height of a student is measured as 1.6m to the nearest tenth of a meter. Find to one significant figure, the greatest possible percentage error
Answer: 7.4
Step-by-step explanation:
Katherine has $8.60 in dimes and quarters. If she has twelve more quarters than dimes, how many dimes does she have? How many quarters does she have?
After addressing the issue at hand, we can state that by function Katherine now has 28 quarters.
what is function?Mathematicians investigate numbers and their varieties, equations and adjacent tissues, shapes but instead their locations, and potential locations for these things. The term "function" refers to the relationship here between set of inputs, each with its own output. A function is a relationship of both inputs and outputs in which each input results in a single, distinct production. Each function has its own domain, codomain, or scope. The letter f is commonly used to denote functions (x). An x represents entry. On functions, each capabilities, so several capabilities, in capabilities, and on operations are the four major types of accessible functions.
Let's represent the unknown quantities with variables.
Let d be the number of dimes Katherine possesses.
Let q represent Katherine's number of quarters.
We can deduce from the problem:
Equation 1: Total dimes and quarters value = $8.60 0.10d + 0.25q = 8.60
Number of quarters = Number of dimes + 12 q = d + 12 Equation 2:
Now we can plug equation 2 into equation 1 to eliminate q and find d:
0.10d + 0.25(d + 12) = 8.60
Katherine now has 16 dimes.
We can use equation 2 to calculate the number of quarters:
q = d + 12 = 16 + 12 = 28
Katherine now has 28 quarters.
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The demand and supply curves are given by y=10-3x³ and y=4+x²+2x (y represents the price and x quantity). Find the equilibrium price and quantity
If the demand and supply curves are given by y=10-3x³ and y=4+x²+2x, the equilibrium quantity is approximately 1.477 units, and the equilibrium price is approximately $5.44 per unit.
To find the equilibrium price and quantity, we need to find the point where the demand curve intersects the supply curve. At this point, the quantity demanded by consumers is equal to the quantity supplied by producers, which means that the market is in equilibrium.
We can set the two equations equal to each other to find the equilibrium quantity:
10 - 3x³ = 4 + x² + 2x
Simplifying the equation, we get:
3x³ + x² - 2x - 6 = 0
We can solve for x using algebraic methods or by using a graphing calculator. Either method will yield three roots for x, but only one of them will be positive and realistic in the context of the problem.
The positive root for x is approximately 1.477, which means that the equilibrium quantity is approximately 1.477 units.
To find the equilibrium price, we can substitute the equilibrium quantity into either the demand or supply equation. Let's use the demand equation:
y = 10 - 3(1.477)³
Solving for y, we get:
y ≈ 5.44
Therefore, the equilibrium price is approximately $5.44 per unit.
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