Answers
the width of the land is reduced by the same percentage as the area.
What is a rectangle?
A rectangle is a four-sided flat shape in which the opposite sides are parallel and equal in length.
To solve this problem, we can use the formula for the area of a rectangle:
Area = length x width
We know that the area of the tennis court is 260.7569 m and the width of the court is 10.97 m. Using these values, we can find the length of the court:
260.7569 = length x 10.97
length = 260.7569 / 10.97
length = 23.7806 m
So, the length of the tennis court is 23.7806 m.
To find the area of the court without the white bands, we need to reduce the length by the width of the bands on top and bottom.
10.97 - (1.37 x 2) = 8.23 m
To find the effective length of the court, we need to reduce the length by 25% of its original value:
length without bands = length - (25% x length)
length without bands = 23.7806 - (0.25 x 23.7806)
length without bands = 17.83545 m
Now, we can find the area of the court without the white bands:
Area without bands = length without bands x effective width
Area without bands = 17.83545 x 8.23
Area without bands = 146.82277 m
Therefore, the area of the court without the white bands is 146.82277 m².
To determine whether the width of the land is also reduced by 25%, we can compare the effective width of the court with the original width:
Effective width = 8.23 m
Original width = 10.97 m
To find the percentage change in width, we can use the formula:
% change = (|new value - old value| / old value) x 100%
% change = (|8.23 - 10.97| / 10.97) x 100%
% change = 25%
The percentage change in width is 25%, which means that the width of the land is reuced by 25% when we do not use the white bands.
Therefore, the width of the land is reduced by the same percentage as the area.
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Related Questions
AOC is a right-angle AOB: BOC - 2:3 what is the size of angle BOC
Answers
Angles AOB and BOC are complimentary angles if AOC is a right angle. Let's use x to represent the angle BOC's size. Next, we have: Angle AOB plus Angle BOC equals 90° (definition of complementary angles).
BOC/AOB angle equals 2/3 (given) Angle AOB may be expressed in terms of angle BOC using the second equation: (3/2) × angle BOC, where angle AOB (multiplying both sides by angle AOB) Angle BOC plus angle (3/2) equals 90 degrees. When we simplify this equation, we obtain: BOC angle (5/2) times equals 90 degrees. By multiplying both sides by 5, we obtain: BOC angle = (2/5) x 90 degrees BOC angle is 36 degrees. Hence, the angle's size Substituting this expression into the first equation, we get: (3/2) x angle BOC + angle BOC = 90 degrees Simplifying this equation, we get: (5/2) x angle BOC = 90 degrees.
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Which of the following equations is equivalent to 2 x + 6 = 30 - x - 3 2 x + 6 = 10 - x - 3 2 x + 6 = 30 - x + 3
Answers
The equation that is equivalent to 2x + 6 = 30 - x - 3 is option (a): 2x + 6 = 30 - x - 3.
What is equation?
In mathematics, an equation is a statement that two expressions are equal, usually written with an equal sign (=) between them. Equations can contain variables, which are symbols that represent unknown or unspecified values.
We can simplify and solve the equation 2x + 6 = 30 - x - 3 as follows:
2x + 6 = 30 - x - 3
Adding x and adding 3 to both sides, we get:
3x + 9 = 30
Subtracting 9 from both sides, we get:
3x = 21
Dividing both sides by 3, we get:
x = 7
So the given equation simplifies to x = 7.
We can now substitute this value of x into each of the answer choices to see which one is equivalent to the given equation:
a) 2x + 6 = 30 - x - 3
Substituting x = 7, we get:
2(7) + 6 = 30 - 7 - 3
14 + 6 = 20
20 = 20
b) 2x + 6 = 10 - x - 3
Substituting x = 7, we get:
2(7) + 6 = 10 - 7 - 3
14 + 6 = 0
20 ≠ 0
Therefore, this equation is not equivalent to the given equation.
c) 2x + 6 = 30 - x + 3
Substituting x = 7, we get:
2(7) + 6 = 30 - 7 + 3
14 + 6 = 26
20 ≠ 26
Therefore, this equation is not equivalent to the given equation.
Therefore, the equation that is equivalent to 2x + 6 = 30 - x - 3 is option (a): 2x + 6 = 30 - x - 3.
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Find the surface area of this triangular prism. Be sure to include the correct unit in your answer.
X
Answers
The surface area of the triangular prism is 2016 [tex]feet ^2[/tex], we get to the answer by adding area of all faces in this prism.
What is surface area ?
Surface area is the sum of the areas of all the faces or surfaces of a 3D object, measured in square units.
To find the surface area of the triangular prism, we need to calculate the area of each of its faces and then add them up.
First, let's find the area of the triangular base.
Area of triangle = (1/2) x base x height
Area of triangle = (1/2) x 18 x 24
Area of triangle = 216 [tex]feet ^2[/tex]
Next, let's find the area of each rectangular face.
Area of rectangle = length x width
Area of rectangle 1 = 24 x 22 = 528 [tex]feet ^2[/tex]
Area of rectangle 2 = 18 x 22 = 396 [tex]feet ^2[/tex]
Area of rectangle 3 = 22 x 30 = 660 [tex]feet ^2[/tex]
Now, we can add up the areas of all three faces to get the total surface area of the prism:
Surface area = area of rectangle (1+2+3) + 2 x area of triangle
Surface area = 528 + 396 + 660 + 2(216)
Surface area = 2016 [tex]feet ^2[/tex]
Therefore, the surface area of the triangular prism is 2016 [tex]feet ^2[/tex].
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can someone please explain?
Answers
It would make it easier for the cafe to adjust prices if necessary, as they would only need to modify the cost per ounce for each size.
What is cost?Cost is the amount of money or resources required to purchase or produce something. It can be the total expenditure on a product, service, or activity. It can also refer to the amount of money or resources consumed in order to maintain or achieve something. Cost can also be the value of a resource lost or sacrificed in order to obtain something.
To make the price of smoothies a function of the size, the sign should be modified to include the following additional information:
8 ounce $2.29/ounce
12 ounce $2.79/ounce
12 ounce. $3.09/ounce
16 ounce $3.69/ounce
20 ounce $4.09/ounce
22 ounce
( Bonus size). $4.09/ounce
This change would make the price of smoothies a function of the size, as each smoothie size would then have its own associated cost per ounce. This would make it easier for customers to compare the cost of different sizes and make an informed decision. Furthermore, it would make it easier for the cafe to adjust prices if necessary, as they would only need to modify the cost per ounce for each size.
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The supervisor at vector control wants your report of how the mosquito population is growing. Do you think your report is better supported by the table above or by a graph of the growth function as show below? WHY? Explain the reasoning behind your conclusion.
Answers
As a result, utilizing the graph of the growth function is preferable for describing the growth of the mosquito population .
what is vector ?A vector is a mathematical concept that possesses both magnitude (or length) and direction. In physics, engineering, and other sciences, physical quantities with both a size and a direction, such as velocity, force, and acceleration, are frequently represented by vectors. In geometry, vectors can be represented as arrows, with the direction of the arrow indicating the vector's magnitude and the length of the arrow indicating its magnitude. In addition to being able to represent points in space and describe curves and surfaces, vectors may also be added, subtracted, and multiplied by scalars to create new vectors.
given
Based on the provided table and the growth function graph, I would argue that the report on the growth of the mosquito population is better supported by the graph.
On the other hand, there is no visual representation of the growth of the mosquito population in the table; it merely displays the data in a tabular format.
Although the table contains the same data as the graph, it is more difficult to understand and evaluate.
As a result, utilizing the graph of the growth function is preferable for describing the growth of the mosquito population .
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please help quickly, this needs to be finished soon
Answers
Accοrding tο the fοrmula fοr the quadratic equatiοn, the maximum height is 98 ft.
What is a quadratic equatiοn?A quadratic equatiοn is a secοnd-degree pοlynοmial equatiοn οf the fοrm:
[tex]ax^2 + bx + c = 0[/tex]
where a, b, and c are cοnstants, and x is the variable. The term "quadratic" cοmes frοm the Latin wοrd "quadratus," meaning square, because the variable is squared in this type οf equatiοn.
Quadratic equatiοns can have οne, twο, οr zerο real sοlutiοns, depending οn the values οf the cοnstants a, b, and c. The sοlutiοns can be fοund using the quadratic fοrmula:
[tex]x = (-b\± \sqrt{(b^2 - 4ac)}) / 2a[/tex] οr by factοring the quadratic expressiοn intο twο linear factοrs.
The quadratic functiοn tο mοdel the vertical mοtiοn is:
[tex]h(t) = -16t^2 + v0t + h0[/tex]
where:
h(t) is the height at time t
t is the time in secοnds
v0 is the initial vertical velοcity in ft/s
h0 is the initial height in ft
Given v0 = 32 ft/s and h0 = 82 ft, the functiοn becοmes:
[tex]h(t) = -16t^2 + 32t + 82[/tex]
Tο find the maximum height, we can use the vertex fοrm οf a quadratic equatiοn:
[tex]h(t) = a(t - t0)^2 + h0[/tex]
where:
a is the cοefficient οf the quadratic term
t0 is the time at which the maximum height is achieved
h0 is the initial height
Cοmparing the twο fοrms, we see that a = -16 and t0 = -b/2a, where b is the cοefficient οf the linear term. In this case, b = 32, sο:
t0 = -32 / (2(-16)) = 1
Therefοre, the maximum height is achieved at t = 1 secοnd. Substituting intο the οriginal equatiοn, we get:
[tex]h(1) = -16(1)^2 + 32(1) + 82 = 98 ft[/tex]
Sο the maximum height is 98 ft.
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Fractions of money question
Answers
1/6 + 1/4= 10/24 (5/12 simplified)
2.50× 12= 30
This is the total sum of money shared.
7/12 is given to Farooq
7/12 of 30 is 17.5
answer= £17.5
There is a bag filled with 5 blue, 2 red and 3 green marbles. A marble is taken at random from the bag, the colour is noted and then it is not replaced. Another marble is taken at random. What is the probability of getting 2 the same colour?
Answers
Answer:
2/9 + 5/36 = 17/36
So the probability of getting 2 marbles of the same color is 17/36 or 0.472.
Answer:
17/36
Step-by-step explanation:
HELP ASAP!!
A kite is flying 10 feet off the ground. It’s line is pulled out in casts a 9 foot shadow, find the length of the line if necessary round to the nearest 10th.
Answers
Answer:
We can use similar triangles to solve this problem. Let's call the length of the kite's line "x". Then, we can set up a proportion:
(length of kite) / (length of shadow) = (height of kite) / (length of shadow)
x / 9 = 10 / 9
To solve for x, we can cross-multiply and simplify:
x = 90 / 9
x = 10
Therefore, the length of the kite's line is 10 feet.
Step-by-step explanation:
Elise saved $184. She bought a scarf, a necklace, and a notebook. After the purchases, she still had $89. 50. The scarf cost three-fifths the cost of the necklace and the notebook cost one-sixth as much as the scarf. How much did the notebook cost?
Answers
The cost of the notebook is $4.50
Let's call the cost of the necklace "N" and the cost of the scarf "S". We know that Elise spent a total of $184 on the scarf, necklace, and notebook, so we can write:
S + N + NB = 184
We also know that after making her purchases, Elise had $89.50 left, so we can write:
89.5 = 184 - (S + N + NB)
Simplifying this equation, we get:
S + N + NB = 94.5
We're also given that the scarf cost three-fifths the cost of the necklace, so we can write
S = (3/5)N
Finally, we're told that the notebook cost one-sixth as much as the scarf, so we can write:
NB = (1/6)S
Now we can the substitution method here
(3/5)N + N + (1/6)(3/5)N = 184 - 89.5
Simplifying the right-hand side
(3/5)N + N + (1/6)(3/5)N = 94.5
Combining like terms on the left-hand side
(21/10)N = 94.5
Multiplying both sides by 10/21
N = 45
So the necklace cost $45. We can use this to find the cost of the scarf
S = (3/5)N = (3/5)($45) = $27
And we can use the cost of the scarf to find the cost of the notebook
NB = (1/6)S = (1/6)($27) = $4.50
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the ratio of students who ade the honor roll to the total number of stoudents is 1:50. if there are 500 students in total how many made the honor roll?
Answers
If there are 500 students in total, the number of students who made the honor roll is 10 students, given that the ratio of students who made the honor roll to the total number of students is 1:50.
The number of students who made the honor roll can be found using proportions. Here's how to do it:
Let X be the number of students who made the honor roll.
The proportion can be set up using the given ratio as follows:
1:50 = X:500
Cross-multiplying this equation and solving for X gives:
50X = 500
X = 10
Therefore, 10 students made the honor roll.
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Find the surface area of the rectangular pyramid.
1 = 12 ft, w = 8 ft, sh = 10 ft
a 194 ft²
b 182 ft²
c 272 ft²
d 296 ft²
Check it
Answers
In response to the stated question, we may state that As a result, the rectangular pyramid has a surface area of 296 ft2. 296 ft2 is the correct answer.
What is rectangle?In Euclidean geometry, a rectangle is a parallelogram with four small angles. It may also be defined as a fundamental rule hexagon or one in which all of the angles are equal. Another alternative for the parallelogram is a straight angle. Four of the vertices of a square are the same length. A quadrilateral with four 90° angle vertices and equal parallel sides has a rectangle-shaped cross section. As a result, it is also known as a "equirectangular rectangle" at times. A rectangle is sometimes referred to as a parallelogram due to the equal and parallel dimensions of its two sides.
To determine the surface area of a rectangular pyramid, first calculate the area of each face and then add them together.
Given the rectangular pyramid's dimensions:
Slant height= 10 ft base length (l) = 12 ft base width (w) = 8 foot
Then, calculate the area of the base. The area of the base is simply l w: because it is a rectangle.
Base area = [tex]12 ft x 8 ft = 96 ft^2[/tex]
A triangle face's area equals 1/2 its base height, where base = w or l and height = sh.
[tex]1/2 *8 ft *10 ft = 40 ft^2[/tex] area of the first triangle face
[tex]1/2 *12 ft *10 ft = 60 ft^2[/tex]area of the second triangular face
Third triangular face area = [tex]1/2 *8 ft *10 ft = 40 ft^2[/tex]
The area of the fourth triangular face is equal to [tex]1/2 *12 ft *10 ft = 60 ft^2.[/tex]
Now put the areas of all the faces together to get the entire surface area:
Total surface area = base area + sum of all triangular face areas
Surface area total =[tex]96 ft^2 + (40 ft^2 + 60 ft^2 + 40 ft^2 + 60 ft^2)[/tex]
296 ft2 total surface area
As a result, the rectangular pyramid has a surface area of 296 ft2.
296 ft2 is the correct answer.
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given the results of the two hypothesis tests, would you reject or fail to reject your null hypotheses (assuming a 0.05 significance level)? what does your decision mean in the context of this problem? would you proceed with changing the design of the shopping cart icon, or would you stay with the original design?
Answers
Assuming a 0.05 significance level, both hypothesis tests would reject the null hypothesis. This means that there is enough evidence to suggest that the shopping cart icon's design affects the users' behavior. Therefore, the design should be changed to improve the user's experience.
Step by step explanation:
The problem is not stated, so we need to make some assumptions. We will assume that the hypothesis tests were done to determine whether a change in the shopping cart icon design would affect the users' behavior.
The null hypothesis (H0) is that the design of the shopping cart icon does not affect the users' behavior, while the alternative hypothesis (Ha) is that the design of the shopping cart icon affects the users' behavior.
The significance level is 0.05, which means that we are willing to accept a 5% chance of making a type I error (rejecting the null hypothesis when it is actually true).
If both hypothesis tests reject the null hypothesis, it means that the p-values were less than 0.05, and there is enough evidence to suggest that the design of the shopping cart icon affects the users' behavior.
Therefore, it is recommended to proceed with changing the design of the shopping cart icon to improve the user's experience.
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Find the slope-intercept form of the line with the slope m= 1/7 which passes through the point (-1, 4).
Answers
Answer:
y = 1/7x + 29/7
Step-by-step explanation:
Slope intercept form is y = mx + b
m = the slope
b = y-intercept
m = 1/7
Y-intercept is located at (0, 29/7)
So, the equation is y = 1/7x + 29/7
A cylindrical tank is one-fifth full of oil. The cylinder has a base radius of 80 cm. The height of the cylinder is 200 cm. 1 litre 1000 cm3 How many litres of oil are in the tank? Round your answer to the nearest litre
Answers
The number of litres (Volume) of oil that is present in the tank of given dimension is calculated to be 806 litres (approximately).
The volume of any cylinder can be calculated using the formula,
V = πr²h
(Here V is the volume, r is the radius of the base, and h is the height of the cylinder)
As, the cylinder is one-fifth full of oil, which means that it is four-fifths empty. Therefore, the volume of oil in the tank is:
Volume of oil = (1/5) x Total Volume
Substituting the given values, we have:
Total Volume = π(80cm)²(200cm) = 4,031,240 cm³
Volume of oil = (1/5) x 4,031,240 cm³ = 806,248 cm³
Converting cm³ to litres, we have:
1 litre = 1000 cm³
Volume of oil = 806,248 cm³ ÷ 1000 = 806.248 litres
Therefore, after rounding of the final volume (806.248 litres) to the nearest litre, the final answer is found to be 806 litres of oil.
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John Paszel took out a loan for 51 months but paid it in full after 25 months. Find the refund fraction he should use to
calculate the amount of his refund.
Answers
Answer: calculate the amount of his refund.
Step-by-step explanation:
Which expression represents the perimeter of a triangle in simplest form that has side lengths: 2x, 3x + 5, x + 2
Answers
Answer:
6x + 7
Step-by-step explanation:
triangle has 3 sides right, which is 2x, 3x+5 and x+2
so basically you just have to add everything up since perimeter is just the total number of each sides combined
2x + (3x+5) + (x+2)
expand from the brackets
2x + 3x + 5 + x + 2
rearrange the numbers to avoid confusion
2x + 3x + x + 5 + 2
add everything up
6x + 7
I NEED HELP ON THIS ASAP!!
Answers
From the graph, the feasible region from the system of linear inequalities is the triangular region bounded by the x-axis, the y-axis, the line x + y = 120, the line x = 60, and the line y = 90.
What is the system of linear inequalitiesa. Let x be the amount of loam soil (in tons) sold, and y be the amount of peat soil (in tons) sold. The system of inequalities representing the constraints of the problem situation is:
x ≥ 0 (non-negative amount of loam soil)
y ≥ 0 (non-negative amount of peat soil)
x + y ≤ 120 (total amount of soil sold is at most 120 tons)
x ≤ 60 (maximum amount of loam soil available is 60 tons)
y ≤ 90 (maximum amount of peat soil available is 90 tons)
To graph these inequalities, we can plot the feasible region (the region that satisfies all the inequalities) in the x-y plane, as shown below;
The feasible region is the triangular region bounded by the x-axis, the y-axis, the line x + y = 120, the line x = 60, and the line y = 90.
b. The profit function P(x, y) for selling x tons of loam soil and y tons of peat soil is:
P(x, y) = 50x + 75y
To maximize profit, we need to find the values of x and y that satisfy the constraints of the problem situation and maximize the profit function P(x, y). One way to do this is to use the method of linear programming, which involves finding the corner points of the feasible region and evaluating the profit function at each corner point.
The corner points of the feasible region are (0, 0), (60, 0), (60, 60), (30, 90), and (0, 90). Evaluating the profit function at each corner point, we get:
P(0, 0) = 0
P(60, 0) = 3000
P(60, 60) = 9000
P(30, 90) = 6750
P(0, 90) = 6750
Therefore, the maximum profit is $9000, which occurs when the company sells 60 tons of loam soil and 60 tons of peat soil.
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determine the smallest integer value of x in -2x+1< -9
Answers
Answer: The smallest integer value of x that satisfies the inequality -2x+1<-9 is x=5.
Step-by-step explanation:
Answer: The smallest integer value of x that satisfies the inequality -2x+1<-9 is x=5.
Explanation:
To solve the inequality, we need to isolate the variable x on one side of the inequality symbol. Here are the steps:
Subtract 1 from both sides of the inequality:
-2x < -10
Divide both sides of the inequality by -2, remembering to reverse the direction of the inequality symbol:
x > 5
Therefore, the smallest integer value of x that satisfies the inequality is x = 5, since any value less than 5 would make the inequality false.
Answer:
x = 6
Step-by-step explanation:
- 2x + 1 < - 9 ( subtract 1 from both sides )
- 2x < - 10
divide both sides by - 2, reversing the symbol as a result of dividing by a negative quantity.
x > 5
since x must be greater than 5, it cannot equal 5
then the smallest integer value of x is x = 6
Austin has a dimes and y nickels, having at most 28 coins worth a minimum of $2
combined. At least 18 of the coins are dimes and no more than 6 of the coins are
nickels. Solve this system of inequalities graphically and determine one possible
solution.
Answers
The solution of system of inequalities solved graphically is (18,6).
What is system of linear inequalities?A group of two or more linear inequalities are graphed together on a coordinate plane to discover the solution that concurrently satisfies all the inequalities. This is known as a system of linear inequalities. The location where all the half-planes overlap is where the system is solved. Each inequality defines a half-plane on the coordinate plane. Every point in this area, which is referred to as the feasible region, fulfils all of the system's inequalities. To identify the optimum solution for an optimization problem given a set of constraints, systems of linear inequalities are frequently utilised.
Let us suppose the number of dimes = a.
Let us suppose the number of nickels = y.
According to the problem we have the following conditions:
a + y ≤ 28 (at most 28 coins)
0.10a + 0.05y ≥ 2 (worth at least $2)
a ≥ 18 (at least 18 dimes)
y ≤ 6 (no more than 6 nickels)
Using different values of a and y plot the points.
The solution of this system of inequality is any point that lies in the feasible region.
One such point is (18, 6).
Hence, the solution of system of inequalities solved graphically is (18,6).
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plese help with the following questions PLESE
Assignment:
Sebastian Salazar opened a Sporting Goods Store. He has some new inventory that needs to be priced. He also has some seasonal inventory that hasn’t sold and he needs to put them on sale.
Help Sebastian with his pricing questions:
Answers
1. The retail prices are: $44.36, $34.10 and $67.57
2. The sales prices are: $263.20 and $65.59
Define the term retail price?Retail price refers to the price at which a product or service is sold to the final consumer by a retailer. This price includes the cost of production, transportation, marketing, and other related expenses, as well as a markup to generate profit for the retailer.
1. New Items - Calculate Retail Prices
Item Wholesale Mark Up Calculation Retail
Cost ($) Percent% Price ($)
a. Louisville $22.75 95% 22.75+(95%×22.75) =$44.36
Slugger bat and
batting glove set
b. Wilson $11.00 210% 11+(210%×11) =$34.10
Basketball
c. Element $26.50 155% 26.50+(155%×26.50) =$67.57
Skateboard
2. Items on sale - Calculate Sale Prices
Item Retail Discount Calculation Sales
price ($) Percent % Price ($)
a. Head $329.00 20% 329-(20%×329) $263.20
Snowboard
b. Kelly $79.99 18% 79.99-(18%×79.99) $65.59
Ski poles
All data is filled in below table.
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It takes 56 minutes for 7 printing machines to
produce a batch of newspapers.
a) How many minutes would it take just 1 machine?
b) How many minutes would it take 8 machines?
Answers
Answer:392
Step-by-step explanation:
a) It would take one machine 392 minutes.
b) It would take one machine 49 minutes.
Define the term proportion?Two ratios are said to be equal when a proportion is stated. When comparing two quantities, ratios are used to divide one quantity by the other.
a) Here given that, to produce a batch of newspaper 7 printing machines needed 56 minutes.
Using this relationship, we can set up a proportion:
as given, 7 printing machine needed = 56 minutes
So, 1 printing machine needed = 7 × 56 minutes = 392 minutes
Therefore, it would take one machine 392 minutes to produce the same batch of newspapers.
b) Similarly, to find out for 8 machines to produce the same batch of newspapers, we can use the same relationship:
1 printing machine needed = 392 minutes
So, 8 printing machine needed = (392 / 8) minutes = 49 minutes
Therefore, it would take one machine 49 minutes to produce the same batch of newspapers.
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three traffic lights on a street span 120 yards. if the second traffic light is 85 yards away from the first, how far in yards is the third traffic light from the seccond
Answers
The distance between the third traffic light from the second traffic light is 35 yards.
What is the distance?Three traffic lights on a street span 120 yards.
If the second traffic light is 85 yards away from the first.
Therefore, the third traffic light is 120 - 85 =35 yards away from the second traffic light.
This means that the third traffic light is directly adjacent to the first traffic light. The third traffic light from the second traffic light is at the same location as the first traffic light.
Thus, the distance between the third traffic light from the second traffic light is 35 yards.
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Design a cylindrical can (with a lid) to contain 1 liter (= 1000 cm3) of water, using the minimum amount of metal.
Answers
To design a cylindrical can (with a lid) to contain 1 liter (= 1000 cm3) of water, using the minimum amount of metal, we need to consider the following parameters:Height and Diameter of the canThickness of the metalMaterial used for making the canLet's assume we use Aluminium as a material. Now, let's start designing the can:Height of the can:
Volume of water = 1000 cm3Volume of cylinder = πr²hVolume of cylinder = π (d/2)² hVolume of cylinder = π (d²/4) hVolume of cylinder = 1000 cm³π (d²/4) h = 1000 cm³d²h = 4000 cm³h = (4000 cm³) / (π d²) h = (4000 cm³) / (3.14 * d²) h = (1273.24) / d²Diameter of the can:
Volume of cylinder = πr²hVolume of cylinder = π (d/2)² hVolume of cylinder = π (d²/4) hVolume of cylinder = 1000 cm³π (d²/4) h = 1000 cm³d²h = 4000 cm³d² = (4000 cm³) / h d² = (4000 cm³) / (1273.24/d²) d² = 3.1425d = 17.8 cmThickness of the metal:We can assume the thickness to be 0.5 mm.Material used for making the can:AluminiumTotal Surface Area of the can:Total Surface Area of cylinder = 2πrhTotal Surface Area of cylinder = 2π(d/2)(1273.24/d²)Total Surface Area of cylinder = 1273.24/d Total Surface Area of lid = πr²Total Surface Area of lid = π (d/2)²Total Surface Area of lid = π (17.8/2)²Total Surface Area of lid = 248.5Total Surface Area of the Can = 1273.24/d + 248.5Now, we can calculate the minimum amount of Aluminium required to make the can by minimizing the Total Surface Area of the can.Total Surface Area of the can = 1273.24/d + 248.5d (in cm)Total Surface Area of the can = 1273.24/7.09 + 248.5(7.09)Total Surface Area of the can = 584.24Therefore, the minimum amount of Aluminium required to make the can is 584.24 cm².
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7. Complete a dilation with scale factor of ½ around the origin and then
reflect over the y-axis. What are the new ordered pair of A'?
Answers
The new ordered pairs of points A', B', and C' after the reflection over the y-axis are (1,-2.5), (0,1.5), and (-3,-1.5), respectively.
WHAT IS AXIS ?
An axis is a straight line around which an object rotates or is symmetrical. In geometry, it is a reference line that is used to measure distances, angles, and other geometric properties of objects. In a two-dimensional plane, there are two axes: the x-axis and the y-axis. The x-axis is the horizontal line that runs from left to right, while the y-axis is the vertical line that runs from bottom to top. Together, the x-axis and y-axis form a coordinate system that is used to plot points and graph functions. In three-dimensional space, there is also a z-axis that runs perpendicular to the x-axis and y-axis
To perform a dilation with a scale factor of 1/2 around the origin, we need to multiply the coordinates of each point by 1/2. This gives us:
A' = (1/2)A = (1/2)(-2,-5) = (-1,-2.5)
B' = (1/2)B = (1/2)(0,3) = (0,1.5)
C' = (1/2)C = (1/2)(6,-3) = (3,-1.5)
The new coordinates of points A, B, and C after the dilation are (-1,-2.5), (0,1.5), and (3,-1.5), respectively.
To reflect each point over the y-axis, we need to change the sign of its x-coordinate, while leaving the y-coordinate unchanged. This gives us:
A" = (-x,y) = (-(-1),-2.5) = (1,-2.5)
B" = (-x,y) = (-0,1.5) = (0,1.5)
C" = (-x,y) = (-3,-1.5) = (-3,-1.5)
The new ordered pairs of points A', B', and C' after the reflection over the y-axis are (1,-2.5), (0,1.5), and (-3,-1.5), respectively.
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At the bookstore, best-sellers are normally $19.95 each. During the store-wide 20% off sale, how much would it cost you, before tax, to buy two best-sellers?
F. $3.99
G. $7.98
H. $15 96
J. $31.92
K. $39.90
Answers
Step-by-step explanation:
20% off means you pay 80 % of the original price for two books
80% * ( 2 x 19.95 ) = .8 ( 39.90) = $ 31.92
The numbers of trading cards owned by 7 middle-school students are given below.
(Note that these are already ordered from least to greatest.)
360, 373, 402, 499, 548, 644, 646
Suppose that the number 646 from this list changes to 639. Answer the following.
Answers
a) If the number 646 from the ordered list changes to 639, c) the median stays the same.
b) a) If the number 646 from the ordered list changes to 639, a) the mean decreases by 1.
What are the median and the mean?The median is the middle value in an ordered list (descending or ascending).
The mean refers to the average value.
The mean or average is computed as the quotient of the division of the total data value by the total number of items in the data set.
The ordered numbers of trading cards owned by 7 middle-school students = 360, 373, 402, 499, 548, 644, 646
The total value (sum) = 3,472
The number of cards = 7
The median = 499
The mean = 496 (3,472/7)
If the number 646 changes too 639:
The total value (sum) = 3,465
The median = 499
The mean = 495 (3,465/7)
Difference in mean = 1 (496 - 495)
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Solve the following proportion for y. 13 11 8 y Round your answer to the nearest tenth. 1 X Ú
Answers
Answer:
Were sorry! Answer is not available right now check in later.
Step-by-step explanation:
anyone know the answer?
Answers
The required value of the base of the triangle is [tex]\frac{7\sqrt{3} }{3}[/tex].
What is right angled triangle?Right-angle triangles are formed when the angle formed by two of their edges is exactly 90 degrees. Obtuse angle triangle: An obtuse angle triangle is one in which the angle formed by two sides is larger than 90 degrees.
According to question:In the given triangle, we will use tangent function to find the value of x.
tan(∅) = Perpendicular/ base
tan(60°) = 7/x
x = 7/tan(60°)
x = 7/√3 ∴ (tan(60°) =√3 )
On rationalizing
x = [tex]\frac{7\sqrt{3} }{3}[/tex]
Thus, required value of x is [tex]\frac{7\sqrt{3} }{3}[/tex].
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12x²+11x-56 box method
Answers
The product of (4x + 7) and (3x - 8) is 12x² + 7x - 56.
WHAT IS BOX METHOD ?
The box method, also known as the grid method, is a visual method used to multiply two numbers or two binomials. It involves creating a grid or box and filling it in with the products of the digits in each row and column. The method works for both single-digit and multi-digit numbers.
To use the box method for multiplying two numbers, we draw a box with two rows and two columns. We write one number along the top row and the other number along the left column. Then, we multiply the digits in each row and column and write the products in the corresponding cell of the box. Finally, we add the numbers in each cell of the box to get the product of the two numbers.
The box method can be used to multiply two binomials, such as (4x + 7) and (3x - 8). To use the box method, we draw a box with four cells, and we write the two binomials along the top and left sides of the box, like this:
| 4x | 7
-------------------
3x | |
-------------------
| |
Then, we fill in the four cells of the box by multiplying the corresponding terms. For example, the top-left cell is filled by multiplying 4x and 3x, which gives 12x². The other cells are filled in a similar way:
| 4x | 7
-------------------
3x | 12x² | 28x
-------------------
| -21x | -56
Next, we combine the terms in each row and column of the box, and write the final answer as the sum of these terms:
12x² + 28x - 21x - 56
Simplifying this expression gives:
12x² + 7x - 56
Therefore, the product of (4x + 7) and (3x - 8) is 12x² + 7x - 56.
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