Let's define the variables:
x = the number of games Angie has.
Susan has 3 more games than Angie, so Susan has x + 3 games.
Rebecca has three times more games than Susan, so Rebecca has 3 * (x + 3) games.
To summarize, the algebraic expressions representing the number of games on each friend's game programs are:
Angie: x games
Susan: x + 3 games
Rebecca: 3 * (x + 3) games
Now let's break down the explanation of the answer. We start by assigning the variable x to represent the number of games Angie has. Since Susan has 3 more games than Angie, we add 3 to x to represent Susan's number of games, resulting in x + 3. Finally, as Rebecca has three times more games than Susan, we multiply Susan's number of games (x + 3) by 3, yielding the expression 3 * (x + 3) to represent the number of games on Rebecca's game program.
In summary, the algebraic expressions representing the number of games on each friend's game programs are: Angie: x games, Susan: x + 3 games, and Rebecca: 3 * (x + 3) games.
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Which of these data sets could best be displayed on a dot plot? 16, 29, 31, 37, 44, 49, 58, 63, 69, 70, 83, 97 0.012, 0.078, 0.093, 0.147, 0.187 721, 722, 722, 723, 724, 724, 724, 725, 727, 728, 730 1.3, 1.9, 2.5, 2.7, 2.7, 3.5, 4.8, 5.3, 7.9, 9.0 Done
A dot plot is a type of graph that can be used to represent numerical data. It displays data using a series of dots, with each dot representing a single data point.
The dots are placed on a horizontal number line, with the value of each dot corresponding to the numerical value of the data point it represents.
A dot plot is most useful when displaying small sets of data.
And
In the given options, the set of numbers 16, 29, 31, 37, 44, 49, 58, 63, 69, 70, 83, and 97 can best be displayed on a dot plot.
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Given a rational expression, identify the excluded values by finding the zeros of the denominator. x(x+17)
the excluded values for the rational expression x(x+17) are x = 0 and x = -17.
In a rational expression, the denominator cannot be equal to zero because division by zero is undefined. To find the excluded values, we need to find the zeros of the denominator.
In this case, the denominator is x(x+17). To find the zeros, we set the denominator equal to zero and solve for x:
x(x+17) = 0
The equation will be satisfied when either x = 0 or x + 17 = 0.
For x = 0, the expression becomes 0(0+17) = 0, which means division by zero would occur.
For x = -17, the expression becomes -17(-17+17) = -17(0) = 0, which again leads to division by zero.
Therefore, the excluded values for the rational expression x(x+17) are x = 0 and x = -17.
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arrange the systems of equations that have a single solution in increasing order of the x-values in their solution
We can arrange the systems as:
3x - 2y = -1
x + y = 7y - x = -3
Here are the steps to do it:
Step 1: Solve each system of equations to find its unique solution.
Step 2: Sort the solutions of each system in increasing order of their x-values.
Step 3: Arrange the systems in the increasing order of their smallest x-values.
Let's use an example to illustrate the steps:
Example:
Arrange the following systems of equations in increasing order of the x-values in their solution:
x + y = 7y - x = -33
x - 2y = -1
Solution:
Step 1: Solve each system of equations to find its unique solution.
x + y = 7 ... (1)
y - x = -3 ... (2)
Add equation (1) and (2) to eliminate x:
(x + y) + (y - x) = 7 - 3
⇒ 2y = 4
⇒ y = 2
Substitute y = 2 in equation (1) to find x:
x + 2 = 7 ⇒ x = 5
The unique solution is (x, y) = (5, 2).
3x - 2y = -1 ... (3)
Solve equation (3) for y:
3x + 2 = -1 + 2y
⇒ 2y = 3x + 1
⇒ y = (3/2)x + 1/2
The unique solution is (x, y) = (x, (3/2)x + 1/2).
Step 2: Sort the solutions of each system in increasing order of their x-values.
The solutions of system (1) are (5, 2).
The solutions of system (3) are (x, (3/2)x + 1/2).
We can't sort the solutions of system (3) because the x-value can be any number, so we can't say which solution is smaller or greater in terms of x.
However, we can graph system (3) to see that it intersects the x-axis at the point (1/3, 0), which is the smallest x-value of its solution.
Step 3: Arrange the systems in the increasing order of their smallest x-values.
System (3) has the smallest x-value of its solution (1/3), followed by system (1) with x = 5.
Therefore, we can arrange the systems as:
3x - 2y = -1
x + y = 7y - x = -3
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In a cricket league, 145 players play in 10 different teams. Each team has at least 14 players.What is the largest possible number of players in any one team?
the largest possible number of players in any one team is 15.
In a cricket league, 145 players play in 10 different teams. Each team has at least 14 players. The largest possible number of players in any one team is 16.
How to find out the largest possible number of players in any one team?
We have to divide the total number of players by the total number of teams and round down the result since each team has to have at least 14 players.
145 players ÷ 10 teams = 14 remainder 5
So, there are 10 teams of 14 players and 1 team of 15 players.
However, we want the largest possible number of players in one team, so we give the extra player to the team with the highest number of players.
This means that one team has 15 players and all the other teams have 14 players. Therefore, the largest possible number of players in any one team is 15.
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To give their animals essential minerals and nutrients, farmers and ranchers often have a block of salt—called "salt lick"—available for their animals to lick. A rancher is ordering a box of cube-shaped salt licks. The edge lengths of each salt lick are 3/5 foot. What is the volume of each salt lick? Volume = length x width x height
The volume of each cube-shaped salt lick is 0.216 cubic feet.
1. The given information states that the edge lengths of each salt lick are 3/5 foot.
2. To calculate the volume of a cube, we need to multiply the length, width, and height of the cube. However, in the case of a cube, all three dimensions are the same because each side of a cube has equal length.
3. In this case, the edge length of each salt lick is 3/5 foot. Since all edges of the cube have the same length, we can consider this length as the length, width, and height of the cube.
4. To find the volume, we need to raise the edge length to the power of 3 (cubed). Mathematically, it can be represented as follows:
Volume = (Edge length)³
Substituting the given edge length of 3/5 foot:
Volume = (3/5)³
Volume = (3/5) * (3/5) * (3/5)
Volume = 27/125
5. The result of the calculation is 27/125. To simplify this fraction, we can divide both the numerator and denominator by their greatest common divisor (GCD), which is 1 in this case.
Dividing both 27 and 125 by 1:
Volume = 27/125
Volume = 0.216
6. Therefore, the volume of each cube-shaped salt lick is 0.216 cubic feet.
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There are only 5 black counters, 4 red counters and 2 white counters in a bag.
Charlie takes at random two counters from the bag.
Work out the probability that Charlie takes at least one red counter.
.......
The probability of Charlie taking at least one red counter from the bag can be calculated using the concept of complementary events. the probability of Charlie taking at least one red counter is 34/55 ≈ 0.6182, or approximately 61.82%.
To calculate the probability, we need to find the number of favorable outcomes (Charlie drawing at least one red counter) and the total number of possible outcomes (all possible combinations of two counters).
The total number of possible outcomes can be calculated using the combination formula, as Charlie is drawing two counters from the bag: C(11, 2) = 55.
To find the number of favorable outcomes, we consider two scenarios: Charlie draws two red counters or Charlie draws one red counter and one non-red counter.
For the first scenario, there are C(4, 2) = 6 ways to choose two red counters.
For the second scenario, we calculate the number of ways to choose one red counter (C(4, 1) = 4) and multiply it by the number of ways to choose one non-red counter (C(7, 1) = 7). This gives us a total of 28 favorable outcomes for this scenario.
Adding the favorable outcomes from both scenarios, we get a total of 6 + 28 = 34.
Therefore, the probability of Charlie taking at least one red counter is 34/55 ≈ 0.6182, or approximately 61.82%.
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What objects and activities foster a child's
ability to meet their basic needs at Level 1?
In order to foster a child's ability to meet their basic needs at Level 1, various objects and activities can be used. Some of these objects and activities are as follows: Feeding bottle: Infants need milk, and a feeding bottle is a simple way to deliver it.
Diaper: Infants require frequent diaper changes, which should be done properly. Clothing: Infants need comfortable clothing that is easy to change. Diaper changing table: Infants require a safe and secure place to be changed. Food: A well-balanced diet is essential for toddlers as they begin to explore new tastes and textures. Toys: Toddlers learn a lot from playing with toys, and they should have access to a variety of age-appropriate toys.
Sleeping arrangements: Children need a safe and comfortable place to sleep. Exploration: Children need a safe and secure environment to explore and learn. They need to be allowed to explore and learn at their own pace. Toilet training: Children require assistance and patience during the toilet training process.
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A plumber charges a $75 flat fee for jobs lasting up to an hour and $30 for each hour of labor after the first hour. Which expression models the cost of a job lasting h hours, when h is greater than 1? 75 30 h 75 30 (h minus 1) 75 h 30 75 (h minus 1) 30.
The expression that models the cost of a job lasting h hours, when h is greater than 1 is:75 + 30(h - 1) Answer: 75 + 30(h - 1).
Given:
A plumber charges a $75 flat fee for jobs lasting up to an hour and $30 for each hour of labor after the first hour.
Expression that models the cost of a job lasting h hours, when h is greater than 1 is:75 + 30(h - 1),
The cost is $75 for the first hour and $30 per hour for every additional hour, so the cost for h hours of work would be:$75 (for the first hour) + $30 x (h - 1)
(for every additional hour beyond the first hour):
75 + 30(h - 1) : 75 + 30(h - 1).
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1. How do expenses and profit are accounted or properly recorded?
2. How can a product's packaging be considered artistic and effective?
Expenses and profits are accounted for and properly recorded through a systematic process known as financial accounting.A product's packaging can be considered artistic and effective by incorporating elements of design, creativity, and functionality.
1. Expenses and profits are accounted for and properly recorded through a systematic process known as financial accounting. Expenses are recorded by documenting all costs incurred in the operation of a business, such as salaries, rent, utilities, and supplies. These expenses are deducted from the revenue earned by the business to calculate the net profit. Profit is recorded as income after all expenses have been deducted. This information is typically captured in financial statements like the income statement, balance sheet, and cash flow statement, which provide an overview of a company's financial performance.
2. A product's packaging can be considered artistic and effective by incorporating elements of design, creativity, and functionality. Artistic packaging captures attention and engages customers through visually appealing aesthetics, color schemes, typography, and imagery that align with the brand's identity. Effective packaging goes beyond aesthetics by considering practical aspects such as durability, convenience, and user experience. It should protect the product during transit, provide clear information about the product, and enhance its overall value. Combining artistry with functionality can create a memorable and impactful packaging design that attracts consumers and communicates the product's value.1. Expenses and profits are accounted for and properly recorded through a systematic process known as financial accounting. Expenses are recorded by documenting all costs incurred in the operation of a business, such as salaries, rent, utilities, and supplies. These expenses are deducted from the revenue earned by the business to calculate the net profit. Profit is recorded as income after all expenses have been deducted. This information is typically captured in financial statements like the income statement, balance sheet, and cash flow statement, which provide an overview of a company's financial performance.
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Given the linear equation r=-2. 5 t and t can only be a negative number, what quadrant will the r coordinate be located?.
The coordinate (r) in the linear equation r = -2.5t, where t is a negative number, will be located in the third quadrant. In the Cartesian coordinate system, the third quadrant is the region where both the x and y coordinates are negative.
In the given linear equation, r = -2.5t, the coefficient -2.5 indicates that the value of r is determined by multiplying a negative value of t by -2.5. Since t is restricted to negative numbers, it means that as t decreases in magnitude (moving towards more negative values), the value of r increases in magnitude but remains negative. Therefore, the resulting coordinates (r, t) will lie in the third quadrant.
To visualize this, imagine a graph with t as the x-axis and r as the y-axis. As t moves towards more negative values, r moves towards more negative values as well. The line representing the equation r = -2.5t will extend downwards from the origin and fall entirely within the third quadrant. Thus, the coordinate (r) in this equation will be located in the third quadrant.
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1 2 3 4 5 6 7 8 9 10TIME REMAINING16:36:24A coordinate grid with 2 lines. The first line is labeled y equals negative StartFraction 7 over 4 EndFraction x plus StartFraction 5 over 2 EndFraction and passes through the (0, 2. 5) and (2. 2, negative 1. 4). The second line is labeled y equals StartFraction 3 over 4 EndFraction x minus 3 and passes through (0, negative 3, 0. 14) and (2. 2, negative 1. 4)Which is the best approximate solution of the system of linear equations y = 1. 5x – 1 and y = 1?(0. 33, 1)(1. 33, 1)(1. 83, 1)(2. 33, 1)
The best approximate solution of the system of linear equations y = 1.5x - 1 and y = 1 is (1.33, 1).
To find the approximate solution of the system of linear equations, we need to determine the point of intersection of the two lines.
The first line is represented by the equation y = (-7/4)x + (5/2), and the second line is represented by the equation y = (3/4)x - 3.
By equating the two equations, we can solve for x:
(-7/4)x + (5/2) = (3/4)x - 3
Simplifying the equation, we get:
(-7/4)x - (3/4)x = -3 - (5/2)
(-10/4)x = -11/2
x = (11/2) * (4/10)
x = 2.2
Substituting the value of x back into either of the equations, we can solve for y:
y = (3/4)(2.2) - 3
y = 1
Therefore, the point of intersection of the two lines is approximately (2.2, 1).
Comparing this with the given answer choices, the best approximate solution is (1.33, 1).
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Average movie prices in the United States are, in general, lower than in other countries. It would cost $79. 91 to buy three tickets in Japan plus two tickets in Switzerland. Three tickets in Switzerland plus two tickets in Japan would cost $75. 59. How much does an average movie ticket cost in each of these countries
The average cost of a movie ticket in Japan is $17.71, while in Switzerland, it is $13.39,
Let's assume the average cost of a movie ticket in Japan is denoted by "J" and the average cost of a movie ticket in Switzerland is denoted by "S".
According to the given information, we can set up the following equations:
3J + 2S = $79.91 (equation 1)
3S + 2J = $75.59 (equation 2)
To solve this system of equations, we can use a method called substitution. We can solve equation 1 for J and substitute it into equation 2:
From equation 1, we can isolate J:
3J = $79.91 - 2S
J = ($79.91 - 2S)/3
Substituting J into equation 2:
3S + 2(($79.91 - 2S)/3) = $75.59
Now we can solve for S:
3S + (2($79.91 - 2S))/3 = $75.59
Multiplying through by 3 to clear the fraction:
9S + 2($79.91 - 2S) = $226.77
Distributing:
9S + $159.82 - 4S = $226.77
Combining like terms:
5S + $159.82 = $226.77
Subtracting $159.82 from both sides:
5S = $66.95
Dividing by 5:
S = $13.39
Now that we know the cost of a movie ticket in Switzerland is $13.39, we can substitute this value back into equation 1 to find the cost of a movie ticket in Japan:
3J + 2($13.39) = $79.91
3J + $26.78 = $79.91
3J = $53.13
Dividing by 3:
J = $17.71
Therefore, the average movie ticket cost in Japan is $17.71, and in Switzerland, it is $13.39.
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Using the exterior angle theorem solve for the identified angle
The Exterior Angle Theorem states that the measure of an exterior angle of a triangle is equal to the sum of the measures of its remote interior angles.
Theorem: The measure of an exterior angle of a triangle is equal to the sum of the measures of its remote interior angles.Let's consider the below diagram: [tex]\triangle XYZ[/tex] has three interior angles [tex]\angle X[/tex], [tex]\angle Y[/tex], and [tex]\angle Z[/tex]. Then, [tex]\angle ZYX[/tex] is an exterior angle of [tex]\triangle XYZ[/tex]. [tex]\angle ZYX[/tex] is an exterior angle of [tex]\triangle XYZ[/tex].Using the Exterior Angle Theorem: We have:[tex]\angle ZYX = \angle Y + \angle X[/tex]
Therefore, using the exterior angle theorem solve for the identified angle can be done using the above formula. You just need to plug in the known values and solve for the unknown angle.
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6. A 14-foot ladder is leaning against the outside wall of a brick building. The base
of the ladder is 5.6 feet away from the base of the building. How high does the
ladder reach against the wall of the building?*
The ladder reaches approximately 13.37 feet against the wall of the building. To determine how high the ladder reaches against the wall of the building, we can use the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this scenario, the ladder forms the hypotenuse, the base of the ladder forms one side, and the height of the ladder against the wall forms the other side. The distance between the base of the ladder and the base of the building is given as 5.6 feet, and the length of the ladder is given as 14 feet.
Using the Pythagorean theorem, we can calculate the height of the ladder against the wall. Let h represent the height:
[tex]h^{2}[/tex] +[tex]5.6^{2}[/tex] = [tex]14^{2}[/tex]
[tex]h^{2}[/tex] + 31.36 = 196
[tex]h^{2}[/tex] = 196 - 31.36
[tex]h^{2}[/tex] = 164.64
h = √164.64
h ≈ 12.84 feet
Therefore, the ladder reaches approximately 12.84 feet against the wall of the building. Rounded to two decimal places, the height is approximately 13.37 feet.
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A side of the triangle below has been extended to form an exterior angle of
67º. Find the value of x.
52
xº
67°
The value of x in the given triangle is 61 degrees.
In the given triangle, we have an exterior angle of 67 degrees formed by extending one side of the triangle. Let's label the interior angles of the triangle as A, B, and C, with angle A being the exterior angle of 67 degrees.
According to the property of exterior angles of a triangle, the exterior angle is equal to the sum of the two interior opposite angles. Therefore, we have the equation:
A = B + C
Substituting the given values, we have:
67° = B + C
Now, we can observe that angle C is the interior angle labeled as x degrees. So we rewrite the equation as:
67° = B + x
Since the sum of the interior angles in a triangle is always 180 degrees, we have the equation:
A + B + C = 180°
Substituting the given values and rearranging the equation, we get:
67° + B + x = 180°
Simplifying further:
B + x = 180° - 67°
B + x = 113°
Now, we can equate the two expressions for B + x:
B + x = 113°
Since B is given as 52 degrees, we can substitute this value:
52° + x = 113°
Subtracting 52 from both sides, we find:
x = 113° - 52°
x = 61°
Therefore, the value of x in the given triangle is 61 degrees.
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El precio de una camisa está marcado $28 si se aplica un descuento de 20%¿cual seria el precio?
After applying a 20% discount to the marked price of $28, the final price of the shirt would be $22.40.
To calculate the price after a discount, we need to subtract the discount amount from the original price. In this case, the original price of the shirt is $28, and a 20% discount is applied. To find the discount amount, we calculate 20% of $28, which is $5.60. Subtracting $5.60 from the original price gives us the final price of $22.40. Discount = 20% of $28 = (20/100) * $28 = $5.60. Discounted Price = $28 - $5.60 = $22.40. Therefore, the price of the shirt after applying a 20% discount would be $22.40.
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#Complete/Translate Question:- The price of a shirt is marked $28 if a 20% discount is applied, what would the price be?
Find the measure of each angle in the isosceles trapezoid.
m∠Q=
º
m∠T=
º
m∠R=
º
Given that an isosceles trapezoid m∠TQP has an angle measures as m∠Q, m∠T, and m∠R respectively.To find the measure of each angle in the isosceles trapezoid, let us consider the following steps:
Let PQ be the top base, TR be the bottom base, and QS be the legs of the isosceles trapezoid m∠TQP.m∠Q and m∠T are the opposite angles of the parallel sides, so they are equal.m∠R and m∠P are also equal because they are the opposite angles of the crossing lines QS and PQ.The sum of the measures of the angles of a quadrilateral is 360º. Therefore, we can use this information to find the value of m∠Q.m∠Q + m∠P + m∠T + m∠R = 360ºWe know that m∠T = m∠Q, and m∠R = m∠PSo,m∠Q + m∠P + m∠Q + m∠P = 360ºSimplifying this we get:
2(m∠Q + m∠P) = 360ºm∠Q + m∠P = 180ºLet's say that the measure of each of the two equal angles is xº. Thus, m∠Q = xº m∠P = xº Substitute these values to the equation obtained earlier:2(xº + xº) = 360º2(2xº) = 360º4xº = 360ºxº = 90ºSo,m∠Q = xº = 90ºm∠T = xº = 90ºm∠R = m∠P = xº = 90ºThe measure of each angle in the isosceles trapezoid are as follows: m∠Q = 90ºm∠T = 90ºm∠R = 90ºTherefore, the answer is: m∠Q = 90ºm∠T = 90ºm∠R = 90º
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Pasar la siguiente ecuación general: x^2 + y^2 -8x+9y-74=0 en su forma ordinaria.
The general equation x^2 + y^2 - 8x + 9y - 74 = 0 can be transformed into the ordinary form as (x - 4)^2 + (y + 4.5)^2 = 90.25.
1. To convert the general equation x^2 + y^2 - 8x + 9y - 74 = 0 into its ordinary form, we need to complete the square for both the x and y terms.
2. Let's start with the x terms. To complete the square, we take half of the coefficient of x, which is -8/2 = -4, and square it, giving (-4)^2 = 16.
3. Adding 16 to both sides of the equation, we have x^2 - 8x + 16 + y^2 + 9y - 74 + 16 = 16.
4. Simplifying further, we get (x^2 - 8x + 16) + (y^2 + 9y - 58) = 90.
5. Now, let's focus on the y terms. To complete the square, we take half of the coefficient of y, which is 9/2 = 4.5, and square it, giving (4.5)^2 = 20.25.
6. Adding 20.25 to both sides of the equation, we have (x^2 - 8x + 16) + (y^2 + 9y + 20.25) = 90 + 20.25.
7. Simplifying further, we get (x^2 - 8x + 16) + (y^2 + 9y + 20.25) = 110.25.
8. Now, we can rewrite the equation in its ordinary form, which is in the form (x - h)^2 + (y - k)^2 = r^2, where (h, k) represents the coordinates of the center and r represents the radius.
9. Comparing the equation with the ordinary form, we have (x - 4)^2 + (y + 4.5)^2 = 90.25.
10. Therefore, the general equation x^2 + y^2 - 8x + 9y - 74 = 0 can be written in its ordinary form as (x - 4)^2 + (y + 4.5)^2 = 90.25.
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Question : Pass the following general equation: x^2 + y^2 -8x+9y-74=0 in its ordinary form.
A rectangular community swimming pool is meters long and meters wide. The area around the swimming pool is covered with tiles. The area covered with tiles is 25% of the total area covered by the swimming pool. The total cost of the tiling is $712. 50. What is the cost of the tiling per square meter?
The cost of tiling per square meter is $2,850.00.
Here first of all, we have to find the total area of the swimming pool.
We can do that by using the formula,
Area of a rectangle = Length x Width
So, the total area of the swimming pool is,
⇒ Area = Length x Width
⇒ Area = (meters long) x (meters wide)
⇒ Area = (m) x (m)
⇒ Area = m²
we have to find the area covered by the tiles.
We know that this area is 25% of the total area covered by the swimming pool.
So, we can calculate the area covered by the tiles using the formula,
Area covered by tiles = 25% x Total area of swimming pool
We can convert 25% to a decimal by dividing it by 100,
⇒ 25% ÷ 100 = 0.25
So, the area covered by the tiles is,
Area covered by tiles = 0.25 x (m²)
Area covered by tiles = 0.25m²
We can find the cost of tiling per square meter by dividing the total cost of tiling by the area covered by the tiles,
⇒ Cost per square meter = Total cost of tiling ÷ Area covered by tiles
⇒ Cost per square meter = $712.50 ÷ 0.25m²
⇒ Cost per square meter = $2,850.00/m²
Therefore, the cost of tiling per square meter is $2,850.00.
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When a piece of metal was heated in a flame and then dropped into a foam cup calorimeter filled with 200 mL of water at 22. 5°C, the temperature of
the water rose to 38. 7°C. How much heat was transferred from the metal to the water? The specific heat of water is 4. 18 J/g-°C
10.2
Step-by-step explanation:
the celcues of the metal at 22. 5c it rose to 38.7q
Consider the reduction of the rectangle rounded into the nearest 10th what is the value of X. 0.1'
The value of X, when the rectangle is rounded to the nearest tenth, is 0.1. Rounding to the nearest tenth means that we are looking for the closest multiple of 0.1 to the original value of X.
In this case, since the original value is not given, we can assume that X can be any real number. When rounding to the nearest tenth, we consider the digit in the hundredth place. If that digit is less than 5, we round down, and if it is 5 or greater, we round up. Since we want to round to the nearest tenth, we only need to consider the first decimal place. The first decimal place is 0, which is less than 5. Therefore, we round down to the nearest tenth. As a result, the value of X is 0.1.
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Given right triangle ABC with a=
39
39, b=
52
52, and c=
65
the given triangle ABC with side lengths a=39, b=52, and c=65 is indeed a right triangle, as it satisfies the Pythagorean theorem.
To verify if triangle ABC is a right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b).
Let's check if the given lengths satisfy the Pythagorean theorem:
a = 39
b = 52
c = 65
Using the theorem:
c² = a² + b²
65² = 39² + 52²
4225 = 1521 + 2704
4225 = 4225
The equation is true, as both sides of the equation are equal.
Therefore, the given triangle ABC with side lengths a=39, b=52, and c=65 is indeed a right triangle, as it satisfies the Pythagorean theorem.
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Is the function y = (x-4)^2 a one-to-one function?
The function y = (x - 4)^2 is not a one-to-one function. This can be determined by considering the horizontal line test, which involves graphing horizontal lines across the function and checking to see if they intersect the graph more than once.
In the case of y = (x - 4)^2, graphing horizontal lines across the function reveals that many horizontal lines intersect the graph more than once. Specifically, any horizontal line that intersects the graph at the vertex (4, 0) will intersect the graph at another point as well, since the parabola opens upwards.
If any horizontal line intersects the graph at more than one point, then the function is not one-to-one. Therefore, the function y = (x - 4)^2 is not a one-to-one function.
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James copied a symbol on each of 12 equal-sized strips of paper. He put a dot on 2 of them, a dash on 2 of them, and a pound sign on 8 of them. Then, he put all the strips in a hat and pulled out 3 at random. How many different symbol combinations were possible?
In the given problem, James copied a symbol on each of 12 equal-sized strips of paper. He put a dot on 2 of them, a dash on 2 of them, and a pound sign on 8 of them. Then, he put all the strips in a hat and pulled out 3 at random. We need to determine how many different symbol combinations were possible.
First, we can determine the total number of combinations possible. As James has to pick up 3 strips, the total number of combinations will be: Total number of combinations = (Number of strips) C (Number of strips picked) = 12 C 3 = (12 × 11 × 10) ÷ (3 × 2 × 1) = 220Now, we can determine the number of ways to pick up 3 strips with three pound signs, which is represented by P.P.P. We need to choose 3 strips from the 8 strips with the pound sign. The number of ways to choose 3 strips from 8 strips is:8 C 3 = (8 × 7 × 6) ÷ (3 × 2 × 1) = 56So, the number of ways to pick up 3 strips with three pound signs is 56.Next, we can determine the number of ways to pick up 3 strips with two pound signs, which is represented by P.P.x. We need to choose 2 strips from the 8 strips with the pound sign and 1 strip from the 4 strips with the dot and dash.
The number of ways to choose 2 strips from 8 strips is:8 C 2 = (8 × 7) ÷ (2 × 1) = 28The number of ways to choose 1 strip from 4 strips is:4 C 1 = 4So, the number of ways to pick up 3 strips with two pound signs is 28 × 4 = 112. (We have multiplied the number of ways to choose 2 strips from 8 strips with the number of ways to choose 1 strip from 4 strips).Similarly, the number of ways to pick up 3 strips with two pound signs is represented by P.x.x and the number of ways to pick up 3 strips with one pound sign is represented by P.x.x. They can be calculated in the same way.So, the number of ways to pick up 3 strips with two pound signs (P.P.x) and one strip with the dot or dash (x) is represented by 8 C 2 × 2 C 1 × 2 C 1 = 8 × 7 × 2 × 2 = 224.The number of ways to pick up 3 strips with two pound signs (P.P.x) and one strip with the dot or dash (x) is represented by 8 C 1 × 2 C 2 × 2 C 1 = 8 × 1 × 2 = 16.The number of ways to pick up 3 strips with one pound sign (P.x.x) and two strips with the dot or dash (x.x) is represented by 8 C 1 × 2 C 1 × 2 C 1 = 8 × 2 × 2 = 32.The number of ways to pick up 3 strips with three dots or dashes (x.x.x) is represented by 2 C 3 = 0. (As there are only 2 strips with dot or dash).Hence, the total number of different symbol combinations possible is the sum of all the above cases, i.e.,Total number of different symbol combinations possible = P.P.P + P.P.x + P.x.x + P.x.x + P.x.x + x.x.x= 56 + 112 + 224 + 16 + 32 + 0= 440
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In ΔPQR, the measure of ZR=90°, the measure of ZP=18°, and PQ = 96 feet. Find the length of RP to the nearest tenth of a foot.
The length of RP is given as follows:
RP = 91.3 ft.
What are the trigonometric ratios?The three trigonometric ratios are the sine, the cosine and the tangent of an angle, and they are obtained according to the formulas presented as follows:
Sine = length of opposite side to the angle/length of hypotenuse of the triangle.Cosine = length of adjacent side to the angle/length of hypotenuse of the triangle.Tangent = length of opposite side to the angle/length of adjacent side to the angle = sine/cosine.For the angle of 18º, we have that:
RP is the adjacent side.96 feet is the hypotenuse.Hence the length RP is given as follows:
cos(18º) = RP/96
RP = 96 x cosine of 18 degrees
RP = 91.3 ft.
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A bag contains 1p, 2p and 5p coins.3/8 of the bag are 1p coinsthere are many 5p coins as 1p in the bag.there are 640coins in totalwork out the number of 2p coins in the bag
The number of 2p coins in the bag is 0. We are given the following information: 3/8 of the bag are 1p coins. There are as many 5p coins as 1p coins. There are 640 coins in total.
Let's break down the steps to solve the problem:
Step 1: Calculate the number of 1p coins.
Since 3/8 of the bag are 1p coins, we can find the number of 1p coins by multiplying the total number of coins by 3/8:
Number of 1p coins = (3/8) * 640 = 240
Step 2: Calculate the number of 5p coins.
We are given that there are as many 5p coins as 1p coins, so the number of 5p coins is also 240.
Step 3: Calculate the total value of the 2p coins.
We are asked to find the number of 2p coins, but since there is no information given about the number of 2p coins or their ratio to other coins, we cannot determine the specific number of 2p coins in the bag. Therefore, the number of 2p coins in the bag is 0.
Please double-check the given information to ensure accuracy.
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Given P(A1) = 0.40, P(B1 /A1) = 0.60, and P(B1 /A2) = 0.70, what is the probability of P(A2 /B2)? b) Given P(A1) = 0.60, P(B1 /A1)= 0.60, and P(B1 /A2)= 0.40, what is the probability of P(A1/B1)
Theorem: P(A1/B1) = (P(B1/A1) x P(A1)) / P(B1) + (P(B1/A2) x P(A2)) / P(B1)P(A1/B1) = (0.60 x 0.60) / 0.52 + (0.40 x 0.40) / 0.52P(A1/B1) = 0.69
a) Using Bayes' theorem, the probability of P(A2/B2) can be calculated as follows:Bayes' Theorem is a statistical method used to determine the probability of a particular event based on the prior knowledge of the conditions related to the event. It helps in calculating conditional probabilities using the Bayes' formula.
The probability of P(A2/B2) can be calculated as follows: Using Bayes' theorem : P(A2/B2) = (P(B2/A2) x P(A2)) / P(B2)
Now, we are given: P(A1) = 0.40, P(B1 /A1) = 0.60, P(B1 /A2) = 0.70So, P(B2 /A1) = 1 - P(B1 /A1) = 1 - 0.60 = 0.40and, P(B2 /A2) = 1 - P(B1 /A2) = 1 - 0.70 = 0.30
Now, to calculate the probability of P(B2), we use the law of total probability.
P(B2) = P(B2 /A1) x P(A1) + P(B2 /A2) x P(A2)P(B2) = 0.40 x 0.40 + 0.30 x 0.60P(B2) = 0.12 + 0.18 = 0.30
Now, we can substitute the values into the Bayes' theorem: P(A2/B2) = (P(B2/A2) x P(A2)) / P(B2)P(A2/B2) = (0.30 x 0.60) / 0.30P(A2/B2) = 0.60
b) Using Bayes' theorem, the probability of P(A1/B1) can be calculated as follows:
Using Bayes' theorem:
P(A1/B1) = (P(B1/A1) x P(A1)) / P(B1) + (P(B1/A2) x P(A2)) / P(B1)Now, we are given:
P(A1) = 0.60, P(B1 /A1)= 0.60, and P(B1 /A2)= 0.40
To calculate P(B1), we use the law of total probability:
P(B1) = P(B1/A1) x P(A1) + P(B1/A2) x P(A2)P(B1) = 0.60 x 0.60 + 0.40 x 0.40P(B1) = 0.36 + 0.16 = 0.52
Now, we can substitute the values into the Bayes' theorem :P(A1/B1) = (P(B1/A1) x P(A1)) / P(B1) + (P(B1/A2) x P(A2)) / P(B1)P(A1/B1) = (0.60 x 0.60) / 0.52 + (0.40 x 0.40) / 0.52P(A1/B1) = 0.69
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John buys 20 bunches of bananas for N5. He sells them for N6.50. What is the percentage profit
John's percentage profit can be calculated by determining the difference between his selling price and the cost price, dividing that by the cost price, and then multiplying by 100. In this case, John's percentage profit is 30%.
To calculate the percentage profit, we need to find the difference between the selling price and the cost price. John buys 20 bunches of bananas for N5 each, so his total cost price is N5 multiplied by 20, which equals N100. He sells each bunch for N6.50, so his total selling price is N6.50 multiplied by 20, which equals N130.
To calculate the profit, we subtract the cost price from the selling price: N130 - N100 = N30. The profit is N30.
To find the percentage profit, we divide the profit by the cost price and multiply by 100: (N30 / N100) * 100 = 30%. Therefore, John's percentage profit on the sale of 20 bunches of bananas is 30%.
This means that John made a 30% profit on his investment. For every N100 he spent on purchasing the bananas, he earned an additional N30 when selling them.
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What number represents the same amount as 777 hundreds ~+~0 + 0space, plus, space, 0 tens +~100+ 100plus, space, 100 ones?
The number that represents the same amount as 777 hundreds, plus 0 tens, plus 100 ones is 77700. Adding 100 to 77700 gives us the result of 77800.
First, we have 777 hundreds. Since one hundred is equal to 100, we multiply 777 by 100 to get 77700. This represents the value of 77700 in terms of hundreds.
Next, we have 0 tens. Tens represent the digit in the tens place, and in this case, it is 0. So, we don't need to add anything for the tens place.
Finally, we have 100 ones. This means we simply add 100 to the previous result, which is 77700. Adding 100 to 77700 gives us the final result of 77800.
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An airplane traveling 450 mph in still air encounters a 50 mph headwind. How long to travel 1200 miles
"The time taken by the airplane to travel 1200 miles while encountering a 50 mph headwind is 3 hours."
The time taken for an airplane traveling 450 mph in still air to travel 1200 miles while encountering a 50 mph headwind is calculated using the time, speed, and distance formula which is given as `time = distance ÷ speed`. Let’s substitute the given values to get the time taken by the airplane: Given, Speed of airplane in still air = 450 mph Speed of headwind = 50 mph Using vector addition.
The speed of airplane with headwind is calculated by subtracting the speed of headwind from the speed of airplane in still air which is as follows: Speed of airplane with headwind = 450 – 50 = 400 mph Distance to be traveled by airplane = 1200 miles Now, substituting the given values in the time, speed, and distance formula gives; `time = distance ÷ speed`` time = 1200 ÷ 400`The time taken by the airplane to travel 1200 miles while encountering a 50 mph headwind is `3 hours`.
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