The point where the three perpendicular bisectors intersect is the circumcenter of the triangle. This point represents the location for the warehouse that is equidistant from all three highways.
To identify the location for the warehouse that is equidistant from the three highways I-20, I-26, and I-95 in South Carolina, we can use the concept of the circumcenter of a triangle. The circumcenter is the center of the circle that passes through all three vertices of the triangle.
Here's how we can determine the location of the warehouse using the circumcenter:
First, locate the intersection point of two highways. In this case, we need to find the intersection points of I-20 and I-26, I-20 and I-95, and I-26 and I-95. These intersection points will serve as two vertices of the triangle.
Once we have the two intersection points, draw the corresponding line segments connecting them. These line segments represent two sides of the triangle.
To find the third vertex of the triangle, locate the intersection point of the remaining highway. This point will complete the triangle.
With all three vertices identified, construct the perpendicular bisectors of the three sides of the triangle. The perpendicular bisectors are the lines that intersect each side at a right angle and divide the sides into two equal parts.
By constructing the triangle and finding its circumcenter, we can precisely determine the location for the warehouse. It's important to note that the accuracy of this method depends on the accuracy of the highway intersections and the construction of the triangle. Additionally, other factors such as zoning regulations, accessibility, and proximity to other facilities should also be considered when selecting the exact location for the warehouse.
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2013 people live on an island. Some of these people are truthtellers and the others are liars. The truthtellers always tell the truth whereas the liars always lie. Each day one of the people says 'when i have left the island the number of truthtellers will be the same as the number of liars. Then he leaves the island. After 2013 days there is no longer anybody living on the island. How many liars were living there to begin with?
There were 671 liars living on the island initially out of 2013 people living on the island.
Let's assume the number of truthtellers is x and the number of liars is y.
According to the given information, each day one person says that when they leave the island, the number of truthtellers will be equal to the number of liars.
This implies that the person speaking must be a liar.
On the first day, if the person speaking is a liar, then the number of liars on the island will increase by one (y+1) and the number of truthtellers will remain the same (x).
The equation can be written as:
x = y + 1
On the second day, if the second person speaking is also a liar, the number of liars will increase by one again (y+2) and the number of truthtellers will remain the same (x).
The equation becomes:
x = y + 2
We can generalize this pattern for each day:
x = y + k
After 2013 days, there is no one left on the island, so x + y = 0.
Substituting this into the equation, we get:
(y + k) + y = 0
Simplifying, we find:
2y + k = 0
Since y represents the number of liars, we want to find a value of y that satisfies this equation.
To do that, we need to find a value of k such that 2013 + k is divisible by 2.
By observing that 2013 is odd, we can conclude that k must be an odd number.
The smallest odd number that satisfies this condition is k = 1.
Substituting k = 1 into the equation, we get:
2y + 1 = 0
Solving for y, we find:
y = -1/2
However, the number of liars cannot be negative, so we can disregard this solution.
Therefore, there were 671 liars living on the island initially.
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A brick is lying on a table in a state of static equilibrium. If the mass of the brick is 7. 52 kilograms, what is the normal force exerted by the table on the brick?.
The normal force exerted by the table on the brick is approximately
73.7 Newtons.
How to determine the normal forceThe weight of the brick can be calculated using the formula:
Weight = mass x acceleration due to gravity
Weight = 7.52 kg x 9.8 m/s²
since the brick is in equilibrium, the normal force exerted by the table on the brick is equal in magnitude but opposite in direction to the weight of the brick.
Therefore, the normal force exerted by the table on the brick is:
Normal force = Weight of the brick
Normal force = 7.52 kg x 9.8 m/s²
Simplifying the calculation:
Normal force ≈ 73.696 N
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Sam has 8 shells and thandeka has 12. What is the ratio,in simplest form,of Sam's shells and thandeka shells?
The ratio of Sam’s shells and Thandeka’s shells, in simplest form is 2:3. To simplify the ratio of Sam’s shells and Thandeka’s shells, we need to divide both numbers by their greatest common factor, GCF.
In this case, we have:Sam’s shells = 8Thandeka’s shells = 12Factors of 8: 1, 2, 4, 8Factors of 12: 1, 2, 3, 4, 6, 12The common factors of 8 and 12 are 1, 2, and 4.
However, we need to find the greatest common factor of 8 and 12 to simplify the ratio. Therefore, the greatest common factor of 8 and 12 is 4.
Hence, dividing both numbers by 4 gives us:
Sam’s shells ÷ GCF = 8 ÷ 4 = 2
Thandeka’s shells ÷ GCF = 12 ÷ 4 = 3
Therefore, the ratio of Sam’s shells and Thandeka’s shells, in simplest form is 2:3.Another way to solve the problem is by finding the ratio between the two numbers.
Thus:Ratio = Sam’s shells :
Thandeka’s shellsRatio = 8 : 12
To simplify the ratio, divide both numbers by the greatest common factor of 8 and 12 which is 4.
Ratio = (8 ÷ 4) : (12 ÷ 4)Ratio = 2 : 3
Therefore, the ratio of Sam’s shells and Thandeka’s shells, in simplest form is 2:3.
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Samuel is playing the Big-Time Builders video game. At the beginning of Samuel's turn, his score was
–
14 points. After building a high-rise apartment building, his score rose to 36 points.
The change in Samuel's score is 50
How to determine the change in Samuel's score?From the question, we have the following parameters that can be used in our computation:
Beginning = -14 points
Final = 36 points
Using the above as a guide, we have the following:
Change = Final - Beginning
Substitute the known values in the above equation, so, we have the following representation
Change = 36 + 14
Evaluate
Change = 50
Hence, the change is 50
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Question
Samuel is playing the Big-Time Builders video game. At the beginning of Samuel's turn, his score was – 14 points. After building a high-rise apartment building, his score rose to 36 points.
What was the change in Samuel's score?
What is the solution of the following system? Use the elimination method. {4x 3y=62x 2y=5 The only solution is (−32, 4). The only solution is (0, 2). There are an infinite number of solutions. There is no solution.
The given system of equations can be solved using the elimination method. The possible solutions to the system are: the only solution is (-32, 4), the only solution is (0, 2), there are an infinite number of solutions, or there is no solution.
To solve the system using the elimination method, we can multiply the first equation by 2 and the second equation by 3 to eliminate the variable x. This gives us the following system:
8x + 6y = 124
6x + 6y = 15
Subtracting the second equation from the first equation, we get:
2x = 109
Dividing both sides by 2, we find:
x = 54.5
Substituting this value of x into either of the original equations, we can solve for y. However, when we substitute x = 54.5 into the second equation, we get a contradiction. The equation becomes:
2(54.5) + 2y = 5
109 + 2y = 5
2y = -104
y = -52
Therefore, the system has no solution. The only solution option that matches this result is "There is no solution."
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nancy used 6 3/4 cups of peanuts and cereal to make a snack mix. she used twice as many peanuts as she did cereal. how many cups of cereal did nancy use?
she used 4/27 cups of cereal to make the snack mix.
Let's say the amount of cereal Nancy used was "x".
Since she used twice as many peanuts as she did cereal, the number of peanuts she used would be "2x".
Total, she used 6 3/4 cups of peanuts and cereal to make the snack mix.
Thus, we can write an equation as follows:6 3/4 = 2x + x
Convert mixed number 6 3/4 to an improper fraction:6 3/4 = (27/4)
Now we can solve the equation: (27/4) = 3x
(combining like terms)
Multiplying both sides by 4/27 gives us:1 = (4/27) * 3x
Now we can solve for "x":x = 4/27Since "x" represents the amount of cereal Nancy used,
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If Triangle ABC was dilated with the center of dilation at (0,0) and a scale factor of 2, what would be the coordinates of A'? Please help :(
When Triangle ABC is dilated with a center of dilation at (0,0) and a scale factor of 2, the coordinates of point A' can be found by multiplying the original coordinates of point A by the scale factor.
In this case, if the coordinates of point A are (x, y), then the coordinates of A' would be (2x, 2y).
Dilation involves scaling an object by a factor while preserving its shape. When the center of dilation is at (0,0), the dilation occurs relative to the origin. By applying a scale factor of 2, the x-coordinate of point A is multiplied by 2, and the y-coordinate of point A is also multiplied by 2. This scaling operation results in the coordinates of A' being (2x, 2y).
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Write the ratio of the first measurement to the second measurement. Compare in millimeters.
diameter of ball A: 33 mm
diameter of ball B: 4.5 cm
So the ratio of the first measurement to the second measurement is approximately 73.33%.
The diameter of ball A is 33 mm.
The diameter of ball B is 4.5 cm.
1 cm = 10 mm
4.5 cm = 4.5 × 10 mm
= 45 mm
To find the ratio of the first measurement (ball A) to the second measurement (ball B), we divide the diameter of ball A by the diameter of ball B.33 mm ÷ 45 mm = 0.7333...
We can simplify this fraction by multiplying both the numerator and denominator by 100 to get a percentage:
0.7333... × 100% = 73.33...%
Ratio of the first measurement to the second measurement = 73.33%.
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The sequence applied to shape I that proves shape I is similar to shape II is a translation blank units right and blank units up and then a dilation by a scale factor of
The sequence applied to shape I that proves shape I is similar to shape II is a translation 4 units right and 3 units up and then a dilation by a scale factor of 2.
For the shapes to be similar, the corresponding angles need to be congruent and corresponding sides need to be proportional. The sequence applied to shape I that proves shape I is similar to shape II involves a translation and a dilation.
Translation: A translation is a transformation in which each point of the shape is moved a certain distance in a certain direction. In this case, Shape I is translated 4 units right and 3 units up to get Shape III. Dilation: A dilation is a transformation in which each point of the shape is stretched or shrunk in size, relative to a fixed point called the center of dilation.
In this case, Shape III is dilated by a scale factor of 2 to get Shape II. Thus, the sequence applied to shape I that proves shape I is similar to shape II is a translation 4 units right and 3 units up and then a dilation by a scale factor of 2.
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They rent a car with insurance for 5 days but lost their coupon. If marven and the three friends spend $75 each, which csr did they rent? Write and solve an equation to justify your answer.
Marven and three of his friends rent a car with insurance for 5 days but lost their coupon. If each person spent $75, then which car did they rent The total amount of money they paid is $75 * 4 = $300.
We can further write the above equation as:250x + 300y + 350z + 400u = 300Based on the given condition, we know that Marven and three of his friends spent $75 each, so the total amount of money they paid is $300. Hence:250x + 300y + 350z + 400u = 300Now we can simplify the equation by dividing each term by 50:5x + 6y + 7z + 8u = 6We have to find the values of x, y, z, and u. The simplest way to solve the equation is by trial and error.
We can substitute values and check if they satisfy the equation. We need to consider the following conditions: The variables x, y, z, and u must be non-negative integers. The sum of x, y, z, and u must be 1.The only set of values that satisfies the above conditions is x = 1, y = 1, z = 0, and u = 0. This means that they rented a compact car and a mid-size car for 5 days each, respectively. Therefore, the car they rented is a compact car and a mid-size car.
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How would you sketch an angle of 210° in standard position in a uv-coordinate system? And then what is the reference angle?
To sketch an angle of 210° in standard position in a UV-coordinate system, you would start by placing the initial side of the angle along the positive x-axis and then rotate the terminal side counter-clockwise by 210°. The reference angle is the acute angle formed between the terminal side of the given angle and the x-axis.
In a UV-coordinate system, the initial side of an angle is placed along the positive x-axis. To sketch an angle of 210°, you would start by drawing a horizontal line (the initial side) extending to the right. Then, you rotate the terminal side of the angle counterclockwise from the initial side. Since 210° is greater than 180°, the terminal side will extend beyond the positive x-axis.
To determine the reference angle, you can subtract the given angle from the nearest multiple of 180°. In this case, the nearest multiple of 180° is 180° itself. Subtracting 210° from 180° gives you 30°. Therefore, the reference angle for the angle of 210° is 30°.
To summarize, you would sketch an angle of 210° in standard position by starting with the initial side along the positive x-axis and rotating the terminal side counterclockwise. The reference angle for this angle is 30°, which is the acute angle formed between the terminal side and the x-axis.
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If my salary is k20,000 monthly and there is an increment of k350 per month,what will be my total amount in the first 2years of my contact?
The total amount earned in the first 2 years of the contract is k488,400
Given that the salary is k20,000 monthly and there is an increment of k350 per month.
To find out the total amount in the first two years of contact, we need to calculate the salary for 24 months and then add the increments earned during those 24 months.
Salary for 24 months = k20,000 × 24= k480,000
Increment for 24 months = k350 × 24= k8,400
Therefore, the total amount earned in the first 2 years of the contract will be the sum of the salary for 24 months and the total increment earned during the same period= k480,000 + k8,400= k488,400
Thus, the total amount earned in the first 2 years of the contract is k488,400.
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The total amount you will have in the first 2 years of your contract is k14,000,000.
If your salary is k20,000 monthly and there is an increment of k350 per month, the total amount you will have in the first two years of your contact can be found using simple interest formula:
I = prt
where I is the interest, p is the principal amount, r is the rate of interest and t is the time in years.Therefore, using the above formula, we have;
I = (20,000)(350)(2)
= 14,000,000
Therefore, the total amount you will have in the first 2 years of your contract is k14,000,000.
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Steve is turning half of his backyard into chicken pen . His backyard is a 24 meter by 45 Metter rectangle
An area of 18 x 30 = 540 square meters, which is half the area of his backyard.
Steve is turning half of his backyard into a chicken pen. Given that his backyard is a 24 meters by 45 meters rectangle, the area of the whole backyard is
24 x 45 = 1080 square meters.
If half of the backyard is to be turned into a chicken pen, then the area of the chicken pen will be
1080/2 = 540 square meters.
Since the area of a rectangle is calculated by multiplying its length by its width, the dimensions of the chicken pen will depend on the desired shape of the pen.
Steve can decide to make the chicken pen a square or a rectangle or any other shape.
However, if he decides to make the pen a rectangle, he will have to make sure that the length and width are such that their product is equal to 540 square meters.
For example, he can make the chicken pen a rectangle with a length of 18 meters and a width of 30 meters.
This will give an area of 18 x 30 = 540 square meters, which is half the area of his backyard.
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Fill in the steps to find the length of the hypotenuse.
b = 5
a = 12
a2 =
and 62 =
2 +6² = 2 =
Take the square root of c2 to find that ca
To find the length of the hypotenuse (c) in a right triangle, you can use the Pythagorean theorem, The length of the hypotenuse (c) is √312.
In this case, you have the lengths of the two sides, b and a, where b = 5a and[tex]a^2[/tex] = 12.
Let's go through the steps to find the length of the hypotenuse (c):
Step 1: Square the value of a
[tex]a^2[/tex] = 12
Step 2: Substitute the value of b in terms of a
b = 5a
Step 3: Square the value of b
[tex]b^2 = (5a)^2 = 25a^2[/tex]
Step 4: Apply the Pythagorean theorem
According to the Pythagorean theorem, [tex]c^2 = a^2 + b^2[/tex]
Substituting the values:
[tex]c^2 = a^2 + b^2\\c^2 = 12 + 25a^2[/tex]
Step 5: Simplify the equation
[tex]c^2 = 12 + 25a^2[/tex]
Step 6: Substitute the value of [tex]a^2[/tex]from Step 1
[tex]c^2 = 12 + 25(12)[/tex]
Step 7: Simplify further
[tex]c^2 = 12 + 300\\c^2 = 312[/tex]
Step 8: Take the square root of both sides to find c
[tex]\sqrt{c^2} = \sqrt{312}\\c = \sqrt{312}[/tex]
The length of the hypotenuse (c) is √312.
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A kayak is traveling across a pond at a spees of 8 meters per second in the direction of S 67 degrees W. Give the speed of the kayak in component form.
The speed of the kayak in component form is approximately 3.112 meters per second in the east-west direction and 7.368 meters per second in the north-south direction.
The speed of the kayak can be represented in component form, which consists of two perpendicular components: one in the east-west direction (x-component) and the other in the north-south direction (y-component).
Given that the kayak is traveling at a speed of 8 meters per second in the direction of S 67 degrees W, we can use trigonometry to determine the x-component and y-component of the speed.
The x-component represents the east-west direction and can be calculated using the cosine function. The y-component represents the north-south direction and can be calculated using the sine function.
To calculate the x-component:
x-component = speed * cosine(angle)
x-component = 8 * cosine(67 degrees)
x-component ≈ 8 * 0.389
x-component ≈ 3.112 meters per second (rounded to three decimal places)
To calculate the y-component:
y-component = speed * sine(angle)
y-component = 8 * sine(67 degrees)
y-component ≈ 8 * 0.921
y-component ≈ 7.368 meters per second (rounded to three decimal places)
Therefore, the speed of the kayak in component form is approximately 3.112 meters per second in the east-west direction and 7.368 meters per second in the north-south direction.
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Use the net to find the lateral area of the prism. Mm^2
The lateral area of the given prism is 450 mm².
The lateral area of any prism is equal to the areas of the sides faces
The base of the prism is triangle
It has 3 side faces
The lengths of the side faces are 5 , 12 , 13 and their height is 15.
The lateral area = (5 × 15) + (12 × 15) + (13 × 15)
The lateral area= 75 + 180 + 195
The lateral area = 450 mm²
Hence, the lateral area of any prism is 450 mm².
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W = Fd. Find the force, F, needed to move a piano given the amount of work applied, W, and distance moved, d. ?
To find the force, F, needed to move a piano given the amount of work applied, W, and distance moved, d, we can use the equation W = Fd.
Rearranging the equation, we can solve for F by dividing both sides of the equation by d.
The equation W = Fd represents the relationship between work (W), force (F), and distance (d).
In this case, we are given the values of W and d and need to find F.
To isolate F, we can rearrange the equation as F = W/d.
By dividing the work (W) by the distance (d), we obtain the force (F) required to move the piano. The unit of force is typically measured in newtons (N), work in joules (J), and distance in meters (m).
It's important to note that this equation assumes a linear motion, where the force applied remains constant throughout the displacement of the piano. In practical situations, however, additional factors such as friction and the piano's weight distribution may affect the force required to move it.
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If 1/5 of 100oranges is given to Olu and 1/4 of the remaining oranges is given to Ade.what fraction of the oranges is left
Given that 1/5 of 100 oranges is given to Olu and 1/4 of the remaining oranges is given to Ade. We have to find what fraction of the oranges are left.
We have 100 oranges.1/5 of 100 oranges is given to Olu= 1/5 × 100= 20 orangesLet's find out how many oranges are remaining after giving 1/5 of 100 oranges to Olu.Therefore, the number of oranges left is = 100 - 20 = 80Now, 1/4 of the remaining oranges is given to Ade= 1/4 × 80= 20 oranges
Now, we have given a total of 20+20= 40 oranges.Hence, the fraction of oranges left is: 60/100 or 3/5.Here, the final answer is "The fraction of oranges left is 3/5.
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If there’s a 70% chance of rain tomorrow, what is the chance it will not rain?
The chance that it will not rain tomorrow can be found by subtracting the probability of rain from 100% or 1 in decimal form. Therefore, if there is a 70% chance of rain, there is a 30% chance it will not rain.
If there is a 70% chance of rain tomorrow, the chance it will not rain can be found by subtracting the probability of rain from 100% (or 1 in decimal form):
Chance of not raining = 100% - Chance of raining
Chance of not raining = 1 - 0.7
Chance of not raining = 0.3 or 30%
Therefore, the chance it will not rain is 30%.
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Nishi invests £2500 at 4% interest a year work out how much she will have after 2 years, 4 years, 8 years and 9 years
Nishi invests £2500 at a 4% interest rate per year. After 2 years, her investment will grow to £2650. The amount will increase further to £2806 after 4 years, £3071 after 8 years, and £3123.84 after 9 years.
1. To calculate the amount Nishi will have after a certain number of years, we can use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the final amount, P is the principal (initial investment), r is the interest rate (expressed as a decimal), n is the number of times interest is compounded per year, and t is the number of years.
2. In this case, Nishi invests £2500 at a 4% interest rate per year. Since the question doesn't specify the compounding frequency, we'll assume it's compounded annually (n = 1). Plugging in the values, we get:
After 2 years:
A = £2500(1 + 0.04/1)^(1*2)
A = £2500(1.04)^2
A ≈ £2650
After 4 years:
A = £2500(1 + 0.04/1)^(1*4)
A = £2500(1.04)^4
A ≈ £2806
After 8 years:
A = £2500(1 + 0.04/1)^(1*8)
A = £2500(1.04)^8
A ≈ £3071
After 9 years:
A = £2500(1 + 0.04/1)^(1*9)
A = £2500(1.04)^9
A ≈ £3123.84
3. Therefore, Nishi will have approximately £2650 after 2 years, £2806 after 4 years, £3071 after 8 years, and £3123.84 after 9 years, assuming an annual compounding frequency.
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The equation of the line shown is y = ax + p, where a and p are real numbers.
What is true about a and p?
The equation of the line is shown as y = ax + p, where a and p are actual numbers. The slope-intercept form of a line is given as y = mx + b, where m is the slope of the line and b is the y-intercept. The line slope-intercept form can be compared with the equation of the line given as y = ax + p.
We know that the equation of a line in slope-intercept form is given as y = mx + b. Here, we are given the equation of the line as y = ax + p, where a and p are real numbers. Thus, the following is true about a and p.The slope of the line in the slope-intercept form is m = a. Therefore, a is the slope of the given line. The y-intercept of the line in the slope-intercept form is b = p.
p is the y-intercept of the given line. Hence, we conclude that in the equation of the line, y = ax + p, where a and p are real numbers, a is the slope of the line and p is the y-intercept of the line.
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Identify the RATE OF CHANGE and INITIAL VALUE from ONE of the equations listed. A. Y = 3x 6 b. Y = -7x 5 c. Y = 9x 4.
The equation Y = 9x + 4 has a rate of change of 9, indicating that for every unit increase in x, y increases by 9. The initial value is 4, representing the y-value when x is zero.
To identify the rate of change and initial value from one of the given equations, let's analyze equation C: Y = 9x + 4.
In this equation, the coefficient of x, which is 9, represents the rate of change. This means that for every unit increase in x, the corresponding value of y will increase by 9 units. Therefore, the rate of change is 9.
To find the initial value, we need to determine the value of y when x is equal to zero. Plugging in x = 0 into the equation, we get:
Y = 9(0) + 4
Y = 0 + 4
Y = 4
Hence, the initial value or y-intercept is 4.
In summary, for the equation Y = 9x + 4, the rate of change is 9, indicating that y increases by 9 units for each unit increase in x, and the initial value is 4, representing the y-value when x is equal to zero.
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If l represents the length of the sidewalk, then the width of the sidewalk is l ÷ 3. Find the true statement.
The true statement is Statement 1: The width of the sidewalk is equal to one-third of its length.
The true statement can be found by examining the relationship between the length of the sidewalk (l) and its width, which is given as l ÷ 3.
Let's consider two possible statements:
Statement 1: The width of the sidewalk is equal to one-third of its length.
Statement 2: The width of the sidewalk is three times its length.
To determine which statement is true, we can substitute a numerical value for the length of the sidewalk (l) and compare the resulting width to the statement.
Let's assume the length of the sidewalk (l) is 9 units.
Statement 1: The width of the sidewalk is 9 ÷ 3 = 3 units.
Statement 2: The width of the sidewalk is 3 × 9 = 27 units.
Comparing the width obtained from the calculation (3 units) with Statement 1 (The width of the sidewalk is equal to one-third of its length), we find that they are equal.
It's important to note that this conclusion is based on the assumption that the relationship between the length and width provided in the question is accurate and consistent.
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If a hiker drops a rock off of a cliff that’s had a height of 150m. How long in seconds does it take for the rock to hit the ground.
The time it takes for the rock to hit the ground can be determined using the equation h(t) = -4.9t^2 + 150, where h(t) represents the height of the rock in meters and t represents time in seconds. By setting h(t) to 0 and solving for t, we can find the time it takes for the rock to hit the ground.
Set the equation h(t) = -4.9t^2 + 150 to 0, since the rock hits the ground when the height is 0.
-4.9t^2 + 150 = 0
Solve the quadratic equation for t by factoring, completing the square, or using the quadratic formula. In this case, let's use the quadratic formula:
t = (-b ± √(b^2 - 4ac)) / (2a)
Plugging in the values for a, b, and c:
t = (-0 ± √(0^2 - 4(-4.9)(150))) / (2(-4.9))
Simplify and calculate the value of t:
t = (√(2940)) / (-9.8) ≈ ±7.23
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A rectangle has a height of 4w^34w
3
4, w, cubed and a width of 5w^2-3w-45w
2
−3w−45, w, squared, minus, 3, w, minus, 4.
To simplify the given expression, we can first simplify the height and width separately.
The height is 4w^3 - 4w. This expression does not have any common factors, so it cannot be simplified further.
The width is 5w^2 - 3w - 4. This expression can be factored as (5w + 1)(w - 4).
Now we can substitute these simplified expressions into the formula for the area of a rectangle, which is A = length × width. The length in this case is the height.
Area = (4w^3 - 4w) × (5w^2 - 3w - 4)
To multiply these expressions, we can use the distributive property:
Area = 4w^3(5w^2 - 3w - 4) - 4w(5w^2 - 3w - 4)
Expanding the multiplication:
Area = 20w^5 - 12w^4 - 16w^3 - 20w^3 + 12w^2 + 16w
Combining like terms:
Area = 20w^5 - 12w^4 - 36w^3 + 12w^2 + 16w
Therefore, the simplified expression for the area of the rectangle is 20w^5 - 12w^4 - 36w^3 + 12w^2 + 16w.
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The area of a rectangular house can be found using the equation A(x)=x2-7x+10 where x is the width of the house in feet.
Calculate the finance charge and new balance using the previous balance method. Previous balance = $179. 32 Annual rate = 16% Finance charge = $ New purchases = $117. 42 Payments/credits = $85. 00 New balance = $.
the finance charge is $28.67 and the new balance is $240.41.To calculate the finance charge and new balance using the previous balance method, we need to consider the previous balance, annual interest rate, new purchases, and payments/credits.
Previous balance = $179.32
Annual rate = 16%
New purchases = $117.42
Payments/credits = $85.00
First, let's calculate the finance charge. The finance charge is the interest charged on the previous balance. We can calculate it by multiplying the previous balance by the annual interest rate:
Finance charge = Previous balance * Annual rate
= $179.32 * 0.16
= $28.67
Next, we can calculate the new balance by adding the finance charge, new purchases, and subtracting the payments/credits:
New balance = Previous balance + Finance charge + New purchases - Payments/credits
= $179.32 + $28.67 + $117.42 - $85.00
= $240.41
Therefore, the finance charge is $28.67 and the new balance is $240.41.
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A television is on sale for $379. That is 18% off the original price. Find the original price of the television. 9. A refrigerator is priced at $1,580. Daniel has a coupon for 10% off. What is the sales price Daniel will pay for the refrigerator? How much will he pay for the refrigerator including 8.875% sales tax. 10. A computer desk sells for $450. Sophia has a coupon for 22% off. What is the sales price Sophia will pay? How much will Sophia pay including 8.875% sales tax? 11. Electronic Depot is selling a car stereo for $140 and 30% off. The Beatbox is selling the same stereo for $135 and 25%. Which store has the better sales price? 12. You buy dinner for your family. The bill comes to $86.00 including tax. You decide you will leave the waitress an 18% tip. How much is the tip?
9. The original price of the television is approximately $462.20. 10. Daniel will pay approximately $1,548.53 for the refrigerator including sales tax. 11. The tip amount is $15.48
9. To find the original price of the television, we can use the formula:
Original price = Sale price / (1 - Discount percentage)
Given:
Sale price = $379
Discount percentage = 18%
Plugging in the values:
Original price = $379 / (1 - 0.18)
Original price = $379 / 0.82
Original price ≈ $462.20
Therefore, the original price of the television is approximately $462.20.
10. To calculate the sales price Daniel will pay for the refrigerator after a 10% discount, we can use the formula:
Sales price = Original price - (Original price * Discount percentage)
Given:
Original price = $1,580
Discount percentage = 10%
Plugging in the values:
Sales price = $1,580 - ($1,580 * 0.10)
Sales price = $1,580 - $158
Sales price = $1,422
Daniel will pay $1,422 for the refrigerator after the 10% discount.
To calculate the total price including 8.875% sales tax, we can use the formula:
Total price = Sales price + (Sales price * Tax percentage)
Given:
Sales price = $1,422
Tax percentage = 8.875%
Plugging in the values:
Total price = $1,422 + ($1,422 * 0.08875)
Total price ≈ $1,548.53
Daniel will pay approximately $1,548.53 for the refrigerator including sales tax.
11. To determine which store has the better sales price for the car stereo, we need to compare the prices after the respective discounts.
Electronic Depot:
Sale price = $140
Discount percentage = 30%
Sales price after discount = $140 - ($140 * 0.30) = $140 - $42 = $98
The Beatbox:
Sale price = $135
Discount percentage = 25%
Sales price after discount = $135 - ($135 * 0.25) = $135 - $33.75 = $101.25
The better sales price is from Electronic Depot, as they offer the stereo for $98 compared to The Beatbox's price of $101.25.
12. To calculate the tip amount, we can multiply the bill amount by the tip percentage:
Tip amount = Bill amount * Tip percentage
Given:
Bill amount = $86.00
Tip percentage = 18%
Plugging in the values:
Tip amount = $86.00 * 0.18
Tip amount = $15.48
The tip amount is $15.48.
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How do I find the measure of AB (Rounded to the nearest tenth.)
The measure of the length AB to the nearest tenth is: 21.8
How to use trigonometric ratios?A right triangle is a triangle with one angle equal to 90 degrees.
The sides and angles of a right triangle can be found using trigonometric ratios.
So, let's find the length AB of the attached right triangle using trigonometry.
Along with that,
Tan ∅ = opposite/adjacent
Opposite side = AB
Adjacent side = 17 units
Along with that,
Tan 52° = AB / 17
multiplication cross
AB = 17 * tan 52
AB = 17 × 1.27994163219
AB = 21.7590077473
For this,
AB ≈ 21.8
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Sir gab borrowed 3,600 to finance his printer repair at a rate of 6.25%for 4.75 years. How much interest did he pay?
Gab paid $855 in interest for the printer repair. Sir gab borrowed 3,600 to finance his printer repair at a rate of 6.25%for 4.75 years.
To calculate the interest Gab paid, we can use the formula for simple interest: Interest = Principal * Rate * Time. In this case, the principal is $3,600, the rate is 6.25% (or 0.0625 as a decimal), and the time is 4.75 years.
Using the formula, we can calculate the interest as follows:
Interest = $3,600 * 0.0625 * 4.75 = $855.
Therefore, Gab paid $855 in interest for the printer repair.
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